Collapse Prevention PDF

Multi-hazard performance of steel moment frame buildings with collapse prevention
systems in the central and eastern United States
Johnn Paul Judd
Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State
University in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Civil Engineering
Finley A. Charney, Chair

Martin C. Chapman
Matthew R. Eatherton
Roberto T. Leon
Adrian Rodriguez-Marek
May 4, 2015
Blacksburg, Virginia
Keywords: Earthquake Engineering, Wind Engineering, Nonlinear Dynamic Analysis,

Structural Steel Buildings, FEMA P-695, FEMA P-58, Risk
Copyright 2015
Multi-hazard performance of steel moment frame buildings with collapse prevention
systems in the central and eastern United States
Johnn Paul Judd
ABSTRACT
This dissertation discusses the potential for using a conventional main lateral-force
resisting system, combined with the reserve strength in the gravity framing, and or
auxiliary collapse-inhibiting mechanisms deployed throughout the building, or enhanced
shear tab connections, to provide adequate serviceability performance and collapse safety
for seismic and wind hazards in the central and eastern United States. While the
proposed concept is likely applicable to building structures of all materials, the focus of
this study is on structural steel-frame buildings using either non-ductile moment frames
with fully-restrained flange welded connections not specifically detailed for seismic
resistance, or ductile moment frames with reduced beam section connections designed for
moderate seismic demands.
The research shows that collapse prevention systems were effective at reducing
the conditional probability of seismic collapse during Maximum Considered Earthquake
(MCE) level ground motions, and at lowering the seismic and wind collapse risk of a
building with moment frames not specifically detailed for seismic resistance. Reserve
lateral strength in gravity framing, including the shear tab connections was a significant
factor. The pattern of collapse prevention component failure depended on the type of
loading, archetype building, and type of collapse prevention system, but most story
collapse mechanisms formed in the lower stories of the building. Collapse prevention
devices usually did not change the story failure mechanism of the building. Collapse
prevention systems with energy dissipation devices contributed to a significant reduction
in both repair cost and downtime. Resilience contour plots showed that reserve lateral
strength in the gravity framing was effective at reducing recovery time, but less effective
at reducing the associated economic losses. A conventional lateral force resisting system
or a collapse prevention system with a highly ductile moment frame would be required
for regions of higher seismicity or exposed to high hurricane wind speeds, but buildings
with collapse prevention systems were adequate for many regions in the central and
eastern United States.
ACKNOWLEDGEMENTS
Many people have contributed to this research. I am grateful most of all to my advisor, Dr.
Finley Charney, for providing an opportunity to do earthquake and wind engineering research
that is both exciting and meaningful, and for the mentoring he has provided throughout my
doctoral studies.
I sincerely appreciate the support of my graduate committee. Thanks to Dr. Roberto Leon for
many thoughtful discussions, for introducing me to forensic engineering and civil engineering
failures, for encouraging me in the field of disaster resilience, and for providing the opportunity
to meet many leaders in our profession. Thanks to Dr. Matthew Eatherton for helping me to be a
better structural engineer, for several insightful comments, and for helping me to be successful in
full-scale experimental testing. Thanks to Dr. Adrian Rodriguez-Marek for introducing me to
risk analysis—it has been both challenging and rewarding. And thanks to Dr. Martin Chapman
for help understanding seismology and earthquake hazards and for his friendship along the way.
I would also like to acknowledge the support of the ASCE/SEI Ad-Hoc Wind Performance-
Based Design Committee, chaired by Don Scott and Larry Griffis. I appreciate the guidance
provided by Larry Griffis of Walter P. Moore Inc. in Austin, Texas on wind engineering and for
driving a big truck with me in Canada. I appreciate the assistance on understanding wind tunnel
testing given by Daryl Boggs of Cermak Peterka Petersen (CPP Inc.) in Fort Collins, Colorado,
and Peter Irwin and Bujar Morova of Rowan Williams Davies and Irwin (RWDI) Inc., in
Guelph, Ontario. I am grateful for the generous assistance of Nicholas Luco (USGS in Golden,
Colorado) in risk analysis, and for Dimitrios Vamvatsikos (National Technical University of
Athens) in supplying hysteresis parameters developed in FEMA P-440A (FEMA 2009b).
This research would not have been possible without time and assistance provided by friends and
family. As in the past, my brother Glenn Judd was an excellent resource for computational
questions. The scheduler he wrote was a life-saver. My wife Sharon spent countless hours
proofreading and giving constructive comments. I also appreciate the support of my graduate
colleagues, Ebrahim Abbas, Adam Phillips, and Chris Galitz in the experimental research, and
Armen Adekristi in furnishing the spectral matching algorithm. I especially appreciate the
support of my research group, Jeena Jayamon, Andy Hardyneic, Francisco Flores, and Jordan
Jarrett. Your help has been invaluable.
This research was supported by the National Institute of Standards and Technology (NIST) grant
No. 60ANB10D107. Financial support was also provided by the Charles E. Via, Jr. Doctoral
Fellowship endowment at Virginia Tech, the Department of Civil and Environmental
Engineering, and Simpson Strong-Tie, Inc. in Pleasanton, California. I would like to express
appreciation to Steven Pryor of Simpson Strong-Tie, and to Igor Marinovic of BlueScope Steel
Ltd., in Memphis, Tennessee, for their support.
I have attempted to eliminate errors, but it is inevitable that there are deficiencies in this
dissertation. Those, along with the opinions and recommendations expressed, are my
responsibility, and do not necessarily reflect views of people and organizations acknowledged.
iii
TABLE OF CONTENTS
TABLE OF CONTENTS ....................................................................................................... iii
LIST OF TABLES ................................................................................................................. iv
LIST OF FIGURES ............................................................................................................... xi
CHAPTER 1 INTRODUCTION ........................................................................................... 1
1.1 Motivation and Background ...................................................................................... 1
1.1.1 Seismic Design .................................................................................................. 2
1.1.2 Wind Design ...................................................................................................... 3
1.1.3 Multi-Hazard Performance ............................................................................... 4
1.1.4 Performance-Based Wind Design ..................................................................... 7
1.2 Objectives and Scope ................................................................................................. 8
1.3 Dissertation Organization .......................................................................................... 10
CHAPTER 2 SEISMIC AND WIND HAZARDS ................................................................ 14
2.1 Seismic Hazards ......................................................................................................... 14
2.1.1 Uniform Hazard Ground Motions .................................................................... 14
2.1.2 Earthquake Rate................................................................................................ 16
2.1.3 Ground Motion Attenuation .............................................................................. 24
2.1.4 Site Response .................................................................................................... 29
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2.1.5 Spectral Shape .................................................................................................. 34
2.2 Wind Hazards............................................................................................................. 36
2.2.1 Uniform Hazard Wind Speeds .......................................................................... 36
2.2.2 Wind Hazards.................................................................................................... 39
2.3 Multi-Hazard Comparison ......................................................................................... 40
2.3.1 Seismic and Wind Elastic Base Shear Forces................................................... 40
2.3.2 Multi-Hazard Performance Example ................................................................ 49
2.4 Discussion .................................................................................................................. 58
CHAPTER 3 ARCHETYPE STRUCTURAL SYSTEMS.................................................... 61
3.1 Collapse Prevention System Concept ........................................................................ 61
3.1.1 Reserve Lateral Strength in Gravity Framing .................................................. 62
3.1.2 Collapse Inhibiting Mechanisms....................................................................... 64
3.1.3 Enhanced Shear Tab Connections .................................................................... 70
3.2 Archetype Buildings .................................................................................................. 75
3.2.1 Type I Archetype Buildings ............................................................................... 76
3.2.2 Type II Archetype Buildings.............................................................................. 80
3.2.3 Type III Archetype Buildings ............................................................................ 82
3.2.4 Collapse Prevention Systems ............................................................................ 83
3.3 Analytical Modeling .................................................................................................. 84
3.3.1 Location of Beam Plastic Hinge ....................................................................... 86
3.3.2 Column Fixity, Splices and Plastic Hinge ........................................................ 87
3.3.3 Fully-Restrained (Moment Frame) Beam-to-Column Connections ................. 88
3.3.4 Partially-Restrained (Shear Tab) Beam-to-Column Connections .................... 96
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3.3.5 Columns and Column Panel Zones ................................................................... 99
3.3.6 Collapse-Inhibiting Mechanisms ...................................................................... 102
3.3.7 Partially-Restrained (Enhanced Shear Tab) Beam-to-Column Connections ... 104
3.4 Nonlinear Analysis Approach .................................................................................... 107
3.4.1 Second-Order Effects ........................................................................................ 107
3.4.2 Damping ............................................................................................................ 107
3.4.3 Analysis Solution Procedures ........................................................................... 111
CHAPTER 4 SEISMIC COLLAPSE ASSESSMENT .......................................................... 116
4.1 Seismic Collapse Vulnerability Procedures ............................................................... 116
4.1.1 Gravity Load Analysis....................................................................................... 117
4.1.2 Frequency (Building Period of Vibration) Analysis ......................................... 118
4.1.3 Nonlinear Static Seismic (“Pushover”) Analysis ............................................. 119
4.1.4 Ground Motion Set for Nonlinear Response History Analysis ......................... 120
4.1.5 Target Spectrum ................................................................................................ 122
4.1.6 Intensity Measure for Seismic Hazard .............................................................. 122
4.1.7 Nonlinear Dynamic Response History Analysis ............................................... 124
4.1.8 Collapse Fragility ............................................................................................. 126
4.2 Seismic Collapse Risk Procedures ............................................................................. 127
4.2.1 Directional Effects ............................................................................................ 127
4.2.2 Site Response .................................................................................................... 131
4.2.3 Integration of Seismic Hazard and Seismic Collapse Vulnerability................. 133
4.3 Results ........................................................................................................................ 137
4.3.1 Type I Non-ductile and Ductile Moment Frame Buildings ............................... 137
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4.3.2 Type II Non-ductile Moment Frame Buildings ................................................. 150
4.3.3 Type III Non-ductile Moment Frame 10-story Building ................................... 154
4.4 Comparison with Traditional Structural Systems ...................................................... 156
4.4.1 Steel Moment Frame ......................................................................................... 156
4.4.2 Steel Braced Frames ......................................................................................... 157
4.4.3 Reinforced Concrete Moment Frames .............................................................. 158
4.4.4 Reinforced Concrete Shear Walls ..................................................................... 159
4.4.5 Reinforced Masonry Shear Walls ..................................................................... 160
4.4.6 Wood (Light-Framed) Shear Walls ................................................................... 161
4.5 Discussion .................................................................................................................. 163
CHAPTER 5 WIND COLLAPSE ASSESSMENT............................................................... 165
5.1 Wind Collapse Vulnerability Procedures................................................................... 165
5.1.1 Gravity Loading ................................................................................................ 167
5.1.2 Frequency (Period) Determination................................................................... 167
5.1.3 Nonlinear Static Wind (“Pushover”) Analysis ................................................. 168
5.1.4 Wind Load Ensemble for Nonlinear Response History Analysis ...................... 170
5.1.5 Intensity Measure for Wind Hazard .................................................................. 172
5.1.6 Nonlinear Dynamic Response History Analysis ............................................... 173
5.1.7 Collapse Fragility ............................................................................................. 175
5.2 Wind Collapse Risk Procedures................................................................................. 177
5.3 Results ........................................................................................................................ 181
5.3.1 Type I Non-ductile and Ductile Moment Frame Buildings ............................... 181
5.3.2 Type II Non-ductile Moment Frame 4-story Building ...................................... 184
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5.3.3 Type III Non-ductile Moment Frame 10-story Building ................................... 185
5.4 Discussion .................................................................................................................. 187
CHAPTER 6 SENSITIVITY OF COLLAPSE ASSESSMENT ........................................... 189
6.1 Seismic Collapse Sensitivity...................................................................................... 189
6.1.1 Panel Zone Representation ............................................................................... 190
6.1.2 Second-Order Effects ........................................................................................ 195
6.1.3 Column Splices.................................................................................................. 199
6.1.4 Ground Motion Spectrum ................................................................................. 201
6.1.5 Intensity Measure Conditioning Period ............................................................ 209
6.1.6 Risk Integration Method ................................................................................... 210
6.1.7 Regional Risk .................................................................................................... 215
6.1.8 Site Response .................................................................................................... 219
6.2 Wind Collapse Sensitivity.......................................................................................... 222
6.2.1 Main Wind-Force Resisting System and Gravity Framing System ................... 225
6.2.2 Static Overstrength ........................................................................................... 228
6.2.3 Damping, Fundamental Period, and Cyclic Degradation ................................ 229
6.2.4 Wind Duration .................................................................................................. 230
6.3 Discussion .................................................................................................................. 234
CHAPTER 7 SEISMIC PERFORMANCE ASSESSMENT ................................................ 237
7.1 General Procedures .................................................................................................... 237
7.1.1 Ground Motion Set for Nonlinear Response History Analysis ......................... 238
7.1.2 Structural and Non-structural Component Fragility ........................................ 239
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7.2 Predicted Seismic Performance ................................................................................. 242
7.2.1 Type I Non-ductile Moment Frame Buildings .................................................. 242
7.2.2 Type II Non-ductile 4-story Moment Frame Building ...................................... 249
7.3 Resiliency Contours ................................................................................................... 253
7.4 Discussion .................................................................................................................. 255
CHAPTER 8 MULTI-HAZARD COLLAPSE ASSESSMENT ........................................... 256
8.1 General ....................................................................................................................... 256
8.1.1 Background ....................................................................................................... 256
8.1.2 Literature Review .............................................................................................. 257
8.2 Procedure ................................................................................................................... 258
8.2.1 Calculation of Multi-Hazard Risk..................................................................... 258
8.2.2 Acceptable Level and Social Amplification of Risk .......................................... 259
8.3 Results ........................................................................................................................ 261
8.4 Discussion .................................................................................................................. 265
CHAPTER 9 CONCULSIONS ............................................................................................. 266
9.1 Summary .................................................................................................................... 266
9.2 Conclusions and Recommendations .......................................................................... 269
9.3 Areas for Future Research ......................................................................................... 271
9.4 Potential Impact of Research ..................................................................................... 274
REFERENCES ...................................................................................................................... 276
APPDENDIX A ANALYSIS VALIDATION ...................................................................... 319
A.1 Computer Software ................................................................................................... 319
A.2 Static Analysis........................................................................................................... 321
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A.2.1 Cantilever Beam ............................................................................................... 321
A.2.2 Second-order effects ......................................................................................... 323
A.2.3 Buckling Analysis ............................................................................................. 325
A.3 Dynamic Analysis ..................................................................................................... 329
A.4 Nonlinear Multi-Degree-of-Freedom Analysis ......................................................... 330
A.5 Collapse prevention systems ..................................................................................... 333
APPENDIX B DESIGN OF TYPE I NON-DUCTILE MOMENT FRAME BUILDINGS . 336
B.1 Design Criteria .......................................................................................................... 337
B.2 Design Gravity Loads................................................................................................ 338
B.3 Seismic Hazard .......................................................................................................... 339
B.4 Wind Hazard ............................................................................................................. 340
B.5 Analyses for Design .................................................................................................. 340
B.6 Example Calculations ................................................................................................ 343
B.6.1 Gravity Design of Girder.................................................................................. 344
B.6.2 Gravity Design of Column ................................................................................ 348
B.6.3 Lateral Design of OMF .................................................................................... 349
B.7 Design Summary ....................................................................................................... 355
APPENDIX C ANALYTICAL MODEL FOR TYPE I NON-DUCTILE MOMENT
FRAME 4-STORY BUILDING ............................................................................................ 358
C.1 Building and Load Model ......................................................................................... 358
C.2 Gravity Load Analysis .............................................................................................. 361
C.3 Frequency (Building Period of Vibration) Analysis ................................................. 361
C.4 Nonlinear Static “Pushover” Analysis ...................................................................... 363
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C.4.1 Seismic Pushover.............................................................................................. 363
C.4.2 Wind Pushover ................................................................................................. 369
C.5 Nonlinear Response History Analysis....................................................................... 371
C.5.1 Seismic Incremental Dynamic Analysis (IDA) ................................................. 371
C.5.2 Wind Incremental Dynamic Analysis ............................................................... 381
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LIST OF TABLES
Table 1.1 Performance objectives in terms of tolerable impact
(adapted from ICC 2012b) ............................................................................. 4
Table 2.1 Average ratio of spectral acceleration (for different MRI)
compared to MCE ground motions ................................................................ 23
Table 2.2 Mean Distance (Magnitude) contributing to MCE ground motion ............... 27
Table 2.3 Performance criteria: tolerable impact in terms of hazard level .................... 50
Table 2.4 Primary contributions to seismic hazard ........................................................ 51
Table 2.5 Effect of structural system on spectral demands............................................ 54
Table 2.6 Estimated drift ratio and probable damage for seismic hazards .................... 55
Table 2.7 Estimated drift ratio and probable damage for windstorm hazards ............... 56
Table 3.1 Archetype structural systems ......................................................................... 75
Table 3.2 Type I archetypical building non-ductile moment frames ............................. 78
Table 3.3 Type I archetypical building gravity framing column sizes .......................... 79
Table 3.4 Type I archetypical building gravity framing beam sizes .............................. 79
Table 3.5 Moment-rotation model parameters for ductile beam-to-column
connections .................................................................................................... 91
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Table 3.6 Moment-rotation model parameters for non-ductile
beam-to-column connections ......................................................................... 94
Table 3.7 Moment-rotation parameters for ductile connections with
composite action ............................................................................................ 96
Table 4.1 Ground motion set (FEMA P-695 Far-Field set) used for
dynamic analysis ............................................................................................ 121
Table 4.2 Qualitative rating used to quantify uncertainties in
seismic collapse assessment ........................................................................... 126
Table 4.3 Ratio of maximum-direction to geomean spectral acceleration .................... 129
Table 4.4 Seismic collapse assessment (for SDC D max ) for Type I non-ductile
moment-frame building (designed for wind, SDC B min ) ............................... 138
Table 4.5 Seismic collapse assessment (for SDC D max ) for Type I ductile
moment-frame building (designed for SDC D min )......................................... 139
Table 4.6 Seismic collapse assessment (for SDC D max ) for Type I ductile
moment-frame building (designed for SDC D max ) ........................................ 139
Table 4.7 Seismic collapse assessment (for SDC Dmax) for Type II non-ductile
moment-frame building (designed for SDC B, design controlled by wind) .. 152
Table 4.8 Seismic collapse assessment for Type III non-ductile 10-story building
(designed for wind and evaluated at SDC Bmin, Cmin, Dmin, and Dmax) .. 155
Table 4.9 Steel moment-frame seismic collapse assessment results ............................. 157
Table 4.10 Steel braced-frame seismic collapse assessment results ................................ 158
Table 4.11 Reinforced concrete moment-frame seismic collapse assessment results ..... 159
Table 4.12 Reinforced concrete shear-wall seismic collapse assessment results ............ 160
xii
Table 4.13 Reinforced masonry shear-wall seismic collapse assessment results ............ 161
Table 4.14 Wood (light-framed) shear-wall seismic collapse assessment results ........... 162
Table 5.1 Qualitative rating used to quantify uncertainties in
wind collapse assessment ............................................................................... 177
Table 5.2 Wind collapse assessment of Type II non-ductile moment frame buildings
(relative to Risk Category II) ......................................................................... 181
Table 5.3 Wind collapse assessment of Type II ductile moment frame buildings
(relative to Risk Category II) ......................................................................... 182
Table 5.4 Wind collapse assessment of Type II non-ductile moment frame building... 184
Table 5.5 Wind collapse assessment of Type III non-ductile moment frame
10-story building (relative to Risk Category II) ............................................ 186
Table 6.1 Sensitivity of collapse assessment (for SDC D max ) for Type I non-ductile
moment-frame building (designed for wind, SDC B min ) to the panel zone
representation ................................................................................................. 192
Table 6.2 Sensitivity of collapse assessment (for SDC D max ) for Type I ductile
moment-frame building (designed for SDC D max ) to the panel zone
representation ................................................................................................. 192
Table 6.3 Sensitivity of collapse assessment (for SDC D max ) for Type I non-ductile
moment-frame building (designed for wind, SDC B min ) to the method
used for second-order effects. ........................................................................ 196
Table 6.4 Sensitivity of collapse assessment (for SDC D max ) for Type I ductile
moment-frame building (designed for SDC D max ) to the method used for
second-order effects ....................................................................................... 196
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Table 6.5 Sensitivity of seismic collapse assessment to column splices
(Type I ductile moment frame 4-story building designed SDC D max ) .......... 199
Table 6.6 Sensitivity of seismic collapse assessment to ground motion spectrum
(Type I non-ductile moment frame buildings designed for SDC B min
evaluated at SDC D max ) ................................................................................. 206
(Type I ductile moment frame buildings designed for SDC D min evaluated
at SDC D max ).................................................................................................. 208
(Type I ductile moment frame 4-story building designed for SDC D min
evaluated at SDC Dmax) ............................................................................... 209
Table 6.9 Collapse risk analysis of PR-CC buildings .................................................... 218
Table 6.10 Effect of Main Wind-Force Resisting Framing System (MWFRS) .............. 226
Table 6.11 Effect of gravity framing system ................................................................... 226
Table 6.12 Effect of lateral strength ratio and ductility ................................................... 228
Table 6.13 Effect of damping and fundamental period on non-ductile moment frame ... 229
Table 6.14 Effect of cyclic degradation ........................................................................... 229
Table 6.15 Effect of duration on ductile moment frame system ...................................... 230
Table 7.1 Ground motion set (FEMA P-695 Far-Field set) used for
dynamic analysis ............................................................................................ 238
Table 7.2 Summary of component fragilities used for Type I non-ductile buildings .... 241
Table 7.3 Serviceability (10% of MCE) performance of Type I non-ductile buildings 245
Table 7.4 Serviceability (10% of MCE) performance of Type I ductile buildings ....... 246
xiv
Table 7.5 Design-level (67% of MCE) performance of Type I ductile buildings ......... 246
Table 7.6 Summary of average performance assessment for Type II non-ductile
4-story building .............................................................................................. 251
Table A.1 Predicted lateral displacement (in.) of typical gravity frame column ............ 324
Table A.2 Critical buckling load (k) ............................................................................... 326
Table A.3 Maximum absolute displacement (in.) ........................................................... 329
Table A.4 Permanent displacement (in.) at time equal to 30 seconds ............................ 329
Table A.5 Nonlinear dynamic response history analysis results for portal frame .......... 335
Table B.1 Deflection and drift performance limits ......................................................... 337
Table B.2 Design dead loads .......................................................................................... 338
Table B.3 Design live loads ............................................................................................ 338
Table B.4 Seismic design hazards .................................................................................. 339
Table B.5 Design parameters for non-ductile moment frames ....................................... 341
Table B.6 Analyses used to design the Type I non-ductile moment frames .................. 343
Table B.7 Inter-story drift ratio and stability ratio for seismic drift analysis
(4-story building, OMF SDC D min ) ............................................................... 351
Table B.8 Ratio of available / required beam strength for seismic strength analysis
Table B.9 Interaction ratio of available and required column flexure and axial
strengths for seismic strength analysis (4-story building, OMF SDC D min ) . 351
Table B.10 Ratio of available and required joint (panel zone) shear strength for
seismic strength analysis (4-story building, OMF SDC D min )....................... 351
Table B.11 Computed periods of vibration (4-story building, OMF SDC D min ) ............. 352
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Table B.12 Inter-story drift ratio and stability ratio for seismic drift analysis
Table B.13 Ratio of available / required beam strength for seismic strength analysis
strengths for seismic strength analysis (4-story building, OMF SDC D min ) . 353
Table B.15 Ratio of available and required joint (panel zone) shear strength for
seismic strength analysis (4-story building, OMF SDC D min )....................... 353
Table B.16 Computed periods of vibration (4-story building, OMF SDC D min ) ............. 353
Table B.17 Inter-story drift ratio for wind drift analysis (4-story building) ..................... 353
Table B.18 Ratio of required / provided beam strength for wind strength analysis
(4-story building) ........................................................................................... 354
strengths for wind strength analysis (4-story building) ................................. 354
Table B.20 Archetype design and member sizes for Type I non-ductile 1-story buildings 355
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LIST OF FIGURES
Figure 2.1 Regional differences in earthquake rate ......................................................... 17
Figure 2.2 Probability of exceeding a 6.7-magnitude earthquake in 100 years .............. 18
Figure 2.3 Ratio of 25-year MRI spectral acceleration compared to
MCE ground motion ...................................................................................... 19
Figure 2.7 Geological regions of United States (background map of geology adapted from
map by Vigil et al. 2000) ............................................................................... 25
Figure 2.8 Geographic extent of perceived ground motion
(adapted from USGS 2012) ........................................................................... 26
Figure 2.9 Conditional mean response spectrum (conditioned on 1.0 second)
for different ground motion prediction equations .......................................... 27
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Figure 2.10 Synthetic ground motions for most likely event based on
a hazard deaggregation .................................................................................. 28
Figure 2.11 Uniform hazard spectrum for a location in San Francisco
(38.0º latitude, -121.7º longitude) with soil site class D
(average 𝑉𝑠30 = 180 m/sec)............................................................................. 30
Figure 2.12 Characteristic uniform hazard response spectra ............................................ 35
Figure 2.13 Design wind speed contours with a 700-year MRI
(special wind regions included) ..................................................................... 37
Figure 2.14 Design wind speed contours with a 700-year MRI
(special wind regions removed) ..................................................................... 37
Figure 2.15 Ratio of service-level wind speed to design wind speed
for ordinary occupancy and use structures (risk category II) ........................ 38
Figure 2.16 Ratio of seismic to wind elastic base shear for 10-year MRI ........................ 42
Figure 2.19 Ratio of seismic to wind elastic base shear for 100-year MRI ...................... 43
Figure 2.20 Ratio of seismic to wind elastic base shear for 700-year MRI ...................... 44
Figure 2.21 Ratio of seismic to wind elastic base shear for 100,000-year MRI ............... 44
Figure 2.22 Ratio of seismic to wind elastic base shear for a short-period building ........ 46
Figure 2.23 Ratio of seismic to wind elastic base shear for a long-period building ......... 46
Figure 2.24 Ratio of seismic to wind elastic base shear for urban terrain
(exposure category B) .................................................................................... 47
xviii
Figure 2.25 Ratio of seismic to wind elastic base shear for open terrain
(exposure category C) .................................................................................... 47
Figure 2.26 Ratio of seismic to wind elastic base shear for extrapolated
ASCE 7-10 wind speeds ................................................................................ 48
Figure 2.27 Ratio of seismic to wind elastic base shear for tornado wind speeds ............ 48
Figure 2.28 Contribution of potential quakes to spectral acceleration, 𝑆𝑎 (𝑇𝑛 = 1.0 𝑠) ... 51
Figure 2.29 Wind pressure and tornado hazards for example structure ............................ 52
Figure 2.30 Seismic hazard curves for potential structural systems ................................. 55
Figure 3.1 Prototypical collapse inhibiting mechanisms................................................. 67
Figure 3.2 Prototypical collapse inhibiting mechanisms equipped with
energy dissipating devices ............................................................................. 67
Figure 3.3 Finite element model of enhanced shear tab connection ............................... 71
Figure 3.4 Finite element model of yield link (T-stub stem) .......................................... 72
Figure 3.5 Finite element model of shear tab with slotted upper and lower bolt holes .. 72
Figure 3.6 Finite element model of enhanced shear tab connection ............................... 74
Figure 3.7 Finite element model of non-constrained buckling restraint mechanism ...... 74
Figure 3.8 Type I non-ductile and ductile moment frame 1-story, 2-story, 4-story,
and 8-story building framing plan.................................................................. 76
Figure 3.9 Type I archetypical building elevation view of structural framing
in longitudinal direction (4-story building shown) ........................................ 77
Figure 3.10 Type II non-ductile moment frame 4-story building plan ............................. 80
Figure 3.11 Type III non-ductile moment frame 10-story building
framing plan and elevation............................................................................. 82
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Figure 3.12 Perspective view of Type I analytical (half-building) models ....................... 84
Figure 3.13 Phenomenological (concentrated plasticity) analytical modeling approach:
moment frame shown for Type I non-ductile moment frame
2-story building .............................................................................................. 85
Figure 3.14 Typical idealized behavior for a ductile fully-restrained beam-to-column
connection: W18x71 beam in Type I ductile moment frame
4-story building .............................................................................................. 89
Figure 3.15 Modified Ibarra-Medina-Krawinkler moment-rotation model ...................... 90
Figure 3.16 Typical idealized behavior for a non-ductile fully-restrained
beam-to-column connection: W16x31 beam in Type I non-ductile
moment frame 4-story building ..................................................................... 93
Figure 3.17 Typical parameter values for non-ductile behavioral model ......................... 94
Figure 3.18 Typical idealized behavior for a shear-tab beam-to-column connection:
W16x31 beam in Type I non-ductile moment frame 4-story building .......... 97
Figure 3.19 Typical idealized behavior for a column plastic hinge: W18x76 column
in Type I non-ductile moment frame 4-story building................................... 99
Figure 3.20 Explicit (Krawinkler) column panel zone model
(reduced beam section shown) ....................................................................... 100
Figure 3.21 Typical idealized behavior for a column panel zone distortion:
W18x76 column in Type I non-ductile moment frame 4-story building ....... 101
Figure 3.22 Axial and moment forces in column with collapse prevention system ......... 104
xx
Figure 3.23 Typical idealized behavior for an enhanced shear tab
beam-to-column connection: W16x31 beam in Type I non-ductile
Figure 3.24 Proportional damping curve for Type I non-ductile moment frame
1-story building .............................................................................................. 108
Figure 3.25 Solution algorithm and maximum number of iterations: seismic analysis of
Type I non-ductile 2-story building with enhanced shear tab connections for
LOS000 ground motion scaled to collapse intensity ..................................... 114
Figure 4.1 Mode shapes and periods of vibration:
Type I non-ductile moment framing 8-story building ................................... 118
Figure 4.2 Seismic pushover response of Type I ductile moment frame
4-story building .............................................................................................. 120
Figure 4.3 Response spectrum for Type I non-ductile 2-story building ......................... 123
Figure 4.4 Spectral acceleration for the 1999 Kocaeli, Turkey earthquake
ground motion recorded at the Duzce station
(FEMA P-695 Far-Field ground motion ID No. 9)........................................ 128
Figure 4.5 Ratio of maximum-direction to geomean 𝑆𝑎 for FEMA P-695 far-field
ground motion set (individual record ratio is indicated by gray lines) .......... 130
Figure 4.6 Ratio of maximum-direction to geomean 𝑆𝑎 for FEMA P-695 near-field
ground pulse ................................................................................................... 130
Figure 4.7 Average shear wave velocity (𝑉𝑠30) based on topographic data .................... 132
Figure 4.8 Seismic hazard data for location in San Francisco (38.0º latitude,
-121.7º longitude) with soil site class D (average 𝑉𝑠30 = 180 m/sec) ............ 132
xxi
Figure 4.9 Seismic collapse risk analysis for Type I non-ductile moment frame
4-story building .............................................................................................. 136
Figure 4.10 Effect of CP system on pushover response of ductile 4-story building ......... 140
Figure 4.11 Representative response of 4-story building with non-ductile
moment frames............................................................................................... 141
Figure 4.12 Response of 4-story building with non-ductile moment frames for LOS000,
with 𝑆𝑎 = 0.36 g ............................................................................................. 142
Figure 4.13 Representative response of 4-story building with non-ductile
moment frames............................................................................................... 143
Figure 4.14 Seismic collapse results for 4-story building with non-ductile
moment frames............................................................................................... 144
Figure 4.15 Regions where seismic collapse risk exceeds 1% in 50 years:
Type I non-ductile .......................................................................................... 145
Figure 4.16 Regions where the probability of seismic collapse (given the MCE)
exceeds 10%: Type I non-ductile moment frame 4-story building with
slack cable collapse prevention system.......................................................... 146
non-ductile 1-story ......................................................................................... 147
xxii
Figure 4.21 Nonlinear dynamic analyses for the Type II non-ductile
moment frame buildings ................................................................................ 150
Figure 4.22 Seismic collapse analyses for the Type II non-ductile
moment frame buildings ................................................................................ 151
Type II non-ductile moment frame 4-story building ..................................... 153
Figure 4.24 Scaled response spectra: Type III non-ductile moment frame
10-story building ............................................................................................ 154
Figure 4.25 Seismic collapse analyses for the Type III non-ductile 10-story building..... 155
Figure 5.1 Equivalent single-degree-of-system force-deformation models .................... 166
Figure 5.2 First mode (𝑇1 = 3.34 s) of Type III non-ductile
moment frame 10-story building ................................................................... 168
Figure 5.3 Wind pushover response of Type III non-ductile
moment frame 10-story building ................................................................... 169
Figure 5.4 Wind tunnel test of a small-scale model of a 46-story building .................... 170
Figure 5.5 Location of pressure taps for Type I archetype building
wind tunnel model.......................................................................................... 171
Figure 5.6 Response of Type I ductile moment frame 8-story building with
enhanced shear tab collapse prevention system for 0° (cross-wind)
(reference wind speed 20 mph) ...................................................................... 174
xxiii
enhanced shear tab connection collapse prevention system
enhanced shear tab collapse prevention system
Figure 5.9 Regions where wind collapse risk exceeds 0.15% in 50 years:
4-story building .............................................................................................. 183
8-story building .............................................................................................. 183
4-story building .............................................................................................. 184
Figure 5.12 Collapse risk analysis for Type I non-ductile moment frame building ......... 186
Figure 6.1 Incremental dynamic analyses: Type I non-ductile
Figure 6.2 Incremental dynamic analyses: Type I ductile
Figure 6.3 Incremental dynamic analyses: Type I non-ductile
Figure 6.4 Incremental dynamic analyses: Type I ductile moment frame 4-story
building .......................................................................................................... 198
Figure 6.5 Response of Type I ductile 4-story building designed for D max .................... 200
xxiv
Figure 6.6 Response histories representative ground motion (FEMA P-695 Far Field
ground motion ID No. 1) ............................................................................... 204
Figure 6.7 Response of representative ground motion (FEMA P-695 Far Field
ground motion ID No. 1) ............................................................................... 205
Figure 6.8 Response of non-ductile 4-story building ...................................................... 206
Figure 6.9 Response of non-ductile 8-story building ...................................................... 207
Figure 6.10 Response of ductile 8-story building ............................................................. 208
Figure 6.11 Seismic hazard, deaggregation of collapse risk, and cumulative risk
(example 4-story ductile moment frame building) ........................................ 213
Figure 6.12 Hazard, deaggregation of risk, and cumulative risk for example structure ... 214
Figure 6.13 Seismic hazards for San Francisco bay area location .................................... 216
Figure 6.14 Seismic hazards for Memphis metropolitan area location ............................. 217
Figure 6.15 Contour regions where the seismic collapse risk exceeds 1% in 50 years,
𝑉𝑠30 = 180 m/s (D/E boundary),
Type I non-ductile moment frame 4-story building....................................... 220
Figure 6.16 Contour regions where the seismic collapse risk exceeds 1% in 50 years,
𝑉𝑠30 based on topographic proxy data, Type I non-ductile
Figure 6.17 Characteristic main wind-force resisting system (MWFRS) ......................... 224
Figure 6.18 Characteristic gravity framing (GF) system .................................................. 225
Figure 6.19 Regions where wind collapse risk exceeds 0.35% in 50 years
(non-ductile MF) ............................................................................................ 227
Figure 6.20 Along-wind (90°) response history for ductile moment frame system .......... 231
xxv
Figure 6.21 Cross-wind (0°) response history for ductile moment frame system............. 232
Figure 6.22 Incremental dynamic analyses curves for ductile moment frame system...... 233
Figure 7.1 Response spectrum for Type I non-ductile 2-story building ......................... 240
Figure 7.2 Median response for 4-story non-ductile moment-frame building at
10% of MCE .................................................................................................. 244
Figure 7.3 Selected component fragilities (sensitivity to ground motion) ...................... 244
Figure 7.4 Serviceability level performance for Type I ductile moment frame 8-story
building .......................................................................................................... 248
Figure 7.5 Profiles of peak IDR and peak floor/roof acceleration .................................. 250
Figure 7.6 Typical component fragility curves ............................................................... 250
Figure 7.7 Typical contributions to repair cost and downtime at 5% of
Figure 7.8 Seismic resilience contour plots..................................................................... 254
Figure 8.1 Regions where multi-hazard collapse risk exceeds 1% in 50 years............... 262
Figure 8.2 Regions where multi-hazard collapse risk exceeds 1% in 50 years............... 264
Figure A.1 Column behavior for second-order analysis methods .................................... 323
Figure A.2 Two-story single-bay frame ........................................................................... 326
Figure A.3 Periods of vibration and mode shapes for the model used in this research ... 331
Figure A.4 Nonlinear static seismic pushover response .................................................. 331
Figure A.5 Free vibration analysis response .................................................................... 332
Figure A.6 Idealized configurations of collapse prevention systems............................... 333
Figure A.7 Collapse-level drift ratio history for portal frame .......................................... 335
Figure B.1 Lateral MWFRS wind loads (4-story building) ............................................. 350
xxvi
Figure B.2 Lateral equivalent seismic loads (4-story building, OMF, SDC D min ) .......... 350
Figure C.1 Finite element model of Type I non-ductile
Figure C.2 Mode shapes and periods of vibration ........................................................... 362
Figure C.3 Seismic pushover response ............................................................................ 368
Figure C.4 Wind pushover response ................................................................................ 370
Figure C.5 Seismic collapse assessment results............................................................... 380
Figure C.6 Wind collapse assessment response for 90° (along-wind) and
𝑉𝑚𝑚ℎ = 256 mph ............................................................................................. 383
xxvii
Chapter 1
INTRODUCTION
This chapter describes the motivation for the research, provides background on seismic design,
multi-hazard performance, and performance-based wind design. The objective and scope of
research are defined. The chapter also summarizes the organization and content of the
dissertation.
1.1 Motivation and Background
Extensive regions of the United States are at risk from multiple hazards. Earthquakes are a
serious threat not only in the western United States, but in much of the central and eastern United
States. For example, the 5.7-magnitude 2011 Virginia earthquake—felt by more people in the
United States than any previous quake—caused damage in excess of $100 million. But large
seismic events are not the only concern. Since 2009, for example, Oklahoma has had over
twenty magnitude 4.0 to 4.8 tremors (USGS-Oklahoma Geological Survey 2014), making the
state more seismically “active” per square mile than California.
Windstorms and related coastal inundation have caused over 4,000 casualties and led to
property losses in excess of $250 billion over the past 16 years (NIST 2014b). The 2012
1
derecho, an intense fast-moving windstorm, is a recent case in point. The windstorm caused
substantial damage and cut power to millions of people in the eastern United States.
Tornadoes alone have devastated communities and caused over 5,000 casualties since
1950—more casualties than for earthquakes and hurricanes combined during the same period
(NIST 2014a). The 2011 Joplin, Missouri Tornado, one of 1,691 tornadoes in the United States
that year, was especially damaging. The Enhanced Fujita (EF) 5 intensity tornado carved a mile-
wide path of destruction, caused 161 fatalities, injured over a thousand, and produced
approximately $3 billion in property losses.
1.1.1 Seismic Design
The conventional practice in seismic resistant design of new buildings in the United
States (FEMA 2009c; ASCE 2010) is to proportion and detail ordinary (Occupancy and Use
Category II) structures such that there is no more than a 10% probability that the structure will
collapse when subjected to the risk-based Maximum Considered Earthquake ground motions
(MCE R ) (ASCE 2010, Table C.1.3.1b), which generally have a return period, or mean recurrence
interval (MRI), of approximately 2,475 years, and that risk of collapse does not exceed 1% in 50
years (FEMA 2009c). While no explicit calculations are required to assess the true likelihood of
collapse performance, safeguards are provided by well-established system configuration and
detailing rules and by limits on computed drift.
The seismic performance expectations for new buildings subjected to ground motions
that occur more frequently than the MCE are loosely stated in the commentary for current design
standards [e.g. ASCE (2010) 7-10; 2009 NEHRP Recommended provisions], but no calculations
are required to assess the adequacy of the building’s performance under such motions. However,
2
there is significant historical evidence that earthquakes along the west coast of the United States
that occur more frequently than the MCE ground motions, and which produce less severe ground
shaking than the MCE ground motions, can cause significant and unacceptable levels of damage.
The 1994 Northridge California Earthquake, which caused an estimated $57 billion in losses
(Seligson and Eguchi 2005), is a case in point. This earthquake had a magnitude of 6.7, and
earthquakes of equivalent size are expected to reoccur once every 35 to 40 years in that area.
Although it is technically incorrect to associate a single event with a return period, Northridge
was one of many moderate-magnitude quakes that caused extensive economic loss in California
during the span of only a few decades (Hamburger et al. 2012). The predicted recurrence of the
ground motions that resulted from these earthquakes was lower than the design recurrence
intervals yet the damage was above acceptable levels. Thus, a significant shortcoming of the
current practice for designing new buildings is that it does not explicitly address the lower
hazard-level ground motions.
1.1.2 Wind Design
The conventional practice in wind resistant design of new buildings in the United States
(ASCE 2010) is to proportion and detail ordinary structures to remain elastic when subjected to
strength-level design wind speeds, which have a 700-year MRI. The design wind speeds
accounts for synoptic wind (regional atmospheric circulation due to high low pressure regions,
including hurricanes). Non-synoptic wind (local wind from thunderstorms and derecho
downbursts and tornado vortices) is not typically accounted. Conventional wind design does
consider more frequently occurring wind speeds, but the probability of wind collapse is not
calculated. Although no target collapse risk for wind has been established, it is assumed that the
3
building code provisions (ASCE 7-10) provide a target annual probability failure rate of 5x10-6
collapses/year to 7x10-7 collapses/year for ordinary structures (ASCE 2010, Table C.1.3.1a).
1.1.3 Multi-Hazard Performance
A broadened design philosophy called performance-based engineering has emerged as a
potential remedy, where the goal is to meet or exceed predefined performance objectives under
different levels of hazard (FEMA 2006, 2012a; ICC 2012b). Typical performance objectives for
buildings are provided in Table 1.1. The objectives described in Table 1.1 were adapted in part
from the International Performance Code (ICC 2012b) rubric and define how a building
structure is expected to perform during an event (earthquake or windstorm) in terms of the
impact, described in terms of a maximum tolerable level of damage.
Table 1.1 Performance objectives in terms of tolerable impact (adapted from ICC 2012b)
Building Occupancy and Use

(Risk Category)
Seismic or Wind Hazard
Probability of Infrequent Ordinary Critical Essential
Event Occurrence Exceedence (I) (II) (III) (IV)
50% in 30 years
Small Frequent Moderate Mild Mild Mild
(43-year MRI)
20% in 50 years
Medium Occasional High Moderate Mild Mild
(225-year MRI)
10% in 50 years
Large (DBE) Rare Severe High Moderate Mild
(475-year MRI)
7% in 50 years
Large Rare High Moderate Mild Mild
(700-year MRI)
3% in 50 years
Very Large Very Rare Severe High Moderate Moderate
(1,700-year MRI)
2% in 50 years
Very Large (MCE) Very Rare Severe Severe High Moderate
(2,475-year MRI)
4
• Mild impact means there is no loss of structural strength and stiffness, and the building is
safe to occupy. Nonstructural systems are fully operational, and the overall extent and
cost of damage is minimal.
• Moderate impact means there is some structural damage, but such damage is limited and
repairable. There may be delay in occupancy. Nonstructural systems are operational but
may require repair. Emergency systems remain fully operational. The extent and cost of
damage is significant in some areas.
• High impact means there is significant damage to structural components (but “no large
falling debris”). Repair is possible, but significant delays in occupancy are expected.
Nonstructural systems are inoperable; emergency systems are significantly damaged, but
remain operational. Severe Impact means there is significant structural damage, but the
gravity-load carrying system is still intact. Occupancy and repair may not be possible or
feasible. There may be multiple casualties.
Although there is general agreement for the recurrence intervals assigned to the large,
Design Basis Earthquake (DBE), and the very large, Maximum Considered Earthquake (MCE)
ground motion events, various performance-based design provisions assign different recurrence
intervals for lower (serviceability and immediate occupancy) level ground motion. [See
commentary on the International Performance Code (ICC 2012b).] These intervals can vary
anywhere from a 25-year MRI to a 72-year MRI. Similarly, wind design of ordinary building
occupancy and use (Category II) structures is associated with large (rare) wind events (700-year
5
MRI). Critical and essential (Category III and IV) structures are associated with very-large (very
rare) wind events (1,700-year MRI). Typical recurrence intervals used for serviceability wind
design vary from 100-year MRI on the high end to 10-year MRI or even less (a 1-year MRI is
often used in design of high-rise buildings).
Traditional performance-based seismic analysis is often based on the characteristics of
the seismicity of tectonic plate boundaries, like the western United States, where it has been the
experience that frequent and occasional earthquakes can be very significant, as was the case with
Northridge. [See, for example, steel frame, reinforced concrete frame, and masonry building
performance assessments reported by Haselton and Churapalo (2012).] While this expectation is
appropriate for the western United States, it is not necessarily correct in the central and eastern
United States. The nature of the overall seismic hazard is quite different in the central and
eastern United States. Large magnitude earthquakes are possible outside the west, but they are
rare.
The implication is that in many areas of the central and eastern United States, the only
seismic limit state of importance is collapse prevention. Ground shaking associated with more
frequently occurring events is not likely to be damaging, and in fact, the gravity and wind system
is going to be capable of resisting the most probable motions (Judd and Charney 2014b). Of
course it is not prudent to ignore the likelihood of a major earthquake, and collapse prevention is
still essential.
Thus, while the goal of less than 10% probability of seismic collapse given the MCE
ground motion is equally applicable in both the western and the central and eastern United
States, and the desire for good performance at lower level shaking is also equally applicable, it
seems that the very distinct differences in the temporal distribution of the level of shaking in the
6
different portions of the country would lead to different conceptual bases for providing
acceptable performance. However, this is not the case because for a given ground motion
intensity, buildings in the central and eastern United States are designed in essentially the same
manner as buildings in the western part of the country.
1.1.4 Performance-Based Wind Design
Performance-based wind engineering has been identified as a national research priority (CTBUH
2014; NIST 2014b). To date, several performance-based frameworks have been developed for
wind engineering (van de Lindt and Dao 2009; Ciampoli et al. 2011; Griffis et al. 2012; Kareem
et al. 2013) and hurricane engineering (Barbato et al. 2013). Aswegan et al. (2015) developed a
procedure for nonstructural damage control of steel buildings under serviceability-level wind.
Nonlinear analysis has been used to determine the structural reliability of tall concrete buildings
(Hart and Jain 2013), and to determine inelastic damage accumulated in tall buildings during
hurricanes (Chen 1999; Chen and Davenport 2000; Gani and Légeron 2011). Muthukumar et al.
(2012) evaluated the performance of an existing concrete shear wall building. Still, general
application of nonlinear analysis to performance-based wind analysis is undeveloped.
One motivation for a performance-based nonlinear wind analysis is that conventional
wind-designed buildings may be overly conservative. Member stresses are limited to the linear
elastic range for strength-level events (700-year MRI for typical occupancy and usage). An
additional motivation for a nonlinear analysis is to determine collapse capacity of buildings—
especially storm shelters (e.g. FEMA 2008a,b) and critical facilities in tornadoes or other
extreme events.
7
Another motivation is that the possibility of employing buildings designed for wind to
achieve adequate seismic performance is economically appealing. More than 80% of the cost of
constructing a new steel building may be attributed to material costs, fabrication labor costs, and
erection labor costs (Carter et al. 2000). The remaining construction costs include special
inspections and other additional costs, such as scheduling constraints. Ductile connections and
detailing drive up construction costs (e.g. Batt and Odeh 2005), and invoking “R=3” provisions
leads to increased demands (and costs), but not necessarily increased performance (Hines and
Fahnestock 2010).
1.2 Objectives and Scope
The objective of this research was to determine the potential for using a conventional main
lateral-force resisting system, combined with the reserve strength in the gravity framing and/or
auxiliary collapse-inhibiting mechanisms deployed throughout the building, or enhanced shear
tab connections—collectively termed a collapse-prevention system—to provide adequate
serviceability performance and collapse safety for seismic and wind hazards in the central and
eastern United States.
While the concept is intended to be applicable to building structures of all materials, the
focus of this study was on structural steel-frame buildings using either non-ductile moment
frames not specifically detailed for seismic resistance, or ductile moment frames designed for
moderate seismic demands. The focus of the research is a proof-of-concept and global behavior
(i.e. building, or region behavior). Design and detailing of specific collapse prevention devices
is outside the scope of this research.
8
The applicability of the concept to steel moment-frame buildings commonly constructed
in the central and eastern United States was determined using a set of archetypical short period
(1-story and 2-story) and long period (4-story, 8-story, and 10-story) office buildings that
employed either a non-ductile moment frame with directly welded flange fully-restrained
moment connections (i.e. AISC 2011a, Figure 12-4a), or a ductile moment frame with a reduced
beam section (RBS) fully-restrained moment connection (i.e. AISC 2011b, Figure 5.1) designed
for moderate seismic demands. The reserve lateral strength in the gravity framing was
considered and collapse inhibiting devices (slack-cables, loose-linkages, or telescoping braces)
were deployed throughout the building. Alternatively, shear tab connections to the strong axis of
the column were enhanced by installing T-stub type flange connectors.
The vulnerability of the archetype structural systems to seismic and wind side-sway
collapse (collapse fragility) was determined by conducting gravity, frequency, nonlinear static
“pushover” analyses, followed by conducting a series of nonlinear dynamic response history
analyses of increasing seismic or wind intensity until side-sway collapse, following the FEMA P-
695 (FEMA 2009a) methodology. Uncertainty in the collapse assessments was considered by
treating separately the inherent variability of seismic and wind hazards (aleatory uncertainity)
and the variability due to imperfect structural modeling, testing, and construction (epistemic
uncertainty) (Ang and Tang 2006). Aleatory uncertainty of seismic and wind demands for the
ground motion and wind record sets was determined directly using record-to-record dispersion in
the structural analysis results. Epistemic uncertainty was determined subjectively, using
qualitative rating systems.
9
Seismic performance was evaluated using a Monte Carlo simulation using the FEMA P-
58 (FEMA 2012a,b,c,d) framework. The sensitivity of the collapse assessments was evaluated
for several key aspects of analytical modeling and hazard uncertainty.
The risk of collapse was determined by integrating collapse fragility and hazard,
accounting for directional effects and site response for seismic hazards, and accounting for non-
synoptic events for wind hazards. The combined seismic and wind (multi-hazard) risk of
collapse was determined and compared with societal levels of acceptable risk.
1.3 Dissertation Organization
This dissertation is organized into nine chapters and three appendices.
• Chapter 1 provides background for the research, and explains the motivation for the
current study. The objectives and scope of the research are defined. The chapter also
gives an overview of the organization of the dissertation.
• Chapter 2 briefly describes important features of seismic and wind hazards in the context
of structural engineering. For seismic hazards, ground motions, earthquake rate, ground
motion attenuation, site response, and spectral shape are discussed. For wind hazards,
basic wind speeds and non-synoptic wind hazards are discussed. Finally, a comparison is
made between elastic seismic and wind base shear forces and multi-hazard performance
of hypothetical buildings.
10
• Chapter 3 describes the collapse prevention system concept and the selection and
development of archetype structural systems. The archetype systems were intended to be
prototypical building configurations with or without collapse prevention mechanisms, in
order to determine the applicability of the CP system concept to steel moment-frame
buildings commonly constructed in the central and eastern United States. Reserve lateral
strength in the gravity framing system is discussed. Delayed-stiffness collapse inhibiting
mechanisms are described, as well as optional energy dissipation devices. Enhanced
shear tab connections, using T-stub type structural fuses, are discussed. The analytical
modeling and nonlinear analysis approach are also included.
• Chapter 4 assesses the seismic collapse safety of the archetype structural systems with
and without collapse prevention systems. The collapse vulnerability (collapse fragility)
was determined using a sequence of gravity, frequency, nonlinear static “pushover”
analyses, followed by nonlinear dynamic response history analyses incrementally scaled,
with respect to a target spectrum, until side-sway collapse. The risk of seismic collapse
was determined by integrating collapse fragility and hazard, accounting for directional
effects and site response. Results of selected archetype systems are discussed. Finally, a
comparison with the seismic collapse assessment of traditional structural systems is
included.
• Chapter 5 assesses the wind collapse safety of the archetype structural systems with and
without collapse prevention systems. The wind collapse vulnerability (collapse fragility)
was determined using a sequence of gravity, frequency, nonlinear static “pushover”
11
analyses, followed by nonlinear dynamic response history analyses incrementally scaled,
using an equivalent single-degree-of-freedom model and with respect to a reference wind
speed, until side-sway collapse. The results of selected archetype systems are discussed.
• Chapter 6 discusses the results of parametric studies used to determine the sensitivity of
seismic and wind collapse assessments to changes in hazard or structural vulnerability via
analytical modeling. The seismic hazard parameters include ground motions, site
response, regional risk, and intensity measures. The seismic modeling parameters
include column panel zone representation, the method used to account for second-order
(P-Delta) effects, column splices, risk integration method, and damping. The wind
hazard parameters consider duration of wind. The wind modeling parameters include
type of lateral system, static overstrength, fundamental building period, and structural
system degradation of stiffness and strength.
• Chapter 7 discusses the seismic performance of archetype structural systems.
Performance, in terms of repair costs and downtime, was assessed at serviceability and
design hazard levels based on the structural and non-structural component fragility using
floor accelerations and inter-story drift from nonlinear response history analyses.
Resilience was quantified by calculating the probable loss in functionality during a
reference time interval. Resilience contours were used to characterize the tradeoff
between construction and repair costs, and the ability to recover rapidly after an
earthquake.
12
• Chapter 8 assesses the multi-hazard (combined seismic and wind) risk of collapse. The
multi-hazard risk was calculated by assuming that the cumulative seismic risk and the
cumulative wind risk are statistically independent. The acceptable level of risk, including
social amplification, is discussed. The results for selected archetype structural system are
used to illustrate a multi-hazard assessment.
• Chapter 9 summarizes the findings of this research study. Conclusions and
recommendations based on the results are discussed, and areas for future research are
identified. The potential impact of the research is suggested.
• Appendix A contains standard analysis examples and benchmark problems to evaluate
the performance of computer software used in this study for structural analysis.
Appendix B discusses the design of the archetype Type I non-ductile moment frame
buildings. Appendix C contains excerpts of the OpenSees (PEER 2012) scripts and
selected modeling results for the Type I non-ductile moment frame 4-story building with
enhanced shear tab connections.
13
Chapter 2
SEISMIC AND WIND HAZARDS
This chapter describes salient features of seismic and wind hazards as they pertain to structural
engineering for buildings. For seismic hazards, ground motions, earthquake rate, ground motion
attenuation, site response, and spectral shape are discussed. For wind hazards, basic wind speeds
and non-synoptic wind hazards are discussed. Finally, a comparison is made between elastic
seismic and wind base shear forces and multi-hazard performance of hypothetical buildings.
2.1 Seismic Hazards
2.1.1 Uniform Hazard Ground Motions
The US Geological Survey (USGS) provides ground motions (spectral accelerations) in the
United States and corresponding maps for various probability levels. This data was based on the
ground shaking from potential earthquakes identified in workshops. The recommendations from
the workshops were then peer-reviewed by several science organizations and two expert panels.
The USGS updates the ground motion values periodically (the latest version of ground motion
values was released in late 2014). The 2008 United States National Seismic Hazard Maps were
adopted by ASCE 7-10 and the 2009 NEHRP provisions. The maps provide 0.2-second and 1.0-
14
second spectral accelerations, respectively, that have a 2% probability of being exceeded in 50
years—corresponding to the MCE ground motion for the “B/C” boundary soil site classification
and 5% of critical damping. Spectral accelerations for other periods and recurrence intervals are
provided (but not mapped).
By way of comparison, in Europe, the Swiss Seismological Service coordinates a
collaborative project—called Seismic Hazard Harmonization in Europe (SHARE)—that provides
ground motion values similar to those provided by the USGS. The SHARE project involves a
core team of over 50 scientists from institutions across Europe, North Africa, and Turkey, along
with additional experts participating in workshops (Giardini et al. 2013a). The European map
provides peak ground accelerations that have a 2% probability of being exceeded in 50 years.
Ground motion values for other probability levels can be accessed through the European Facility
for Earthquake Hazard and Risk (EFEHR) (Giardini et al. 2013b).
Ground motions for seismic design have traditionally been defined to provide a uniform
hazard. Typically the ground motions have a 2% to 10% probability of being exceeded in 50
years, depending on occupancy and use of the structure, and the building code and region
involved (ASCE 2005; FEMA 2009c; Bommer and Pinho 2006). However, it is the probability
of structural collapse that is of paramount concern (ATC 1978; ATC 1984; FEMA 2009c) and,
as a result, the goal of a uniform risk of collapse has replaced uniform hazard in recent design.
The chief example of this is the current ASCE 7-10 ground motion maps for the United States,
which are intended to provide a uniform risk of collapse of 1% probability in 50 years (Luco et
al. 2007; FEMA 2009c; ASCE 2010). Another example of uniform risk design is the ASCE 43-
05 approach for designing nuclear power plants (Kennedy 2011).
15
The difference between uniform-hazard and uniform-risk design ground motions depends
on the convolution of two factors: the shape of the ground motion spectral acceleration versus
annual frequency of exceedence curve (termed the “seismic hazard curve”) and the structural
sensitivity or vulnerability of collapse to ground motion (termed the “fragility curve”). For new
construction it is implied that the design using uniform-hazard maps of ground motion leads to
structures with fragility curves where the probability of collapse is consistent at a given hazard
level. Thus, the difference between uniform-hazard and uniform risk design maps is primarily a
reflection of the underlying differences in seismic hazard, discussed in the following section for
the United States.
Seismic hazard varies within many regions of the world. In the United States differences
between hazard curves in the western United States (tectonic plate boundary area) and hazard
curves in the central and eastern United States (intra-plate area) are well documented (FEMA
2009c; Levendecker et al. 2000; Judd and Charney 2014a). Similar but less dramatic differences
exist in Italy (tectonic plate boundary area) (Crowley et al. 2009). Of course, within some
regions—especially smaller regions—the seismic hazard curves do not vary greatly. In France,
for example, the shapes of the seismic hazard curves are similar (Douglas et al. 2013), and thus
the distinction between a uniform-hazard and uniform-risk map is less pronounced.
2.1.2 Earthquake Rate
The rate of earthquake recurrence varies across the United States. In general, earthquakes of a
given magnitude occur more frequently in the western United States than in the central and
eastern United States. The cumulative earthquake rates and seismic hazard curves for four high-
seismic locations shown in Figure 2.1 are used to illustrate this fact. The earthquake rate (Figure
16
2.1a) is estimated using the Gutenberg-Richter relationship (1944) and the magnitude and
number of events in 4° latitude by 2° longitude regions based on seismic events recorded in the
Advanced National Seismic System (ANSS 2013) global earthquake catalog. The earthquake
rate for Memphis is approximately corrected by removing double events.
The difference in earthquake recurrence rate is also evident in the shape of seismic hazard
curves (Figure 2.1b), which graphically depict the annual rate of exceeding a ground motion.
Based on the 2008 USGS National Seismic Hazard Map data for 5% damping on rock (soil site
class B/C boundary), the 0.2-second spectral acceleration during very large events (2,475-year
MRI) in Memphis and Charleston is comparable to San Francisco and Los Angeles. Yet the
intensity of shaking for small and medium events in the central and eastern United States is only
a small fraction of that in the western United States.
The lower recurrence rates in the central and eastern United States mean that the
dominate contributions to the overall seismic hazard come from smaller-magnitude events,
compared to western United States. This difference is thought to be a reflection of a wider
distribution of faults in the intra-plate region compared to tectonic boundaries.
a) b)
a) Cumulative earthquake rate (b) Seismic hazard curves
Figure 2.1 Regional differences in earthquake rate
17
The impact of the difference in earthquake rate is further illustrated in Figure 2.2, which
shows the probability over the next 100 years of a 6.7-magnitude earthquake occurring in Los
Angeles, California compared to Charleston, South Carolina, calculated using the USGS 2009
earthquake probability mapping application (USGS 2010). A Northridge-sized earthquake
(M6.7) is expected in California within the next 30 years (SCEC 2007) and the probability over
the next 100 years of a 6.7-magnitude earthquake occurring in Los Angeles is extremely high (as
high as 100% in many locations), but is less than 15% in Charleston, South Carolina, although
strong quakes of this size are possible in both locations. For comparison, a Mineral, Virginia-
sized earthquake (M5.8) is expected to occur in the northern Virginia area every 752 years or so
(Chapman 2015).
Differences between seismic ground shaking are plainly evident in many regions and
across a wide range of low-intensity hazard levels (Judd and Charney 2014a). For example,
Figure 2.3 to Figure 2.6 shows maps (contour lines of constant values) of the ratio of spectral
accelerations for different MRI compared to the MCE (2,475-year MRI) ground motion. The top
map compares the 0.2-sec spectral accelerations (𝑆𝑠 ), and the bottom map compares the 1.0-sec
spectral accelerations (𝑆1).
a) Los Angeles, California b) Charleston, South Carolina
Figure 2.2 Probability of exceeding a 6.7-magnitude earthquake in 100 years
18
Seattle 7.8%
Boston 2.1%
New York 1.2%
San Francisco 11%
𝑆𝑎25𝑀𝑀𝑀 Los Angeles 7.7%

