Using Incremental Dynamic Analysis to Visualize the Effects of
Viscous Fluid Dampers on Steel Moment Frame Drift
Stephanie J. Kruep
Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of
Master of Science
in
Civil Engineering
Approved:
Dr. Finley A. Charney Committee Chairman
Dr. Samuel Easterling Dr. Elisa Sotelino Committee Member Committee Member
July 3, 2007
Blacksburg, Virginia
Keywords: Damping, Drift, Incremental Dynamic Analysis, Passive Energy, Seismic Design, Steel Structures, Structural Dynamics
Using Incremental Dynamic Analysis to Visualize the Effects of
Viscous Fluid Dampers on Steel Moment Frame Drift
by
Stephanie Jean Kruep
Committee Chairman: Dr. Finley A. Charney
This thesis presents the details of a study regarding both the use of linear viscous fluid
dampers in controlling the interstory drift in steel moment frames, and the use of
incremental dynamic analysis as a method of visualizing the behavior of these moment
frames when subjected to seismic load effects. Models of three story and nine story steel
moment frames were designed to meet typical strength requirements for office buildings
in Seattle, Washington. These models were intentionally designed to violate seismic
interstory drift restrictions to test the ability of the linear viscous fluid dampers to reduce
these drifts to the point of code compliance. Dampers were included in one bay of every
story in each model. These devices were used to produce total structural damping ratios
of 5%, 10%, 20%, and 30% of critical. Undamped, traditional stiffness controlled models
of both three stories and nine stories were also created for comparison purposes.
Incremental dynamic analysis was used to subject these models to ten ground motions,
each scaled to twenty incremental levels. Two new computer applications were written
to facilitate this process. The results of these analyses were studied to determine if the
linear viscous fluid dampers were able to cause compliance with codified drift limits.
Also, incremental dynamic analysis plots were created to examine the effects of the
dampers on structural behavior as damping increased from inherent to 30% of critical. It
was found that including linear viscous fluid dampers in steel moment frame design can
satisfactorily control interstory drift, and incremental dynamic analysis is a beneficial tool
in visualizing dynamic structural behavior.
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Acknowledgements First and foremost, I would like to thank my parents, Dale and Carol Kruep. They taught
me the value of knowledge and hard work, and to never accept less than my best effort. I
would not be earning my second degree without their love and encouragement.
Dr. Finley A. Charney served as my major advisor and committee chair. I wish to
express my appreciation for his wisdom and patience over the past year and a half, and
especially for his guidance and constructive criticism during the writing of this thesis. It
has been a privilege to work for a professor who is so dedicated not only to research, but
to education as well. I am also grateful for the time and effort Dr. Samuel Easterling and
Dr. Elisa Sotelino spent reviewing this thesis and serving on my committee.
Finally, I would like to thank Taylor Devices, Inc. for funding this project, which
provided me with the opportunity to learn more about the application of computer
programming and passive energy dissipation to structural analysis and design.
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Table of Contents
TABLE OF CONTENTS........................................................................................................................... IV LIST OF FIGURES.................................................................................................................................... VI LIST OF TABLES.................................................................................................................................... XII CHAPTER 1: INTRODUCTION ............................................................................................................... 1
1.1 BACKGROUND ...................................................................................................................................... 1 1.2 LITERATURE SURVEY OF DAMPING IN STEEL MOMENT FRAMES.......................................................... 2 1.3 LITERATURE SURVEY OF INCREMENTAL DYNAMIC ANALYSIS ............................................................. 7 1.4 OBJECTIVE AND SCOPE ....................................................................................................................... 13
CHAPTER 2: MODELS............................................................................................................................ 14 2.1 OVERVIEW.......................................................................................................................................... 14 2.2 MODEL GEOMETRY ............................................................................................................................ 14
2.2.1 Three Story Model Geometry .................................................................................................... 14 2.2.2 Nine Story Model Geometry...................................................................................................... 16
2.3 GRAVITY LOADS AND MASSES ........................................................................................................... 18 2.4 REGIONAL PARAMETERS, DESIGN ASSUMPTIONS, AND LATERAL LOADS........................................... 19
2.4.1 Seismic Design Loads................................................................................................................ 19 2.4.2 Wind Design Loads.................................................................................................................... 24
