Characterization of Multi-Phase Performance-Based Passive Control Systems 
 
by 
 
Taylor A. Rawlinson 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 12th, 2011 
 
 
 
 
Keywords:  performance-based, earthquake, multi-phase,  
structures, engineering 
 
 
Copyright 2011 by Taylor Rawlinson 
 
 
Approved by 
 
Justin D. Marshall, Chair, Assistant Professor of Civil Engineering 
Mary L. Hughes, Instructor of Civil Engineering 
James S. Davidson, Associate Professor of Civil Engineering 
 
 
 
 
 
ii 
 
Abstract 
 
Typical passive control devices have inherent strengths and weaknesses as 
seismic protection systems.  A Multi-phase Passive Control System (MPCS) combines 
two types of passive control devices in a system in order to offset the weaknesses of each 
system individually and to optimize structural performance.  The performance-based 
nature of a MPCS in structural design allows the structure to respond effectively to 
varying levels of lateral loading.  Previous work indicates the effectiveness of combining 
passive control devices but the fundamental understanding of the system is lacking.  A 
single-degree-of-freedom (SDOF) non-linear dynamic study was performed in order to 
more clearly define multi-phase behavior and identify important parameters affecting 
response.  Seismic hazard, system arrangement, system strength, system components, and 
material properties were all varied in order to fundamentally understand which 
parameters had significant effects on response.  An incremental dynamic analysis was 
performed on the SDOF systems for a suite of scaled strong ground motions representing 
an array of site characteristics.  Important response quantities included total acceleration, 
base shear, element ductility demand, and drift.  Compared to the baseline systems, 
overall structural performance showed improved behavior with multi-phase 
configurations.  The results of this study offer significant insight towards future work 
involving MPCS. 
 
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Acknowledgments 
 
 First, I would like to thank Dr. Marshall for giving me the opportunity to further 
myself at Auburn University.  His advice and guidance throughout this research has been 
very beneficial to my success.  Always making himself available and offering valuable 
feedback and passion towards the research, Dr. Marshall has been a very enjoyable 
person to work alongside.  I look forward to our continued research over the next few 
years as I continue my studies.   
 I would also like to acknowledge the rest of my committee.  Dr. Hughes has been 
a tremendous help throughout the duration of my graduate career.  Whether it be a 
research question, class work question, or just general chit-chat, her positive attitude and 
willingness to help is extremely appreciated.  Dr. Davidson has provided me with useful 
information applied throughout this research in the 3 courses I have taken with him here 
at Auburn.  I truly appreciate the time and feedback they have devoted to this project.  In 
addition to my committee members, I would also like to thank Dr. LaMondia who 
devoted time to helping me when I was struggling with the statistical aspects of the 
research. 
 I would also like to thank my family, especially my mother, whose love and 
support throughout the duration of my schooling have helped me grow as an individual.  
iv 
 
My mother?s strong work ethic and determination have provided me a strong disposition 
for success.  In addition to my mother, my girlfriend Alana Resmini has provided me
with a tremendous amount of support.  I would also like to thank my fellow graduate 
students and friends whose camaraderie has made Auburn a very enjoyable place to study 
and live the last two years. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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Table of Contents 
Abstract .......................................................................................................................... ii 
Acknowledgments ......................................................................................................... iii 
List of Tables............................................................................................................... viii 
List of Figures ............................................................................................................... ix 
Chapter 1 Introduction .....................................................................................................1 
1.1 Defining the Problem.........................................................................................1 
1.2 The Proposed Solution .......................................................................................2 
1.3 Scope of Work...................................................................................................4 
1.4 Organization of Thesis .......................................................................................5 
Chapter 2 Literature Review ............................................................................................7 
2.1 Introduction .......................................................................................................7 
2.2 Active Control Devices......................................................................................8 
2.3 Semi-Active Control Devices ............................................................................9 
2.4 Passive Control Devices .................................................................................. 11 
2.5 Hybrid Control Devices ................................................................................... 23 
2.6 Multi-Phase Passive Control Devices .............................................................. 23 
2.7 Multi-Phase Behavior ...................................................................................... 24 
2.8 Summary ......................................................................................................... 33 
Chapter 3 Parametric Study Development and Analysis Plan ......................................... 34
 
vi 
 
3.1 Introduction ..................................................................................................... 34 
3.2 Velocity-Dependent Device ............................................................................. 35 
3.3 Displacement-Dependent Device ..................................................................... 36 
3.4 System Arrangement ....................................................................................... 37 
3.5 Baseline Systems ............................................................................................. 41 
3.6 Transition Phase (Gap Size) ............................................................................. 46 
3.7 Seismic Hazard ................................................................................................ 46 
3.8 Natural Period ................................................................................................. 48 
3.9 Experimental Design ....................................................................................... 49 
3.10 System Names ............................................................................................. 51 
3.11 Summary ..................................................................................................... 51 
Chapter 4 Nonlinear SDOF Response History Analysis ................................................. 53 
4.1 Introduction ..................................................................................................... 53 
4.2 System Parameters .......................................................................................... 53 
4.3 Earthquake Records ......................................................................................... 54 
4.4 Modeling Details ............................................................................................. 58 
4.5 Incremental Dynamic Analysis ........................................................................ 65 
4.6 Response Quantities ........................................................................................ 66 
4.7 Summary ......................................................................................................... 67 
Chapter 5 Preliminary Analysis ..................................................................................... 69 
5.1 Introduction ..................................................................................................... 69 
5.2 Preliminary Analysis ....................................................................................... 69 
5.2 Reduction of the Research Scope ..................................................................... 76 
 
vii 
 
5.3 Summary ......................................................................................................... 83 
Chapter 6 Full Factorial Analysis ................................................................................... 85 
6.1 Introduction ..................................................................................................... 85 
6.2 Comparison to Baselines ................................................................................. 85 
6.3 Comparison Between Natural Periods .............................................................. 91 
6.4 Comparison Between Multi-Phase Systems ..................................................... 96 
6.5 Acceleration Spikes ....................................................................................... 127 
6.6 Residual Drifts .............................................................................................. 131 
6.7 Summary ....................................................................................................... 132 
Chapter 7 Summary and Conclusions .......................................................................... 135 
7.1 Summary ....................................................................................................... 135 
7.2 Conclusions ................................................................................................... 137 
7.3 Future Work .................................................................................................. 140 
References ................................................................................................................... 143 
Appendix A. Preliminary Design ............................................................................. 148 
Appendix B. Final Design ....................................................................................... 170
 
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List of Tables 
Table 3-1:  Multi-Phase Systems and Abbreviations ...................................................... 37 
Table 3-2:  Dual System Stiffness Derivation................................................................. 45 
Table 3-3:  System Naming Scheme .............................................................................. 51 
Table 4-1:  Los Angeles Record Selection Summary...................................................... 55 
Table 4-2:  Memphis Record Selection Summary .......................................................... 56 
Table 4-3:  Link Element Backbone Curve Values (ASCE/SEI, 2007) ........................... 60 
Table 4-4:  Response Quantity Summary ....................................................................... 67 
Table 5-1:  Connecting Letters Report ........................................................................... 79 
 
 
 
ix 
 
List of Figures 
Figure 2-1:  Typical Performance Curve (Ghobarah, 2001) ..............................................7 
Figure 2-2:  Magnetorheological Fluid Damper (Spencer Jr. & Nagarajaiah, 2003) ........ 10 
Figure 2-3:  Velocity-dependent Hysteresis Comparison ................................................ 12 
Figure 2-4:  Typical Viscous Fluid Damper (Lee & Taylor, 2001) ................................. 14 
Figure 2-5:  Viscoelastic Device Configuration (Aiken et al., 1993) ............................... 15 
Figure 2-6:  VE Devices in All Stories (Kim et al., 2006) .............................................. 16 
Figure 2-7:  Displacement-Dependent Hysteresis Comparison ....................................... 17 
Figure 2-8:  Typical ADAS Configuration (Alehashem et al., 2008) .............................. 18 
Figure 2-9:  Acceleration Response Comparison with ADAS Device             
(Tehranizadeh, 2001) ......................................................................................... 19 
 
Figure 2-10:  BRB Schematic with Hysteretic Behavior (Sabelli et al, 2003) ................. 20 
Figure 2-11:  Typical Slotted Bolted Connection (Balendra et al., 2001) ........................ 22 
Figure 2-12:  Pall Friction Device (Aiken et al., 1993) ................................................... 23 
Figure 2-13:  Sequential Connection Schematics (Weidlinger & Ettouney, 1993) .......... 25 
Figure 2-14:  Benefits of Sequential Coupling (Weidlinger & Ettouney, 1993) .............. 26 
Figure 2-15:  Stiffening Single-Degree-of-Freedom System                                      
(Motlagh & Saadeghvaziri, 2001) ...................................................................... 27 
 
Figure 2-16:  Stiffening Single-Degree-of-Freedom Comparison to Baseline (Motlagh & 
Saadeghvaziri, 2001) .......................................................................................... 27 
 
Figure 2-17:  Finite Element Model of the VPD (Ibrahim et al., 2007) ........................... 28 
 
x 
 
Figure 2-18:  Multi-Phase Passive Control Device (Marshall, 2008) .............................. 29 
Figure 2-19:  High-damping Rubber Sandwich Damper Schematic (Marshall, 2008) ..... 30 
Figure 2-20:  Possible Arrangements of Multi-Phase Systems (Marshall, 2008) ............. 31 
Figure 2-21:  Acceleration Response Comparison (Marshall, 2008) ............................... 32 
Figure 2-22:  DBE Residual Displacement Comparison (Marshall, 2008) ...................... 32 
Figure 3-1:  BRB Yield Length (Lopez & Sabelli, 2004) ............................................... 37 
Figure 3-2:  Multi-Phase Passive Control Systems ......................................................... 38 
Figure 3-3:  Elastomeric Device (Karavasilis et al., 2010) .............................................. 41 
Figure 3-4:  Comparison of Two Systems with Different Baselines (Marshall, 2008) ..... 42 
Figure 3-5:  Moment Frame Stiffness/Strength Comparison ........................................... 43 
Figure 3-6:  Buckling Restrained Brace Frame Stiffness/Strength Comparison .............. 44 
Figure 3-7:  Comparison of the Design Response Spectrums ......................................... 48 
Figure 3-8:  Design Spectrums with System Natural Periods .......................................... 49 
Figure 3-9:  System Combinations ................................................................................. 50 
Figure 4-1:  Rayleigh Damping ...................................................................................... 54 
Figure 4-2:  Los Angeles Ground Motion Selection and Scaling .................................... 57 
Figure 4-3:  Memphis Ground Motion Selection and Scaling ......................................... 58 
Figure 4-4:  Special Moment Frame Component Breakdown ......................................... 59 
Figure 4-5:  Link Backbone Behavior (ASCE/SEI, 2007) .............................................. 60 
Figure 4-6:  Modeled Baseline System ........................................................................... 61 
Figure 4-7:  Gap Element Modeling ............................................................................... 62 
Figure 4-8:  Modeling of the Series Systems .................................................................. 63 
Figure 4-9:  EMD Hysteretic Slip Behavior ................................................................... 64 
 
xi 
 
Figure 4-10:  Modeling of the Parallel Systems .............................................................. 65 
Figure 5-1:  Acceleration Results for 0.5T Los Angeles Systems ................................... 71 
Figure 5-2:  Base Shear Results for 0.5T Los Angeles Systems ...................................... 71 
Figure 5-3:  Moment Frame Ductility Results for 0.5T Los Angeles Systems ................ 72 
Figure 5-4:  BRB Ductility Results for 0.5T Los Angeles Systems................................. 72 
Figure 5-5:  Hierarchal Nesting Issue ............................................................................. 75 
Figure 5-6:  1T-M70B30-1.0-HYFR Seismic Hazard Comparison ................................. 77 
Figure 5-8:  Moment Frame Ductility Comparison between Dual System Ratios ........... 80 
Figure 5-9:  M-S-2.5T-M50B50-HPCD-VFD Gap Size Comparison ............................. 81 
Figure 5-10:  Full Factorial Experimental Design........................................................... 83 
Figure 6-1:  Multi-Phase System Acceleration Comparison to Baseline (1T-M50B50) .. 87 
Figure 6-2:  Multi-Phase System Base Shear Comparison to Baseline (1T-M50B50) ..... 87 
Figure 6-3:  Multi-Phase System Moment Frame Ductility Comparison to Baseline      
(1T-M50B50) ..................................................................................................... 88 
 
Figure 6-4:  Multi-Phase System Brace Ductility Comparison to Baseline                     
(1T-M50B50) ..................................................................................................... 89 
 
Figure 6-5:  Acceleration Comparison of Multi-Phase Systems to Baselines (0.25T) ..... 92 
Figure 6-6:  Acceleration Comparison of Multi-Phase Systems to Baselines (2.5T) ....... 93 
Figure 6-7:  Brace Ductility Comparison of Multi-Phase Systems to Baselines (0.25T) . 93 
Figure 6-8:  Brace Ductility Comparison of Multi-Phase Systems to Baselines (2.5T) ... 94 
Figure 6-9:  Gap Element Displacement Comparison ..................................................... 95 
Figure 6-10:  HPCD 1T Comparison to Baselines .......................................................... 98 
Figure 6-11:  HPCD 1T Moment Frame Ductility .......................................................... 99 
Figure 6-12:  HPCD 1T Acceleration Response ........................................................... 101 
 
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Figure 6-13:  HPCD 1T Base Shear Response.............................................................. 101 
Figure 6-14:  HPCD 1T Brace Ductility ....................................................................... 102 
Figure 6-15:  HPCD-VFD 1T Comparison to Baselines ............................................... 103 
Figure 6-16:  HPCD-VFD 1T Moment Frame Ductility ............................................... 105 
Figure 6-17:  HPCD-VFD 1T Acceleration Response .................................................. 106 
Figure 6-18:  HPCD-VFD 1T Base Shear Response..................................................... 107 
Figure 6-19:  Gap Element Comparison for M50B50-1T (DZC270 DBE) .................... 107 
Figure 6-20:  HPCD-VFD 1T Brace Ductility .............................................................. 108 
Figure 6-21:  HPCD-VFD Damping Ratio Comparison ............................................... 110 
Figure 6-22:  HPCD vs. HPCD-VFD (M40B60-1.0-1T) .............................................. 111 
Figure 6-23:  HYFR 1T Comparison to Baselines ........................................................ 112 
Figure 6-24:  HYFR 1T Moment Frame Ductility ........................................................ 113 
Figure 6-25:  HYFR 1T Acceleration Response ........................................................... 115 
Figure 6-26:  HYFR 1T Base Shear Response.............................................................. 116 
Figure 6-27:  HYFR 1T Brace Ductility Response ....................................................... 117 
Figure 6-28:  HPCD vs. HYFR Performance ............................................................... 118 
Figure 6-29:  HYFR-VFD Comparison to Baselines .................................................... 119 
Figure 6-30:  HYFR-VFD 1T Moment Frame Ductility ............................................... 121 
Figure 6-31:  HYFR-VFD 1T Acceleration Response .................................................. 122 
Figure 6-32:  HYFR-VFD 1T Base Shear Response..................................................... 123 
Figure 6-33:  HYFR-VFD 1T Brace Ductility .............................................................. 124 
Figure 6-34:  HYFR-VFD Damping Ratio Comparison ............................................... 125 
Figure 6-35:  System Arrangement Comparison........................................................... 126 
 
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Figure 6-36:  a) HYFR-VFD-0.25T-1.0 Gap-M40B60 Acceleration Response History    
b) HYFR-VFD-1T-1.0 Gap-M40B60 Acceleration Response History .............. 128 
 
Figure 6-37:  a) HPCD-0.25T-1.0 Gap-M40B60 Acceleration Response History               
b) HPCD-1T-1.0 Gap-M40B60 Acceleration Response History ....................... 130  
 
Figure 6-38:  Residual Deformations ........................................................................... 132 
Figure A- 1:  Los Angeles 0.25T Acceleration ............................................................. 148 
Figure A- 2:  Los Angeles 0.25T Base Shear ............................................................... 148 
Figure A- 3:  Los Angeles 0.25T Moment Frame Ductility .......................................... 149 
Figure A- 4:  Los Angeles 0.25T Brace Ductility ......................................................... 149 
Figure A- 5:  Memphis 0.25T Acceleration .................................................................. 150 
Figure A- 6:  Memphis 0.25T Base Shear .................................................................... 150 
Figure A- 7:  Memphis 0.25T Moment Frame Ductility ............................................... 151 
Figure A- 8:  Memphis 0.25T Brace Ductility .............................................................. 152 
Figure A- 9:  Los Angeles 0.5T Acceleration ............................................................... 152 
Figure A- 10:  Los Angeles 0.5T Base Shear ............................................................... 153 
Figure A- 11:  Los Angeles 0.5T Moment Frame Ductility .......................................... 153 
Figure A- 12:  Los Angeles 0.5T Brace Ductility ......................................................... 154 
Figure A- 13:  Memphis 0.5T Acceleration .................................................................. 154 
Figure A- 14:  Memphis 0.5T Base Shear .................................................................... 155 
Figure A- 15:  Memphis 0.5T Moment Frame Ductility ............................................... 155 
Figure A- 16:  Memphis 0.5T Brace Ductility .............................................................. 156 
Figure A- 17:  Los Angeles 1T Acceleration ................................................................ 156 
Figure A- 18:  Los Angeles 1T Base Shear .................................................................. 157 
Figure A- 19:  Los Angeles 1T Moment Frame Ductility ............................................. 157 
 
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Figure A- 20:  Los Angeles 1T Brace Ductility ............................................................ 158 
Figure A- 21:  Memphis 1T Acceleration ..................................................................... 159 
Figure A- 22:  Memphis 1T Base Shear ....................................................................... 159 
Figure A- 23:  Memphis 1T Moment Frame Ductility .................................................. 160 
Figure A- 24:  Memphis 1T Brace Ductility ................................................................. 160 
Figure A- 25:  Los Angeles 2.5T Acceleration ............................................................. 161 
Figure A- 26:  Los Angeles 2.5T Base Shear ............................................................... 161 
Figure A- 27:  Los Angeles 2.5T Moment Frame Ductility .......................................... 162 
Figure A- 28:  Los Angeles 2.5T Brace Ductility ......................................................... 162 
Figure A- 29:  Memphis 2.5T Acceleration .................................................................. 163 
Figure A- 30:  Memphis 2.5T Base Shear .................................................................... 163 
Figure A- 31:  Memphis 2.5T Moment Frame Ductility ............................................... 164 
Figure A- 32:  Memphis 2.5T Brace Ductility .............................................................. 164 
Figure A- 33:  Los Angeles 4T Acceleration ................................................................ 165 
Figure A- 34:  Los Angeles 4T Base Shear .................................................................. 165 
Figure A- 35:  Los Angeles 4T Moment Frame Ductility ............................................. 166 
Figure A- 36:  Los Angeles 4T Brace Ductility ............................................................ 167 
Figure A- 37:  Memphis 4T Acceleration ..................................................................... 167 
Figure A- 38: Memphis 4T Base Shear ........................................................................ 168 
Figure A- 39:  Memphis 4T Moment Frame Ductility .................................................. 168 
Figure A- 40:  Memphis 4T Brace Ductility ................................................................. 169 
Figure B- 1:  Los Angeles 0.25T HYFR Acceleration .................................................. 170 
Figure B- 2:  Los Angeles 0.25T HYFR-VFD Acceleration ......................................... 170 
 
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Figure B- 3:  Los Angeles 0.25T HPCD Acceleration .................................................. 171 
Figure B- 4:  Los Angeles 0.25T HPCD-VFD Acceleration ......................................... 171 
Figure B- 5:  Los Angeles 0.25T HYFR Base Shear .................................................... 172 
Figure B- 6:  Los Angeles 0.25T HYFR-VFD Base Shear............................................ 172 
Figure B- 7:  Los Angeles 0.25T HPCD Base Shear .................................................... 173 
Figure B- 8:  Los Angeles 0.25T HPCD-VFD Base Shear............................................ 173 
Figure B- 9:  Los Angeles 0.25T HYFR Moment Frame Ductility ............................... 174 
Figure B- 10:  Los Angeles 0.25T HYFR-VFD Moment Frame Ductility .................... 174 
Figure B- 11:  Los Angeles 0.25T HPCD Moment Frame Ductility ............................. 175 
Figure B- 12:  Los Angeles 0.25T HPCD-VFD Moment Frame Ductility .................... 175 
Figure B- 13:  Los Angeles 0.25T HYFR Brace Ductility ............................................ 176 
Figure B- 14:  Los Angeles 0.25T HYFR-VFD Brace Ductility ................................... 176 
Figure B- 15:  Los Angeles 0.25T HPCD Brace Ductility ............................................ 177 
Figure B- 16:  Los Angeles 0.25T HPCD-VFD Brace Ductility ................................... 177 
Figure B- 17:  Los Angeles 0.5T HYFR Acceleration .................................................. 178 
Figure B- 18:  Los Angeles 0.5T HYFR-VFD Acceleration ......................................... 178 
Figure B- 19:  Los Angeles 0.5T HPCD Acceleration .................................................. 179 
Figure B- 20:  Los Angeles 0.5T HPCD-VFD Acceleration ......................................... 179 
Figure B- 21:  Los Angeles 0.5T HYFR Base Shear .................................................... 180 
Figure B- 22:  Los Angeles 0.5T HYFR-VFD Base Shear............................................ 180 
Figure B- 23:  Los Angeles 0.5T HPCD Base Shear .................................................... 181 
Figure B- 24:  Los Angeles 0.5T HPCD-VFD Base Shear............................................ 181 
Figure B- 25:  Los Angeles 0.5T HYFR Moment Frame Ductility ............................... 182 
 