𝑆𝑎𝑀𝑀𝑀
100%
63%
Memphis 0.8%
40% Charleston 0.2%
25%
16%
10%
6.3%
a) 0.2-second spectral acceleration (𝑆𝑠 )
4%
2.5% Seattle 6.2%
1.6% Boston 2.6%
1%
New York 1.2%
San Francisco 9.1%
Los Angeles 8.5%
Memphis 0.7%
Charleston 0.3%
b) 1.0-second spectral acceleration (𝑆1)
Figure 2.3 Ratio of 25-year MRI spectral acceleration compared to MCE ground motion
19
Seattle 12%
Boston 3.8%
New York 2.2%
San Francisco 18%
𝑆𝑎43𝑀𝑀𝑀
Los Angeles 12%
100%
63%
40% Memphis 1.7%

Charleston 0.5%
25%
16%
10%
6.3%
4%
2.5% Seattle 10%

1.6%
Boston 4.7%
1%
New York 4.2%
San Francisco 15%
Los Angeles 13%
Memphis 1.3%
Charleston 0.7%
20
Seattle 18%
Boston 6.5%
New York 4.0%
San Francisco 25%
𝑆𝑎72𝑀𝑀𝑀
Los Angeles 16%
100%
63%
40% Memphis 3.0%

Charleston 1.2%
25%
16%
10%
6.3%
4%
2.5%
Seattle 15%
1.6%
Boston 8.0%
1%
New York 7.2%
San Francisco 21%
Los Angeles 18%
Memphis 2.3%
Charleston 1.4%
21
Seattle 35%
Boston 18%
New York 13%
San Francisco 45%
𝑆𝑎225𝑀𝑀𝑀 Los Angeles 33%

100%
63%
Memphis 11%
40%
Charleston 7%
25%
16%
10%
6.3%
4%
2.5% Seattle 32%

1.6%
Boston 21%
1%
New York 19%
San Francisco 41%
Los Angeles 34%
Memphis 8.2%
Charleston 5.8%
22
Generally speaking, spectral demand with a 72-year MRI, is approximately 10% of the
MCE ground motion for the central and eastern United States, and 20% of the MCE ground
motion for the western United States. Of course, for soft soil (site classes D and E), low-
frequency ground motion is amplified more compared to high-frequency ground motion. The
effect of site response is considered later in this chapter.
A summary of average spectral acceleration compared to the uniform-hazard MCE-level
spectral acceleration is given in Table 2.1. Ratios for all map grid locations (every 0.05°) was
defined using 106° W longitude as the boundary between western United States and central and
eastern United States regions (Wald and Allen 2007). Deterministic limits on the ground motion
were not considered because the focus of the comparison was on probabilistic demands (and not
on design demands). The summary shows that ratios in the central and eastern United States
were roughly half that of the western United States. Comparing only population centers in the
west coast with the central and eastern United States, and not including the intermountain region
and outlier locations (e.g. Charleston, Memphis, and Miami), the ratios in the central and eastern
United States were 3 to 4 times smaller than the western United States.
Table 2.1 Average ratio of spectral acceleration (for different MRI)
compared to MCE ground motions
All map (gridded) locations Population centers

MRI
(years) Western United Central and Eastern West Coast of the Central and Eastern
States United States United States United States
25 0.07 0.03 0.08 0.02
43 0.12 0.06 0.13 0.04
72 0.19 0.11 0.19 0.07
225 0.44 0.34 0.36 0.20
23
Based on these results, for most locations in the central and eastern United States the
spectral demand associated with the 43-year event is approximately 5% of the MCE, compared
to 13% of the MCE for the western United States. The service-level (43-year MRI) spectral
acceleration of 13% of the MCE ground motion for population centers in the western United
States confirms that used in previous seismic performance studies (Atlayan and Charney 2014;
Jarrett et al. 2015). For the 72-year event, spectral demand is approximately 10% and 20% for
the central and eastern United States and western United States, respectively.
2.1.3 Ground Motion Attenuation
In general, the newer, more fractured and jointed bedrock in the western United States dissipates
seismic waves more over a given distance compared to the older central and eastern United
States bedrock. As well, there are significant regional aspects to ground motion attenuation.
Figure 2.7 shows major geological regions and their Quality (Q) factors, which are inversely
proportional to attenuation. The western United States generally has a low Q factor (e.g.
sedimentary basins). Seismic waves attenuate less in the Great Plains, where there is a high Q
factor, and generally in the Midwest, although this region is complex and difficult to generalize
(Conn 2013; PEER 2013).
Ground motion is attenuated somewhat less along the Atlantic Coastal Plain (moderately-
high Q factor), but considerably damped along the Gulf Coastal Plain (low 𝑄 factor). Indeed,
differences in regional attenuation of ground motion were dramatic during the 2011 Mineral,
Virginia earthquake. Ground motion propagated efficiently in the northeast, but was sharply
attenuated in the Gulf States (Chapman 2015).
24
Great Plains
(high 𝑸)
Midwest (complex,
Western United States
moderately-high 𝑸)
(complex, low 𝑸 in active
tectonic areas and
sedimentary basins)
Appalachians
(high 𝑸)
Atlantic Coastal Plain

(moderately low 𝑸)
Gulf Coastal
Plain (low 𝑸)
Figure 2.7 Geological regions of United States (background map of geology adapted from map
by Vigil et al. 2000)
Thus, earthquakes of a given magnitude attenuate much less rapidly in the central and
eastern United States compared to the western United States. This leads to a larger “felt area”
and potential for a more damaging impact. The difference between the geographic extents of
perceived ground motion is shown in Figure 2.8 for the 2011 Mineral, Virginia earthquake and a
similar magnitude earthquake in California (the 2004 Parkfield earthquake). The Virginia
earthquake was felt by more people in the United States than any previous quake in an area
encompassing a third of the country’s population (Horton 2012). The larger felt area in the
central and eastern United States is noteworthy, considering that half of the U.S. population lives
within 600 miles of Tennessee.
25
2011 Virginia
Earthquake
(magnitude 5.8)
2004 Parkfield
Earthquake
(magnitude 6.0)
Figure 2.8 Geographic extent of perceived ground motion (adapted from USGS 2012)
The difference in ground motion attenuation also affects the way earthquakes contribute
to the hazard at a location, in terms of magnitude and distance. Table 2.2 shows the mean
distance and magnitude of events that contribute to MCE ground motion (2,475-year MRI) for
selected locations, based on the 2008 USGS Interactive Deaggregation Tool (USGS 2013). In
the western United States, the hazard is dominated by earthquakes that are close by, due to a
higher density of faults. By contrast, in the central and eastern United States, as the spectral
period increases, the seismic hazard is increasingly dominated by distant earthquakes, sometimes
as far away as 300 miles or more. There are more known faults in western United States than in
the central and eastern United States, and these known sources have high seismic potential. For
these reasons, distributed seismicity contributes little to the hazard in the western United States
but is a strong contributor in the central and eastern United States.
26
Table 2.2 Mean Distance (Magnitude) contributing to MCE ground motion
Spectral Period (s)

Location
0.2 1.0 2.0
Los Angeles 5 km (6.66) 6 km (6.72) 12 km (6.87)
Western US
Las Vegas 16 km (6.14) 41 km (6.59) 77 km (6.96)
Chicago 115 km (5.86) 376 km (7.09) 455 km (7.38)
Nashville 203 km (7.41) 221 km (7.52) 226 km (7.57)
Boston 62 km (5.97) 165 km (6.61) 229 km (6.8)
Central and
New York 36 km (5.81) 119 km (6.44) 212 km (6.7)
Eastern US
Philadelphia 56 km (5.89) 169 km (6.53) 290 km (6.8)
Washington, D.C. 126 km (6.16) 286 km (6.77) 386 km (6.97)
Charlotte 143 km (6.77) 196 km (7.1) 242 km (7.21)
Another consideration is that ground motion attenuation is more uncertain in the CEUS.
This uncertainty is manifest by the dispersion in response spectrum, especially in the high
frequency (very short period) range for ground motion prediction equations. For example,
Figure 2.9 shows the mean response spectrum (conditioned for 1.0-second spectral period) for
Las Vegas and Nashville using different ground motion prediction equations based on the 2008
USGS Interactive Deaggregation Tool (USGS 2013).
0.4 0.4
Chiou-Youngs 2008
0.35
Campbell-Bozorgnia 2008 Frankel et al. 1996
0.35
Mean
Spectral Acceleration (g)
Spectral Acceleration (g)
0.3 0.3 Silva 1-corner

Boore-Atkinson 2008
0.25 0.25 Tavakoli and Pezeshk 05
0.2 0.2 Campbell CEUS Hybrid
Mean
0.15 0.15
0.1 0.1
Somerville Rifted FinFlt
0.05 0.05 Toro et al. 1997
0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Period (s) Period (s)
a) Las Vegas b) Nashville
Figure 2.9 Conditional mean response spectrum (conditioned on 1.0 second) for different ground
motion prediction equations

27
In the western United States, the ground motion prediction equations are well defined,
compared to the central and eastern United States. The underlying cause of uncertainty in the
central and eastern United States is the lower earthquake rates and scarcity of strong motion data
(Nikolaou et al. 2012).
The likely duration of ground motion is longer in the central and eastern United States.
For example, Figure 2.10 compares synthetic ground motions that are generated based on the
most likely (modal magnitude and distance) event for Las Vegas and Nashville. The ground
motions are generated using a stochastic model and deaggregation analysis (for 1.0-second
spectral period in Table 2.2).
0.3
Las Vegas (M6.6, 9 km)
0.2
Acceleration (g)
0.1
0
-0.1
-0.2
-0.3
20 25 30 35 40 45 50 55 60
Time (s)
0.3
Nashville (M7.7, 222 km)
0.2
Acceleration (g)
0.1
0
-0.1
-0.2
-0.3
20 25 30 35 40 45 50 55 60
Time (s)
Figure 2.10 Synthetic ground motions for most likely event based on a hazard deaggregation
28
Although a more realistic physics-based model (e.g. that by Somerville et al. 2001) is
needed to realistically represent source and path effects, including near-fault directivity (NIST
2011), the comparison shows that the overall duration of ground motion in the central and
eastern United States is predicted to be significantly longer than in the western United States.
The difference in duration is primarily due to the different distances from the fault sources.
The implication for performance-based design is that, all other factors being equal, the
longer duration of strong ground motion will likely mean: (1) structural components will be
subjected to additional cycles of deformation; and (2) collapse capacity will be lower
(Chandramohan et al. 2013). This is especially important for components susceptible to low-
cycle fatigue, such as pre-Northridge beam-to-column connections (Kanvinde and Deierlein
2004) and steel frames in buildings not specifically detailed for seismic resistance.
2.1.4 Site Response
The conventional NEHRP and ASCE 7 procedure to account for local site soil response
(amplification) is based on correlating shear wave velocity in the top 30 meters of the soil, 𝑉𝑠30
with ground motion records in the San Francisco bay area (Borcherdt 1994). Response
resolution was limited to two spectral period bands, short periods (near 0.2 seconds) and medium
range periods (near 1.0 seconds), because the design spectra was anchored these two periods.
Although a finer resolution of spectral periods, updated attenuation relationships, or similar
refinements have been proposed (Huang et al. 2010b; Seyhan and Stewart 2012), the original
two-band method has been shown to be adequate for the western United States (Borcherdt 2002).
For example, Figure 2.11 shows a comparison of the uniform hazard spectrum for a location in
San Francisco using the NEHRP/ASCE 7-10 procedure and the Huang et al. (2010b) procedure.
29
1.3
NEHRP/ASCE 7-10 site
1.2 response procedure
1.1
Site response procedure
Spectral acceleration (g)

1
based on Huang et al. (2010b)
0.9
0.8
0.7
0.6
0.5
0.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Spectral period (seconds/cycle)
Figure 2.11 Uniform hazard spectrum for a location in San Francisco (38.0º latitude, -121.7º
longitude) with soil site class D (average 𝑉𝑠30 = 180 m/sec)
The Eurocode 8 procedure is similar to the NEHRP procedure, except that site response
factors are applied to the entire spectrum (instead of period bands), and that there are some
differences in defining soil classifications. Improvements have been suggested for both the
classifications and the amplification factors (Pitilakis and Riga 2012), and for incorporating
some knowledge of the type and depth of the soil column (Pitilakis and Riga 2013).
Nevertheless, site response is complex. Ground motion amplification depends on the
shear wave velocity profile and thickness of the soil column, bedrock characteristics, the
magnitude and depth of the soil-to-bedrock impedance contrast, and topographic effects, among
other factors (Kramer 1996). This is especially true in the central and eastern United States. As
a consequence, various alternative site response procedures have been proposed (Rodriguez-
Marek and Bray 2001; Pitilakis and Riga 2013; Kottke et al. 2012).
30
Bedrock Characteristics
Bedrock in the western United States sedimentary basins exhibits 𝑉𝑠 of generally 2,000 m/s.
Bedrock in the central and eastern United States is typically harder, with 𝑉𝑠 consistently higher
than 3,000 m/s (Nikolaou et al. 2012). The implication for seismic performance-based design is
that site response in the central and eastern United States is better represented using 𝑉𝑠 = 2,000
m/s data (i.e. 2010 Revision III update of the 2008 USGS data) for bedrock motion, instead of
the conventional 𝑉𝑠 = 760 m/s data corresponding to the “B/C boundary” assumed for the
western United States.
Soil-Bedrock Impedance Contrast
An important consequence of bedrock characteristics is that the soil-bedrock impedance contrast
is typically larger in the central and eastern United States, compared to the western United
States. As seismic shear waves move upward through a layer contrast, the transmitted wave is
amplified. (See Kramer 1996; Aki and Richards 1980; Schnabel et al. 1972.) The response at
the free surface (ground) is the compounded effect of transmitted up-going waves and reflected
down-going waves. In the absence of resonance,
2𝜌𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑉𝑠,𝑏𝑏𝑏𝑏𝑏𝑏𝑏
Ground / bedrock motion = (2.1)
𝜌𝑠𝑠𝑠𝑠 𝑉𝑠,𝑠𝑠𝑠𝑠
Assuming a single layer contrast, no attenuation in the soil layer, and no damping (𝑄
equal to ∞), the minimum amplification is 2.0 at the free surface. For a typical rock (𝑉𝑠 = 1,000
m/s and density, 𝜌 = 2 gm/cc) and bedrock (𝜌 = 2.5 gm/cc), the maximum amplification at the
ground would be 5.0 in the western United States and 7.0 or greater in the central and eastern
United States. Resonance occurs in proportion to the location of the layer contrast relative to the
31
surface. An actual soil profile has multiple layers and a finite 𝑄, so the amplification is damped
out after the first harmonic.
Thus, site response is simply an application of the principle of conservation of energy.
One way to think of site response is to consider that seismic waves traveling towards the ground
surface are like ocean waves approaching the shoreline. As the ocean wave slows down, the
ocean wave amplitude increases. In California most of the population is in sedimentary basins
and active tectonic areas, and the velocity contrast is roughly 2. In the central and eastern United
States the velocity contrast can be much higher. In fact, a high impedance contrast is true for
many locations along the east coast and in the Midwest.
The velocity profile is also gradual in the western United States, but in the central and
eastern United States the contrast is often sudden. Site response studies in Washington, D.C.
following the Virginia earthquake showed “sharp velocity contrasts” (Godfrey et al. 2012).
Short and mid-range period amplification are consistently higher along the eastern
Coastal plains than the conventional procedure predicts (Nikolaou et al. 2012; Amine et al.
2012). Generally speaking, there is a 20% increase in high-frequency motion and no increase in
low-frequency (long period) motion in central and eastern United States compared to the western
United States (Hashash and Moon 2011; Amine et al. 2012).
Depth of Soil-Bedrock Impedance Contrast
It is not uncommon in the central and eastern United States to have a significant impedance
contrast located within the top 100 feet. In such locations, the shallow depth of a high
impedance contrast can generate damaging surface waves during an earthquake, much like a
tsunami. Thus, even if most of the soil profile can be generalized (bedrock characteristics,
32
contrast between bedrock and lower layers) the last layer to the surface can govern site response.
As a result, it may not be practical to generalize site response. South Carolina is a case in point.
Site response is very different in Columbia and Charleston, but even within Columbia, response
is very different west of the fall line in the Piedmont, compared to the Coastal Plain in the east
(Amine et al. 2012).
As previously mentioned, the USGS uniform-hazard ground motions reference a shear
wave velocity, 𝑉𝑠 = 760 m/s. This corresponds to the boundary of the ASCE 7-10 soil
classification of “rock” (site class B) and “very dense soil and soft rock” (site class C). Although
the actual bedrock shear wave velocity in the central and eastern US is much higher—three times
or more (Nikolaou et al. 2012)—site class B was selected because it represented an average of
the rock sites used in the western United States attenuation relationships (FEMA 2003).
Soil-Structure Interaction
The importance of soil-structure interaction may be indicated by the superstructure-to-soil
“velocity” ratio, expressed in Equation 2.2.
𝐻 ⁄𝑇1
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑟𝑟𝑟𝑟𝑟 = (2.2)
𝑉𝑠30
where 𝐻 is taken as 2/3 of the building height and 𝑇1 is the fundamental period of vibration of
the building.
When the ratio is on the order of 0.1, soil-structure interaction is an important factor in
site response (NIST 2012a). In general, for braced frame or shear wall structures, the ratio is
between 0.1 and 0.5. For moment frames on stiff rock, the ratio will be less than 0.1 (Stewart et
al. 1999). Thus, soil-structure interaction is not expected to be significant for the buildings
analyzed in this research.
33
2.1.5 Spectral Shape
The combined effect of earthquake rate, ground motion attenuation, and site response results in a
central and eastern United States spectral shape that is distinguished from the western United
States by added high-frequency content (NIST 2011).
For example, Figure 2.12 shows the characteristic uniform hazard spectrum for 12 major
population centers in the western United States (and the average spectrum) and for 25 major
population centers the central and eastern United States (and the average spectrum) for both the
43-year MRI (upper plots) and the 2,475-year MRI MCE ground motion (lower plots). The
spectra in Figure 2.11 were normalized with respect to the peak ground acceleration and plotted
on a log-log scale. The spectra demonstrate both the spectrum shift toward higher frequencies
(especially at the MCE-level) and the wider variability in the central and eastern United States.
The difference in spectrum is significant because high frequency content in ground
motion affects building performance. Existing buildings, wind-designed buildings, and braced-
frame buildings—all common in the central and eastern United States—are sensitive to high
frequencies due to high stiffness and lack of ductility. For example, an analytical study of a 9-
story low-ductility chevron braced frame building (Hines et al. 2011) indicated that higher-mode
effects caused significant damage. In general, short-period buildings exhibit poor collapse safety
performance (NIST 2012b).
An implicit assumption of the uniform-hazard response spectrum is that a single event
may produce the spectral values (ordinates in the response spectrum). As an alternative, the
conditional mean spectrum (Baker 2011), which is the probabilistic expected (mean) response
spectrum conditioned on a target period and corresponding spectral acceleration, can be used.
34
If all ordinates in the uniform hazard response spectrum were dominated by the same
very-large event, the uniform hazard and conditional mean spectrum would be essentially the
same (Baker 2011). Unlike the western United States, in the central and eastern United States
often a small close event dominates the high-frequency while a large distant event dominates
low-frequency. For these reasons, and due to the fact that multiple modes often contribute
(NIST 2011), the uniform hazard response spectrum is thought to be a suitable (i.e. not an overly
conservative) target for ground motion selection and scaling (Lin et al. 2013) in the central and
eastern United States. Nevertheless, the further research is required to confirm this statement.
43-year MRI 43-year MRI

Normalized (Sa/PGA) (g)
Average
0
Average 0
10 10
-1 0 -1 0
10 10 10 10
2,475-year MRI 2,475-year MRI

0 0
10 10
-1 0 -1 0
10 10 10 10
a) Western United States b) Central and eastern United States
Figure 2.12 Characteristic uniform hazard response spectra
35
2.2 Wind Hazards
2.2.1 Uniform Hazard Wind Speeds
Uniform hazard wind speed values for the United States and corresponding maps for selected
probability levels are provided in ASCE 7-10 and in digital format by the Applied Technology
Council (ATC 2011). These values correspond to a synoptic basic wind speed (in mph) for a 3-
second gust at 33 feet above the ground for terrain exposure category C (unobstructed, open
country) and, as a consequence, they do not account for topographic effects. Non-synoptic wind,
especially tornadic wind, is not accounted for in the ASCE 7-10 mapped values. The basis is
twofold. First, spatially the probability of occurrence of a tornadic wind speed is significantly
lower compared to the basic wind speed. Second, measurements of wind speed during actual
tornados indicate that the wind speed is often (more than half the time) lower compared to the
basic wind speed (ASCE 2010). The effect of tornados is considered in more depth in the next
section, and the effect of tornados on the collapse risk of building is examined in Chapter 5.
Figure 2.13 shows the design wind speed for a 700-year MRI (used for ordinary
occupancy risk category II structures). The figure resembles Figure 26.5-1.A in ASCE 7-10 and
includes “special wind regions,” where a design value is not provided. Figure 2.14 shows the
corresponding wind hazard map used in this research, which is identical to Figure 2.13 except
regional values of wind speed were applied to the special wind regions. (In design special wind
regions should be examined for unusual wind conditions.) Figure 2.15 compares service-level
wind speeds to the design wind speed (700-year MRI) for the central and eastern United States.
In contrast to ground motion, service-level wind is a significant percent of the design-level.
36
𝑉𝑚𝑚ℎ
200 mph
h
190 mph
180 mph
Special wind
regions 170 mph
h
160 mph
h
150 mph
140 mph
h
130 mph
120 mph
h
110 mph
100 mph
h
Figure 2.13 Design wind speed contours with a 700-year MRI (special wind regions included)
Seattle 110 mph 𝑉𝑚𝑚ℎ

200 mph
Boston 128 mph
190 mph
New York 115 mph
180 mph
Special wind h
regions removed 170 mph
San Francisco 110 h
160 mph
150 mph
Los Angeles 110 mph h
140 mph
h
130 mph
Memphis 115 mph 120 mph

h
Charleston 146 mph
110 mph
h
100 mph
h
Miami 169 mph
Figure 2.14 Design wind speed contours with a 700-year MRI (special wind regions removed)
37
Boston 62%
Boston 70%
New York 66%

New York 74%
Memphis 66%
Memphis 73%
Charleston 52%
Charleston 61%
𝑉𝑚𝑚ℎ
700𝑀𝑀𝑀
𝑉𝑚𝑚ℎ
100%
95%
Miami 53%
Miami 67%
90%
85%
a) 10-year MRI / 700-year MRI b) 25-year MRI / 700-year MRI 80%
75%
Boston 76% Boston 81% 70%
65%
New York 78% New York 83%
60%
55%
50%
Memphis 78% Memphis 83%

Charleston 69% Charleston 77%
Miami 76% Miami 82%
a) 50-year MRI / 700-year MRI b) 100-year MRI / 700-year MRI
Figure 2.15 Ratio of service-level wind speed to design wind speed for ordinary occupancy and
use structures (risk category II)
38
2.2.2 Wind Hazards
Wind hazards are inherently different compared to seismic hazards. Wind loads are
generated by wind pressures applied to the building envelope, whereas seismic loads are inertial
forces generated by ground movement. The characteristics of wind pressure depend primarily on
the shape of the building and the terrain exposure. Wind loads also depend on the type of
windstorm (e.g. hurricane, extra-tropical cyclone, downburst, and tornado). This differs from
seismic load characteristics which depend largely on the mass and stiffness of the building and
the tectonic environment, fault mechanism, and epicenteral distance.
Wind load is a random phenomenon that is stationary in the short term, and is often
described as mean load with superimposed random fluctuations (gusts) that tend to increase
during a windstorm in a ratcheting pattern. By contrast, earthquake ground motion is non-
stationary and reflects combinations of compression and shear seismic waves. As a result,
seismic loads are essentially symmetric, but the average along-wind load is non-zero. Cross-
wind loads generated by vortex shedding and harmonic effects are not symmetric, and are
important in taller structures.
Another difference is that a wind event is significantly longer in duration than an
earthquake. A typical strong windstorm (excepting tornados) may be 45 to 60 minutes long or
even longer (e.g. Gani and Legeron 2012). A particular building model may sustain extreme
wind loads for an hour prior to collapse (as shown through analysis in this study), but the same
building model subjected to earthquake ground motions may sustain only 10-20 seconds of
strong shaking.
Additionally, the frequency content of wind loads is typically broader compared to the
earthquake load spectrum, but contains less high-frequency content (Boggs and Dragovich
39
2006). Structural damage during an earthquake lengthens the fundamental period, which in turn
can lower demands or increase demands, depending on the shape of the response spectrum (Naga
and Eatherton 2014). In a windstorm, softening of a structure induces greater flexibility and
demands. On the other hand, wind-borne debris (missile impact) can likewise change the
character of the wind load.
2.3 Multi-Hazard Comparison
2.3.1 Seismic and Wind Elastic Base Shear Forces
A comparison between elastic seismic and wind base shear forces generated by equal likelihood
events indicates that steel frame buildings designed for wind may have the essential strength
required for small and medium seismic events. A hypothetical 8-story building with a height of
100 feet, assuming a 12.5-ft story height, is used for illustration. The building width (dimension
perpendicular to the wind direction) is taken as 90 feet, to represent three 30-ft long bays. The
building length (dimension parallel to the wind direction) is taken as 60 feet, to represent two 30-
ft long bays. The building “density” is assumed to be 8 pounds per cubic foot. The building
structural system is assumed to employ steel moment frames for lateral resistance, and to provide
about 1% damping for dynamic wind forces. The building is assumed to be located on rock
(ASCE 7-10 soil site class B) and in open terrain (ASCE 7-10 wind exposure terrain type C).
Elastic seismic base shear force was calculated using the equivalent lateral force
procedure (ASCE 7-10 Chapter 12.8), where the minimum base shear requirements were not
invoked, and the response modification factor was set to 1.0. Spectral accelerations were based
on the 2008 USGS National Seismic Hazard Map data.
40
The wind base shear force was calculated using the directional procedure (“all heights”
method) for the main wind force resisting system (ASCE 7-10 Chapter 27). Basic wind speeds
were based on the digitized version (ATC 2011) of the ASCE 7-10 wind speed maps (Figures
26.5-1.A through C, and Figures CC1 through CC4), except that regional values were applied to
“special wind regions.” For wind forces, the fundamental period of vibration was estimated
using the wind procedures. As a result, the period calculated was slightly longer compared to the
estimated values used for seismic forces.
Spectral accelerations and basic wind speeds with return periods in between mapped data
return periods were interpolated or extrapolated based on the nearest interval. (For a given
probability of exceedence, the corresponding return periods for wind and seismic hazards differ
slightly, but not significantly.)
Figure 2.16 to Figure 2.21 compare elastic seismic and wind base shear forces for the
hypothetical 8-story building in the conterminous United States for the range of event return
period, or median return interval (MRI), used for wind serviceability design. The maps show
contour lines of constant values (white space does not represent zero). The value of the base
shear ratio is indicated by the color (exponential scale). This comparison indicates that for
serviceability applications, the wind elastic base shear force is 10 times the seismic force or
more, outside the western United States.
41
𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ⁄𝑉𝑤𝑤𝑤𝑤
32
Seattle 17%
Boston 0.8%
10
New York 0.8%

3.2
San Francisco 35%
1.0
Los Angeles 42%
0.32
Memphis 1.1% 0.1
Charleston 0.4%
8-story moment frame building (90 0.032

feet wide, 60 feet deep, 100 feet tall)
with soil site class B in open terrain
(exposure category C)
0.01
Figure 2.16 Ratio of seismic to wind elastic base shear for 10-year MRI
32
Seattle 39%
Boston 1.7%
10
New York 1.8%

3.2
San Francisco 79%
1.0
Los Angeles 82%

0.32
Memphis 2.9% 0.1
Charleston 1.2%

(exposure category C) 0.01
42
32
Seattle 62%
Boston 3.1%
10
New York 3.3%

3.2
San Francisco 124%
1.0
Los Angeles 119%

0.32
Memphis 5.9% 0.1
Charleston 2.6%
(exposure category C)
0.01
32
Seattle 90%
Boston 5.3%
10
New York 5.8%

3.2
San Francisco 185%
1.0
Los Angeles 170%

0.32
0.1
Memphis 11%
Charleston 5.2%

(exposure category C) 0.01
43
Figure 2.21 Ratio of seismic to wind elastic base shear for 100,000-year MRI
44
The sensitivity of the conclusions to building period, soil type, and terrain exposure is
shown in Figure 2.22 to Figure 2.25, where a constant 100-year MRI (39% probability of
exceedence in 50 years) and assuming stiff soil (site class D) is used for comparison. Seismic
design controls in many areas for short-period buildings, but wind design controls for long-
period buildings. The effect of terrain on the wind pressure is less significant. The effect of
hurricane wind is evident along the southern and eastern coastlines.
Figure 2.26 shows the comparison of the base shear for seismic activity, assuming soft
soil (site class D) with the base shear for extreme winds estimated by extrapolating ASCE wind
speed data. Figure 2.27 shows the same comparison of the base shear, except that the extreme
wind speeds are based on tornados. Tornado wind speed was estimated by using the number of
tornados that have been cataloged for 2°×2° regions and correlating the tornado intensity factor
with a wind speed (Ramsdell and Rishel 2007). For rare events (MRI much greater than 100
years), seismic force controls. Using tornado data was conservative for locations in the interior
of the United States (such as in Memphis), but extrapolated wind data was more conservative for
non-tornado prone regions or regions with exposed to hurricane wind speeds.
45
32
Boston 52%
10
3.2
San Francisco 1,640%
1.0
0.32
Memphis 108% 0.1
2-story eccentric braced frame

building with soil site class D in 0.032
open terrain (exposure category C)

for a 100-year MRI
0.01
Figure 2.22 Ratio of seismic to wind elastic base shear for a short-period building
32
Boston 13% 10
3.2
San Francisco 400%
1.0
0.32
Memphis 26% 0.1
12-story moment frame building

with soil site class D in open 0.032
terrain (exposure category C) for

a 100-year MRI
0.01
Figure 2.23 Ratio of seismic to wind elastic base shear for a long-period building
46
32
Boston 17%
10
3.2
San Francisco 545%
1.0
0.32
Memphis 36% 0.1
8-story moment frame

building with soil site class D 0.032
for a 100-year MRI
0.01
Figure 2.24 Ratio of seismic to wind elastic base shear for urban terrain (exposure category B)
32
Boston 13% 10
3.2
San Francisco 400%
1.0
0.32
Memphis 26% 0.1
8-story moment frame

0.032
building with soil site class D
for a 100-year MRI
0.01
Figure 2.25 Ratio of seismic to wind elastic base shear for open terrain (exposure category C)
47
32
Seattle 492%
Boston 170%
10
New York 331%

3.2
San Francisco 471%
1.0
Los Angeles 377%

0.32
Memphis 445% 0.1
Charleston 83%
8-story moment frame building (90 feet
wide, 60 feet deep, 100 feet tall) with soil 0.032
site class D in open terrain (exposure

category C) for a 100,000-year MRI
0.01
Figure 2.26 Ratio of seismic to wind elastic base shear for extrapolated ASCE 7-10 wind speeds
32
Seattle 2,720%
Boston 441%
10
New York 525%

3.2
San Francisco 2,090%
1.0
Los Angeles 2,080%

0.32
Memphis 348% 0.1
Charleston 276%
8-story moment frame building (90 feet
wide, 60 feet deep, 100 feet tall) with soil 0.032
site class D in open terrain (exposure

category C) for a 100,000-year MRI
0.01
Figure 2.27 Ratio of seismic to wind elastic base shear for tornado wind speeds
48
2.3.2 Multi-Hazard Performance Example
An example structure is used to illustrate the multi-hazard performance of a building located in
the central and eastern United States for a variety of structural systems. The example
(hypothetical) structure is a children’s hospital located to be located in Cape Girardeau, Missouri
(37.3º latitude, -89.52º longitude) with soil site class D. A discussion of site response in Cape
Girardeau is provided by Hoffman (2001).
The hospital has six stories above grade with one basement level (15 feet below grade).
The building is 125 feet wide (N-S direction), 175 feet deep (E-W direction) and 85 feet tall.
The first story height is 17.5 feet and upper story height is 13.5 feet. The design live load is 60
psf on the main floors, and 20 psf on the roof.
Performance Objectives
The set of performance goals (objectives) selected for the hospital are summarized in Table 2.3.
It is assumed that the seismic and wind hazard levels, defined in terms of the mean-recurrence
interval (MRI), were set by the stakeholders. In this example, the MRI for small and medium
magnitude events was longer (i.e. conservative) compared to the 2012 International
Performance Code (ICC 2012b). Mild damage is tolerated for most hazard levels (43-year to
475-year MRI). Moderate damage is tolerated for the maximum considered earthquake (MCE)
ground motion hazard level (2,475 MRI). High damage is not tolerated for any hazard levels. It
is intended that the structural design will prevent collapse and protect the life of the occupants.
Since the children’s hospital is an essential facility, the overarching performance objective goes
beyond safeguarding life to reducing damage and ensuring that the hospital is operable during
earthquakes and windstorms.
49
Table 2.3 Performance criteria: tolerable impact in terms of hazard level
Earthquake Event (Hazard Level) Maximum Damage Limit

Magnitude Occurrence MRI (years) (Tolerable Impact)
Small Frequent 43 Mild
Medium Less Frequent 225 Mild
Large Rare 475 Mild
Very Large Very Rare 2,475 Moderate
Seismic Hazards
The USGS national seismic hazard maps and data (Petersen et al. 2008) and seismic
deaggregation tools were used to determine the seismic hazards. Figure 2.28 shows the
contribution potential of earthquakes (described by magnitude and distance from the source to
site) for the spectral acceleration at 1.0 seconds/cycle [𝑆𝑎 (𝑇𝑛 = 1.0 𝑠)] for each hazard level.
This long-period spectral response is nearest the estimated fundamental period of the building
(approximately between 1.0 and 1.5 seconds/cycle).
The seismic hazard is dominated by a magnitude 7.7 rupture on the New Madrid fault at a
distance of less than 50 km from the children’s hospital, except for small levels of hazard
(frequent seismicity, 43 MRI) where a 5.4 magnitude quake farther away (124 km) is the primary
contributor along with widespread background seismicity.
Table 2.4 summarizes the spectral acceleration, modal event, and source for each
earthquake hazard level. The epsilon values for each magnitude (M) and distance (D) pair
indicate the degree of uncertainty (values within -0.5 to 0 are less uncertain). Contributions of
the hazard not arising from the New Madrid fault are from the central and eastern United States
(CEUS) area source. Taken together, Figure 2.28 and Table 2.4 show that ground shaking was
not expected to be significant, except for a rare earthquake.
50
a) 43-year MRI b) 225-year MRI
c) 475-year MRI d) 2,475-year MRI
Figure 2.28 Contribution of potential quakes to spectral acceleration, 𝑆𝑎 (𝑇𝑛 = 1.0 𝑠)
Table 2.4 Primary contributions to seismic hazard
Sa(Tn=1.0 s) Modal Event (Earthquake)

MRI (years) (g) Contribution M D (km) Epsilon Source
43 0.005 3% 5.4 124 -0.5 to 0 CEUS (91%)
225 0.034 20% 7.7 43 less than -2 New Madrid FZ (43%)
475 0.097 35% 7.7 43 -2 to -1 New Madrid FZ (75%)
2,475 0.441 40% 7.7 41 0.5 to 1.0 New Madrid FZ (94%)
51
Wind Hazards
Windstorm hazards were determined using the ASCE 7-10 methods. Figure 2.29a shows the
basic wind pressure values for design of the structural system. The location of the children’s
hospital is in an area of the United States that has historically been very susceptible to tornadoes.
Figure 2.29b shows the predicted 3-second gust wind speeds (mph) for the contiguous United
States (corresponding to a 100,000-year MRI), based on a typical structure size and the number
of tornado events that have been cataloged for 2°×2° regions (Ramsdell and Rishel 2007).
An examination of the seismic and wind hazards for this location reveals that the
magnitude of expected earthquake hazards is unlikely to be significant, and that windstorms may
actually dominate the most performance levels (i.e. the lower performance levels, serviceability).
40
35
Vmph
Wind pressure (psf)
30
25
20
15
0 500 1000 1500 2000 2500
Return period (yrs)
a) Design MWFRS wind pressure (psf) b) 3-second tornado gust wind speed (mph)
Figure 2.29 Wind pressure and tornado hazards for example structure
52
Comparison of Structural Systems
Four types of structural systems (defined in general terms) were considered for the children’s
hospital:
• Steel moment frames
• Reinforced concrete (R/C) moment frames
• Steel eccentrically braced frames (EBF), steel buckling restrained braced (BRB) frames
• All other systems. Broadly includes a variety of materials and systems (e.g. shear walls)
An optimal structural system is to selected based on (1) reducing the spectral demands on
the structural system; (2) comparing the relative structural performance based on seismic and
wind drift analyses; and (3) considering the historical performance, cost-effectiveness, and
architectural viability of the system.
Table 2.5 demonstrates how the choice of structural system effects the spectral demands
in terms of the estimated spectral acceleration at the fundamental period of the hospital. Since
the approximate fundamental period of the hospital (based on the ASCE 7-10 empirical method)
is a function of the structural system, stiffer systems lead to lower periods and higher seismic
design demands.
The corresponding values of spectral acceleration account for bidirectional effects of
ground shaking (maximum-direction spectrum instead of geometric mean spectrum) as well as
ground motion amplification at the site based on the soil (using the NEHRP/ASCE 7 factors).
Although the amplification factors in NEHRP/ASCE 7 were developed for the western United
States, recent analysis (Hashash and Moon 2011) suggests that the magnitude of amplification is
appropriate for long period structures in the Mississippi embayment, such as the hospital.
53
Table 2.5 Effect of structural system on spectral demands
Structure Spectral Acceleration, Sa(Ta)

System Ct x Ta 43 MRI 225 MRI 475 MRI 2,475 MRI
Steel moment frame 0.028 0.8 0.98 0.012 0.077 0.222 0.745
R/C moment frame 0.016 0.9 0.87 0.014 0.089 0.251 0.855
Steel EBF 0.03 0.75 0.84 0.015 0.092 0.257 0.882
Steel BRB 0.03 0.75 0.84 0.015 0.092 0.257 0.882
All other 0.02 0.75 0.56 0.019 0.113 0.308 1.066
Figure 2.30 compares the seismic hazard curves for each structural system. The curves
include the geometric mean spectrum hazard (gray line), maximum-direction spectrum hazard
(red line), and the soil-amplified maximum-direction spectrum hazard (blue line), discussed in
detail in Chapter 4. Seismic hazard levels are indicted by horizontal lines (from top to bottom,
43-year, 225-year, 475-year, and 2,475-year MRI) and MCE values are indicated by vertical
lines.
Compared to a steel moment frame system, concrete moment frame or braced frame
systems “attract” 13% to 22% more spectral acceleration, depending on the hazard level and
system. This increase in spectral acceleration is due to the shape of the response spectrum and
the flexibility of the system. All other factors aside, this comparison supports the selection of a
steel moment frame system.
A simple analysis was used to compare the relative performance of potential structural
systems. Table 2.6 shows the estimate of roof drift based on the drift-controlled structural
system being designed using ASCE 7-10, and based on a linear relationship between drift and
spectral acceleration. Damage is based on approximate drift ratio limits adapted from Griffs
(1993), Galambos and Ellingwood (1986), and ASCE (1986). In Table 2.6, “high damage” is
indicated in orange.
54
-1
Mean annual rate of exceedance, λ (1/year) 10
-2
10
-3
10
-4
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Spectral acceleration, Sa(T=0.98s) (g)
a) Steel moment frame b) Reinforce concrete (R/C) moment frame
c) Steel EBF or BRB d) “All other” structural systems
Figure 2.30 Seismic hazard curves for potential structural systems
Table 2.6 Estimated drift ratio and probable damage for seismic hazards
Drift Ratio
System 43-year MRI 225-year MRI 475-year MRI 2,475-year MRI
Steel moment frame 0.000246 0.001554 0.00447 0.015
R/C moment frame 0.000253 0.001565 0.004395 0.015
Steel EBF 0.000254 0.001567 0.004365 0.015
Steel BRB 0.000254 0.001567 0.004365 0.015
All other 0.000266 0.001596 0.00434 0.015
55
The analysis suggests that the hospital is unlikely to experience any kind of significant
damage due to earthquakes. Yet, should the New Madrid fault have a very-rare large magnitude
rupture at the MCE hazard level, high damage is expected. The hospital is expected to survive,
but likely it will be badly damaged. It may be difficult to repair and there may be significant
downtime during those repairs.
The analysis method for this example is manifestly approximate, and is not intended to
provide a precise or final assessment. Yet given that limitation, the analysis would suggest there
is no advantage in terms of seismic drift control for one structural system above another.
However, wind drift control is another matter.
Table 2.7 shows an estimate of the damage expected due to windstorms. The estimate is
based on the ratio of wind base shear to seismic base shear, where the seismic base shear is
calculated including the 𝑅 value and importance factor, but not the 2/3 factor for the design basis
earthquake demands. Tornadoes are a threat for this area of the country, but the effects do not
alter the projected wind speeds until longer return periods.
Table 2.7 Estimated drift ratio and probable damage for windstorm hazards
Drift Ratio
Structural Lateral Force-Resisting System 43 MRI 225 MRI 475 MRI 2,475 MRI
Type Ct x Tw 89 mph 103 mph 110 mph 122 mph
Steel moment frame 0.045 0.8 1.57 0.0021 0.0028 0.0032 0.0035
R/C moment frame 0.023 0.9 1.25 0.0018 0.0025 0.0028 0.0031
Steel EBF 0.030 0.75 0.84 0.0018 0.0024 0.0027 0.0030
Steel BRB 0.030 0.75 0.84 0.0018 0.0024 0.0027 0.0030
All other 0.013 1 1.13 0.0015 0.0020 0.0023 0.0025
56
The results indicate that it is very possible for the children’s hospital to experience mild
damage, especially for more flexible structures. Steel moment frames are especially vulnerable.
Thus, a realistic selection of a structural system requires an evaluation of the likely damage due
to windstorm hazards. Steel moment frames are favorable in terms of historical performance in
earthquakes. Steel moment frames are especially cost-effective for 6-story to 9-story structures,
compared to other systems, if the gravity system is utilized (Elnashai and Di Sarno 2008).
57
2.4 Discussion
In many ways, seismic hazard in the central and eastern United States is different compared to
the western United States. Although earthquakes of a given magnitude occur less frequently in
the central and eastern United States, ground motion is felt over a much broader area. Strong
ground motion in the central and eastern United States is likely to be of long duration, which is
important for non-ductile structures and components that are prone to low-cycle fatigue. Also,
the uniform hazard response spectrum is likely a conservative target for ground motion selection
and scaling. Large magnitude earthquakes are rare outside the western United States. As a
consequence, even for communities in the New Madrid high-seismic area, the impact of
frequently occurring earthquakes (serviceability-level seismic hazard) is the primary concern, not
life safety (Olshansky et al. 2003).
Of course it is recognized that any “micro-zonation” or generalization concerning seismic
hazard is inherently inexact. There are significant regional aspects to ground motion attenuation,
and, in addition to topographic effects, site response is dependent on bedrock characteristics, the
soil velocity profile, and the magnitude and depth of the soil-to-bedrock impedance contrast.
Bedrock in most of the central and eastern United States is harder than the bedrock in
populated areas of the west coast, and in evaluating site response, ground motion data
corresponding to 𝑉𝑠 = 2,000 m/s is more appropriate compared to B/C boundary data. Soil-
structure interaction is important for stiff buildings located on a stiff soil site, and should be
considered in the site response of braced-frame and shear wall buildings on hard rock sites,
common in the central and eastern United States. Although site response informed by regional
geology may provide a first-order estimate (e.g. Kottke et al. 2012), a geotechnical site
investigation is recommended where feasible.
58
The spectral demands associated with the 43-year and 72-year events in the central and
eastern United States are approximately 5% and 10% of the MCE, respectively, roughly half of
the comparable demands in the western United States. This is noteworthy considering that in
ASCE 7-10 drift limit is 0.02 for the DBE (defined as two-thirds of the MCE) for buildings with
ordinary use and occupancy.
For example, assuming a structure was designed using ASCE 7-10 and a linear
relationship between drift and ground motion intensity, a building in the western United States
would experience, on average, an inter-story drift ratio of approximately 0.10×0.02/(2/3) = 0.003
in the 43-year event. According to typical observed behavior (i.e. Griffis 1993) this magnitude
of drift ratio would be visible and would cause architectural damage. The drift ratio
corresponding to the 72-year event is 0.006, and could be expected to damage many
nonstructural components, including partition walls and windows. The latter is especially
significant for wind engineering, where penetration of the building envelope can lead to water
infiltration and serious habitability problems (Kwok et al. 2015).
In the central and eastern United States, the same building would experience, on average,
a 43-year MRI drift ratio of only 0.05×0.03=0.0015 times the story height, which is near the
threshold of expected damage for nonstructural components (Griffis 1993). Thus, in contrast
with the western United States, ground motions during small and medium events, used to design
for serviceability limit states, are unlikely to be significant for new buildings in the central and
eastern United States. In contrast, service-level wind loads are expected to be significant.
59
As a consequence, it is possible that buildings designed for wind can provide adequate
performance in many regions. In high-seismic zones, like New Madrid and Charleston, where
very large rare quakes are possible, a structural system (i.e. a collapse prevention system) could
be devised to exploit the unique shape of seismic and wind hazard curves in the central and
eastern United States. Of course it should be recognized that large events are possible not only
in New Madrid and Charleston, but all over the central and eastern United States. The historical
events in New Madrid and Charleston stand out in the catalog because of the scarcity of large-
magnitude events, but the earthquakes were not exceptional in terms of magnitude. In fact,
almost all of the central and eastern United States is capable of generating a magnitude 7.5
earthquake (Chapman 2014).
60
Chapter 3
ARCHETYPE STRUCTURAL SYSTEMS
This chapter describes the collapse prevention system concept and the selection and development
of archetype structural systems. In order to determine the applicability of the collapse prevention
system concept to steel moment-frame buildings commonly constructed in the central and
eastern United States, the archetype systems were intended to be prototypical building
configurations with or without collapse prevention mechanisms. Reserve lateral strength in the
gravity framing system is discussed. Delayed-stiffness collapse inhibiting mechanisms are
described, as well as optional energy dissipation devices. Enhanced shear tab connections, using
T-stub type structural fuses, are discussed. The analytical modeling and nonlinear analysis
approach are also discussed.
3.1 Collapse Prevention System Concept
The concept of a collapse-prevention system consists of two aspects. First, the main lateral-force
resisting system is designed for wind (or low to moderate seismicity), and, where required,
together with the gravity framing system it is used to provide adequate performance under low to
moderate level ground motions and service-level wind events. Second, the main lateral-force
resisting system (and the reserve lateral strength in the gravity framing where applicable) is used
61
in tandem with a back-up collapse-inhibiting mechanism, or enhanced shear tab connections, to
provide life safety under extreme ground motions (i.e. the MCE-level ground motions) and
extreme wind events. When necessary, serviceability performance is improved by augmenting
collapse-prevention systems with auxiliary energy dissipation devices.
3.1.1 Reserve Lateral Strength in Gravity Framing
The concept of utilizing gravity framing as a back-up or “reserve” lateral system is a concept that
has emerged in post-Northridge years (Liu and Astaneh-Asl 2000; Ariyaratana and Fahnestock
2011; NIST 2012c).
Gravity framing can serve as a reserve lateral system for two reasons: First, gravity frame
connections have lateral strength. Composite concrete-slab and steel beam-to-column (shear tab)
connections are partially restrained and inherently have lateral strength and stiffness. Liu and
Astaneh-Asl (2000, 2004) showed that simple gravity beam-to-column connections may provide
significant lateral strength and act as a ductile back-up system by engaging the concrete slab.
Similarly, reserve lateral strength also exists in braced frame systems where gusset plates at
pinned ends of braces create rotational restraint at the beam-to-column connection (Stoakes and
Fahnestock 2011; Ariyaratana and Fahnestock 2011).
Second, the quantity of gravity connections in a moment-frame building can be
significant compared to the number of fully-restrained (moment) connections, depending on the
building column layout and the gravity column orientation. Thus, although the lateral strength of
a shear tab connection is typically a fraction of the moment-frame connection strength (on the
order of 10% to 30%), taken in aggregate the gravity framing strength may be significant.
62
Analytical studies have shown that the gravity system may contribute in a significant way
to the performance of steel moment frame structures, in terms of strength and stiffness
(Eatherton and Hajjar 2011), serviceability (Flores and Charney 2014), and collapse resistance
(NIST 2010b; Flores and Charney 2014; Judd and Charney 2014b; Flores 2015). Incorporating
the gravity system in a non-linear response history analysis (at 3 times the MCE) of a 4-story
building (NIST 2010b), for example, reduced median roof drift ratio from 4.9% to 3.4%, and
reduced the number of collapses in 44 analyses from 22 to 11. Post-earthquake reconnaissance
has also confirmed the concept of reserve lateral capacity in gravity framing. Observations of
two low-rise steel buildings after the 1994 Northridge quake concluded that the perimeter
moment frames had failed, but the gravity framing likely had prevented collapse (Leon 1998).
An analytical study after the quake also confirmed that this might be the case (Astaneh-Asl et al.
1998).
The availability of reserve lateral strength in the graving framing has led to the idea of
using dual systems for lateral resistance, such as a conventional lateral force resisting system (i.e.
a moment or braced frame) for primary resistance, and a gravity framing system as a back-up
lateral resisting system (Nelson et al. 2006; Hines et al. 2009; Hines and Fahnestock 2010). The
effect of reserve strength in the gravity framing has been shown to be greater for non-ductile
lateral systems than for ductile lateral systems (Wen et al. 2013). This study considers the
reserve strength due to the gravity framing columns and gravity framing beams (shear tab
connections).
63
3.1.2 Collapse Inhibiting Mechanisms
Literature Review
Collapse mechanisms with delayed strength and stiffness mechanisms are an attractive back-up
system. The intent of such a mechanism is to not add stiffness to the structure prior to the time
the mechanism is needed. In terms of seismic design, added stiffness reduces the period of
vibration, and in turn, a reduced period of vibration typically increases the base shear demand
(depending on the ordinate of the response spectrum).
Delayed-stiffness collapse inhibiting mechanisms have been used in the past, particularly
in large-scale seismic experiments where conventional structures are tested to near collapse, but
for safety and other reasons it is not acceptable for the test specimen to fully collapse. For
example, slack cables were used to prevent full collapse of a full-scale 4-story steel moment-
frame structure that was tested on a shake table at the E-Defense facility in Japan (Lignos et al.
2013).
Research using delayed stiffness is limited compared to other types of lateral protection
schemes. Saunders (2004) investigated brace devices made of hyper-elastic materials used to
provide passive seismic protection of buildings. As the term suggests, hyperelastic materials
deform nonlinearly, stiffen under load, and unload elastically. Hyperelastic devices behave
similar to the way nonlinear fluid viscous dampers perform (Oesterle 2002). Thus, while
hyperelastic braces may not increase base shear forces at service level loads, they are able to
stabilize a structure and prevent collapse. Saunders employed two sets of cubic polynomial
functions to define the hyperelastic material stress-strain relationship. The first set exhibits
higher early stiffness. The second set exhibits higher later stiffness. Saunders’ cubic polynomial
functions were based on a preliminary study by Jin (2003). Jin examined the effect of
64
hyperelastic elements on maximum displacement, residual displacement, and maximum base
shear, and combined these results to determine the optimum cubic polynomial functions.
Saunders’ analytical results showed that delayed-stiffness devices (e.g. a slack-cable) are
effective at controlling the behavior of unstable systems, while at the same time avoiding too
much contribution to stiffness (and thus higher component force demands).
Saunders work was also the basis for subsequent research by Chittur Krishna Murthy
(2005) who investigated one of two prototype hyperelastic devices proposed by Saunders. In
Chittur Krishna Murthy’s study, a visco-hyperelastic device consisting of motorcycle tires was
placed between two steel rings. The results showed the device successfully dissipated energy.
Ryan (2006) investigated structures using double-braided synthetic fiber ropes to improve
the seismic performance of steel moment frames. The investigation included experimental tests,
1:3-scale dynamic tests and 1:6-scale shake-table tests and nonlinear dynamic analytical studies.
The 1:6-scale experiments suggested the ropes considerably improved performance, since
maximum and residual drift were reduced with minimal increase to the maximum base shear.
Although the original intent of Ryan’s work was to evaluate the “cable snapping” energy-
dissipation potential of the ropes, the upshot was that ropes could stabilize structures that have
significant residual drift. In a related application, used slack chains to prevent displacement in a
“beyond-design level earthquake” of a building located in Los Angeles County (Kelly 2004).
Ibrahim, et al. (2005) developed an energy dissipation device called a “viscoplastic”
damper. This device consisted of two steel plates that were pre-bent (pre-buckled), so when
loaded axially in tension or compression, the axial stiffness was reduced. Between the plates
was a high damping viscoelastic solid material that was stressed in tension when the plates were
in compression, and stressed in compression when the plates were in tension. The changes in
65
strain (deformational velocity) in the viscoelastic material provided damping at low-level
displacements, and the flexural yielding in the plates at higher levels of deformation provided the
needed energy dissipation under strong ground shaking. The device had a nonlinear force-
displacement relationship while the steel was still elastic, with the stiffness increasing with axial
force.
Marshall (2008) and Marshall and Charney (2010a, 2010b, 2012) developed a device that
acts like a low-axial stiffness viscoelastic damper at low levels of deformation, and then stiffens
to act like a steel buckling restrained brace at higher levels of deformation. This device was
tested both analytically and experimentally, and proved to be very effective in controlling low-
level response (via damping) and high level response (via inelastic yielding). A similar device
was also tested by Yamamoto and Sone (2014). These devices are a prototype of one of the
“advanced telescoping brace” collapse prevention mechanisms described in this study.
A variety of designs could form a collapse inhibiting mechanism (Figure 3.1 and Figure
3.2). [See also Judd and Charney (2014e).] The simplest mechanisms consist of a pair of slack
cables (Figure 3.1a,b) or loose linkages (Figure 3.2a) that provide no resistance or stiffness until
the building story deformation reaches some limit, such as 2% interstory drift. Then, at the
predefined deformation, the slack cable (SC) or loose linkages (LL) become taut and augment
the residual building system strength to prevent dynamic instability. This study will consider
slack cables in knee-brace arrangement and loose linkages.
Selected mechanisms can be equipped with energy dissipating devices, such as small
viscous fluid dampers or viscoelastic solid high-damping rubber material, to enhance
serviceability performance under wind or small seismic events. Energy dissipating devices are
effective for seismic design (Symans et al. 2008). In fact, a previous investigation of steel
66
moment-frame buildings (Atlayan and Charney 2011) indicated that adding even a small amount
of damping is advantageous (e.g. increasing the equivalent system damping from 5% to 10%
critical). In the case of collapse-prevention systems, this added damping would primarily be
used to control behavior up until the point that the collapse inhibiting mechanism engages.
Gusset plate (with stiffener if

required to transfer force
from cable or link)
Structural cables
a) Full-bay slack-cable X-bracing b) Slack-cable (SC) knee bracing
Figure 3.1 Prototypical collapse inhibiting mechanisms
Telescoping HSS with