2.5 P-DELTA EFFECTS............................................................................................................................... 25 2.6 JOINT MODELING................................................................................................................................ 26 2.7 STRENGTH CONTROLLED FRAME DESIGN........................................................................................... 27 2.8 DAMPING............................................................................................................................................ 33 2.9 STIFFNESS CONTROLLED FRAME DESIGN ........................................................................................... 36 2.10 COMPUTER AIDED STRUCTURAL MODELING USING NONLINPRO..................................................... 38
CHAPTER 3: INCREMENTAL DYNAMIC ANALYSIS DEVELOPMENT ..................................... 39 3.1 OVERVIEW.......................................................................................................................................... 39 3.2 GROUND MOTION SELECTION ............................................................................................................ 39 3.3 INTENSITY MEASURES ........................................................................................................................ 40 3.4 ENGINEERING DEMAND PARAMETERS................................................................................................ 41 3.5 COMPUTER AIDED IDA DEVELOPMENT.............................................................................................. 41
3.5.1 NICC Requirements................................................................................................................... 42 3.5.2 NICC Collection Format and Specifications.............................................................................. 42 3.5.3 NICC Ground Acceleration Record Scaling .............................................................................. 46 3.5.4 NICC Ground Acceleration History and Response Spectra Visualization................................. 46
3.6 IDA DEVELOPMENT FOR THE CURRENT STUDY.................................................................................. 49 CHAPTER 4: INCREMENTAL DYNAMIC ANALYSIS APPLICATION ........................................ 61
4.1 OVERVIEW.......................................................................................................................................... 61 4.2 IDA CURVES ...................................................................................................................................... 61 4.3 LIMIT STATES ..................................................................................................................................... 62 4.4 COMPUTER AIDED IDA VISUALIZATION............................................................................................. 64
4.4.1 NIVA Requirements .................................................................................................................. 64 4.4.2 NIVA Main Window and *.ida Files ......................................................................................... 64 4.4.3 NIVA IDA Plotting Functions ................................................................................................... 66 4.4.4 NIVA Performance Objectives and Response Histories ............................................................ 66
CHAPTER 5: RESULTS AND DISCUSSION ........................................................................................ 69 5.1 OVERVIEW.......................................................................................................................................... 69
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5.2 CODE COMPLIANCE ............................................................................................................................ 70 5.2.1 Three Story Strength Design Code Compliance ........................................................................ 70 5.2.2 Nine Story Strength Design Code Compliance.......................................................................... 71 5.2.3 Base Shear and Feasibility ......................................................................................................... 72
5.3 BENEFITS OF INCREMENTAL DYNAMIC ANALYSIS.............................................................................. 74 5.3.1 IDA Studies of Stiffness Designed Models................................................................................ 75 5.3.2: IDA Studies of Strength Designed Models ............................................................................... 77
CHAPTER 6: CONCLUSION .................................................................................................................. 89 6.1 SUMMARY .......................................................................................................................................... 89 6.2 LIMITATIONS AND SUGGESTIONS FOR FUTURE WORK........................................................................ 91
REFERENCES ........................................................................................................................................... 93 APPENDIX A: USER’S GUIDE TO THE NONLINPRO IDA COLLECTION CREATOR AND THE NONLINPRO IDA VISUALIZATION APPLICATION.............................................................. 95 APPENDIX B: IDA STUDIES ................................................................................................................ 125 VITA.......................................................................................................................................................... 189