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Figure B- 26:  Los Angeles 0.5T HYFR-VFD Moment Frame Ductility ...................... 182 
Figure B- 27:  Los Angeles 0.5T HPCD Moment Frame Ductility ............................... 183 
Figure B- 28:  Los Angeles 0.5T HPCD-VFD Moment Frame Ductility ...................... 183 
Figure B- 29:  Los Angeles 0.5T HYFR Brace Ductility .............................................. 184 
Figure B- 30:  Los Angeles 0.5T HYFR-VFD Brace Ductility ..................................... 184 
Figure B- 31:  Los Angeles 0.5T HPCD Brace Ductility .............................................. 185 
Figure B- 32:  Los Angeles 0.5T HPCD-VFD Brace Ductility ..................................... 185 
Figure B- 33:  Los Angeles 1T HYFR Acceleration ..................................................... 186 
Figure B- 34:  Los Angeles 1T HYFR-VFD Acceleration ............................................ 186 
Figure B- 35:  Los Angeles 1T HPCD Acceleration ..................................................... 187 
Figure B- 36:  Los Angeles 1T HPCD-VFD Acceleration ............................................ 187 
Figure B- 37:  Los Angeles 1T HYFR Base Shear ....................................................... 188 
Figure B- 38:  Los Angeles 1T HYFR-VFD Base Shear .............................................. 188 
Figure B- 39:  Los Angeles 1T HPCD Base Shear ....................................................... 189 
Figure B- 40:  Los Angeles 1T HPCD-VFD Base Shear .............................................. 189 
Figure B- 41:  Los Angeles 1T HYFR Moment Frame Ductility .................................. 190 
Figure B- 42:  Los Angeles 1T HYFR-VFD Moment Frame Ductility ......................... 190 
Figure B- 43:  Los Angeles 1T HPCD Moment Frame Ductility .................................. 191 
Figure B- 44:  Los Angeles 1T HPCD-VFD Moment Frame Ductility ......................... 191 
Figure B- 45:  Los Angeles 1T HYFR Brace Ductility ................................................. 192 
Figure B- 46:  Los Angeles 1T HYFR-VFD Brace Ductility ........................................ 192 
Figure B- 47:  Los Angeles 1T HPCD Brace Ductility ................................................. 193 
Figure B- 48:  Los Angeles 1T HPCD-VFD Brace Ductility ........................................ 193 
 
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Figure B- 49:  Los Angeles 2.5T HYFR Acceleration .................................................. 194 
Figure B- 50:  Los Angeles 2.5T HYFR-VFD Acceleration ......................................... 194 
Figure B- 51:  Los Angeles 2.5T HPCD Acceleration .................................................. 195 
Figure B- 52:  Los Angeles 2.5T HPCD-VFD Acceleration ......................................... 195 
Figure B- 53:  Los Angeles 2.5T HYFR Base Shear .................................................... 196 
Figure B- 54:  Los Angeles 2.5T HYFR-VFD Base Shear............................................ 196 
Figure B- 55:  Los Angeles 2.5T HPCD Base Shear .................................................... 197 
Figure B- 56:  Los Angeles 2.5T HPCD-VFD Base Shear............................................ 198 
Figure B- 57:  Los Angeles 2.5T HYFR Moment Frame Ductility ............................... 198 
Figure B- 58:  Los Angeles 2.5T HYFR-VFD Moment Frame Ductility ...................... 198 
Figure B- 59:  Los Angeles 2.5T HPCD Moment Frame Ductility ............................... 199 
Figure B- 60:  Los Angeles 2.5T HPCD-VFD Moment Frame Ductility ...................... 199 
Figure B- 61:  Los Angeles 2.5T HYFR Brace Ductility .............................................. 200 
Figure B- 62:  Los Angeles 2.5T HYFR-VFD Brace Ductility ..................................... 201 
Figure B- 63:  Los Angeles 2.5T HPCD Brace Ductility .............................................. 201 
Figure B- 64:  Los Angeles 2.5T HPCD-VFD Brace Ductility ..................................... 201 
 
1 
 
Chapter 1  Introduction 
1.1 Defining the Problem 
Catastrophic seismic events in recent times have received global attention and 
have increased concern about the resilience of structures.  While engineers are prepared 
to design for life safety for such events, the need and motivation to evolve design to be 
more efficient and create greater resiliency is stronger than ever.   
The two primary types of loading engineers are faced with in designing a 
structure include gravity and lateral loads.  Within the scope of lateral loading, design is 
focused on elastic design for service level wind conditions and relies on inelastic 
behavior for the dissipation of energy for earthquake loading.  Relying on elastic 
behavior for design level earthquake resistance is impractical and uneconomical given the 
large inertial forces exerted on the structure and the relatively infrequent occurrence of 
seismic events within the life of the structure.  For these reasons, the emphasis of the 
design codes is primarily on life safety rather than structural resilience after an event.  
The 1994 Northridge and 1995 Kobe earthquakes demonstrated the need for a 
monumental shift in the design philosophy.  More recently, 2011 New Zealand and 2011 
Japan events have commanded worldwide attention for the protection of structures from 
seismic events.  Although structures provided adequate life safety, the economic losses 
were far too great.   
This research seeks to find a solution to seismic design that is able to provide life 
safety in addition to damage control.  Limiting damage to a replaceable element and 
 
2 
 
minimizing non-structural damage would be an attractive option to building owners who 
want to return to business as quickly as possible after a seismic event. 
Most structures rely on the structural system to dissipate the majority of the 
earthquake energy while ensuring post-event safety.  When additional energy dissipation 
is needed, supplemental passive control devices such as viscous fluid dampers, 
viscoelastic solid dampers, metallic yielding devices, and friction dampers are paired 
with the structural system.  However, the problem lies within the inherent strengths and 
weaknesses of these devices.  Each device performs well under certain loading conditions 
but is not ideal for a range of loadings.  For instance, viscous dampers are efficient at 
dissipating energy for wind and small to moderate seismic events but can become 
uneconomical when they are needed for a larger amount of supplemental damping.  
Alternatively, braces are efficient at dissipating large amounts of energy and are 
relatively inexpensive, but experience large accelerations, base shears, and possible 
inelastic deformations in small to moderate seismic events.  This could require costly 
replacement following an event.  
 
1.2 The Proposed Solution 
The solution proposed in this work combines two different passive control 
devices working together as a system to create multi-phase behavior that utilizes the 
strengths of each device.  There are three primary elements of a multi-phase passive 
control system:  1) a velocity-dependent damper, 2) a displacement-dependent energy 
dissipation device, and 3) a phase transition mechanism.  Combining these elements with 
a moment frame creates two-phased behavior.  The first phase involves the velocity-
 
3 
 
dependent damper paired with a special moment frame for initial stiffness which reduces 
response through supplemental damping for severe wind events and low to moderate 
seismic events.  The second phase involves the transition mechanism which engages at a 
displacement less than the yield displacement of the moment frame.  After the transition, 
the displacement-dependent device adds significant stiffness and energy dissipation 
capability in the final phase.  This phase would be utilized in moderate to severe events.    
Many options exist for the multi-phase passive control systems and there is a need 
for research to understand the fundamental system behavior.  The type of velocity-
dependent or displacement-dependent energy dissipation devices needed in a multi-phase 
system is unclear.  An extensive review of passive control devices to be included in a 
multi-phase system needs to be completed in order to find a solution.  Many 
combinations of devices are available but the best-performing, most practical, reliable 
and economical combination is largely unknown.  Arrangement of the phases in parallel 
or series also provides an interesting aspect to the research.  By combining the phases in 
parallel, the damping in the first phase can happen concurrently with the significant 
energy dissipation in the second phase, a potentially appealing attribute.  Other system 
characteristics, such as the transitional gap size and moment-frame-to-hysteretic-device 
strength ratio have a potential to largely affect response.  All of these options need to be 
thoroughly researched in order to work towards an effective multi-phase passive control 
system.  
The result of the multi-phase behavior is essentially a structure that is pre-
programmed to respond to varying levels of lateral loading, ranging from service level 
wind conditions to major seismic events.  A system that responds to varying levels of 
 
4 
 
loading is not a unique idea.  However, a multi-phase passive control system which 
requires no electricity, maintenance, or controllers has tremendous potential to impact 
seismic design.  The improvement in structural response would result in a decrease in the 
likelihood of structural damage within the design life of the structure while improving 
life safety.  From an engineering standpoint, this is a marketable and viable option. 
1.3 Scope of Work 
Previous research demonstrates the effectiveness of combining passive control 
systems but the fundamentals of system behavior are unclear.  A single-degree-of-
freedom (SDOF) non-linear dynamic study was performed to clearly define multi-phase 
behavior and to identify important parameters affecting response.  Because most 
structures respond primarily in the first mode of vibration, a SDOF study is initially 
sufficient to examine the fundamental system behavior.  The research is completed in 
three main stages:  1) parametric development and analysis plan, 2) model development 
and nonlinear dynamic SDOF analytical study, and 3) interpretation of results. 
  The parametric development involves choosing the parameters and their range of 
acceptable values.  An extensive literature review provides insight as to the type of 
parameters and values that should be involved in the study.  The analysis plan involves a 
statistical experimental design in which the number of system combinations is reduced, 
yet the interactions are still captured between the parameters and the response.  The 
model development is completed using SAP 2000 Version 14 (CSI, 2009).  Models 
include linear and nonlinear elements to represent system and material behavior.  The 
nonlinear dynamic SDOF study is completed using an incremental dynamic analysis for a 
suite of scaled ground motions representing various site conditions (Vamvatsikos & 
 
5 
 
Cornell, 2002).  The interpretation of results evaluates the statistical significance of 
parameters on total acceleration, base shear, moment frame ductility, and displacement-
dependent device ductility.  The systems are also compared against baseline models to 
illustrate the benefits of adding supplemental damping and a transitional gap element.  
Other areas of concern such as acceleration spikes and residual deformations are also 
investigated.   
The study seeks to reduce the range of possible combinations of devices to be 
combined in a multi-phased system.  With a reduction in the range of qualified devices, 
the study can be expanded into a multi-degree of freedom (MDOF) study and then tested 
within a lab setting.  This research provides the groundwork for a system that could 
largely change design philosophy.  
   
1.4 Organization of Thesis 
Chapter 2 provides a literature review on the development of passive control 
systems and their application to structures.  Various types of passive control systems are 
reviewed in order to illustrate strengths and weaknesses of the systems.  The need for 
multi-phase behavior of the systems is also demonstrated. 
Chapter 3 presents the single-degree-of-freedom system development.  Each 
parameter of the study is briefly discussed and an acceptable range of response values are 
chosen.  Arrangement of the multi-phase systems are also discussed and illustrated.  The 
statistical basis for the research is also described. 
 
6 
 
Chapter 4 describes the analytical study.  The modeling of the system and 
material behavior is discussed.  Details on ground motion selection and scaling are also 
presented.  
Chapter 5 organizes the results from the preliminary SDOF study and investigates 
the statistical significance.  The scope of the study is reduced to a reasonable range for a 
full factorial study to be completed. 
Chapter 6 shows the results from the full factorial study developed in Chapter 5.  
Systems are compared to each other and also to baseline systems in order to demonstrate 
the benefits of multi-phase behavior.  Other behavior elements, such as acceleration 
spikes and residual deformations are analyzed for a select group of systems. 
Chapter 7 summarizes the findings of the study and offers recommendations for 
future work involving multi-phase passive control systems.  
 
7 
 
Chapter 2  Literature Review 
2.1 Introduction 
 Conventional structural design provides life safety but in recent years there has 
been a push towards performance-based design. The 1994 Northridge and 1995 Kobe 
earthquakes were very significant seismic events, yet structures performed well from a 
life safety point-of-view.  Unfortunately, the economic loss and cost of repair was much 
higher than expected, leading to a need for a fundamental change in the code towards 
performance-based design.  Creating performance objectives in response to certain 
seismic hazards, a performance-based design seeks to provide additional life safety in 
addition to damage control (Ghobarah, 2001).  The typical performance curve for a 
structure is indicated in Figure 2-1.   
 
Figure 2-1:  Typical Performance Curve (Ghobarah, 2001) 
 
The Japanese seismic design code has already moved towards a performance-
based engineering approach, first concerned with life safety and secondly with damage-
 
8 
 
limitation levels.  The life safety limit state is concerned with preventing an individual 
story and entire structure from collapsing.  The damage limit state seeks to prevent 
damage and limit inelastic behavior only to the energy dissipation devices (Midorikawa, 
et al., 2000).  Performance-based design essentially breaks design into three main parts: 
the seismic hazard, the structural system, and loss.  The hazard and loss domains provide 
design constraints while the structural system provides design alternatives (Krawinkler et 
al., 2006).   
The multi-phase passive control systems analyzed in this research are a prime 
example of performance-based design oriented lateral systems.  Since the field of 
performance-based seismic engineering is relatively new, the results from the multi-phase 
passive control study could provide great strides towards improved design.  A 
performance-based system could involve a large array of structural control systems.  The 
following is an in-depth look at structural control systems in order to more clearly 
understand the options available for multi-phase control systems.   
 
2.2 Active Control Devices 
 Active control devices utilize actuators, such as an active mass damper, to add or 
dissipate energy in a structure.  Physical sensors relay information to the actuators which 
respond accordingly to reduce structural response.  The first full-scale use of an active 
control device was in 1989 in Tokyo, using two active mass dampers.  The role of this 
system was to reduce building vibration for strong winds and moderate earthquakes and 
to increase the comfort of the building occupants (Spencer Jr. & Nagarajaiah, 2003).   
 
9 
 
The primary problem with an active control device is that it uses an external 
power source to run the system.  In load cases in which structural control would be most 
critical, such as strong wind or earthquakes, it is likely that electricity would be lost, 
making the building very vulnerable to damage (Asteris, 2008).  The reliability and 
stability of the sensor system is an area of concern in active control and for most 
structures, the systems are not always cost effective or necessary for energy dissipation, 
leading to the use of semi-active or passive control devices. 
 
2.3 Semi-Active Control Devices 
 Semi-active control is a rapidly developing area in the field of civil engineering.  
The devices do not add any mechanical energy to the structural system, but have 
properties that can be altered in order to reduce the structural response.  Examples 
include controllable fluid dampers, controllable friction devices, variable stiffness 
devices, and variable-orifice fluid dampers.  Many semi-active devices are able to operate 
on battery power, making it an appealing option because of the adaptability of the 
systems without the use of an external power source (Asteris, 2008). 
 Controllable fluid dampers offer simplicity and reliability to semi-active control 
in the form of electrorheological (ER) and magnetorheological (MR) devices.  Reversible 
behavior between a viscous fluid and a semi-solid fluid is achieved by inducing an 
electric or magnetic field as needed to dissipate energy (Spencer Jr. & Nagarajaiah, 
2003).  ER fluids have been thoroughly researched and remain limited in use due to a 
limited yield stress range, high voltage requirements, low level of safety, and 
intolerability to fluid impurities.  In recent years, magnetorheological (MR) fluid 
 
10 
 
dampers, as illustrated in Figure 2-2,  have become a more attractive option for semi-
active controllable fluid dampers.  MR fluid is able to achive much higher yield stresses 
than ER fluids in addition to requiring much less power, and exhibiting resilience to 
temperature changes and fluid impurities (Spencer Jr. & Sain, 1997). 
 
Figure 2-2:  Magnetorheological Fluid Damper (Spencer Jr. & Nagarajaiah, 2003) 
  
Due to that fact that this is a developing field, there are still many inherent 
problems to be resolved.  Complex algorithms that are not yet optimal are involved in 
relaying information from sensors to the control center.  Also, when using a 
displacement-dependent or accumulated semi-active hydraulic damper, the time delay 
between the sensor and controller is about 0.11 to 0.13 seconds.  Therefore, when the 
frequency is greater than 1.0 Hz, the device will lose the efficiency of semi-active control 
and could possibly amplify response (Shih & Sung, 2010).   Maintenance costs, design 
costs, and the reliability of vibration sensors over time are other issues that could deter 
the use of a semi-active system in its current state. 
 
11 
 
 
 
2.4 Passive Control Devices 
 Passive control devices, the first and most common structural control device, 
utilize relative displacement between two attachment points to dissipate energy.  
Examples of passive control devices include base isolation systems, viscoelastic dampers, 
viscous fluid dampers, tuned mass dampers, metallic yielding devices, and friction 
devices.  These devices are often favored in design due to low maintenance costs, 
stability, and absence of an external power source (Spencer Jr. & Nagarajaiah, 2003).  
The use of passive control devices also minimizes structural damage by restricting the 
energy dissipation and damage to the device, making it favorable for post-event repairs.  
Behavior of passively controlled systems is also widely understood and accepted in 
structural design for dynamic resistance.  The major drawback of typical passive control 
devices is that they are unable to adapt to structural load changes, from service level 
loading to extreme wind or seismic events.  Design of a passive system that effectively 
handles all of these load conditions is currently far from optimal, yet necessary for life 
safety (Asteris, 2008). 
2.4.1 Base Isolation 
 Base isolation is a passive control mechanism used in low-to-mid-rise structures.  
In the most common base isolation system, the structure is connected to the ground using 
layers of material that are stiff under gravity loads, yet flexible under lateral loads.  The 
horizontal flexibility gives the structure a much longer natural period than a fixed-base 
structure.  This substantially reduces the expected forces within the first mode of 
 
12 
 
response.  Deformation is primarily concentrated in the isolation system and therefore the 
structural system experiences minimal drifts (Chopra, 2007).  Problems associated with 
the large deformations in the isolation system are the mechanical, electrical, and 
plumbing materials at the base which must be specially detailed to avoid damage.  The 
cost of this isolation system is often a deterrent for a typical structure.  Base isolation is 
typically used for historical retrofits and important structures in areas of high seismicity. 
2.4.2 Velocity-Dependent Passive Control Devices 
 Velocity-dependent, often referred to as rate-dependent, passive control devices 
rely on relative motion for energy dissipation.  They are typically cost effective and can 
be used in the design of a new structure or added to existing structures to provide 
additional protection (Chopra, 2007).  The two most typical rate-dependent devices are 
viscous fluid dampers (VFD) and viscoelastic dampers (VED).  The typical hysteretic 
behavior of these devices is found in Figure 2-3.   Damping values can vary largely 
depending on the type and implementation of damping device.  The damping coefficients 
used in this research will be discussed within the parametric development in Chapter 3. 
 
Figure 2-3:  Velocity-dependent Hysteresis Comparison 
 
13 
 
 
 
 
2.4.2.1 Viscous Fluid Dampers 
 Viscous fluid dampers consist of a cylinder filled with a fluid, typically silicon, 
and a piston with orifices on the face (Figure 2-4).  The travel of the piston through the 
fluid inside the cylinder dissipates energy.  Although the device is operational and stable 
at various temperatures and frequencies, the viscous properties of the damper do vary 
(Reinhorn et al., 1995).  Viscous fluid dampers can be either linear or nonlinear 
depending on the arrangement of the orifices on the face of the piston.  The linear 
hysteresis loop has an elliptical shape (Figure 2-3) but as the nonlinear exponent 
approaches 0.3, the hysteresis loop is nearly rectangular (Lee & Taylor, 2001).  Inclusion 
of viscous fluid dampers in an elastic steel structure shaking table experiment have 
shown to reduce story drift and shear forces by 30% to 70% in addition to improving drift 
response in inelastic systems (Reinhorn et al., 1995).   
 
 
14 
 
 
Figure 2-4:  Typical Viscous Fluid Damper (Lee & Taylor, 2001) 
 
 
2.4.2.2 Viscoelastic Dampers 
 Viscoelastic devices utilize layers of polymers to dissipate energy in shear 
deformation (Chopra, 2007).  Figure 2-5 illustrates a typical configuration for a VE 
device which utilizes a viscoelastic material, such as high-damping natural rubber, 
sandwiched between two metal plates.  That ability to reach strains up to 500% before 
failure means that the device can dissipate energy over a large range of deformation 
(Marshall, 2008).  
 