Optional supplemental optional energy dissipation
energy dissipation device system (e.g. high-damping
(i.e. viscous fluid damper) rubber)
Steel links
a) Loose linkages (LL) b) Telescoping brace (TB)
Figure 3.2 Prototypical collapse inhibiting mechanisms equipped with
energy dissipating devices
67
Loose linkages may be used alone as a collapse inhibiting mechanism (left corner in
Figure 3.2a) or may be used in association with a damper (right corner in Figure 3.2a), to act as a
true toggle brace damper system. In fact, the loose-linkage mechanism can be thought of as a
toggle brace without the damper. The idea behind a toggle brace is that deformations acting
parallel to the braces are amplified in the transverse direction, thereby increasing the efficiency
of dampers (Constantinou et al. 2001).
The toggle brace system is useful in stiff structures, for reduction of wind vibrations, or
to reduce the size of the damper device. By amplifying displacement and velocity, smaller and
lower-cost dampers may be used. The amplification allows dampers to be used in the short-
period range, as well as for wind applications. Amplification systems may use gear mechanisms
(Berton and Bolander 2005) or “toggle braces” and “scissor jacks” (Whittaker and Constantinou
2004).
Charney and McNamara (2008) show that a toggle system is “generally more efficient
when compared to the diagonal system.” Huang and McNamara (2006) investigated both toggle-
brace and scissor-jack systems. The conclusion was that the effectiveness of the system is
directly related to the stiffness of the brace. Hwang et al. (2008) derived new design formulas
for structures with supplemental viscous dampers by modifying the existing design formulas to
account for the effects of combined shear and flexural deformation of the structure.
Constantinou et al. (2001) demonstrated the use of three types of toggle brace mechanisms that
may be utilized effectively in application of small structural drift, using shake table testing of a
large scale steel modal structure and analysis, and discussed some applications.
Huang (2004) derived the amplification factor by including the brace elongation, and
discussed configurations for different design parameters, including target story drifts, brace
68
stiffness, joint reduction, and damping value. The conclusion was that “conventional placed
damper device may be not efficient under normal wind condition due to small story drift” and
“the efficiency of [toggle brace damper] devices is very sensitive to the design parameters, such
as geometric configuration, relative brace stiffness and damping values, and other parameters.”
Also, “the stronger and stiffer brace members always have better performance for the [toggle
brace damper] system. The larger viscous damper force may not produce larger energy
dissipation.” Hwang et al. (2005) provided design procedures for “upper” and “lower” toggle-
brace-damper systems with dampers directly installed to beam-column joints, and performed
shake table tests on a scaled-down three-story steel model. The result is the system was more
efficient in controlling the seismic response of the model structure compared to a diagonal-
braced damper system.
Hwang et al. (2006) showed that viscous toggle-braced dampers are effective in
reinforced concrete structures with walls, as well as such structures without walls. Lee et al.
(2007) studied toggle brace systems using magnetorheological dampers. Based on analytical and
experimental results, the study concluded that structural performance is enhanced compared to
magnetorheological dampers not installed in an amplifying brace system. Di Paola and Navarra
(2009) propose a “pendulum” type toggle brace damper system.
A more complex collapse inhibiting mechanism is the telescoping brace (TB) shown in
Figure 3.2b. In this mechanism two steel tubes telescope over each other and can elongate
without resistance until a “stop” mechanism causes the brace to go into tension. The brace
cannot carry compression. The telescoping brace described here is an adaptation of the hybrid
passive energy dissipation device developed by Marshall and Charney (Marshall and Charney
2010a,b; Marshall and Charney 2012) discussed in the previous section.
69
A key aspect of the collapse-prevention system concept is the size of the mechanisms: the
slack-cable and loose-linkage configurations can be compact and unobtrusive. Where a compact
configuration is used, the collapse inhibiting mechanisms could be distributed throughout the
building. A larger mechanism, such as the telescoping brace, on the other hand, would likely be
installed in only selected bays. Another important aspect of the collapse-prevention system is
that the mechanisms may be deployed in both the moment frame and the gravity frame. Indeed,
collapse inhibiting mechanisms are envisioned to work as a supplement to the conventional
lateral-force resisting system (e.g. moment frame or braced frame) in conjunction with reserve
lateral strength in the gravity framing system.
3.1.3 Enhanced Shear Tab Connections
As discussed previously, the lateral force-resisting capacity of a conventional gravity-frame
beam-to-column connection is often small, on the order of 10% - 30% of a comparable moment-
frame connection, and is not typically utilized for seismic protection. An alternate collapse-
prevention system (in lieu of utilizing the existing reserve lateral strength in shear tab
connections and a collapse inhibiting mechanism) is proposed in this section that enhances the
lateral-force resisting capacity of conventional gravity-frame connections.
The method consists of modifying the existing shear tab connection (as a retrofit or in
new construction) and installing T-stub type flange connectors in order to create a ductile
partially-restrained beam-to-column connection (Figure 3.3). The existing beam flanges and the
T-stub connector are used to form a buckling-restraint mechanism that allows a reduced-width
segment of the T-stub stem, or “yield-link” (Figure 3.4), to act as a structural fuse in a seismic or
extreme wind event. The application is based on the Yield-Link™ components used in Strong-
70
Frame® special moment frame system (Pryor and Murray 2013; ICC-ES 2013). Such enhanced
shear tab connections have the added benefit that beam flange bracing is not required.
Moreover, the connection is highly repairable because damage is limited to the fuses while other
components of the connection remain elastic.
In the enhanced shear tab connection, a single plate shear connection is used to transfer
shear, and a pair of buckling restraint mechanisms (one at the top beam flange, one at the
bottom) is used to transfer flexure. The single plate shear connection uses a coped beam web, a
center standard bolt hole, and upper and lower slotted bolt holes, to permit a true hinge
mechanism (Figure 3.5).
T-sub type flange connector

Buckling restraint plate
Gravity framing beam
Gravity framing column
Single plate shear connection
Figure 3.3 Finite element model of enhanced shear tab connection
71
Reduced region
Flange bolt holes
Figure 3.4 Finite element model of yield link (T-stub stem)
Slotted bolt holes
Standard bolt hole
Figure 3.5 Finite element model of shear tab with slotted upper and lower bolt holes
72
The buckling restraint mechanism consists of the T-stub type flange connectors, an outer
restraining plate, inner spacer plates, and restraint bolts. Figure 3.6 shows a finite element
representation of the enhanced shear tab connection during a monotonic load analysis. The T-
stub structural fuse is bolted to the beam flange, it has a flange that is bolted to the column
flange, and a stem (with a reduced region) designed to yield in both tension and compression.
Compression yielding of the T-stub stem is achieved by using the beam flange and the outer
restraining plate to force the reduced region of the link stem into high-mode buckling (rippling).
Figure 3.7 shows a finite element model representation enhanced shear tab connection with a
buckling restraint plate that is too thin to constrain the buckling of the reduced region, during a
monotonic load analysis.
The inner spacer plates limit friction between the restraint plate and the T-stub stem, and
limit transverse movement of the T-stub stem during yielding. Snug-tight bolts pass through the
restraint plate, each spacer plate, and the beam flange to encapsulate the mechanism. The
remaining bolts are fully pre-tensioned. In concept, the buckling restraint mechanism provided
by the restraint plate and beam flange is similar to that used in all-steel buckling restrained brace
(BRB) frames (Genna and Gelfi 2012a,b, 2014).
73
Figure 3.6 Finite element model of enhanced shear tab connection
Figure 3.7 Finite element model of non-constrained buckling restraint mechanism
74
3.2 Archetype Buildings
Table 3.1 summarizes the building archetypes. Three types of archetypical structural systems
were included. The buildings employed either a non-ductile moment frame, or a ductile moment
frame designed for moderate seismic demands. Building design criteria was based on the
building codes and standards in current use (described in detail in Appendix B).
Table 3.1 Archetype structural systems
with Viscous Fluid
Braces with High-

strength in shear
Damping Rubber
Enhanced shear
tab connections
tab connections
Loose Linkages
Loose Linkages
Reserve lateral
Slack Cables
Telescoping
Dampers
Total
Archetype Number
(Seismic Design of
Category) Stories
Type I
1 ● ● ● ● ● ●
Non-ductile 2 ● ● ● ● ● ●
(SDC B min ) 4 ● ● ● ● ● ●
8 ● ● ● ● ● ●
1 ● ● ● ● ● ●
Ductile 2 ● ● ● ● ● ●
(SDC D min ) 4 ● ● ● ● ● ●
8 ● ● ● ● ● ●
Type II
Non-ductile
(SDC B)
4 ●
Type III
Non-ductile
(SDC B)
10 ●
75
3.2.1 Type I Archetype Buildings
The first type (“Type I”) was archetypical short period (1-story and 2-story) and long period (4-
story and 8-story) office buildings that employed either a non-ductile moment frame, with fully-
restrained flange welded connections, or a ductile moment frame with reduced beam section
(RBS) connections. The building configuration and overall plan layout for Type I are shown in
Figure 3.8 and Figure 3.9. The building plan used 20-ft bays and perimeter moment frames. The
first story height (measured to the top of the beam) was 15 ft. Upper story height was 13 ft. 1-
story and 2-story moment frame columns were considered pinned at the base, taller columns
were considered fixed. The layout, story heights, and gravity loads match the special steel
moment framing building archetypes developed in the ATC-76 project (NIST 2010a).
Main lateral-force resisting

system (steel moment frames)
Frame C
Tributary area for gravity loads on
moment frame
Frame B
Frame A
Figure 3.8 Type I non-ductile and ductile moment frame 1-story, 2-story, 4-story, and 8-story
building framing plan
76
Steel moment frame (three bays), typical Gravity framing
13-ft story height

(upper story,
typical)
15-ft story height

(first story)
Figure 3.9 Type I archetypical building elevation view of structural framing in longitudinal
direction (4-story building shown)
Gravity columns were considered pinned at the base, and were spliced 4 ft above the third
and sixth floors. The ATC-76 evaluation (NIST 2010a) did not model gravity framing and, as a
result, the gravity framing layout shown, including the direction and spacing of filler beams
every 10 ft, column splices, and gravity column orientation, were developed in this study. The
gravity frame columns were oriented with the strong axis in the same direction as the moment
frames (the longitudinal direction), and thus the reserve lateral strength observed in this study
represents an upper bound on the gravity framing contribution for this building configuration.
The first building type was developed following the procedure recommended in FEMA
P-695 (FEMA 2009a). The non-ductile steel moment frames were not detailed for seismic
resistance and were designed for a wind hazard corresponding to non-coastal location in the
United States and low seismicity [Seismic Design Category (SDC) B min , meaning the lowest
spectral accelerations corresponding SDC B].
77
Table 3.2 provides the structural members for the non-ductile moment frame buildings.
Moment frame design was based on meeting drift requirements and providing a column moment
of inertia between 1 and 2 times the beam moment of inertia (Hamburger et al. 2009; Bruneau et
al. 2011). The frame was designed without considering the collapse prevention system. Initial
beam and column sizes were adjusted when required to meet strength and stability requirements.
Column sizes were selected from W14, W18, and W24, depending on the loads. To reduce cost,
column sizes were increased to avoid specifying double plates.
The gravity framing selection (Table 3.3 and Table 3.4) was based on considering both
composite and non-composite (construction) strength. Gravity members were not designed for
lateral loads, except members that form part of the steel moment frames were subsequently
designed for lateral loads. The final column member sizes used match the gravity columns used
in a related study (Flores 2015).
Table 3.2 Type I archetypical building non-ductile moment frames
No. of Column size Controlling

stories Story Beam size Exterior Interior criteria
1 1 W18X35 W14X82 W14X82 Stability
1 W21X44 W18X71 W18X76

2 Stability
2 W16X31 W18X71 W18X76
1 W16X40 W18X76 W18X86

2 W21X44 W18X76 W18X86
4 Stability
3 W18X35 W18X40 W18X46
4 W16X31 W18X40 W18X46
1 W21X48 W24X146 W24X146

2 W24X68 W24X146 W24X146
3 W24X76 W24X76 W24X103
4 W24X55 W24X76 W24X103
8 Wind strength
5 W24X55 W24X55 W24X62
6 W21X48 W24X55 W24X62
7 W18X35 W24X55 W24X55
8 W18X35 W24X55 W24X55
78
Table 3.3 Type I archetypical building gravity framing column sizes
Column Size
No. of Frame Line A Frame Line C
stories Story Lines 1, 6 Lines 2, 5 Lines 3, 4
1 1 W14x43 W14x90 W14x61
1 W14x43 W14x90 W14x61

2
2 W14x43 W14x90 W14x61
1 W14x43 W14x90 W14x61

2 W14x43 W14x90 W14x61
4
3 W14x30 W14x90 W14x61
4 W14x30 W14x90 W14x61
1 W14x61 W14x120 W14x74

2 W14x61 W14x120 W14x74
3 W14x43 W14x90 W14x68
4 W14x43 W14x90 W14x68
8
5 W14x34 W14x90 W14x68
6 W14x34 W14x90 W14x68
7 W14x30 W14x90 W14x68
8 W14x30 W14x90 W14x68
Table 3.4 Type I archetypical building gravity framing beam sizes
Beam Size
Frame Line A Frame Line C
Bays 1, 5 Bays 1, 5 Bays 2, 3, 4
All stories W24x68 W24x68 W16x31
The Type I ductile moment frame archetypes employed a ductile moment frame designed
for moderate seismic demands. The ductile special steel moment frames (SMF) with reduced
beam sections (RBS) were designed for the FEMA P-695 Seismic Design Category (SDC) D min ,
and previously developed in the ATC-76 project (NIST 2010a). SMF designed for SDC D max
are also used for purposes of comparison. The details of the design and member sizes are
available in Appendix D of the ATC project report. The ATC-76 project did not consider wind
loads. The gravity framing was identical to that used in the Type I non-ductile buildings.
79
3.2.2 Type II Archetype Buildings
The second type (“Type II”) was an archetypical long period (4-story) office building that
employed a non-ductile moment frame with fully-restrained flange welded connections. This
building was selected from the AISC (2013) Design Examples to illustrate the behavior of a
typical mid-rise steel building in the central United States where the building design is controlled
by moderate wind loads and has low seismic loads.
The building configuration and overall plan layout is shown in Figure 3.10. The building
is a 4-story steel-frame structure comprised of seven 30-ft bays in the longitudinal (East-West)
direction and one 30-ft and four 22.5-ft bays in the transverse (North-South) direction. The story
height is 13.5 ft., except the fourth story height is 14 ft.
Main lateral-force resisting

system (steel moment frames)
(Filler beams not shown)
Approximate tributary area for

gravity loads on moment frame
Figure 3.10 Type II non-ductile moment frame 4-story building plan
80
The building uses steel moment frames along the perimeter for lateral resistance in the
longitudinal direction, and braced frames in the transverse direction. Columns in the gravity
frame are spliced 4 feet above the 3rd story floor level. Each floor consisted of a composite 6-
inch concrete slab on 3-inch steel deck system. The roof consisted of a steel deck and steel joist
system.
The building was designed for wind loads based on a basic wind speed of 115 mph, and
for seismic loads based on 𝑆𝑠 = 0.121 g, 𝑆1 = 0.060 g, and soil site class D (Seismic Design
Category B). The design was controlled by wind (where the seismic 𝐶𝑠 is equal to 0.043). A
detailed description of the building, its loads, and the selection and design of the gravity and
lateral systems is provided in the Design Examples (AISC 2013), except that in this research
fully-restrained flange welded connections were used instead of bolted connections.
81
3.2.3 Type III Archetype Buildings
The third type (“Type III”) was an archetypical long period (10-story) office building that
employed a non-ductile moment frame with fully-restrained flange welded connections. Figure
3.11 shows the structural plan and elevation of the building. Moment frames consist of fully
rigid, wide-flange girder welded to a wide-flange column with single plate bolted shear
connection. Only the longitudinal (moment frame) direction was modeled.
The building was designed for a generic location in the United States where wind loads
control strength (basic wind speed of 115 mph and ASCE 7-10 terrain exposure category C) and
seismic detailing is not required. In the moment-frame direction, the wind base-shear force, 𝑉
equal to 494 k. Based on an estimated building weight, 𝑊 equal to 10,920 k, this corresponds to
a wind base shear coefficient, C wind (V/W) equal to 0.045.
Figure 3.11 Type III non-ductile moment frame 10-story building framing plan and elevation
(Plan and elevation drawing by Larry Griffis)
82
3.2.4 Collapse Prevention Systems
Reserve lateral strength in the shear tab connections was considered for both Type I and Type II
archetypical buildings. In the Type III archetypical building, the gravity columns are oriented in
the weak-axis (with respect to the moment frames), so reserve lateral strength was not
considered. Enhanced shear tab connections were considered only in Type II archetypical
buildings. The enhanced connections used a 0.5-in thick by 3.5-inch wide yield region. The
reduced region length was 6 inches for W16x31 beams, and 8.25 inches for W24x68 beams. The
length of the reduced region was based on limiting the strain demand to 0.085 in./in.
Additionally, in Type I archetypical buildings, slack-cable and loose-linkage mechanisms
were deployed in bays 1–5 along frame A, and in bays 2–4 along frame C. Full-bay slack-cable
X bracing was not included in this study. Telescoping brace mechanisms were used in bays 2
and 4 along frame A. Using the capacity based design described in the next section, the
structural cables ranged from 21-mm diameter and 79 k breaking force, to 45-mm diameter and
434 k breaking force, with properties based on Ronstan Galfan full-locked structural cables
(www.ronstan.com). The links consisted of A992 steel bars with an effective net area, 𝐴𝑒 that
ranged from 1.0 in.2 to 8.4 in.2. The telescoping brace (9x9x1/4 HSS A1085) area was 8.03 in.2.
The expected yield strength was used, but no material overstrength was included.
A nonlinear static (pushover) analysis was used to determine the target drift at which
collapse inhibiting mechanisms become engaged, typically between 2% to 4%. When utilized,
energy dissipating devices (small viscous fluid dampers or viscoelastic solid high-damping
rubber) were sized to provide 10% equivalent system damping (see Charney and McNamara
2008), based on a free-vibration analysis.
83
3.3 Analytical Modeling
Archetypical buildings were idealized using two-dimensional half-building models and
OpenSees (PEER 2012) finite element software. Figure 3.12 shows a perspective view of the
Type I analytical (half-building) models.
Structural framing members were modeled using a phenomenological (concentrated
plasticity) approach (Figure 3.13). Beams and columns were represented using an assembly of
rotational springs (zero-length elements) and elastic beam-column elements in series to simulate
the potential for plastic behavior to be developed near the end of each member. The formation of
a plastic hinge in the column or beam at the location of a collapse inhibiting component (cable or
link) connection was precluded by employing a capacity-based design approach (limiting the
component capacity based on member limit states).
In the beam or column assembly was defined using a method proposed by Ibarra and
Krawinkler (2005), where the rotational spring stiffness, 𝐾𝑠 was defined relative to elastic beam-
column rotational stiffness, 𝐾𝑏𝑏 in order to permit the secondary stiffness (strain hardening) to be
expressed as a function of the initial elastic stiffness.
𝐾𝑠 = 𝑛𝐾𝑏𝑏 (3.1)
Moment frame (black)
Gravity frame (blue)
500
1-story 2-story 4-story 8-story
Figure 3.12 Perspective view of Type I analytical (half-building) models
84
Beams Columns
Beam-column joints
(panel zones)
Figure 3.13 Phenomenological (concentrated plasticity) analytical modeling approach: moment
frame shown for Type I non-ductile moment frame 2-story building
The rotational stiffness of the beam or column assembly 𝐾𝑚𝑚𝑚 , was then calculated as
1 1 −1
𝐾𝑚𝑚𝑚 = � + � (3.2)
𝐾𝑠 𝐾𝑏𝑏
For fully-restrained (moment) connections and plastic column hinges, the ratio of spring
to elastic beam-column stiffness, 𝑛 was taken as 10. This value of the ratio was selected in
order to avoid numerical instability when the ratio is large (Ibarra and Krawinkler 2005).
The rotational stiffness of the assembly 𝐾𝑚𝑚𝑚 , was based on a conjugate-beam analysis.
For members subjected single-curvature bending (i.e. columns pinned at the base, or columns
that are spliced) the assembly stiffness was calculated using Equation 3.3.
3𝐸𝐸
𝐾𝑚𝑚𝑚 = (3.3)
𝐿
For members subjected to double-curvature bending (i.e. beams, fixed-based columns)
the assembly stiffness was calculated using Equation 3.4.
6𝐸𝐸
𝐾𝑚𝑚𝑚 = (3.4)
𝐿
85
In this method for beam or column assembly, one of two conditions of curvature in
bending (the moment gradient) was assumed a priori and was assumed to remain constant
through the analysis. Thus, a column splice could only be modeled as a fully-rigid joint (no
splice) or true hinge column splice (no rotational capacity). Similarly, a plastic hinge in the
beam or column at the location of the collapse prevention system component connection could
not be employed because it requires a change in the moment gradient. This limitation is
discussed later in this chapter (see also Figure 3.22).
3.3.1 Location of Beam Plastic Hinge
In this research, the assumed location of the plastic hinge depended on the type of beam-to-
column connection. In previous research, the assumed location of the plastic hinge varied
depending on the researcher (e.g. Rojas 2003, Lee 2003, and others). Interestingly, regardless of
the actual distribution of plasticity and the assumed location of the plastic hinge, previous studies
(e.g. Ibarra and Krawinknler 2005) have shown that the global response of the building frame
was relatively insensitive to the precise location of the plastic beam hinge (column plastic hinges
controlled global collapse).
For modeling purposes, for beam-to-column connections without flange reduction or
reinforcement, the plastic hinge was assumed to occur at the face of the column (PEER/ATC
2010). In actuality, first yielding of the beam occurs at the face of the column. The center of
rotation eventually migrates into the beam span with a “final” center of rotation located at
approximately half the beam depth from the column. This includes both ductile and non-ductile
(pre-Northridge) connections. For reduced beam section (“RBS”) beam-to-column connections,
the plastic hinge occurs at the centerline of the radius-cut reduced section.
86
For ductile beam-column connections with flange reinforcement (e.g. haunches or cover
plates) the plastic hinge occurs away from the column face a distance depending on the particular
type of connection. This distance may be determined using procedures given in AISC 358-10
(AISC 2011b). In this research, the NEES structural component databases (Lignos and
Krawinkler 2012) were used to determine moment-rotation deterioration parameters of the
connections, but it is noted that ductile reinforced beam-to-column connections were excluded
from the regression analysis used to determine connection parameters (Lignos and Krawinkler
2011). For simple shear (gravity) connections including composite action, the hinge was
assumed to occur at the column face.
3.3.2 Column Fixity, Splices and Plastic Hinge
In this research, the assumed location of the plastic hinge was at the top or bottom of the column.
Columns participating in the moment frame were idealized as fixed at the base (except the 1-
story frames); all other columns (gravity frame columns) were idealized as pinned. Column
splices (at story 3 and story 5) were modeled as a pinned connection. In this study, column
splices were assumed to have no rotational capacity, and column bases were assumed to be either
fixed (rigid) or hinged (fully flexible). Partial fixity was not modeled. The analytical model
could be refined to represent the base as a partial restraint (e.g. Hamburger et al. 2009), but this
was beyond the scope of this study. The sensitivity of the seismic collapse assessment to the
inclusion of gravity column splices is discussed in Chapter 6. Interaction between axial and
flexure (P-M interaction) is described in the next section.
87
3.3.3 Fully-Restrained (Moment Frame) Beam-to-Column Connections
Ductile connections
The moment-rotation behavior of ductile beam-to-column connections (Figure 3.14) was
represented using the Bilin uniaxial material with parameters based on regression analysis of
test data (Lignos and Krawinkler 2011).
The modified Ibarra-Medina-Krawinkler moment-rotation model (PEER/ATC 2010;
Lignos and Krawinkler 2011) was used in this study. In this model, cyclic degradation is
considered directly in the hysteresis behavior. The moment-rotation behavior follows the
monotonic response and is reduced or degrades as a typical cyclic analysis progresses. The
hysteresis behavior is rule-based (Judd 2005). The primary parameters for the moment-rotation
model are shown in Figure 3.15. (For non-symmetric behavior, these parameters are defined for
both positive and negative directions.)
The model also requires Λ = reference cumulative rotation capacity, 𝑐 = empirical

R
parameter taken as 1.0, and 𝐷 = decrease rate of cyclic deterioration. Parameter values depend
on the ductility of the connection or plastic hinge. For steel beams, different values of Λ (for
R
different modes of cyclic deterioration) do not significantly improve the model (Lignos and
Krawinkler 2011), so one value was used in this study.
88
6000 Monotonic
W18X71 envelope
4000
Moment (k-in.)
2000
-2000
-4000
Fully-reversed cyclic
response (hysteresis)
-6000
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Rotation (rad)
Figure 3.14 Typical idealized behavior for a ductile fully-restrained beam-to-column
connection: W18x71 beam in Type I ductile moment frame 4-story building
The plastic moment, 𝑀𝑝 was based on the expected yield strength, 𝐹𝑦 𝑅𝑦 (where 𝑅𝑦 = 1.1)
and the plastic section modulus, 𝑍. For RBS beams, 𝑍 was based on the centerline of the RBS
cut using AISC 358-10 Equation 5.8-4 (AISC 2011b). For non-RBS beams, 𝑍 was as given in
the AISC Steel Construction Manual (AISC 2011a).
Isotropic hardening was included in the model in an approximate way by increasing the
plastic moment to an “effective” yield strength, 𝑀𝑦 = 1.1 𝑀𝑝 (see Lignos and Krawinkler 2011).
This strength represented an “average” strain hardening (Lignos 2008) but did not account for
cyclic hardening.
89
𝑀𝑐
6000 𝑀𝑦
4000
𝑀𝑟
Moment (k-in.)
2000
0
𝜃𝑢
-2000
-4000
-6000
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Rotation (rad)
a) Modified Ibarra-Medina-Krawinkler moment-rotation model
𝑀 / 𝑀𝑦
1.1
𝜃𝑝𝑝 = 0.2
0.4
θ
θu= 0.2
θp= 0.02
b) Typical parameter values
Figure 3.15 Modified Ibarra-Medina-Krawinkler moment-rotation model
90
The post-yield strength ratio (𝑀𝑐 /𝑀𝑦 ) was calculated as the ratio of the capping strength
to the effective yield strength. This is similar to the strain hardening ratio, as expressed by the
𝐶𝑝𝑝 factor. This factor accounts for the peak strength (see AISC 358-10 page 9.2-6). Therefore,
the 𝐶𝑝𝑝 factor is similar to 𝑀𝑐 /𝑀𝑦 ratio, except 𝑀𝑦 incorporates average strain hardening.
In this study, the parameters for the modified Ibarra-Medina-Krawinkler moment-rotation
model (Table 3.5) were based on statistical analysis of a database of experimental testing (Lignos
and Krawinkler 2011). In that statistical analysis, beam-to-column connections were classified
as RBS or non-RBS (which includes a variety of connection types). The statistical analysis
indicated that pre-capping plastic rotation 𝜃𝑝 is small (about 0.02 rad), but post-capping
deformation 𝜃𝑝𝑝 is large. As a result, loss in strength is predicted to be slow after the peak
strength (PEER/ATC 2010).
Yield and capping moment parameters represent mean values. Average values (used in
ATC-76) are about 1.10 for both normalized yield and capping moments. The normalized
residual moment was an approximate value suggested by Lignos and Krawinkler (2011).
Table 3.5 Moment-rotation model parameters for ductile beam-to-column connections
Normalized strength Deformation Hysteresis

My / Mc / θp θ pc θu Λ
Connection Mp My Mr / My (rad) (rad) (rad) (rad) D
(b)
RBS rad 1.06 1.09 (a) (a) (0.06 to 0.07) (a)
Eqn. Eqn. (b) Eqn.
Non-RBS 1.17 1.11 0.4 (0.05 to 0.06) 1.0
(~0.02) (~0.20) (~1.0)
ATC-76 1.10 1.10 0.2
(a) Regression equation in Lignos and Krawinkler (2011).
(b) Depends on loading history. Range shown is for symmetric cyclic loading protocols.
91
In this study, the ultimate rotation capacity 𝜃𝑢 was taken as 0.2, but it was recognized that
the actual ultimate rotation capacity depends on the loading protocol. For monotonic loading the
value may be three times larger than the value for symmetric cyclic loading, and larger values
may be expected for near-fault loading or for ratchet loading in one direction, such as occurs in
side-sway dynamic instability (Lignos and Krawinkler 2011). For example, ultimate rotation
capacity was observed to be 0.37 rad for shake table testing of scale model steel frames (Lignos
2008). Thus, in ATC-76 (NIST 2010a) an assumed value of 0.20 rad was used.
In this research, 𝑀𝑐 /𝑀𝑦 =1.1. In the ATC-76 project, 𝑀𝑐 /𝑀𝑦 =1.1 (see NIST 2010a, page
D-8). The average of the mean values from the statistical analysis of the database of testing were
𝑀𝑐 /𝑀𝑦 = 1.09 for RBS, and 𝑀𝑐 /𝑀𝑦 = 1.11 for non-RBS connections (see Lignos and Krawinkler
2011, Table 3). In AISC 358-10, Equation 2.4.3-2 is used to calculate 𝐶𝑝𝑝 . Based on AISC 2010
Manual Table 2-4, 𝐹𝑦 = 50 ksi and 𝐹𝑢 = 65 ksi. Therefore, 𝐶𝑝𝑝 = 1.15. (There are three factors
used in the ATC-76 report that all equal 1.10.) The 𝑀𝑐 /𝑀𝑦 ratio was used instead of 𝐶𝑝𝑝 .
Non-Ductile Connections
The moment-rotation behavior of the non-ductile beam-to-column connections (Figure 3.16) was
represented using a tri-linear loading and unloading rule-based hysteresis model (Lowes et al.
2004) that includes degradation of stiffness and strength. The model was incorporated in the
analysis using the Pinching4 and MinMax uniaxial materials in OpenSees, with load-
deformation and hysteresis parameters based on FEMA P-440A (FEMA 2009b), ASCE 41
(ASCE 2006, 2014), and FEMA 355D (FEMA 2000b).
Beam-column connections in steel moment frames not detailed for seismic resistance
(“R=3” systems) were assumed to exhibit non-ductile behavior, and the moment-rotation
92
parameters were based on the performance of fully-restrained flange welded connections
designed prior to the 1994 Northridge earthquake (so-called “pre-Northridge” connections).
Stojadinovic et al. (2000) performed experimental tests of pre-Northridge connections.
Shi (1997) developed a connection model for non-ductile connections, and Shi and Foutch
(1997) implemented the model in DRAIN-2DX (Prakash et al. 1993). Foutch and Yun (2002)
used this model to predict the performance of steel moment frames with non-ductile and ductile
connections, as well as simple shear connections (Yun et al. 2002). Lee (2000) and Lee and
Foutch (2002) also used the model to predict performance of pre-Northridge type buildings.
Parameters for the model are given in Table 3.6. Typical values are shown in Figure
3.17. It is noted that the empirical equations in ASCE 41-13 (ASCE 2014) and previous versions
of the standard, as well as the pre-standard, for non-ductile (pre-Northridge or WUF)
connections were based the analysis used in FEMA 355D (2000b).
5000
W16X40
Moment (k-in.)
Monotonic response (hysteresis)
envelope
-5000
-0.1 -0.05 0 0.05 0.1
Rotation (rad)
Figure 3.16 Typical idealized behavior for a non-ductile fully-restrained beam-to-column
connection: W16x31 beam in Type I non-ductile moment frame 4-story building
93
The non-ductile connections lose strength immediately after yielding in positive moments
(simulating fracture of the bottom flange) and more gradually in negative moments. The
connections exhibit cyclic degradation of both stiffness and strength, within a 15% residual
strength boundary until approximately 4% drift, after which the rotational stiffness and flexural
strength of the connection is zero.
Table 3.6 Moment-rotation model parameters for non-ductile beam-to-column connections
Normalized strength Deformation

Connection θp θ pc Hysteresis
(Moment) My / Mp Mc / My Mr / My (rad) (rad) θ u (rad) parameters
Pre-Northridge WUF
+ (a) (b)
M 1.10 1.00 0.001 0.001
Eqn. − θ p
(b) (c) (d)
- (a) (a) 0.15 (c)
M 1.10 1.10 0.011 Eqn.
(a) Approximate value based on average of ductile connections in Lignos and Krawinkler (2011).
(b) Residual moment based on FEMA P440A Page 3-15 (FEMA 2009b).
(c) Equation 2-12a in FEMA 355D (FEMA 2000b). See also ASCE 41-13 (ASCE 2014).
(d) Parameters from FEMA P440A (FEMA 2009b): displacement ratio = 0.2, reloading force ratio = 0.4,
unloading force ratio = 0.05, cyclic strength degradation parameters = 0.0, except gF2 = 0.7, gF4 =
0.5, and gFLim = 0.8, and maximum cyclic to monotonic energy displacement ratio = 10.
M / My
1.0
θ+pc= 0.0
0.15
θ−p= 0.02
θ
θu= 0.05
θ−pc= 0.03
Figure 3.17 Typical parameter values for non-ductile behavioral model
94
Fully-Restrained Beams with Composite Action
The stiffness and moment-rotation of beams mechanically fastened to a concrete slab on a steel
deck (“composite beams”) can be significant due to composite action. For example, Lignos et al.
(2011) performed an experimental shake-table test and an analytical study of a 4-story building
with a steel moment using composite beams and showed that composite action significantly
affected side-sway collapse capacity.
Experimental tests of composite beams with fully-restrained RBS beam-to-column
connections (Tremblay et al. 1997; Engelhardt et al. 2000; Ricles et al. 2004) exhibit asymmetric
moment-rotation behavior, whereas similar tests of bare steel beams for ductile beam-column
connections (Uang et al. 2000) exhibit symmetric moment rotation behavior.
Although the effect of composite action between the beam and the concrete slab has been
shown to generally enhance the seismic behavior of ductile (RBS) connections (Elkady and
Lignos 2013, 2014) the influence on non-ductile connections has not yet been determined. As a
result, composite action was not included in this study.
For purposes of comparison, in Table 3.7 the moment-rotation parameters for ductile
connections were modified to account for composite action based on analysis by Lignos (2008)
and Lignos et al. (2011). Tabulated parameters with a dash instead of a value were not modified
by composite action. The flexure strength of composite beams is predicted to be 25% to 30%
higher than the strength of the bare steel beams. Furthermore, the composite beam pre-capping
plastic positive and negative rotations 𝜃𝑝 are modified by a factor 2 and 0.9, respectively, and
𝜃𝑝𝑝 is increased by a factor of 1.5, compared to bare steel beams. The reduction in positive
rotation is due to lateral torsion of the bottom flange (Lignos et al. 2011).
95
The stiffness of composite beams may be estimated in various ways. One method is to
use the lower-bound elastic moment of inertia, which only includes the portion of the concrete
slab used to balance the shear force transferred by the shear stud anchors (AISC 2011a, page 3-
13). Thus, the quantity of shear stud anchors (or the degree of composite action) must be
assumed or specified.
Table 3.7 Moment-rotation parameters for ductile connections with composite action
Normalized strength Deformation Hysteresis

relative to bare steel relative to bare steel relative to bare steel
Sub-assembly θp θ pc θu Λ
(Moment) My Mc Mr (rad) (rad) (rad) (rad) D
Exterior
+
M
M
- 1.20 1.25 2.0 1.5 1.0
-- -- 1.0
1.10 1.10 0.9 1.0 1.0
Interior
+
M
M
- 1.25 1.30 2.0 1.5 0.85
-- -- 1.0
1.15 1.10 0.9 1.0 1.0
Slab / column
face gap
+
M 1.0 1.20 2.0 1.5 1.0
M
- -- -- 1.0
1.0 1.05 1.0 1.0 1.0
3.3.4 Partially-Restrained (Shear Tab) Beam-to-Column Connections
Literature related to the analytical modeling of partially-restrained gravity framing connections is
limited compared to fully-restrained connections. One modeling approach has been to simply
assume the flexural strength of the connection is a percentage of the beam plastic strength (Hines
et al. 2009; Flores et al. 2012). Another approach has been to “lump” the gravity framing
(individual beam-to-column connections are not explicitly modeled) (Lee and Foutch 2002;
NIST 2010b; Eatherton and Hajjar 2011). Explicit modeling has been centered on rule-based
96
hysteresis (Barber 2011; Zhang 2012; Wen et al. 2013) and complex models (Rassati et al. 2004)
using commercial finite element software [i.e. Abaqus (Dassault Systèmes)].
In this research, the moment-rotation behavior of the shear tab connections (Figure 3.18)
was represented using the tri-linear loading and unloading rule-based hysteresis model (Lowes et
al. 2004), implemented using the Pinching4 and MinMax uniaxial materials in OpenSees,
with load-deformation and hysteresis parameters based on test data of shear tab connections (Liu
and Astaneh-Asl 2000), corresponding analytical models (Liu Astaneh-Asl 2004; Wen et al.
2013), and FEMA P-440A. The shear tab connection behavior is asymmetric due to the effect of
composite action with the concrete slab. The connections exhibit cyclic degradation of both
stiffness and strength, until approximately 10% to 12% drift, after which the rotational stiffness
and flexural strength of the connection is zero. The negative-moment capacity boundary
(monotonic envelope) was based on the behavior of the bare steel beam.
500
W16X31 Monotonic
envelope
Moment (k-in.)
-500
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Rotation (rad)
Figure 3.18 Typical idealized behavior for a shear-tab beam-to-column connection: W16x31
beam in Type I non-ductile moment frame 4-story building
97
Experimental data and finite element analyses (Wen et al. 2013) have shown that a linear-
elastic stress distribution is developed at the negative yield moment (Equation 3.5), and a
uniform plastic stress distribution is developed at the negative ultimate moment (Equation 3.6),
based on the geometry of the shear tab connection, where 𝑑𝑠𝑠 is the height of shear tab (taken as
𝑑𝑏𝑏𝑏𝑏 – 6 inches), 𝑡𝑠𝑠 is shear tab thickness (taken as 3/8 inches), 𝑅𝑦 = 1.1, and 𝐹𝑦 = 50 ksi.
1
𝑀𝑦 − = 𝑑 2𝑡 𝑅 𝐹 (3.5)
6 𝑠𝑠 𝑠𝑠 𝑦 𝑦
1
𝑀𝑢 − = 𝑑𝑠𝑠 2 𝑡𝑠𝑠 𝑅𝑦 𝐹𝑦 (3.6)
4
The positive-moment capacity boundary was based on observations of experimental data
(Liu and Astaneh-Asl 2004) that indicate maximum strength for positive moment (Equation 3.7)
is twice that for negative moment, and positive-moment yield strength (Equation 3.8) is a quarter
of maximum strength.
𝑀𝑦 + = 0.25 𝑀𝑢 + (3.7)
𝑀𝑢 + = 2 𝑀𝑢 − (3.8)
The total (ultimate) rotational capacity (Equation 3.9) for positive and negative moment
was based on the gap, 𝑔 between the beam flange and the column, and distance from the mid-
height of the shear tab to the beam flange, 𝑑𝑏𝑏𝑏𝑏 /2 (Liu and Astaneh-Asl 2004).
𝑔
𝜃𝑇𝑇𝑇𝑇𝑇 = (3.9)
𝑑 ⁄2
As was assumed in FEMA P-440A, the displacement ratio was 0.5, reloading force ratio
was 0.25, unloading force ratio was 0.05, cyclic strength degradation parameters 𝑔𝑔 = 𝑔𝑔 = [0.0
0.1 0.0 0.0 0.2], 𝑔𝑔 = [0.0 0.4 0.0 0.4 0.9], and maximum cyclic to monotonic energy
displacement ratio = 10.
98
3.3.5 Columns and Column Panel Zones
Column Plastic Hinge
Column behavior was idealized similarly to beam behavior, except column plastic hinging
moment-rotation behavior (Figure 3.19) was represented using the Bilin uniaxial material with
parameters based on regression analysis of test data (Lignos and Krawinkler 2011), and with an
approximate reduction to account for axial load interaction. The reduction was based on AISC
360-10 Equations H1-1a and H1-1b (AISC 2010a) using a constant axial load resulting from the
gravity load plus half the lateral load calculated in a nonlinear static (pushover) analysis under
wind or seismic loads. This was the same method used in the ATC-76 project (NIST 2010a). A
fiber model was not used in order to make incremental dynamic analyses feasible.
8000
W18X76 Monotonic
6000 envelope
4000
Moment (k-in.)
2000
-2000
-4000
-6000 Fully-reversed cyclic

-8000
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Rotation (rad)
Figure 3.19 Typical idealized behavior for a column plastic hinge: W18x76 column in Type I
non-ductile moment frame 4-story building
99
This is the same approximate approach used in other collapse assessments (e.g. NIST
2010a,b; Deierlein et al. 2010), and was necessary not only because the finite element model
representation could not capture axial and flexure interaction directly, but was also necessary
because both the moment-rotation models and the experimental data used to define the column
hinge moment rotation behavior do not account for variation in axial load (see section 6.5.4 of
NIST 2010a).
Column Panel Zones
Beam-to-column joints to the weak-axis connections (no panel zone) were represented using a
centerline joint model. Column panel zones (beam connections to the strong axis of the column)
were explicitly represented using the Krawinkler joint model (Krawinkler 1978; Charney and
Marshall 2006). Figure 3.20 shows the finite element model corresponding to the Krawinkler
joint model. The Krawinkler model consisted of 8 rigid beam elements connected by hinges and
one spring. The spring represented the combined contributions of the panel zone (column web
plus doubler plate, where added) and the column flanges.
True hinge,
Zero-length spring element
typical
(panel zone shear distortion)
(beam plastic hinge)
(8) Rigid elastic beam-column elements

(column plastic hinge)
Figure 3.20 Explicit (Krawinkler) column panel zone model (reduced beam section shown)
100
The shear-distortion behavior of column panel zones (Figure 3.21) was represented using
the Hysteretic uniaxial material option, with a tri-linear envelope curve and bilinear
hysteresis behavior (Gupta and Krawinkler 1999) based on the column depth 𝑑𝑐 , the panel zone
thickness (column web thickness plus doubler plate thickness, if specified) 𝑡𝑝𝑝 , the shear
modulus 𝐺, the column flange width 𝑏𝑓𝑓 , column flange thickness 𝑡𝑓𝑓 , and beam depth 𝑑𝑏 :
𝑉𝑦 = 0.55 (𝑅𝑦 𝐹𝑦 ) 𝑑𝑐 𝑡𝑝𝑝
𝐾𝑒 = 0.95 𝐺 𝑑𝑐 𝑡𝑝𝑝
𝐾𝑝 = �0.95 𝐺 𝑏𝑓𝑓 𝑡𝑓𝑓 2 � ⁄𝑑𝑏
Degradation of the joint model was neglected because experimental research has
indicated that it is unlikely to occur, unless there is shear buckling (PEER/ATC 2010). The
intent was to preclude shear buckling by designing the panel zone using AISC 360-10.
500
Monotonic
W18X76 envelope
Shear Force (k)
-500
-0.05 0 0.05
Shear Distortion (rad)
Figure 3.21 Typical idealized behavior for a column panel zone distortion: W18x76 column in
Type I non-ductile moment frame 4-story building
101
3.3.6 Collapse-Inhibiting Mechanisms
Slack-cable collapse inhibiting mechanisms were represented using truss elements with a multi-
linear elastic material behavior (to simulate initial slackness) until fracture at the cable breaking
load. The loose-linkage collapse inhibiting mechanism was represented using corotational truss
elements that are elastic until fracture, approximated as the tensile yield limit state of the links.
Energy dissipating devices (small viscous fluid dampers or viscoelastic solid high-damping
rubber) were idealized using viscous corotational truss elements.
The model representation for beams and columns did not admit a change in the moment
gradient, as previously discussed. Therefore, the formation of a plastic hinge in the column or
beam at the location of the cable or link connection was precluded by limiting the axial capacity
of the collapse prevention system component (cable or link). The limiting capacity was based on
two limit states: (1) interaction of axial load and moment at the location of the brace-to-column
or brace-to-beam connection, as described in AISC 360-10 section H1.1; and (2) shear yielding
of the column or beam web, as described in AISC 360-10 section G2.1. The size of the collapse
prevention system component was based on the lower value obtained according to the two limit
states for either the beam or column.
The nominal axial strength, 𝑃𝑛 was determined according to AISC 360-10 section E3.
The column effective flexural strength, 𝑀𝑛 was calculated by increasing the expected plastic
moment, 𝑀𝑝 (Equation 3.10) to account for isotropic hardening by the ratio 𝑀𝑦 /𝑀𝑝 and average
strain hardening by the ratio 𝑀𝑐 /𝑀𝑦 in Equation 3.11, based on information extracted from a
database of experimental testing of steel components (Lignos and Krawinkler 2011).
𝑀𝑝 = 𝑅𝑦 𝐹𝑦 𝑍 (3.10)
102
𝑀𝑐 𝑀𝑦
𝑀𝑛 = � � � � 𝑀𝑝 (3.11)
𝑀𝑦 𝑀𝑝
The nominal flexural strength at each end of the column was reduced to account for
flexure and axial load, 𝑃 interaction, as previously discussed. The nominal flexural strength at
the connection location, 𝑀𝑎 was determined according to AISC 360-10 section F2 and adjusted
according to the moment gradient using the lateral-torsional buckling modification factor, 𝐶𝑏 :
𝐶𝑏 = 1.60 for double curvature
= 1.36 for single curvature
The interaction of axial load and moment at the location of the brace-to-column or brace-
to-beam connection was determined using AISC 360-10 section H1.1 (Equation 3.12) based on
the axial and moment force diagram shown in Figure 3.22.
�𝑃 − 𝐹𝑦 � (𝑀𝑎 + 𝑀𝑥 )
1 = 𝛼 +𝛽 (3.12)
𝑃𝑛 𝑀𝑛
where
0.5 𝑖𝑖 �𝑃 − 𝐹𝑦 �/𝑃𝑛 < 0.2

𝛼 = � (3.13)
1.0 𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒
𝛽 = 1.0 𝑖𝑖 �𝑃 − 𝐹𝑦 �/𝑃𝑛 < 0.2 (3.14)

�
8/9 𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒
The maximum capacity of the collapse prevention system component, for interaction of axial and
moment forces, was then back-calculated using (Equation 3.15):
𝑃𝑛 𝑀𝑛 − 𝛼𝑀𝑛 𝑃 − 𝛽𝑃𝑛 𝑄𝑀𝑦

𝐹𝑚𝑚𝑚1 = 𝛽𝑃 𝑎(𝐿 − 𝑎) 𝛼𝑀𝑛 (3.15)
� 𝑛 �−
𝐿√2 √2
where
(𝐿 − 2𝑎)/𝐿 𝑑𝑑𝑑𝑑𝑑𝑑 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑄 = � (3.16)
(𝐿 − 𝑎)/𝐿 𝑠𝑠𝑠𝑠𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
103
𝑃
𝐹𝑦 𝐹
𝑎 𝑀𝑦
𝐹𝑥 𝑀𝑎 𝑀𝑥
𝑀𝑦
a) Structural member b) Moments due to double curvature c) Moments due to device
Figure 3.22 Axial and moment forces in column with collapse prevention system
Shear yielding of the column or beam web was determined using AISC 360-10 section
G2.1, 𝑉𝑛 = 0.6�𝐹𝑦 𝑅𝑦 �𝐴𝑤 , where 𝐴𝑤 is the area of the web (web thickness times the section
depth). Ultimately, the lowest value of the two limit states (minimum of 𝑉𝑛 √2, 𝐹𝑚𝑚𝑚1 ) was used
to size the collapse-prevention system component.
3.3.7 Partially-Restrained (Enhanced Shear Tab) Beam-to-Column Connections
The moment-rotation behavior of the enhanced shear-tab connections (Figure 3.23) was
represented using the Pinching4 and MinMax uniaxial materials in OpenSees, with load-
deformation and hysteresis parameters based on test data of T-stub type flange connections
(Pryor and Murray 2013) and FEMA P-440A. The connections exhibit cyclic degradation of
both stiffness and strength, until 9% drift, after which the rotational stiffness and flexural
strength of the connection is zero (based on monotonic tests results).
104
3000
W16X31
2000 Monotonic
envelope
1000
Moment (k-in.)
-1000
-2000 Fully-reversed cyclic