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List of Figures Figure 1.1: Viscous Fluid Dampers in a Chevron Brace Configuration ............................ 3 Figure 1.2: Viscous Fluid Dampers Exposed in a Building ............................................... 3 Figure 1.3: Single IDA Curve ............................................................................................ 7 Figure 1.4: Multiple Earthquake IDA Study ...................................................................... 9 Figure 1.5: Multiple Parameter IDA Study ........................................................................ 9 Figure 2.1: Three Story Model Elevation ........................................................................ 15 Figure 2.2: Three Story Model Floor Plan ....................................................................... 15 Figure 2.3: Nine Story Model Elevation .......................................................................... 17 Figure 2.4: Nine Story Model Floor Plan ........................................................................ 17 Figure 2.5: Design Response Spectra .............................................................................. 23 Figure 2.6: P-delta “Ghost Frame” .................................................................................. 26 Figure 2.7: Krawinkler Joint Model ................................................................................. 27 Figure 2.8: Elevation of the Three Story Seattle Model Designed for Strength .............. 29 Figure 2.9: Elevation of the Nine Story Seattle Model Designed for Strength ............... 30 Figure 2.10: Elevation of the Three Story Boston Model Designed for Strength ........... 31 Figure 2.11: Elevation of the Nine Story Boston Model Designed for Strength ............. 32 Figure 2.12: Damping “Ghost Frame” ............................................................................. 34 Figure 2.13: Elevation of the Three Story Seattle Model Designed for Stiffness ........... 37 Figure 2.14: Elevation of the Nine Story Seattle Model Designed for Stiffness ............. 38 Figure 3.1: NICC Main Window ..................................................................................... 44 Figure 3.2: Collection Specifications Section for a Multiple Earthquake IDA ............... 45 Figure 3.3: Collection Specifications Section for a Multiple Parameter IDA ................. 45 Figure 3.4: NICC Scaling Options Window .................................................................... 47 Figure 3.5: NICC Ground Acceleration History Plot Window ........................................ 48 Figure 3.6: NICC Response Spectra Plot Window .......................................................... 49 Figure 3.7: Unscaled 5% Damped Ground Acceleration Response Spectra ................... 50 Figure 3.8: Ground Acceleration History for Mendocino, 1992 ..................................... 51 Figure 3.9: Ground Acceleration History for Erzinican Meteorological Station, 1992 ... 51 Figure 3.10: Ground Acceleration History for Olympia Highway Test Lab, 1949 ......... 52 Figure 3.11: Ground Acceleration History for Olympia Highway Test Lab, 1965 ......... 52 Figure 3.12: Ground Acceleration History for Llolleo, Chile, 1985 ............................... 53 Figure 3.13: Ground Acceleration History for Vina del Mar, Chile, 1985 ...................... 53 Figure 3.14: Ground Acceleration History for Deep Interplate (simulation) .................. 54 Figure 3.15: Ground Acceleration History for Miyagi-oki, 1978 .................................... 54 Figure 3.16: Ground Acceleration History for Shallow Interplate 1 (simulation) ........... 55 Figure 3.17: Ground Acceleration History for Shallow Interplate 2 (simulation) ........... 55 Figure 3.18: 5% Damped Ground Acceleration Response Spectra Scaled to 0.32g
at T = 1.565s for Three Story Strength Design ........................................... 57 Figure 3.19: 5% Damped Ground Acceleration Response Spectra Scaled to 0.48g
at T = 1.042s for Three Story Stiffness Design .......................................... 58 Figure 3.20: 5% Damped Ground Acceleration Response Spectra Scaled to 0.17g
at T = 2.964s for Nine Story Strength Design ............................................ 59
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Figure 3.21: 5% Damped Ground Acceleration Response Spectra Scaled to 0.19g at T = 2.634s for Nine Story Stiffness Design ............................................ 60
Figure 4.1: Typical IDA Curve Characteristics ............................................................... 62 Figure 4.2: NIVA Main Window ..................................................................................... 65 Figure 4.3: NIVA Create New Project Group Window ................................................... 65 Figure 4.4: NIVA IDA Curve and Performance Objective Example .............................. 67 Figure 4.5: NIVA Response History Viewing Window .................................................. 68 Figure 5.1: IDA Study for 2nd Story Drift of Three Story Stiffness Design .................... 76 Figure 5.2: IDA Study for 5th Story Drift of Nine Story Stiffness Design ...................... 76 Figure 5.3: IDA Study of 2nd Story Drift for Three Story Strength Design
with Inherent Damping ............................................................................... 78 Figure 5.4: IDA Study of 2nd Story Drift for Three Story Strength Design
with 5% Damping ....................................................................................... 78 Figure 5.5: IDA Study of 2nd Story Drift for Three Story Strength Design
with 10% Damping ..................................................................................... 79 Figure 5.6: IDA Study of 2nd Story Drift for Three Story Strength Design
with 20% Damping ..................................................................................... 79 Figure 5.7: IDA Study of 2nd Story Drift for Three Story Strength Design
with 30% Damping ..................................................................................... 80 Figure 5.8: IDA Study of 5th Story Drift for Nine Story Strength Design
with Inherent Damping ................................................................................81 Figure 5.9: IDA Study of 5th Story Drift for Nine Story Strength Design