15 
 
 
Figure 2-5:  Viscoelastic Device Configuration (Aiken et al., 1993) 
 
Variation in temperature can significantly impact the performance of a 
viscoelastic device.  An increase of 10?C can alter material storage and loss modulus 
from 30% to 50% at low frequencies and even more at higher frequencies, meaning that a 
fluctuation in temperature could largely affect the energy dissipation capability (Reinhorn 
et al., 1995).  This is typically not an issue for seismic events because of the short 
duration but can cause problems for strong wind events due to a build-up of heat over 
repeated strain cycles.  The development of newer rubber materials has decreased the 
variability in performance and increased the energy dissipation capacity (Marshall, 2008).  
As evident in Figure 2-3, viscoelastic devices do provide additional stiffness to a system.  
Although this could decrease the natural period of the structure and thus increase the 
seismic response, the period is typically only shortened by about 10% to 20%, which is 
much less than the effect of most metallic displacement-dependent devices (Chopra, 
2007).   
 
16 
 
Although primarily used for wind excitation, considerable research has been 
performed in recent years on VE dampers for seismic protection. One dynamic analysis 
demonstrates the effectiveness of installing VE dampers between seismic joints or sky 
bridges between structures. As evident in Figure 2-6, displacements were significantly 
decreased, especially if the natural frequencies of the connected structures were different 
(Kim et al., 2006). 
 
Figure 2-6:  VE Devices in All Stories (Kim et al., 2006) 
 
 
 
2.4.3 Displacement-Dependent Passive Control Devices 
 Another type of passive control, which is rate-independent (or velocity-
independent), is often referred to as ?hysteretic?.  Use of these rate-independent devices 
significantly affects seismic response due to a high elastic stiffness which can drastically 
shorten the natural period of the structure.  Although the seismic hazard may significantly 
increase, the large inelastic capabilities are appealing for energy dissipation.  The two 
 
17 
 
most common classes of hysteretic devices are metallic yielding devices and friction 
devices.  The hysteretic behavior of each is represented in Figure 2-7. 
 
Figure 2-7:  Displacement-Dependent Hysteresis Comparison 
 
2.4.3.1 Metallic Yielding Devices 
 Metallic yielding devices rely heavily on the inelastic action of the metal, 
typically mild steel, to dissipate energy.  Numerous devices and configurations have been 
designed, researched, and implemented with success.  One such application involves 
adding damping and stiffness (ADAS) elements as a link at the top of a chevron braced 
configuration (Figure 2-8). 
 
18 
 
 
Figure 2-8:  Typical ADAS Configuration (Alehashem et al., 2008) 
 
 Multiple plates are arranged in a parallel formation and dissipate energy through 
flexural yielding.  The unique tapered design of the plate is intended so that the plates can 
act in double curvature, yielding across the entirety of the plate and therefore dissipating 
more energy (Alehashem et al., 2008).  A reduction of almost 50% in acceleration can be 
seen in Figure 2-9 with the addition of an ADAS device to a 4-story building 
(Tehranizadeh, 2001).  The TADAS (Triangular Added Damping and Stiffness) device is 
similar except it utilizes a triangular shaped plate and therefore single curvature to 
dissipate energy.   
 
19 
 
 
Figure 2-9:  Acceleration Response Comparison with ADAS Device (Tehranizadeh, 
2001) 
 
 Recent seismic events such as Northridge 1994 and Loma Prieta 1989 raised 
concerns about typical braced frames due to poor performance under cyclic loading 
(Sabelli et al., 2003).  Buckling restrained braces (BRB) offer a solution to this problem 
by encasing a steel core in a concrete filled tube in order to restrain the brace from lateral 
buckling.  BRBs are beneficial because they are able to dissipate roughly the same 
amount of energy in both tension and compression, eliminating the erratic and inefficient 
behavior of typical concentrically braced frames.  Figure 2-10 shows the typical 
arrangement and hysteresis loops for a typical BRB.  The design of the steel core may 
vary depending on the manufacturer but the fundamentals of behavior remain the same.  
Nonlinear dynamic analyses and experimental testing of the braces have demonstrated 
reliable behavior with improved interstory drifts and substantial ductility capability 
(Sabelli et al., 2003).  
 
20 
 
 
Figure 2-10:  BRB Schematic with Hysteretic Behavior (Sabelli et al, 2003) 
 
 Another metallic device involves the use of shape memory alloys (SMA), utilized 
in wire braces installed diagonally in a frame.  During excitation, the braces dissipate 
energy through stress-induced solid-to-solid phase transformation (Song et al., 2006).  
Change in stress causes a phase transition from austenite to martensite and then back 
again to austenite, resulting in a hysteretic behavior. SMAs perform well in large strain 
cycle fatigue, are corrosion resistant, and require no maintenance.  The main advantage of 
using a SMA system is the self-centering capability which would provide safety after a 
seismic event.  Unfortunately, the energy dissipation achieved by the SMA devices is not 
sufficient to limit deformation to the SMA element itself.  Costly strengthening of other 
structural elements would be a deterrent to most structural applications (Dolce et al., 
2000). 
2.4.3 Friction Devices 
 Friction devices are another commonly used means for dissipating large amounts 
of energy. Once the device reaches a ?slip force?, friction is utilized as two solid bodies 
slide against one another.  The mechanism slips in both tension and compression and 
 
21 
 
creates a rectangular hysteresis behavior, which is evident in Figure 2-7.  Although the 
devices do add stiffness to the system, the natural periods are only shortened by about 
10% to 20% (Chopra, 2007).  The devices are often favored in design due to reliable 
behavior under varying load amplitude and frequencies (Reinhorn et al., 1995).   
 Slotted bolted connections (SBC) are a type of friction device often used due to 
the relative ease of design, construction, and availability of commercial materials (Levy 
et al., 2000).  As seen in Figure 2-11, the bolts connect two plates together with a 
compression force.  Once the slip force is reached, the coefficient of friction and bolt 
compression dissipate energy through heat.  Initially SBCs used two steel surfaces to 
generate friction but experimental results showed that brass on steel contact creates a 
more uniform behavior (Levy et al., 2000).  Retrofit of a moment resisting frame building 
with a SBC in a chevron configuration provided a much greater energy dissipation 
capacity and limited inelastic action in the friction device (Aiken et al., 1993).  More 
recently, SBCs have been utilized at the beam-to-column moment connection in order to 
dissipate energy and provide self-centering capabilities after a seismic event (Tsai et al., 
2008). 
 
22 
 
 
Figure 2-11:  Typical Slotted Bolted Connection (Balendra et al., 2001) 
 
 A specific type of friction damper known as a Pall friction damper is located at 
the intersection of diagonal brace elements, utilizing friction at the interface of the two 
cross braces, as shown in Figure 2-12.  Horizontal and vertical links attach the two braces 
to ensure that the slip deformation is equal in both compression and tension in order to 
maintain stability (Aiken et al., 1993). The performance of a 9-story steel moment 
resisting frame structure showed marked improvement by the addition of Pall devices, 
with reliable behavior and increasing energy absorption with increasing input energy 
(Aiken et al., 1993). 
 
23 
 
 
Figure 2-12:  Pall Friction Device (Aiken et al., 1993) 
 
2.5 Hybrid Control Devices 
Hybrid control devices combine active and passive control systems in order to 
offset inherent weaknesses of each system.  An example of a hybrid system is a base 
isolated system with supplemental actively controlled actuators to enhance the overall 
performance of the system.  Although the active system is still subject to power failure, 
the major benefit of the hybrid system is that the passive component is still present for 
backup protection (Asteris, 2008). The demand for external energy is also reduced 
because of the presence of the passive control systems (Marshall, 2008).  Similar to 
active control systems, hybrid control systems are simply not cost effective for most 
structures. 
 
2.6 Multi-Phase Passive Control Devices 
Typical passive control devices have inherent strengths and weaknesses that are 
considered in design.  A multi-phase passive control device seeks to combine two types 
 
24 
 
of passive control devices in a system in order to offset the weaknesses of each and to 
optimize structural performance (Marshall, 2008).  This can essentially create a 
performance-based approach that can allow the structure to react differently to varying 
levels of lateral force.  If implemented correctly, a multi-phase passive control system 
could potentially have all the benefits of a semi-active active system without need for an 
external power source, control algorithm, and structural monitoring system.  The low 
maintenance cost and improved reliability are appealing features in comparison to semi-
active devices. 
As previously discussed, the more commonly used passive control devices 
include viscous fluid dampers, viscoelastic solid dampers, metallic yielding devices, and 
friction dampers.  The focus of the research involves combining these more commonly 
used devices into a multi-phase system in order to improve structural response.  
 
2.7 Multi-Phase Behavior 
 The multi-phase nature of multi-phase passive control systems has been explored 
in the past, showing promising results in many different applications.  A sequential 
coupling system was one of the first introductions of dynamic slip and multi-phase 
behavior in order to improve response.  Using a repeated slip-resistance sequence within 
a structural system, a significant reduction in deformation response was achieved.  This 
can be accomplished by properly detailing special connections, such as bolts in slotted 
holes, in steel, reinforced concrete, and prestressed concrete structures, as illustrated in 
Figure 2-13 (Weidlinger & Ettouney, 1993). 
 
25 
 
  
Figure 2-13:  Sequential Connection Schematics (Weidlinger & Ettouney, 1993) 
 
A relatively simple SDOF example of this sequential coupling is evident in Figure 
2-14.  System A, which is representative of a parallel (conventional) system and system 
B, which is representative of a sequential system, are equivalent in both strength (RO) and 
mass (M). Combinations of the ? value (secondary stiffness value) and ? (percentage of 
yield displacement) were optimized in order to achieve the best response. Both systems 
were subjected to the same seismic event and the results of the sequential connection had 
a displacement response of 70% of the standard system and a residual displacement that 
was only 10% of the standard system (Weidlinger & Ettouney, 1993). 
 
26 
 
 
Figure 2-14:  Benefits of Sequential Coupling (Weidlinger & Ettouney, 1993) 
 
 Another example of multi-phased passive control behavior involves an analysis 
performed on a multi-span simply supported bridge (Figure 2-15).  When excited, the 
system increases in stiffness as the displacement increases, which mainly results from the 
closure of the gap between the end span and abutment (Motlagh & Saadeghvaziri, 2001).  
This is referred to as a stiffening single-degree-of-freedom system whereas a baseline 
single-degree-of-freedom system would only consist of the bridge without the stiffness 
added from the abutment. 
 
27 
 
 
Figure 2-15:  Stiffening Single-Degree-of-Freedom System (Motlagh & 
Saadeghvaziri, 2001) 
  
 Figure 2-16 clearly demonstrates the multi-phase nature of the stiffening SDOF 
system in comparison to the baseline system.  For most periods, the stiffening system had 
much lower ductility demands than the baseline system yet the hysteretic energy and 
damage index were often higher (Motlagh & Saadeghvaziri, 2001).  Further research was 
recommended to quantify the effects of yield strength, stiffness, and gap size on response 
in order to minimize damage while maintaining the decreased ductility demand. 
 
Figure 2-16:  Stiffening Single-Degree-of-Freedom Comparison to Baseline 
(Motlagh & Saadeghvaziri, 2001) 
 
28 
 
More recently, a structural application of a multi-phase passive system has been 
developed that sandwiches a high-damping viscoelastic material between two steel plates 
or channels, as shown in Figure 2-17.  The visco-plastic device (VPD) utilizes the 
displacements across the viscoelastic material to increase damping as the steel plates 
subject it to tension and compression forces.  As the forces increase, the steel elements 
yield in order to dissipate more energy.  The primary benefit of this system is that it will 
respond elastically to low level excitation yet still possess the energy dissipation 
capability for large events (Ibrahim et al., 2007).  The cost of manufacturing this device is 
a potential drawback of this system. 
 
 
Figure 2-17:  Finite Element Model of the VPD (Ibrahim et al., 2007) 
 
Stemming from the visco-plastic research, a multi-phase passive control device 
was developed combining a viscoelastic high-damping rubber sandwich damper and a 
buckling restrained brace in series in order to utilize the strengths of each system (Figure 
2-18).  The system is backed up with a moment resisting frame in order to provide initial 
stiffness and redundancy to the system.  Although other passive control devices and 
arrangements were considered, the VE and BRB provided the most reliable and practical 
option for construction (Marshall, 2008).   
 
29 
 
 
Figure 2-18:  Multi-Phase Passive Control Device (Marshall, 2008) 
 
The behavior of the system is comprised of three main phases.  The first phase, 
involving the VE sandwich damper and moment frame, is designed to provide sufficient 
stiffness and damping for service level wind conditions and small to moderate seismic 
events.  The next phase involves the transition from the VE device to the BRB, which 
occurs at a specified gap size that is a percentage of the moment frame yield 
displacement.  The lockout of the secondary phase occurs due to a slotted bolted 
connection on the outer plates of the sandwich damper (Figure 2-19).  The final phase 
involves the BRB, which adds significant stiffness and energy dissipation capacity to the 
system for larger seismic events.  The overall result is a device that can variably respond 
to levels of lateral force and primarily restrict damage to a replaceable BRB (Marshall, 
2008). 
 
30 
 
 
Figure 2-19:  High-damping Rubber Sandwich Damper Schematic (Marshall, 2008) 
 
An analytical study was performed on a 9-story steel moment frame designed 
with a hybrid passive control device (HPCD) and other multi-phase arrangements.  
Viscous fluid dampers as well as a range of transition gap sizes were also considered.  
Other arrangements of the system were also considered (Figure 2-20).  Arranging a 
system in a parallel formation provides damping throughout the entire duration of 
excitation, whereas the series formation only allows damping in the first phase (Marshall, 
2008).   
 
31 
 
 
Figure 2-20:  Possible Arrangements of Multi-Phase Systems (Marshall, 2008) 
 
Response parameters such as acceleration, base shear, drift, and residual 
displacements all showed marked improvement over conventional systems.  Figure 2-21 
shows the results of an incremental dynamic analysis (IDA) that demonstrates significant 
decreases in acceleration response of an HPCD system in comparison to the baseline 
buckling restrained brace framed system. Figure 2-22 demonstrates the re-centering 
capability of a parallel system (HYFR) due to the presence of the elastic high-damping 
rubber throughout the entirety of the excitation (Marshall, 2008).  This could provide 
tremendous post-event safety after a design basis earthquake in which secondary 
moments are often a concern for taller structures. 
 
 
32 
 
 
Figure 2-21:  Acceleration Response Comparison (Marshall, 2008) 
 
 
Figure 2-22:  DBE Residual Displacement Comparison (Marshall, 2008) 
 
Although the research produced many beneficial results, the fundamental 
understanding of the systems was lacking.  In order to find a better performing device, it 
was recommended that an exhaustive SDOF study be performed to identify some of the 
more important variables influencing response (Marshall, 2008).  A larger range of gap 
sizes, natural periods, and hysteretic-device-to-moment-frame strength ratios need to be 
 
33 
 
investigated in different system arrangements and subjected to a larger suite of ground 
motions.  In doing this, a range of values could be established for a given situation. 
 
2.8 Summary  
The potential for multi-phase passive control devices to improve structural 
performance is clearly demonstrated within the literature.  Ideally a system could be 
optimized to remain elastic for the duration of a small to moderate seismic event, while 
still providing life safety, and to minimize damage for a large scale seismic event.  
Multiple options exist for multi-phase passive devices but the best-performing 
combination is still unknown.  Although multi-phase systems have shown improved 
structural response, the fundamental understanding of this improvement is unclear.  This 
SDOF study seeks to explore these multi-phase system combinations and clarify 
important variables that affect response.  By accomplishing this feat, the study can be 
expanded into a multi degree-of-freedom study with a much smaller range of variables.  
Subsequently, lab testing and implementation would provide results leading to a device 
that could substantially change the way structures react to seismic loading.  This research 
can provide valuable insight and lay the groundwork for these goals. 
 
34 
 
Chapter 3     Parametric Study Development and Analysis Plan 
3.1 Introduction 
 Numerous factors are involved in each multi-phase control system: a velocity-
dependent damping device, displacement-dependent device, system arrangement, 
hysteretic-device-to-moment-frame strength ratio, seismic hazard, natural period, and 
transition gap size.  The feasibility of testing all combinations of these factors and the 
ranges of values is simply impractical.  Therefore, an analysis of all the variables was 
performed and narrowed down to an acceptable range.  Passive control devices reviewed 
in Chapter 2 were analyzed and chosen based on energy dissipation capability, damping 
characteristics, reliability, and constructability within a multi-phase device.   
Each multi-phase system should be subjected to various seismic hazards to show 
the versatility of the systems.  This chapter details the selection of the seismic hazards 
and natural periods to be tested within the scope of the research.  The hysteretic-device-
to-moment-frame strength ratio and the corresponding transitional gap size are thought to 
be important factors in the response of the multi-phase control systems.  The ranges of 
values for these variables are also discussed within this chapter.  With the large number 
of variables present in each multi-phase system, a systematic naming scheme had to be 
developed in order to keep the extensive data organized.  The details of this naming 
scheme are also detailed in this chapter. 
 
 
 
 
35 
 
3.2 Velocity-Dependent Device 
 Two main types of velocity-dependent damping devices were reviewed and 
considered for a multi-phase system:  viscous fluid dampers (VFD) and viscoelastic 
dampers (VED). Both systems can provide substantial damping within a multi-phase 
system.  Marshall (2008) demonstrated the potential of both systems but a clear favorite 
was not evident.  For this reason, both devices were examined within the scope of this 
research.  As a control, some systems were designed with no supplemental damping, so 
that show the benefits of a velocity-dependent device could be shown in comparison. 
The VFD used in the multi-phase system was similar to the one in Figure 2-4, 
utilizing a piston displacing fluid in an enclosed cylinder.  A linear viscous damper was 
used for simplicity in analysis.  For a nonlinear damper, a range of nonlinear exponents 
would have to be tested as well.  Since the results prove that a multi-phase system with a 
VFD is beneficial, further study should be conducted to investigate the possible benefits 
of a nonlinear VFD.  The VED used utilized high-damping rubber as the viscoelastic 
material, in the form of a sandwich damper, as illustrated in Figure 2-19, and other 
configurations to be discussed in Section 3.4.   
Once the damping device is established, appropriate damping values have to be 
determined for the system.  Typical buildings have about 2%-3% inherent damping but 
the addition of a supplemental damper significantly adds to the damping capacity.  For a 
structure with a uniform distribution of mass and stiffness, a necessary assumption for a 
SDOF system, total damping of 16% of critical damping is expected for a viscous damper 
(Occhiuzzi, 2009).  This recommended value would suggest that the viscous damper is 
contributing about 13% of the damping, which was the value used for design of the multi-
 
36 
 
phase systems.  Using this damping ratio, along with the mass and stiffness of the system, 
the damping coefficient for the systems can be calculated.   
As part of Marshall?s (2008) investigation, extensive material testing was 
performed on the viscoelastic high-damping rubber (HDR) component utilized in the 
sandwich damper.  The butyl rubber tested had a loss factor of about 0.36 at a frequency 
of 2.0 hertz which is able to provide about 8% of critical damping, a value used for this 
analysis (Marshall, 2008).  Although damping values for the VED are less than the VFD, 
the initial stiffness provided by the high-damping rubber could help to reduce 
displacements. 
 
3.3 Displacement-Dependent Device 
Buckling restrained braces (BRBs), slotted bolted friction devices, and Pall 
friction devices were all considered for displacement-dependent elements of the multi-
phase system.  For simplicity, only one device was chosen.  A device with reliable 
hysteresis behavior, large energy dissipation, and a large ductility capacity for moderate 
to large seismic events was desirable.  Therefore, a BRB was chosen as the displacement-
dependent device. 
Once the BRB was chosen, some important parameters had to be established.  The 
hysteresis loop for the BRB is not quite symmetric for tension and compression, resulting 
in the need for adjustment factors. The tension strength adjustment factor, ?, was taken 
as 1.0 while the compression overstrength adjustment factor, ?, was taken as 1.1 to 
account for slightly larger compression stresses typically seen in BRBs.  Additionally, a 
generally accepted range of core yield strengths is 38 ksi to 46 ksi; therefore, 42 ksi was 
 
37 
 
used in design (Robinson, 2009).  A BRB core yield length varies between manufacturers 
depending on connection detail and frame configuration (Figure 3-1). A standard 
connection length of 48? from work point to yielding core was used on each side of the 
brace to calculate the yield length for each frame configuration.  Average yield length 
was 60% of the work-point length, a reasonable approximation for a chevron 
configuration.  These design values are important for the development of the strength and 
stiffness relationships developed later in the research.  
 
Figure 3-1:  BRB Yield Length (Lopez & Sabelli, 2004) 
 
3.4 System Arrangement 
 Using the variables defined above, essentially 5 multi-phase systems were 
created, the details of which are outlined in Table 3-1 and shown in Figure 3-2. 
 