-3000
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Rotation (rad)
Figure 3.23 Typical idealized behavior for an enhanced shear tab beam-to-column connection:
W16x31 beam in Type I non-ductile moment frame 4-story building
The axial strength of the T-stub stem was calculated based on the reduced region.
𝑃𝑦 = 𝐴𝑦 �𝑅𝑦 𝐹𝑦 � (3.17)
𝑃𝑢 = 𝐴𝑦 (𝑅𝑡 𝐹𝑢 ) (3.18)
The moment strength of the connection was calculated based on the axial force couple,
where 𝑑 is the beam depth and 𝑡 is the stem plate thickness.
𝑀𝑦 = 𝑃𝑦 (𝑑 + 𝑡) (3.19)
𝑀𝑢 = 𝑃𝑢 (𝑑 + 𝑡) (3.20)
The yield rotation of the connection 𝜃𝑦 was calculated based on the effective rotational
stiffness of the connection 𝐾𝑒𝑒𝑒 (ICC-ES 2013).
2𝑃𝑦
𝜃𝑦 = (3.21)
𝐾𝑒𝑒𝑒 (𝑑 + 𝑡)
105
The ultimate and failure rotations were estimated to be 0.02 rad and 0.05 rad, respectively, based
on test data.
Two limit states were considered for the design of the T-stub stem: yielding of the
reduced region of the stem, and high-mode buckling of the reduced region of the stem. The stem
was proportioned so that inelasticity was limited primarily to the reduced region. The yield
length was determined based on a target strain demand. The theoretical lateral out-of-plane
thrust forces exerted on the restraint plate and beam flange during high-mode buckling of the
weak-axis of the reduced region of the link stem were calculated. Similarly, the theoretical
lateral in-plane thrust forces exerted on the spacer plates during high-mode buckling of the
strong-axis was calculated. The out-of-plane thrust force was used to determine the required
thickness of the restraint plate.
The thrust forces were predicted based on constrained buckling theory (Bleich 1952; Chai
1998; Chai 2001; Chai 2002; Genna and Bregoli 2014). A lower and upper bound on the thrust
force was based on classical inelastic column theory (Shanley 1947; Chen and Lui 1987; Gere
and Timoshenko 1990). A detailed description of the design procedure for the enhanced shear
tab connections is available in a separate report (Judd and Charney 2015b).
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3.4 Nonlinear Analysis Approach
Archetypical structural systems were analyzed in OpenSees (PEER 2012). This section
describes the general procedures used to include second-order effects, damping, and the solution
strategy used to solve the non-linear equations of motion. Specific analysis procedures for
seismic loads are described in Chapter 4, and specific analysis procedures for wind loads are
described in Chapter 5.
3.4.1 Second-Order Effects
Second-order (P-∆) effects were included using the “corotational” approach, where the local
element frame continuously rotates with the element to capture large displacements, and small-
strain constitutive relationships are applied. Instead of a “leaning column,” the gravity framing
was explicitly represented. The effect of the approach used to include second-order effects is
examined in Chapter 6.
3.4.2 Damping
When a building vibrates, energy is dissipated by various mechanisms (Chopra 2012;
PEER/ATC 2010; Deierlein et al. 2010). This energy dissipation is commonly referred to as
damping. Inherent damping (damping not explicitly modeled through component hysteresis in
the finite element model) is caused by a variety of structural and non-structural mechanisms,
such as loading and reloading of components, internal friction of deformed components, friction
between structural components, foundation-soil interaction, and so on. In contrast to inherent
damping, active, semi-active, or passive energy dissipation devices can provide added damping
107
to the building. Such added supplemental energy dissipation devices (e.g. linear viscous
dampers) were not considered “inherent damping.”
Mathematical Model for Damping
This study used a viscous model for damping. This model is mathematically convenient since
the damping matrix in the equation of motion can be assembled as a linear combination of the
mass and stiffness matrices (“Rayleigh” damping). For example, Figure 3.24 shows the damping
curve for the Type I non-ductile moment frame 1-story building.
The viscous model is also convenient in the sense that damping may be expressed as a
fraction of critical damping. Also, reconnaissance and field studies often report building
damping using a percent of critical viscous damping.
0.1
0.09
0.08
0.07
“Rayleigh” damping, 𝛼𝑴 + 𝛽𝑲
Modal damping ratio
0.06
0.05
20% of
1st mode second mode
0.04
Target 0.03 Stiffness proportional damping, 𝛽𝑲

damping
ratio 0.02
Mass proportional damping, 𝛼𝑴
0.01
0
0 10 20 30 40 50
Natural circular frequency (rad/sec)
Figure 3.24 Proportional damping curve for Type I non-ductile moment frame 1-story building
108
It was recognized that invoking viscous damping to capture damping that is not explicitly
incorporated in the model is problematic, at best, and may be inaccurate. Many researchers
(Bernal 1994; Medina and Krawinkler 2003; Hall 2006; Priestly and Grant 2007; Powell 2008;
Charney 2008; Bowland and Charney 2010; Zareian and Medina 2010; Jehel et al. 2011;
Puthanpurayil et al. 2011; Hardyneic 2014) have demonstrated the complications with using
viscous damping in inelastic models. Namely, viscous damping tends to over-estimate internal
forces (e.g. unrealistic damping forces) and under-estimate deformations under inelastic
behavior. A primary cause of these errors is the deterioration of component force-deformation
relationships. The explicitly modeled hysteresis damping degrades and no longer contributes
toward dissipating energy.
Commonly proposed solutions to these concerns maintain viscous damping, but with a
varying degree of stiffness-proportional damping. For example, Petrini et al. (2008) verified the
use of viscous damping in elastic analysis using experimental data from concrete piers. Among
other approaches, for example, Charney (2008) recommends using tangent stiffness-based
viscous damping with solution procedures, such as a small time step, to ensure equilibrium.
Using initial stiffness may lead to over-damping (e.g. Priestly et al. 2007) and, on the other hand,
using tangent stiffness is computationally expensive and may lead to numerical instability. Thus,
Zareian and Medina (2010) proposed using a modified initial stiffness by excluding structural
elements that may behave inelastically. Similarly, Deierlein et al. (2010) suggest excluding or
minimizing the effect of components with degradation or artificial stiffness (such as “rigid”
beams or links). In addition to excluding degrading components (i.e. plastic hinges), Ibarra and
Krawinkler (2005) increase the stiffness-proportional damping of the internally modified elastic
109
beam-column elements. Some researchers (e.g. Lignos et al. 2013) advocate using only mass-
proportional damping (no stiffness-proportional damping).
Other researchers have altered or completely discarded the assumption of viscous
damping. Bowland and Charney (2010) proposed two methods: in the first method, damping
was modeled through a rigid-link “ghost element” with rotational dampers, attached to the
structure; in the second method, damping was based on internal stresses, a so-called
instantaneous viscous damping. Puthanpurayil et al. (2011) showed that a non-viscous model
may be more appropriate. Using a relaxation function, a mathematical expression was used that
varied from viscous to non-viscous, depending on the dissipation constant (e.g. large value was
viscous, small value was non-viscous). The difficulty with this model was that an appropriately
tuned value for seismic analysis was undetermined.
For the above reasons, in this research, Rayleigh damping was only applied to linear
elastic components of the finite element model.
Critical Damping Ratio
This research assumed 2.5% critical damping ratio, except that in a wind strength design analysis
1% damping was assumed (ASCE 2010), and 1% damping was used in a wind collapse analysis
(see Chapter 5). Mass and stiffness proportional (“Rayleigh”) damping was defined using the
fundamental building period and a period corresponding to 20% of the second mode period of
the building (see Figure 3.24). It is noted that this definition of proportional damping (NIST
2010a) differs from the recommendation by Smyrou et al. (2011) for nonlinear dynamic analyses
to use the first mode and the 𝑛-th mode, where 𝑛 = number of stories of the building. A free
vibration analysis was used to verify the model damping.
110
It was recognized that the appropriate amount of proportional damping depends on the
structure and hazard intensity considered. Traditionally, 2% to 5% total damping has been used
for seismic analysis of buildings. However, this overestimates the damping for nonlinear
analysis because some of the damping is already explicitly modeled via component hysteresis.
The assumed damping in this research falls in the range between 1% and 5%, but not greater than
3% for tall buildings, where the damping effect of foundations and nonstructural cladding is
small relative to the structural characteristics, recommended by FEMA P-58 (FEMA 2012a,b).
3.4.3 Analysis Solution Procedures
For nonlinear static analysis, the finite element system of equations was solved using static load
control for gravity analysis, and displacement control (Batoz and Dhatt 1979; Ramm 1981) for
seismic or wind pushover analysis. For nonlinear response history analysis, the system of
equations was solved using the implicit integration method proposed by Newmark (1959) with
the special case of average acceleration (Tedesco et al. 1999), where the corresponding
integration parameters are 𝛾 = 1/2 and 𝛽 = 1/4. The integration method is unconditionally
stable for linear analysis (Bathe 1996), however stability for nonlinear analysis has not been
proven (Belytschko et al. 2014, pages 356 to 357). Explicit integration was not used for two
reasons. The first reason is that the stable time increment (Equation 3.22) required for an explicit
integration scheme was very small and may lead to impractical run-time.
2
∆𝑡 ≤ + ��1 + 𝜉𝑚𝑚𝑚 2 − 𝜉𝑚𝑚𝑚 � (3.22)
𝜔𝑚𝑚𝑚
In Equation 3.22, 𝜉𝑚𝑚𝑚 is the critical damping ratio in the mode with the highest
frequency. The consequence is that damping in the analysis actually reduces the stable time
111
increment (Dassault Systèmes 2011b). Nevertheless, previous experience suggests that much
larger time steps can still be used for an implicit scheme, compared to an explicit scheme
(Belytschko et al. 2014).
The second reason is that the explicit integration necessitates the inclusion of mass at
each degree of freedom in the finite element model (Carr 2004), but the model used in this study
employed a lumped mass approach. The primary disadvantage of an implicit integration scheme
is the high-computational cost and insufficient robustness for rough response.
Thus, a self-adaptive solution strategy (Appendix C) was required to solve the non-linear
equations. The Newton-Raphson method was the initial default solution algorithm. The default
convergence tolerance (based on absolute energy balance) was between 10-4 and 10-5 depending
on the analysis type (static gravity, pushover, or dynamic) and the solution algorithm.
• In the first step of the strategy, the Newton-Raphson method was used. This method was
computationally expensive in that it required the tangent stiffness matrix to be
reformulated, but the method was robust.
• In the second step of the strategy, if required, the analysis time step was reduced.
• In the third step, the solution strategy tried the following solution algorithms (in this
order). A Newton-Raphson with Line Search was used to improve slow convergence
with the Newton-Raphson algorithm. An initial interpolated line search was used with
tolerance = 0.8, max number of iterations = 10, minimum root to the solution function,
η min = 0.1, and maximum root to the solution function, η max = 10.0. A Newton-Raphson
112
with Krylov subspace accelerator (a low-rank least-squares analysis) was used to improve
slow convergence by identifying where the largest changes in structural state occurred
and then correcting for smaller changes at the remaining degrees of freedom (Scott and
Fenves 2010) using an initial tangent stiffness matrix. As an alternative to the Newton-
Raphson methods for dynamic analyses (Bathe and Cimento 1980), a secant
approximation of the stiffness matrix was employed using the Broyden–Fletcher–
Goldfarb–Shanno (BFGS) matrix-updating (quasi-Newton) method. Successive rank-one
updates of the tangent stiffness matrix were used based on the first iteration of the current
time step using the Broyden method. The Newton-Raphson algorithm was modified (the
stiffness matrix was not reformulated) using initial stiffness solution iterations. In the
fourth step of the strategy, the TRBDF2 integrator (Bathe 2007) was temporarily applied.
Finally, the convergence tolerance was temporarily loosened.
As an example, Figure 3.25 compares the solution information for nonlinear static
“pushover” analysis and nonlinear dynamic response history analysis of the Type I non-ductile
2-story building with enhanced shear tab connections. The colors indicate the final algorithm
that was used to achieve a solution. The number of iterations shown in the lower plots refers
only to the final algorithm, and does not include the number of algorithms tried and the number
of iterations attempted for those analyses.
In the static analysis, at approximately 3% roof drift the solution algorithm switch from
the default (Newton-Raphson) to include a line search. At approximately 7% the Krylov
subspace accelerator was used. Finally, at approximately 8% the solution returned to using
default algorithm. The static analysis required up to 63 iterations to achieve a solution.
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0.25 0.05
0
0.2
Normalized Base Shear (V/W)
-0.05
Roof Drift Ratio

0.15
-0.1
0.1
-0.15
0.05
-0.2
0 -0.25
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 2 4 6 8 10 12 14 16 18 20
Roof Drift Ratio Time (s)
70 120
60
100
Number of Solution Iterations
Number of Solution Iterations

50
80
40
60
30
40
20
20
10
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 2 4 6 8 10 12 14 16 18 20
Roof Drift Ratio Time (s)
a) Nonlinear static pushover analysis b) Nonlinear response history analysis
Newton-Raphson (default algorithm)
Newton-Raphson with line search
Newton-Raphson with Krylov subspace accelerator
Broyden–Fletcher–Goldfarb–Shanno (BFGS)
Figure 3.25 Solution algorithm and maximum number of iterations: seismic analysis of Type I
non-ductile 2-story building with enhanced shear tab connections for LOS000 ground motion
scaled to collapse intensity
114
In the dynamic analysis, a similar pattern of algorithm switching was observed but more
iterations (up to 120) were typically required.
Thus, the appropriate algorithm and number of steps depended on the nonlinear equations
that were solved. Depending on the structure, these equations varied considerably, and it was not
apparent which solution algorithm was most appropriate. In fact, previous research of nonlinear
analysis of framed structures (Vamvatsikos and Cornell 2004; Bathe 1996; Vamvatsikos 2011;
Hardyniec 2014; Hardyneic and Charney 2015) have employed similar ad-hoc self-adaptive
solution strategies.
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Chapter 4
SEISMIC COLLAPSE ASSESSMENT
This chapter assesses the seismic collapse safety of the archetype structural systems with and
without collapse prevention systems. The collapse vulnerability (collapse fragility) was
determined using a sequence of gravity, frequency, nonlinear static “pushover” analyses,
followed by nonlinear dynamic response history analyses incrementally scaled, with respect to a
target spectrum, until side-sway collapse. The risk of seismic collapse was determined by
integrating collapse fragility and hazard, accounting for directional effects and site response.
Results of selected archetype systems are discussed. Finally, a comparison with the seismic
collapse assessment of traditional structural systems is included.
4.1 Seismic Collapse Vulnerability Procedures
The probability of building seismic collapse given the MCE was assessed following the FEMA
P-695 methodology (FEMA 2009a) with two adaptations appropriate for the collapse prevention
systems approach and for the central and eastern United States.
116
• First, the computed (model) fundamental period of vibration was used for both
referencing spectral accelerations and for estimating the inherent damping (taken as
2.5%) in the building that was not explicitly modeled through component hysteresis.
• Second, incremental dynamic analyses were run until all ground motions caused collapse
and the measured record-to-record dispersion was used when incorporating uncertainty.
The collapse assessment consisted of several analysis procedures. A gravity load
analysis was first conducted. An eigenvalue analysis was then used to determine the period of
vibration used as a reference for ground motion scaling and used as a reference for damping.
Nonlinear static seismic (pushover) analyses were conducted to determine the axial loads used in
the column plastic hinge approximation and to determine period-based ductility. Finally,
nonlinear dynamic response history analyses were completed. Appendix C contains excerpts of
the OpenSees (PEER 2012) scripts and selected seismic modeling results for the Type I non-
ductile moment frame 4-story building with enhanced shear tab connections.
4.1.1 Gravity Load Analysis
Vertical gravity roof and floor dead (D) and floor live (L) loads were calculated using the load
combination given in Equation 4.1. The gravity loads are defined in Appendix B.
Total load = 1.05𝐷 + 0.25𝐿 (4.1)
The load combination was intended to represent the expected gravity loads present in the
building during an earthquake [see ASCE 7-10 Table C4-2 (ASCE 2010); FEMA (2009a)].
Second-order effects were included in the gravity load analysis.
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4.1.2 Frequency (Building Period of Vibration) Analysis
After the gravity pre-load analysis, an eigenvalue frequency analysis was used to determine the
periods of vibration of the building and associated mode shapes. For example, Figure 4.1 shows
the first four modes of vibration for the Type I non-ductile moment frame 8-story building.
a) Mode 1 (𝑇1 = 2.85 seconds/cycle) b) Mode 2 (𝑇2 = 1.00 seconds/cycle)
c) Mode 3 (𝑇3 = 0.55 seconds/cycle) d) Mode 4 (𝑇4 = 0.33 seconds/cycle)
Figure 4.1 Mode shapes and periods of vibration: Type I non-ductile moment framing
8-story building
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4.1.3 Nonlinear Static Seismic (“Pushover”) Analysis
In the nonlinear static seismic “pushover” response analysis, the building model was subjected to
a static lateral force at each story. Pushover analysis serves three purposes: it provides
information regarding dynamic response (see below), the post-peak negative slope is a predictor
of P-D instability (Humar et al. 2000), and it provides a method to verify that the analytical
modeling (i.e. story collapse mechanisms are reasonable).
In this research, the distribution of lateral forces was proportioned to match the mode
shape corresponding to the fundamental period of vibration of the building (previously
discussed). The lateral forces were applied using a displacement-control solution strategy until
the roof displacement of the building exceeded at least the displacement corresponding to a 20%
loss in lateral strength of the building. For example, Figure 4.2 shows the seismic pushover
response for the Type I ductile moment frame 4-story building.
The seismic pushover analysis was used to determine the static overstrength, Ω and the
period-based ductility, 𝜇 𝑇 . The static overstrength was calculated as the ratio of the maximum
base shear resistance to the design base shear force (Equation 4.2).
𝑉𝑚𝑚𝑚
Ω = (4.2)
𝑉𝑑𝑑𝑑𝑑𝑑𝑑
The period based ductility was calculated based on the ratio of ultimate roof displacement
to effective yield roof displacement (Equation 4.3), where a single-degree-of-freedom (SDOF)
displacement is correlated to the building roof displacement, using 𝐶0 as calculated in ASCE 41-
13 (ASCE 2014).
119
𝛿𝑢
𝜇𝑇 =
𝛿𝑦,𝑒𝑒𝑒
= 𝛿𝑢 (4.3)
𝑉 𝑔
�𝐶0 𝑉 𝑚𝑚𝑚 � 2 � [𝑚𝑚𝑚(𝐶𝑢 𝑇𝑎 , 𝑇1 )]2 �
𝑑𝑑𝑑𝑑𝑑𝑑 4𝜋
0.16
max V/W = 0.1414

0.14
MF+GF
80% of
0.12 MF max V/W
ΩSeismic = 1.80
0.1
Cs = 0.079
0.08
0.06
0.04
0.02
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Roof Drift Ratio
Figure 4.2 Seismic pushover response of Type I ductile moment frame 4-story building
4.1.4 Ground Motion Set for Nonlinear Response History Analysis
Response history analysis of a structure requires the use of an input ground motion, and these
input ground motions can be legitimately derived from a variety of sources (see discussion in
Chapter 6). In this study, the FEMA P-695 “Far-Field” ground motion set (Table 4.1) was used.
It is recognized that this choice is imperfect. It has been shown in this study that ground
motions in the central and eastern United States have different characteristics—namely
120
frequency content—compared to ground motions in the western United States or from other
tectonic boundary regions. [See Baker et al. (2011) for example ground motion set for tectonic
boundary regions.] Moreover, due to the scarcity of large-magnitude earthquakes and the lack of
strong motion instrumentation, we know less about earthquakes outside the western United
States.
Table 4.1 Ground motion set (FEMA P-695 Far-Field set) used for dynamic analysis
FEMA P-695 ID Record Name Earthquake Magnitude

1 Beverly Hills - Mulhol 1994 Northridge 6.7
2 Canyon Country-WLC USC 1994 Northridge 6.7
3 Bolu ERD 1999 Duzce, Turkey 7.1
4 Hector SCSN 1999 Hector Mine 7.1
5 Delta UNAMUCSD 1979 Imperial Valley 6.5
6 El Centro Array 1979 Imperial Valley 6.5
7 Nishi-Akashi CUE 1995 Kobe, Japan 6.9
8 Shin-Osaka CUE 1995 Kobe, Japan 6.9
9 Duzce ERD 1999 Kocaeli, Turkey 7.5
10 Arcelik KOERI 1999 Kocaeli, Turkey 7.5
11 Yermo Fire Station CDMG 1992 Landers 7.3
12 Coolwater SCE 1992 Landers 7.3
13 Capitola CDMG 1989 Loma Prieta 6.9
14 Gilroy Array #3 1989 Loma Prieta 6.9
15 Abbar BHRC 1990 Manjil, Iran 7.4
16 El Centro Imp. 1987 Superstition Hills 6.5
17 Poe Road (temp) 1987 Superstition Hills 6.5
18 Rio Dell Overpass 1992 Cape Mendocino 7
19 CHY101 CWB 1999 Chi-Chi, Taiwan 7.6
20 TCU045 CWB 1999 Chi-Chi, Taiwan 7.6
21 LA - Hollywood 1971 San Fernando 6.6
22 Tolmezzo -- 1976 Friuli, Italy 6.5
In this research, two overriding considerations in choosing ground motions for analysis
were (1) that the ground motions match (more or less) the spectral shape expected for the
location, and (2) a wide-range of motion based on the spectral shape should be used to account
121
for the lack of known constraints on the motion. The selected ground motion set was considered
to be a reasonable choice since the primary interest was in the comparison between structural
systems, as opposed to an attempt to accurately predict collapse for an actual site location.
4.1.5 Target Spectrum
In this study, the ASCE 7-10 design spectrum was used as the target spectrum. This approach
follows the approach used in the prevailing seismic collapse assessment method (FEMA P-695).
It is recognized that in the western United States a conditional mean spectrum is
theoretically an appropriate target, whereas in the central and eastern United States, the uniform
hazard spectrum is theoretically more appropriate. This is the case because outside the western
United States the uniform hazard and conditional mean spectrums do not differ much. This lack
of dissimilarity is due to the fact that the same earthquake event is the dominant contributor to
hazard across the range of spectral periods (Baker 2011). However, the objective is to compare
structural systems, so the design spectrum was used in this research.
As an example, Figure 4.3 shows the response spectrum for the Type I non-ductile 2-
story building. The analytical model included reserve lateral strength in the gravity framing.
4.1.6 Intensity Measure for Seismic Hazard
In this study, the spectral acceleration at the fundamental period of vibration was selected as the
seismic hazard intensity measure. The sensitivity of the collapse assessment to the conditioning
period used for the intensity measure is discussed in Chapter 6.
Various intensity measures can be used in a seismic collapse assessment, including single
parameter measures, such as peak ground acceleration (PGA), peak ground velocity (PGV), and
122
peak ground displacement (PGD), and multiple parameter measures, or so-called vector intensity
measures (e.g. Baker and Cornell 2005). A vector intensity measure using spectral acceleration
and epsilon (difference between observed and expected lognormal spectral accelerations in terms
of standard deviations) has been shown to be an effective intensity measure for predicting
seismic damage in ductile steel frame buildings, whereas a vector intensity measure using peak
ground displacement and peak ground velocity (PGD, PGV) has been shown to be more suited
for seismic collapse predictions of ductile steel frame buildings (Olsen et al. 2014; Buyco 2014).
Interestingly, a related study indicated that applying a low-pass Butterworth filter to the peak
ground acceleration with a cutoff period larger than the fundamental building period (termed a
“peak filtered acceleration”), in order to isolate the long-period component of the ground motion,
is another effective intensity measure for seismic collapse of ductile steel frame buildings (Song
2014; Buyco 2014). Notwithstanding, perhaps the most commonly used single-parameter
seismic intensity measure for structural engineering is spectral acceleration at the fundamental
period of vibration [i.e. FEMA P-695 (FEMA 2009a); FEMA P-58 (FEMA 2012a,b)].
4.5
Scaled FEMA P-695 Far-Field
Ground Motion Set
4
Pseudo-acceleration, Sa (g)
3.5
Median spectrum
3
Target spectrum (SDC Dmax)
2.5
1.5 Target period, T1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds/cycle)
Figure 4.3 Response spectrum for Type I non-ductile 2-story building
123
4.1.7 Nonlinear Dynamic Response History Analysis
In the nonlinear dynamic response history analysis, the FEMA P-695 “Far-Field” ground motion
set (shown in Table 4.1) was collectively scaled so that the median response spectrum matched
the target spectrum (SDC D max ) at the reference period. Each building model was subjected to
the ground motion set in successive incrementally increasing levels of intensity (as measured by
the spectral acceleration at the fundamental period) until all ground motions caused side-sway
collapse, assumed to occur when the maximum interstory drift ratio is at least 0.2.
This procedure of conducting nonlinear dynamic response history analyses with
increasing hazard intensities is commonly called an incremental dynamic analysis (IDA).
Although the concept of incremental dynamic analyses is not new (e.g. Nassar and Krawinkler
1991; Elnashai and Di Sarno 2008), it was impractical for the computational resources of the
time and was not commonly done until Vamvatsikos and Cornell (2004). It was recognized that
the linear scaling approach used in the IDA leads to a loss in accuracy for large ground motions
(Baker 2013), but at the same time the IDA approach was the most viable approach when
collapse is to be assessed in numerous locations with variations in the underlying seismic hazard,
as is considered in this study.
In an IDA, the ground motion scaling is relative to a reference magnitude. The scaling
procedure was a multi-step scaling process. The ground motion record was first scaled (in
FEMA P-695) by a factor to normalize the velocity of the ground motion set. Next the record
was scaled so that the median of the record set matches the target design spectrum. Finally, the
record is incrementally scaled relative to the normalization factor times the anchor factor. The
following scheme was used to determine the anchor factor. (An alternate scheme was used for
seismic performance assessment in Chapter 7.)
124
Each ground motion record was scaled relative to the original record intensity. (For
example, the record was multiplied by 2, 3, 4, and so on.) The advantage of this method is that
the scaling was independent of a target spectrum (which target depends on several factors,
including the building location, seismic design category (SDC), and period of vibration).
Additionally, this scaling method allowed the IDA results to be independent of the sub-set of
motions selected from the full set (since the normalization factor is a function of the set of
motions considered). Another advantage was that this scaling method allowed the seismic
collapse fragility curve to exhibit non-vertical data points (since ground motions are not being
run at the same spectral acceleration intensity for a given period).
Moreover, the intensity factor correlates to how much the magnitude of original ground
motion has been altered, whereas the intensity factor for anchored scaling (used for performance
assessment in Chapter 7) does not show the normalization and anchoring factors. A
disadvantage of this scaling scheme is that the individual response for a given ground motion is
not necessarily calculated at exactly the DBE, MCE, or some other hazard intensity level.
The anchor record reference scheme was used for response history analyses when used as
part of a collapse assessment using the FEMA P-695 procedure, for the reasons previously
outlined. However, the anchor reference scheme is used for performance assessment using the
FEMA P-58 framework, since this scheme calculates response at exactly the hazard level of
interest, as previously noted.
The nonlinear dynamic analyses were advanced in the IDA scaling procedure using
parallel processing with a bisection approach (Vamvatsikos 2011; Hardyniec and Charney 2015).
Each ground motion was assigned to one processor and incremental analyses were run until
completion of the IDA for that ground motion.
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4.1.8 Collapse Fragility
The seismic vulnerability of the building to side-sway collapse (seismic collapse fragility) was
determined by fitting individual collapse points (spectral acceleration at the reference period and
corresponding probability of collapse for a one scaled ground motion record) with a curve,
assuming a lognormal cumulative distribution function. The lognormal cumulative distribution
function was defined by two parameters: the median collapse spectral acceleration with reference
to the ground motion set 𝑆𝑎 (𝑇1 ), and the standard deviation of the natural logarithm 𝛽
(dispersion due to variability and uncertainty). Prior analytical studies suggest that the
lognormal distribution is appropriate for seismic collapse fragility (Ibarra and Krawinkler 2005;
Bradley and Dhakal 2008; Ghafory-Ashtiany et al. 2011; Eads et al. 2013).
The median collapse spectral acceleration was adjusted (increased) to account for spectral
shape, estimated using period-based ductility, 𝜇 𝑇 and the total dispersion, 𝛽𝑇𝑇𝑇𝑇𝑇 in collapse
capacity was calculated using Equation 4.4.
𝛽𝑇𝑇𝑇𝑇𝑇 = �𝛽𝑅𝑅𝑅 2 + 𝛽𝐷𝐷 2 + 𝛽𝑇𝑇 2 + 𝛽𝑀𝑀𝑀 2 (4.4)
In Equation 4.4, 𝛽𝑅𝑅𝑅 was the measured (record-to-record) dispersion in the nonlinear
seismic response history analyses. Epistemic uncertainty was incorporated by assigning
dispersion due to design 𝛽𝐷𝐷 , test data 𝛽𝑇𝑇 , and modeling uncertainty 𝛽𝑀𝑀𝑀 . The qualitative
ratings (using FEMA P-695 rubric) given in Table 4.2 were used in this study.
Table 4.2 Qualitative rating used to quantify uncertainties in seismic collapse assessment
Non-ductile moment frame Ductile moment frame

Design requirements B (β =0.20) A (β =0.10)
Test data C (β =0.35) B (β =0.20)
Analytical model C (β =0.35) B (β =0.20)
126
For non-ductile moment frame buildings, 𝛽𝐷𝐷 = 0.2 (“Good”), and 𝛽𝑇𝑇 = 𝛽𝑀𝑀𝑀 = 0.35
(“Fair”). For ductile moment frame buildings, 𝛽𝐷𝐷 = 0.1 (“Superior”), and 𝛽𝑇𝑇 = 𝛽𝑀𝑀𝑀 = 0.2
(“Good”).
The ASCE 7-10 (ASCE 2010) target is that the average conditional collapse probability
for a group of similar archetypical structures does not exceed 10%, and the FEMA P-695 (2009a)
target is that the conditional collapse probability for any individual building does not exceed
20%.
4.2 Seismic Collapse Risk Procedures
Seismic collapse risk (probability of collapse considering the likelihood of seismicity) was
calculated by integrating the seismic collapse fragility and seismic hazard and by accounting for
directional effects and site response. The ASCE 7-10 (ASCE 2010) target risk is 1% in 50 years.
4.2.1 Directional Effects
Ground motion is a three-dimensional phenomenon that can be described in terms of three
components: one component in the vertical direction and two orthogonal horizontal components.
Relative to a structure, the direction of ground motion and spectral acceleration may be based on
the geometric mean (“geomean”) of two horizontal components. The USGS ground motions use
the geomean due to the ground motion attenuation models used. See FEMA P-750 (FEMA
2009c) and Abrahamson and Shedlock (1997). Alternatively, the direction may be based on the
square root of the sum of the squares (SRSS) of the two horizontal components, or on the
“maximum-direction” of the two components. Maximum-direction spectral acceleration is
determined by calculating the maximum spectral acceleration based on both horizontal
127
components for an entire orbit (orientations from 0° to 360°). The maximum direction is the
orientation with the maximum spectral demand (identified by the point on the orbit farthest from
the origin) (Huang et al. 2008; Huang et al. 2010a).
To illustrate, Figure 4.4 compares the geomean, SRSS, and maximum-direction spectra
for the 1999 Kocaeli, Turkey earthquake ground motion recorded at the Duzce station (FEMA P-
695 Far-Field ground motion ID No. 9). The maximum-direction spectrum envelopes the
component and geomean spectra, but is less than the SRSS spectrum.
As would be expected, the direction of ground motion affects structural response. Three-
dimensional analyses of buildings, subjected to two orthogonal components of ground motion
simultaneously, systematically show that structural collapse is predominately in the direction of
the stronger component. See FEMA P-750 (FEMA 2009c). As a consequence, the overall
structural failure rate is higher for three-dimensional analyses compared to two-dimensional
analyses, all other factors being equal.
1.6 X-Component
Y-Component
1.4
Pseudo-acceleration (g)
Geomean
1.2 SRSS
Maximum Direction
1
0.8
0.6
0.4
0.2
0
0.5 1 1.5 2 2.5 3 3.5 4
Period (s)
Figure 4.4 Spectral acceleration for the 1999 Kocaeli, Turkey earthquake ground motion
recorded at the Duzce station (FEMA P-695 Far-Field ground motion ID No. 9)
128
To remove this non-conservative bias in collapse capacity, the ASCE 7-10 ground motion
design data has been adjusted (increased) from the USGS geomean uniform-hazard spectral
accelerations to approximate maximum-direction demand. See FEMA P-751 (FEMA 2012e).
The ASCE 7-10 (NEHRP) approximation is based on the ratio of maximum-direction to
geomean spectral demand for near-field ground motions in the western United States (Huang et
al. 2008).
Table 4.3 gives the ratio of maximum-direction to geomean spectral demand for sets of
ground motions used in FEMA P-695 and in the development of ASCE 7-10. The ratios reflect
the fact that the maximum-direction spectral acceleration depends on the ground motions. The
ratios for far-field ground motion sets and for ground motion sets intended for the central and
eastern United States can be quite different from each other. For far-field ground motions in the
western United States, the median ratio is 1.20 and 1.27, for 0.2-second and 1.0-second spectral
accelerations, respectively. In the central and eastern United States, the 0.2-second ratio is equal
to 1.28 and the 1.0-second ratio is equal to 1.35.
Table 4.3 Ratio of maximum-direction to geomean spectral acceleration
P-695 Huang et al. (2010)

Near-Field Western US Central and
T (s) Far-Field Pulse No Pulse Far-Field Near-Field Eastern US NEHRP
0 1.2 1.21 1.25 1.18 1.21 1.23 1.1
0.2 1.29 1.24 1.31 1.2 1.22 1.28 1.1
0.5 1.32 1.26 1.31 1.23 1.29 1.32 1.2
1 1.3 1.27 1.37 1.27 1.31 1.35 1.3
2 1.39 1.41 1.4 1.27 1.31 1.39 1.3
3 1.34 1.33 1.31 1.27 1.31 1.35 1.35
4 1.27 1.48 1.35 1.31 1.37 1.4 1.5
129
Figure 4.5 and Figure 4.6 compare the ratio of maximum direction to geomean spectral
acceleration for the three FEMA P-695 ground motion sets with the NEHRP approximation.
Note that the ratios using the FEMA P-695 method will differ for these periods compared to the
NEHRP approximation.
FEMA P-695 Far-Field

Ground Motion Set
Average
NEHRP / ASCE 7-10
Figure 4.5 Ratio of maximum-direction to geomean 𝑆𝑎 for FEMA P-695 far-field ground motion
set (individual record ratio is indicated by gray lines)
FEMA P-695 Near-Field Ground FEMA P-695 Near-Field Ground

(Pulse) Motion Set (No Pulse) Motion Set
a) Near-field ground pulse b) Near field no pulse
Figure 4.6 Ratio of maximum-direction to geomean 𝑆𝑎 for FEMA P-695 near-field ground pulse
130
Based on data from Huang et al. (2010a), maximum-direction to geomean spectral
acceleration ratios of 1.2 and 1.3 are appropriate in the western United States, whereas ratios of
1.3 and 1.4 may be more appropriate in the central and eastern United States, for 0.2-second and
1.0-second spectral accelerations, respectively.
4.2.2 Site Response
A coarse estimate of ground motion amplification can be correlated using geological data
(Kottke et al. 2012), topographic data as a proxy for 𝑉𝑠30 (Wald and Allen 2007; Allen and Wald
2009), or a combination thereof (Magistrale et al. 2012). Such an estimate is especially useful in
situations where it is not feasible to know site conditions with certainty (such as when generating
a ground motion map for code adoption). In fact, ground motion maps along these lines are
proposed for Italy (Crowley et al. 2009).
Figure 4.7 shows a map of 𝑉𝑠30 for the conterminous United States based on topographic
data. An important consideration using the topographic proxy method is that the effect of
sediment thickness is not included (among other effects), and that the proxy method tends to
under-predict 𝑉𝑠30 for hard rock sites (Kottke et al. 2012).
In the ASCE 7-10 approach to risk, site amplification of ground motion is not considered
until after calculation of the risk-targeted motions. Site amplification is dependent on the
spectral acceleration, however, due to soil non-linearity, and so the amplification varies for
different intensities of seismic hazard. For example, Figure 4.8 shows the effect of soil
amplification on both the seismic hazard curve and the ground motion spectrum for a location in
San Francisco.
131
𝑉𝑠30
1 760 m/s
0 702 m/s
0 644 m/s
0 586 m/s
0 528 m/s
0 470 m/s
0 412 m/s
0 354 m/s
0 296 m/s
0 238 m/s
0 180 m/s
Figure 4.7 Average shear wave velocity (𝑉𝑠30) based on topographic data
-1
10 1.4
Maximum-direction Maximum-direction
1.2
Mean annual rate of exceedance, λ (1/year)
-2
10 with site response with site response
1
Spectral acceleration
-3
10
0.8
Maximum-direction
MCE
-4 0.6
10
Maximum-direction Geomean
0.4
-5
10
Geomean
0.2
-6
10 0
0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Spectral acceleration, Sa(T=1.33s) (g) Spectral period
a) Seismic hazard curves b) uniform hazard spectra
Figure 4.8 Seismic hazard data for location in San Francisco (38.0º latitude, -121.7º longitude)
with soil site class D (average 𝑉𝑠30 = 180 m/sec)
132
Clearly, a more accurate seismic risk analysis requires a geotechnical investigation
(where possible), or an estimate of site response using proxy data, to obtain the soil-amplified
hazard curve before integrating hazard and vulnerability.
4.2.3 Integration of Seismic Hazard and Seismic Collapse Vulnerability
Seismic hazard (the occurrence of earthquakes) is commonly described as a Poisson’ process
(FEMA 2012a), that assumes events (e.g. earthquakes) occur randomly and independent of other
events (earthquakes). Although the Poisson process is an inaccurate description for
characteristic earthquake sources, where other descriptions may be more accurate (Matthews et
al. 2002), the description is generally useful (Cornell and Winterstein 1988) and was employed
in this research. For a Poisson process, the probability of occurrence of an event, 𝑁 in 𝑡 years is
𝑃(𝑁 ≥ 1) = 1 − 𝑒 (−𝜆𝑎𝑡) (4.5)
where 𝜆𝑎 is the mean hazard exceedence frequency corresponding to an intensity measure (i.e.
spectral acceleration), the probability that the intensity of an earthquake, A will exceed some
level, a in a given year.
𝜆𝑎 = 𝑃(𝐴 > 𝑎 | 𝑡 = 1𝑦𝑦) (4.6)
For low annual hazard rates, Equation 4.5 is numerically equivalent to the hazard curve
(inverse of MRI) expressed by Equation 4.6.
𝑃(𝑁 ≥ 1) = 𝜆𝑎 𝑡
= 𝜆𝑎
As noted earlier, the collapse fragility curve is simply the probability of collapse or
failure, F conditioned on the occurrence of a spectral acceleration value: 𝑃(𝐹|𝐴 < 𝑎) =

𝑎
∫−∞ 𝑓(𝑡)𝑑𝑑, where f(t) is the probability density function of collapse.
133
Calculation of collapse risk requires the integration of seismic hazard curves and
structural collapse vulnerability (fragility) curves. Integrating hazard and fragility depends on
the overall approach. For example, in a “deterministic” analysis, each fragility ordinate is
multiplied by the corresponding hazard probability (Wang 2011). In probabilistic seismic hazard
analysis (PSHA), there are three analytically equivalent methods to integrate hazard and fragility.
These methods are discussed in Chapter 6. Each method leads to some approximation, and an
alternate form of the risk integral that does not require differentiating the hazard curve is
attractive. This alternate method was used by the USGS to create risk-targeted ground motion
maps (Luco 2006). The alternate form may be derived as follows. Given the risk integral:
+∞
𝑑𝜆𝑎
𝜆𝐹 = −� 𝑃(𝐹|𝑎) � � 𝑑𝑑
0 𝑑𝑑
Let
𝑢 = 𝑃(𝐹|𝑎)
𝑑𝑑 = 𝑑𝑑(𝐹|𝑎)
𝑑𝑑
where the latter is the same as
𝑑𝑑 = 𝑓(𝑎) 𝑑𝑑
and let
𝑑𝜆𝑎
𝑑𝑑 = � � 𝑑𝑑
𝑑𝑑
𝑣 = 𝜆𝑎
Invoking definite integration by parts:

+∞
𝜆𝐹 = −� 𝑢𝑢𝑢
0
+∞
= − �𝑢𝑢|+∞
0 − � 𝑣𝑣𝑣�
0
134
+∞
=
−[𝑃(𝐹|𝑎) 𝜆𝑎 ]+∞
0 + � 𝜆𝑎 𝑓(𝑎) 𝑑𝑑
0
+∞
=
−[(1)(0) − (0)(1)] + � 𝜆𝑎 𝑓(𝑎) 𝑑𝑑
0
+∞
= (4.7)
� 𝜆𝑎 𝑓(𝑎) 𝑑𝑑
0
Note that this form of the risk integral (Equation 4.7) requires the derivative of the
fragility curve—the CDF, which yields the probability density function (PDF). This was a more
stable approach than taking the derivative of the hazard curve. It is important to note that there is
not a closed form solution to the risk integral regardless of the method used, and in practice the
integral is performed numerically. The cumulative risk (𝑃𝐹 ) to seismic collapse during the
building lifetime (𝑡 in years) was calculated using Equation 4.8.
𝑃𝐹 = 1 − 𝑒 (−𝜆𝐹 𝑡) (4.8)
The seismic risk analysis procedures are illustrated in Figure 4.9 for two locations. The
first location is in Saint Louis, Missouri and the second location is in Charleston, South Carolina.
The hazard curves in the top plots correspond to the spectral acceleration for the building without
considering the gravity framing (black) and with the gravity framing (blue).
The hazard curve was based on the USGS 2008 United States National Seismic Hazard
Maps, adjusted for the maximum-direction spectrum of the FEMA P-695 Far-Field Set and
adjusted for soil amplification using the NGA correlation between shear wave velocity, 𝑉𝑠30 and
bedrock motion (Huang et al. 2010b), assuming soil site class D and 𝑉𝑠30 = 180 m/s.
135
-1 -1
10 10
Hazard Curves
Mean Annual Rate of Exceedance, λ (1/year)

Mean Annual Rate of Exceedance, λ (1/year)
-2 -2
10 10
-3 -3 MF+GF
10 10
MCE
-4 -4
10 10
MF
-5 -5
10 10
-6 -6
10 10
-3 0x 10-3 05 1 15 2
x 10
4 4
3.5
Risk Deaggregation 3.5
Collapse Rate, P(C|Sa)*|dλ/dSa| (1/g/year)

Collapse Rate, P(C|Sa)*|dλ/dSa| (1/g/year)
3 3
2.5 2.5
2 2
1.5 1.5
1 1
0.5 0.5
0 0
0.05 0.05 0 05 1 15 2
0.045 Collapse Risk 0.045
0.04 0.04
MF
Probability of Collapse, P
0.035
Probability of Collapse, P
0.035
0.03 0.03
0.025 0.025
0.02 0.02
0.015 MF+GF 0.015
0.01 0.01
With slack cables
0.005 0.005
0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Spectral Acceleration, Sa(T=1.7s), g Spectral Acceleration, Sa(T=1.7s), g
a) Saint Louis, Missouri b) Charleston, South Carolina
Figure 4.9 Seismic collapse risk analysis for Type I non-ductile moment frame 4-story building
136
4.3 Results
4.3.1 Type I Non-ductile and Ductile Moment Frame Buildings
The collapse assessment results are summarized in Table 4.4 for non-ductile and Table 4.5 for
ductile moment frames. Table 4.6 provides comparative results for ductile frames designed for
SDC D max . It is noted that the fundamental period values determined in the eigenvalue analysis,
𝑇1 are high compared to empirical estimates of actual buildings. Nevertheless, the periods are
similar to those reported in the ATC-76 report (NIST 2010a).
The static pushover results are described in terms of the seismic base shear coefficient 𝐶𝑠
and static “overstrength” Ω for SDC D max , and period-based ductility, 𝜇 𝑇 described in FEMA P-
695. The dynamic IDA results are shown relative to SDC D max and include the intensity
measure (the spectral acceleration corresponding to the MCE ground motion 𝑆𝑎𝑎𝑎𝑎 ), collapse
margin ratio (CMR), Spectral Shape Factor (SSF), adjusted CMR (ACMR), record-to-record
dispersion, 𝛽𝑅𝑅𝑅 total dispersion, 𝛽𝑇𝑇𝑇𝑇𝑇 and the probability of collapse conditioned on the MCE
level ground motion (𝑃𝑐 |𝑆𝑎 𝑀𝑀𝑀 ). Results relative to SDC D min are not shown.
Figure 4.10a shows the contribution of the moment frame (MF), gravity frame (GF), and
slack cable (SC) mechanism to the pushover response of the 4-story ductile-frame building. The
slack-cables engage at approximately 2% drift, and the cables fail at approximately 6% drift.
The pattern of collapse prevention component failure depends on the loading and archetype
building.
For example, the sequence of mechanism failures is described in Figure 4.10b for the
loose-linkage (LL) mechanism. At 4% drift, the initial linkage failure occurs in story 1 of the
gravity frame. At 6% drift, five additional linkage failures occur in both the moment and gravity
137
framing. Just prior to 7% drift, 14 linkages pairs have failed, and a building collapse mechanism
forms at story 2. The story-2 collapse mechanism was formed in this building model regardless
of the inclusion of gravity frame reserve lateral strength or collapse inhibiting mechanism
deployed.
Table 4.4 Seismic collapse assessment (for SDC D max ) for Type I non-ductile moment-frame
building (designed for wind, SDC B min )
Static Pushover Dynamic IDA

SaMCE
Archetype T1 (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal Pc | MCE
1-Story
MF 1.52 0.33 0.41 1.16 0.59 0.81 1.10 0.90 0.38 0.65 57%
MF+SST 1.14 0.33 0.66 2.69 0.79 1.11 1.25 1.39 0.38 0.65 31%
MF+GF 1.14 0.33 0.66 2.72 0.79 1.11 1.25 1.39 0.38 0.65 31%
+SC 1.13 0.33 0.75 3.13 0.80 1.30 1.28 1.66 0.37 0.65 22%
+LL 1.14 0.33 0.75 2.42 0.79 1.25 1.23 1.54 0.34 0.64 25%
2-Story
MF 1.87 0.33 0.28 1.89 0.48 0.59 1.22 0.72 0.38 0.66 69%
MF+SST 1.33 0.33 0.73 4.11 0.68 1.65 1.37 2.26 0.33 0.63 10%
MF+GF 1.58 0.33 0.39 1.45 0.57 0.95 1.16 1.10 0.36 0.64 44%
+SC 1.58 0.33 0.39 3.26 0.57 1.42 1.34 1.91 0.34 0.63 15%
+LL 1.58 0.33 0.44 3.30 0.57 1.24 1.35 1.67 0.33 0.63 21%
4-Story
MF 2.38 0.21 0.33 2.90 0.38 0.74 1.32 0.98 0.37 0.65 51%
MF+SST 1.67 0.21 0.60 5.26 0.54 1.22 1.47 1.80 0.32 0.62 17%
MF+GF 2.01 0.21 0.41 3.94 0.45 0.93 1.39 1.30 0.37 0.65 34%
+SC 2.01 0.21 0.42 6.00 0.45 1.28 1.51 1.93 0.35 0.64 15%
+LL 2.01 0.21 0.41 4.01 0.45 1.00 1.40 1.39 0.36 0.64 30%
8-Story
MF 3.16 0.12 0.43 3.26 0.28 0.65 1.34 0.87 0.44 0.69 58%
MF+SST 2.47 0.12 0.73 3.01 0.36 0.91 1.33 1.21 0.49 0.72 40%
MF+GF 2.85 0.12 0.55 2.35 0.32 0.87 1.27 1.10 0.34 0.63 44%
+SC 2.86 0.12 0.56 1.99 0.32 1.03 1.23 1.27 0.36 0.64 36%
+LL 2.85 0.12 0.55 3.10 0.32 0.78 1.33 1.04 0.33 0.63 48%
138
Table 4.5 Seismic collapse assessment (for SDC D max ) for Type I ductile moment-frame
building (designed for SDC D min )

SaMCE
1-Story
MF 1.46 0.13 1.38 2.97 0.62 1.53 1.32 2.01 0.44 0.53 9%
MF+SST 0.92 0.13 3.44 5.15 0.98 2.12 1.34 2.84 0.34 0.45 1%
MF+GF 1.11 0.13 2.16 3.43 0.81 1.64 1.29 2.12 0.43 0.52 7%
+SC 1.11 0.13 2.53 2.88 0.81 1.74 1.26 2.19 0.40 0.50 6%
+LL 1.11 0.13 2.16 3.43 0.81 1.71 1.29 2.21 0.42 0.51 7%
2-Story
MF 1.55 0.13 1.28 3.66 0.58 1.33 1.37 1.82 0.47 0.56 14%
MF+SST 1.20 0.13 2.29 4.16 0.75 1.99 1.35 2.68 0.39 0.49 2%
MF+GF 1.36 0.13 1.73 3.98 0.66 1.71 0.43 2.34 0.43 0.53 5%
+SC 1.36 0.13 1.83 4.85 0.66 1.85 1.42 2.63 0.37 0.48 2%
+LL 1.36 0.13 1.73 3.98 0.66 1.78 1.37 2.44 0.40 0.50 4%
4-Story
MF 1.75 0.08 1.48 5.06 0.51 1.17 1.46 1.71 0.34 0.46 12%
MF+SST 1.42 0.08 2.24 4.05 0.63 1.64 1.38 2.27 0.36 0.47 4%
MF+GF 1.60 0.08 1.80 4.92 0.56 1.45 1.45 2.11 0.32 0.44 5%
+SC 1.60 0.08 1.80 6.19 0.56 1.63 1.52 2.48 0.36 0.47 3%
+LL 1.60 0.08 1.79 5.19 0.56 1.48 1.47 2.17 0.34 0.45 4%
8-Story
MF 3.18 0.05 1.15 3.04 0.28 0.66 1.33 0.88 0.37 0.48 61%
MF+SST 2.50 0.05 1.76 3.49 0.36 0.95 1.36 1.29 0.40 0.50 30%
MF+GF 2.88 0.05 1.31 3.44 0.31 0.87 1.36 1.18 0.34 0.46 36%
+SC 2.88 0.05 1.34 3.99 0.31 1.03 1.39 1.43 0.34 0.46 22%
+LL 2.88 0.05 1.31 3.52 0.31 0.96 1.36 1.31 0.34 0.45 27%
Table 4.6 Seismic collapse assessment (for SDC D max ) for Type I ductile moment-frame
building (designed for SDC D ma x )

SaMCE
4-Story
MF+GF 1.36 0.08 2.26 5.63 0.66 1.93 1.46 2.82 0.35 0.46 1%
139
0.16 0.16
First link pair fails
0.14 0.14 (Frame C, story
1, Line 2)
0.12
MF+GF 0.12

0.1 0.1
MF
0.08 0.08
0.06 0.06
Six link pairs failed in stories

0.04 CP system only 0.04
1 and 2, Frame A and C
0.02 0.02 Story 2 collapse mechanism:
14 link pairs failed
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Roof Drift Ratio Roof Drift Ratio
a) Effect of GF and slack cables b) Effect of loose links
Figure 4.10 Effect of CP system on pushover response of ductile 4-story building
The basic process of assessing collapse is illustrated in Figure 4.11 through Figure 4.13
for the 4-story building with non-ductile moment frames. Figure 4.11a shows the scaled
response spectra for the moment-frame and gravity-frame (MF+GF) archetype model.
Figure 4.11b shows the interstory drift response at each story of the moment-frame (MF)
model at the collapse intensity for the 1994 Northridge earthquake Canyon Country Component
1 (LOS000) record.
Figure 4.11c compares the response history of the MF and MF+GF models and shows
that the reserve lateral strength in the shear-tab connections prevents collapse at 𝑆𝑎 = 0.36 g.
Figure 4.11d compares the MF+GF response to the same building model incorporating loose-
linkages (+LL). For this ground motion record, the collapse prevention system prevents collapse
at 𝑆𝑎 = 0.39 g. Figure 4.12 shows the response of the 4-story building with non-ductile moment
frames at 𝑆𝑎 = 0.36 g. Figure 4.12a compares the deformed (and-undeformed) configurations of
the MF, MF+GF, and +LL models. At this shaking intensity, the reserve strength in the shear tab
connections is sufficient to prevent collapse.
140
8 0.2
Story 1
7 Scaled FEMA P-695 Far- 0.15 Story 2
Field Ground Motion Set Story 3
6 0.1 Story 4
5 0.05
IDR
4 0
3 Median spectrum -0.05

2 -0.1
1 -0.15
0 -0.2
0 1 2 3 4 0 5 10 15 20
Period (seconds/cycle) Time (s)
a) Scaled response spectra b) Drift for LOS000, with 𝑆𝑎 = 0.36 g
0.04 0.04
MF MF+GF
0.02 MF+GF 0.02 +LL
0 0
-0.02 -0.02
IDR
IDR
-0.04 -0.04
-0.06 -0.06
-0.08 -0.08
-0.1 -0.1
-0.12 -0.12
0 5 10 15 20 0 5 10 15 20
Time (s) Time (s)
c) Story 2 drift for LOS000, 𝑆𝑎 = 0.36 g d) Story 2 drift for LOS000, 𝑆𝑎 = 0.39 g
Figure 4.11 Representative response of 4-story building with non-ductile moment frames
The addition of the back-up mechanism (loose-linkages) prevents failure of the non-
ductile beam-to-column connection (Figure 4.12b) in the first story. The behavior of a typical
shear tab connection (Figure 4.12c) and a typical column panel zone (Figure 4.12d) is shown for
the three models. The +LL model reduces building side-sway and utilizes less ductility in the
shear-tab connection, which leads to increased panel zone deformations.
141
MF
Deformed configuration
Beam: Frame 1 Story 1, Bay 3

5000
MF+GF 4000 Elastic

3000
response
for +LL
2000
Moment (k-in.)
1000
-1000
+LL -2000
-3000
-4000
-5000
-0.05 0 0.05
Rotation (rad)
a) Perimeter frame configuration b) Non-ductile connection
Beam: Frame 1 Story 1, Bay 5 Joint: Frame 1 Story 1, Line 4

3000 500
400
2000
300
200
1000
Moment (k-in.)
100
Shear (k)
0 0
-100
-1000
-200
-300
-2000
-400
-3000 -500
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1
Rotation (rad) Distortion (rad)
c) Shear-tab connection d) Column panel zone
Figure 4.12 Response of 4-story building with non-ductile moment frames for LOS000,
with 𝑆𝑎 = 0.36 g
142
Figure 4.13a shows individual incremental dynamic analysis (IDA) curves representing
the response of different building models to the same ground motion record. The spectral
acceleration (for the MF+GF building) corresponding to SDC D max and D min is shown for
reference. (Note that in an IDA plot, the spectral acceleration refers to the median of the ground
motion set, which generally is not the same as the spectral acceleration of each individual ground
motion.) In contrast, Figure 4.13b shows the IDA curves for the entire ground motion set for one
(MF+GF) building model. The median spectral acceleration at collapse (red line) is shown
relative to the SDC D max spectral acceleration (black horizontal line).
Figure 4.14a compares the collapse fragility curves for the MF, MF+GF, and the same
building model incorporating slack-cables (+SC). The median collapse spectral acceleration was
adjusted (increased) to account for spectral shape, estimated using period-based ductility, 𝜇 𝑇 and
the total dispersion, 𝛽𝑇𝑇𝑇𝑇𝑇 in collapse capacity was calculated as previously described. The
adjusted seismic collapse fragility curves are shown in Figure 4.14b.
0.5 1
MCE SDC Dmax
Spectral Acceleration Sa(T=2), g
0.4 0.8
Sa[T=2] (g)
0.3 0.6
MCE SDC Dmax

0.2 0.4
MCE SDC Dmin MF Median
MF+GF collapse
0.1 0.2
+LL
+SC
0 0
0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1
Maximum IDR Maximum Interstory Drift Ratio
a) LOS000 IDA curves b) IDA curves for MF+GF archetype
Figure 4.13 Representative response of 4-story building with non-ductile moment frames
143
1 1
MF+GF MCE (MF)
MCE (Other)
0.8 0.8 MF
MF
P(Fail|x=Sa[T=2])
P(Fail|x=Sa[T=2])
0.6 0.6 MF+GF
+SC
+SC
0.4 0.4
Measured
0.2 0.2
Lognormal distribution
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Sa[T=2] (g) Sa[T=2] (g)
a) Collapse fragility curves b) Collapse fragility curves with 𝛽𝑇𝑇𝑇𝑇𝑇
Figure 4.14 Seismic collapse results for 4-story building with non-ductile moment frames
The reserve lateral strength in the shear-tab connections reduced the collapse probability
considerably compared to moment frames alone. Employing collapse prevention mechanisms
improved the collapse safety, but the amount of improvement depended on the number of stories
and the collapse inhibiting mechanism. Collapse prevention systems with a non-ductile moment-
frame passed the FEMA P-695 acceptance criteria for SDC D min . For collapse prevention
systems with ductile moment-frames, the short-period (1-story, 2-story) performance group and
the 4-story buildings passed the acceptance criteria for SDC D max .
A risk analysis was used to illustrate areas where collapse prevention systems are
applicable for the Type I archetype building. Collapse risk was calculated by integrating
collapse fragility (from Table 4.4 and Table 4.5) and seismic hazard—based on 2008 USGS data,
and adjusted for site amplification based on a correlation between shear wave velocity, 𝑉𝑠30 and
bedrock motion using Next Generation Attenuation (NGA) relationships (Huang et al. 2010b).
This risk analysis was repeated for every 0.5-degree latitude and longitude to generate a map of
risk values in the conterminous United States. Soil site class D (𝑉𝑠30 = 180 m/s) is assumed.
144
Figure 4.15 shows regions (shaded contours) where the seismic collapse risk exceeds 1%
in 50 years for the non-ductile moment frame building. Blue and red shaded areas in the central
and eastern United States indicate (for this particular building archetype) where the collapse
prevention system is needed, compared to the moment frame alone. Yellow shaded areas
indicate where the collapse prevention system using slack cables is not sufficient. Major
metropolitan areas (dots) are shown based on 2011 population estimate using 2010 census data.
The maps show that the slack cable collapse prevention system with non-ductile moment
frames is adequate for many regions in the central and eastern United States. Although buildings
with non-ductile frames were not suitable for the maximum intensity possible in SDC D, the
collapse prevention systems were viable for the major portion of the SDC D regions.
MF
MF+GF
+SC
a) 2-story b) 8-story
Figure 4.15 Regions where seismic collapse risk exceeds 1% in 50 years: Type I non-ductile
145
For example, consider the non-ductile moment frame 4-story building. Figure 4.16
shows contour lines where the probability of collapse given the MCE exceeds 10% (gray
contours correspond to SDC boundaries). Memphis, Tennessee and Charleston, South Carolina
are the only major cities in the central and eastern United States not reached by the slack cable
collapse prevention system (orange contour lines).
Figure 4.17 to Figure 4.20 show the applicability of using enhanced shear tab connections
(SST) as a collapse prevention system in non-ductile moment frame buildings. (Blue shaded
areas indicate where the collapse prevention system is needed; red shaded areas indicate where
the enhanced shear tab connection collapse prevention system is not sufficient.)
SDC A
SDC B
SDC C
SDC D
CP system GF contribution
Figure 4.16 Regions where the probability of seismic collapse (given the MCE) exceeds 10%:
Type I non-ductile moment frame 4-story building with slack cable collapse prevention system
146
MF
MF+SST
Figure 4.17 Regions where seismic collapse risk exceeds 1% in 50 years: non-ductile 1-story
MF
MF+SST
147
MF
MF+SST
MF
MF+SST
148
The maps show that collapse prevention systems are adequate for many regions in the
central and eastern United States, but the applicability depends on both the ductility of the
primary moment frame, the building height (building stories) and the type of collapse prevention
mechanism employed. The collapse prevention system concept was predicted to be viable for a
major portion of the SDC D regions.
149
4.3.2 Type II Non-ductile Moment Frame Buildings
The Type II non-ductile moment frame buildings with and without considering the lateral
strength in the gravity framing were subjected to the FEMA P-695 “Far-Field” ground motion set
(Figure 4.21a), and the set was incrementally scaled (relative to the median response spectrum
and target spectrum SDC D max ) until collapse (Figure 4.21b). The collapse points (spectral
acceleration at the reference period and corresponding probability of collapse) were fit with a
curve assuming a lognormal cumulative distribution function (Figure 4.22a), and the median
collapse spectral acceleration is adjusted to account for spectral shape. Spectral shape effects are
estimated using period-based ductility (𝜇 𝑇 ). The total uncertainty (𝛽𝑇𝑇𝑇𝑇𝑇 ) in collapse capacity
(Figure 4.22b) was calculated by dispersion in the response history analysis (record-to-record
dispersion 𝛽𝑅𝑅𝑅 ) together with a “rated” dispersion due to design, test data, and modeling
uncertainty. Design requirements were rated ‘(B)’; test data and model quality were each rated
‘(C)’.
7 2
Scaled FEMA P-695 Far-
Spectral Acceleration Sa(T=1.6), g
6 Field Ground Motion Set

1.5
5
4 Median collapse
1
3 Median spectrum
2
0.5
1 MCE
0 0
0 1 2 3 4 0 0.05 0.1 0.15 0.2
Period (s) Maximum Interstory Drift Ratio
a) Scaled response spectrum b) Incremental dynamic analyses
Figure 4.21 Nonlinear dynamic analyses for the Type II non-ductile moment frame buildings
150
Conditional Probability of Collapse 1 1
Conditional Probability of Collapse

CDF curve including
0.8 0.8 spectral shape effect and
total uncertainty, βTotal
0.6 0.6
Cumulative distribution
function (CDF) curve for
0.4 0.4
lognormal distribution
MCE
0.2 0.2
0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Spectral Acceleration Sa(T=1.6), g Spectral Acceleration Sa(T=1.6), g
a) Measured / fitted collapse fragility b) Total fitted collapse fragility
Figure 4.22 Seismic collapse analyses for the Type II non-ductile moment frame buildings
The collapse assessment results for the east-west direction (moment frames) are
summarized in Table 4.7. The computed fundamental period of the analytical model, 𝑇1 is 1.64
seconds. This is reasonable, but larger than both the empirically determined period for wind
analysis (𝑇𝑤 = 1.11 seconds) and the empirically determined period for seismic analysis (𝐶𝑢 𝑇𝑎 ),
which ranges from 0.97 seconds (SDC D max ) to 1.18 seconds (SDC B min ). The values of Ω
shown are relative to 𝐶𝑠 for SDC D max . Relative to 𝐶𝑠 equal to 0.043 used to design the building
(see Design Examples, page III-51) the overstrength, Ω is equal to 2.64. Seismic pushover
analysis showed that the period-based ductility, 𝜇 𝑇 values are dominated by the panel zones.
Reserve strength in the gravity framing increased overstrength and reduced the conditional
probability of collapse by 3%, which was enough to “pass” the 10% conditional collapse
criterion set by FEMA P-695.
151
Table 4.7 Seismic collapse assessment (for SDC D max ) for Type II non-ductile moment-frame
building (designed for SDC B, design controlled by wind)
Dynamic IDA
Static Pushover Sa[T 1 ] (g)
Model T 1 (s) Cs Ω µT MCE Collapse SSF ACMR β Total P c |MCE
MF 1.77 0.21 0.46 8.71 0.51 0.65 1.61 2.05 0.61 12%
MF+GF 1.64 0.21 0.54 8.26 0.55 0.80 1.61 2.33 0.61 8%
A risk analysis is used to display areas where the Type II non-ductile moment frame 4-
story building would provide a 1% or less risk of seismic collapse in 50 years. The probability
of collapse, 𝑃𝑐 was computed in both directions and the total probability (risk of collapse) was
computed using Equation 4.9.
𝑃𝑐−𝑇𝑇𝑇𝑇𝑇 = 𝑃𝑐−𝐸𝐸 + 𝑃𝑐−𝑁𝑁 – (𝑃𝑐−𝐸𝐸 )( 𝑃𝑐−𝑁𝑁 )

R (4.9)
This is repeated for every 0.5-degree latitude and longitude to generate the map shown in
Figure 4.23. The shaded areas in the figure show regions where seismic collapse risk exceeds
1% in 50 years.
The prototype building provides adequate seismic life-safety for many regions in the
central and eastern United States, except the Mid-America and Charleston high-seismic areas.
Note that the Type II non-ductile moment frame 4-story building was designed for moderate
wind, and buildings designed for higher wind pressures along the hurricane-prone gulf and
eastern coasts have an even lower risk of seismic collapse.
152
Seattle 15%
Boston 0.3%
Salt Lake City 8.4% Chicago 0.2%
San Francisco 19%

Saint Louis 1.5%
New York 0.4%
Nashville 1.1%
Las Vegas 1.7%
Memphis 4.0%
Charleston 4.1%
Los Angeles 29%
Probability of seismic collapse

exceeds 1% in 50 years
Figure 4.23 Regions where seismic collapse risk exceeds 1% in 50 years: Type II non-ductile
moment frame 4-story building
153
4.3.3 Type III Non-ductile Moment Frame 10-story Building
The Type III non-ductile moment frame 10-story building was subjected to the FEMA P-695
“Far-Field” ground motion set (Figure 4.24a). The median spectrum of the ground motion set
was incrementally scaled relative to four target spectrums, SDC B min , SDC C min , SDC D min , and,
as in previous analyses, SDC D max , until collapse (Figure 4.24).
1 3
0.9
Scaled FEMA P-695 Far-
2.5
0.8 Field Ground Motion Set
0.7
2
0.6
0.5 1.5
Median spectrum
0.4
1
0.3 Target spectrum (SDC Cmin)
Target spectrum (SDC Bmin)
0.2
0.5
0.1
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds/cycle) Period (seconds/cycle)
a) Target spectrum: SDC B min b) Target spectrum: SDC C min
3 10
9
2.5
8
7
2
6
1.5 5
4
1
Target spectrum (SDC Dmin) 3
2
0.5
1
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds/cycle) Period (seconds/cycle)
c) Target spectrum: SDC D min d) Target spectrum: SDC D max
Figure 4.24 Scaled response spectra: Type III non-ductile moment frame 10-story building
154
The collapse points were fit with a curve assuming a lognormal cumulative distribution
function (Figure 4.25a) and adjusted to account for spectral shape and total uncertainty 𝛽𝑇𝑇𝑇𝑇𝑇 in
collapse capacity (Figure 4.25b). The collapse assessment results are summarized in Table 4.8
relative to the four target applications (SDC B min , SDC C min , SDC D min , and SDC D max ). The
building was viable for SDC B and most of SDC C, but was inadequate (as would be expected)
for higher seismic regions.
1 1
0.9 0.9
CDF curve including
0.8 0.8 spectral shape effect and

0.7 0.7
total uncertainty, βTotal
Cumulative distribution
0.6 function (CDF) curve for 0.6
0.5
lognormal distribution 0.5
0.4 0.4
0.3 0.3 MCE

SDC Dmax
0.2 0.2
0.1 0.1
0 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
a) Measured / fitted collapse fragility b) Total fitted collapse fragility
Figure 4.25 Seismic collapse analyses for the Type III non-ductile 10-story building
Table 4.8 Seismic collapse assessment for Type III non-ductile 10-story building
(designed for wind and evaluated at SDC B mi n , C mi n , D mi n , and D max )
Dynamic IDA
Static Pushover Sa[T 1 ] (g)
T1
SDC (s) T w (s) T e (s) Cs Ω µT MCE Collapse SSF ACMR β Total P c |MCE
B min 2.41 0.01 7.45 0.03 0.2%
C min 2.32 0.02 3.63 0.06 3%
3.34 2.28 4.12 0.52 1.40 0.73 0.64
D min 2.13 0.03 2.21 0.09 11%
D max 1.98 0.10 0.69 0.27 69%
155
4.4 Comparison with Traditional Structural Systems
The collapse assessment for seismic hazards of traditional lateral-force resisting structural
systems for new buildings in the United States is examined in the context of comparing FEMA
P-695 evaluations reported to-date in the literature. Although the focus of this research is steel
moment-frame structures, also included in the comparison are steel moment frame and braced-
frame, reinforced concrete moment-frame and shear wall, reinforced masonry shear wall, and
light-frame wood shear wall structures.
In a FEMA P-695 evaluation, a structure is deemed to “pass” if (1) the average
conditional collapse probability for a group of similar archetypical structures does not exceed
10%, and if (2) the conditional collapse probability for any individual structure does not exceed
20%. As discussed previously, FEMA P-695 includes the effect of modeling and design
uncertainties in the evaluation, and it incorporates an estimate of the effect of spectral shape on
collapse capacity. In the tables shown, for each Performance Group (PG) the dispersion,
overstrength, Ω, Adjusted Collapse Margin Ratio (ACMR) accounting for the effect of spectral
shape, and the acceptable ACMR corresponding to 10% probability of collapse are given.
4.4.1 Steel Moment Frame
The vulnerability of steel moment frame structures is summarized in Table 4.9. Three types of
steel moment structures are examined: special steel moment frames (SMF) (NIST 2010a),
partially-restrained composite connection (PR-CC) steel moment frames (Bozorgmehr 2012;
Bozorgmehr and Leon 2012), and cold-formed steel bolted moment frames (Sato and Uang
2013). All steel SMF systems are adequate except one performance group: the steel SMF long-
period SDC D max performance group does not pass (but is not far off from passing the criteria).
156
Table 4.9 Steel moment-frame seismic collapse assessment results
PG Accept.
Lateral Force Resisting System (LFRS) β Ω ACMR
No. 10%
0.5 1 4.16 2.97 1.9
0.45 2 3.67 1.94 1.75
0.475 3 2.55 2.53 1.81
0.45 4 4.27 3.13 1.77
Ave 4.27 2.64
Steel special moment frame (R=8, Ω=3)
0.5 1 4.7 2.91 1.9
0.475 2 2.61 1.76 1.81
0.45 3 2.84 2.72 1.78
0.475 4 2.93 3.28 1.84
Ave 4.7 2.67
1 1.39 2.19
2 1.57 2.89
3 1.58 3.99
2.16
Steel PR-CC frame (R=6, Ω=3) 0.6 4 1.59 3.96
5 1.78 4.74
6 1.63 4.25
Ave 1.78 3.67
1 1.9 2.2
2 2.09 2.16
Cold-form steel Special bolted MF (R=3.5, Ω=3) 0.5 3 3.14 3.66 1.9
4 5.59 4.98
Ave 5.59 3.25
4.4.2 Steel Braced Frames
The vulnerability of steel braced-frame structures is summarized in Table 4.10. Two types of
steel braced-frames are considered (NIST 2010a): steel special concentrically braced frames
(CBF), and buckling restrained braced (BRB) frames. For further consideration of BRB frames,
see also Ariyaratana and Fahnestock (2011).
All steel braced-frame structures satisfy the FEMA P-695 requirements, except one
performance group: the CBF short-period SDC D max performance group did not pass. However,
a recent study of special CBF buildings (Hsiao et al. 2013) indicates that 3-story and 20-story
buildings also do not pass. In fact, short-period systems often do not pass the FEMA P-695
criterion, regardless of the type of structure (Charney et al. 2012; NIST 2012b).
157
Table 4.10 Steel braced-frame seismic collapse assessment results
PG Accept.
No. 10%
1 1.42 1.63
2 1.67 3.37
Steel Special CBF (R=6, Ω=2) 0.525 3 1.9 2.93 1.96
4 1.87 4.73
Ave 1.9 3.17
1 1.4 3.13
2 1.21 4.12
Steel BRB (R=8, Ω=2.5) 0.525 3 1.77 2.86 1.96
4 1.29 4.19
Ave 1.77 3.58
4.4.3 Reinforced Concrete Moment Frames
The vulnerability of reinforced concrete moment frame structures is summarized in Table 4.11.
Two types of moment-frames are included: special (SMF) and ordinary (OMF) based on the
FEMA P-695 supporting study (FEMA 2009a).
Most concrete frame structures pass FEMA P-695 requirements. However, SMF frames
taller than 4 stories (the long-period perimeter frame performance groups) do not. The long-
period performance group for OMF frames also fails to pass. Accordingly, the study suggested
that a height limit is needed for SMF frames and that OMF frames should not be allowed.
The reinforced concrete moment frame results and recommendations underscore a
weakness of the assumption for the current uniform risk-targeted maps: structures designed using
ASCE 7-10 do not necessarily have less than a 10% probability of collapse given the MCE.
158
Table 4.11 Reinforced concrete moment-frame seismic collapse assessment results
PG Accept.
No. 10%
1 1.7 1.9
2 1.9 1.84
Reinforced concrete SMF (R=8, Ω=3) 0.5 3 3.5 2.66 1.9
4 2.8 2.36
Ave 3.5 2.19
1 2.2 3.86
2 6 4.58
3 1.6 2.2
4 3.2 2.44
Ave 6 3.27
Reinforced concrete OMF (R=3, Ω=3) 0.575 2.09
1 1.6 2.2
2 3.2 2.44
3 1.5 1.48
4 2.4 2.12
Ave 3.2 2.06
4.4.4 Reinforced Concrete Shear Walls
The vulnerability of reinforced concrete shear wall structures is summarized in Table 4.12. Two
types of shear walls are considered: special and ordinary (NIST 2010a). The results indicate that
long-period performance groups pass, but short-period performance groups do not. One and two
story structures collapsed due to shear failures at low drift levels (about 1.5%). The study notes
that in past earthquakes, collapse of low-rise concrete shear wall buildings has only been
observed in precast parking type structures where the diaphragm failed, yet “insufficient
information exists to establish more liberal failure criteria.”
159
Table 4.12 Reinforced concrete shear-wall seismic collapse assessment results
PG Accept.
No. 10%
1 1.98 1.5
2 1.54 3.18
3 2.41 1.5
4 3.88 5.71
1.96
Reinforced concrete Special SW (R=5, Ω=2.5) 0.525 5 2.08 1.75
6 1.7 3.2
7 2.41 1.5
8 3.52 4.65
Ave 3.88 3.05
1 2.85 1.77
2 3.43 5.8
3 3.25 2.28
4 5.2 8.23
1.96
Reinforced concrete Ordinary SW (R=4, Ω=2.5) 0.525 5 2.85 1.77
6 2.37 6.42
7 3.25 2.28
8 3.37 9.38
Ave 5.2 5.06
4.4.5 Reinforced Masonry Shear Walls
The vulnerability of reinforced masonry shear wall structures is summarized in Table 4.13.
Again, two types of shear walls are considered: special and ordinary (NIST 2010a). The results
indicate that many reinforced masonry structures do not pass the FEMA P-695 criteria. 1-story,
2-story, and 4-story OMF shear wall buildings with low gravity loads pass, but high gravity
loads do not. Part of the poor performance is attributed to the low ductility capacity of short
shear walls. Regardless of the reason for performance, the results again demonstrate that
structures designed using ASCE 7-10 do not necessarily meet the 10% probability of collapse
assumption.
160
Table 4.13 Reinforced masonry shear-wall seismic collapse assessment results
PG Accept.
No. 10%
1 2 1.41
2 1.75 2.3
3 2.12 1.69
4 1.75 2.25
1.96
Reinforced masonry Special SW (R=5, Ω=2.5) 0.525 5 1.8 1.71
6 1.53 2.33
7 1.71 1.95
8 1.5 2.28
Ave 2.12 1.99
1 1.89 1.51 2.23
2 2.08 1.54 2.38
3 1.41 1.46 2.16
4 1.99 1.96 2.38
Reinforced masonry Ordinary SW (R=2, Ω=2.5) 0.525 5 1.91 1.98 2.23
6 1.67 2.69 2.38
7 1.37 1.94 2.16
8 1.64 3.19 2.38
Ave 1.99 2.20
4.4.6 Wood (Light-Framed) Shear Walls
The vulnerability of light-frame wood shear wall structures (i.e. residential and small commercial
buildings) is summarized in Table 4.14. The table is based on the results from the P-695
supporting study (FEMA 2009a). All performance groups pass, except the short-period low-
aspect-ratio performance group. However, a recent study shows that the collapse margins of
wood buildings in the western United States are significantly lower than those in the central and
eastern United States due to regional construction practices (Li et al. 2010). In this manner, it is
possible that wood structures may not necessarily have the performance implied by conformance
with ASCE 7-10.
161
Table 4.14 Wood (light-framed) shear-wall seismic collapse assessment results
PG Accept.
No. 10%
0.5 1 2.2 1.89 1.9
0.675 2 3.4 2.48 2.38
Wood light-frame wood panels (R=2, Ω=2.5) 0.675 3 4.1 2.91 2.38
0.675 4 3.6 3.18 2.38
Ave 4.1 2.62
162
4.5 Discussion
The seismic collapse safety was assessed for archetypical buildings with and without collapse
prevention systems. The results indicated that collapse prevention systems could (1) effectively
reduce the probability of collapse during MCE-level ground motion, and (2) lower the seismic
collapse risk of a building with moment frames not specifically detailed for seismic resistance.
Reserve lateral strength in the gravity framing, specifically in the shear tab connections,
was a significant factor in the success of the collapse prevention system. In most buildings,
simply utilizing the reserve strength in the shear tab connections significantly reduced the
probability of collapse. The pattern of collapse prevention component failure depended on the
loading and archetype building. Generally speaking, the collapse prevention devices did not
change the story failure mechanism, compared to the moment frame alone, but the opposite was
observed for the shear tab connections. Reserve lateral strength in the gravity framing or
enhanced shear tab connections sometimes changed the story failure mechanism for the building.
Collapse prevention systems using non-ductile moment frames were adequate for many
regions in the central and eastern United States, but a conventional lateral resisting system, or a
collapse prevention system with a ductile moment frame designed for moderate seismic
demands, was required for several regions of higher seismicity (namely, New Madrid and
Charleston areas). The region of the United States where the results suggest that collapse
prevention systems are applicable was wide, and covers up to a quarter of the United States
population for some building archetypes.
Seismic collapse assessments reported in the literature, according to the available P-695
evaluations, indicate that on average, the assumed ASCE 7-10 fragility curve was conservative in
terms of the variability in structural vulnerability (seismic collapse fragility), at least for
163
structures that have been detailed for seismic resistance. Nevertheless, in some cases the
conditional probability of collapse during MCE-level ground motion may exceed 10%, even for
structures detailed for seismic resistance using ASCE 7-10. It is important to note that the
seismic collapse assessments surveyed did not calculate collapse risk.
164
Chapter 5
WIND COLLAPSE ASSESSMENT
This chapter assesses the wind collapse safety of the archetype structural systems with and
without collapse prevention systems. The wind collapse vulnerability (collapse fragility) was
determined using a sequence of gravity, frequency, and nonlinear static “pushover” analyses,
followed by nonlinear dynamic response history analyses incrementally scaled, with respect to a
reference wind speed, until side-sway collapse.
5.1 Wind Collapse Vulnerability Procedures
The probability of wind collapse was determined using an approach (Judd and Charney 2015a)
similar to the prevailing method utilized for seismic loads (FEMA P-695) adapted in Chapter 4.
A gravity load analysis was first conducted. Equivalent single-degree-of-freedom models were
used to represent the hysteretic behavior, including in-cycle degradation, of typical main wind-
force resisting systems (MWFRS). Single-degree-of-freedom modeling has been used by a
several researchers in wind engineering (e.g. Tsujita et al. 1997; Chen and Davenport 2000;
Hong 2004; Gani and Légeron 2011). Multiple-degree-of-freedom modeling in the literature is
more limited (Muthukumar et al. 2012). The single-degree-of-freedom models reflected the
overall response characteristics of structural subassemblies expected to be present in
165
corresponding real buildings, although these simplified and idealized models obviously are not a
detailed representation of the structure. Notwithstanding these limitations, similar simplified
equivalent single-degree-of-freedom models have been shown to demonstrate salient features of
dynamic behavior for earthquake ground motion (FEMA 2009b).
Figure 5.1 shows the monotonic envelope and fully-reversed cyclic behavior assumed for
the characteristic main wind-force resisting systems and gravity framing system (shear tab
connections). Force-deformation behavior parameters used in this study, including in-cycle
degradation, matched those used in FEMA P-440A (FEMA 2009b).
1 Monotonic 1
Non-ductile MF Ductile MF
(MWFRS) envelope (MWFRS)
0.5 0.5
Moment (k-in.)
Moment (k-in.)
0 0
Fully-reversed
-0.5 -0.5
cyclic response
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1

Rotation (rad) Rotation (rad)
1 Ductile GF
0.5
Moment (k-in.)
-0.5
-1
-0.1 -0.05 0 0.05 0.1

Rotation (rad)
Figure 5.1 Equivalent single-degree-of-system force-deformation models
166
An eigenvalue analysis was used to determine the fundamental period of vibration
associated with the equivalent single-degree-of-freedom model. Nonlinear static wind
“pushover” analysis was used to determine the strength of the equivalent single-degree-of-
freedom model.
Nonlinear dynamic response history analysis of the equivalent single-degree-of-freedom
model was completed using an ensemble of wind load records from boundary-layer wind tunnel
tests applied to capture both along-wind and cross-wind effects on buildings. Wind loads were
then scaled (intensified corresponding to increasing hazard levels) using an incremental dynamic
analysis (IDA) approach until lateral instability and collapse occurs. The risk of collapse was
quantified by incorporating epistemic uncertainty and integrating collapse fragility with ASCE 7-
10 (ASCE 2010) wind speed data. Appendix C contains excerpts of the OpenSees (PEER 2012)
scripts for a Type I non-ductile moment frame 4-story building.
5.1.1 Gravity Loading
Vertical gravity roof and floor dead (𝐷) and floor live (𝐿) loads were calculated using the same
load combination used in seismic collapse assessment (Equation 4.1). The load combination was
intended to represent the expected gravity loads present in the building during a wind event.
Second-order effects were included in the gravity load analysis.
5.1.2 Frequency (Period) Determination
After the gravity pre-load analysis, an eigenvalue frequency analysis was used to determine the
periods of vibration of the building and associated mode shapes. This was the same procedure
used for seismic collapse assessment.
167
For example, Figure 5.2 shows the fundamental period and mode of vibration as
determined by computer analysis for the Type III non-ductile moment frame 10-story building.
As expected, the fundamental period estimated using ASCE 7-10 (ASCE 2010) Equation 26.9-2,
is shorter (2.28 seconds). Note that, in contrast to seismic analysis, however, the longer period
from the computer analysis is the more conservative value for wind analysis.
Figure 5.2 First mode (𝑇1 = 3.34 s) of Type III non-ductile moment frame 10-story building
5.1.3 Nonlinear Static Wind (“Pushover”) Analysis
In the nonlinear static wind “pushover” response analysis, the building model was subjected to a
static lateral force at each story. The distribution of lateral forces was proportioned to match the
wind-exposure C atmospheric boundary layer wind (synoptic wind) profile, based on the ASCE
7-10 directional procedure. This method for wind pushover analysis differed from the
distribution used in seismic pushover analysis, which was proportioned to match the first mode
shape of the building. The lateral forces were applied using a displacement-control solution
strategy until the roof displacement of the building exceeded at least the displacement
corresponding to a 20% loss in lateral strength of the building.
168
The wind pushover analysis was used to determine the wind static overstrength. The
static overstrength was calculated as the ratio of the maximum base shear resistance to the design
base shear force (Equation 5.1).
𝑉𝑚𝑚𝑚
Ω𝑊𝑊𝑊𝑊 = (5.1)
𝑉𝑑𝑑𝑑𝑑𝑑𝑑
For example, Figure 5.3 shows the pushover response of the Type III non-ductile moment
frame 10-story building. Figure 5.3b shows the deformed “pushover” shape of the building
frame. The frame yielding was distributed over several stories. The loss in strength was due to a
combination of beam, column, and panel zone yielding. The maximum wind pushover capacity
normalized by the building weight, (𝑉𝑚𝑚𝑚 /𝑊) equal to 0.10. Based on the wind base shear
coefficient, the static wind overstrength, Ω𝑊𝑊𝑊𝑊 is equal to 2.22.
Un-deformed
shape (gray) Gravity frame (blue)
Moment frame (black)
0.1
0.09
0.08
ΩWind = 2.22
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0 0.005 0.01 0.015 0.02 0.025 0.03
Roof Drift Ratio
(a) Wind pushover curve (b) Wind pushover deformation
Figure 5.3 Wind pushover response of Type III non-ductile moment frame 10-story building
169
5.1.4 Wind Load Ensemble for Nonlinear Response History Analysis
An ensemble of wind loads was created using records generated from boundary-layer wind
tunnel testing of small-scale building models. A representative wind tunnel building model is
shown in Figure 5.4. This study used a database of wind tunnel data from Tokyo Polytechnic
University (http://www.wind.arch.t-kougei.ac.jp). The database has previously been used to
study wind effects of buildings (e.g. Tamura et al. 1999; Huang and Chen 2007). The database
contains time series data of point wind pressure coefficients on the surface of small-scale
aeroelastic (nominally rigid) building models. Force (base) balance building models were not
used.
Figure 5.4 Wind tunnel test of a small-scale model of a 46-story building
(Photograph provided by RWDI Inc., Guelph, Ontario.)
170
For the Type I and Type II moment frame buildings, the data corresponded to the “low-
rise” model database. The low-rise model contained 144 to 288 wind pressure taps (depending
on the model size) uniformly distributed over the surfaces of the models. Each wall had 2 to 8
layers of pressure taps (depending on the model size), with 5 pressure taps per layer.
For example, Figure 5.5 shows the location of pressure taps for the Type I archetype
building wind tunnel model. The simulated terrain corresponded to ASCE 7-10 terrain category
B and C (terrain exponent, 𝛼 = 1/4), and the wind tunnel length scale was 1/400. In order to
capture along-wind and cross-wind effects, the wind direction for each test ranged from 0°
(cross-wind) to 90° (along-wind) in 15° increments. Wind pressures were sampled every 0.0667
seconds for a total of 9,000 data points (10 minutes).
Figure 5.5 Location of pressure taps for Type I archetype building wind tunnel model
(Figure from http://www.wind.arch.t-kougei.ac.jp)
171
For the Type II moment frame building, the data corresponded to the “high-rise” model
database. The high-rise model contained 240 wind pressure taps uniformly distributed over the
vertical surfaces of the models. Each wall had 8 layers of pressure taps, with 10 pressure taps
per layer. The simulated terrain corresponded to ASCE 7-10 terrain category B and C (terrain
exponent, 𝛼 = 1/4), and the wind tunnel length scale was 1/400. The wind direction for each test
ranged from 0° (cross-wind) to 90° (along-wind) in 5° increments. Wind pressures were sampled
every 0.00128 seconds for a total of 32,768 data points (about 42 minutes).
The wind pressure data depends primarily on the shape and aspect ratios of the building.
This has been observed to be the case for actual buildings, where for a given synoptic or non-
synoptic wind event actual wind loads are essentially independent of the spatial location of the
building (with the exception that real-world locations have predominate wind directions). Such
location independence is a contrast to ensembles of seismic loads that are used for nonlinear
analysis, such as the FEMA P-695 Far-Field ground motion set (FEMA 2009a), that depend on
the spatial location (intra-plate versus plate boundary, for example) but do not depend on the
shape or aspect ratio of the building.
5.1.5 Intensity Measure for Wind Hazard
In this study, the basic wind speed in miles per hour (V𝑚𝑚ℎ ) was selected as the wind hazard
intensity measure. Although this study is the first of its kind (i.e. a wind IDA), and there is no
precedent for the wind intensity measure, the basic wind speed has been commonly used in other
studies as an intensity measure (e.g. ASCE 2010; Yeo et al. 2014).
172
5.1.6 Nonlinear Dynamic Response History Analysis
The wind pressure exerted on the surface of the building was calculated using Bernoulli’s
equation, 𝑝 = 0.5𝜌𝑉𝑚𝑚ℎ 2 for the density of the air, 𝜌 at standard temperature (59° F), and
barometric pressure (29.92 in. Hg). The wind load history was then calculated using the wind-
tunnel test pressure coefficient history data, scaled from the model to the building size and
hazard intensity of interest. As a result, the wind speed record is not the same for different
hazard levels. For example, if the wind speed is doubled, the equivalent data sample rate is also
doubled, and the record length is only half as long.
In order to maintain the same duration of loading during an incremental dynamic
analysis, the wind load record was replayed. For the response history analysis, the wind load was
linearly ramped for the initial record segment of the loading. Finally, for the purposes of the
single-degree-of-freedom model, windward and leeward forces at each story in the building were
aggregated into a single equivalent (generalized) lateral load.
Structural analysis of the equivalent single-degree-of-freedom model was performed
using OpenSees finite element software (PEER 2012). As previously discussed, the single-
degree-of-freedom model was subjected to full-scale wind load records that were scaled
(intensified) corresponding to increasing hazard levels (higher wind speeds), and the wind speed
was used as the intensity measure. For example, Figure 5.6 shows the response just prior to
collapse and at collapse for the Type I ductile moment frame 8-story building with the enhanced
shear tab connection collapse prevention system with a reference wind speed of 20 mph. A
single IDA curve (wind speed versus drift for one wind record) is also shown for 0° (cross-
wind).
173
1 Maximum strength-
0.05
0.04 0.8 level demand
0.03 0.6
Normalized base shear (F/Fy)

Normalized base shear (F/W)
0.02 0.4
0.01 0.2
0 0
-0.01 Reference -0.2
-0.02 Strength-Level (115 mph) -0.4
-0.03 Prior to Collapse -0.6

-0.04 Collapse -0.8
-0.05
-1
0 2 4 6 8 10 12 14 16 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
Time (min) Roof drift ratio
a) Wind load history b) SDOF force-deformation
0.1 250
0.08 Collapse
(194 mph) 200
0.06
Wind speed, V (mph)
Roof drift ratio
150
0.04
100
0.02
50
0
-0.02 0
0 2 4 6 8 10 12 14 16 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (min) Roof drift ratio
c) Roof drift ratio d) Single IDA
Figure 5.6 Response of Type I ductile moment frame 8-story building with enhanced shear tab
collapse prevention system for 0° (cross-wind) (reference wind speed 20 mph)
The incremental dynamic analyses were continued until lateral instability and presumed
collapse, when the drift ratio exceeds 0.2. The equivalent single-degree-of-freedom drift was
converted to a multi-degree-of-freedom roof drift using Equation 5.2 based on ASCE 41-13
(ASCE 2014). See also FEMA P-695 Equation 6-8 and Appendix B (2009a), where 𝑚 is the
mass, and 𝜑 is the mode shape of the building (an array the size of the number of stories).
174
∆𝑅𝑅𝑅𝑅 = 𝐶0 ∆𝑅𝑅𝑅𝑅
= ∑𝑁=𝑛𝑛𝑛𝑛𝑛𝑛
1
𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑚𝑠𝑠𝑠𝑠𝑠 𝜑1,𝑠𝑠𝑠𝑠𝑠 (5.2)
�𝜑1,𝑟𝑟𝑟𝑟 𝜑 2 � ∆𝑅𝑅𝑅𝑅
∑1 1,𝑟𝑟𝑟𝑟 𝑚𝑠𝑠𝑠𝑠𝑠 �𝜑1,𝑠𝑠𝑠𝑠𝑠 �
For simplicity, it was assumed that the building envelope remained intact, although it is
recognized that at higher hazard levels, wind-borne debris and missile impact would likely
compromise the cladding and fenestration integrity.
The appropriate ratio of critical damping for conventional structures for inelastic wind
analysis was estimated to be 2.5%, half that used for linear seismic analysis (5%). Damping was
incorporated in the analysis in two parts. First, energy dissipation was explicitly modeled
through the nonlinear hysteretic behavior, which is a function of the wind intensity. Second,
stiffness and mass proportional (“Rayleigh”) equivalent viscous damping was conservatively set
at 1% to account for the non-explicitly modeled part of the damping. The effect of damping is
considered in Chapter 6.
As previously discussed, if the wind speed increases, the time-interval (sample rate)
decreases, and the record duration is inversely reduced. Thus, unlike in a seismic IDA, the
duration must be defined in a wind IDA. In this study, a constant loading duration was
maintained by adjusting the record length relative to an initial reference intensity wind speed.
For the baseline condition, the reference wind speed and duration was 100 mph and 28 min.
5.1.7 Collapse Fragility
The wind vulnerability of the building to side-sway collapse (wind collapse fragility) was
determined by fitting individual collapse points (wind speed in miles per hour and corresponding
probability of collapse for a one scaled wind load record) with a curve assuming a lognormal
175
cumulative distribution function. A Kolmogorov-Smirnov “goodness-of-fit” test (Massey 1951)
at the 1% confidence level was used to verify that the fragility curve could be assumed to have a
lognormal distribution. The lognormal cumulative distribution function was defined by two
parameters: the median collapse wind speed, and the standard deviation of the natural logarithm
𝛽 (dispersion due to variability and uncertainty).
For example, Figure 5.7 shows the incremental dynamic analyses and wind collapse
fragility curves for the Type I ductile moment frame 8-story building with enhanced shear tab
connection collapse prevention system with reference wind speed of 20 mph.
Since wind loads are a random vibration, variability in the response was generated by
wind directionality (angle of attack). Such variation provided a practical way to incorporate
epistemic uncertainties in the incremental dynamic analysis. This “directional” variation differs
from the variation used in seismic load ensembles, which were generated using actual records
from a range of earthquake magnitude-distance pairs for (mostly) independent events.
250 1
0.9
Measured collapse point
200 0.8
0.7
Wind speed, V (mph)
150 0.6
mph
P |V
0.5
CDF curve including
c
100 0.4 spectral shape effect and

0.3 total uncertainty, βTotal
50 0.2
0.1
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 120 140 160 180 200 220 240
Roof drift ratio Wind speed, Vmph
a) Incremental dynamic analyses b) Wind collapse fragility curve
connection collapse prevention system (reference wind speed 20 mph)
176
The total dispersion, 𝛽𝑇𝑇𝑇𝑇𝑇 in collapse capacity was calculated using Equation 5.3,
following the method adopted in FEMA P-58 (FEMA 2012a,b):
𝛽𝑇𝑇𝑇𝑇𝑇 = �𝛽𝑅𝑅𝑅 2 + 𝛽𝐶 2 + 𝛽𝑄 2 (5.3)
In Equation 5.3, 𝛽𝑅𝑅𝑅 was the measured (record-to-record) dispersion in the nonlinear
wind response history analyses. Epistemic uncertainty was incorporated by assigning dispersion
due to construction uncertainty 𝛽𝐷𝐷 , and analytical model quality uncertainty 𝛽𝑄 . The
qualitative ratings (using FEMA P-58 rubric) given in Table 5.1 were used in this study. The
dispersion values in the table correspond to new buildings constructed with rigorous quality
assurance and a sufficiently accurate analytical model.
Table 5.1 Qualitative rating used to quantify uncertainties in wind collapse assessment
Non-ductile moment frame Ductile moment frame

Construction β =0.10 β =0.10
Analytical model β =0.10 β =0.10
5.2 Wind Collapse Risk Procedures
Wind collapse risk (probability of collapse considering the likelihood of wind speed) was
calculated by integrating the wind collapse fragility and wind hazard. A target risk of 0.15% in
50 years for ordinary occupancy was based on ASCE 7-10 Table C.1.3.1a (ASCE 2010).
Wind hazard (the occurrence of windstorms) may be described as a Bernoulli sequence or
process, that assumes events (e.g. windstorms) occur randomly, independently, and the
probability of occurrence is constant. For “well behaved climates away from the hurricane
coast” the probability of occurrence may be describe using an extreme value type I distribution
177
(Boggs and Peterka 1992). Assuming a geometric distribution, the probability of occurrence of
an event, 𝑁 in 𝑡 years is
𝑃(𝑁 ≥ 1) = 1 − (1 − 𝜆𝑎 )𝑡 (5.4)
where 𝜆𝑎 is the mean hazard exceedence frequency corresponding to an intensity measure (i.e.
wind speed in miles per hour), the probability that the intensity of windstorm, A will exceed
some level, a in a given year: 𝜆𝑎 = 𝑃(𝐴 > 𝑎 | 𝑡 = 1𝑦𝑦). As in the seismic collapse assessment, for
low annual hazard rates, Equation 5.4 is numerically equivalent to the hazard curve (inverse of
MRI), so that 𝑃(𝑁 ≥ 1) = 𝜆𝑎 .
Integration of the wind hazard (wind speed) curve and the structural collapse
vulnerability (wind collapse fragility) curve followed the process used for seismic analysis. The
vulnerability of the structure to the wind hazard (conditional probability of failure), in terms of
an annual failure rate, was calculated using the Equation 5.5.

+∞
𝜆𝐹 = � 𝜆𝑎 𝑓(𝑎) 𝑑𝑑 (5.5)
0
As before, this form of the risk integral requires the derivative of the fragility curve—the
CDF, which yields the probability density function (PDF). This was a more stable approach than
taking the derivative of the hazard curve. And, as before, the integral was performed
numerically. In contrast to seismic risk analysis in Chapter 4, directional effects and site
response were not included in the wind risk analysis. The cumulative risk (𝑃𝐹 ) to wind collapse
during the building lifetime (𝑡 in years) was calculated using Equation 5.6.
𝑃𝐹 = 1 − (1 − 𝜆𝐹 )𝑁 (5.6)
Equation 5.6 is different than the equation used to calculate cumulative seismic risk
(Equation 4.8), but produces similar values for low annual failure rates and typical exposure
times.
178
The wind collapse risk analysis procedures are illustrated in Figure 5.8 for Type I ductile
moment frame 8-story building with enhanced shear tab connection collapse prevention system,
with a reference wind speed 20 mph. Wind hazard (Figure 5.8a,b) was based on the ASCE 7-10
wind speed data (ATC 2011) for the interior of the conterminous United States (see Chapter 2).
Extreme hazard, where the mean recurrence interval (MRI) exceeds 1,700 years, was based on
extrapolation.
The ASCE 7-10 data does not include downdrafts and tornadoes. Tornado hazard was
estimated by using the number of tornado events that have been cataloged for 2°-latitude×2°-
longitude regions and correlating the tornado scale factor with a wind speed (Ramsdell and
Rishel 2007). The wind hazard curves shown in Figure 5.8 are only for the extrapolated data,
and do not include tornado data.
Where the hazard curve incorporated tornado effects, it is important to note that this
integration reflected the building vulnerability (collapse fragility) to straight-line wind forces of
long duration, not to a tornado-like wind force vortex of short duration. Experimental studies of
high-rise buildings (Yang et al. 2011) and low-rise buildings (Haan et al. 2010) subjected to a
tornado vortex suggest that the wind pressure coefficients is on the order of 1.5 times larger
compared to the straight-line effects.
A deaggregation of wind collapse risk (Figure 5.8c) indicates the wind speeds that
contribute the most to the annual risk rate. The cumulative risk to wind collapse (Figure 5.8d)
during the building lifetime was calculated using Equation 5.6.
179
-1
250 10
-2
10
Mean annual rate of exceedance, λ

200
mph
-3
10
Basic wind speed, V
-4
150 10
-5
10
100
-6
10
-7
50 10
0 200 400 600 800 1000 1200 1400 1600 50 100 150 200 250
Mean recurrance interval (yr) Basic wind speed, Vmph
a) Wind hazard (wind speed versus MRI) b) Wind hazard (λ versus wind speed)
-8 -5
x 10 x 10
2 5
| (1/mph/year)
1.8 4.5
1.6 4
1.4 3.5
mph
f
Collapse risk, P
)*|dλ/dV
1.2 3
1 2.5
mph
Collapse rate, P(c|V
0.8 2
0.6 1.5
0.4 1
0.2 0.5
0 0
50 100 150 200 250 50 100 150 200 250
Wind speed, Vmph Wind speed, V (mph)
c) Deaggregation of wind collapse risk d) Cumulative wind collapse risk
collapse prevention system (reference wind speed 20 mph)
180
5.3 Results
5.3.1 Type I Non-ductile and Ductile Moment Frame Buildings
The collapse assessment results, relative to risk category II (115 mph basic wind speed), are
summarized in Table 5.2 for non-ductile and Table 5.3 for ductile moment frames. The
empirical period, 𝑇𝑤 and calculated period, 𝑇1 from an eigenvalue analysis are given. As in the
seismic evaluation, the fundamental period values determined in the eigenvalue analysis, 𝑇1 are
high compared to empirical estimates of actual buildings, even for wind evaluation. The static
pushover results are described in terms of the wind base shear coefficient 𝐶𝑠−𝑊𝑊𝑊𝑊 and static
“overstrength” Ω. The dynamic IDA results include the collapse margin ratio (CMR), record-to-
record dispersion 𝛽𝑅𝑅𝑅 , total dispersion 𝛽𝑇𝑇𝑇𝑇𝑇 , and the risk of wind collapse (unconditional)
based on a location in the interior of the United States.
The reserve lateral strength in the shear-tab connections reduced the risk of collapse
noticeably compared to moment frames alone.
Table 5.2 Wind collapse assessment of Type II non-ductile moment frame buildings
(relative to Risk Category II)

Archetype Tw (s) T1 (s) Cs,wind Ω CMR βRTR βTotal Pf,50
4-Story
MF 2.38 2.99 1.43 0.104 0.176 0.57%
MF+GF 1.10 2.01 0.03 3.02 1.46 0.105 0.176 0.42%
MF+SST 1.67 5.22 1.69 0.107 0.178 0.05%
8-Story
MF 3.16 2.10 1.44 0.046 0.149 0.20%
MF+GF 1.88 2.85 0.03 2.45 1.37 0.057 0.153 0.48%
MF+SST 2.47 2.96 1.48 0.036 0.146 0.12%
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Table 5.3 Wind collapse assessment of Type II ductile moment frame buildings

4-Story
MF+GF 1.10 1.60 0.03 3.34 2.30 0.060 0.154 0.00%
MF+SST 1.10 1.60 0.03 7.35 2.56 0.109 0.179 0.00%
8-Story
MF+GF 1.88 2.88 0.03 2.45 1.62 0.080 0.162 0.05%
MF+SST 1.88 2.50 0.03 2.71 1.88 0.075 0.160 0.00%
Employing enhanced shear tab connection collapse prevention systems decreased the risk
dramatically. Without collapse prevention systems, only the ductile buildings passed the target
risk (0.15%). With collapse prevention systems, all buildings easily passed the target risk.
Maps are used to illustrate areas where collapse prevention systems are applicable for the
Type I archetype non-ductile building. Wind collapse risk was calculated by integrating collapse
fragility (from Table 5.2 and Table 5.3) and wind hazard based on extrapolated ASCE 7-10 wind
speed data. The wind risk analysis was repeated for every 0.5-degree latitude and longitude to
generate a map of risk values in the conterminous United States. Major metropolitan areas (dots)
are shown based on 2011 population estimate using 2010 census data.
Regions where the wind collapse risk exceeds 0.15% in 50 years (shaded contours) are
shown in Figure 5.9 for the 4-story non-ductile building, and in Figure 5.10 for the 8-story non-
ductile building. The maps show that the enhanced shear tab connection (SST) collapse
prevention system with non-ductile moment frames is necessary for all of United States, except
the west coast, for the 4-story building. For both the 4-story and 8-story buildings, the collapse
prevention system was not suitable for use in high wind regions along the hurricane coastline and
extending up along the eastern seaboard to New York and Boston.
182
MF
MF+SST
Type I non-ductile MF
Figure 5.9 Regions where wind collapse risk exceeds 0.15% in 50 years (4-story building)
MF
MF+SST
Type I non-ductile MF
183
5.3.2 Type II Non-ductile Moment Frame 4-story Building
The wind collapse assessment results are summarized in Table 5.4 for the non-ductile 4-story
building, relative to Risk Category II. As before, the reserve lateral strength in the shear-tab
connections reduced the risk of collapse significantly. The building easily passed the target risk
of 0.15%. Figure 5.11 shows regions where the wind collapse risk exceeds 0.15% in 50 years
(shaded contours). The wind collapse risk exceeds 0.15% only in areas of high hurricane hazard.
Table 5.4 Wind collapse assessment of Type II non-ductile moment frame building

MF+GF 1.11 1.64 0.02 6.27 1.84 0.086 0.165 0.0%
MF+GF
Type II non-ductile MF
184
5.3.3 Type III Non-ductile Moment Frame 10-story Building
The wind collapse assessment results are summarized in Table 5.5 for the Type III non-ductile
10-story building. This building structural plan was configured such that there were no shear tab
connections with columns oriented in the strong direction, thus no reserve strength comparison
was made. The results indicate that the building does not pass the target risk (0.15%) by a large
margin.
Figure 5.12 illustrates the process of calculating the wind collapse risk. Wind hazard
(Figure 5.12a) was based on the ASCE 7-10 wind speed data (ATC 2011) for the interior of the
conterminous United States. Extreme hazard, where the mean recurrence interval (MRI) exceeds
1,700 years, was based on extrapolation. Hazard curves for the west coast of the United States
and for Jacksonville, Florida (on the hurricane-prone east coast) are also shown. The effect of
tornado hazard is shown for Jacksonville and Oklahoma City. The plot indicates that tornado
hazards dominate extreme events for the interior of the United States, whereas hurricanes pose a
greater hazard along the eastern seaboard.
Building vulnerability, or the collapse fragility (Figure 5.12b), was integrated with the
wind hazard using the derivative of the fragility curve.
The contribution of hazards to the annual rate of collapse risk (𝜆𝐹𝐹𝐹𝐹 ), or so-called
deaggregation, displayed in Figure 5.12c shows that the effect of extrapolating wind speed data
was negligible for the non-ductile moment frame building for most locations in the interior of the
United States. Even in Oklahoma City and Jacksonville, where tornadoes or the effect of wind
speed data extrapolation are significant, non-extreme wind events (wind events with less than a
1,700-year MRI) still contribute the most to the annual risk rate for wind collapse.
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Table 5.5 Wind collapse assessment of Type III non-ductile moment frame 10-story building

MF 2.28 3.34 0.05 2.21 1.20 0.069 0.158 3.3%
10
-1 1
Interior of United States 0.9
10
-2 Measured collapse points
0.8
fit with a lognormal
Mean annual rate of exceedance, λ
Oklahoma City
0.7 cumulative distribution
-3 (Tornados)
10 1,700 MRI function (CDF) curve
0.6
Pc | Vmph
-4
Jacksonville
10 0.5
West coast
0.4 Collapse
-5
of United
10 States 0.3 fragility curve
using βTotal
-6 0.2
10
Jacksonville 0.1
-7
(Tornados)
10 0
80 100 120 140 160 180 200 80 100 120 140 160 180 200
Basic wind speed, Vmph Wind speed, V mph
a) Wind hazard b) Wind collapse fragility

-5
x 10
1 0.02
Collapse rate, P(c|V mph)*|dλ/dVmph| (1/mph/year)
0.9 Contribution from 0.018

extrapolated data Addition from extrapolated data
0.8 0.016
0.7 Interior of 0.014

United
Collapse risk, Pf
0.6 0.012
States
0.5 0.01
0.4 0.008
Addition from tornados
0.3 0.006
Contribution ASCE 7-10
0.2 from tornados 0.004 target
0.1 0.002
Interior of United States
0 0
80 100 120 140 160 180 200 80 100 120 140 160 180 200
Wind speed, V mph Wind speed, V (mph)
c) Wind collapse risk deaggregation d) Cumulative risk of wind collapse
Figure 5.12 Collapse risk analysis for Type I non-ductile moment frame building
186
5.4 Discussion
Wind collapse assessments indicated that the probability of collapse was acceptably low for most
archetypical structural systems in the interior (and west coast) of the United States. Taller
buildings, however, had a higher risk, and one archetype (the Type III non-ductile moment frame
10-story building) did not pass the suggested 0.15% target risk. Collapse prevention systems are
needed and viable in the interior of the United States, but along the hurricane-prone coastline the
risk of collapse often exceeded the target risk, depending on the location and type of archetype
structural system.
In seismic analysis, the conditional probability of collapse is often used to determine
structural safety: the building collapse probability should not exceed 10% given the Maximum
Considered Earthquake (MCE) ground motions. The conditional probability may be appropriate
for seismic engineering for the reason that the seismic risk reflects the underlying seismic
hazard, and thus the seismic risk changes dramatically from one site to another site, even in the
same general location. In other words, calculation of seismic risk may not enable a uniform
comparison of structural response to earthquakes.
In wind analysis, on the other hand, there is no equivalent “Maximum Considered Wind”
speed event. The closest such event is the design wind speed. In ASCE 7-10, for risk category II
structures the design wind speed (115 mph in the interior of the United States) is associated with
a 700-year MRI. For risk category III and IV structures the design wind speed (120 mph in the
interior of the United States) is associated with a 1,700-year MRI. This suggests that a
“Maximum Considered Wind” could take on various wind speeds.
187
Moreover, a target for the conditional probability of wind collapse given such an event
has not been established. The results in this chapter suggest that such a target would need to be
much less than 10% (used for seismic), perhaps on the order of 1% to 2%.
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Chapter 6
SENSITIVITY OF COLLAPSE ASSESSMENT
This chapter discusses the sensitivity of seismic and wind collapse assessments to parametric
changes in hazard or structural vulnerability via analytical modeling. The seismic hazard
parameters included ground motions, site response, regional risk, and intensity measures. The
seismic modeling parameters included column panel zone representation, the method used to
account for second-order (P-∆) effects, column splices, and the risk integration method. The
wind hazard parameters included duration of wind. The wind modeling parameters included
type of lateral system, static overstrength, fundamental building period, and structural system
degradation of stiffness and strength.
6.1 Seismic Collapse Sensitivity
In the analytical modeling approach (Chapter 3) used in this study, beams and columns were
represented using an assembly of rotational springs and elastic beam-column elements in order to
simulate the potential for inelastic behavior at or near the end of the member. Aside from
component behavior, key aspects of analytical modeling are the beam-column joint (panel zone)
representation, the method used to take into account second-order (P-∆) effects, modeling of
189
column splices, spectral matching between the ground motion record and the target response
spectrum, risk integration method, regional risk, and site response.
This section discusses the sensitivity of the seismic collapse assessment to these
parameters for the Type I archetype structural systems. Three types of moment-frame designs
were considered: a non-ductile moment frame designed for FEMA P-695 Seismic Design
Category (SDC) B min , and a ductile moment frame using a reduced-beam section designed for
SDC D min or SDC D max . Although the scope of the sensitivity study was limited to these specific
structures, related sensitivity studies of second-order effects and damping have shown similar
effects for a braced-frame and an 8-story moment-frame building (Hardyniec 2014).
6.1.1 Panel Zone Representation
Background
Shear distortion in the panel zone of a beam-to-column connection has been shown to be an
important factor in the seismic analysis of steel moment-frame buildings (Charney and
Horvilleur 1995; Charney and Johnson 1986; FEMA 2000a; Charney and Pathak 2007). The
panel zone may be represented analytically in a variety of ways. In the simplest representation,
the steel frame is modeled using centerline dimensions and rigid joints. In this “centerline”
model the shear distortion in the panel zone behavior is not explicitly considered, but is
approximated (the underestimated shear and overestimated bending moment within the joint
region tend to cancel out as “compensating errors”). More importantly, the centerline model
does not account for inelastic deformation. Another representation is the “scissors” model,
where the panel zone is modeled using a beam and a column, with rigid links at each end,
connected by a hinge with a spring. In this model, the spring rotation is equal to the shear
190
distortion of the panel zone. A more correct representation was proposed by Krawinkler (1978).
In the “Krawinkler” model, the panel zone is modeled using rigid beam elements connected by
hinges and springs that form a parallelogram. It should be noted that the kinematic behavior
differs for scissors and Krawinkler models, and the properties for springs are not the same
(Charney and Marshall 2006). Although it is clear that the kinematic behavior of the Krawinkler
model is closer to the true connection behavior (Charney and Marshall 2006), the scissors and
centerline models require fewer degrees of freedom. The number of degrees of freedom has a
significant impact on the computational demand for seismic collapse analyses, which, as
previously discussed, involve multiple ground motions run at increasing intensity levels until
collapse.
Results
The sensitivity of the seismic collapse assessment to the panel zone representation is summarized
in Table 6.1 for the Type I non-ductile moment frame 4-story building, and in Table 6.2 for the
Type II ductile moment-frame 4-story building designed for SDC D max . The results are shown
relative to the Krawinkler model (the “baseline” or reference model). The fundamental period,
𝑇1 was based on the eigenvalue analysis. The static response is described in terms of the seismic
base shear coefficient 𝐶𝑠 , the “overstrength”, Ω, and the period-based ductility, 𝜇 𝑇 . The dynamic
response is described in terms of the seismic intensity measure (spectral acceleration at the
fundamental period corresponding to the MCE-level ground motion, 𝑆𝑎𝑎𝑎𝑎 ), the collapse margin
ratio (CMR), the measured record-to-record dispersion (𝛽𝑅𝑅𝑅 ), the total dispersion (𝛽𝑇𝑇𝑇𝑇𝑇 )
dispersion including epistemic uncertainties), and the conditional probability of seismic collapse
(failure conditioned on occurrence of the MCE-level ground motion intensity).
191
Table 6.1 Sensitivity of collapse assessment (for SDC D max ) for Type I non-ductile moment-
frame building (designed for wind, SDC B min ) to the panel zone representation

SaMCE Pc |
Model Aspect T1 (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal MCE
Baseline (Reference) Model
Krawinkler 2.01 0.21 0.41 3.94 0.45 0.93 1.39 1.30 0.37 0.65 34.0%
Alternate Panel Zone Model
Centerline 1.44 0.21 0.43 3.65 0.62 1.04 1.36 1.41 0.30 0.61 28.8%
Scissors 1.99 0.21 0.40 4.33 0.45 0.93 1.42 1.32 0.36 0.64 33.4%
Table 6.2 Sensitivity of collapse assessment (for SDC D max ) for Type I ductile moment-frame
building (designed for SDC D ma x ) to the panel zone representation

SaMCE Pc |
Krawinkler 1.36 0.08 2.26 5.63 0.66 1.89 1.46 2.75 0.33 0.45 1.2%
Alternate Panel Zone Model
Centerline 1.01 0.08 2.03 11.66 0.89 1.89 1.46 2.76 0.36 0.47 1.5%
Scissors 1.35 0.08 2.24 5.88 0.67 1.87 1.47 2.74 0.33 0.45 1.2%
A comparison of CMR values from each model indicates that the non-ductile moment
frame building assessment was more sensitive than the ductile frame building to the change in
the panel zone model representation. The total dispersion of the collapse results, represented by
𝛽𝑇𝑇𝑇𝑇𝑇 , was similar for both panel zone models, and the conditional probability of collapse was
similar. Overall, the CMR, static overstrength, and period-based ductility values were greater for
the ductile frames, while the conditional probability and dispersion were greater for the non-
ductile frames, which were expected based on the design considerations for the two frames.
192
A comparison of the incremental dynamic analyses for the non-ductile moment frame
buildings (Figure 6.1) and ductile moment frame buildings (Figure 6.2) augments the results
from the previous tables. The CMR values, calculated from the spectral acceleration associated
with the median collapse and the spectral acceleration at the MCE level, represented by the red
and black lines, respectively, were generally near 1.0 for the non-ductile frames and near 2.0 for
the ductile frames. The greater ductility of the ductile moment frames was also apparent in the
higher interstory drift ratios that the models reached before collapse.
7 1.6
Scaled response spectra 1.4
Krawinkler
6
Pseudo-acceleration Sa(g)
5 1.2
1
4
0.8
3
0.6
2
0.4
1 0.2
0 0
0 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 0.08 0.1
1.6 1.6
Centerline Scissors
1.4 1.4
1.2 1.2
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1
Maximum Interstory Drift Ratio Maximum Interstory Drift Ratio
Figure 6.1 Incremental dynamic analyses: Type I non-ductile moment frame 4-story building
193
7 6
Scaled response spectra Krawinkler

6 5
5
4
4
3
3
2
2
1 1
0 0
0 0.5 1 1.5 2 2.5 0 0.05 0.1 0.15 0.2
6 6
Centerline Scissors

5 5
4 4
3 3
2 2
1 1
0 0
0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2
Figure 6.2 Incremental dynamic analyses: Type I ductile moment frame 4-story building
194
6.1.2 Second-Order Effects
Background
Second-order effects are also known to be an important factor in the analysis of flexible
structures like steel moment frames, especially for seismic collapse analysis (Gupta and
Krawinkler 2000; Christoph et al. 2004). In a first-order analysis, the displaced configuration of
a structure is not considered, and equilibrium is calculated based on the undeformed
configuration. However, the undeformed configuration cannot be used to satisfy equilibrium as
displacements increase. The effects of these equilibrium unbalances are commonly referred to as
second-order effects. To reduce the equilibrium unbalances induced by large displacements,
geometric nonlinearity approaches are incorporated.
For small displacements, second-order effects can be reasonably estimated using a P-∆
approximation, where lateral (transverse) member displacements are considered, but axial
(longitudinal) member displacements are ignored (referred to as the Euler-beam theory “large-
displacement” assumption). The “corotational” method is one way to account for large
displacements.
In the corotational method, the local element coordinate system continuously rotates with
the element (Balling and Lyon 2011). In its usual form, the corotational method assumes small-
strain relationships. The small-strain assumption is valid for collapse analysis of steel moment-
frame buildings, where the ultimate plastic rotation of the beam-to-column connection does not
exceed 0.15 radians (Lignos and Krawinkler 2011).
195
Results
The sensitivity of the collapse assessment to the second-order method is summarized in
Table 6.3 for the Type I non-ductile moment frame 4-story building, and in Table 6.4 for the
Type I ductile moment-frame 4-story building. A comparison of CMR values from each model
indicates that the seismic collapse assessment of both types of moment frame buildings were
very sensitive to a change from a first-order (linear) to a second-order modeling approach.
Table 6.3 Sensitivity of collapse assessment (for SDC D max ) for Type I non-ductile moment-
frame building (designed for wind, SDC B min ) to the method used for second-order effects