Table 3-1:  Multi-Phase Systems and Abbreviations 
Abbreviation System Description 
HPCD Special moment frame with a multi-phase passive control device utilizing a BRB and high-damping rubber sandwich damper 
HPCD-VFD Special moment frame with a multi-phase passive control device utilizing a BRB and linear viscous fluid damper 
HPCD-None Special moment frame with a multi-phase passive control device with no damper 
 
38 
 
HYFR Special moment frame with a multi-phase frame configuration utilizing an BRB and compressed elastomeric device 
HYFR-VFD Special moment frame with a multi-phase frame configuration utilizing a BRB and viscous fluid damper 
 
 
Figure 3-2:  Multi-Phase Passive Control Systems 
 
 The HPCD is composed of a high-damping rubber damper in series with a 
buckling restrained brace.  The transition from viscoelastic damping to BRB yielding is 
dependent upon a lockout mechanism, which is a slotted bolted rubber sandwich damper 
as illustrated in Figure 2-11.  The initial stiffness of the system is provided by the 
 
39 
 
moment frame and damper stiffness.  This transition mechanism is reliant upon a 
displacement-based gap size which can be varied in design.  Damping is only present 
before the mechanism is locked out.  The HPCD-VFD is exactly the same as the HPCD 
system except a VFD is utilized as a means of damping instead of the high-damping 
rubber.  The difference between the two systems is that the high-damping rubber provides 
initial stiffness, while the VFD does not provide initial static stiffness but can achieve 
higher damping capacity at a lower cost.  The importance of these inherent properties was 
investigated in this research effort.  The HPCD-None system is only a BRB in series with 
a lockout mechanism; no supplemental damping is provided. Simple schematics of the 
systems are provided in Figure 3-2a, 3-2b, and 3-2c.  
The HYFR and HYFR-VFD configurations are considered to be parallel systems 
because the damping device is utilized throughout the duration of excitation, even while 
the BRB is yielding.  The damper and BRB on opposite sides of the chevron 
configuration means that one is in tension and one is in compression, requiring two 
frames and symmetry for equal action in each direction.  The ability to model and utilize 
a high-damping rubber for large displacements and corresponding strains is not very 
practical due to the highly nonlinear behavior of rubber.  A parallel arrangement with a 
HDR could experience large strains and complex nonlinear rubber behavior.  The SDOF 
study demands simplicity to understand the fundamental behavior of the multiphase 
systems, so modeling the complex nonlinear behavior of the high-damping rubber is not 
desirable, and was not attempted in this study.   
A new system was investigated for parallel action of damping and yielding for the 
HYFR configuration in order to reduce the complexity of the model.  Karavasilis et al. 
 
40 
 
(2010) offered a system that could be utilized in a parallel design.  The device proved 
beneficial in reducing drifts and floor acceleration and could be substantially beneficial 
when paired with a BRB.  This device consists of precompressed high-damping rubber 
wrapped around a longitudinal bar and wrapped in a steel tube (Figure 3-3).  The rubber 
is bonded to the longitudinal bar, which is subsequently wrapped in a steel tube but not 
bonded to the steel tube.  At a specified force and displacement the steel tube slips until 
the load is reversed.  Behavior is very similar to a friction device, with the added benefit 
of VE damping prior to slipping.  Since the rubber remains elastic, a simple linear model 
gives a reasonable approximation.  The BRB element of this arrangement has a specified 
gap size before the yielding takes place.  Similar to the HPCD, the damping and stiffness 
provided could significantly reduce response except the HYFR high-damping rubber can 
be utilized throughout the duration of excitement.   
The HYFR-VFD system is the same as the HYFR configuration except a VFD is 
used as the damping device instead of a high-damping rubber (Figure 3-2d and Figure 
3-2e).  Every system is backed up by a special moment frame that resists a portion of the 
lateral force in addition to the BRB.  The details of the ?baseline? system are given in the 
next section. 
 
41 
 
 
Figure 3-3:  Elastomeric Device (Karavasilis et al., 2010) 
 
3.5 Baseline Systems 
The baseline systems considered consisted of conventional lateral force resisting 
systems; a special moment frame, a braced frame, and a combination of the two in a dual 
frame.  These systems are often favored in seismic design due to their large ductility 
capacity and corresponding reduction in design forces (response modification factor of 8 
in some cases).  Special moment frames are often controlled by drift rather than strength 
due to inherent flexibility and a deflection amplification factor (Cd) of 5.5.  Pairing the 
special moment frame with a buckling restrained brace adds stiffness and redundancy to 
the system and reduces the Cd to 5, allowing the system to be controlled by strength 
rather than stiffness.  Code minimum requires that the moment frame must resist at least 
25% of the lateral force in a dual frame (ASCE, 2006).  Previous research indicates that a 
special moment frame resisting 25% of the force is inadequate in a multi-phase passive 
system because it does not provide enough initial stiffness to allow the first phase of the 
multi-phase system to be active long enough to provide sufficient damping (Marshall & 
Charney, 2010).   
 
42 
 
Figure 3-4 illustrates the inadequacy of a system with a relatively weak moment 
frame.  The dual system with the smaller portion of the lateral force being resisted by the 
moment frame (VFD10-3-M25B75) experiences larger displacements.  For this reason, 
the range of stiffness ratios for dual systems used in this study were limited to 5 values: 
Moment frame resisting 40% of the lateral force and buckling restrained brace resisting 
60% of the lateral force (M40B60), M50B50, M60B40, M70B30, and M80B20.  This 
provides a large range of dual system arrangements but if it becomes evident that another 
combination may provide better performance within the study, the range can be modified. 
 
Figure 3-4:  Comparison of Two Systems with Different Baselines (Marshall, 2008) 
 
The inherent behavior of a moment frame coupled with a buckling restrained 
brace creates different strength-to-stiffness ratios for each of the baseline systems.  A 
moment frame is more flexible than a buckling restrained brace therefore a multi-phase 
system containing a M80B20 dual system would be more flexible than a M40B60 system 
designed for the same seismic hazard.  To clearly define the properties of these dual 
systems, it was important to find the numerical relationship between the strength and 
 
43 
 
stiffness of each component in the system.  Once the relationship was found, separate 
force-displacement plots could be developed for the moment frame and BRB elements.  
Together, the overall strength of these elements will equal the required design strength, 
yet the overall stiffness will vary depending on the baseline ratios.  In order to find the 
strength/stiffness ratios, moment frames were designed at 7 different strength levels for 5 
typical bent sizes. The resulting stiffness from the models were recorded and plotted 
against strength (Figure 3-5).  Strength and stiffness increase in a linear fashion.  The 
relationship between strength and stiffness is given in the legend for each bent size. 
 
 
Figure 3-5:  Moment Frame Stiffness/Strength Comparison 
 
Similar to the moment frame analysis, buckling restrained brace frames (BRBFs) 
were designed for 7 different strength levels and 5 different frame configurations.  The 
design of the frames was carried out using the BRB design parameters defined earlier.  
 
44 
 
The resulting stiffness was plotted against strength in Figure 3-6.  A linear relationship 
between strength and stiffness was also found for the BRBFs. 
 
 
Figure 3-6:  Buckling Restrained Brace Frame Stiffness/Strength Comparison 
 
After the relationship between strength and stiffness for each component was 
established, the same relationship had to be created for a dual system.  One could infer 
that the strength and stiffness relationship in a dual system would simply be a weighted 
average of system components but this hypothesis was tested to ensure its validity.  
Twelve systems were designed and the strength and stiffness of the dual frames were 
compared to a weighted average.  The values for strength, frame size, and dual frame 
ratio were generated randomly and designed accordingly.  Error! Reference source not 
 
45 
 
found. shows the relationship between the design stiffness and weighted average 
stiffness.   
 
 
Table 3-2:  Dual System Stiffness Derivation 
System Results 
Strength 
(kips) Frame Size 
Dual System 
Configuration 
Designed 
Stiffness 
(k/in) 
Weighted 
Stiffness 
(k/in) 
Percent 
Difference (%) 
213 25' x 12.5' M62.5B37.5 323.56 329.35 -1.76 
351 20' x 12.5' M25B75 756.14 760.16 -0.53 
347 30' x 12.5' M62.5B37.5 512.8 519.73 -1.33 
289 40' x 12.5' M75BM25 326.66 329.64 -0.90 
341 35' x 12.5' M62.5B37.5 477.7 476.16 0.32 
199 20' x 12.5' M37.5B62.5 399.3 394.35 1.26 
295 35' x 12.5' M37.5B62.5 558.66 558.06 0.11 
211 35' x 12.5' M62.5B37.5 305.29 304.53 0.25 
274 30' x 12.5' M50B50 478.97 472.32 1.41 
122 30' x 12.5' M62.5B37.5 188.29 202.42 -6.98 
393 35' x 12.5' M50B50 636.9 639.82 -0.46 
205 25' x 12.5' M37.5B62.5 437.3 423.56 3.24 
 
The 99% confidence interval was -2.28 to 1.38 percent for the difference between 
a weighted average stiffness and designed system stiffness.  This small range indicates 
that a weighted average is a good indicator of the stiffness to strength ratio of a dual 
system.  The stiffness-to-strength ratios used for the design of the baseline systems were 
chosen based on the 30? x 12.5? bent size, a typical structural frame size.   
 Once the weighted average issue was resolved, a simple multi-phase design 
process was used for the moment frame and BRB strength-to-stiffness ratios.  The dual 
system design strength was comprised of the appropriate ratio for a given multi-phase 
system (i.e. M50B50), while the stiffness for the elements were calculated using a 
 
46 
 
weighted average of the linear equations in Figure 3-5 and Figure 3-6.  Once the strength-
to-stiffness ratio of the elements was developed, the transitional gap size was considered. 
 
 
3.6 Transition Phase (Gap Size) 
 As stated before, each multi-phase system has a transition phase before the BRB 
becomes active.  The gap needs to be less than the yield displacement of the moment 
frame in an attempt to limit yielding to the replaceable BRB.  The gap also has to be large 
enough to allow damping to be effective before the mechanism locks out.  This research 
looks to strike a balance in order to increase damping of the system and reduce moment 
frame yielding, which is designed to first occur in the beam element. These gap sizes are 
specified as a percentage of the moment frame yield displacement:  20%, 40%, 60%, 
80%, and 100%.  Depending on the dual system used in the multi-phase control system, 
the yield displacement varies depending on the strength of the moment frame required for 
lateral resistance.  A gap in a high-damping rubber system has a stiffness that is a 
function of the damper size while the VFD has no initial stiffness.  All of the gap size 
properties are a function of the design strength, which is dependent on the seismic hazard, 
the next topic of discussion.. 
 
3.7 Seismic Hazard 
 The systems were designed to resist two different seismic hazard levels: those of 
Los Angeles, CA and Memphis, TN.  The systems were designed with an Occupancy 
Importance Factor of II, on Site Class D soil, and were considered vertically and 
 
47 
 
horizontally regular.  Los Angeles, CA (34.05?,-118.25?) was chosen to evaluate the 
seismic hazard of a populous city near the San Andreas Fault, a transform fault located in 
California.  The 1994 M6.7 Northridge earthquake caused $20-$40 billion dollars in 
damage in the Los Angeles area, and the potential for another earthquake of significance 
is relatively large (U.S. Geological Survey 2008).   For a Site Class B soil, short period 
spectral acceleration is 2.17g and the 1 second period spectral acceleration is 0.727g.  
Modified for site class and the design basis earthquake, short period and 1 second period 
spectral accelerations changed to 1.447g and 0.727g, respectively (ASCE, 2006).  The 
design spectrum according to ASCE 7-05 provisions is shown in Figure 3-7. 
Memphis, TN (35.65, -90.22) was chosen to evaluate the seismic hazard induced 
in a populous city near the New Madrid Fault, an intra-plate fault near the border of 
Tennessee and Missouri.  The largest seismic event in the continental United States 
(M8.7) occurred at the New Madrid Fault in 1812.  Although the reoccurrence of events 
is over a much larger time scale than the San Andreas Fault, the seismic hazard is still an 
important issue for design in this populous area.  For a Site Class B soil, short period 
acceleration is 1.415g and the 1 second period acceleration is 0.385g.  Modified for site 
class and the design basis earthquake, short period and 1 second period spectral 
accelerations are 0.943g and 0.444g, respectively (ASCE, 2006).  The design spectrum 
according to ASCE 7-05 provisions is shown in Figure 3-7. 
 
48 
 
 
Figure 3-7:  Comparison of the Design Response Spectrums 
 
 
3.8 Natural Period 
 After evaluating the design response spectrums for each location, it was 
determined that systems should be designed for 5 different natural periods.  The periods 
chosen were:  0.25 seconds, 0.5 seconds, 1 seconds, 2.5 seconds, and 4 seconds.  These 
natural periods are representative of most buildings within these seismic locations and 
were chosen to test the feasibility of multi-phase behavior in both long and short periods.  
The design accelerations for these periods are indicated in Figure 3-8. 
 
49 
 
 
Figure 3-8:  Design Spectrums with System Natural Periods 
 
3.9 Experimental Design 
After the variables and range of their characteristic values to use in the study were 
established, the next step was to choose the multi-phase systems for the analytical study.  
A full factorial design in which all the combinations of variables would be tested would  
involve 1250 systems (Montgomery, 2009).  Modeling, analyzing, and organizing data 
from 1250 systems is simply impractical, therefore an experimental design had to be 
performed in order to reduce this number, while still maintaining statistical significance.  
The hierarchy showing all the possible combinations of systems is shown in Figure 3-9 
for clarity.   
The statistical software used for analysis was JMP Version 8 (SAS Institute Inc., 
2009).  Using a D-Optimal experimental design, the number of systems needed to capture 
all the main effects and two-way interactions of the variables was 103, a much more 
 
50 
 
reasonable scope for this study.  To include more statistical evidence, 135 systems were 
ultimately analyzed. 
 
 
Figure 3-9:  System Combinations 
 
 
 
 
 
 
Gap Sizes System Ratios 
Velocity 
Dependent 
Damping 
Device 
System 
Arrangement 
Natural 
Period 
Seismic 
Hazard 
Los 
Angeles 
or 
Memphis
(2 Levels) 
0.25, 0.5, 
1.0, 2.5,  or 
4 Seconds   
(5 Levels) 
Parallel 
VE Rubber 
M40B60- 
M80B20  
(5 Levels) 
20%-100% of 
SMF Yield 
Displacement    
(5 Levels) 
VFD 
M40B60- 
M80B20  
(5 Levels) 
20%-100% of 
SMF Yield 
Displacement    
(5 Levels) 
Series 
VE Rubber 
M40B60- 
M80B20  
(5 Levels) 
20%-100% of 
SMF Yield 
Displacement    
(5 Levels) 
VFD 
M40B60- 
M80B20  
(5 Levels) 
20%-100% of 
SMF Yield 
Displacement    
(5 Levels) 
None M40B60- 
M80B20  
(5 Levels) 
20%-100% of 
SMF Yield 
Displacement    
(5 Levels) 
 
51 
 
3.10 System Names 
 After the systems were generated in an experimental design, it was important to 
come up with a naming convention in order to effectively organize the extensive data.  As 
outlined in the previous sections, each system contains a seismic hazard, multi-phase 
system arrangement, natural period, gap size, baseline system, and velocity-dependent 
damping device.  Examples of the naming scheme are outlined in Table 3-3. 
 
Table 3-3:  System Naming Scheme 
Seismic 
Hazard 
System 
Arrangement 
Natural 
Period (sec) 
Gap 
Size 
Strength 
Ratio 
System 
Configuration System Name 
Los Angeles Parallel 0.25 40% M50B50 HYFR LA-P-0.25T-0.4-M50B50-HYFR 
Los Angeles Series 2.5 80% M60B40 HPCD LA-S-2.5T-0.8-M60B40-HPCD 
Los Angeles Series 1 60% M80B20 HPCD-None LA-S-1T-0.6-M80B20-HPCD-None 
Memphis Parallel 4 100% M40B60 HYFR-VFD M-P-4T-1.0-M40B60-HYFR-VFD 
Memphis Series 0.5 20% M70B30 HPCD-VFD M-S-0.5-0.2-M70B30-HPCD-VFD 
 
3.11 Summary 
This chapter has provided a thorough explanation of the parametric development 
and analysis plan.  Velocity-dependent devices, such as a viscous fluid damper and 
viscoelastic damper, were chosen, and the corresponding properties were discussed.  A 
BRB was chosen as the displacement-dependent device and the pertinent properties to 
include in the analysis were also discussed.  Once the two damping device types were 
chosen, the multi-phase arrangements were developed and discussed in detail.  Other 
system components such as the dual frame strength ratios were reduced to an acceptable 
 
52 
 
range of values.  Relationships between the strength and stiffness of the dual frame 
components were developed.  The gap size responsible for the transition of phases was 
also briefly discussed.  The seismic locations, which are indicative of the seismic hazard 
level, and natural periods included in the scope of the research were chosen to adequately 
represent an array of seismic hazards.  A naming scheme was also formed so that data 
collection could be performed in an organized manner.  Once the parametric development 
was complete, the modeling and response history analysis criteria were developed and the 
analysis was performed. 
 
53 
 
Chapter 4         Nonlinear SDOF Response History Analysis 
4.1 Introduction 
Measuring the earthquake response of buildings using a single degree of freedom 
system is common.  This research is intended to identify the fundamental behavior of 
multi-phase systems; therefore, an approximation of a regular building as a single-degree 
of freedom system is desirable. An analysis of system parameters and their affect on 
structural response was used to reduce the number of viable multi-phase systems.  The 
analysis of fundamental system behavior provided insight towards a MDOF analysis.  
Considering the multi-phase control device?s current state of knowledge, statistical 
inferences of a MDOF system would be exhaustive, clouded, and difficult to 
comprehend.  Additionally, attributing response to a certain system parameter would not 
be nearly as straightforward as it would be for a SDOF system because of the relatively 
complex behavior involved with a MDOF system.  This chapter details the SDOF system 
parameters, in addition to the modeling process.  Other aspects such as ground motion 
selection and scaling are also detailed in this chapter. 
 
4.2 System Parameters 
The SDOF system seeks to represent the whole structure but fails to account for 
the significant redundancy that would be present in a MDOF system.   Since the first 
yield of a structure may happen early in a SDOF system, rendering it relative weak in 
seismic capacity, the use of an overstrength factor (? = 2.5) was justified for modeling 
the systems (NEHRP, 2003).  Inherent damping, another item to be included in SDOF 
 
54 
 
modeling, was represented using mass and stiffness proportional damping (Rayleigh 
damping).  The damping ratio was kept between 1.5% and 2.3% of critical damping from 
a 0.25 second natural period (Tn) to 1.5Tn of the system (Figure 4-1).   
 
 
Figure 4-1:  Rayleigh Damping 
 
4.3 Earthquake Records 
 A suite of ground motions had to be selected that represented a variety of ground 
motion types:  far field, near field with an acceleration pulse, and near field without an 
acceleration pulse.  Eleven ground motions were chosen for each seismic hazard location 
and three sources were used for the selection of the ground motions.  The Los Angeles 
ground motions were chosen from a list of motions recommended in FEMA-P695 based 
on characteristics such as source magnitude, source type, site conditions, and distance 
from source (FEMA, 2009).  The eleven records chosen for response history analysis 
were comprised of 5 far field records, 3 near field with acceleration pulse records, and 3 
near field without acceleration pulse records and were downloaded from the PEER 
 
55 
 
database (PEER, 2000).  The records chosen for the response history analysis of the 
multi-phase systems are detailed in Table 4-1. 
Table 4-1:  Los Angeles Record Selection Summary 
Earthquake 
Record Location Source Year Magnitude 
Duration 
(Seconds) 
Scale 
Factor 
Far Field Records 
DZC270 Duzce, Turkey PEER 1999 7.5 27.19 1.924 
BPOE270 Superstition Hills PEER 1987 6.5 22.3 1.861 
HE11140 Imperial Valley PEER 1979 6.5 39.04 2.06 
BICC000 Superstition Hills PEER 1987 6.5 40 2.233 
ABBARL Manjil, Iran PEER 1990 7.4 53.52 1.624 
Near Field with Pulse Acceleration 
DZC180 Duzce, Turkey PEER 1999 7.1 25.89 1.146 
ERZEW Erzican, Turkey PEER 1992 6.7 20.78 1.672 
STG090 Loma Prieta PEER 1989 6.9 39.955 2.036 
Near Field without Pulse Acceleration 
CPM000 Cape Mendocino PEER 1992 7.0 30 1.409 
TCU067N Chi-Chi, Taiwan PEER 1999 7.6 90 1.66 
STC180 Northridge PEER 1994 6.7 30 1.782 
 
The approach for record selection in the Memphis location was slightly different 
than for the Los Angeles area due to the unavailability of historic ground motion data.  
The use of near field ground motions is not practical in the Memphis area because of the 
 
56 
 
distance from the New Madrid Fault.  Numerous synthetic motions have been developed 
for the Memphis area by Fernandez (2007) and the Engineering Seismology Laboratory 
(2005) and were included in the suite of motions.  Of the eleven ground motions, 5 were 
far-field motions obtained from FEMA-P695, 4 were Memphis synthetic records, and 2 
were Charleston, SC synthetic records, chosen to represent another East coast seismic 
hazard.  The records chosen for the Memphisresponse history analysis of the multi-phase 
systems are detailed in Table 4-2. 
Table 4-2:  Memphis Record Selection Summary 
Earthquake 
Record Location Source Year Magnitude 
Duration 
(Seconds) 
Scale 
Factor 
Far Field Records 
BOL000 Duzce, Turkey PEER 1999 7.1 55.9 1.21 
ABBARL Manjil, Iran PEER 1990 7.4 53.52 1.348 
DZC270 Kocaeli, Turkey PEER 1999 7.5 27.19 1.432 
CHY101N Chi-Chi, Taiwan PEER 1999 7.6 90 1.016 
TCU045W Chi-Chi, Taiwan PEER 1999 7.6 90 1.686 
Charleston Synthetic Records 
Cacc401bc Charleston, SC MCEER N/A 7.3 21.78 1.685 
Cacc105bc Charleston, SC MCEER N/A 7.3 22.78 1.061 
Memphis Synthetic Records 
Acc510bc Memphis MCEER N/A 8.0 51.34 1.234 
Acc101bc Memphis MCEER N/A 8.0 51.34 1.25 
MEM97507 Memphis Fernandez N/A 7.65 59.715 1.802 
 
57 
 
MEM97504 Memphis Fernandez N/A 7.65 85.63 1.513 
 
Once a suite of motions was selected, each had to be scaled appropriately to 
match the design spectrum.  The geometric mean of the motions had to be kept above the 
design spectrum from a natural period of 0.25 seconds to 4 seconds to ensure that the 
input energy was greater than the design strength at all levels modeled.  The scaled 
earthquake records for the Los Angeles and Memphis ground motions are detailed in 
Figure 4-2 and Figure 4-3.  Each scaled record was input as an acceleration function in 
SAP2000. 
 
 
Figure 4-2:  Los Angeles Ground Motion Selection and Scaling 
 
 
58 
 
 
Figure 4-3:  Memphis Ground Motion Selection and Scaling 
 
4.4 Modeling Details 
 With the ground motions and systems selected, the details of the modeling had to 
be established.  Each element had to be accurately represented so that system behavior 
could be analyzed.  The following sections detail the modeling process for each system.  
4.4.1 Baseline Systems 
The baseline systems consisted of a dual seismic resisting system and were 
analyzed to demonstrate the benefits of adding a transitional gap phase.  The multi-phase 
systems also contain the baseline elements, but included the addition of other elements 
representing gap, rubber, and damping behavior, depending on the system arrangement.  
Each baseline system has a moment frame and buckling restrained brace element, 
represented with a multilinear plastic link in SAP2000.  Using data from the moment 
 
59 
 
frame design discussed earlier in the research, a ?backbone? curve was developed ofr the 
link elements.  A trilinear force-displacement relationship would be expected as the beam 
yields first, the column yields, then both strain harden together.  Since it would be 
somewhat difficult to represent this sequential yielding with strain hardening, two 
bilinear relationships, one for the moment frame beam and one for the column were used 
in parallel instead (Figure 4-4).   
Post-yield p-delta effects were neglected because the practicality of use within a 
SDOF study is simply not realistic.  P-delta effects can add large secondary moments to 
the structure throughout the duration of excitement, especially after yielding because of 
the decrease of system stiffness.  Because, for a SDOF system, the mass is lumped at a 
single point, including secondary moments associated the displacement is not realistic.  
Although neglecting p-delta effects improves system performance, it is a necessary 
assumption within the scope of the research.  Investigating p-delta effects would be an 
area of interest, especially with longer period structures, in a MDOF study.   
Similar to the moment frame, the buckling restrained brace frame backbone curve 
was generated using the strength and stiffness data presented in the previous chapter. 
 
 
Figure 4-4:  Special Moment Frame Component Breakdown 
 
60 
 
 
The backbone curves for the links in the models were created in accordance with 
ASCE Standard 41-06 ?Seismic Rehabilitation of Existing Buildings? (ASCE, 2007).  
Figure 4-5 details the typical behavior of the elements, including criteria for yielding, 
strain hardening (3% of the elastic slope), plastic deformation, and residual strength.  
Values taken from Table 5-6 and Table 5-7 in ASCE Standard 41-06 are outlined in 
Table 4-3.   
 
Table 4-3:  Link Element Backbone Curve Values (ASCE/SEI, 2007) 
 Plastic Rotation Angle or Deformation Residual Strength Ratio 
Link Element a b c 
Moment Frame Beam for 
Flexure 9?y 11?y 0.6 
Moment Frame Column for 
Flexure 9?y 11?y 0.6 
Buckling Restrained Brace in 
Tension 11?T 14?T 0.8 
 
 
Figure 4-5:  Link Backbone Behavior (ASCE/SEI, 2007) 
 
In the model, the multilinear plastic links for the SMRF and BRB are situated on 
either side of the SDOF mass (Figure 4-6).  These plastic links are comprised of elastic 
 
61 
 
and inelastic behavior and are representative of the force-displacement behavior of the 
SMRF and BRB elements.  Varying the SDOF mass and the link stiffnesses, the natural 
period of the system can be changed.  Other modeling elements will be detailed in further 
sections as they are encountered in the multi-phase systems. 
 
 
Figure 4-6:  Modeled Baseline System 
 
4.4.2 Series Systems 
 The three series systems to be modeled include the HPCD, HPCD-VFD, and 
HPCD-None systems.  These systems include the link elements previously described for 
the SMRF and BRBF, with the addition of a gap element and linear viscous damper.  The 
gap element for the HPCD system is represented with a multilinear elastic link element 
that accounts for the high-damping rubber stiffness and lockout mechanism.  The 
stiffness during the transition action is dependent on the damper size but after the desired 
 
62 
 
displacement is reached, the element essentially becomes infinitely stiff when the 
mechanism locks out.  Marshall (2008) found the shear storage modulus (G?) to be 87 psi 
during the mechanical testing of a high-damping butyl rubber to be utilized in an HPCD; 
therefore this value was used in this research as well.  The gap for the HPCD-VFD and 
HPCD-None (also represented with a multilinear elastic link element) theoretically has 
no stiffness but a value of 0.5 kips/inch was used to account for friction in the slotted 
connection.  Detailed gap element behavior can be found in Figure 4-7. 
 
 
Figure 4-7:  Gap Element Modeling 
 
Damping in the high-damping rubber and viscous fluid damper was modeled 
using a linear viscous dashpot element.  The damping coefficient, c, is changed 
depending on the system properties and damping material (8% for the HDR and 13% for 
the VFD).  In the series systems, viscous or viscoelastic damping is only present while 
the gap is active; therefore it is placed in parallel with the gap element.  The HPCD-None 
 
63 
 
system has no supplemental damping and therefore no linear viscous damper.  Details of 
the system arrangements are shown in Figure 4-8. 
 
Figure 4-8:  Modeling of the Series Systems 
 
4.4.3 Parallel Systems 
 The parallel systems were a little more complex to model and had to allow for 
damping during all phases of excitation.  The HYFR system included the SMRF elements 
in parallel with a BRB and gap element in series on one side of the system. The other side 
 
64 
 
included the compressed elastomeric device (EMD) described in Chapter 3.  The encased 
high-damping rubber in the EMD is represented using a multilinear elastic link element, 
linear viscous dashpot, and a multilinear plastic element.  The HDR stiffness is 
represented the same as it was in the HPCD system, in parallel with the viscous damper 
with a damping coefficient that creates 8% of critical damping.  Karavasilis et al. (2010) 
found slip behavior in the EMD to occur at approximately 2/3 of an inch, meaning that a 
?slip force? can be found that would initiate a friction device behavior with little 
resistance until force direction reverses.  This slip behavior is represented with a 
multilinear plastic link element that does not become active until the slip force is reached; 
this behavior is evident in a hysteresis loop resulting from a representative model in 
Figure 4-9.   
 
Figure 4-9:  EMD Hysteretic Slip Behavior 
  
The HYFR-VFD system utilizes a VFD placed in parallel with a BRB and gap 
element acting in series. The other side of the system is the typical moment frame 
-400 
-300 
-200 
-100 
0 
100 
200 
300 
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -1E-15 0.1 0.2 0.3 0.4 0.5 0.6 
For
ce 
(ki
ps)
 
Displacement (inches) 
 
65 
 
configuration seen in all the other systems.  The modeling schematics for the parallel 
systems are represented in Figure 4-10.  Both systems can utilize damping even while the 
BRBF link is yielding, a potentially appealing option that was investigated in this study.   
 
 
Figure 4-10:  Modeling of the Parallel Systems 
 
4.5 Incremental Dynamic Analysis 
 The primary means for analyzing the data was in the form of an incremental 
dynamic analysis (IDA).  This method is widely accepted and has been adopted as an 
acceptable means of analysis in the FEMA guidelines (Vamvatsikos & Cornell, 2002).  In 
the scope of this research, the IDAs were created by 1) scaling the ground motions as 
detailed earlier in the chapter, 2) scaling the ground motions further by factors of 0.1, 0.2, 
0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 (DBE), 3) running each scale factor for the model, 
 
66 
 
and 4) plotting the maximum absolute value for each response quantity.  The values used 
in the IDAs were typically an average response of the 11 ground motions at each scale 
factor.  General trends, such as yielding of an element, were noticed as the IDA plots 
changed shape.  Comparing multi-phase system IDAs to baseline system IDAs is also a 
useful means of analysis.  Observing response in an IDA is a great means for evaluating a 
large set of data in a quick fashion. As better performing multi-phase systems were 
identified using the IDA data, more rigorous comparisons were made.  Acceleration 
spikes and residual displacements were also analyzed using a representative set of 
response histories. 
 
4.6 Response Quantities 
The four primary response quantities used to evaluate the systems were 
acceleration, base shear, moment frame ductility, and buckling restrained brace ductility.  
It was felt that the magnitudes of these four characteristics could adequately describe the 
overall performance of the multi-phase systems.  In order to compare the systems, 
normalization of the response parameters into unitless quantities was desirable.  
Acceleration response consisted of the total nodal acceleration divided by the 
gravitational constant (386.4        ).  Base shear response was determinedby dividing the 
lateral base reaction (kips) by the weight (kips) of the system.  
Since the moment frames were designed to ensure strong column-weak beam 
response, the moment frame ductility was determined using the moment frame beam link 
response.  The moment frame ductility is also a measure of drift since the moment frame 
displacement is the absolute displacement of the system.  The normalized moment frame 
 
67 
 
ductility value (?M) consisted of the actual beam displacement value divided by the beam 
yield displacement. Similarly, the buckling restrained brace ductility (?B) was calculated 
by dividing the buckling restrained brace link displacement by the brace yield 
displacement.  The quantities used to determine these normalized responses are detailed 
in Table 4-4. 
 
Table 4-4:  Response Quantity Summary 
Response Quantity Unitless Response 
Acceleration (g)                                    
Base Shear                           
Moment Frame Ductility (?M)                                                                   
Buckling Restrained Brace 
Ductility (?B) 
                                      
                                            
 
4.7 Summary 
 This chapter provided a description for the response history analysis that was 
performed for the multi-phase passive control systems.  Important aspects of the study 
were established such as the suite of ground motions and the appropriate scaling levels 
for the ground motion records.  Modeling aspects for all of the multi-phase systems were 
discussed, and the arrangement of the systems was described.  Multi-linear plastic link 
elements, multi-linear elastic link elements, and linear viscous dashpots were all used to 
represent the multi-phase behavior.  In addition to modeling techniques, analysis criteria 
were described for the results of the response history analyses.  Four primary response 
 
68 
 
quantities were chosen to be analyzed in the form of an incremental dynamic analysis.  
After the completion of the model development, the multi-phase system models were run 
in SAP2000 and the results are discussed within the next section. 
 
69 
 
Chapter 5  Preliminary Analysis 
5.1 Introduction 
 The groundwork for the study has been clearly defined in the previous chapters.  
Multiple multi-phase passive control device combinations have been proposed and 
demonstrated to be beneficial in previous studies (Marshall, 2008).  The goal of this study 
was to identify the important factors controlling response.   This chapter provides the 
results of the study outlined in the previous chapters and some conclusions are drawn 
about the behavior of passive multi-phase systems.  The chapter consists of the 
description a preliminary analysis, in which the range of variables was narrowed down 
into a reasonable range, for which a full factorial analysis could be conducted.  The 
ultimate goal was to narrow the scope of the research into an acceptable range of values 
so that a MDOF study may be performed in the next part of the multi-phase system 
development.  In doing so, important system responses were identified and fundamental 
multi-phase behavior was uncovered.  As outlined in previous chapters, an extensive 
nonlinear response history analysis was completed using SAP2000.  The graphical results 
of data collected in the preliminary analyses can be found in Appendix A. 
 
5.2 Preliminary Analysis 
As described in Chapter 3, the scope of the study potentially involved 1250 
possible combinations for the multi-phase systems.  In order to complete the study in a 
timely manner and still capture the significance of the results, the results of an 
experimental design reduced the scope of the study to 135 systems.  This representative 
 
70 
 
subset of the 1250 possible systems was meant to capture the statistical significance of 
each of the system parameters.  This was difficult to determine due to the hierarchal 
structure inherently present within the multi-phase systems.  The factors are statistically 
?nested? within each other, an important variable that was unintentionally ignored in the 
experimental design.  This means that individually variable performance could not be 
compared to each other because the performance was dependent on other variables within 
the hierarchal structure.  The scope of this analysis was simply too large to draw finite 
conclusions about the statistical significance of multi-phase systems, but general 
conclusions were made.  In this section, some results from the preliminary analysis are 
presented, general observations about multi-phase systems are provided, and a solution to 
the nesting issue is offered.   
Figure 5-1 through 5-4 show representative sets of data generated from the 
preliminary analysis with the four response quantities of concern are plotted.  The system 
names follow the convention given in Section 3.10. 
 
 
71 
 
 
Figure 5-1:  Acceleration Results for 0.5T Los Angeles Systems 
 
Figure 5-2:  Base Shear Results for 0.5T Los Angeles Systems 
 
 
72 
 
 
Figure 5-3:  Moment Frame Ductility Results for 0.5T Los Angeles Systems 
 
Figure 5-4:  BRB Ductility Results for 0.5T Los Angeles Systems  
 
73 
 
In comparing the graphical results, there were no multi-phase systems that clearly 
stood out as outstanding performers across all scale factors and response quantities, but 
general trends were noticed.  Even though systems had noticeable differences in 
response, the reasons for the differences were difficult to pinpoint due to the nesting of 
the system variables.  For many of the multi-phase systems, better performance in one of 
the response quantity amounts to sacrificial performance in another. 
Generally speaking, the transition gap allows for better acceleration and base shear 
shear performance in the lower scale factors.  This was noticed as the plots with the 
larger gap sizes have a lower acceleration response in the lower scale factors and 
delayed transition into higher acceleration values in the upper scale factors.  To a 
degree, this is noticed across all natural periods, multi-phase systems, and both 
hazards.  The presence of supplemental damping and a reduction in initial stiffness 
would be present in a dual system is the reason for this marked improvement in 
Figure 5-1 and  
Figure 5-2:  Base Shear Results for 0.5T Los Angeles Systems 
 
 show the poor performance of the HPCD-None systems, demonstrating the need 
for supplemental damping and therefore a transition gap phase with supplemental 
damping.  Yielding in the HPCD-None systems occurs quicker than the systems with 
supplemental damping.  The overall performance seems to be very sensitive to the 
strength/stiffness ratio and gap size pairing.   
No discernable difference could be found between the two types of supplemental 
damping.  The high-damping rubber provides more stiffness, and therefore higher 
 
74 
 
acceleration, in the lower scale factors for the series systems, but also potentially delays 
the transition into the secondary phase and reduces displacements. The high-damping 
rubber in the parallel arrangement provides more stiffness throughout all scale factors and 
therefore can experience a larger acceleration throughout all scale factors.  Although this 
is a drawback of a parallel multi-phase system, it also means that more damping and 
energy dissipation is present to protect the system elements. 
Although these general observations are helpful in understanding the fundamental 
multi-phase behavior, statistical significance and proof of beneficial multi-phase behavior 
was not evident.  The difficulty in identifying the beneficial factors arose because of the 
great independence of each of the factors on one another.  Figure 5-5 illustrates the 
hierarchical path taken to get to two plausible multi-phase systems:  LA-S-4T-0.4-
M50B50-HPCD-None and LA-P-0.5T-0.6-M80B20-HYFR-VFD.  Simply comparing the 
response parameters from the two gap sizes or system ratios is not feasible because the 
response is also reliant on the higher levels in the hierarchal structure.  Trying to find 
statistical significance this far down the hierarchal arrangement with data from 135 
systems out of the 1250 combinations was not possible due to this nesting issue.    
 
 
 
 
75 
 
 
 
Figure 5-5:  Hierarchal Nesting Issue 
 
A full factorial design on a smaller range of variables would allow statistical 
observations to be made if significance were present.  At the very least, since the research 
was deterministic in nature and all the multi-phase combinations were exhausted, the data 
from a full factorial design would allow one to make observations between the systems, 
 
76 
 
knowing that a better performing multi-phase system is not available within the scope the 
research variables.  The following sections detail the reduction of the research scope in 
order to accomplish these goals.  
 
5.2 Reduction of the Research Scope 
Although the analysis was intended to be the only analysis, it ultimately served as 
a preliminary analysis used to narrow the scope of the study into a more useful range of 
values.  Instead of performing another experimental design and analyzing a representative 
set of the multi-phase system population, the goal was to eliminate certain factors, and 
perform a full factorial analysis using the remaining factors, for which the whole 
population was analyzed.  Since the analysis was deterministic in nature, this full 
factorial analysis was a desirable option for determining the variables that controlled the 
response, and for identifying the systems that showed superior performance.  As stated in 
Chapter 3, a full factorial design which exhausts all possible options would consist of 
1250 systems. The following sections details the techniques used to systematically reduce 
the number of factors varied in the study. 
5.2.1 Seismic Hazard 
 Results of the preliminary analysis demonstrated similar response magnitudes for 
the two seismic hazards, as evident in Figure 5-6a through Figure 5-6d.  In this figure, 
results for two multi-phase systems that had the same multi-phase configuration, but were 
designed and exposed to both seismic hazards, are compared.  Although the systems were 
subjected to a different suite of ground motions, the general shape of the IDA curves is 
somewhat similar, suggesting similar behavior across seismic hazards.  Ductility values 
 
77 
 
were also found to be statistically similar for the analysis, further backing this assertion.  
These observations hold true across the preliminary analyses for multi-phase systems 
with differing gap sizes. 
 
 
Figure 5-6:  1T-M70B30-1.0-HYFR Seismic Hazard Comparison 
 
Since there are only two seismic hazards and seismic hazard is near the top of the 
hierarchy, reducing the seismic hazard to one location would reduce the number of 
possible systems from 1250 to 625 systems.  Evaluating the responses for the seismic 
hazard of each location, it was determined that Los Angeles would be a more suitable 
 
78 
 
location for the rest of the analyses, because the intensity and frequency of seismic events 
in Los Angeles make the location a more marketable and viable option for the multi-
phase systems.  Once a range of multi-phase systems are identified as good performers at 
the end of the study, their performance can be validated in other locations. 
5.2.2 Natural Period 
 The preliminary analysis included 5 natural periods of interest:  0.25, 0.5, 1.0, 2.5, 
and 4.0 seconds.  In order to reduce the number of natural periods, similarities in 
response behavior were sought. 
Error! Reference source not found. shows a connecting letters report for the 
longer natural periods for the report.  A Tukey is used test to compare the means and to 
test for significant differences.  The Tukey test has been demonstrated as an excellent 
post-hoc test method for an Analysis of Variance (ANOVA) (Montgomery, 2009). The 
report shows that moment frame and brace ductilities are not significantly different for 
the two periods, suggesting that only one of the periods needs to be tested in the future.  
The total acceleration and base shear responses are not connected in a similar manner, 
which is expected due to different input energies at the two natural periods.  Conclusions 
drawn for a 2.5 second period could reasonably be extended for a 4 second period in the 
next analysis.  Once a range of acceptable multi-phase systems are established at the end 
of the study, their performance can be validated for a 4 second natural period if needed.  
This would probably not be the case within the scope of an MDOF study, but for the 
scope of this research it is no longer necessary to include both periods.  Eliminating the 4 
second period from the study reduced the scope of interest from 625 to 500 systems. 
 
 
79 
 
Table 5-1:  Connecting Letters Report 
 
 
 5.2.3 System Arrangement 
 The preliminary analysis involved 5 different multi-phase system 
HPCD, HPCD-VFD, HPCD-None, HYFR, and HYFR-VFD.  As alluded to earlier 
shown in Figure 5-1 and  
Figure 5-2:  Base Shear Results for 0.5T Los Angeles Systems 
 
, the HPCD-None system demonstrated poor acceleration and base shear performance in 
comparison to the other systems.  Yielding of elements, as the ductility values exceed 1, 
also occurred earlier in comparison to the other multi-phase systems.  For these reasons, 
the HPCD-None system was eliminated from further analyses.  As expected, damping 
does play a valuable role in the protection of structures using the multi-phase systems.  
No valid arguments could be made for the elimination of other systems.  The 
parallel systems did experience high acceleration and base shear response in the higher 
scale factors in comparison to the series systems, but the great ductility response made 
those systems a viable to option to be included in the next analysis.   The elimination of 
the HPCD-None system reduced the scope of the study from 500 to 400 systems. 
5.2.4 System Ratios 
 
80 
 
The preliminary analysis involved 5 different dual system ratios:  M40B60, 
M50B50, M60B40, M70B30, and M80B20.  Moment frame ductility is largely 
dependent on the moment frame strength and gap size.  The larger the portion of the dual 
system resisted by the moment frame, the more ductility is present in the moment frame 
element.  Since the primary goal of the study was to limit the ductile behavior to a 
replaceable ?link? element, the ductile behavior of the moment frame was not desirable.  
This ductility could be reduced by limiting the gap size to 20%-40% of the moment 
frame yield, but that would not allow the supplemental damping to be fully utilized to 
reduce accelerations.   
 