SaMCE Pc |
Corotational 2.01 0.21 0.41 3.94 0.45 0.93 1.39 1.30 0.37 0.65 34.0%
Alternate Second-Order Method
Linear (first-order) 1.91 0.21 0.51 2.32 0.47 2.22 1.27 2.81 0.43 0.69 6.6%
P-∆ approximation 2.00 0.21 0.41 3.81 0.45 0.95 1.38 1.31 0.38 0.65 34.1%
Table 6.4 Sensitivity of collapse assessment (for SDC D max ) for Type I ductile moment-frame
building (designed for SDC D ma x ) to the method used for second-order effects

SaMCE Pc |
Corotational 1.36 0.08 2.26 5.63 0.66 1.89 1.46 2.75 0.33 0.45 1.2%
Alternate Second-Order Method
Linear (first-order) 1.33 0.08 2.64 7.72 0.68 4.01 1.55 6.20 0.40 0.50 0.0%
P-∆ approximation 1.36 0.08 2.25 5.60 0.66 1.79 1.46 2.60 0.34 0.45 1.8%
196
As in the previous sensitivity study, the CMR, static overstrength, and period-based
ductility values were greater for the ductile frames while the conditional probability and
dispersion were greater for the non-ductile frames. The predicted conditional probability of
collapse was much less using a first-order model.
A comparison of the incremental dynamic analyses for the non-ductile moment frame
buildings (Figure 6.3) and ductile moment frame buildings (Figure 6.4) supplements the results
from the previous tables. Higher dispersion, related to 𝛽𝑅𝑅𝑅 , was evident in the incremental
dynamic analyses for first-order model.
7 1.6
6 Scaled response spectra 1.4 Corotational

5 1.2
1
4
0.8
3
0.6
2
0.4
1 0.2
0 0
0 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 0.08 0.1
1.6 1.6
Linear P-∆ approximation
1.4 1.4
1.2 1.2
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1
Figure 6.3 Incremental dynamic analyses: Type I non-ductile moment frame 4-story building
197
7 6
Scaled response spectra Corotational

6 5
5
4
4
3
3
2
2
1 1
0 0
0 0.5 1 1.5 2 2.5 0 0.05 0.1 0.15 0.2
6
Linear P-∆ approximation

5
0
0 0.05 0.1 0.15 0.2
Maximum Interstory Drift Ratio
Figure 6.4 Incremental dynamic analyses: Type I ductile moment frame 4-story building
198
6.1.3 Column Splices
The sensitivity of the seismic collapse assessment of the Type I ductile moment frame 4-story
building, designed SDC D max , to the inclusion of splices in the gravity columns is determined in
this section. Columns participating in the moment frame were idealized as fixed at the base.
Gravity frame columns were idealized as pinned at the base. Column splices were located at
story 3. Column splices were assumed to have no rotational capacity (a pinned connection).
Partial rotational capacity was not modeled.
The sensitivity study results are summarized in Table 6.5. As a supplement, Figure 6.5
shows the seismic pushover response, story collapse mechanism, and incremental dynamic
analyses including column splices (left column of figure) and not including splices (right column
of figure). The collapse assessment was sensitive to the inclusion of column splices, both in
terms of static overstrength and probability of collapse at the MCE-level ground motion
intensity. The inclusion of column splices changed the predicted static collapse story mechanism
from story 4 to story 3.
These sensitivity analysis results confirm a previous study of steel moment frame
buildings with column splices (Flores 2015) that utilized a lumped column approach.
Table 6.5 Sensitivity of seismic collapse assessment to column splices
(Type I ductile moment frame 4-story building designed SDC D max )

Column T1 SaMCE Pc |
Splices (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal MCE
4-Story
Included 1.60 0.08 1.80 4.92 0.56 1.45 1.45 2.11 0.32 0.44 5%
Non included 1.36 0.08 2.30 6.54 0.66 2.09 1.50 3.15 0.32 0.44 0%
199
0.2 0.2
0.18 0.18
0.16 0.16

0.14 0.14
0.12 0.12
0.1 0.1
0.08 0.08
0.06 0.06
0.04 0.04
0.02 0.02
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Roof Drift Ratio Roof Drift Ratio
Seismic Pushover Response
Pushover Story Collapse Mechanisms
4 4
3.5 3.5
3 3
2.5 2.5
2 2
1.5 1.5
1 1
0.5 0.5
0 0
0 0.05 0.1 0.15 0 0.05 0.1 0.15
Incremental Dynamic Analyses
a) Column splices b) No column splices
Figure 6.5 Response of Type I ductile 4-story building designed for D max
200
6.1.4 Ground Motion Spectrum
The sensitivity of the seismic collapse assessment of the Type I non-ductile moment frame 4-
story and 8-story building, and the ductile 8-story building, to the ground motion spectrum, of
the ground motion set relative to the target spectrum, was determined by comparing the response
obtained using spectral matched ground motions to the original (un-matched) response.
Background
Nonlinear response history analysis of a structure requires the use of an input ground motion, and
the input ground motion can be derived from a variety of sources:
• real strong-motion ground recordings,
• real recordings that have the amplitude linearly-scaled to match a target spectrum,
acceleration or other measure,
• real recordings that have been modified in terms of frequency content, duration,
amplitude (and so forth),
• synthetic ground motions based on a “seed” real recording, and
• stochastic ground motions generated using a variety of methods that may or may not be
based on physical models.
A set of ground motions (also referred to as an ensemble or suite of ground motions) is then used
to capture response variability due to frequency and other attributes of ground motion (Liel et al.
2009). Such variability is termed “record-to-record” (RTR) variability. An alternative approach
is to use one ground motion and account for record-to-record variability elsewhere, i.e. in a First
Order Second Moment (FOSM) method.
201
NIST (2011) gives an overview of ground motions, various methods in selecting and
scaling ground motions, and the use of ground motions in analysis. Baker et al. (2011) give
recommendations for the western United States. Various scaling procedures have been proposed
including, for instance, a modal-pushover-based ground-motion scaling procedure (Kalkan and
Chopra 2011).
Ground motions in the central and eastern United States, however, differ from ground
motions in the western United States due to geological dissimilarities between the two regions,
as discussed in Chapter 2. Namely, the central and eastern ground motions have higher
frequency content (NIST 2011; GEER Team 2012), owing to various factors: hazard
contributions tend to come from smaller-magnitude earthquakes that have less low-frequency
content ground motion for a given hazard level; earthquakes have more high-frequency energy;
attenuation of motion (especially high-frequencies) is slower due to a high 𝑄 factor; and the
target uniform hazard spectral shape for a site is shifted towards higher frequencies because the
reference ground motion often corresponds to a hard-rock condition, and high-frequency motion
is not attenuated as much by near-surface site effects (NIST 2011).
Thus, various ground motion sets have been proposed for structures located in the central
and eastern United States. For example, while developing a ground motion prediction model for
the central and eastern United States, Somerville et al. (2001) generated a set of ground motions
using a physics-based simulation procedure. Fernández (2007), Rix and Fernandez (2006),
developed a synthetic ground motion ensemble for the Mississippi embayment area. Celik
(2007) used ground motions by Fernández in his analysis of the central and eastern United States
in order to capture nonlinear soil behavior (i.e., damping) in site response and resonance in the
soil column, and concluded that other ground motions (developed by Wen and Wu 2001)
202
overestimate the ground motion intensity at low periods and do not capture soil column
resonance at higher periods.
Huang et al. (2010a) formed a set of ground motions based on real recordings, mostly
from the United States, but augmented with records from Canada and elsewhere in the world
where there were large intra-plate earthquakes. Some of the recordings were from the western
United States where it was determined that the fault mechanism and high-velocity sedimentary
layer were appropriate for the eastern United States.
Hines et al. (2011) propose an ensemble of ground motions for the eastern United States.
Their ensemble does not employ amplitude scaling. Instead, the motions were selected from a
United States Nuclear Regulatory Commission (NUREG) database (McGuire et al. 2001). In the
NUREG database, real recordings (mostly from the western United States) were modified
(scaled using theoretical transfer functions) as to be appropriate for the tectonic environment of
the central and eastern United States: the modified records exhibit higher spectral accelerations
and peak in a higher frequency range compared to the original records.
Since high-frequency ground motions are largely stochastic (Hanks and McGuire 1981;
Boore 2003), there is no perceived problem (at least theoretically) with modifying ground
motions, although synthetic ground motions may lead to differences in the predicted structural
response (e.g. Milburn 2009). Synthetic ground motions were obtainable using deaggregation
software at the USGS website (http://earthquake.usgs.gov/research/hazmaps). As of 2015, these
USGS simulated ground motions were based on 2002 deggregation data. (Simulations based on
2008 data were not yet available.)
203
Results
The ground motion set was spectral matched to the FEMA P-695 SDC D max target spectrum by
employing an algorithm using wavelets and Broyden updating developed by Adekristi (2013).
Figure 6.6 shows a comparison of the acceleration, velocity, and displacement response
histories of the original (un-matched) and spectral matched ground motion for a representative
record (FEMA P-695 Far Field ground motion ID No. 1). Figure 6.6 shows that realistic
physical behavior (i.e. zero velocity and minimal displacement) was maintained in the matching
process for this ground motion. This comparison is in line with recommendations for assessing
the adequacy of the spectral-matching process (Grant and Diaferia 2012).
(a) Original Acceleration Time Series (b) Modified Acceleration Time Series
Acceleration (g)
Acceleration (g)
0.5 0.5
0 0
-0.5 -0.5
0 10 20 30 40 0 10 20 30 40
Time (sec) Time (sec)
(c) Original Velocity Time Series (d) Modified Velocity Time Series
Velocivty (m/s)
Velocivty (m/s)
1 1
0 0
-1 -1
0 10 20 30 40 0 10 20 30 40
(e) Original Displacement Time Series (f) Modified Displacement Time Series
Displacement (m)
Displacement (m)
0.2 0.2
0 0
-0.2 -0.2
0 10 20 30 40 0 10 20 30 40
Figure 6.6 Response histories representative ground motion
(FEMA P-695 Far Field ground motion ID No. 1)
204
For the same ground motion, Figure 6.7 shows a comparison of the response spectrum and
normalized arias intensity (acceleration of transient waves) of the original (un-matched) and
spectral matched ground motion. The figure shows that the matching process also produced a
ground motion that was very similar, in terms of spectral response and ground shaking intensity.
The sensitivity study results are summarized in Table 6.6 for the 4-story and 8-story non-
ductile building (with Figure 6.8 and Figure 6.9, respectively), and in Table 6.7 (with Figure
6.10) for the 8-story ductile building. The seismic collapse assessment was sensitive to the
ground motion variability (with respect to the target spectrum) and, in general, the matched
ground motions led to a higher CMR value and consequently a lower probability of collapse.
Interestingly, the dispersion in response was much wider for the matched ground motions. A
possible cause for the increased dispersion could be attributed to the fact that the high frequency
content of ground motions did not match the target spectrum at low periods. To a lesser extent,
the low frequency content also did not always match the target spectrum (e.g. Figure 6.8a).
Response Spectra Arias Intensity

1.6 1
Original Response Original Response
Matched Response 0.9 Proposed Method
1.4 Target
0.8
Normalized Arias Intensity (m/s)
1.2
0.7
1
Acceleration (g)
0.6
0.8 0.5
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0 0
0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 35 40
Period (sec) t (sec)
a) Response spectrum b) Normalized arias intensity
Figure 6.7 Response of representative ground motion
(FEMA P-695 Far Field ground motion ID No. 1)
205
(Type I non-ductile moment frame buildings designed for SDC B min evaluated at SDC D max )

Ground T1 SaMCE Pc |
Motion Set (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal MCE
4-Story (MF+GF)
Original 0.93 1.39 1.30 0.37 0.65 34%
2.01 0.21 0.41 3.94 0.45
Matched 1.08 1.39 1.50 0.34 0.63 26%
8-Story (MF+GF)
Original 0.87 1.27 1.10 0.34 0.63 44%
2.85 0.12 0.55 2.35 0.32
Matched 1.39 1.36 1.90 0.39 0.66 17%
4.5 Original ground motions 1.2 Original ground motions

4
1
3.5
3 0.8
2.5
0.6
2
1.5 0.4
1
0.2
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Period (seconds/cycle) Maximum Interstory Drift Ratio
4.5 Spectral-matched ground motions 1.2 Spectral-matched ground motions

4
1
3.5
3 0.8
2.5
0.6
2
1.5 0.4
1
0.2
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
a) Response spectrum b) Incremental dynamic analyses
Figure 6.8 Response of non-ductile 4-story building
206
5 0.8
4.5 Original ground motions Original ground motions

0.7
4

0.6
3.5
0.5
3
2.5 0.4
2
0.3
1.5
0.2
1
0.1
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
5 0.8
4.5 Spectral-matched ground motions Spectral-matched ground motions

0.7
4

0.6
3.5
0.5
3
2.5 0.4
2
0.3
1.5
0.2
1
0.1
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Figure 6.9 Response of non-ductile 8-story building
207
(Type I ductile moment frame buildings designed for SDC D min evaluated at SDC D max )

Ground T1 SaMCE Pc |
Motion Set (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal MCE
8-Story
Original 0.87 1.36 1.18 0.34 0.46 36%
2.88 0.05 1.31 3.44 0.31
Matched 1.12 1.36 1.52 0.37 0.48 19%
5 0.8
4.5 Original ground motions 0.7

Original ground motions
4

0.6
3.5
0.5
3
2.5 0.4
2
0.3
1.5
0.2
1
0.1
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.02 0.04 0.06 0.08 0.1
5 0.8
4.5 Spectral-matched ground motions 0.7

Spectral-matched ground motions
4
0.6
3.5
0.5
3
2.5 0.4
2
0.3
1.5
0.2
1
0.1
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.02 0.04 0.06 0.08 0.1
Figure 6.10 Response of ductile 8-story building
208
6.1.5 Intensity Measure Conditioning Period
The sensitivity of the seismic collapse assessment of the Type I ductile moment frame 4-story
building to the conditioning period used to define the seismic hazard intensity measure (spectral
acceleration) was determined.
The sensitivity study results are summarized in Table 6.8. Three definitions of spectral
acceleration were considered, based on fundamental building period (1) calculated from an
eigenvalue analysis 𝑇1 , and determined empirically for (2) wind analysis 𝑇𝑤 using ASCE 7-10,
or (3) for seismic analysis 𝑇𝑒 = 𝐶𝑢 𝑇𝑎 using ASCE 7-10.
The results indicate that using a longer period to define the spectral acceleration intensity
measure slightly increased the collapse margin ratio and decreased the conditional probability of
collapse. The difference in response could be attributed to the nature of the response spectrum
for typical ground motions (and as a corollary, ground motion sets) that exhibit higher
accelerations for lower periods. Thus, all other factors being equal, a lower value for the
conditioning period would be expected to suggest a higher vulnerability to seismic collapse.
(Type I ductile moment frame 4-story building designed for SDC D min evaluated at SDC D max )

Seismic
Intensity SaMCE Pc |
Measure (IM) T (s) Cs Ω µT (g) CMR SSF ACMR βRTR βTotal MCE
4-Story
Sa(T1) 1.36 0.08 2.26 5.63 0.66 1.89 1.46 2.75 0.33 0.45 1.2%
Sa(Tw) 1.10 0.08 2.26 5.63 0.82 1.89 1.40 2.64 0.34 0.45 1.6%
Sa(Te) 0.95 0.08 2.26 5.63 0.94 1.87 1.37 2.56 0.34 0.45 1.9%
209
6.1.6 Risk Integration Method
This section uses the collapse risk of a 4-story ductile moment frame building as an example to
determine the sensitivity of seismic collapse assessment to the method used to integrate hazard
and risk. [See also Judd and Charney (2014c).]
For purposes of comparison (i.e. with Eads et al. 2013), the ground motion hazard was
determined using the 2002 USGS hazard data for a location in Los Angeles. The fundamental
building period, 𝑇1 = 1.33 seconds, and seismic collapse fragility were based on Eads et al.
(2013).
Background
In probabilistic seismic hazard analysis, there are three analytically equivalent methods to
integrate hazard and fragility.
Method 1: Numerical Derivative of Hazard Curve
The integration of hazard and fragility is shown in the following equation and is the so-called
“risk integral” which calculates an annual rate of failure, 𝜆𝐹 :

+∞
𝑑𝜆𝑎
𝜆𝐹 = −� 𝑃(𝐹|𝑎) � � 𝑑𝑑 (6.1)
0 𝑑𝑑
The failure rate usually refers to the collapse rate, 𝜆𝑐 which can also be used to calculate
the risk of collapse in an exposure time (such as calculating the probability of collapse in 50
years). The minus sign accounts for the negative slope of the hazard curve (in PSHA the hazard
curve is the probability of exceeding a value so it decreases as the demand parameter increases).
An equivalent version of the risk integral could use an absolute value instead of a minus sign.
210
The risk integral equation represents the concept that the probability of failure is the
probability of the ground motion times the probability of building failure given that level,
integrated over all possible levels of hazard (Kennedy 2011). The equation assumes ergodicity,
meaning hazard and fragility (conditional failure) are independent and “the structure does not
deteriorate” and is “instantaneously restored to its original state after each damaging
earthquake.” This approximation is only accurate as long as the failure rate is small. For
probabilities of failure greater than 1%, the approximation overestimates risk (Der Kiureghian
2005).
The hazard curve is not commonly represented using a continuous function, but instead a
discrete data set is used, so in practice the derivative is approximated numerically. See, for
example, FEMA P-58 (FEMA 2012a).
Method 2: Derivative of Fitted Hazard Curve
An alternative approach to using the discrete set of hazard data points is to fit the hazard curve
with a function (usually a polynomial) and then take the derivative of that function when
calculating Equation 6.1 (see Eads et al. 2013).
Method 3: Derivative of Fragility Curve
As shown before
+∞
𝜆𝐹 = � 𝜆𝑎 𝑓(𝑎) 𝑑𝑑 (6.2)
0
Note that this form of the risk integral (Equation 6.2) requires the derivative of the
fragility curve—the CDF, which yields the probability density function (PDF). This is a more
stable approach than taking the derivative of the hazard curve.
211
Results
A comparison between risk calculated using numerical derivative (Method 1) and curve fitting
(Method 2) is shown in Figure 6.11. For Method 2, various degree polynomials were fit to the
hazard curve. The effect of the methods to determine the slope of the hazard curve is shown in
Figure 6.11a. For the hazard curve, the black line was linearly interpolated in log-log space. For
the risk deaggregation curves (Figure 6.11b) the gray line was based on the incremental slope,
and colors represent a 3-degree (cyan), 4-degree (blue), 5-degree (magenta), and 6-degree
(green) polynomial curve fit for the hazard curve.
A 4-degree or more polynomial curve fit converges to the same cumulative risk (Figure
6.11c). For very small spectral accelerations (spectral acceleration less than 0.1g), a 5-degree
polynomial is a very bad fit (this effect is not visible in Figure 6.11a). Using the derivative of
the fitted polynomial hazard curve gives the collapse rate (number of predicted collapses per
year) 𝜆𝑐 = 3.51×10-4 and the seismic collapse risk of 1.74% in 50 years (green line) for the Los
R
Angeles location considered. Using the incremental derivative of hazard curve gives 𝜆𝑐 =
3.97×10-4 and the seismic collapse risk of 1.97% in 50 years.
Figure 6.12 shows a comparison between Method 1, Method 2 using a 4-degree
polynomial fit, and Method 3 (integration by parts and the derivative of the fragility curve).
Using Method 3 gives 𝜆𝑐 = 3.97×10-4 and the seismic collapse risk of 1.97% in 50 years (red
line). For reference, the seismic collapse assessment by Eads et al. (2013) using a 4-degree
polynomial curve fit determined that the collapse rate was 𝜆𝑐 = 3.51×10-4.
212
Numerical Derivative
of Hazard Curve
Derivative
of Fitted
Hazard
Curves
MCE
a) Seismic hazard b) Deaggregation of risk
c) Cumulative collapse risk over exposure time (50 years)
Figure 6.11 Seismic hazard, deaggregation of collapse risk, and cumulative risk
(example 4-story ductile moment frame building)
The method used to calculate risk may significantly affect the collapse assessment. Both
the contribution of different hazards to this risk (the deaggregation shown in the Figure 6.12a)
and the cumulative value of risk calculated (Figure 6.12b) varied. The derivative of the fragility
curve (Method 3) was a more stable approach compared to using the other methods, because the
213
derivative of the hazard curve was avoided. Besides, using a curve-fit (Method 2) was not
necessarily more accurate, because the derivative of the curve was unstable.
The deaggregation of the risk was also different in each method because the numerical
integration of incremental hazard (𝑑𝑑) differed for each method. Thus, Method 1 and Method 3
produced the same value of risk, but differed in terms of hazard contributions, which is easily
visualized using deaggregation. Deaggregation of collapse risk was analogous to using
deaggregation of ground motion to ascertain magnitude and distance pairs that are primary
contributors to hazard (Chapman 1995).
Using Method 2, risk may be over- or under-estimated, depending on the shape of the
hazard curve relative to the fragility curve. Hazard curve points are derived from interpolated
data, so the validity of using a fitted curve is questionable. Furthermore, fitted curves were
sensitive at low values of spectral accelerations. This may be an additional concern for
ascertaining multi-hazard performance at lower intensity levels (i.e. serviceability and immediate
occupancy levels).
MCE
Derivative of Fragility Curve
Numerical Derivative
of Hazard Curve
Derivative of Fitted
Hazard Curve
a) Deaggregation of risk b) cumulative risk (50 years)
Figure 6.12 Hazard, deaggregation of risk, and cumulative risk for example structure
214
6.1.7 Regional Risk
The sensitivity of the seismic collapse assessment to regional risk was explored by contrasting
two locations: a location with frequent seismicity, in the San Francisco bay area (38.0° latitude,
-121.7° longitude), and a location with infrequent seismicity, in the Memphis metropolitan area
(35.2° latitude, -89.9° longitude).
The deaggregation of seismic hazard (spectral acceleration) corresponding to a long-
period structure (T = 1.0 seconds) is shown in Figure 6.13 and Figure 6.14 for both locations.
For San Francisco (Figure 6.13) the dominant contribution to hazard was along one fault line
producing magnitude 5.0 to 7.0 earthquakes. For Memphis (Figure 6.14) the dominant hazard
was one fault (New Madrid) about 60 km away. Compared to San Francisco, however, in
Memphis there are large uncertainties with respect to source and size of potential earthquakes.
Structural vulnerability results for partially-restrained composite-connection (PR-CC)
moment frame buildings (summarized earlier in Chapter 4 Table 4.9) indicate the lateral system
static overstrength is somewhat less than anticipated, keeping in mind that the overstrength factor
Ω in ASCE 7-10 is a conservative upper bound intended to protect vulnerable components. The
primary collapse mechanism of the buildings is generally column hinging of the lower story
columns (see Chapter 4). The low collapse margin ratios adjusted for spectral shape and period
elongation (as reflected in the ACMR) for the 4 story buildings (performance groups 1 and 2)
suggest that the mid-rise buildings were more sensitive to collapse than higher-rise buildings.
215
Figure 6.13 Seismic hazards for San Francisco bay area location
(Generated using USGS utility https://geohazards.usgs.gov/deaggint/2008/)
Table 6.3 gives the collapse risk for each building performance group. Site response was
included based on the NEHRP relationship and topographic data. Seismic collapse risk was
calculated based on achieving the ACMR values in Table 4.9. It is noted that this definition of
fragility (achieving the ACMR) represents the predicted sensitivity of code-conforming PR-CC
buildings in general, not the sensitivity of the specific buildings proportioned in the analytical
study by Bozorgmehr (2012). For this reason, building fragility was not constant (it increased or
decreased geographically) and was for a consistent safety margin.
216
Figure 6.14 Seismic hazards for Memphis metropolitan area location
(Generated using USGS utility https://geohazards.usgs.gov/deaggint/2008/)
The assessment was fairly insensitive to the 𝑉𝑠30 , but highly sensitive to the method used
to calculate the risk (𝜆𝑐 = 2.57×10-4 collapses per year using the derivate of the fragility curve,
compared to 𝜆𝑐 = 7.44×10-4 collapses per year using the derivative of the fitted hazard curve).
All the PR-CC buildings meet the acceptable risk objective of the building code (seismic
collapse risk not greater than 1% in 50 years), except for 4-story buildings with a 12-foot story
height in the San Francisco location. Surprisingly, for 6- to 8-story buildings, the risk of collapse
in the Memphis location was greater than in the San Francisco location.
217
Importantly, a deaggregation of the seismic collapse risk (not shown in Table 6.9) reveals
that the contribution to risk shifts from likely events (earthquakes with return periods less than
2,475 years) to unlikely events (earthquakes with return periods greater than 2,475 years).
Table 6.9 Collapse risk analysis of PR-CC buildings
Performance Group Summary Risk analysis (Prob. collapse in 50 years)
No. Stories Hx (ft) Te (s) ACMR SF Memphis

1 4 12 0.87 2.19 1.30% 0.76%
2 4 14 0.98 2.89 0.45% 0.39%
3 6 12 1.2 3.99 0.12% 0.17%
4 6 14 1.36 3.96 0.12% 0.17%
5 8 12 1.51 4.74 0.05% 0.10%
6 8 14 1.71 4.25 0.08% 0.14%
218
6.1.8 Site Response
This section explores the effect of site response on the seismic collapse assessment of the Type I
4-story non-ductile moment frame building. The maps were generated by integrating seismic
hazard and collapse fragility at every 0.5-degree latitude and longitude.
Figure 6.15 compares the sensitivity of the seismic collapse assessment to the method
used to correlate the average shear wave velocity with soil amplification of ground motion,
assuming 𝑉𝑠30 = 180 m/s (D/E boundary). The response not including the lateral reserve strength
of the shear tab connections is indicated in blue. The response including the reserve lateral
strength from the shear tab connections is indicated in purple. The response including both
reserve lateral strength and a slack cable collapse prevention system is indicated in orange.
Figure 6.15a shows contoured regions where the risk of collapse exceeds 1% in 50 years
using the NEHRP/ASCE 7-10 (ASCE 2010) soil amplification method. Figure 6.15b shows
contoured regions where the collapse risk exceeds 1% in 50 years using the NGA WUS soil
amplification method and assuming 𝑉𝑠30 = 180 m/s (D/E boundary). The predicted difference in
seismic collapse risk was significant in the central and eastern United States.
The sensitivity of the assessment to using topographic data as a proxy for average shear
wave velocity in the top 100 feet of the soil is shown in Figure 6.16. Again the predicted
difference in conditional collapse was significant, but to a lesser extent.
219
a) NEHRP/ASCE 7-10 soil amplification method
b) NGA WUS soil amplification method
Figure 6.15 Contour regions where the seismic collapse risk exceeds 1% in 50 years
𝑉𝑠30 = 180 m/s (D/E boundary), Type I non-ductile moment frame 4-story building
220
a) NEHRP/ASCE 7-10 soil amplification method
b) NGA WUS soil amplification method
Figure 6.16 Contour regions where the seismic collapse risk exceeds 1% in 50 years
𝑉𝑠30 based on topographic proxy data, Type I non-ductile moment frame 4-story building
221
6.2 Wind Collapse Sensitivity
This section discusses the sensitivity of the wind collapse assessment to the characteristic
equivalent single-degree-of-freedom model used to represent the main wind-force resisting
system (MWFRS) and the gravity framing system, to the static overstrength of the building
determined in a wind pushover analysis, to damping, to the fundamental period of vibration of
the building, to cyclic degradation of the characteristic system behavior, and to the duration of
the wind event.
The Type III non-ductile moment frame 10-story building is considered. As previously
discussed (in Chapter 3), the building was a composite steel-frame building designed for a basic
wind speed of 115 mph and ASCE 7-10 terrain exposure category C. The equivalent lateral
strength of the main wind-force resisting system relative to the building weight, (𝑉𝑚𝑚𝑚 /𝑊) was
0.1, based on a wind pushover analysis of the Type II 10-story building (Chapter 5). Although it
is acknowledged that the lateral pushover strength is building-specific, the 0.1 value was used as
a baseline for comparison of differing main wind-force resisting systems in the sensitivity study.
When considering the effects of gravity framing, the lateral strength contribution from gravity
framing was conservatively assumed to be 10% compared to the MWFRS (Judd and Charney
2014b). This value was also recognized to be building-specific and was only used to establish a
baseline for comparison in the sensitivity study.
The fundamental period, 𝑇𝑤 was approximated by the building height, 𝐻/75 = 1.8
seconds, based on ASCE 7-10 (ASCE 2010) Equation C26.9-7. This equation is valid for up to
300-ft tall buildings. Building “density” was estimated to be 8 pcf based on the building weight,
𝑊 equal to 16,200 kips. The wind base-shear force, 𝑉𝑤𝑤𝑤𝑤 was equal to 515 kips, and the
corresponding wind base shear coefficient, 𝐶𝑠−𝑤𝑤𝑤𝑤 was equal to 0.032.
222
Figure 6.17 shows the monotonic envelope and fully-reversed cyclic behavior of the
characteristic main wind-force resisting systems investigated. Three types of steel moment
frame (MF) systems (non-ductile, semi-ductile, and ductile) were considered. The non-ductile
moment frame was intended to be representative of a fracturing steel moment frame. The semi-
ductile moment frame was intended to be similar to the intermediate moment frame (“IMF”)
system used in structures detailed for seismic resistance. The ductile moment frame was
intended to be representative of special moment frame (“SMF”) seismic systems, such as steel
moment frames with reduced-beam-sections. Stiff non-ductile (braced) frames, and shear wall
main wind-force resisting systems were also considered for purposes of comparison.
The potential effect of three types of gravity framing (GF) systems, non-ductile, semi-
ductile, and ductile (typical gravity framing with shear-tab connections) was incorporated.
Characteristic behavior of the gravity framing systems is shown in Figure 6.18.
Force-deformation behavior parameters used in this study, including in-cycle
degradation, matched those parameters used in FEMA P-440A (FEMA 2009b), except for the
parameters for the semi-ductile main wind-force resisting system, which were used for
comparison purposes in this study. The semi-ductile main wind-force resisting system
parameters used in this study were based on the AISC Seismic Design Manual (AISC 2012)
story drift ratio requirement (0.02) for intermediate moment frames, and a monotonic envelope
approximately halfway between the ductile and non-ductile responses.
The results of the sensitivity studies are summarized in Table 6.10 to Table 6.15 (shown
in subsequent pages) for the baseline duration (28 minutes) and a reference wind speed of 20
mph.
223
1 Monotonic 1 Semi-ductile MF
Non-ductile MF
envelope
0.5 0.5
Moment (k-in.)
Moment (k-in.)
0 0
Fully-reversed
-0.5 cyclic response -0.5
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1

1 Ductile MF 1 Braced Frame
0.5 0.5
Moment (k-in.)
Moment (k-in.)
0 0
-0.5 -0.5
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1

1 Shear Wall
0.5
Moment (k-in.)
-0.5
-1
-0.1 -0.05 0 0.05 0.1

Rotation (rad)
Figure 6.17 Characteristic main wind-force resisting system (MWFRS)
224
1 Non-ductile 1 Semi-ductile
0.5 0.5
Moment (k-in.)
Moment (k-in.)
0 0
-0.5 -0.5
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1

1
Ductile
0.5
Moment (k-in.)
-0.5
-1
-0.1 -0.05 0 0.05 0.1

Rotation (rad)
Figure 6.18 Characteristic gravity framing (GF) system
6.2.1 Main Wind-Force Resisting System and Gravity Framing System
The sensitivity of wind collapse assessment to the characteristic main wind-force resisting
system was determined. Table 6.10 shows that all the characteristic main wind-force resisting
systems passed the target risk (established based on ASCE 7-10, as described in Chapter 5),
except for the non-ductile moment frame system. It should be emphasized that the results are
intended for comparative purposes only. The results were partly subjective due to the
incorporation of epistemic uncertainty. Moreover, the tabulated results were only for the interior
225
of the United States without consideration of tornado wind hazards. Figure 6.19a shows regions
of the United States where the wind collapse risk exceeds 0.35% for the non-ductile moment
frame system. Figure 6.19b shows the effect of including tornado hazards. The non-ductile
moment frame system has a high wind-collapse risk in much of central United States and along
the southern and eastern coastlines.
The results in Table 6.10 suggest that some ductility or moderate degree of reserve
capacity was effective at reducing risk, but highly ductile systems may not necessarily reduce the
wind collapse risk.
The effect of the type of gravity framing system is given in Table 6.11. The reserve
strength of the gravity framing always increased the CMR and lowered the collapse risk,
compared to the main wind-force resisting system alone (Table 6.10), but the type (ductility) of
the gravity frame system was not significant relative to the moment-frame type (ductility).
Table 6.10 Effect of Main Wind-Force Resisting Framing System (MWFRS)
MWFRS Tw (s) CMR βRTR βTotal Pf,50

Non-ductile MF 1.41 0.047 0.149 0.30%
Semi-ductile MF 1.55 0.060 0.154 0.08%
Ductile MF 1.80 1.60 0.064 0.155 0.05%
Braced Frame 1.55 0.040 0.147 0.06%
Shear Wall 1.55 0.056 0.152 0.07%
Table 6.11 Effect of gravity framing system
Gravity Frame (GF) MF/GF CMR βRTR βTotal Pf,50

Non-ductile Moment Frame (MF)
Ductile 1.46 0.042 0.147 0.16%
Semi-ductile 0.10 1.48 0.047 0.149 0.14%
Non-ductile 1.48 0.046 0.149 0.14%
Ductile Moment Frame (MF)
Ductile 1.63 0.067 0.156 0.03%
Semi-ductile 0.10 1.65 0.053 0.151 0.02%
Non-ductile 1.63 0.060 0.154 0.03%
226
Wind collapse
risk exceeds
0.35% in 50 years
a) Extrapolated ASCE 7-10 wind hazards
Wind collapse
risk exceeds
0.35% in 50 years
b) Extrapolated based on tornado wind hazards
Figure 6.19 Regions where wind collapse risk exceeds 0.35% in 50 years (non-ductile MF)
227
6.2.2 Static Overstrength
The effect of strength and ductility for steel moment frame systems is examined in Table 6.12.
The assumed lateral strength ratio was varied from the baseline condition, 0.1 up to 0.7 in order
to examine if a moderately-ductile system with a reduced relative strength provides the same
wind collapse safety as a stronger non-ductile system. (The lateral strength ratio is roughly
equivalent to the inverse of an “R” value for wind.) The results, based on an equivalent single-
degree-of-freedom model and a target wind collapse risk of 0.15% in 50 years, lead to a
maximum wind R equal to 1.10, for the Type III non-ductile moment frame 10-story building.
Table 6.12 Effect of lateral strength ratio and ductility
MWFRS Fmax/W CMR βRTR βTotal Pf,50

Non-ductile MF 0.100 1.41 0.047 0.149 0.30%
0.100 1.55 0.060 0.154 0.08%
0.095 1.53 0.057 0.153 0.09%
0.090 1.48 0.053 0.151 0.15%
Semi-ductile MF 0.085 1.46 0.063 0.155 0.21%
0.080 1.43 0.060 0.154 0.29%
0.075 1.39 0.059 0.153 0.41%
0.070 1.34 0.058 0.153 0.71%
228
6.2.3 Damping, Fundamental Period, and Cyclic Degradation
The effect of damping and the fundamental period is shown in Table 6.13, and the effect of
cyclic degradation is shown in Table 6.14. For comparison with the baseline model, the
fundamental period was calculated using ASCE 7-10 (ASCE 2010) Equation 26.9-2 through
Equation 26.9-4. These equations relate to the lower-bound of measured natural frequency data
of actual buildings.
The CMR, dispersion, and the collapse risk were sensitive to the level of damping
assumed in the analysis, as expected, but were less sensitive to the fundamental period
estimation. The effect of cyclic degradation in the characteristic system (gravity frame was not
included) was significant, doubling the risk of wind collapse.
Table 6.13 Effect of damping and fundamental period on non-ductile moment frame
MWFRS CMR βRTR βTotal Pf,50

ζ=1.0% 1.41 0.047 0.149 0.30%
Damping
ζ=2.5% 1.50 0.046 0.149 0.11%
T w =1.80s 1.41 0.047 0.149 0.30%
Fundamental Period
T w =2.28s 1.39 0.042 0.147 0.34%
Table 6.14 Effect of cyclic degradation
Cyclic Degradation CMR βRTR βTotal Pf,50

Non-ductile Moment Frame (MF)
Included 1.41 0.047 0.149 0.30%
Not included 1.50 0.065 0.156 0.14%
Ductile Moment Frame (MF)
Included 1.60 0.064 0.155 0.05%
Not included 1.69 0.067 0.156 0.02%
229
6.2.4 Wind Duration
The effect of wind load duration is shown in Table 6.15. For illustration, the along-wind (Figure
6.20) and cross-wind (Figure 6.21) responses, respectively, are shown for four intensity levels:
reference, strength-level, prior to collapse, and at collapse wind speeds. The left column of each
figure shows the responses for the baseline duration (28 minutes). The right columns show the
responses for the 138-minute (2.3 hours) duration. The wind load history is shown in the upper
plot. Load values are normalized in terms of the building weight. The hysteresis behavior is
shown in the middle plot. Load values are normalized relative to the lateral strength of the
equivalent single-degree-of-freedom model. The drift ratio history is shown in the lower plot.
Ratcheting of the lateral load was especially evident in the along-wind response. For the ductile
moment frame model, collapse was imminent for drift ratios between 0.02 and 0.04.
Figure 6.22 shows the incremental dynamic analyses for both durations. The collapse
margin ratio (CMR) was calculated as the ratio of the median collapse intensity to the strength-
level intensity (115 mph for Risk Category II). Duration led to a 6% difference in CMR.
Clearly, the duration had a profound effect (evident in Figure 6.20 and Figure 6.22), but
the relationship between duration and risk was not predictable. It is postulated that the
unpredictable effect of duration may be caused, in part, due to the replayed wind load history
records. A more robust study, however, is required to better understand the relationship.
Table 6.15 Effect of duration on ductile moment frame system
MWFRS CMR βRTR βTotal Pf,50

28 1.60 0.064 0.155 0.05%
55 1.51 0.059 0.153 0.11%
Duration (min.)
138 1.50 0.049 0.150 0.12%
257 1.44 0.036 0.146 0.18%
230
0.1 0.1
0.08 0.08
0.06 0.06

0.04 0.04
0.02 0.02
0 0
-0.02 -0.02
-0.04 -0.04
-0.06 -0.06
-0.08 -0.08
-0.1 -0.1
0 5 10 15 20 0 10 20 30 40 50 60 70 80
Time (min) Time (min)
1 1
0.8 0.8
0.6 0.6

0.4 0.4
0.2 0.2
0 0
-0.2 -0.2
-0.4 -0.4
-0.6 -0.6
-0.8 -0.8
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1
Drift ratio Drift ratio
a) 28-minute duration b) 138-minute duration
Figure 6.20 Along-wind (90°) response history for ductile moment frame system
231
0.1 0.1
0.08 0.08
0.06 0.06

0.04 0.04
0.02 0.02
0 0
-0.02 -0.02
-0.04 -0.04
-0.06 -0.06
-0.08 -0.08
-0.1 -0.1
0 5 10 15 20 25 0 20 40 60 80 100
1 1
0.8 0.8
Maximum strength-
0.6 0.6
level demand

0.4 0.4
0.2 0.2
0 0
-0.2 -0.2
-0.4 -0.4
-0.6 -0.6
-0.8 -0.8
-1 -1
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1
Drift ratio Drift ratio
0.05 0.05
0.04 0.04 Collapse (174 mph)

0.03 0.03
0.02 0.02
0.01 0.01
Drift ratio
Drift ratio
0 0
-0.01 -0.01
-0.02 -0.02
-0.03 -0.03
-0.04 Collapse (194 mph) -0.04
-0.05 -0.05
0 5 10 15 20 25 0 20 40 60 80 100
Figure 6.21 Cross-wind (0°) response history for ductile moment frame system
232
220 220
Median
200 200
collapse
180 180
160 160
CMR = 1.60
Wind speed, V (mph)
Wind speed, V (mph)

140 140 CMR = 1.50
120 (Risk Category II) 120
100 100
80 80
60 60
40 40
20 20
0 0
0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05
Maximum drift ratio Maximum drift ratio
Figure 6.22 Incremental dynamic analyses curves for ductile moment frame system
233
6.3 Discussion
Collapse assessments were generally sensitive to parametric changes in hazard or analytical
modeling. The seismic collapse assessment was sensitive to the inclusion of column splices and
the inclusion of splices changed the predicted static collapse story mechanism. The seismic
collapse assessment was sensitive to the ground motion variability. Measured dispersion in
incremental dynamic analysis curves was much wider for ground motions spectrally matched to
the target spectrum, compared to the original (un-matched) FEMA P-695 Far Field set), a
probable reflection of high and low frequency content outside the matching bounds. Spectral
acceleration intensity measures defined by longer periods slightly decreased the conditional
probability of seismic collapse.
The method used to integrate hazard and collapse fragility significantly affected both the
predicted contribution of different hazards to the annual risk rate, and the calculated cumulative
value of collapse risk. When applied in seismic analysis, the collapse risk prediction was
sensitive to the method used to incorporate site response.
For seismic analysis, the methods used to represent panel zones and to account for
second-order effects were most significant. The differences in response from the ductile and
non-ductile frames originate in the details for the design of each frame. The non-ductile frame
was designed with components that cannot sustain large ductility demands without failure, as
opposed to the detailing for the ductile frame. As is observed from comparing the incremental
dynamic analysis curves, the ductile frame buildings were capable of sustaining greater
interstory drift ratios than the non-ductile frame buildings. Increasing the drift in the stories of
the ductile frame increased the ductility demand on the hinges in the beams and columns, which
caused collapse at lower ground motion intensity values. Therefore, analytical modeling
234
approaches that increased interstory drift ratios had a larger effect on the non-ductile frame
buildings. In addition, the inability for the connections in the non-ductile frame to sustain large
ductility demands increased the sensitivity of the seismic collapse assessment when considering
variations in ground motion records. The higher sensitivity was demonstrated by higher β Total
values from the non-ductile frame compared to the values from the ductile frame buildings.
Comparing the collapse response of the baseline non-ductile model to the response of the
models with the centerline and scissors approaches for the panel zone indicates the effect of
stiffening the panel zone joint. The centerline approach stiffened the structure compared to the
Krawinkler and scissors approaches, as was indicated by comparing the fundamental periods of
vibration. Stiffening the structure increased the spectral acceleration associated with the median
collapse value, but the collapse margin ratio was similar to the collapse margin ratio from the
models with the Krawinkler and scissors joints because of the increase in spectral acceleration at
the MCE-level ground motion.
As anticipated, changing from a second-order analysis to a first-order analysis in the non-
ductile frame had a large effect on the collapse response. The first-order approach was incapable
of modeling the destabilizing effects of the gravity loads, which effects reduced the interstory
drift ratios in the model and increased the collapse resistance. The inability of the non-ductile
frame buildings to sustain large, repeated interstory drift ratios prevented the systems from
reaching large interstory drift ratios where the differences between the corotational and P-∆
approximation are amplified before the building collapses.
As with the non-ductile frame buildings, the largest differences in response for the ductile
frame among changes in modeling approaches occurred for the change from a first-order to
second-order approach. However, the ability for the ductile frame to reach higher interstory drift
235
ratios before collapse amplified the differences in modeling approaches, as demonstrated by the
conditional collapse probability values at MCE level ground motion intensity. The larger
interstory drift ratios also enabled the building to demonstrate differences in the collapse
resistances between employing the corotational and P-∆ approximation. The ability for the
corotational approach to model large displacements enabled the ductile frame building model to
better distribute ductility demand throughout the structure, increasing the collapse resistance of
the building.
Changing from the Krawinkler or scissors panel zone joint model to a centerline model
stiffened the ductile frame, as was observed for the non-ductile frame building. The increased
collapse resistance from the centerline model also did not have a large effect on the collapse
margin ratio because of the larger spectral acceleration associated with the MCE-level ground
motion. However, the building with the Krawinkler joint representation had a greater collapse
margin ratio than the frame using the scissors approach. The differences in response between the
models with the Krawinkler and scissors panel zone were due to the larger deformations in the
beam-to-column joints (Charney and Marshall 2006).
Wind analysis was similar to seismic analysis in that the inelastic behavior and
subsequent collapse risk was sensitive to the ratio of critical damping assumed, the incorporation
of cyclic degradation, and the inclusion of the gravity framing in the model.
For the specific building studied, ductility or reserve capacity was effective at increasing
the collapse safety and reducing the risk of collapse. Highly ductile systems did not necessarily
lead to matching improvements in response. Adding a limited degree of ductility to the moment
frame system, similar to that provided by a so-called intermediate moment frame in seismic
design, could justify the use of a wind response modification factor “R”.
236
Chapter 7
SEISMIC PERFORMANCE ASSESSMENT
This chapter discusses the seismic performance of archetype structural systems. Performance, in
terms of repair costs and downtime, was assessed at serviceability and design hazard levels based
on the structural and non-structural component fragility using floor accelerations and inter-story
drift from nonlinear response history analyses. Resilience was quantified by calculating the
probable loss in functionality during a reference time interval. Resilience contours were used to
characterize the tradeoff between construction and repair costs, and the ability to recover rapidly
after an earthquake.
7.1 General Procedures
The improved seismic performance of the Type I non-ductile and ductile moment-frame
buildings was assessed using the FEMA P-58 framework (FEMA 2012a,b,c) and companion
software, Performance Assessment Calculation Tool (PACT) (FEMA 2012d). The non-ductile
moment framing buildings (designed for wind, SDC B min ) were assessed for serviceability
considering reserve lateral strength in the gravity framing, and with collapse inhibiting
mechanisms augmented with energy dissipation devices. The ductile moment frame buildings
237
(designed for SDC D max ) were assessed for both serviceability and design-level performance
(DBE level ground motions), considering reserve lateral strength.
This assessment was accomplished in a two-tier process. First, the structural response for
a given hazard intensity level was determined (using the same analytical models used for the
collapse assessment). Second, the sensitivity of structural components, non-structural
components, and other critical components of the building to ground shaking was determined
using PACT and the structural response results.
7.1.1 Ground Motion Set for Nonlinear Response History Analysis
A subset (Table 7.1) of the FEMA P-695 “Far-Field” ground motion set was used. The scaling
procedure was a multi-step scaling process. The ground motion record was first scaled (in
FEMA P-695) by a factor to normalize the velocity of the ground motion set. Next the ground
motion record was scaled so that the median of the record set spectral acceleration was equal to
the target design spectrum spectral acceleration at the target period. Finally, the record was
incrementally scaled relative to the normalization factor times the anchor factor.
Table 7.1 Ground motion set (FEMA P-695 Far-Field set) used for dynamic analysis
FEMA P-695 ID Record Name Earthquake Magnitude

1 Beverly Hills - Mulhol 1994 Northridge 6.7
2 Canyon Country-WLC USC 1994 Northridge 6.7
11 Yermo Fire Station CDMG 1992 Landers 7.3
15 Abbar BHRC 1990 Manjil, Iran 7.4
17 Poe Road (temp) 1987 Superstition Hills 6.5
18 Rio Dell Overpass 1992 Cape Mendocino 7
21 LA - Hollywood 1971 San Fernando 6.6
238
The ground motion records were scaled relative to an anchor magnitude of intensity. The
anchor magnitude of intensity was the scaling value applied to the ground motion record in order
for the ground motion record to match a target spectral acceleration for a target period of
vibration. This differed from the scaling procedure used in a seismic collapse assessment
(Chapter 5).
The advantage of the anchor scaling method used in this Chapter was that the response
was determined at exactly the hazard level of interest for the intensity measure. A disadvantage
was that the results were not conveniently converted to other anchor spectrums. Also, the
fragility curve will show equal-intensity measured collapse points (vertical “dots” in the fragility
figure) since ground motions are applied at discrete intensity levels (so failure is shown at
discrete intensity levels).
As an example, Figure 7.1 shows the response spectrum for the Type I non-ductile
moment frame 2-story building including reserve strength in the gravity framing. The sub set of
ground motions was normalized using the FEMA P-695 Toolkit (Hardyneic 2014).
7.1.2 Structural and Non-structural Component Fragility
The component fragilities used in the assessment were determined using the FEMA P-58
Normative Quantity Estimation Tool. As an example, Table 7.2 summarizes the component
fragilities used in the assessment of the Type I non-ductile moment frame buildings. Structural
components consisted of beam-to-column connections, column splices, and base plates.
Although components of the collapse-inhibiting mechanism, such as cables, links, and HSS
members could not be included (since the fragility test data was not yet available), it is likely that
the ease of access and size would mitigate (lower) costs, compared to other components. Non-
239
structural components included a variety of items, ranging from mechanical, electrical, and
plumbing (MEP) to exterior cladding and partition walls. Earthquake ground shaking intensity
was correlated to component performance by median demand 𝜃, and dispersion, 𝛽 parameters.
Structural components used interstory drift ratio (IDR). Non-structural components used
floor or roof acceleration. All IDR parameters were directional, meaning that the performance
depended on the direction of ground motion relative to the principal directions of the building
(longitudinal or transverse), and all accelerations are non-directional.
Quantities of components were estimated using the FEMA P-58 spreadsheet tools
(FEMA 2012c) and depended on the number of stories and the component type. For example,
buildings with the moment frame columns not fixed at the base (1- and 2-story buildings) did not
utilize the base plate fragility.
4.5
4
Scaled sub-set of FEMA P-695
Far-Field Ground Motion Set

3.5
3
Median spectrum
2.5
2
1.5
Target period, T1
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds/cycle)
Figure 7.1 Response spectrum for Type I non-ductile 2-story building
240
Table 7.2 Summary of component fragilities used for Type I non-ductile buildings
Demand
Component Description (FEMA P-58 Fragility ID) Quantity
Parameter
Structural Components
Non-ductile, Pre-Northridge WUF-B, single sided (B1035.041) 4 IDR
Beam-to-column connections Non-ductile, Pre-Northridge WUF-B, double sided

4 IDR
(B1035.051)
Gravity frame, bolted shear tab (B1031.001) 32 IDR
Base plates with column W < 150 plf (B1031.011a) 8 IDR
Moment frame columns
Column W < 150 plf (B1031.021a) 8 IDR
Non-Structural Components
Curtain Walls (B2022.001) 4,200 sf IDR
Wall Partition (C1011.001a) 1,400 lf IDR
Prefabricated steel stair (C2011.001b) 2 ea IDR
Wall Partition (C3011.001a) 106 lf IDR
Raised Access Floor (C3027.001) 10,500 sf Acceleration
Suspended Ceiling (C3032.001a) 12,600 sf Acceleration
Independent Pendant Lighting (C3034.001) 210 ea Acceleration
All stories Cold Water Piping (D2021.011a) 210 lf Acceleration
HVAC Metal Ducting (D3041.011a) 1,050 lf Acceleration
HVAC Metal Ducting (D3041.012a) 280 lf Acceleration
HVAC Drops (D3041.031a) 126 ea Acceleration
(VAV) box (D3041.041a) 98 ea Acceleration
Fire Sprinkler Water Piping (D4011.021a) 2,800 lf Acceleration
Fire Sprinkler Drop (D4011.031a) 126 ea Acceleration
Low Voltage Switchgear (D5012.021a) 225 ea Acceleration
1st story Traction Elevator (D1014.011) 4 ea Acceleration
Chiller (D3031.011a) 360 tn/ea Acceleration
Cooling Tower (D3031.021a) 360 tn/ea Acceleration
Roof
Air Handling Unit (D3052.011a) 88,200 cf Acceleration
Motor Control Center (D5012.013a) 6 ea Acceleration
241
7.2 Predicted Seismic Performance
Comprehensive building seismic performance for Type I buildings and Type II buildings was
predicted in PACT using 200 Monte Carlo simulations using the results from the structural
analysis (interstory drift ratio and floor/roof accelerations) and the median demand values and
dispersion for all component fragilities and associated damage consequences.
7.2.1 Type I Non-ductile Moment Frame Buildings
A sub-set of 7 ground motion component pairs was selected from the FEMA P-695 Far-Field
Suite. For serviceability-level performance, the ground motions were scaled to 10% of the
spectral acceleration corresponding to the MCE ground motion level. As previously discussed in
Chapter 2, this intensity level generally corresponds to a 72-year MRI for the central and eastern
United States. For design-level (DBE) performance, the ground motions were scaled to 67% of
the spectral acceleration corresponding to the MCE ground motion level (with roughly a 475-
year MRI). A similar evaluation at other intensity levels was performed in a related study
(Jarrett et al. 2015).
Figure 7.2 shows median peak interstory drift ratio (IDR) and accelerations for the 4-
story non-ductile moment-frame building. The collapse prevention system using loose-linkages
with dampers limited the drift ratio below the threshold limit for visual damage under wind loads
(0.003) (Griffis 1993). Accelerations exceed the threshold for human comfort (0.025 g) at high-
frequency motion in an office building (Griffis 1993; Murray et al. 2003; Griffis et al. 2012),
although this is probably not an issue for the short duration of shaking.
The sensitivity to ground motion for two selected components is shown in Figure 7.3. In
FEMA P-58 sensitivity is described in terms of “damage” consequences. There are three
242
damage states and associated consequences for wall partitions, but only one damage state for
chillers. Based on comparing the fragility curves with the median peak interstory drift ratio and
acceleration response, the collapse prevention system using loose-linkages with dampers
eliminated moderate and significant damage to wall partitions. Damage to shear-tab connections
is unlikely to be important at this intensity level, but serious damage to the chiller is possible.
For reference, exterior cladding damage fragility (not shown) has a median demand, 𝜃 = 0.04
interstory drift ratio and dispersion, 𝛽 = 0.4. Thus, no damage to glazing is expected.
Table 7.3 to Table 7.5 summarize the seismic performance (relative to SDC D max ) in
terms of the median repair cost, 𝐶𝑅𝑅𝑅𝑅𝑅𝑅 and time, 𝑡𝑅𝑅𝑅𝑅𝑅𝑅 , and the probability of unsafe placards
determined in the PACT analyses. Design level performance was only assessed for the ductile
moment frame buildings. Resilience, R was calculated using Equation 7.1 originally proposed
by Bruneau and Reinhorn (2007) and used by Cimellaro et al. (2010). In Equation 7.1 the
reference time, 𝑡𝑐 was taken as 60 days.

𝑡𝑐
𝑅 = � [1 − 𝑄(𝑡)]𝑑𝑑 (7.1)
𝑡0
1 𝐶𝑅𝑅𝑅𝑅𝑅𝑅 + 𝑃 𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐶𝑇𝑇𝑇𝑇𝑇𝑇 𝑡𝑅𝑅𝑅𝑅𝑅𝑅

= 1− � ��
2 𝐶𝑇𝑇𝑇𝑇𝑇 𝑡𝑐
The total replacement cost, 𝐶𝑇𝑇𝑇𝑇𝑇 of a moment-frame building has been suggested in the
literature (RSMeans 2013; ENR 2011; Zareian 2012) to be anywhere from 150-350 dollars/sf,
where the upper end of cost was representative of construction on the west coast. In this study,
the focus was on steel-framed buildings constructed in a low or moderate seismic area in the
central and eastern United States, so the total replacement cost for the prototype building was
estimated at 230 dollars/sf with 30% attributed to the core and shell (building cost excluding
tenant improvements, 𝐶𝑇𝑇𝑇𝑇𝑇𝑇 ) (Cheever 2013).
243
4 4
MF
MF
3 3
Story
Story
MF+GF
+LL +LL
MF+GF
2
(ζ=10%) 2
(ζ=10%)
1 1
0 0.002 0.004 0.006 0.008 0.01 0.012 0 0.05 0.1 0.15 0.2
IDR Floor Acceleration
a) Median inter-story drift ratio (IDR) b) Median peak floor acceleration (g)
Figure 7.2 Median response for 4-story non-ductile moment-frame building at 10% of MCE.
1 1
Minor cracking of wall
board or tape
0.8 0.8
Moderate cracking or
P(Fail|x=IDR)
P(Fail|x=a)
0.6 crushing of wall board 0.6
0.4 0.4
Significant cracking and/or Damaged, inoperative
crushing of wall board, buckling
0.2 of studs and tearing of tracks 0.2
0 0
0 0.002 0.004 0.006 0.008 0.01 0.012 0 0.05 0.1 0.15 0.2
IDR Peak Floor Acceleration, a (g)
a) Wall partition fragilities b) Chiller fragility
Figure 7.3 Selected component fragilities (sensitivity to ground motion).
An implicit assumption of Equation 7.1 was a linear recovery “trajectory” (relationship
between recovery time and functionality). The linear trajectory was intended to represent an
average post-earthquake response, but the equation could easily be re-derived for trigonometric
and exponential recovery trajectories, representative of a below or above average post-
earthquake response, respectively (e.g. Cimellaro et al. 2010).
244
Table 7.3 Serviceability (10% of MCE) performance of Type I non-ductile buildings
Repair Prob. of
Archetype Unsafe Resilience
Model Cost ($) Time (days) Placards R
1-story
MF 277,500 50 0.49 0.82
MF+GF 220,000 32 0.26 0.93
+LL (ζ=10%) 108,500 19 0.10 0.98
+TB (ζ=10%) 115,000 20 0.10 0.98
2-story
MF 330,000 36 0.21 0.94
MF+GF 266,250 32 0.15 0.96
+LL (ζ=10%) 181,250 23 0.05 0.99
+TB (ζ=10%) 172,000 23 0.05 0.99
4-story
MF 666,667 40 0.19 0.94
MF+GF 490,000 27 0.09 0.98
+LL (ζ=10%) 211,000 14 0.01 1.00
+TB (ζ=10%) 196,875 14 0.01 1.00
8-story
MF 1,192,000 48 0.10 0.95
MF+GF 775,000 29 0.03 0.99
+LL (ζ=10%) 458,333 18 0.01 1.00
+TB (ζ=10%) 445,000 18 0.01 1.00
The repair costs embedded in PACT and the FEMA P-58 documentation reflect costs for
northern California in 2011 (FEMA 2012b). The cost data was adjusted to reflect the national
average commercial construction costs by computing the national average cost (RSMeans 2013)
relative to the average cost of ten population centers in northern California (ranging from Santa
Rosa in the north, to San Jose in the south). A result, for use with PACT the region cost
multiplier was 0.867 and the date cost multiplier was 1.064. The repair time for the building was
estimated using typical construction schedules based advice from practitioners and the number of
stories (Jarrett et al. 2015), ranging from 357 days for 1-story and 2-story buildings, 392 days for
4-story buildings, and 462 days for 8-story buildings.
245
Table 7.4 Serviceability (10% of MCE) performance of Type I ductile buildings
Repair Prob. of
Unsafe
Archetype Cost ($) Time (days) Placards Resilience
1-story
MF 1,510,000 228 0.96 0.28
MF+GF 1,310,000 181 0.94 0.47
2-story
MF 1,540,000 137 0.87 0.68
MF+GF 1,560,000 142 0.87 0.67
4-story
MF 2,585,714 148 0.93 0.65
MF+GF 2,388,889 139 0.88 0.69
8-story
MF 4,100,000 162 0.87 0.65
MF+GF 3,800,000 156 0.85 0.68
Table 7.5 Design-level (67% of MCE) performance of Type I ductile buildings
Repair Prob. of
Unsafe
Archetype Cost ($) Time (days) Placards Resilience
1-story
MF 1,510,000 228 0.96 0.28
MF+GF 1,310,000 181 0.94 0.47
2-story
MF 1,540,000 137 0.87 0.68
MF+GF 1,560,000 142 0.87 0.67
4-story
MF 2,585,714 148 0.93 0.65
MF+GF 2,388,889 139 0.88 0.69
8-story
MF 4,100,000 162 0.87 0.65
MF+GF 3,800,000 156 0.85 0.68
246
The maximum number of workers per square foot (used to calculate repair time) was one
worker per 1,000 square feet (the default value in PACT). The ratio of repair cost to building
replacement cost, or “total loss threshold” was taken as 1.0 (the default value in PACT). A single
random seed value equal to 5 was used so that the analysis was repeatable. (Using a random
seed value equal to zero would lead to a unique simulation for each analysis that was not
repeatable.)
For the serviceability performance, the lateral strength in shear tab connections and the
collapse prevention system with energy dissipation devices contributed to a significant reduction
in both repair cost and downtime. The improvement was most dramatic in the 1-story building.
For the 1-story, 2-story, and 4-story buildings, the probability of an unsafe placard (“red tag”) for
the conventional building (moment frame only) is primarily due to the probability of structural
damage to the non-ductile moment frame connections. Collapse prevention systems were highly
resilient compared to the conventional building.
For the Type I ductile moment frame 8-story building designed for SDC D min , most
repair costs were caused by damage to the gypsum wall partitions. The reserve lateral strength
from the gravity framing reduced repair costs by 22%. The time required for repairs is correlated
to repair costs, and was dominated by repair time for the gypsum wall partitions. Figure 7.4
contrasts the repair times considering only the moment frame and including the reserve lateral
strength in the gravity framing. The bar colors indicate different component performance
groups. Interestingly, including the gravity framing actually increased the probable repair time
for some components (chiller). Placarding was caused due to prefabricated steel stair systems
with steel treads and landings without seismic joints. Reserve strength reduced the probability of
placarding from 9% to 3%.
247
Chiller Chiller
Wall partitions Type II Wall partitions Type II
a) Moment-frame only b) With reserve lateral strength
Figure 7.4 Serviceability level performance for Type I ductile moment frame 8-story building
For the Type I ductile moment frame 8-story building designed for SDC D max , most
repair costs were caused by damage to the gypsum wall partitions, as before, but there were other
significant contributions to repair costs, such as bolted shear tab gravity connections, and
unanchored chiller and air handling units. The reserve lateral strength from the gravity framing
reduced repair costs by 13%.
Repair time was dominated by gypsum wall partitions, but many other fragility
performance groups were significant contributors. The reserve lateral strength from the gravity
framing reduced the predicted mean repair time by 6 days (4%).
Unsafe placarding was mostly due to the prefabricated steel stair systems without seismic
joints, but there were several other components that contributed to the probability of unsafe
placards. Reserve strength slightly reduced the probability, with most improvement in reducing
placard associated with unbraced fire sprinkler water piping.
248
7.2.2 Type II Non-ductile 4-story Moment Frame Building
A sub-set of 7 ground motion component pairs was selected from the FEMA P-695 Far-Field
Suite. To investigate serviceability-level performance the ground motions were scaled to 5% and
10% of the spectral acceleration corresponding to the MCE ground motion level. As previously
discussed, these intensity levels generally correspond to a 43-year MRI and a 72-year MRI,
respectively, for the central and eastern United States. For comparison, similarly occurring
intensities would generically be 13% and 20% for the western United States.
Figure 7.5 displays average peak inter-story drift ratio (IDR) and acceleration profiles.
For these intensity levels, the relationship between ground acceleration, drift, and acceleration is
essentially linear. The 5% of MCE response is below the threshold for visual damage (0.003).
Accelerations exceed the threshold for human comfort (0.025 g) at high-frequency motion in an
office building (Griffis 1993; Murray et al. 2003; Griffis et al. 2012) at both intensity levels, as
expected. However, this is probably not an issue for the short duration of shaking.
Compared to the moment-frame direction, the performance of the building in the braced-
frame direction is less robust and highly sensitive to even small drifts (on the order of 0.2%).
This observation matches a previous comparison of braced frames and moment frames (Nelson
et al. 2006) and a related study (Hines et al. 2009) that concluded that braced frames are
particularly sensitive to variations in ground motion as well as building system characteristics.
Figure 7.6 shows typical component performance fragility curves documented in FEMA
P-58. Performance is judged in terms of “damage” consequences. For example, there are three
damage states and associated consequences for non-ductile beam-to-column connections
(Deierlein and Victorsson 2008), but only one damage state for braced frames and chillers.
249
4 4
5% of MCE
3 3
Story
Story
10% of MCE
5% of MCE
2 2
10% of MCE
1 1
0 0.005 0.01 0 0.1 0.2 0.3 0.4
Peak IDR Peak Acceleration (g)
Figure 7.5 Profiles of peak IDR and peak floor/roof acceleration.
1 1
Braced frame: brace and
gusset are severely damaged, Chiller: repair chiller
0.8 require replacement. Yielding 0.8 and attached piping
P(Fail|x=Accel)
and local buckling of beams

P(Fail|x=IDR)
and columns may be repaired.

0.6 0.6
0.4 0.4
Non-ductile
0.2 Beam-to-column 0.2
connection
0 0
0 0.005 0.01 0 0.1 0.2 0.3 0.4
IDR Acceleration (g)
Figure 7.6 Typical component fragility curves.
Based on comparing the fragility curves with the average IDR and acceleration profiles,
damage to non-ductile connections is unlikely to be important, but serious damage to the braced
frame and chiller are expected. For reference, exterior cladding damage fragility (not shown) has
a median demand, 𝜃 = 0.04 IDR and dispersion, 𝛽 = 0.4. Thus, no damage to glazing is
expected.
250
Comprehensive building performance was predicted in PACT, and the PACT analysis
was run twice (component directions are switched in the second run). The average results of the
PACT analyses are summarized in Table 7.6. The color shading in the table correlates with
performance objectives in terms of the tolerable level of damage (see Table 1.1 in Chapter 1).
Repair cost is expressed as a percent of the total replacement cost. As before, in this study the
focus is on steel-framed buildings constructed in a low or moderate seismic area in the central
and eastern United States, so the total replacement cost for the prototype building was estimated
at 230 dollars/sf with 30% attributed to the core and shell (building cost excluding tenant
improvements). The impact of damages and losses is suggested by color: mild impact (green),
moderate impact (yellow), and high impact (orange).
Sample contributions to median cost and downtime are shown in Figure 7.7. Note that
contributions to repair costs change for each realization in the PACT Monte Carlo simulation.
Generally speaking, common contributors are wall partitions, chillers, and air handling units that
are not anchored. Similarly, downtime can often be attributed to the elevators, pendant lighting,
chillers, and air handling units.
Table 7.6 Summary of average performance assessment for Type II non-ductile 4-story building
Median Response (PACT)

Repair Cost
(% of Total Probability
Replacement Downtime of Unsafe
Seismic Performance Level Cost) (days) Placards
Small event (43-year MRI, 5% of MCE) 2% 10 11%
Medium event (72-year MRI, 10% of MCE) 5% 33 65%
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Air Handling Unit
Roof
Chiller
Floor 4
Wall
Partitions
Type I
Floor 3
Pendant
lighting
Wall Raised Floor 2
partitions access
Type II floor
Floor 1
0 1 2 3 4 5 6 7 8 9
Time (Days)
(Weighted Average of Realizations 134 and 90)
Figure 7.7 Typical contributions to repair cost and downtime at 5% of MCE ground motion
The probability of an unsafe placard during small events is due to the non-seismically
detailed braced frames. During medium events, the braced frame contributes the most. (A 5%
contribution is from prefabricated stairs without seismic joints, and a 1% contribution is from
non-ductile beam-to-column connections.)
For the small event (43-year MRI), repair cost is fairly minimal (mild impact), although
there is likely to be some delay in re-occupancy (moderate impact). For the medium event (72-
year MRI), there is likely to be moderate repair costs and significant delays (high impact). Thus,
relative to SDC D max , the building is probably adequate for small events, but not for medium
events. For low and moderate seismic areas (i.e. SDC C max and lower), improved performance
(reduced impact in terms of lower costs and usage delays) is probable.
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7.3 Resiliency Contours
The repair cost plus the non-functionality loss caused by unsafe placarding, normalized with
respect to the replacement cost of the building, or the “initial loss index,” L associated with a
given level of resilience, R was computed using Equation 7.2 in terms of normalized repair
(recovery) time, T.
𝑡𝑐
𝑅 = � [1 − 𝑄(𝑡)]𝑑𝑑
𝑡0
1 𝐶𝑅𝑅𝑅𝑅𝑅𝑅 + 𝑃 𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐶𝑇𝑇𝑇𝑇𝑇𝑇 𝑡𝑅𝑅𝑅𝑅𝑅𝑅

= 1− � ��
2 𝐶𝑇𝑇𝑇𝑇𝑇 𝑡𝑐
= 1 − 𝐿𝐿/2
2(1 − 𝑅)
𝐿 = (7.2)
𝑇
Using Equation 7.2, resilience contours are plotted in Figure 7.8 for the non-ductile and
ductile moment frame buildings. Each contour in the plots represents a constant value of
resilience. Mathematically, each contour is described by an equilateral hyperbola (Equation 7.2),
and each point on the plot represents a unique scenario of recovery time and loss (Zobel and
Khansa 2014). The simulated resilience (the values in Table 7.3 and Table 7.4) of archetype
buildings without reserve strength is indicated by points designated with empty symbols;
resilience of buildings with reserve lateral strength is indicated by points with filled symbols.
The utility of the contour plots is twofold. First, the relative magnitude of improvement
in resilience is readily identified. For example, at the serviceability intensity level the reserve
lateral strength was a significant factor for archetype buildings with non-ductile moment frames
or with SMF designed for SDC D min , but it was insignificant for buildings with SMF designed
for SDC D max . At the design intensity level, the reserve lateral strength was only effective for
253
the 1-story building. The second advantage of the contour plots is that the optimal direction to
improve resilience can be discerned, i.e. orthogonal to the contour lines (green arrows). For
example, it is apparent at the serviceability level intensity that an improvement in the initial loss
index is the most effective way to increase resilience. In other words, the gradient represented
by the contour lines could be used to determine how to get the most benefit for the least cost. Of
course, Equation 7.1 relies on the method used to incorporate the probability of unsafe
placarding, and this method needs to be carefully evaluated.
0.5 90% 85% 80% 0.5 90% 85% 80%
0.4 0.4
Initial Loss Index
Initial Loss Index
0.3 0.3
1-story
0.2 0.2 1-story
2-story 2-story
0.1 4-story 0.1
Optimal direction 4-story
8-story
8-story
0 0
15 20 25 30 35 40 45 50 15 20 25 30 35 40 45 50
Recovery Time (days) Recovery Time (days)
a) Serviceability Level (Non-Ductile MF) b) Serviceability Level (SMF D min )
0.5 1.2
90% 85% 80% 65% 60% 55% 50% 45% 40%
0.4 1.1 1-story

Optimal
Initial Loss Index
Initial Loss Index
0.3 1
0.2 0.9
2-story
1-story
2-story 4-story
0.1 4-story 0.8
8-story
8-story
0 0.7
15 20 25 30 35 40 45 50 120 140 160 180 200 220 240
Recovery Time (days) Recovery Time (days)
c) Serviceability Level (SMF D max ) d) Design Level (SMF Designed for D max )
Figure 7.8 Seismic resilience contour plots
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7.4 Discussion
The seismic resilience of Type I archetype buildings generally increased when considering the
reserve lateral strength contributed by the shear tab connections (in the gravity framing), but the
improvement depended on the type and design of the lateral-force resisting system and the
number of stories. For archetype buildings with non-ductile moment frames and special moment
frames designed for SDC D min , reserve lateral strength in the shear tab connections was a
significant factor in improving resilience. Reserve lateral strength from shear tab connections
was less significant as the design strength of the lateral-force resisting system increased.
The results suggest that Type II steel moment-frame buildings designed for wind may
provide adequate performance under frequent and occasional ground motions in many areas of
the central and eastern United States. The performance is attributed in part to reserve strength in
both wind and gravity systems, ductility in the column panel zone, and the relative insensitivity
of non-ductile connections to service-level seismic hazard. Further research is needed to
examine the seismic performance of braced-frame buildings designed for wind, and to evaluate
the effects of building irregularity.
Collapse prevention systems with energy dissipation devices contributed to a significant
reduction in both repair cost and downtime. The resilience contour plots showed that for Type I
buildings the reserve lateral strength was most effective at improving (reducing) recovery time,
but less effective at reducing the associated economic losses. The comparison also illustrated the
usefulness of resiliency contours in identifying optimal strategies for improving resilience [see
also Judd and Charney (2014e)]. Thus, resilience contour plots could provide a pragmatic
approach to visualize the tradeoff between improving robustness (reducing loss) and speeding
recovery time, and to easily identify the best path to develop resilience.
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Chapter 8
MULTI-HAZARD COLLAPSE ASSESSMENT
This chapter assesses the multi-hazard (combined seismic and wind) risk of collapse. The multi-
hazard risk was calculated by assuming that the cumulative seismic risk and the cumulative wind
risk are statistically independent. The acceptable level of risk, including social amplification of
acceptable risk, is discussed. The results for selected archetype structural system are used to
illustrate a multi-hazard assessment.
8.1 General
8.1.1 Background
Multi-hazard risk analysis may be thought of as encompassing four basic elements: hazard,
exposure, vulnerability, and consequence (World Bank 2010). Hazard refers to the likelihood of
a natural phenomenon that can produce damaging impacts (NAP 2012), but it may also be
expanded to include the potential for blasts and technological threats (terrorism). In this study,
the focus is on performance-based structural engineering, and hazards were defined as the
potential for strong ground motions (caused by earthquakes) and strong wind pressure (caused by
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extreme winds, such as hurricanes and tornados). Other events that cause structural hazards
(such as fire, for example) are not considered in this study.
Exposure refers to people and assets subject to the damaging impacts from a hazard
(NAP 2012). In structural engineering, the focus is on the people and infrastructure that are
exposed. The degree of exposure involves the type, quantity, and location of assets and the
distribution in terms of both space and time of occupants. Vulnerability refers to the sensitivity
of buildings, bridges, and other structures to hazards (NAP 2012). Structural vulnerability is a
function of the structural design and construction methods. Vulnerability is generally described
in terms of one or more consequences, but in this study the focus is on side-sway collapse of
buildings.
8.1.2 Literature Review
In the literature, collapse assessments of building structures have been almost exclusively
concerned with a single hazard—usually seismic hazard. To date, there are few collapse
assessments for a wind hazard, or multi-hazard collapse assessments or performance assessments
(e.g. Li 2012).
Freeman et al. (2005) studied the structural efficiency and life-cycle costs of tall (49-
story) buildings subjected to multiple hazards. Crosti and Duthinh (2011) and Duthinh and
Simiu (2010) proposed a “risk-consistent” approach to the design of steel moment-frame
buildings designed in accordance with AISC specifications and ASCE 7-10. The results showed
that for the 10-story building studied by these researchers, the risk of exceeding the MCE level
lateral drift limit was not significantly reduced by employing ductile (reduced beam section)
beam-to-column connections, compared to welded-unreinforced-flange bolted connections.
257
Chen (2012) determined the structural response of mid-rise and high-rise steel-frame
buildings subjected to earthquake and wind hazards using two-dimensional nonlinear static
(pushover) and dynamic response history analyses. The buildings were a combination of
moment frames and eccentrically braced frames. The analyses indicated that the seismically
designed buildings have an inherent wind resistance for wind speeds up to 127 mph, while the
wind designed buildings have inherent seismic resistance for spectral accelerations up to 0.34 g.
8.2 Procedure
8.2.1 Calculation of Multi-Hazard Risk
Risk (the probability of side-sway building collapse considering the likelihood of wind or
seismic hazards) was calculated by integrating the respective collapse fragility and hazard curves
and calculating the cumulative risk for a given exposure time, 𝑡.
Annual seismic hazard failure rate:

+∞
𝜆𝐹,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = � 𝜆𝑎,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑓𝑆𝑆𝑆𝑆𝑆𝑆𝑆 (𝑎) 𝑑𝑑 (8.1)
0
Cumulative seismic risk for exposure time:
𝑃𝐹,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 1 − 𝑒 �−𝜆𝐹,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑡� (8.2)
Annual wind hazard failure rate:

+∞
𝜆𝐹,𝑊𝑊𝑊𝑊 = � 𝜆𝑎,𝑊𝑊𝑊𝑊 𝑓𝑊𝑊𝑊𝑊 (𝑎) 𝑑𝑑 (8.3)
0
Cumulative wind risk for exposure time:

𝑡
𝑃𝐹,𝑊𝑊𝑊𝑊 = 1 − �1 − 𝜆𝐹,𝑊𝑊𝑊𝑊 � (8.4)
258
The total (aggregate) collapse risk was calculated by combining the cumulative seismic and wind
collapse risks for a given exposure time.
𝑃𝐹 = 𝑃𝐹,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝑃𝐹,𝑊𝑊𝑊𝑊 − �𝑃𝐹,𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ��𝑃𝐹,𝑊𝑊𝑊𝑊 � (8.5)
It was assumed in Equation 8.5 that the cumulative seismic risk and the cumulative wind
risk are uncorrelated (statistically independent).
8.2.2 Acceptable Level and Social Amplification of Risk
Background
Society’s acceptance of risk is constantly changing due to various factors. Uncertainty in the
acceptable level of risk may be categorized as being a reflection of at least three factors:
irrationality, prior experience, and perception of risk. The use of alternative histories and (to
some extent) risk management provides ways to control expectations. The interaction of hazards
and vulnerability and the corresponding calculated risk may be amplified or attenuated by public
response. In other words, in addition to quantifying risk, an assessment of total risk must also
include political, psychological, sociological, and cultural factors (Kasperson 2012; Robinson
2012).
Political factors usually amplify risk. When structures or systems are “messy,” scientific
knowledge and calculated risk “become unavoidably enmeshed in political disputes” (Metlay
and Sarewitz 2012). For example, in recent years, government budget cuts in the United States
led to significant flight delays for commercial airliners (Wald 2013). Seismic risk is
compounded by megacities, which have a “concentration and buildup of populations and
infrastructure in cities” (Aster 2012) that portends magnification of risk (Bilham 2009) including
significant casualties (Holzer and Savage 2013). Wind risk has similar complications.
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Compared to the western United States, a large-magnitude earthquake is possible in most
the central and eastern United States (Chapman 2014), but such an event is rare. The rarity of
the such events increases the uncertainty of the seismic hazard (see Stein and Stein 2013). Thus,
one researcher has concluded, “All told, we should expect that globally we will experience more
such surprising (and even astounding) low-probability and potentially very high-impact Black
Swan” events (Aster 2012; see also Taleb 2007). In this study, a preliminary target collapse risk
was established with these factors in mind.
Target Collapse Risk
In Chapter 4, the ASCE 7-10 target collapse risk of 1% in 50 years was used to evaluate
structural safety under seismic loads. In Chapter 5, the target of 0.15% in 50 years was applied
to structural collapse and used to evaluate structural safety under wind loads. The target risk in
ASCE 7-10 Table C.1.3.1a was originally established based on the threshold of human risk
acceptance (see commentary to ASCE 7-10, Pate-Cornell 1994), and therefore its application to
structural collapse assessment was considered reasonable.
In this research, a target multi-hazard collapse risk of 1% in 50 years is suggested. The
target risk was established based on lowering a combined risk of 1.15% (seismic and wind) to
account for social amplification of risk, and specifically for perception of risk. This value is
much larger than the minimum risk generally considered by society, 0.00005% (Ellingwood and
Dusenberry 2005). Moreover, recent studies have shown that targets of acceptable risk may need
to be revisited in light of modern data regarding risk aversion of building owners, code-
enforcement organizations, and other stakeholders (Cha and Ellingwood 2014).
260
8.3 Results
The multi-hazard collapse risk of the Type I non-ductile moment frame 4-story and 8-story
buildings were assessed. Multi-hazard collapse risk was calculated using Equation 8.5. Seismic
collapse fragility was determined using parameters from Table 4.4. Seismic hazard was based on
2008 USGS data, adjusted for site amplification based on a correlation between shear wave
velocity 𝑉𝑠30 , and bedrock motion using NGA relationships. Wind collapse fragility was
determined using parameters from Table 5.2. Wind hazard was based on the ASCE 7-10 wind
speed data, and was extrapolated for extreme wind speeds. This integration was calculated for
every 0.5-degree latitude and longitude to generate a map of risk values in the conterminous
United States.
Figure 8.1a (upper map) shows shaded contours regions where the multi-hazard collapse
risk exceeds 1% in 50 years for the 4-story building, assuming soil site class D (𝑉𝑠30 = 180 m/s)
everywhere, and not including tornado wind hazards. Blue shaded areas in the central and
eastern United States indicate (for this particular building archetype) where the enhanced shear
tab collapse prevention system is needed, compared to the moment frame alone. Red shaded
areas indicate where the enhanced shear tab collapse prevention system is not sufficient to meet
the acceptable multi-hazard risk target (set at 1%). Major metropolitan areas (dots) are shown
based on 2011 population estimate using 2010 census data. The upper map shows that the
building is effective for a large portion of the central and eastern United States, but not for
hurricane prone locations.
261
Type I non-ductile 4-story building
MF collapse
risk exceeds
1% in 50 years
MF+SST collapse
risk exceeds 1% in
50 years
a) assuming soil site class D and extrapolated ASCE 7-10 wind hazards
Type I non-ductile 4-story building Type I non-ductile 4-story building
b) Site response using topographic proxy c) Inclusion of tornado wind hazards with proxy
Figure 8.1 Regions where multi-hazard collapse risk exceeds 1% in 50 years
262
Figure 8.1b and Figure 8.1c (lower maps) show regions where the risk exceeds 1% in 50
years, using topographic data as a proxy for the average shear wave velocity to estimate site
response, and considering synoptic wind hazards (left map) or including tornado wind hazards
(right map). The collapse prevention system is shown to be viable for many locations in the
central and eastern United States.
Figure 8.2a (upper map) shows where the multi-hazard collapse risk exceeds 1% in 50
years for the 8-story building, assuming soil site class D (𝑉𝑠30 = 180 m/s), and not including
tornado wind hazards. The upper map shows that, for this particular collapse prevention system
and building type, the applicable area is more restricted for the 8-story building compared to the
4-story building. The risk exceeds the target for large swaths of the southern and eastern
coastlines of the United States.
Figure 8.2b and Figure 8.2c (lower maps) show regions where the risk exceeds 1% in 50
years, using topographic proxy data and considering synoptic wind hazards (left map), or
including tornado wind hazards (right map). Although the banded region is much smaller for the
collapse prevention system, the area still contains several major metropolitan areas, extending
from Atlanta in the south, to Chicago in the north.
263
Type I non-ductile 8-story building
MF collapse risk
exceeds 1% in
50 years
MF+SST collapse
risk exceeds 1% in
50 years
a) assuming soil site class D and extrapolated ASCE 7-10 wind hazards
Type I non-ductile 8-story building Type I non-ductile 8-story building
b) Site response using topographic proxy c) Inclusion of tornado wind hazards with proxy
Figure 8.2 Regions where multi-hazard collapse risk exceeds 1% in 50 years
264
8.4 Discussion
Multi-hazard collapse assessments suggested that the probability of collapse due to seismic and
wind hazards is significant in much of the United States. Enhanced shear tab collapse prevention
systems dramatically improve (reduce) the collapse risk for the Type I non-ductile moment
frame building, depending on the number of stories. Collapse prevention systems are needed and
viable in much of the interior of the United States, but a ductile moment frame designed for high
seismic demands or a conventional lateral resisting system would be necessary in regions of high
seismicity (such as the in much of the western United States), or a high-wind designed main
wind-force resisting system would be necessary along segments of the hurricane-prone
southeastern United States.
The quantification of risk predicted in this Chapter should be tempered by considering
the uncertain nature of both of the hazards, structural vulnerability, and the acceptable level of
risk. The calculation of multi-hazard risk is like the following gambling strategy (Taleb 2005).
Suppose one has a 999/1,000 probability of wining one dollar, and a 1/1,000 probability of losing
$10,000 dollars. Here the probability is analogous to multiple hazards, and the amount of dollars
won or lost is analogous to the tolerable impact of those hazards when combined with structural
fragility. The expected result can be obtained by multiplying each probability by each outcome.
Thus, the expectation would be that one will lose nine dollars. But the frequency or probability,
in and by itself, is totally irrelevant. The probability needs to be judged in connection with the
magnitude of the outcome. In the same way, calculating multi-hazard risk in structural
engineering needs to be evaluated in the context of disproportionate impact. An examination of
the acceptable level of multi-hazard risk is warranted.
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Chapter 9
CONCULSIONS
This chapter summarizes the findings of this research study. Conclusions and recommendations
based on the results are discussed, and areas for future research are identified. The potential
impact of the research is discussed.
9.1 Summary
An examination of seismic and wind hazards in the United States confirmed that extensive
regions of the United States are at risk from both hazards. However, the examination revealed
that in many locations of the central and eastern United States, wind performance was most
crucial for frequently occurring events, and the only seismic limit state of consequence was life
safety. The spectral accelerations associated with the 43-year and 72-year events in the central
and eastern United States were approximately 5% and 10% of the MCE-level spectral
accelerations, respectively, roughly half of the comparable demands in the western United States.
The collapse prevention system concept explored in this study may provide a cost-effective
solution for these locations. The collapse prevention system concept relies on components that,
working together with the primary lateral force-resisting system and gravity framing, are
specifically intended to prevent collapse.
266
The seismic and wind collapse safety of archetypical buildings with and without collapse
prevention systems was evaluated. For wind analysis, ensembles of wind load records for
nonlinear response history analyses were based on wind tunnel testing. Variability in the wind
load records was generated by wind directionality, and this provided a convenient way to
incorporate epistemic uncertainties in the analysis. A straight-line wind and a reasonable
duration of the wind event were assumed. These aspects of wind collapse analysis differ
significantly from the procedures used to select ground motions for seismic collapse analysis.
For the buildings in this study, collapse prevention systems were effective at reducing the
conditional probability of seismic collapse (during MCE-level ground motion) and at lowering
the seismic collapse risk of a building with moment frames not specifically detailed for seismic
resistance. The results indicated that the wind collapse risk was acceptably low for most of the
buildings considered in this study if located in the interior (and west coast) of the United States,
and if reserve strength in the shear tab connections was included. Taller buildings, however, had
a higher wind collapse risk, and the non-ductile moment frame 10-story building did not pass the
suggested target of 0.15% chance of collapse in 50 years. Compared to using only the main
wind force resisting system, collapse prevention systems were needed and viable in the interior
of the United States, but were not sufficient for some locations along the southeastern coast,
depending on the location and type of archetype structural system.
Buildings with collapse prevention systems using non-ductile moment frames with fully-
rigid flange welded connections passed the FEMA P-695 seismic criteria for SDC D min .
Buildings with collapse prevention systems were adequate for many regions in the central and
eastern United States, but a conventional lateral force resisting system or a collapse prevention
system with a ductile moment frames with reduced beam section connections would be required
267
for regions of higher seismicity (such as the New Madrid and Charleston areas) and for some
regions exposed to high hurricane wind speeds.
Reserve lateral strength in the gravity framing, specifically in the shear tab connections,
was a significant factor in the success of the collapse prevention system. In most buildings,
simply utilizing the reserve strength in the shear tab connections significantly reduced the
probability of seismic or wind collapse. The pattern of collapse prevention component failure
depended on the type of loading, archetype building, and type of collapse prevention system, but
most story collapse mechanisms formed in the lower stories of the building. Collapse prevention
devices usually did not change the story failure mechanism of the building, compared to the
primary moment frame alone, except for the “holistic” collapse prevention systems: reserve
lateral strength in the gravity framing and enhanced shear tab connections, which in some cases
did alter the story failure mechanism for the building.
Collapse prevention systems were highly resilient. Collapse prevention systems with
energy dissipation devices contributed to a significant reduction in both repair cost and
downtime. Resilience contour plots showed that reserve lateral strength was effective at
reducing recovery time, but less effective at reducing the associated economic losses.
Seismic and wind collapse assessments were sensitive to hazard and analytical modeling
parameters. The inclusion of gravity column splices, for example, changed the predicted static
collapse story mechanism. The seismic collapse assessment was also sensitive to the ground
motion variability, relative to the target response spectrum, due to the inevitability of uncaptured
frequency content in the spectral matching process. The method used to represent column panel
zones and to account for second-order effects in the analytical model had a significant impact on
the collapse assessments. Using the centerline modeling approach stiffened the structure
268
compared to the Krawinkler and scissors approaches. Stiffening the structure then increased the
spectral acceleration associated with the median collapse spectral acceleration. Changing from a
second-order analysis to a first-order analysis in the non-ductile frame also had a large effect on
the collapse response. The first-order approach was incapable of modeling the destabilizing
effects of the gravity loads, and thus predicted reduced interstory drift ratios and increased
collapse resistance. Such an effect was less pronounced with non-ductile moment frame
buildings, because these systems were typically not able to sustain large, repeated interstory drift
ratios. This behavior prevented the non-ductile buildings from reaching large interstory drift
ratios where the differences between the corotational and P-∆ approximation are amplified
before the building collapses.
The method used to integrate seismic or wind hazard and the respective collapse fragility
significantly affected both the contribution of different hazards to the annual risk rate, and the
calculated cumulative value of collapse risk. When applied in seismic analysis, collapse risk was
sensitive to the method used to incorporate site response.
Steel moment-frame buildings designed for wind may provide adequate seismic
performance under frequent and occasional ground motions in many areas of the central and
eastern United States. The performance was attributed in part to reserve strength in both wind
and gravity systems, ductility in the column panel zone, and the relative insensitivity of non-
ductile connections to service-level seismic ground motion intensity.
9.2 Conclusions and Recommendations
The research leads to four general recommendations for performance-based analysis and design
in earthquake and wind engineering.
269
• The first recommendation is that gravity framing should be included in structural analysis
when feasible. The inherent added stiffness and strength have profound effects on
collapse capacity behavior.
• A thorough understanding of the sensitivity of modeling aspects is needed when
analyzing steel moment frame buildings to collapse. For example, the collapse responses
from analytical models with the Krawinkler and scissors panel zone representations were
quite different for the ductile frame buildings with high interstory drift ratios, but the
differences were minimal for the ductile frame with low interstory drift ratios. The
results suggest that employing the scissors model may be a valid way to reduce the
number of degrees of freedom in the model and the analysis run time for some structural
systems (i.e. non-ductile systems).
• It is recommended to use the derivative of the collapse fragility curve when calculating
collapse risk. Using the derivative of the hazard curve to calculate risk is more
computationally expensive, unstable, inaccurately determines the contribution of hazard,
and, depending on the method used, may lead to grossly inaccurate values of risk.
• For performance-based wind engineering, adding a limited degree of ductility to the
moment frame system, similar in magnitude to that provided by intermediate moment
frames in seismic design, could justify the use of a response modification factor for wind
and inelastic design for strength-level wind speeds.
270
The research leads to two specific observations for the collapse prevention system concept.
• It is expected that collapse prevention systems are applicable principally in the central
and eastern United States and are not likely to be amenable to the western United States.
• Reserve lateral strength provided by the shear tab beam-to-column connections was a
significant factor in the success of the collapse prevention system. This conclusion
reflects the fact that shear tab connections can contribute in a significant way to the
stiffness, strength, and ductility of the building, depending on the number of connections
compared to the number of fully-restrained moment connections.
9.3 Areas for Future Research
Several aspects of the research are important areas for future research. It should be stressed that
the results discussed herein are preliminary in nature. Similar to collapse analyses for seismic
loads, a detailed study is required that involves a variety of multi-degree of freedom archetypical
models representative of actual buildings, as well as consideration of taller buildings and other
building shapes. Further research is needed to examine the seismic performance of braced-frame
buildings designed for wind, and to evaluate the effects of building irregularity.
Wind collapse analyses exhibit special challenges compared to seismic collapse analyses.
In order to meet these challenges, a comprehensive database of wind loads, a method to
incorporate the non-stationary, long-term nature of wind loads (a sustained wind load was used
in this research), rational methods for estimating the non-explicitly modeled part of damping,
and calibration epistemic uncertainties are needed to advance the state-of-the-art.
271
The effect of the gravity framing on the response leads to the recommendation that three-
dimensional modeling, including torsional effects, may be needed to realistically predict collapse
behavior of buildings. Data mining procedures need to be developed for collapse assessments in
order to glean from the numerical results and promote an understanding of the behavior of
building components.
The procedures used to show applicable areas for collapse prevention systems should be
reviewed and compared to studies that concentrate on central and eastern United States geology
and seismicity, particularly in the highest hazard regions (Charleston and Memphis), and that
focus on the windstorms of those areas (especially tornados and hurricanes). Eventually, regions
outside the United States for which the collapse prevention system is viable should be identified,
and the applicability of the method to those regions should be assessed.
Incremental dynamic analyses and ground motion sets should be developed that reflect
the hazard and fault mechanisms likely found in central and eastern United States. A central and
eastern United States companion for the FEMA P-695 Far-Field Set should be developed to
better understand the vulnerability of structures outside the western United States.
Incremental dynamic wind analysis procedures need to be continued to be developed.
The ramping of wind loads needs to be investigated. Reference wind speeds and wind durations
need to be established.
Collapse prevention systems need to be optimized. In this research, the strength of the
collapse prevention systems was limited by the size of the gravity frame beams and columns, and
future research should investigate collapse prevention systems with slightly larger gravity
framing members (especially column sizes). This research also revealed that ductility may have
a larger impact than strength on the collapse performance of the collapse prevention system.
272
Accordingly, it may be advantageous to utilize other aspects of buildings that are inherently
ductile (such as panel zone yielding). Collapse prevention systems with distributed forms of
damping (such as friction dampers) could also be investigated.
The focus of this research was primarily a proof-of-concept. Essential aspects related to
the design and the behavior of collapse prevention systems need to be addressed before
implementation of the concept. For example, except for the enhanced shear tab connections, the
proposed collapse prevention devices (and their connecting elements) need to be detailed.
Similarly, the demands imposed on the gravity framing (such as increased base shear forces)
need to be addressed.
A comprehensive cost-benefit analysis should look at material, labor, and inspection
costs for deployed collapse prevention mechanisms. Collapse prevention systems are not
expected to be implemented in actual construction until it is demonstrated that the new system is
economically viable, improves performance, and produces reliable expectations of that
performance.
A “Design Guide” should be developed for steel structures where the main gravity and
wind system is either a moment frame or a braced frame (instead of just a moment frame). The
methodology for assessing the strength of the system without the collapse prevention mechanism
should be provided along with procedures for designing the collapse prevention mechanism and
assessing the performance of the complete collapse prevention system.
It is likely that current retrofit methodologies as outlined in ASCE 41-13 will not be
applicable to buildings with collapse prevention systems. This arises from differences identified
in the seismic and wind hazards of the central and eastern United States compared to the western
United States, and is a result of the concept that the main lateral force-resisting system and
273
gravity framing is expected to provide adequate performance at all limit states except life-safety
and collapse. This lack of applicability should be assessed and recommendations should be
made for the future development of guidelines for implementation in existing buildings.
An approach similar to the FEMA P-58 framework used to assess seismic performance
needs to be developed in order to better understand the risk of life, as well as occupancy and
economic losses that could occur during a wind event. Unlike seismic performance, wind
performance encompasses a host of concerns besides building motions that need to be addressed,
such as habitability, aero-acoustics, and water infiltration.
9.4 Potential Impact of Research
It is possible that buildings designed for wind can provide adequate multi-hazard performance in
many regions. In in the central and eastern United States, where very large, rare earthquakes are
possible, a structural system (i.e. a collapse-prevention system) could be devised to exploit the
unique shape of seismic and wind hazard curves.
Resilience contour plots could provide a pragmatic approach for practicing structural
engineers to visualize the tradeoff between improving robustness (reducing loss) and speeding
recovery time, and to easily identify the best path to develop resilience. The approach explored
in this research also has the potential to minimize design office errors introduced by
implementing ever-evolving seismic code provisions (Cheever and Hines 2010), that were
envisioned for use in high-seismic areas, in low-seismic high-wind areas.
The focus of this study was steel moment-frame structures, however the results suggest
that reinforced concrete and masonry shear wall structures could be viable primary systems for a
secondary collapse prevention system. The demands imposed on the gravity framing columns
274
suggest that composite gravity frame columns could provide necessary capacity to meet the
demands imposed by the collapse prevention system on the gravity framing.
The collapse prevention system concept is equally relevant (and perhaps more attractive)
for the repair and retrofit of existing buildings. An important advantage in using collapse
prevention systems for rehabilitation (compared to a traditional retrofit) is that the collapse
prevention mechanism need not be part of the main lateral load resisting system. A related
advantage is that the collapse prevention system concept has less reliance on added deformation
capacity, which is a key factor in older construction. For that reason, collapse prevention
systems could likewise be used to prevent collapse of a damaged building during a strong
aftershock.
This research has the potential to facilitate a “technology transfer” from seismic
performance-based design, to wind performance-based design, and to multi-hazard performance-
based design. The potential impact of this research will be best realized if the collapse
prevention concept becomes part of a larger effort to mitigate the impact of disasters. Instead of
a silver bullet, the goal of the collapse prevention concept is to improve, in a cost-effective way,
community preparedness for seismic and wind risk by improving the structural performance of
older construction and implementing resilient new construction.
275
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318
Appendix A
ANALYSIS VALIDATION
This appendix contains analysis examples used to evaluate the performance of computer
software and the analysis procedures used in this research. All examples used the Open Systems
for Earthquake Engineering Simulation (OpenSees) software (McKenna et al. 2000-2011; PEER
2012). For some examples and problems, additional software was used, including Nonlin
(Charney 2010), Quick (Judd 2006), and Abaqus (Dassault Systèmes 2011a), depending on the
problem considered and software capabilities.
A.1 Computer Software
The primary software used in this study was OpenSees (PEER 2012). There were a number of
advantages to using OpenSees. First, OpenSees was computationally powerful. It was amenable
to a variety of structural configurations, and included various material behaviors, a wide
selection of phenomenological models, element types, as well as a good selection of possible
analyses and solution algorithms. Part of this power is owed to the engaged community of users
that also play the role of developers. Many aspects of the software have been user added.
Implied here is that the software is accurate, and the subsequent example and benchmark
problems in part support this assertion.
319
The second advantage to using OpenSees was that the software has been used by many
researchers in the earthquake engineering field at the time of this study. The open source code
and the low cost (at least in terms of purchase price) was probably the primary driver behind the
usage. Using the same software, in this case OpenSees, facilitates collaborative work and speeds
the creative process.
There were also disadvantages to using OpenSees. It may have been as expensive, or
more expensive, than comparable finite element software, in terms of labor costs. The man-
hours required to climb the steep learning curve and endure the bug-de-bug development cycle
create a high cost, despite the initial purchase price. Three factors contribute to these costs. The
first factor is that the software was not WYSIWYG. Pre- and post-processing was text based or
handled by other software, namely MATLAB (2011). The second factor is that the software was
not made in a for-profit environment. Much of the code and functionality is ad-hoc, ongoing,
and made by a turn-over of temporary student code writers. Documentation suffers in addition to
code. Compared to commercially maintained software, both the implementation and the
documentation were clunky. The third factor is that OpenSees required the use of the TCL script
language. The choice of script language was unfortunate because modern script languages, such
as PYTHON—used by Abaqus (Dassault Systèmes 2011a) software, for example—avoid many
of the pitfalls that must be traversed using TCL.
For this study, the advantages of using OpenSees were judged to outweigh the
disadvantages. OpenSees worked well for structures where a GUI was not essential, such as
framed structures with regular and repeated geometry, or other structures that were relatively
simple (e.g. portal frames).
320
Additional software was used for comparison with OpenSees. For dynamic analysis of
single degree of freedom (SDOF) structural systems, Nonlin software (Charney 2010) was used.
Nonlin was developed primarily as educational software for earthquake engineering, and has the
capability to model nonlinear structural behavior including damping, ductility, and energy
dissipation. Also used for dynamic analysis of SDOF systems, Quick (Judd 2006) has the
capability to include various hysteresis models. Quick was originally developed to study the
dynamic response of light-frame wood shear walls and diaphragms (Judd 2006; Judd and
Fonseca 2006). For some problems, Abaqus (Dassault Systèmes 2011) was used. Abaqus is a
commercially developed multi-purpose finite element software.
A.2 Static Analysis
Standard analyses examples are discussed in this section to verify some of the basic capabilities
of OpenSees. Not all analysis capabilities were verified or demonstrated. The software
documentation (Mazzoni et al. 2011) provides a more comprehensive introduction to OpenSees
and its use of the TCL script language. This section also includes a second order analysis [see
Charney (2015)] and an eigenvalue buckling analysis example.
A.2.1 Cantilever Beam
A 2D cantilever beam with a point load at the end (Hibbeler 1995) was analyzed using
OpenSees. The input file is shown below.
# DESCRIPTION: OpenSees2.3.1 input file for analysis of a 2D cantilever beam

# with a point load at the end from Example 8-3 (Hibbeler 1995).
#
wipe
model basic -ndm 2 -ndf 3
# nodal coordinates
321
node 1 0 0
node 2 360 0
# bondary conditions
fix 1 1 1 1
fix 2 0 0 0
# transformation
geomTransf Linear 1
#
# elements
element elasticBeamColumn 1 1 2 38.5 29000 600 1
# recorders
recorder Node -file Node2.out -time -node 2 -dof 1 2 3 disp
recorder Element -file Element1.out -time -ele 1 force
#
# gravity loads
pattern Plain 1 Linear {
load 2 0.0 2.0 0.0
}
# analysis
constraints Plain
numberer Plain
system BandGeneral
algorithm Linear
integrator LoadControl 1.0
analysis Static
#
analyze 1
#
puts "Finished analysis"D
The analysis results in two output files: displacements at node 2, and forces in element 1.
The displacement results are shown below (time value followed by displacements).
1 0 1.78759 0.00744828
The calculate slope at the end of the cantilevered beam matches the theoretical slope at
the end of the beam using the moment-area analysis method.

𝐵
𝑀
𝜃𝐴𝐴 = � 𝑑𝑑
𝐴 𝐸𝐸
(−900 𝑘 ∗ 𝑓𝑓)(144 𝑖𝑖.2 /𝑓𝑓)

=
(29,000 𝑘𝑘𝑘)(600 𝑖𝑖.4 )
= −0.00745 𝑟𝑟𝑟
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A.2.2 Second-order effects
The effect of the approach used to include second-order effects on a static analysis was
determined by examining a typical (W14x82) gravity column. For purposes of illustration, the
height of the column is 12.5 feet, and the boundary conditions of the column are idealized as
fixed at the base and free at the top. A lateral load V of 10 kips was applied.
The columns was analyzed with a vertical load 𝑃 equal to 15%, 80%, or 99.9% of the
elastic critical buckling load, 𝑃𝑐𝑐 of the column. The column was modeled using OpenSees and
using a MATLAB routine. The model consisted of one or four elements, depending on the
analysis.
Figure A.1 shows the column behavior for the various methods used to model second-
order effects. In a first order analysis of the column the displacement, ∆ is equal to 𝑃ℎ3 /3𝐸𝐸 =
2.62 inches. An estimate of the second-order effect was determined using a linearized geometric
stiffness matrix, 𝐾𝑔𝑔𝑔 . = −𝑃/ℎ, based on a straight-line deformed column configuration. This
assumption in the configuration of the deformed shape causes an incorrect increase in the
stiffness the system.
Figure A.1 Column behavior for second-order analysis methods
323
The second-order effect was more accurately determined using a consistent geometric
stiffness matrix, 𝐾𝑔𝑔𝑔 , based on a cubic shape function for both the elastic stiffness and
geometric stiffness. Lastly, the second-order effect was determined using the corotational
formulation, where the system stiffness is updated to reflect the deformed shape. Such an
analysis will report a vertical deflection of the column. However, the corotational formulation
does not include the P-δ effect unless more than one element is used to model the column.
The predicted lateral displacement is summarized in Table A.1. The linearized geometric
stiffness with 15% of 𝑃𝑐𝑐 corresponded to an increase in displacement compared to the first order
displacement. Using four elements to model the column resulted in larger displacements
compared to modeling the column using one element. There was a small increase in
displacements when the consistent geometric stiffness model is used, but interestingly, the results
for the correlational model are the same as with linearized geometric stiffness because the
corotational model using one element does not include the P-δ effect, and because the column
rotation is small.
Table A.1 Predicted lateral displacement (in.) of typical gravity frame column
Number of Second-order method

P/Pcr Elements 1st Order Linear K geo Consistent K geo Corotational
1 2.62 2.97 3.05 2.97
0.15
4 2.62 3.04 3.05 3.04
1 2.62 7 10.7 6.97
0.8
4 2.62 10.4 10.8 10.3
1 2.62 12.3 51.0+ 12.1+
0.999
4 2.62 46.1 58.8* 34.0**
+ Vertical displacement =0.0 in.
* Vertical displacement = -0.1 in.
** Vertical displacement = -4.88 in.
324
When the axial load is 80% of 𝑃𝑐𝑐 , the increase in displacements was significant, and the
predicted lateral displacements differ widely. As before, the results from the corotational model
are similar to those obtained using linearized geometric stiffness. As the axial P approaches 𝑃𝑐𝑐 ,
the choice of analytical model and the level of discretization of the model has a profound effect.
Note that the one-element corotational model was inaccurate at this level of axial load
due to the inability to represent P-δ . However, the four-element corotational model was more
accurate because the vertical displacement (-4.88 inches) was captured. The smaller lateral
displacement (34 inches) for the correctional model relative to that obtained for the consistent
geometric stiffness model (58.8 inches) was due to the fact that the length of the column using
the corotational model was constant. A study by Denavit and Hajjar (2013) reached similar
conclusions.
A.2.3 Buckling Analysis
The critical buckling load of a two-story single-bay frame was analyzed using MATLAB
routines, OpenSees, and Abaqus. (Input scripts and files are shown on the following pages.)
Two analysis approaches were used. In the first analysis approach, a constant transverse load 𝑉
= 0.001 k and a gradually increasing axial load P were applied until reaching the critical buckling
load, 𝑃𝑐𝑐 . In the second analysis approach, 𝑃𝑐𝑐 was determined using the first mode of an
eigenvalue analysis.
The nonlinear response is summarized in Table A.2. Using a consistent geometric
stiffness formulation, both analysis approaches accurately predict the critical buckling.
325
W27x129
W24x146 W24x146
W27x129
W24x146 W24x146
Figure A.2 Two-story single-bay frame
Table A.2 Critical buckling load (k)
Analysis Approach P cr (k)
Constant V=0.001, gradually increase P until reaching P cr 3,770
OpenSees using corrotational formulation 3,829
Eigen analysis: V=1, and P = 1. Solve for P times lambda (P cr ) 3,800
Abaqus 3,790
326
OpenSees input script:
wipe
# Input parameters
# Vertical (P) and lateral (V) loads
set P 10.0
set V 0.001
# Material (steel)
set E 30000.0
# Column section (W24x146)
set Ac 43.0
set Ic 4580.0
# Beam and rafter section (W27x129)
set Ab 37.8
set Ib 4760.0
# Node coordinates
node 1 -240.0 0.0
node 2 -240.0 90.0
node 3 -240.0 180.0
node 4 -240.0 252.0
node 5 -240.0 324.0
node 6 -120.0 372.0
node 7 0.0 180.0
node 8 0.0 420.0
node 9 120.0 372.0
node 10 240.0 0.0
node 11 240.0 90.0
node 12 240.0 180.0
node 13 240.0 252.0
node 14 240.0 324.0
# Boundary conditions
fix 1 1 1 0
fix 10 1 1 0
# Transformation
geomTransf Corotational 1
# Element material, type, and connectivity
element elasticBeamColumn 1 1 2 $Ac $E $Ic 1
element elasticBeamColumn 5 5 6 $Ab $E $Ib 1
# Recorders
recorder Node -file Node14.out -time -node 14 -dof 1 2 3 disp
# Loads
timeSeries Linear 1
pattern Plain 1 1 {
# load $nodeTag (ndf $LoadValues)
load 8 0.0 [expr -$P*2] 0.0
load 14 0.0 -$P 0.0
load 14 $V 0.0 0.0
}
# Analysis parameters
constraints Plain
numberer Plain
system BandGeneral
test NormDispIncr 1.0e-8 10
algorithm Newton
analysis Static
analyze 3829
327
Abaqus input file:
*HEADING
** NODE DEFINITIONS
**
*RESTART,WRITE,FREQUENCY=999
*NODE, NSET=FRAME_NODES
1, -240.0, 0.0, 0.0
2, -240.0, 90.0, 0.0
3, -240.0, 180.0, 0.0
4, -240.0, 252.0, 0.0
5, -240.0, 324.0, 0.0
6, -120.0, 372.0, 0.0
7, 0.0, 180.0, 0.0
8, 0.0, 420.0, 0.0
9, 120.0, 372.0, 0.0
10, 240.0, 0.0, 0.0
11, 240.0, 90.0, 0.0
12, 240.0, 180.0, 0.0
13, 240.0, 252.0, 0.0
14, 240.0, 324.0, 0.0
*ELEMENT,TYPE=B21, ELSET=FRAME_ELEMENTS_1
1,1,2
2,2,3
3,3,4
4,4,5
5,5,6
6,6,8
7,8,9
8,9,14
9,3,7
10,7,12
11,10,11
12,11,12
13,12,13
14,13,14
*BEAM GENERAL SECTION, SECTION=GENERAL, ELSET=FRAME_ELEMENTS_1
43.0, 4580.0
0.0,0.0,-1.0
30000.0
37.8, 4760.0
0.0,0.0,-1.0
30000.0
43.0, 4580.0
0.0,0.0,-1.0
30000.0
*BOUNDARY
1, 1
1, 2
10, 1
10, 2
*STEP
*BUCKLE
1,
*CLOAD
8, 2, -2.0
14, 2, -1.0
*END STEP
328
A.3 Dynamic Analysis
In this section the time-history response of an elastoplastic SDOF system (Chopra 2012) was
compared to the responses of three computer programs: Nonlin, OpenSees, and Quick.
The maximum and permanent displacements are summarized in Table A.3 and Table
A.4. The SDOF system is defined with 𝑇𝑛 = 0.5 sec, 5% damping, and various bilinear
R
elastoplastic behaviors, defined using the response modification factor, R. The SDOF system was
subjected to the El Centro ground motion record (𝑎𝑚𝑚𝑚 = 0.32 g) as described by Chopra (2012).
Table A.3 Maximum absolute displacement (in.)
Response modification factor, R

Method R=1 R=2 R=4 R=8
Chopra (Fig. 7.4.2) 2.25 1.62 1.75 2.07
Nonlin 2.24 1.62 1.74 2.06
OpenSees 2.24 1.63 1.77* 2.07
Quick 2.24 1.63 1.76* 2.07
Duhamel’s (MATLAB) 2.26
*Reached at a different time, compared to Chopra.
Table A.4 Permanent displacement (in.) at time equal to 30 seconds
Response modification factor, R

Method R=1 R=2 R=4 R=8
Chopra (Fig. 7.4.2) 0 0.17 1.1 1.13
Nonlin 0.02 0.17 1.1 1.13
OpenSees 0.04 0.2 1.14 1.1
Quick 0.04 0.2 1.14 1.1
329
A.4 Nonlinear Multi-Degree-of-Freedom Analysis
In this section the nonlinear response of the 4-story ductile moment frame building designed for
SDC D max is compared to the response for a similar building model reported in NIST (2010b).
The models differ in at least the following aspects:
• OpenSees was used in this research, whereas the comparison model used Drain-2DX
(Prakash et al. 1993).
• In this research, the gravity framing was explicitly modeled and includes gravity columns
and beams, whereas the comparison model employed a single leaning column to account
for second-order effects.
• The beam-to-column joint model was geometrically accurate in this research (the top of
adjacent beams was at the same elevation), whereas it was not in the comparison model.
• The comparison model story elevations were based on beam centerlines, except the first
story height was measured from the ground to the top of a trial beam used to establish the
first story elevation (not necessarily the actual beam size).
The vibration response is shown in Figure A.3. The reference study’s first four periods
of vibration were 1.56, 0.50, 0.27, and 0.17 seconds/cycle. The nonlinear static seismic pushover
response is shown in Figure A.4. (The red dashed line is the response of the comparative
model.)
330
Figure A.3 Periods of vibration and mode shapes for the model used in this research
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0 0.01 0.02 0.03 0.04 0.05 0.06
Roof Drift Ratio
a) Model used in this research b) Comparative model (from NIST 2010b)
Figure A.4 Nonlinear static seismic pushover response
331
Figure A.5 shows the results from a free vibration analysis to verify the inherent (non-
explicitly modeled) damping in the finite element analysis. (The comparative study did not
conduct a free vibration analysis.) In the analysis, the building was subjected to the first 2
seconds of the 1941 El Centro ground motion record (Chopra 2012), scaled to 10% of the
original record intensity, followed by 58 seconds of free vibration. The equivalent damping ratio
was approximately 2.5% (the target damping ratio was 2.5%).
-4
x 10
0.1 8
0.09
6
0.08
4
0.07
Modal damping ratio
2
Roof drift ratio
0.06
0.05 0
0.04
-2
0.03
-4
0.02
-6
0.01
0 -8
0 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 60
Natural circular frequency (rad/sec) Time (sec)
a) Rayleigh damping curve b) Free vibration response history