Figure 5-7:  Moment Frame Ductility Comparison between Dual System Ratios 
 
Figure 5-7 is a random sample of ductility responses of multi-phase systems at 
different system ratios.  The IDA curves illustrate the relatively poor performance of the 
systems with a larger moment frame percentage (M70B30 and M80B20).  Moment frame 
yielding occurs as early as 40% of the design basis earthquake (DBE) for these systems 
 
81 
 
as opposed to 60%-90% of the DBE for the M40B60 and M50B50 systems.  For this 
reason, the secondary analysis was concentrated on the range of M40B60 to M60B40 in 
order to reduce moment frame ductility.  This reduced the scope of the study from 400 to 
240 multi-phase systems. 
5.2.5 Transitional Gap Size 
 The preliminary analysis involved 5 different transitional gap sizes:  20%, 40%, 
60%, 80%, and 100% of the special moment frame yield displacement.  The multi-phase 
system behavior was very sensitive to the system ratio paired with the gap size.   
 
Figure 5-8:  M-S-2.5T-M50B50-HPCD-VFD Gap Size Comparison 
 
Figure 5-8a through Figure 5-8d demonstrate the importance of the gap size on 
the response of the multi-phase systems, comparing the same multi-phase arrangement 
with two different gap sizes.  Significant differences in magnitude can be seen between 
 
82 
 
the two systems across all of the response quantities.  The smaller gap size does not allow 
for significant damping because it closes too quickly and increases acceleration and base 
shear due to the increase in stiffness.  Buckling restrained brace behavior is also much 
more desirable for the larger gap size, delaying yielding until about 50% of the DBE as 
opposed to 20% of the DBE in the multi-phase system with the smaller gap size.  The one 
drawback of the larger gap size is the slightly worse moment frame ductility behavior, a 
response quantity identified earlier as very important.  This problem could potentially be 
resolved with a smaller gap size, such as 60% or 80% of moment frame yield 
displacement, which should still allow for significant damping but also protect the 
moment frame.  Similar behavior was observed across all of the multi-phase systems, and 
therefore justified the reduction of the scope of the study to only include gap sizes from 
60%-100% of moment frame yield displacement.   
This decision reduced the scope of the study from 240 to 144 systems, a number 
that was much more reasonable to analyze in a timely manner than 1250 systems.  With 
the reduction of variable levels to a reasonable scope for a full factorial analysis, the next 
set of analyses was completed.  The hierarchal structure of the full factorial analysis is 
given in Figure 5-9.  Although nesting was still present due to the inherent hierarchal 
structure of the data, the overall multi-phase system performance was more evident at the 
end of the analysis. 
 
83 
 
 
Figure 5-9:  Full Factorial Experimental Design 
 
5.3 Summary 
This chapter provided a significant amount of preliminary information for multi-
phase systems.  Although the work was intended to be the only analysis, the results were 
unclear, and an additional analysis was required.  Some general observations were made 
but the fundamental understanding of multi-phase behavior was still lacking.  The 
preliminary analysis did help in reducing the range of variables to an acceptable range for 
a full factorial analysis to be performed.  Each variable was analyzed and the range of 
variable values to be studied was reduced using a statistical analysis or empirical 
observations.  The number of possible systems was reduced from 1250 to 144 multi-
Gap Sizes System Ratios 
Velocity 
Dependent 
Damping 
Device 
System 
Arrangement 
Natural 
Period 
Seismic 
Hazard 
Los 
Angeles 
(1 Level) 
0.25, 0.5, 
1.0, & 2.5 
Seconds   
(4 Levels) 
Parallel 
VE Rubber 
M40B60- 
M60B40  
(3 Levels) 
60%-100% of 
SMF Yield 
Displacement    
(3 Levels) 
VFD 
M40B60- 
M60B40  
(3 Levels) 
60%-100% of 
SMF Yield 
Displacement    
(3 Levels) 
Series 
VE Rubber 
M40B60- 
M60B40  
(3 Levels) 
60%-100% of 
SMF Yield 
Displacement    
(3 Levels) 
VFD 
M40B60- 
M60B40 
(3 Levels) 
60%-100% of 
SMF Yield 
Displacement    
(3 Levels) 
 
84 
 
phase arrangements, a number reasonable for a full factorial analysis.  Similar to models 
described in this chapter, the new models required for the full factorial analysis were 
assembled and run in SAP2000.  The following chapter details the results of this analysis. 
 
85 
 
Chapter 6  Full Factorial Analysis 
6.1 Introduction 
 Chapter 6 describes the steps taken to identify the fundamental behavior of multi-
phase systems.  With the range of variables narrowed as detailed in the previous chapter, 
a full factorial analysis was completed in order to find significant differences in the 
system responses.  The original intention of the research was to provide a statistical 
analysis of the system results, but since the data is deterministic in nature, a full factorial 
analysis will allowed a direct comparison between systems.  First, an overall comparison 
of the multi-phase systems to baseline systems was accomplished to demonstrate the 
benefits of a multi-phase system.  Once this was completed, the ultimate goal became 
narrowing the scope of the study into an acceptable range of values so that a MDOF 
study can be performed in the next phase of multi-phase system development.  This goal 
was accomplished by comparing the responses of multi-phase systems in a variety of 
ways.  Responses for different natural periods, system arrangements, and system strength 
ratio and gap size combinations were all compared in order to identify the systems that 
performed the best.  Other aspects of multi-phase behavior, such as acceleration spikes 
and residual deformations, were also investigated.  The complete set of data collected for 
the full factorial analysis can be found in Appendix B.  
  
6.2 Comparison to Baselines 
 In order to demonstrate the benefits of a multi-phased system, their performances 
were compared to the baseline systems for all response quantities.  For appropriate 
 
86 
 
comparisons to be made, all multi-phase systems were compared to their corresponding 
baseline system, which were comprised of only the dual frames. Figure 6-1 through 
Figure 6-4 show the performance of all the multi-phase systems for a 1 second natural 
period with an M50B50 dual frame.  This is a representative selection of multi-phase 
systems but similar observations were made across all of the multi-phase systems 
evaluated in this analysis. 
The responses of the baseline systems were represented with a solid line.  Box 
plots were used to depict the spread in the multi-phase system responses.  Using the five 
number summary (minimum value, lower quartile, median, upper quartile, and maximum 
value), variability and skewness in the responses were readily identified.  Since these 
comparisons included all of the multi-phase systems, large error bars or a high level of 
skewness may be apparent in some system combinations, indicating poor performance.  
Initially, this was a useful means to evaluate the multi-phase performance, but more 
detailed analyses were used in further sections to further evaluate system behavior. 
 
87 
 
 
Figure 6-1:  Multi-Phase System Acceleration Comparison to Baseline (1T-M50B50) 
 
Figure 6-2:  Multi-Phase System Base Shear Comparison to Baseline (1T-M50B50) 
 
88 
 
 
Figure 6-3:  Multi-Phase System Moment Frame Ductility Comparison to Baseline   
(1T-M50B50) 
 
 
89 
 
 
Figure 6-4:  Multi-Phase System Brace Ductility Comparison to Baseline   (1T-
M50B50)  
As seen in Figure 6-1, relative to the baseline system (solid line), poor 
performance was seen for the upper scale factors with 40% more acceleration for the 
median multi-phase system.  This poor performance is probably partially due to larger 
second phase stiffness present once the gap is closed and yielding of the displacement 
device takes place.  Another reason for the poor performance could also be a result of 
large acceleration spikes that may occur as the multi-phase systems transition from the 
first to second phase.  These acceleration spikes were evaluated in more detail later in the 
study to determine if they were a controlling factor in acceleration performance of the 
multi-phase systems.   
The mid-scale factors exhibited a tremendous amount of variability in 
acceleration response, depending on the system arrangement.  Some systems performed 
better than the baselines, while others performed worse.  This is due to the transition of 
 
90 
 
phases as the gap locks out and the system becomes stiffer.  The most evident and 
convincing benefit of the multi-phase systems is present in the lower scale factors.  
Regardless of the multi-phase arrangement, improved performance was observed from 
10% to 40% of the DBE.  The supplemental damping and lower stiffness present in the 
initial phase of the multi-phase arrangements is probably responsible for the improved 
behavior. 
Base shear performance for the multi-phase systems, in comparison to the 
baseline dual frame, was very similar to that for the acceleration performance, as seen in 
Figure 6-2.  Relatively poor performance was seen in the upper scale factors but the 
systems were not as variable and median performance was only about 20% worse than 
the baseline system.  Similar to acceleration response, the mid-scale factors showed the 
most variability in response due to the transition of phases.  Responses for lower scale 
factors had very little variability and demonstrated as low as 35% of baseline shear 
responses in some cases. 
Although the variability in moment frame ductility response was relatively low 
and therefore led to somewhat predictable performances, overall performance of the 
multi-phase systems for moment frame ductility was worse than the baseline performance 
across all of the scale factors.  Ductility values ranged from 20% to 70% higher than the 
baseline ductility values, with the multi-phase systems remaining elastic up to a 60% 
DBE, as opposed to 80% of the DBE with the baseline system.  The response is sensitive 
to the frame stiffness ratio and gap size pairing, but even if optimized in this regard, 
moment frame ductility was worse than baseline values.  Although the displacement 
device performs extremely well in the multi-phase system, it is at a slight cost to the 
 
91 
 
performance of the moment frame.  A few solutions to be discussed later could improve 
the moment frame integrity, while also maintaining the improved displacement device 
behavior. 
The brace ductility performance in comparison to the performance of the baseline 
system is by far the most appealing aspect of the multi-phase systems.  Unfortunately, 
this outstanding performance often comes at the cost of moment frame ductility.  Every 
system remained elastic at 40% of the DBE, and about half of them remained elastic up 
to 50% of the DBE which is much better than the baseline system, which yields before 
20% of the DBE.  Even beyond the elastic range, brace ductility was still markedly 
improved in comparison to the baseline system, with median ductility values of only 70% 
of the baseline value at the DBE.   
 In conclusion, the multi-phase systems offer many advantages in comparison to 
the baseline dual frames.  This better performance comes at the cost, though, of higher 
accelerations and base shears in the mid to high scale factors, and of poor moment frame 
ductility response. Since the displacement device is the replaceable link in the system, 
more investigation into limiting the moment frame ductility will need to be performed.  
The multi-phase system arrangements offer too many advantages in comparison to the 
baseline dual systems to be ignored as an option for seismic protection.  The following 
sections describe the narrowing of a range of multi-phase systems to those that offer the 
best performance across all response quantities.  A reduction into a smaller range of 
multi-phase systems will allow further research into optimizing system performance. 
 
6.3 Comparison Between Natural Periods 
 
92 
 
 Multi-phase system performance has been proven to be beneficial in some cases, 
but the extent of the benefits and the variability of performance across natural periods 
were not evident.  This section describes the effort to clarify the relationship between 
multi-phase system performance and natural period.  Figure 6-5 through Figure 6-8 show 
comparisons of multi-phase system responses from a 0.25 second period system and 2.5 
second period system, the two extremes of the analysis.  
 
 
Figure 6-5:  Acceleration Comparison of Multi-Phase Systems to Baselines (0.25T) 
 
93 
 
 
Figure 6-6:  Acceleration Comparison of Multi-Phase Systems to Baselines (2.5T) 
  
 
Figure 6-7:  Brace Ductility Comparison of Multi-Phase Systems to Baselines 
(0.25T) 
 
94 
 
 
Figure 6-8:  Brace Ductility Comparison of Multi-Phase Systems to Baselines (2.5T) 
 
The acceleration performances of the 0.25 second period multi-phase systems 
were worse than the baseline dual system for almost all scale factors, whereas the 2.5 
second system showed improved performance up to 50% of the DBE, as evident in 
Figure 6-5 & Figure 6-6, respectively.  Similar results were observed for the brace 
element ductility responses for the multi-phase systems.  The shorter period systems 
barely outperformed the baseline systems, while the longer period systems experienced 
up to only 30% of the baseline ductility in some cases, as shown in Figure 6-7 & Figure 
6-8, respectively.  These observations lead to question the validity of using multi-phase 
systems for shorter period systems, an issue that needs to be further investigated.   
 
 
95 
 
 
Figure 6-9:  Gap Element Displacement Comparison 
 
 Figure 6-9 shows a comparison of the gap element behavior of two of the same 
multi-phase arrangements designed with different natural periods and subjected to the 
same ground motion.  Each plateau represents the changing of phases as the gap element 
locks out and the secondary phase begins.  The 0.25 second period system experiences 
about 50 phase transitions throughout the duration of the 90 second ground motion, 
compared to 8 phase changes for the 2.5 second period multi-phase system.  Ultimately, 
the greater number of phase transitions could lead to reliability issues with repeated 
closing of the link and large acceleration spikes for the lower periods.  Failure of the 
transition element could lead to catastrophic failure of the overall system, therefore the 
0.25 second period systems may not be a viable option for the rest of the multi-phase 
system analysis.  Also, overall performance of the shorter period systems did not offer 
many benefits in contrast to the baseline systems making the multi-phase systems an 
undesirable option, especially considering the higher costs associated with the fabrication 
and design of the devices.  Further research could provide a solution for multi-phase 
behavior in shorter period systems but that is beyond the scope of this study.   
 
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Performance of the 0.5 and 1.0 second period systems were statistically different 
than the 0.25 second period systems for all response quantities. Overall results were also 
observed to be much better than 0.25 period systems; therefore it was determined to 
include the 0.5 and 1.0 period systems in the rest of the analysis.   
 
6.4 Comparison Between Multi-Phase Systems 
 With the scope of the multi-phase systems reduced into a reasonable range, it 
became important to establish selection criteria for the systems.  Because there are four 
response quantities of interest, good performance in one was often offset by poor 
performance in another.  Setting criteria for the selection of the better-performing 
systems created a consistent, systematic way of analyzing the data.   
The first, and most important criteria, is moment frame protection.  As stated 
earlier, the goal of a multi-phase system is to efficiently dissipate energy as well as to 
limit yielding to a replaceable element.  Damage to the moment frame requires expensive 
and time-consuming repairs after an event.  Another important criterion is good 
performance in the low-to-mid scale factors for the acceleration and base shear responses. 
Protection of acceleration and shear sensitive elements in the low-to-mid scale factors 
could mean immediate occupancy after an event.  Lastly, the BRB ductility performance 
must be checked.  Most of the multi-phase systems showed great performance in this 
regard, remaining elastic anywhere from 30%-70% of the design basis earthquake.  
Similar to the previous criterion, protecting a displacement-dependent device in the low-
to-midscale factors would allow immediate occupancy after an event.   
 
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Although this type of performance is ideal in regards to occupancy, as the ground 
motion intensity increases, it becomes important to strike a balance between brace 
ductility and other response quantities.  Higher brace ductility values in the mid-to-upper 
scale factors would be acceptable because of the extensive energy dissipation capabilities 
and the ability to replace the device after an event.   
This section looks at each system arrangement and follows the selection criteria 
outlined above in order to identify the better performing systems.  If a system 
demonstrated potential but was lacking in a certain response quantity, solutions were 
investigated and the results are discussed.  The 1 second natural period systems were 
analyzed as a representative set for this next section but observations made were similar 
for each natural period.  Generally speaking, as natural period increased, the performance 
of the multi-phase systems increased.   
 
 
6.4.1  HPCD Analysis 
 The HPCD systems described in Table 3-1 were the first to be analyzed.  Figure 
6-10 illustrates the system performance relative to the baseline systems. 
 
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Figure 6-10:  HPCD 1T Comparison to Baselines 
 
Median moment frame ductility was over 30% more than the baseline response 
for each scale factor, but was still reasonable at 1.6 times the yield displacement at the 
DBE.  The plots show that yielding of the moment frame would be expected at about 
60% of the DBE, as opposed to 80% to 100% of DBE for the baselines.  Acceleration and 
base shear responses were much better for the low scale factors when compared to the 
baseline systems.  A median response of 50% of the baseline response for the 0.1 and 0.2 
scale factors can be attributed to the significant supplemental damping provided by the 
high-damping rubber.  Greater responses than the baseline responses were exhibited at 
high scale factors, but only by about 10%-15%.  Brace behavior remained elastic up to 
 
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almost 50% of the DBE, and far exceeded baseline performance in the upper scale 
factors. 
In regards to the system-to-system comparisons, Figure 6-12 through Figure 6-14 
demonstrate the relationships for the four response quantities.  The moment frame 
ductility presented in Figure 6-11 shows relatively no difference in response until about 
40% of the DBE, and then a slight dispersion is noticed.  Regardless of the gap size, the 
larger system ratio (M60B40) performed the worst out of all the systems.  As one would 
expect, the larger gap sizes also performed the worst.  Moment frame ductility values 
were very close for the lower scale factors and showed only a 20% difference from the 
worst performer to the best performer for the upper scale factors.  The M40B60 paired 
with the 0.6 gap size was the best overall performer in terms of moment frame ductility. 
 
Figure 6-11:  HPCD 1T Moment Frame Ductility 
 
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Acceleration and base shear responses were very similar across all of the scale 
factors, as shown in Figure 6-12 and Figure 6-13.  For the lower scale factors, the lower 
system ratio (M40B60) performed the best due to the flexibility present in the first phase.  
As the scale factor increased, the higher system ratios became the more attractive option, 
probably due to a lower stiffness present in the second phase of the control device.  The 
dispersion between the responses for the various systems for the upper scale factors is not 
very significant, exhibiting approximately a 10% difference between the best and worst 
performers for acceleration.  As far as gap size is concerned, the larger the gap, the better 
the performance across all of the scale factors.  This is probably due to a longer first 
phase duration which allows more damping from the high-damping rubber.  Overall, the 
best performer in regards to acceleration and base shear is the M40B60, paired with the 
1.0 gap size. 
 
 
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Figure 6-12:  HPCD 1T Acceleration Response 
 
 
Figure 6-13:  HPCD 1T Base Shear Response 
 
 Lastly, the brace ductility behavior exhibited much more dispersion between 
systems than the other response quantities, with over 70% difference in response in the 
upper scale factors.  Yielding occurs anywhere from 40% to 60% of the DBE, depending 
on the system ratio and gap size combination.  The smaller system ratios performed the 
best out of all of the systems.  As the gap size increased, the brace ductility decreased, 
due to less energy dissipation required from the hysteretic braces.  Combining the 
observations regarding system ratios and gap sizes, the M40B60 system with the 1.0 gap 
size is the best performer regarding brace ductility of the group of HPCD systems for all 
scale factors.  
 
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Figure 6-14:  HPCD 1T Brace Ductility 
 
 Notwithstanding a slight compromise in the moment frame ductility (less than 
10% of the best performing system), the M40B60 system with the 1.0 gap size is clearly 
the best performer for the HPCD systems.  The large gap size allows for more damping in 
the first phase and a significant improvement in response in the low-to-mid scale factors 
in comparison to the baseline system.  The only drawback of the system is the yielding of 
the moment frame at 60% of the DBE, as opposed to yielding at100% of the DBE for the 
baseline system (M40B60).  A solution to address moment frame ductility is a must for 
all of the HPCD systems before they are completely viable for implementation. 
6.4.2  HPCD-VFD Analysis 
 
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Many of the observations made for the HPCD system would be expected to be the 
same for the HPCD-VFD systems.  Any differences would be attributed to higher 
damping present in the VFD relative to the high-damping rubber, and the lack of stiffness 
present in the first phase of the VFD devices.  Figure 6-15 presents the HPCD-VFD 
system responses compared to the baseline system responses for a system period of 1 
second. 
 
Figure 6-15:  HPCD-VFD 1T Comparison to Baselines 
 
Similarly to the HPCD systems, the median moment frame ductility was over 
30% more than the baseline response at the DBE but was still reasonable at about 1.6 
times the yield displacement.  Yielding of the moment frame was exhibited at about 60% 
to 70% of the DBE as opposed to 80% to 100% of DBE for the baselines.  Acceleration 
 
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and base shear responses were much better in the low-to-mid scale factors when 
compared to the baseline systems.  Although there was a large dispersion for the lower 
scale factors, the median acceleration and base shear responses did not become larger 
than the baseline systems until about 60% of the DBE.  The higher scale factors exhibited 
a higher response than the baselines but only by about 15%-20%.  Brace behavior 
remained elastic up to almost 60% of the DBE and far exceeded baseline performance for 
the upper scale factors. 
Also, similar to the HPCD systems, the moment frame ductility (Figure 6-16) 
shows relatively no difference in response until about 40% of the DBE, and then a slight 
dispersion is noticed.  Regardless of the gap size, the larger system ratio (M60B40) 
performed the worst out of all the systems.  Similar to the HPCD systems, the larger gap 
sizes also performed the worst but the difference was small for each system ratio.  
Moment frame ductility values were very close in the lower scale factors and showed 
only a 15% difference from the worst performer to the best performer in the upper scale 
factors.  Very little difference between the M40B60 systems was noticed across all the 
scale factors and each of those systems could be considered the best performers.  The 
M50B50 system with the smallest gap size also offered comparable moment frame 
protection.  
 