-4
x 10
8 0.038
6 0.036
4
0.034
Equivalent Damping Ratio
2
0.032
Drift Ratio
0
0.03
-2
0.028
-4
-6 0.026
-8 0.024
0 10 20 30 40 50 60 0 5 10 15 20 25 30 35 40 45
Time (sec) Abridged Time (sec)
c) Half-cycle response history d) Equivalent damping ratio
Figure A.5 Free vibration analysis response
332
A.5 Collapse prevention systems
In this section the potential effect of a collapse prevention system is demonstrated through
analysis of a portal frame. The portal frame (Figure A.6) was idealized as shear-structure (rigid
beam relative to the columns). Inelastic column behaviour was modelled using a concentrated
plasticity approach. Members were rigid elastic beam-column elements, and beam-to-column
connections were zero-length rotational elastic-plastic springs. The spring stiffness was
calculated such that the lateral stiffness of the frame was equal to a frame with fixed columns
and a rigid beam. Columns were pinned (free to rotate) at the base and a lean-on column (not
shown in Figure A.6) was used to incorporate gravity load columns that are indirectly stabilized
by the frame.
(a) without a collapse prevention system (b) with full-bay slack-cables
(c) with loose linkages (d) loose linkages, viscous fluid dampers
Figure A.6 Idealized configurations of collapse prevention systems
333
The portal frame height, H, was 10 feet and the frame length (bay length) was 20 feet.
The frame weight, W and lateral stiffness, K were selected such that the fundamental period of
vibration was 0.5 seconds. The gravity load stabilized was 1.0 times the load directly supported
by the frame. The ductility supply to demand ratio was 8, and the inherent damping was
estimated to be 5% of critical damping.
Nonlinear dynamic response history analysis was performed using OpenSees (PEER
2012). The portal frame was subjected to the Imperial Valley (1940) El Centro ground motion
record, scaled to match various hazard intensity values (spectral acceleration) at the fundamental
period of vibration. For a structure located in Charleston, South Carolina (with 32.8° latitude,
-80.0° longitude) the damped 0.5-sec. spectral acceleration values are, respectively 0.02 g, 0.29
g, and 1.43 g for serviceability (50% probability of being exceeded in 30 years), life safety (10%
probability of being exceeded in 50 years), and collapse prevention (2% probability of being
exceeded in 50 years).
The collapse-level drift ratio history is shown in Figure A.7 for the portal frame with and
without slack-cables. The slack in the cable was selected so that the peak drift ratio was 3%.
Similarly, the geometry of the loose linkages was configured to limit the peak drift to 3%. The
hybrid collapse prevention system using viscous dampers was selected such that 5% or 10% of
equivalent damping was added to the overall structure.
Table A.5 summarizes the potential benefit of incorporating a collapse prevention system
in the portal frame. An earthquake hazard level equal to 2/3 of the maximum considered
earthquake (MCE) ground motion level was included for comparison of the design basis
earthquake (DBE) ground motions. The results show that for this portal frame structure and this
location (Charleston, South Carolina), life safety and collapse prevention were the most relevant
334
performance objectives for seismic design. Employing a collapse prevention system to meet the
predetermined limit (3% drift ratio) reduced residual drifts by about half, while only increasing
the base shear ratio (base shear divided by frame weight) by 10% to 30%, depending on the
collapse prevention system. Viscous fluid dampers reduced residual drift. For this particular
frame and analysis, adding 10% compared to 5% of equivalent damping to the system did not
improve the performance.
Slack-cables
No collapse prevention system
Figure A.7 Collapse-level drift ratio history for portal frame
Table A.5 Nonlinear dynamic response history analysis results for portal frame
Ratio (%)
Seismic
Frame Description Hazard level ∆ peak /H ∆ residual /H V base /W
Serviceability 0.03 0.00002 0.29
Life safety 0.34 0.03 4.33
Without CPS
DBE 1.54 1.31 13.5
MCE 5.39 5.20 20.0
Slack cables 3.00 2.68 21.9
Loose linkages (LL) 3.00 2.63 25.4
MCE
LL with dampers (5% damping) 3.00 2.79 23.1
LL with dampers (10% damping) 3.00 2.79 23.1
335
Appendix B
DESIGN OF TYPE I NON-DUCTILE MOMENT FRAME BUILDINGS
This appendix discusses the design of the archetype Type I non-ductile moment frame buildings.
The archetype buildings were intended to be prototypical building configurations that are
representative of possible building configurations to be used with the collapse prevention system
concept. The development followed the general procedure recommended in FEMA P695,
Quantification of building seismic performance factors (FEMA 2009a). Building design criteria
was based on current (2015) codes and standards. Design gravity loads (dead loads and live
loads) were based on realistic materials and standard occupancy and use. Buildings were
evaluated for several hazard levels, considering both wind and seismic hazards. Building
configuration was based on common story elevations and plan layouts, and a range of building
heights. The intent of archetype development was to reasonably predict general performance of
a broad class of buildings based on the performance of the limited set of buildings designed here.
Ordinary moment frame (OMF) buildings were also designed, although these buildings
were not used in Chapter 3 and subsequent evaluations. The design of the OMF buildings is
included in this appendix because it illustrates the procedures used to design the Type I non-
ductile moment frame buildings.
336
B.1 Design Criteria
The non-ductile buildings were designed to meet the load requirements (including dead, live,
wind, and seismic loads) and load combinations provided in ASCE/SEI 7-10, Minimum design
loads for buildings and other structures (ASCE 2010).
The design of structural steel systems was based on ANSI/AISC 360-10, Specification for
structural steel buildings (AISC 2010a) and the AISC Steel construction manual (AISC 2011a).
The design of structural seismic force resisting systems (i.e. the steel moment frames) was based
on ANSI/AISC 341-10, Seismic provisions for structural steel buildings (AISC 2010b).
Member deflections and building drifts satisfy the performance limits given in Table B.1.
Deflections of members under gravity loads were limited to common applications as specified in
the International building code (IBC) (ICC 2012a). Building drift limit for wind loads was based
on a 10-year MRI. Building drift limit for seismic loads was based on 2% allowable drift for
Risk Category II steel structures in ASCE/SEI 7-10, Table 12.12-1.
Table B.1 Deflection and drift performance limits
Analysis Deflection / drift limit

Member live load L/360
Member total load L/240
Member construction total load L/360
Building wind elastic drift (10-year MRI) H/400
Building seismic inelastic drift (DBE) H/50
337
B.2 Design Gravity Loads
The uniform dead and live loads used to design the archetype buildings are given in Table B.2
and Table B.3. The total loads were targeted to match the design loads used in Chapter 6 and
Appendix D of the FEMA P-695 evaluation report (NIST 2010a). The dead loads are generally
representative of typical design dead loads used in practice, except that a composite steel deck
and concrete slab is used instead of a steel-joist and steel-deck system for the roof.
The live loads were representative of the occupancy and use of commercial office
buildings. A constant uniform live load was used, matching the live load used in the FEMA
evaluation report (i.e. lobby, corridor, stair, and exit area live loads are not used). Construction
phase (pre-composite) live load is 25 psf (ASCE 2002). Reduction of roof and floor live loads is
applied in accordance with ASCE 7 section 4.7.
Table B.2 Design dead loads
Description Uniform load (psf)

5.5-inch slab (2-inch normal weight concrete cover on 3-inch steel deck) 51
Partitions (floor) or ballast material (roof) 20
Structural steel members 9
Superimposed dead load (ceiling, mechanical, electrical, plumbing) 10
Total design dead load: 90
Table B.3 Design live loads
Use or occupancy Uniform load (psf)

Roofs (ordinary maintenance) 20
Floors (offices) 50
Construction phase 25
338
B.3 Seismic Hazard
Archetype buildings were designed for seismic hazard levels described in Table B.4. For each
hazard level, the target Seismic Design Category (SDC) design basis earthquake (DBE) spectral
acceleration values from ASCE/SEI 7-10, Table 11.6-1 and Table 11.6-2 were used to determine
the corresponding risk-based Maximum Considered Earthquake (MCE) ground motion spectral
acceleration values (2% probability of being exceeded in 50 years (or 2,475-year MRI), based on
soil site class D, and the mapped MCE values.
A hazard level corresponding to SDC D max (shown in FEMA P695 Table 5-1A and Table
5-1B) is included in the design, even though the archetype lateral force resisting system—steel
ordinary moment frames (OMF) and steel moment frames not detailed for seismic resistance (so
called “R=3” systems)—are not permitted by ASCE/SEI 7-10, Table 12.2-1 in SDC D, for the
full range of archetype building height (greater than 65 feet) and material weight (roof and wall
dead load in excess of 20 psf). The purpose of including these in the design was to allow for a
comparison between the response of non-ductile (OMF and R=3) and ductile (SMF and IMF)
frames determined in related studies (Jarrett 2013; Flores 2015).
Table B.4 Seismic design hazards
Spectral Acceleration
Mapped MCE DBE
Seismic Design
Category (SDC) S S (g) S 1 (g) S MS (g) S M1 (g) S DS (g) S D1 (g)
B min 0.156 0.042 0.25 0.10 0.17 0.07
C min 0.330 0.083 0.51 0.20 0.34 0.13
D min 0.550 0.132 0.75 0.30 0.50 0.20
D max 1.500 0.684 1.50 0.90 1.00 0.60
339
B.4 Wind Hazard
Archetype buildings are designed for a wind hazard corresponding to non-coastal location in the
United States. This provides a typical wind speed for design (avoiding the lower design wind
speed on the west coast, and the higher wind speeds along the eastern coast). Service level wind
speed (76 mph) and strength level wind speed (115 mph) are based on the 10-year MRI (ASCE
7-10 Figure CC-1) and 700-year MRI (ASCE 7-10 Figure 26.5-1A), respectively.
The buildings are designed for terrain exposure category C (open terrain without
obstructions). The effect of wind gust is included based on 1% damping (inherent damping not
explicitly modeled) for service level drift, and 2% damping for strength level drift.
B.5 Analyses for Design
For design purposes, story heights were based on beam centerlines, including the first story.
This definition of story height differs from the definition of story height in the FEMA P-695
evaluation report (NIST 2010a). In the evaluation report, elevations were based on beam
centerlines, except the first story height was measured from the ground to the top of the beam
(NIST 2010a Appendix A; NIST 2010b). In that study, the beam size used to establish the first
story elevation was not necessarily the final beam size used in the design. (It was likely a trial
size). For example, all the 1-story buildings in the evaluation report use a first-story elevation
based on a W18X16 first story beam, but only one archetype design actually used that size beam
for the first story.
Tributary areas and loads were based on beam and column centerlines. The evaluation
report also used beam centerlines when calculating tributary dead loads, but ignored the first
story height definition used to determine elevation lines.
340
Parameters used to design the steel moment frames are summarized in Table B.5. The
estimated (empirical) period of vibration for wind analyses is shown. This value differs from the
empirical period of vibration used for seismic analyses and is closer to a lower bound on
observed data of building periods. The wind base shear force for drift analysis (10-year MRI)
and strength analysis (700-year MRI) are shown in Table B.5. For each seismic design category,
the base shear force and base shear coefficient, 𝐶𝑠 (base shear force normalized by the total
weight of the building) is given based on the estimated period of vibration (T = C u T a ).
Table B.5 Design parameters for non-ductile moment frames
Wind Seismic
Archetype No. of V (k)
ID stories T (s) 10-yr MRI 700-yr MRI SDC T (s) Cs V (k)
R3-20-1A B min 0.42 0.054 72.8
R3-20-1B C min 0.40 0.111 150
1 0.39 8.44 19.3
R3-20-1C D min 0.37 0.166 224
R3-20-1D D max 0.34 0.333 450
R3-20-2A B min 0.68 0.033 90.5
R3-20-2B C min 0.66 0.067 186
2 0.65 24.8 56.8
R3-20-2C D min 0.60 0.110 305
R3-20-2D D max 0.56 0.333 922
R3-20-4A B min 1.16 0.019 108
R3-20-4B C min 1.11 0.040 223
4 1.10 64.6 149
R3-20-4C D min 1.02 0.065 365
R3-20-4D D max 0.95 0.210 1,175
R3-20-8A B min 1.99 0.011 127
R3-20-8B C min 1.91 0.023 261
8 1.88 159 369
R3-20-8C D min 1.75 0.038 428
R3-20-8D D max 1.64 0.122 1,378
R3-20-12A B min 2.73 0.008 139
R3-20-12B C min 2.63 0.017 285
12 2.59 269 624
R3-20-12C D min 2.41 0.028 468
R3-20-12D D max 2.25 0.089 1,505
Table B.6 summarizes the lateral load resisting system drift, strength, and seismic
stability analyses used for design. Load combinations and load factors for these requirements
were based on ASCE 7-10. Note that in contrast to gravity load combinations, roof live load was
not included in the lateral combinations except in a wind strength analysis.

341
Second-order effects (P-∆ effects) were included in a centerline-model analysis using the
Direct Design Method (AISC 360-10). The reduced stiffness that is required by the Direct
Design Method was employed only in strength analyses, not in drift or vibration (eigenvalue
frequency-determination) analyses (commentary to AISC 2010a; commentary to AISC 2010b).
The equivalent lateral forces used to check the drift requirement was based on the
computed fundamental period of vibration from an eigenvalue analysis, per ASCE 7-10 section
12.8.6.2, which are lower compared to the forces used for strength analysis shown in Table B.5.
The stability ratio is back-calculated based on first order and second order interstory drift ratios
(Charney 2014). The maximum allowable stability ratio is 0.5/𝐶𝑑 (story overstrength factor β is
taken as 1.0).
342
Table B.6 Analyses used to design the Type I non-ductile moment frames
Hazard Analysis Comments Load combination
Vibration Centerline joint modeling (rigid joints). 1.0D
Lateral forces based on the computed

Drift fundamental period from vibration
(eigenvalue) analysis.
Seismic
Strength Stiffness (modulus of elasticity) reduced 20%. (1.2 + 0.2*S DS )D + 0.5L + E
Stability ratio θ calculated directly based on

Stability first and second order drift analyses:
θ = 1 – ∆1st order / ∆2nd order.
Drift -- D + 0.5L + W 10
Wind
Strength Stiffness (modulus of elasticity) reduced 20%. 1.2D + L + 0.5L r + W 700
B.6 Example Calculations
This section provides example calculations for the Type I 4-story non-ductile archetype building
with an ordinary moment frame (OMF) system. Included are gravity design calculations for a
typical girder, typical column, and lateral design results for the moment frame members.
343
B.6.1 Gravity Design of Girder
The gravity design included live load reductions and considers composite action between the
roof and floor concrete slab and the bare steel beams. Camber (where required) was only used
on interior beams. Exterior beams have no camber.
Composite member
Geometry
Member span L= 40 ft
Dist. to adjacent left member sR = 20 ft
Dist. to adjacent right member sL = 20 ft
Concrete
Concrete cover above deck t= 4.5 in.
Steel deck depth td = 3 in.
Steel deck orientation = Parallel to steel member
Steel
W-Shape = W24X68 in.
Camber c= 1 1/4 in.
PNA location = 5 (BFL)
Loads
Dead Loads
Pre-composite (construction) CDL = 60 psf
Composite (service) DL = 30 psf
Live Loads
Pre-composite (construction) CLL = 25 psf
Composite (service) LL = 50 psf
Live Load Reduction
Live load type = Floor
Tributary area AT = 800 sf
Live load reduction factor = 0.63 ASCE/SEI 7 Section 4.7
Pre-composite (construction) CLL = 16 psf
Composite (service) LL = 31 psf
Materials
Steel
Yield strength Fy = 50 ksi
Modulus of elasticity E= 29,000 ksi
Concrete
Concrete F'c = 4 ksi
Weight = Normal weight
Headed stud anchor (HSA)
Diameter = 3/4 in.
Single anchor strength Qn = 21.5 k
344
Deflection limits
Pre-composite DL L/ 360 AISC Design guide 3
Composite (service) LL L/ 360 2009 IBC Table 1604.3
Pre-composite (construction) design

Required strength
Uniform load (factored) wu = 1.94 klf
Simple-span moment Mu = 388 k-ft
Design strength
Resistance factor φb = 0.90
Plastic section modulus Zx = 177 in.3
Plastic strength φMn = 664 k-ft
Available strength φMn = 585 k-ft AISCM Table 3-10
Flexure strength φMn = 585 k-ft OK Pass by 51%
Deflection
Moment of intertia Ix = 1,830 in.4
DL deflection (unfactored) ∆DL = 1.30 in.
DL deflection limit ∆limit = 1.33 in.
Required camber ∆c = 0.00 in.
Provided camber c= 1.25 in. OK Pass by1%
Composite design
Required strength
Uniform load (factored) wu = 3.16 klf
Simple-span moment Mu = 632 k-ft
Concrete
Effective width of concrete b1 = 120 in.
b2 = 240 in.
bmin = 120 in.
Total slab depth Ycon = 7.5 in.
345
Plastic neutral axis
PNA location = 5 (BFL)
Steel flange thickness tf = 0.585 in.
Steel flange width bf = 8.97 in.
Distance from TFL to PNA Y1 = 0.5850 in.
Area of W-shape As = 20.1 in.2
Steel web thickness tw = 0.415 in.
Lower bound parameters (location 7)
Lower bound composite action = 25% AISCM Page 3-13
Lower bound horizontal shear fo ΣQn = 251 k AISCM Fig. 3-3
Steel shape depth d= 23.7 in.
Steel web fillet k1 = 1.09 in.
Steel web area Aw = 8.93 in.^2 AISCM Page 3-13
Kdep = 0.505 in. AISCM Page 3-13
Karea = 0.34 in.^2 AISCM Page 3-13
Lower bound Y1 Y1 (LB) = 5.7958 in.
Bottom of flange parameters (location 5)
Bottom of flange Y1 Y1 (BFL) = 0.5850 in.
Area of W-shape in tension At = 14.85 in.^2
Horizontal shear force @ locatio ΣQn = 480 k AISCM Fig. 3-3
Location 6 parameters
Horizontal shear force @ locatio ΣQn = 366 k AISCM Fig. 3-3
Steel web depth d= 23.7 in.
Steel web fillet k1 = 1.09 in.
Steel web area Aw = 8.93 in.^2 AISCM Page 3-13
Kdep = 0.505 in. AISCM Page 3-13
Karea = 0.34 in.^2 AISCM Page 3-13
Location 6 Y1 Y1 (L6) = 3.0367 in.
Composite W-shape parameters
Area of W-shape in tension At = 14.85 in.^2
Steel tension force T= 743 k
Area of W-shape in compresion Ac = 5.25 in.^2

Steel compression force Cs = 262 k
Horizontal shear force at interfa ΣQn = 480 k
Dist. from TOS to conc. flange f a= 1.177 in. AISCM Eq. 3-7
Dist. from TFL to conc. force Y2 = 6.911 in. AISCM Eq. 3-7
Conc. compressive force C= 480 k

Max steel tension force T= 1,005 k
346
Composite flexure strength PNA locat Y1 At M(-) (k-in)
1 (TFL) 0.000 20.1 0.0

2 0.146 18.8 9.6
3 0.293 17.5 38.4
4 0.439 16.2 86.3
5 (BFL) 0.585 14.9 153.5
6 3.037 13.7 348.4
7 5.796 12.6 854.1
φMp = 1,131 k-ft OK Pass by 79%

Deflection
Dist. From TFL to conc force d1 = 6.911 in.
Dist. From TFL to steel force d3 = 11.850 in.
Elastic neutral axis YENA = 17.916 in.
Ix, Lower bound ILB = 4,118 in.4
DL deflection (unfactored) ∆DL = 0.30 in.
DL deflection limit ∆limit = 1.33 in. OK Pass by 342%
Number of HSA
Number from zero to Mmax n1 = 23
Total number of anchors n= 46
Result summary
Composite member = W24X68 with c=1.25 in. and (46) HSA
Pre-composite (construction)
Strength = OK Pass by 51%
Deflection = OK Pass by1%
Composite
Strength = OK Pass by 79%
Deflection = OK Pass by 342%
347
B.6.2 Gravity Design of Column
Loads
Dead Loads
Floor/roof dead load DL = 90 psf
Exterior wall dead load WDL = 25 psf
Live Loads
Roof live load (construction) RLL = 25 psf
Floor live load FLL = 50 psf
Column factored dead load (k) per level

Column ID 1 2 3 4 5 6
Trib A (sf) 900 600 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 97 65 47 71 27 47
3 14 97 65 52 77 34 52
2 14 97 65 52 77 34 52
1 13 97 65 51 77 33 51
Column factored live load (k) per level

Column ID 1 2 3 4 5 6
Trib A (sf) 900 600 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 36 24 21 32 16 21
3 14 36 24 27 41 25 27
2 14 36 24 27 41 25 27
1 13 36 24 26 40 24 26
Column total factored load (Pu, k) per level

Column ID 1 2 3 4 5 6
Trib A (sf) 900 600 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 133 89 68 102 43 68
3 14 133 89 79 118 59 79
2 14 133 89 79 118 59 79
1 13 133 89 77 116 57 77
Column load (Pu, k) cummulative

Column ID 1 2 3 4 5 6
Trib A (sf) 800 400 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 133 89 68 102 43 68
3 14 266 178 147 221 102 147
2 14 400 266 226 339 161 226
1 13 533 355 303 455 218 303
348
Column tributary area (sf)
Column ID 1 2 3 4 5 6
Story KLL 4 4 4 4 4 4
4 800 400 400 600 200 400
3 1,600 800 800 1,200 400 800
2 2,400 1,200 1,200 1,800 600 1,200
1 3,200 1,600 1,600 2,400 800 1,600
Column Live Load Reduction factor

Column ID 1 2 3 4 5 6
Story KLL 4 4 4 4 4 4
4 0.60 0.80 0.80 0.60 1.00 0.80
3 0.63 1.00 1.00 0.68 1.00 1.00
2 0.52 0.63 0.63 0.56 1.00 0.63
1 0.47 0.56 0.56 0.50 0.68 0.56
Column reduced factored live load (k) per level

Column ID 1 2 3 4 5 6
Trib A (sf) 900 600 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 22 19 17 19 16 17
3 14 23 24 27 28 25 27
2 14 19 15 17 23 25 17
1 13 17 13 15 20 16 15
Column total load (Pu, k) cummulative including live load reduction

Column ID 1 2 3 4 5 6
Trib A (sf) 800 400 400 600 200 400
Story Trib W (ft) 0 0 20 30 30 20
4 6.5 119 84 64 90 43 64
3 14 239 173 143 195 102 143
2 14 354 253 211 295 161 211
1 13 468 331 277 391 211 277
Gravity only columns

Column 1 2 5
Story Hmax (ft) W-Shape φPn W-Shape φPn W-Shape φPn
3 to 4 13 W8X31 266 W8X31 266 W8X31 266
1 to 2 15 W8X67 523 W8X48 367 W8X31 230
B.6.3 Lateral Design of OMF
Lateral design loads for the 4-story frame are shown below. Figure B.1 shows the MWFRS wind
loads (for the 10-year MRI), and Figure B.2 shows equivalent lateral seismic loads (for the OMF
349
frame in SDC D min / C max ). For modeling purposes, the lateral load was applied at each beam-
column joint: half load at exterior joints, whole load at interior joints (not entirely at the exterior
frame joint as depicted below).
The seismic analysis results using centerline modeling is shown in Table B.7 to Table
B.11. Inter-story drift values shown have been amplified to represent inelastic drift values
(multiplied by 𝐶𝑑 ).
9.82 k
18.9 k
18.0 k
17.9 k
Base shear = 64.6
Figure B.1 Lateral MWFRS wind loads (4-story building)
129 k
96.7 k
59.8 k
27.4 k
Base shear = 313
Figure B.2 Lateral equivalent seismic loads (4-story building, OMF, SDC D min )
350
Table B.7 Inter-story drift ratio and stability ratio for seismic drift analysis: 4-story building,
OMF SDC D mi n
Inter-story drift ratio Stability ratio, θ

∆1st order ∆2nd order
(1 – ∆ /∆
1st order 2nd order
Story )
4 0.0070 0.0077 0.086
3 0.0103 0.0117 0.123
2 0.0093 0.0107 0.134
1 0.0067 0.0077 0.129
Drift limit = 0.0200 θ max = 0.167
Table B.8 Ratio of available / required beam strength for seismic strength analysis: 4-story
building, OMF SDC D mi n
Bay
Story 1 2 3
4 0.41 0.36 0.33
3 0.69 0.60 0.61
2 0.89 0.80 0.83
1 0.92 0.84 0.88
Table B.9 Interaction ratio of available and required column flexure and axial strengths for
seismic strength analysis: 4-story building, OMF SDC D mi n
Column
Story 1 2 3 4
4 0.41 0.52 0.47 0.37
3 0.82 0.88 0.85 0.90
2 0.39 0.52 0.51 0.55
1 0.80 0.76 0.76 0.97
Table B.10 Ratio of available and required joint (panel zone) shear strength for seismic strength
analysis: 4-story building, OMF SDC D mi n
Column
Story 1 2 3 4
4 0.45 0.34 0.30 0.37
3 0.94 0.71 0.67 0.82
2 0.87 0.62 0.61 0.81
1 0.80 0.59 0.59 0.76
351
Table B.11 Computed periods of vibration: 4-story building, OMF SDC D mi n
Period (sec/cycle)
Analytical model T1 T2 T3 T4
Centerline 2.15 0.71 0.39 0.24
For purposes of comparison, the seismic analysis results based on explicit joint modeling
(using the Krawinkler panel zone model) are shown in Table B.12 to Table B.16. The archetype
designs were not based on explicit joint modeling.
Table B.12 Inter-story drift ratio and stability ratio for seismic drift analysis: 4-story building,
OMF SDC D mi n
Inter-story drift ratio Stability ratio, θ

∆1st order
∆2nd order
(1 – ∆ /∆
1st order 2nd order
Story )
4 0.0073 0.0080 0.090
3 0.0099 0.0112 0.118
2 0.0092 0.0106 0.131
1 0.0068 0.0078 0.127
Drift limit = 0.0200 max = 0.167
Table B.13 Ratio of available / required beam strength for seismic strength analysis: 4-story
building, OMF SDC D mi n
Bay
Story 1 2 3
4 0.42 0.34 0.35
3 0.64 0.50 0.58
2 0.84 0.71 0.78
1 0.88 0.76 0.84
352
seismic strength analysis: 4-story building, OMF SDC D mi n
Column
Story 1 2 3 4
4 0.41 0.50 0.46 0.38
3 0.76 0.73 0.72 0.85
2 0.34 0.45 0.43 0.51
1 0.80 0.76 0.76 0.98
Table B.15 Ratio of available and required joint (panel zone) shear strength for seismic strength
analysis: 4-story building, OMF SDC D mi n
Column
Story 1 2 3 4
4 0.40 0.58 0.54 0.34
3 0.72 0.97 0.97 0.65
2 0.64 0.88 0.85 0.59
1 0.56 0.80 0.78 0.53
Table B.16 Computed periods of vibration: 4-story building, OMF SDC D mi n
Period (sec/cycle)
Analytical model T1 T2 T3 T4
Centerline 2.12 0.69 0.35 0.21
A summary of the wind analysis results using centerline modeling is shown in Table B.17
to Table B.19. The wind analysis results (not shown) were based on explicit joint modeling
(using the Krawinkler panel zone model) but are not significantly different.
Table B.17 Inter-story drift ratio for wind drift analysis: 4-story building
Inter-story drift ratio

Story ∆1st order ∆2nd order
4 0.0005 0.0005
3 0.0010 0.0011
2 0.0011 0.0012
1 0.0009 0.0010
Drift limit = 0.0025 (H/400)
353
Table B.18 Ratio of required to provided beam strength for wind strength analysis: 4-story
building
Bay
Story 1 2 3
4 0.11 0.08 0.04
3 0.22 0.17 0.13
2 0.34 0.29 0.28
1 0.40 0.35 0.36
wind strength analysis: 4-story building
Column
Story 1 2 3 4
4 0.17 0.16 0.11 0.11
3 0.53 0.36 0.32 0.52
2 0.36 0.27 0.25 0.38
1 0.58 0.47 0.47 0.64
354
B.7 Design Summary
A summary of the design analyses is provided in Table B.20 to Table B.23. For each archetype,
the beam and column sizes, the design criteria (strength, drift, or stability) that controlled the
overall design, and the computed fundamental period of vibration (based on centerline modeling)
used in seismic drift analyses is given.
Table B.20 Archetype design and member sizes for Type I non-ductile 1-story buildings
Column size Controlling Computed

Design Story Beam size Exterior Interior criteria Period, T 1
OMF / B max 1 W18X40 W14X90 W14X99 Strength 1.50
OMF / C max 1 W21X44 W14X109 W14X132 Strength 1.27
R=3 / A max 1 W18X35 W14X82 W14X82 Stability 1.67

1 W21X55 W18X71 W18X76

OMF / B max Strength 1.99
2 W16X31 W18X71 W18X76
1 W24X55 W18X97 W18X143

OMF / C max Strength 1.62
2 W16X31 W18X97 W18X143
1 W21X44 W18X71 W18X76

R=3 / A max Stability 2.13
2 W16X31 W18X71 W18X76
355

1 W16X40 W18X76 W18X97

OMF / 2 W21X44 W18X76 W18X97
Stability 2.44
B max 3 W18X35 W18X40 W18X50
4 W16X31 W18X40 W18X50
1 W21X44 W18X86 W18X106

OMF / 2 W21X48 W18X86 W18X106
Strength 2.15
C max 3 W21X44 W18X40 W18X50
4 W18X35 W18X40 W18X50
1 W16X40 W18X76 W18X86

2 W21X44 W18X76 W18X86
R=3 / A max Stability 2.49
3 W18X35 W18X40 W18X46
4 W16X31 W18X40 W18X46
356

1 W21X48 W24X146 W24X146

2 W24X68 W24X146 W24X146
3 W24X76 W24X76 W24X103
OMF / 4 W24X55 W24X76 W24X103
Stability 3.32
B max 5 W24X55 W24X55 W24X62
6 W21X48 W24X55 W24X62
7 W18X35 W24X55 W24X55
8 W18X35 W24X55 W24X55
1 W21X48 W24X131 W24X162

2 W24X76 W24X131 W24X162
3 W24X76 W24X76 W24X103
OMF / 4 W24X55 W24X76 W24X103
Strength 3.27
C max 5 W21X55 W24X55 W24X68
6 W21X55 W24X55 W24X68
7 W18X35 W24X55 W24X55
8 W18X35 W24X55 W24X55
1 W21X48 W24X146 W24X146

2 W24X68 W24X146 W24X146
3 W24X76 W24X76 W24X103
4 W24X55 W24X76 W24X103
R=3 / A max Wind strength 3.32
5 W24X55 W24X55 W24X62
6 W21X48 W24X55 W24X62
7 W18X35 W24X55 W24X55
8 W18X35 W24X55 W24X55
357
Appendix C
ANALYTICAL MODEL FOR TYPE I NON-DUCTILE MOMENT FRAME
4-STORY BUILDING
This appendix contains excerpts of the OpenSees (PEER 2012) scripts and selected modeling
results for the Type I non-ductile moment frame 4-story building with enhanced shear tab
connections.
C.1 Building and Load Model
The following is an excerpt from the OpenSees script used to define the building, materials,
connection and plastic hinge behavior, and gravity loads. Figure C.1 shows a perspective view
of the finite element model.
Figure C.1 Finite element model of Type I non-ductile moment frame 4-story building
358
# OpenSees input file generated using MATLAB
#
# General information
wipe
geomTransf Linear 1
geomTransf PDelta 2
geomTransf Corotational 3
#
# Frame 1 Base line 1
node 100010100 0.000000 0.000000
fix 100010100 1 1 0
#
# Frame 1 Joint line 1 story 1
node 101020101 6.850000 180.000000
node 101020102 6.850000 180.000000
node 101020103 6.850000 168.150000
node 101020104 6.850000 156.300000
node 101020105 6.850000 156.300000
node 101020106 0.000000 156.300000
node 101020107 -6.850000 156.300000
node 101020108 -6.850000 156.300000
node 101020109 -6.850000 168.150000
node 101020110 -6.850000 180.000000
node 101020111 -6.850000 180.000000
node 101020112 0.000000 180.000000
equalDOF 101020101 101020102 1 2
equalDOF 101020104 101020105 1 2
equalDOF 101020107 101020108 1 2
equalDOF 101020110 101020111 1 2
element elasticBeamColumn 101020101 101020102 101020103 1000.000000
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
29000.000000 100000.000000 3
uniaxialMaterial Hysteretic 101020109 2995.671113 0.002855 3199.604513
0.011419 11827.137317 0.285481 -2995.671113 -0.002855 -3199.604513 -0.011419
-11827.137317 -0.285481 1.000000 1.000000 0.000000 0.000000 0.000000
element zeroLength 101020109 101020101 101020102 -mat 101020109 -dir 6
[…]
# Frame 3 Beam bay 5 story 4

equalDOF 101020209 301020209 1
equalDOF 102020209 302020209 1
equalDOF 103020209 303020209 1
359
equalDOF 104020209 304020209 1
equalDOF 101020309 301020309 1
[…]
mass 101020109 0.154110 0.000000 0.000000

mass 101020103 0.154110 0.000000 0.000000
mass 101020209 0.154110 0.000000 0.000000
mass 101020203 0.154110 0.000000 0.000000
mass 101020309 0.154110 0.000000 0.000000
mass 101020303 0.154110 0.000000 0.000000
mass 101020409 0.154110 0.000000 0.000000
mass 101020403 0.154110 0.000000 0.000000
mass 101020509 0.154110 0.000000 0.000000
mass 101020503 0.154110 0.000000 0.000000
mass 101020609 0.154110 0.000000 0.000000
[…]
#
# Gravity load time series
timeSeries Constant 1 -factor 1.000000
pattern Plain 101020109 1 {
load 101020109 0.000000 -16.212500 0.000000
}
load 101020103 0.000000 -16.212500 0.000000
}
load 101020209 0.000000 -37.612500 0.000000
}
[…]
360
C.2 Gravity Load Analysis
The following is the script used to define the gravity (pre-load) analysis.

#
# Define source file (finite element model and loads)
source exampleInput.tcl
#
constraints Plain
numberer Plain
system UmfPack
test EnergyIncr 1.000000e-005 20
algorithm Newton
analysis Static
set ok [analyze 10 1.000000]
loadConst -time 0.000000
C.3 Frequency (Building Period of Vibration) Analysis
The following is the script used to define the frequency analysis. Figure C.2 shows the first four
mode shapes and periods of vibration.

#
# Define source file (gravity analysis)
source exampleGravityInput.tcl
#
constraints Plain
numberer Plain
system UmfPack
algorithm Newton
#
# Define response recorders
recorder Node -file exampleVibrationRecorderNodeeigeni.out -time -dof 1 2 3
eigen i
set lambda [eigen -generalized -fullGenLapack 4]
set fidwrite [open eigenValue.out w]
foreach lam $lambda {
puts $fidwrite $lam
}
analysis Static
set ok [analyze 1 1.000000]
361
Figure C.2 Mode shapes and periods of vibration
362
C.4 Nonlinear Static “Pushover” Analysis
C.4.1 Seismic Pushover
The following is the script used to define the seismic pushover analysis. Figure C.3 shows the
seismic pushover response and the deformed shape.

#
#
# Lateral Seismic pushover profile load time series
timeSeries Linear 2 -factor 1.000000
load 101020209 0.317256 0.000000 0.000000
}
load 102020209 0.594542 0.000000 0.000000
}
load 103020209 0.842210 0.000000 0.000000
}
load 104020209 0.995724 0.000000 0.000000
}
#
constraints Plain
numberer Plain
system UmfPack
algorithm Newton
#
recorder Node -file exampleSeismicPushoverRecorderNodedisp.out -time -dof 1 2
3 disp
recorder Node -file exampleSeismicPushoverRecorderNodereaction.out -time -dof
1 2 3 reaction
integrator DisplacementControl 104020209 1 0.100000
set fidwrite2Name examplePushoversummary2.out
set fidwrite2 [open examplePushoversummary2.out w]
close $fidwrite2
#
# Solution strategy
set integratorType DisplacementControl
set ok 0
363
set step 1
set fidwrite2Name exampleSeismicPushoversummary2.out
set fidwrite2 [open $fidwrite2Name w]
close $fidwrite2
set numIncr 300
set dt 1
set testType EnergyIncr
set tol 0.0001
set maxIter 20
analysis Static
set algorithmType Newton
while {$ok == 0 && $step <= $numIncr} {
set subStep $dt
set tempIntegratorType $integratorType
set ok [analyze 1 $subStep]
if {$ok != 0} {
puts "Try 1/4 time step"
set subStep 0.25
if {$ok == 0} {puts "That worked .. back to regular time step"}
if {$ok != 0} {
set subStep 0.125
if {$ok == 0} {puts "That worked .. back to 1/4 time step"}
if {$ok != 0} {
set subStep 0.0625
if {$ok == 0} {puts "That worked .. back to 1/8 time step"}
if {$ok != 0} {
set subStep 0.03125
if {$ok == 0} {puts "That worked .. back to 1/16 time
step"}
set subStep 0.0625
}
set subStep 0.125
}
set subStep 0.25
}
set subStep $dt
}
if {$ok != 0 && $algorithmType != "NewtonLineSearch"} {
puts "Try Newton Line Search for this step"
test $testType $tol [expr $maxIter*10]
algorithm NewtonLineSearch
set algorithmType NewtonLineSearch
if {$ok == 0} {puts "That worked .. continue with Newton Line Search"}
}
if {$ok != 0 && $algorithmType != "KrylovNewton"} {
puts "Try Krylov-Newton for this step"
algorithm KrylovNewton -initial
set algorithmType KrylovNewton
364
if {$ok == 0} {puts "That worked .. continue with Krylov-Newton"}
}
if {$ok != 0 && $algorithmType != "BFGS"} {
puts "Try BFGS for this step"
algorithm BFGS
set algorithmType BFGS
if {$ok == 0} {puts "That worked .. continue with BFGS"}
}
if {$ok != 0 && $algorithmType != "Broyden"} {
puts "Try Broyden for this step"
algorithm Broyden 8
set algorithmType Broyden
if {$ok == 0} {puts "That worked .. continue with Broyden"}
}
if {$ok != 0 && $algorithmType != "ModifiedNewton"} {
puts "Try Modified Newton for this step"
algorithm ModifiedNewton
set algorithmType ModifiedNewton
if {$ok == 0} {puts "That worked .. continue with Modified Newton"}
}
if {$ok != 0 && $algorithmType != "ModifiedNewtonInitial"} {
puts "Try initial stiffness for this step"
algorithm ModifiedNewton -initial
set algorithmType ModifiedNewtonInitial
if {$ok == 0} {puts "That worked .. continue with initial stiffness"}
}
if {$ok == 0} {set tempTol $tol}
if {$ok != 0} {
puts "Try tolerance*10 "
set tol 0.001
if {$ok != 0 && $algorithmType != "NetwonLineSearch"} {
if {$ok == 0} {puts "That worked .. continue with Newton Line
Search"}
}
365
}
algorithm BFGS
}
algorithm Broyden 8
}
if {$ok != 0} {
set tol 0.01
Search"}
Search"}
}
if {$ok == 0} {puts "That worked .. continue with Krylov-
Newton"}
}
algorithm BFGS
}
366
algorithm Broyden 8
}
if {$ok != 0} {
set tol 0.1
Search"}
Search"}
}
Newton"}
}
algorithm BFGS
}
algorithm Broyden 8
}
puts "Back to tolerance*100 "
set tol 0.01
}
set tol 0.001
}
puts "Back to original tolerance "
367
set tol 0.0001
}
if {$ok == 0} {
puts $step
set currentTime [getTime]
set numIteratons [testIter]
set fidsolutioninfo [open $fidwrite2Name a]
puts $fidsolutioninfo "$step $tempIntegratorType $currentTime
$algorithmType $numIteratons $tempTol"
close $fidsolutioninfo
set step [expr $step + 1]
}
}
0.14
0.12
Response without considering

0.1 interaction of axial and flexure
0.08
Response with reduction in
moment strength due to
interaction of axial and flexure
0.06
0.04
0.02
0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Roof Drift Ratio
Figure C.3 Seismic pushover response
368
C.4.2 Wind Pushover
The following is an excerpt from the script used to define the wind pushover analysis. Figure
C.4 shows the seismic pushover response and the deformed shape.

#
#
# Lateral Wind pushover profile load time series
timeSeries Linear 2 -factor 1.000000
load 101020209 -41.223884 0.000000 0.000000
}
load 102020209 -41.464717 0.000000 0.000000
}
load 103020209 -43.627370 0.000000 0.000000
}
load 104020209 -22.650376 0.000000 0.000000
}
#
constraints Plain
numberer Plain
system UmfPack
algorithm Newton
#
recorder Node -file exampleWindPushoverRecorderNodedisp.out -time -dof 1 2 3
disp
recorder Node -file exampleWindPushoverRecorderNodereaction.out -time -dof 1
2 3 reaction
integrator DisplacementControl 104020209 1 0.050000
set fidwrite2Name examplePushoversummary2.out
set fidwrite2 [open examplePushoversummary2.out w]
close $fidwrite2
#
# Solution strategy
[...]
369
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Roof Drift Ratio
Figure C.4 Wind pushover response
370
C.5 Nonlinear Response History Analysis
C.5.1 Seismic Incremental Dynamic Analysis (IDA)
The following is an excerpt from the script used to define a typical seismic IDA.

#
#
# Ground motion
timeSeries Path 3 -dt $dtValue -filePath $filePathValue -factor $factorValue
pattern UniformExcitation 1 1 -accel 3
#
# Inherent non-explicitly-modeled damping
region 101020101 -ele 101020101 -rayleigh 0.156410 0.000000 0.002220 0.000000
[…]
constraints Plain
numberer Plain
system UmfPack
algorithm Newton
recorder Node -file
exampleDynamicIDA.$recordName.runNo$runNo.RecorderNode101020209disp.out -time
-node 101020209 -dof 1 2 3 disp
recorder Node -file
-node 102020209 -dof 1 2 3 disp
recorder Node -file
-node 103020209 -dof 1 2 3 disp
recorder Node -file
-node 104020209 -dof 1 2 3 disp
integrator Newmark 0.500000 0.250000
#
# Solution strategy
set integratorType Newmark
set ok 0
set step 1
371
set numIncr $points
set dt $dtValue
set minNumSubStep 10
set testType EnergyIncr
set tol 0.0001
set maxIter 20
analysis VariableTransient
set dtMin [expr $dt/$minNumSubStep]
set dtMax $dt
set Jd 1
set algorithmType Newton
while {$ok == 0 && $step <= $numIncr} {
set subStep $dt
set tempIntegratorType $integratorType
set ok [analyze 1 $subStep $dtMin $dtMax $Jd]
if {$ok != 0} {
puts "Temporarily try reduced (1/10) dtMin"
set ok [analyze 1 $subStep [expr $minNumSubStep/10] $dtMax $Jd]
}
if {$ok != 0 && $algorithmType != "NewtonLineSearch"} {
}
}
algorithm BFGS
}
algorithm Broyden 8
}
if {$ok != 0 && $algorithmType != "ModifiedNewton"} {
puts "Try Modified Newton for this step"
algorithm ModifiedNewton
set algorithmType ModifiedNewton
372
if {$ok == 0} {puts "That worked .. continue with Modified Newton"}
}
if {$ok != 0 && $algorithmType != "ModifiedNewtonInitial"} {
puts "Try initial stiffness for this step"
algorithm ModifiedNewton -initial
set algorithmType ModifiedNewtonInitial
if {$ok == 0} {puts "That worked .. continue with initial stiffness"}
}
if {$ok != 0} {
puts "Temporarily try TRBDF2"
integrator TRBDF2
set integratorType TRBDF2
if {$ok == 0} {puts "That worked .. back to Newmark"}
if {$ok == 0} {set tempIntegratorType $integratorType}
set integratorType Newmark
}
if {$ok != 0} {
set tol 0.001
Search"}
}
}
algorithm BFGS
}
373
algorithm Broyden 8
}
if {$ok != 0} {
set tol 0.01
Search"}
Search"}
}
Newton"}
}
algorithm BFGS
}
algorithm Broyden 8
}
if {$ok != 0} {
set tol 0.1
Search"}
374
Search"}
}
Newton"}
}
algorithm BFGS
}
algorithm Broyden 8
}
set tol 0.01
}
set tol 0.001
}
puts "Back to original tolerance "
set tol 0.0001
}
if {$ok == 0} {
puts $step
set currentTime [getTime]
set numIteratons [testIter]
set fidsolutioninfo [open $fidwrite2Name a]
puts $fidsolutioninfo "$step $tempIntegratorType $currentTime
$algorithmType $numIteratons $tempTol"
close $fidsolutioninfo
set step [expr $step + 1]
}
}
375
The following is the script used to advance the IDA analysis for a typical ground motion
(LOS000 ground motion record). Figure C.5 shows the scaled response spectra, IDA curves, and
the measured seismic collapse fragility curve.
# OpenSees IDA input file generated using MATLAB

#
# Initialization parameters
set recordName LOS000
set dtValue 0.010000
set points 1999
set filePathValue LOS000.tcl
set g 386.088000
set collapseIDR 0.200000
set collapseFlag 0
set maxCounter 200
set scaleFactor 0.200000
set scaleIncr 0.200000
set scaleTol 0.010000
set runNo 0
set fidwrite [open exampleDynamicIDALOS000summary.out w]
close $fidwrite
#
# Execute and evaluate dynamic response until collapse (IDA)
while {$scaleIncr >= $scaleTol && $runNo <= $maxCounter} {
#
# Initialize variables in run
set runNo [expr {$runNo + 1}]
set maxIDR 0.0
set maxIDRstoryNo 0
set factorValue [expr $scaleFactor*$g]
#
# Execute dynamic analysis
set fidwrite2Name exampleDynamicIDALOS000.runNo$runNo.summary.out
set fidwrite2 [open $fidwrite2Name w]
close $fidwrite2
source exampleDynamicIDAInput.tcl
wipe
#
# Evaluate response for each story
set prevStoryDisp 0.0
#
# Story 1
set storyHeight1 180.000000
set fidread1 [open
exampleDynamicIDA.$recordName.runNo$runNo.RecorderNode101020209disp.out r]
#
# Extract data from each row of recorder output
set lineCount 0
set minX1 0
set maxX1 0
while {[gets $fidread1 line] >= 0} {
376
set fields [split $line " "]
lassign $fields \
time x y z
if {$x < $minX1} {set minX1 $x}
if {$x > $maxX1} {set maxX1 $x}
}
#
# Calculate maximum story displacement
set absMinX1 [expr abs($minX1)]
if {$absMinX1 > $maxX1} {
set storyDisp1 $absMinX1
} else {
set storyDisp1 $maxX1
}
#
# Calculate maximum story drift
set storyDrift1 [expr $storyDisp1 - $prevStoryDisp]
#
# Calculate story IDR
set storyIDR1 [expr $storyDrift1/$storyHeight1]
#
# Save if this is the maximum IDR of the building
if {$storyIDR1 > $maxIDR} {
set maxIDR $storyIDR1
set maxIDRstoryNo 1
}
#
# Save this story displacement as the previous story disp
set prevStoryDisp $storyDisp1
close $fidread1
#
# Story 2
set fidread2 [open
#
set lineCount 0
set minX2 0
set maxX2 0
lassign $fields \
time x y z
}
#
} else {
}
#
377
#
#
set maxIDRstoryNo 2
}
#
close $fidread2
#
# Story 3
set fidread3 [open
#
set lineCount 0
set minX3 0
set maxX3 0
lassign $fields \
time x y z
}
#
} else {
}
#
#
#
set maxIDRstoryNo 3
}
#
close $fidread3
#
# Story 4
378
set fidread4 [open
#
set lineCount 0
set minX4 0
set maxX4 0
lassign $fields \
time x y z
}
#
} else {
}
#
#
#
set maxIDRstoryNo 4
}
#
close $fidread4
#
# Output information to stdout
puts "$runNo $scaleFactor $maxIDR $maxIDRstoryNo"
#
# IDA output information (runNo,scaleFactor,maxIDR)
set fidwrite [open exampleDynamicIDALOS000summary.out a]
puts $fidwrite "$runNo $scaleFactor $maxIDR"
close $fidwrite
set fidwrite3 [open exampleDynamicIDALOS000summaryMaxIDRstoryNo.out a]
puts $fidwrite3 "$runNo $scaleFactor $maxIDR $maxIDRstoryNo"
close $fidwrite3
#
# Check to see if this analysis had a collapse
if {$maxIDR >= $collapseIDR} {
set scaleFactor [expr {$scaleFactor - $scaleIncr}]
set scaleIncr [expr $scaleIncr/2]
set scaleFactor [expr {$scaleFactor + $scaleIncr}]
set collapseFlag 1
379
} else {
# Check to see if previously collapsed
if {$collapseFlag == 0} {
} else {
set scaleIncr [expr $scaleIncr/2]
}
}
}
7 1.5

5
1
0.5
2
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
a) Scaled response spectrum: SDC D max b) IDA curves
1 1
0.9 0.9
0.8 0.8
0.7 Measured collapse 0.7
0.6 points 0.6
0.5 0.5
0.4 0.4
0.3 0.3 Adjusted seismic

0.2 0.2
collapse fragility
0.1 0.1
0 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
c) Measure seismic collapse fragility d) Adjusted seismic collapse fragility
Figure C.5 Seismic collapse assessment results
380
C.5.2 Wind Incremental Dynamic Analysis
The following is the script used to define the wind response history analysis for the along wind
direction (90°) and the wind speed intensity at collapse (256 mph). Figure C.5 shows the scaled
response spectra, IDA curves, and the measured seismic collapse fragility curve.

# 15-Apr-2015 by Johnn Judd
# wipe
#
# Node coordinates
node 1 0 0
node 2 0 0
#
# Boundary conditions
fix 1 1 1 1
fix 2 0 1 1
#
# SDOF system input parameters
set intensityFactor 1.000000
set Tn 1.673800
set zeta 0.010000
#
set pi 3.14159265359
set omega [expr 2*$pi/$Tn]
set k 10.000000
set m [expr $k/pow($omega,2)]
set c [expr 2*$m*$omega*$zeta]
set fy 1.0
#
# Node masses
mass 2 $m 0. 0.
#
# Node damping
rayleigh $c 0.0 0.0 0.0
#
# Coordinate transformation
geomTransf Linear 1
#
# Materials
set material "atc62_spring2a"
set degflag 1
set i 1
set N 1.000000
source materialList.tcl
set material "atc62_spring1a"
set degflag 1
set i 2
381
set N 0.744098
source materialList.tcl
#
# Element type, connectivity, and material
#
# Response recorders
recorder Node -file Cp_ts_g12040090.matInput55Node2.out -time -node 2 -dof 1
disp
recorder Element -file Cp_ts_g12040090.matInput55Element1.out -time -ele 1
force
recorder Element -file Cp_ts_g12040090.matInput55Element2.out -time -ele 2
force
recorder EnvelopeNode -file Cp_ts_g12040090.matInput55Node2Denvelope.out -
time -node 2 -dof 1 disp
#
# Loads for forced motion
set normFactor 0.873328
set scaleFactor [expr $normFactor*$intensityFactor]
timeSeries Path 1 -dt 0.008869 -filePath Cp_ts_g12040090.mat.tcl -factor
$scaleFactor
pattern Plain 1 1 {
load 2 1 0 0
}
#
constraints Plain
numberer Plain
system BandGeneral
test NormDispIncr 1.0e-8 10
algorithm Newton
analysis Transient
#
# Execute analysis
analyze 115201 0.008869
#
puts "Finished nonlinear dynamic response-history analysis:
Cp_ts_g12040090.matInput55"
382
0.08
1
0.8 0.06
0.6
0.04
0.4
0.02
Roof drift ratio

0.2
0 0
-0.2
-0.02
-0.4
-0.04
-0.6
-0.8 -0.06
-1
-0.08
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0 2 4 6 8 10 12 14 16 18 20 22
Roof drift ratio Time (min)
a) SDOF force-deformation b) Roof drift ratio
300 1
0.9
250
Measured collapse
0.8
points
0.7
200
Wind speed, V (mph)
0.6
mph
Adjusted wind
P |V
150 0.5
c
0.4 collapse fragility

100
0.3
0.2
50
0.1
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 50 100 150 200 250 300
Roof drift ratio Wind speed, Vmph
c) Wind IDA curves d) Wind collapse fragility
Figure C.6 Wind collapse assessment response for 90° (along-wind) and 𝑉𝑚𝑚ℎ = 256 mph
383

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Multi-hazard performance of steel moment frame buildings with collapse prevention

systems in the central and eastern United States

Johnn Paul Judd

Finley A. Charney, Chair

Keywords: Earthquake Engineering, Wind Engineering, Nonlinear Dynamic Analysis,

Johnn Paul Judd

TABLE OF CONTENTS ....................................................................................................... iii

LIST OF TABLES ................................................................................................................. iv

LIST OF FIGURES ............................................................................................................... xi

CHAPTER 1 INTRODUCTION ........................................................................................... 1

1.1 Motivation and Background ...................................................................................... 1

1.1.1 Seismic Design .................................................................................................. 2

1.1.2 Wind Design ...................................................................................................... 3

1.1.3 Multi-Hazard Performance ............................................................................... 4

1.1.4 Performance-Based Wind Design ..................................................................... 7

1.2 Objectives and Scope ................................................................................................. 8

1.3 Dissertation Organization .......................................................................................... 10

CHAPTER 2 SEISMIC AND WIND HAZARDS ................................................................ 14

2.1 Seismic Hazards ......................................................................................................... 14

2.1.1 Uniform Hazard Ground Motions .................................................................... 14

2.1.2 Earthquake Rate................................................................................................ 16

2.1.3 Ground Motion Attenuation .............................................................................. 24

2.1.4 Site Response .................................................................................................... 29

2.2 Wind Hazards............................................................................................................. 36

2.2.1 Uniform Hazard Wind Speeds .......................................................................... 36

2.2.2 Wind Hazards.................................................................................................... 39

2.3 Multi-Hazard Comparison ......................................................................................... 40

2.3.1 Seismic and Wind Elastic Base Shear Forces................................................... 40

2.3.2 Multi-Hazard Performance Example ................................................................ 49

2.4 Discussion .................................................................................................................. 58

CHAPTER 3 ARCHETYPE STRUCTURAL SYSTEMS.................................................... 61

3.1 Collapse Prevention System Concept ........................................................................ 61

3.1.1 Reserve Lateral Strength in Gravity Framing .................................................. 62

3.1.2 Collapse Inhibiting Mechanisms....................................................................... 64

3.1.3 Enhanced Shear Tab Connections .................................................................... 70

3.2 Archetype Buildings .................................................................................................. 75

3.2.1 Type I Archetype Buildings ............................................................................... 76

3.2.2 Type II Archetype Buildings.............................................................................. 80

3.2.3 Type III Archetype Buildings ............................................................................ 82

3.2.4 Collapse Prevention Systems ............................................................................ 83

3.3 Analytical Modeling .................................................................................................. 84

3.3.1 Location of Beam Plastic Hinge ....................................................................... 86

3.3.2 Column Fixity, Splices and Plastic Hinge ........................................................ 87

3.3.3 Fully-Restrained (Moment Frame) Beam-to-Column Connections ................. 88

3.3.4 Partially-Restrained (Shear Tab) Beam-to-Column Connections .................... 96

3.3.6 Collapse-Inhibiting Mechanisms ...................................................................... 102

3.3.7 Partially-Restrained (Enhanced Shear Tab) Beam-to-Column Connections ... 104

3.4 Nonlinear Analysis Approach .................................................................................... 107

3.4.1 Second-Order Effects ........................................................................................ 107

3.4.2 Damping ............................................................................................................ 107

3.4.3 Analysis Solution Procedures ........................................................................... 111

CHAPTER 4 SEISMIC COLLAPSE ASSESSMENT .......................................................... 116

4.1 Seismic Collapse Vulnerability Procedures ............................................................... 116

4.1.1 Gravity Load Analysis....................................................................................... 117

4.1.2 Frequency (Building Period of Vibration) Analysis ......................................... 118

4.1.3 Nonlinear Static Seismic (“Pushover”) Analysis ............................................. 119

4.1.5 Target Spectrum ................................................................................................ 122

4.1.6 Intensity Measure for Seismic Hazard .............................................................. 122

4.1.7 Nonlinear Dynamic Response History Analysis ............................................... 124