 
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Figure 6-16:  HPCD-VFD 1T Moment Frame Ductility 
 
Acceleration and base shear responses were very similar across all of the scale 
factors (Figure 6-17 & 6-18).  The lower system ratio (M40B60) performed the best due 
to the flexibility present in the first phase.  The dispersion between the systems in the 
upper scale factors is not very significant, exhibiting approximately a 10% difference 
between the best and worst performers for acceleration, and virtually no difference at the 
DBE for base shear response.  As far as gap size goes, the larger the gap, the better the 
performance across all of the scale factors.  The 0.6 gap size consistently performed the 
worst out of the systems most likely due to the relatively small amount of damping in the 
first phase compared to that for the larger gap size.  The VFD provides very little 
stiffness to the system and therefore allows the transition into the second phase to happen 
 
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quicker with smaller gap sizes.  This is illustrated in Figure 6-19, in which the gap 
displacement response histories are presented for two M50B50 HPCD-VFD systems with 
different gap sizes.  The smaller gap size goes through over 10 phase transitions, as 
opposed to 5 transitions for the larger gap size.  Overall, the best performer in regards to 
acceleration and base shear is the M40B60, paired with the 1.0 gap size. 
 
Figure 6-17:  HPCD-VFD 1T Acceleration Response 
 
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Figure 6-18:  HPCD-VFD 1T Base Shear Response 
 
 
Figure 6-19:  Gap Element Comparison for M50B50-1T (DZC270 DBE) 
 
 
108 
 
Similar to the HPCD system response, the brace ductility behavior for the HPCD-
VFD systems exhibited much more dispersion than the other response quantities, with 
over 90% difference in response for the upper scale factors.  Yielding occurred anywhere 
from 40% to 70% of the DBE, depending on the system ratio and gap size combination.  
The smaller system ratios performed the best out of all of the systems.  As the gap size 
increased, the brace ductility decreased due to less energy dissipation required from the 
hysteretic braces.  Similar to the HPCD systems, the M40B60 system with the 1.0 gap 
size was the best performer out of the group of HPCD-VFD systems for all scale factors 
regarding brace ductility.  
 
 
Figure 6-20:  HPCD-VFD 1T Brace Ductility 
 
 
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 The M40B60 system with the 1.0 gap size is clearly the best performer for the 
HPCD-VFD systems.  The large gap size allows for more damping in the first phase, and 
a significant improvement in response in the low-to-mid scale factors when compared to 
the same responses for the baseline system.  
 Similar to the HPCD system, the only drawback of the M40B60 HPCD-VFD 
system is the yielding of the moment frame at 70% of the DBE, as opposed to 100% of 
the DBE for the baseline system (M40B60).  One possible solution to this issue is to add 
more damping to the system, an option that is feasible for a VFD.  The systems with the 
smallest gap sizes were analyzed again with a damping ratio equal to 25% including 
inherent damping, as opposed to the 15% value used in the original models, to see if there 
was a significant increase in performance (Figure 6-21).  Improved performance was seen 
across all response quantities, but only approximately a 10% improvement in moment 
ductility performance was realized.  More significant improvements were seen in other 
response quantities, but the extra costs associated with a higher damping ratio may not be 
worthwhile, especially since the moment frame performance wasn?t significantly 
improved.  Other solutions for moment frame protection need to be investigated. 
 
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Figure 6-21:  HPCD-VFD Damping Ratio Comparison 
 
Although the performance of the HPCD and HPCD-VFD systems were very 
similar, there were some differences.  Figure 6-22 shoes a comparison of responses for 
the two best systems (M40B60 with 1.0 gap size) from both series configurations.  The 
HPCD-VFD outperformed the HPCD systems for all response quantities.  Moment frame 
ductility response was about 10% better in the upper scale factors, yielding at 70% of the 
DBE, as opposed to yielding at 60% of the DBE with the HPCD system.  Acceleration 
response wass up to 70% better for mid-scale factors.  The brace remained elastic up to 
70% of the DBE as opposed to 60% for the HPCD system.  These results suggest that the 
damping capability is the most important aspect of the series configurations.  
 
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Figure 6-22:  HPCD vs. HPCD-VFD (M40B60-1.0-1T) 
 
6.4.3  HYFR Analysis 
 Although the series systems needed to be fundamentally analyzed, their behavior 
was somewhat intuitive.  The parallel systems add another element to the multi-phase 
behavior that may not be as intuitive, but could be potentially advantageous.  The 
damping present throughout the duration of the ground motion offers both positive and 
negative attributes that are described in the HYFR and HYFR-VFD sections.   
The HYFR performance compared to baseline performance is presented in Figure 
6-23.  Slightly better than the two series systems, the median moment frame ductility at 
the DBE was only about 15% more than the baseline response, measuring approximately 
1.4 times the yield displacement.  From the plot it can be seen that yielding of the 
 
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moment frame would be expected at about 70% to 80% of the DBE, as opposed to 80% 
to 100% of DBE for the baselines.  Acceleration and base shear responses were much 
better for the lower factors when compared to the baseline systems.  A large variability in 
acceleration in the mid-to-upper scale factors suggests that HYFR systems are more 
sensitive to system ratio and gap size than the series systems.  The median acceleration 
response is much larger than the baseline response for the upper scale factors, up to over 
60% larger.  Similar to the series systems, the HYFR brace ductility behavior remained 
elastic up to almost 60% of the DBE and far exceeded baseline performance for the upper 
scale factors. 
 
 
Figure 6-23:  HYFR 1T Comparison to Baselines 
 
 
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Data for moment frame ductility for the various HYFR systems, presented in 
Figure 6-24, shows relatively no difference in response until about 60% of the DBE, and 
then a slight dispersion is noticed.  Regardless of the gap size, the larger system ratio 
(M60B40) performed the worst out of all the systems.  The larger gap sizes also 
performed the worst but the difference was small for each system ratio.  The two best 
performers were the M40B60 and M50B50 systems with the 0.6 gap size, but the 
variance between the best and worst performers was less than 15%.  
 
 
Figure 6-24:  HYFR 1T Moment Frame Ductility 
 
Acceleration and base shear responses showed a large amount of variability 
across all of the scale factors, especially the base shear response (Figure 6-25 & Figure 
 
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6-26).  Unlike the series systems, the acceleration and base shear responses differed 
slightly for a system-to-system comparison.  In regards to acceleration, the lower system 
ratios performed the best throughout all scale factors.  Base shear performance was the 
best for the lower-to-mid scale factors with the lower system ratio (M40B60), but this 
performance trend was reversed in the upper scale factors.  Similar to the series systems, 
the largest gap size allowed for better response regarding both acceleration and base 
shear.   
Because of the variability in response and difference between acceleration and 
base shear, it is difficult to pick the best overall system for this selection criterion.  
Although not the best performing system at all times, the M50B50 system with a 1.0 gap 
size offers the best overall performance. 
 
 
115 
 
 
Figure 6-25:  HYFR 1T Acceleration Response 
 
116 
 
 
Figure 6-26:  HYFR 1T Base Shear Response 
 
The brace ductility response, presented in Figure 6-27, showed a significant 
amount of dispersion through the mid-to-upper scale factors.  Yielding occurred 
anywhere from 50% to 70% of the DBE, depending on the system ratio and gap size 
combination.  The brace ductility performance is largely dependent on the gap size, with 
the largest gap sizes performing the best.  The performance was much less dependent on 
the system ratio, although the M50B50 system showed a slightly better response for all 
three gap sizes.  All three system ratios with the largest gap size would be a viable option 
in regards to brace ductility, with yielding delayed beyond 60% of the DBE. 
 
 
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Figure 6-27:  HYFR 1T Brace Ductility Response 
 
 With a slight sacrifice of moment frame ductility (less than 10%), the M50B50 
system with a 1.0 gap size would be the most viable option for a HYFR system.  The 
large gap size allows for significant damping for the lower scale factors. Once again, the 
major drawback of the system is the moment frame ductility response for the upper scale 
factors.  In comparison to the series systems, moment frame ductility is significantly 
better but far from ideal.  Further solutions need to be investigated for moment frame 
behavior in the HYFR systems as well. 
To demonstrate the differences in responses between the HPCD and HYFR 
arrangements, a comparison between the two better-performing high-damping rubber 
systems was made (Figure 6-28).  Performance varies across the different response 
 
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quantities without a clear advantage for either system.  The parallel system offers slightly 
more moment frame protection in the mid-to-upper scale factors but still yields at 70% of 
the DBE.  Acceleration and base shear responses are very similar for the lower scale 
factors but the HPCD system has an advantage for the upper scale factors.  Brace 
ductility responses are fairly close, but the HYFR system offers slightly more brace 
protection across all scale factors.  An argument could be made in favor of parallel or 
series arrangements, but the differences may become clearer after the analysis of the 
HYFR-VFD systems. 
 
Figure 6-28:  HPCD vs. HYFR Performance 
 
  
 
 
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6.4.4 HYFR-VFD Analysis 
 With the HPCD-VFD clearly performing better than the HPCD, as described 
earlier, the HYFR-VFD offered an intriguing final option for the multi-phase devices.  A 
comparison of the HYFR-VFD system responses to the baseline responses is shown in 
Figure 6-29.   
 
Figure 6-29:  HYFR-VFD Comparison to Baselines 
 
The median moment frame ductility was over 20% more than the baseline 
response at a ductility of about 1.5 times the yield displacement.  It appears that yielding 
of the moment frame for the hybrid system would be expected at about 70% of the DBE, 
 
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as opposed to 80% to 100% of DBE for the baselines.  Similar to the other multi-phase 
systems, acceleration and base shear responses were much better for the low scale factors 
in comparison to the baseline systems.  Similar to the other parallel system, the 
acceleration and base shear performances were relatively poor in comparison to the 
baselines, with an acceleration response exceeding 70% more than the baseline response 
at the DBE.  Although variable across all the systems, brace ductility performance far 
exceeded baseline performance across all of the scale factors.  The median response 
indicated that the brace would stay elastic up to 50% of the DBE. 
The HYFR-VFD moment frame ductility, presented in Figure 6-30, shows 
relatively more dispersion in response across all of the systems when compared to the 
other multi-phase devices.  The HYFR-VFD systems with the lower system ratios 
(M40B60 and M50B50) showed superior performance.  Similar to the other multi-phase 
arrangements, the systems with smaller gap sizes exhibited the best performance for all of 
the system ratios.  The two best performers were the M40B60 with the 0.6 and 0.8 gap 
sizes. 
 
 
 
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Figure 6-30:  HYFR-VFD 1T Moment Frame Ductility 
 
Similar to the HYFR systems, acceleration and base shear responses showed a lot 
of variability across all of the scale factors, as demonstrated in Figure 6-31 and Figure 
6-32.  The larger system ratio (M60B40) performed the worst out of the three system 
ratios.  The larger gap sizes allowed for more damping throughout the duration of the 
multi-phase action and provided better overall response for both acceleration and base 
shear.  With the exception of the upper scale factors in acceleration, the M40B60 system 
with the 1.0 scale factor consistently performed the best for these selection criteria.  This 
system offers significantly better performance in the low-to-mid factors for both 
acceleration and base shear. 
 
 
122 
 
 
 
Figure 6-31:  HYFR-VFD 1T Acceleration Response 
 
123 
 
 
Figure 6-32:  HYFR-VFD 1T Base Shear Response 
The brace ductility response, presented in Figure 6-33, shows a significant 
amount of dispersion through the mid-to-upper scale factors.  Yielding occurs anywhere 
from 40% to 70% of the DBE, depending on the system ratio and gap size combination.  
The brace ductility performance is largely dependent on the gap size, with the largest gap 
sizes performing the best.  Generally speaking, the M60B40 systems perform worse than 
the M40B60, with the M50B50 performance in the middle.  The M40B60 system with 
the 1.0 gap was consistently the best performer at all scale factors, remaining elastic 
beyond 60% of the DBE. 
 
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Figure 6-33:  HYFR-VFD 1T Brace Ductility 
 
 Similar to the two series systems, the M40B60 system with the 1.0 gap sizewould 
be the best option for an HYFR-VFD system.  The larger gap size allows for significant 
damping throughout the duration of the ground motion excitement for a parallel system.  
Like all the other multi-phase systems, the major drawback of the system is the relatively 
poor moment frame ductility observed in the upper scale factors.   
Similarly to the HPCD-VFD systems, the HYFR-VFD systems with a higher 
damping ratio were evaluated to see if the damping made a significant difference in 
response (Figure 6-34).  Improved performance was seen across all response quantities 
for the systems with increased damping, especially for the M60B40 system which saw 
improved performance across all response quantities for all scale factors.  Most 
 
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importantly, the moment frame ductility performance drastically improved, remaining 
elastic up to 90% of the DBE.  The cost of adding damping may be more worthwhile in 
the case of the parallel VFD systems than for the series systems.  Additionally, larger gap 
sizes may provide even better performance, while still protecting the moment frame.  
 
Figure 6-34:  HYFR-VFD Damping Ratio Comparison 
 6.4.5  System Comparison 
 Although some comparisons were previously made between systems, it is useful 
to compare them all at once.  The four best performing systems identified earlier in the 
research were all compared with each other in order to make comparisons between 
system arrangements and damping type (Figure 6-35). 
 
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Figure 6-35:  System Arrangement Comparison 
  
 The moment frames in all four systems were observes to yield anywhere from 
60% to 70% of the DBE, with the HYFR system exhibiting the best performance.  
Acceleration and base shear exhibited the most variability in response from the four 
systems.  The parallel systems both experienced higher responses in the upper scale 
factors.  Brace performance for all of the systems remained elastic until at least 50% of 
the DBE.  The HPCD system was the first to yield, while the other three systems 
remained elastic until 60% of the DBE.   
Overall, the systems offer many benefits in relationship to the baselines.  The one 
major drawback is the poor moment frame ductility behavior, which could potentially be 
resolved by adding more damping to the systems.  Other potential drawbacks of the 
 
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multi-phase systems could result from acceleration spikes at the phase transitions.  This 
issue is described in more detail in the next secion. 
 
6.5 Acceleration Spikes 
The multi-phase systems are possibly subjected to large acceleration spikes as the 
gap element closes and the system becomes stiffer.  These acceleration spikes could be 
responsible for poor acceleration and base shear responses observed in some of the IDA 
plots, especially those for the near-field ground motion records.  Comparing the 
acceleration response to the gap link element would give some insight into whether the 
closing of the gap element was the source of the larger accelerations.  If this is the case, 
further investigation of the stiffness transition region could prove helpful in finding a way 
to reduce these spikes, and to improve the overall multi-phase system response.   
The following is a detailed look at the acceleration spikes for various multi-phase 
systems and ground motions.  The Erzican, Turkey DBE record was chosen to evaluate 
acceleration spikes for the 0.25 and 1.0 second period systems because it is a near source 
motion with an acceleration response spectrum similar to design values at the periods of 
concern.  The M40B60-1.0-HYFR-VFD system was evaluated first because of the 
superior performance it demonstrated earlier in the chapter (Figure 6-36).  As alluded to 
earlier, the poor performance of the 0.25 second multi-phase system could be attributed 
 
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to the acceleration spikes.
 
Figure 6-36:  a) HYFR-VFD-0.25T-1.0 Gap-M40B60 Acceleration Response History 
b) HYFR-VFD-1T-1.0 Gap-M40B60 Acceleration Response History 
 
 Acceleration and gap element behavior are very closely related.  When the gap 
element is closed, an acceleration spike is sometimes observed.  This is apparent in 
Figure 6-36A; shortly after 5 seconds, the gap closes and the acceleration response has 
two clear spikes.  Figure 6-36B shows multiple instances of acceleration spikes, most 
notably at 5, 10 and 14 seconds.  Although the 0.25 second system goes through more 
phase transitions, it seems as though the 1 second period system is subjected to more 
 
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violent acceleration spikes.  This may occur because the duration of the gap closure is 
longer for the 1 second systems.   These spikes may have resulted from an increase in 
ground motion energy input while the gap is closed rather than a spike caused by the 
phase transition.   
The poor response observed in the 0.25T second systems may be due to the large 
number of phase transitions rather than acceleration spikes due to phase transitions.  
Although acceleration spikes would be more likely to occur in a VFD system due to a 
more drastic stiffness transition, this phenomenon was also investigated for the HPCD 
systems (Figure 6-37).    
 
 
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Figure 6-37:  a) HPCD-0.25T-1.0 Gap-M40B60 Acceleration Response History       
b) HPCD-1T-1.0 Gap-M40B60 Acceleration Response History 
 
 Similar to the response observed for the other system, the acceleration and gap 
element behavior coincided.  Records for systems with both periods showed a slight 
shock at about 4 seconds, but not as substantial as that observed for the VFD systems.  
The 0.25 second HPCD system also experienced a smaller number of phase transitions 
than the VFD system, a potentially appealing aspect if an effective solution for multi-
 
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phase behavior is found for lower periods.  Overall, it seemed that acceleration spikes did 
not seem to have a large affect on acceleration response for the HPCD systems.   
6.6 Residual Drifts 
 In addition to investigating the effects of acceleration spikes on the responses of 
multi-phase systems, it is also important to analyze the residual drifts for the different 
system arrangements.  Inelastic behavior of the buckling restrained brace element or the 
moment frame could lead to permanent residual deformation in the system.  Residual 
deformation is an important factor in post-event safety of the structure and therefore was 
investigated for the multi-phase systems.  Although residuals may not be directly 
applicable to a real structure as a SDOF system, the relative residuals for each system can 
still be compared to demonstrate which multi-phase systems perform the best.  
Four ground motions were chosen to evaluate residual deformations for the four 
best-performing systems (M40B60-1T-1.0-HPCD, M40B60-1T-1.0-HPCD-VFD, 
M50B50-1T-1.0-HYFR, & M40B60-1T-1.0-HYFR-VFD).  Figure 6-38 shows the 
residual deformations for the four systems.  Displacements were normalized by the 
moment frame yield displacement in order to consistently compare results from the 
different system ratios.  Yield displacements ranged from 7.3 inches to 8.4 inches.  
Relatively large residual drifts were observed in response to only one ground motion 
(ERZEW).  The HYFR system, which in included the parallel arrangement paired with 
the high-damping elastomeric device, demonstrated self-centering capabilities.  This is 
evident in all of the ground motions by observing the relatively small residual 
deformations for this system when comparison to the other systems.  The HYFR system 
also is the most effective at damping out the energy after the duration of the ground 
 
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motion.  The HPCD-VFD and HYFR-VFD behaved very similarly in response to all four 
ground motions, while the HPCD exhibited the highest overall residual deformations.  
More research should be performed regarding the minimization of residual deformations 
in the MDOF system study.   
 
 
Figure 6-38:  Residual Deformations 
 
6.7 Summary 
 An extensive analysis of the multi-phase behavior of the various hybrid systems 
was presented in this chapter.  Given the range of system parameters that had been 
narrowed considerably from the initial set, this chapter described the efforts to identify 
the best performing systems from the remaining systems.  In order to demonstrate the 
benefits of multi-phase behavior, results for the multi-phase systems were compared to 
 
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those for baseline systems.  Then the multi-phase systems were evaluated to determine 
the effectiveness at different natural periods.  The systems were then divided into system 
arrangements and their responses were evaluated in detail.  Selection criteria were 
developed to identify the most promising systems considering multiple response 
quantities.  The effects of system ratio and gap size on response were identified and the 
most desirable systems were chosen.  Comparisons were made between damping type 
and system arrangements.  Other aspects of response, such as acceleration spikes and 
residual deformations, were also considered and compared between systems.   
In comparison to the baseline systems, the multi-phase systems offer many 
benefits.  Once the systems were compared in the full factorial analysis, the following 
four systems were identified as the best-performing systems: 
? HPCD:  M40B60 with a 1.0 gap size 
? HPCD-VFD:  M4060 with a 1.0 gap size 
? HYFR: M50B50 with a 1.0 gap size 
? HYFR-VFD:  M40B60 with a 1.0 gap size 
Acceleration and base shear for these were largely reduced in the lower scale 
factors.  Their brace behavior remained elastic up 60%-70% of the DBE, compared to 
20% for the baseline systems.  The major drawback of these systems is poor moment 
frame ductility performance for the upper scale factors.  Moment frame yielding occurs 
as early as 60% of the DBE, compared to 90%-100% of the DBE for the baseline 
systems.  The beneficial acceleration, base shear, and brace ductility behavior is not 
useful unless the moment frame can be protected.  The inclusion of additional damping 
was observed to improve the moment frame performance to an acceptable level, but this 
 
134 
 
option could be costly.  Overall, large steps were made towards improving the 
fundamental understanding of multi-phase passive control systems, but more research 
needs to be completed to realize the true potential of multi-phase passive control systems. 
 
 
135 
 
Chapter 7  Summary and Conclusions 
7.1 Summary 
The goal of this research was to understand the fundamental behavior of multi-
phase passive control devices.  The first step was to perform a literature review in order 
to explore the options for multi-phase systems.  A review on active control, semi-active 
control, and passive control was performed.  Within the scope of passive control, possible 
options for multi-phase systems were analyzed.  Other uses of multi-phased devices in 
past research were also reviewed.  Beyond the literature review, the research was split 
into three primary sections: 1) Parametric development and analysis plan, 2) Model 
development and nonlinear dynamic SDOF analytical study, and 3) Interpretation of 
results. 
The parametric development and analysis draws from the options presented in the 
literature review and chooses appropriate parameters for multi-phase use.  Two velocity-
dependent devices were chosen, a linear viscous fluid damper and viscoelastic high-
damping rubber.  A buckling-restrained brace was chosen for the displacement dependent 
device due to the reliable hysteretic behavior and significant energy dissipation 
capabilities.  Relationships between the moment frame strength and hysteretic brace 
strength were developed for the system design.  The transition phase and corresponding 
gap size was developed as a function of the moment frame yield displacement.  Two 
locations and natural periods were developed in order to test the feasibility of multi-phase 
systems in different seismic hazards.  Once a range of parameters were developed, an 
 
136 
 
experimental design meant to capture statistical significance and reduce the number of 
systems was completed.     
The next step of the research involved the model development and nonlinear 
dynamic SDOF study.  Important aspects of the response history analysis were 
established such as the suite of ground motions and the appropriate scaling for the 
motions.  The arrangement of the multi-phase systems and the corresponding modeling 
details were developed.  Appropriate configurations of the multi-phase systems involved 
multi-linear plastic link elements, multi-linear elastic link elements, and linear viscous 
dashpots.  Four response quantities were developed to compare the performance of the 
systems.  The completion of the model development phase of the research allowed the 
systems to be run in SAP2000 and the results were interpreted.  
 The analysis of the results was completed in two phases; the preliminary analysis 
and a full factorial analysis.  Although the preliminary analysis was intended to be the 
only analysis, the statistical significance was difficult to evaluate due to the inherent 
nesting of the multi-phase system components.  The preliminary analysis did provide 
valuable insight towards the research and allowed the scope of the analysis to be reduced.  
Using statistical and empirical observations, the range of variables was able to be reduced 
to provide 144 systems in a full factorial analysis, a number that was feasible for analysis.   
 The full factorial analysis provided an extensive look at multi-phase behavior and 
identified some of the better performing system combinations.  Systems were compared 
to baseline systems in order to demonstrate the benefits of multi-phase behavior.  Beyond 
this comparison, systems were also compared at different natural periods to determine the 
effectiveness at different natural periods.  A detailed look at each system arrangement 
 
137 
 
was done to identify the key components affecting response.  At the completion of this 
analysis, the systems were compared to each other to identify the effects of damping type 
and system arrangements.  Other aspects of system response, such as acceleration spikes 
and residual deformations were analyzed to demonstrate other possible benefits or 
drawbacks of multi-phase behavior.   
 Overall, the fundamental behavior of multi-phase systems was evident by the end 
of the research.  Multi-phase systems provide an interesting aspect to structural design in 
that they allow the structure to be more resilient and essentially preprogrammed for 
ground motion excitement.  This idea has been explored in the past, but the 
implementation using passive control devices is relatively new and appealing for 
structural design.  The work provided in this research provides significant groundwork 
for multi-phase research in the future.  Using the range of variables from this analysis, an 
MDOF system can be developed and tested analytically.  Once the system performance is 
verified analytically, the study can be tested experimentally and hopefully implemented 
in design.  
 
7.2 Conclusions 
Specific conclusions were given within Chapter 5 and Chapter 6 but this section 
provides a broader set of conclusions for the multi-phase systems.  Compared to the 
baseline systems, multi-phase passive control devices offer many benefits, especially in 
the higher periods (1 second to 4 seconds).  The first phase provides a significant 
decrease in acceleration and base shear in the lower scale factors.  The brace behavior is 
another appealing aspect of the multi-phase devices, remaining elastic up to 60%-70% of 
 
138 
 
the DBE in some cases.  As the period decreases (0.25 seconds and 0.5 seconds), the 
beneficial multi-phase behavior decreases and therefore the extra costs associated with a 
multi-phase system may not be justified.  More research needs to be done to investigate 
the feasibility of a multi-phase system in lower natural periods. 
The major drawback of the multi-phase behavior lies in the protection of the 
moment frame.  The beneficial protection of the brace element is only appealing if the 
moment frame remains elastic.  Variability was not very large for moment frame ductility 
but was consistently poor in comparison to the baseline systems.  Even in the best 
performing systems, yielding occurs as early as 60% of the DBE compared to 90%-100% 
for the baseline systems.  The two VFD arrangements were analyzed with larger damping 
ratios for extra moment frame protection.  This proved to be very beneficial to the 
parallel arrangement.  
Once the systems were compared to each other in the full factorial analysis, 
standout performers were noticed for each system arrangement: 
? HPCD:  M40B60 with a 1.0 gap size 
? HPCD-VFD:  M4060 with a 1.0 gap size 
? HYFR: M50B50 with a 1.0 gap size 
? HYFR-VFD:  M40B60 with a 1.0 gap size 
Other options for multi-phase systems are obviously feasible and could provide similar 
responses.  A range of good performing system traits is evident within each section. 
 The results presented with this research clearly show the beneficial capabilities of 
multi-phase behavior.  The better performing systems within the research provided elastic 
behavior of all elements up to 60% of the design basis earthquake which is much better 
 
139 
 
than the baseline system which experience yielding at 20% of the DBE.  In addition to 
ductility performance, the acceleration and base shear were drastically decreased in the 
lower scale factors in comparison to the baselines.  With the resolution of the poor 
acceleration, base shear, and moment frame performance in the upper scale factors, 
multi-phase systems become a very viable option for implementation in design. 
 
Other conclusions drawn are detailed below: 
? The statistical analysis of a multi-phase system in which the components are 
in a hierarchal arrangement is difficult with a limited amount of data.  The 
reduction of the scope of the study into a range in which a full factorial 
analysis can be performed is a more desirable approach for this research. 
? Acceleration spikes did not play as large of a role in response as anticipated.  
Spikes were present but not always due to the phase transition. 
? The HYFR system had the best residual deformation performance but further 
research into this behavior is required in the MDOF study.  
? Overall, the multi-phase systems have a favorable response to increased 
damping.  Generally speaking the VFD systems performed better than the 
HDR systems.  Also, the parallel arrangements had a favorable affect on 
moment frame performance.  A parallel VFD system with the large gap size 
may be the best option for future research. 
 
 
  
 
140 
 
7.3 Future Work 
 Since this research is only meant to provide the groundwork for multi-phase 
control systems, there is obviously a need for future research.  Like most research, 
assumptions were made and problems arose throughout the duration of the project.  These 
recommendations for future work seek to eliminate these uncertainties and better develop 
multi-phase systems. 
As alluded to many times in the research, this analysis is meant to provide the 
groundwork for a MDOF system analysis.  Although the SDOF analysis offers significant 
insight towards the fundamentals of the system, it is not a completely accurate 
representation of structural response.  Participation in other modes of vibration in an 
MDOF system could reduce overall base shears or increase story accelerations and 
shears.  P-delta forces, which were excluded for the SDOF systems, could potentially 
play a large role in response.  The HYFR system which is more effective at reducing 
residual deformations may become a more appealing system.  The MDOF system 
analysis could be accomplished in the form of a three story shear building and then 
expanded into a larger analytical model using the multi-phase system recommendations 
given in this research.  Whichever system demonstrates the most appealing behavior in an 
MDOF study should be further tested experimentally to verify results.  Design criteria 
would also have to be developed if the system were to be implemented into structural 
design.  Other recommendations are detailed below:  
 
 
141 
 
? The most pressing issue with the multi-phase systems is moment frame 
protection.  Options were suggested (such as adding more supplemental damping) 
but further research is needed to investigate this aspect of response. 
? A cost-benefit analysis of the systems would also have to be performed to ensure 
the validity of the multi-phase systems in a practical application. 
? A weighted response criterion for the MDOF analysis should be developed.  
Comparing the four response quantities at 10 different scale factors is a difficult 
task unless there is a systematic approach developed. 
? One of the main issues with the parallel systems is the excessive acceleration and 
base shear in the upper scale factors most likely due to the strain hardening of the 
system components and forces from the velocity-dependent device.  By 
implementing a friction device rather than a BRB, the forces would essentially be 
capped and possibly resolve this issue. 
? Linear viscous damping was used in order to reduce the number of variables in 
the research.  Nonlinear viscous damping should also be investigated.  In addition, 
damping values may be able to be increased for the viscous fluid damper and 
high-damping rubber.  Research into feasible damping values should also be 
performed. 
? A detailed analysis was done for the 1 second period although the data was 
present for 4 natural periods.  Although the system behavior was observed to be 
similar for each period, further research could be performed to find any 
significant differences if present. 
 
142 
 
? The focus of this analysis was mostly in the form of an incremental dynamic 
analysis.  Although this is a widely used method of analysis, more conclusions 
may have been able to be drawn by looking at the individual response history for 
each ground motion. Some of the better performing systems could be analyzed in 
more detail for each ground motion. 
? The HYFR system involving a compressed elastomeric device is a relatively new 
concept.  More research involving the ?slip? behavior of the device should be 
completed before it is fully implemented in a multi-phase system. 
? The phase transition behavior is the most important aspect of the multi-phase 
device.  The reliability of the phase transition mechanism must be evaluated 
further to ensure adequate behavior. 
? The overstrength and response modification factors (2.5 and 8 respectively) used 
in this study need to be investigated further to see if they are appropriate for 
multi-phase systems.  
These are just a few recommendations for the further development of multi-phase 
systems.  The tendency of design codes is moving towards a performance-based approach 
which will demand research in the field of multi-phase behavior.  Engineers? ingenuity 
and creativeness will surely find many uses and make developments for multi-phase 
passive control devices. 
 
 
 
 
 
143 
 
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Appendix A. Preliminary Design 
Appendix A presents the results for all of the preliminary design presented in Chapter 5. 
 
Figure A- 1:  Los Angeles 0.25T Acceleration 
 
 
Figure A- 2:  Los Angeles 0.25T Base Shear 
 
149 
 
 
 
 
Figure A- 3:  Los Angeles 0.25T Moment Frame Ductility 
 
 
 
Figure A- 4:  Los Angeles 0.25T Brace Ductility 
 
 
150 
 
 
 
 
Figure A- 5:  Memphis 0.25T Acceleration 
 
 
Figure A- 6:  Memphis 0.25T Base Shear 
 
 
151 
 
 
 
 
 
Figure A- 7:  Memphis 0.25T Moment Frame Ductility 
 
 
 
152 
 
 
Figure A- 8:  Memphis 0.25T Brace Ductility 
 
 
 
 
Figure A- 9:  Los Angeles 0.5T Acceleration 
 
 
 
153 
 
 
Figure A- 10:  Los Angeles 0.5T Base Shear 
 
 
 
 
Figure A- 11:  Los Angeles 0.5T Moment Frame Ductility 
 
 
154 
 
 
 
Figure A- 12:  Los Angeles 0.5T Brace Ductility 
 
 
 
 
Figure A- 13:  Memphis 0.5T Acceleration 
 
 
155 
 
 
 
Figure A- 14:  Memphis 0.5T Base Shear 
 
 
 
 
Figure A- 15:  Memphis 0.5T Moment Frame Ductility 
 
 
156 
 
 
 
Figure A- 16:  Memphis 0.5T Brace Ductility 
 
 
 
 
Figure A- 17:  Los Angeles 1T Acceleration 
 
 
157 
 
 
 
Figure A- 18:  Los Angeles 1T Base Shear 
 
 
 
 
Figure A- 19:  Los Angeles 1T Moment Frame Ductility 
 
158 
 
 
 
 
Figure A- 20:  Los Angeles 1T Brace Ductility 
 
 
 
 
159 
 
 
Figure A- 21:  Memphis 1T Acceleration 
 
 
 
Figure A- 22:  Memphis 1T Base Shear 
 
 
 
 
160 
 
 
Figure A- 23:  Memphis 1T Moment Frame Ductility 
 
 
 
Figure A- 24:  Memphis 1T Brace Ductility 
 
 
 
 
161 
 
 
Figure A- 25:  Los Angeles 2.5T Acceleration 
 
 
 
Figure A- 26:  Los Angeles 2.5T Base Shear 
 
 
 
 
162 
 
 
Figure A- 27:  Los Angeles 2.5T Moment Frame Ductility 
 
 
 
Figure A- 28:  Los Angeles 2.5T Brace Ductility 
 
 
 
 
163 
 
 
Figure A- 29:  Memphis 2.5T Acceleration 
 
 
 
Figure A- 30:  Memphis 2.5T Base Shear 
 
 
 
164 
 
 
Figure A- 31:  Memphis 2.5T Moment Frame Ductility 
 
 
 
Figure A- 32:  Memphis 2.5T Brace Ductility 
 
 
 
165 
 
 
 
Figure A- 33:  Los Angeles 4T Acceleration 
 
 
 
Figure A- 34:  Los Angeles 4T Base Shear 
 
 
166 
 
 
 
 
 
Figure A- 35:  Los Angeles 4T Moment Frame Ductility 
 
 
 
 
167 
 
 
Figure A- 36:  Los Angeles 4T Brace Ductility 
 
 
 
Figure A- 37:  Memphis 4T Acceleration 
 
 
 
168 
 
 
 
Figure A- 38: Memphis 4T Base Shear 
 
 
 
Figure A- 39:  Memphis 4T Moment Frame Ductility 
 
 
169 
 
 
 
 
Figure A- 40:  Memphis 4T Brace Ductility 
 
170 
 
Appendix B. Final Design 
Appendix B presents the results for all of the full factorial design presented in Chapter 6. 
 
Figure B- 1:  Los Angeles 0.25T HYFR Acceleration 
 
 
 
Figure B- 2:  Los Angeles 0.25T HYFR-VFD Acceleration 
 
171 
 
 
Figure B- 3:  Los Angeles 0.25T HPCD Acceleration 
 
 
 
Figure B- 4:  Los Angeles 0.25T HPCD-VFD Acceleration 
 
 
 
 
172 
 
 
Figure B- 5:  Los Angeles 0.25T HYFR Base Shear 
 
 
 
Figure B- 6:  Los Angeles 0.25T HYFR-VFD Base Shear 
 
 
 
 
173 
 
 
Figure B- 7:  Los Angeles 0.25T HPCD Base Shear 
 
 
 
Figure B- 8:  Los Angeles 0.25T HPCD-VFD Base Shear 
 
 
 
 
174 
 
 
Figure B- 9:  Los Angeles 0.25T HYFR Moment Frame Ductility 
 
 
 
Figure B- 10:  Los Angeles 0.25T HYFR-VFD Moment Frame Ductility 
 
 
 
 
175 
 
 
 
Figure B- 11:  Los Angeles 0.25T HPCD Moment Frame Ductility 
 
 
 
Figure B- 12:  Los Angeles 0.25T HPCD-VFD Moment Frame Ductility 
 
 
 
176 
 
 
 
Figure B- 13:  Los Angeles 0.25T HYFR Brace Ductility 
 
 
 
Figure B- 14:  Los Angeles 0.25T HYFR-VFD Brace Ductility 
 
 
 
177 
 
 
 
Figure B- 15:  Los Angeles 0.25T HPCD Brace Ductility 
 
 
 
Figure B- 16:  Los Angeles 0.25T HPCD-VFD Brace Ductility 
 
 
 
178 
 
 
 
Figure B- 17:  Los Angeles 0.5T HYFR Acceleration 
 
 
 
 
Figure B- 18:  Los Angeles 0.5T HYFR-VFD Acceleration 
 
 
179 
 
 
 
Figure B- 19:  Los Angeles 0.5T HPCD Acceleration 
 
 
 
 
Figure B- 20:  Los Angeles 0.5T HPCD-VFD Acceleration 
 
 
180 
 
 
 
Figure B- 21:  Los Angeles 0.5T HYFR Base Shear 
 
 
 
 
Figure B- 22:  Los Angeles 0.5T HYFR-VFD Base Shear 
 
 
181 
 
 
 
Figure B- 23:  Los Angeles 0.5T HPCD Base Shear 
 
 
 
 
Figure B- 24:  Los Angeles 0.5T HPCD-VFD Base Shear 
 
 
182 
 
 
 
Figure B- 25:  Los Angeles 0.5T HYFR Moment Frame Ductility 
 
 
 
 
Figure B- 26:  Los Angeles 0.5T HYFR-VFD Moment Frame Ductility 
 
 
183 
 
 
 
 Figure B- 27:  Los Angeles 0.5T HPCD Moment Frame Ductility  
 
 
 
 
Figure B- 28:  Los Angeles 0.5T HPCD-VFD Moment Frame Ductility 
 
 
184 
 
 
Figure B- 29:  Los Angeles 0.5T HYFR Brace Ductility 
 
 
 
Figure B- 30:  Los Angeles 0.5T HYFR-VFD Brace Ductility 
 
 
 
 
185 
 
 
Figure B- 31:  Los Angeles 0.5T HPCD Brace Ductility 
 
 
 
 
Figure B- 32:  Los Angeles 0.5T HPCD-VFD Brace Ductility 
 
 
 
186 
 
 
Figure B- 33:  Los Angeles 1T HYFR Acceleration 
 
 
 
 
Figure B- 34:  Los Angeles 1T HYFR-VFD Acceleration 
 
 
 
187 
 
 
Figure B- 35:  Los Angeles 1T HPCD Acceleration 
 
 
 
 
Figure B- 36:  Los Angeles 1T HPCD-VFD Acceleration 
 
 
 
188 
 
 
Figure B- 37:  Los Angeles 1T HYFR Base Shear 
 
 
 
 
Figure B- 38:  Los Angeles 1T HYFR-VFD Base Shear 
 
 
 
189 
 
 
 
Figure B- 39:  Los Angeles 1T HPCD Base Shear 
 
 
 
 
 Figure B- 40:  Los Angeles 1T HPCD-VFD Base Shear  
 
 
190 
 
 
 
Figure B- 41:  Los Angeles 1T HYFR Moment Frame Ductility 
 
 
 
 
Figure B- 42:  Los Angeles 1T HYFR-VFD Moment Frame Ductility 
 
 
191 
 
 
 
Figure B- 43:  Los Angeles 1T HPCD Moment Frame Ductility 
 
 
 
 
Figure B- 44:  Los Angeles 1T HPCD-VFD Moment Frame Ductility 
 
 
192 
 
 
 
 
 Figure B- 45:  Los Angeles 1T HYFR Brace Ductility  
 
 
 
 
Figure B- 46:  Los Angeles 1T HYFR-VFD Brace Ductility 
 
193 
 
 
 
Figure B- 47:  Los Angeles 1T HPCD Brace Ductility 
 
 
 
 
Figure B- 48:  Los Angeles 1T HPCD-VFD Brace Ductility 
 
 
194 
 
 
 
Figure B- 49:  Los Angeles 2.5T HYFR Acceleration 
 
 
 
 
Figure B- 50:  Los Angeles 2.5T HYFR-VFD Acceleration 
 
 
195 
 
 
 
 
Figure B- 51:  Los Angeles 2.5T HPCD Acceleration 
 
 
 
 
Figure B- 52:  Los Angeles 2.5T HPCD-VFD Acceleration 
 
196 
 
 
 
 
Figure B- 53:  Los Angeles 2.5T HYFR Base Shear 
 
 
 
 
Figure B- 54:  Los Angeles 2.5T HYFR-VFD Base Shear 
 
197 
 
 
 
 
 
Figure B- 55:  Los Angeles 2.5T HPCD Base Shear 
 
 
 
 
 
198 
 
Figure B- 56:  Los Angeles 2.5T HPCD-VFD Base Shear 
 
 
Figure B- 57:  Los Angeles 2.5T HYFR Moment Frame Ductility 
 
 
 
 
Figure B- 58:  Los Angeles 2.5T HYFR-VFD Moment Frame Ductility 
 
199 
 
 
 
 
Figure B- 59:  Los Angeles 2.5T HPCD Moment Frame Ductility 
 
 
 
 
Figure B- 60:  Los Angeles 2.5T HPCD-VFD Moment Frame Ductility 
 
200 
 
 
 
 
 
Figure B- 61:  Los Angeles 2.5T HYFR Brace Ductility 
 
 
 
 
 
201 
 
Figure B- 62:  Los Angeles 2.5T HYFR-VFD Brace Ductility 
 
 
Figure B- 63:  Los Angeles 2.5T HPCD Brace Ductility 
 
 
 
 
Figure B- 64:  Los Angeles 2.5T HPCD-VFD Brace Ductility 
 
202