with 5% Damping ....................................................................................... 81 Figure 5.10: IDA Study of 5th Story Drift for Nine Story Strength Design
with 10% Damping ..................................................................................... 82 Figure 5.11: IDA Study of 5th Story Drift for Nine Story Strength Design
with 20% Damping ..................................................................................... 82 Figure 5.12: IDA Study of 5th Story Drift for Nine Story Strength Design
with 30% Damping ..................................................................................... 83 Figure 5.13: IDA Study of Roof Displacement for Three Story Strength Design
Subject to se02fp0 ....................................................................................... 84 Figure 5.14: IDA Study of Roof Displacement for Nine Story Strength Design
Subject to se02fp6 ....................................................................................... 84 Figure 5.15: IDA Study of Total Base Shear for Three Story Strength Design
Subject to se02fp1 ....................................................................................... 86 Figure 5.16: IDA Study of Total Base Shear for Three Story Strength Design
Subject to se02fp9 ....................................................................................... 86 Figure 5.17: IDA Study of Total Base Shear for Nine Story Strength Design
Subject to se02fp1 ....................................................................................... 87 Figure 5.18: IDA Study of Total Base Shear for Nine Story Strength Design
Subject to se02fp9 ....................................................................................... 88 Figure A.1: NICC Main Window .................................................................................... 97 Figure A.2: Collection Format Section ............................................................................ 98 Figure A.3: Collection Specifications Section for a Multiple Earthquake IDA .............. 99 Figure A.4: Collection Specifications Section for a Multiple Parameter IDA ................ 99 Figure A.5: NICC Scaling Options Window ................................................................. 103
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Figure A.6: Scale to a Specified Period and Pseudo-Acceleration ................................ 104 Figure A.7: Scale According to the NEHRP Provisions ................................................ 105 Figure A.8: NEHRP Spectrum Parameters Window ..................................................... 106 Figure A.9: Scale to the Best Fit of the NEHRP Design Spectrum
over a Range of Periods ............................................................................ 107 Figure A.10: NICC Response Spectra Plot Window...................................................... 109 Figure A.11: NICC Ground Acceleration History Plot Window ................................... 111 Figure A.12: NICC File Writing Complete Message Box ............................................. 112 Figure A.13: NIVA Main Window ................................................................................ 114 Figure A.14: NIVA Create New Project Group Window .............................................. 114 Figure A.15: NIVA Input File Viewing Window .......................................................... 116 Figure A.16: NIVA Available Earthquakes Grid .......................................................... 117 Figure A.17: NIVA Node/Element Group Selection ..................................................... 118 Figure A.18: NIVA Expanded Node/Element Group Selection .................................... 118 Figure A.19: NIVA Expanded Node Selection .............................................................. 119 Figure A.20: NIVA Damage Measure Selection ........................................................... 120 Figure A.21: NIVA Graphing Button ............................................................................ 120 Figure A.22: NIVA IDA Curves .................................................................................... 121 Figure A.23: NIVA Response History Plot Window ..................................................... 122 Figure A.24: NIVA Performance Objectives ................................................................. 123 Figure A.25: NIVA IDA Study with Performance Objectives ...................................... 124 Figure B.1: 1st Story Drift for Three Story Stiffness Design ......................................... 125 Figure B.2: 2nd Story Drift for Three Story Stiffness Design ........................................ 126 Figure B.3: 3rd Story Drift for Three Story Stiffness Design ......................................... 126 Figure B.4: Base Shear for Three Story Stiffness Design ............................................. 127 Figure B.5: 1st Story Drift for Three Story Strength Design with Inherent Damping ... 128 Figure B.6: 2nd Story Drift for Three Story Strength Design with Inherent Damping .. 128 Figure B.7: 3rd Story Drift for Three Story Strength Design with Inherent Damping ... 129 Figure B.8: Base Shear for Three Story Strength Design with Inherent Damping ........ 129 Figure B.9: 1st Story Drift for Three Story Strength Design with 5% Damping ........... 130 Figure B.10: 2nd Story Drift for Three Story Strength Design with 5% Damping ........ 130 Figure B.11: 3rd Story Drift for Three Story Strength Design with 5% Damping ......... 131 Figure B.12: Base Shear for Three Story Strength Design with 5% Damping .............. 131 Figure B.13: 1st Story Drift for Three Story Strength Design with 10% Damping ....... 132 Figure B.14: 2nd Story Drift for Three Story Strength Design with 10% Damping ...... 132 Figure B.15: 3rd Story Drift for Three Story Strength Design with 10% Damping ....... 133 Figure B.16: Base Shear for Three Story Strength Design with 10% Damping ............ 133 Figure B.17: 1st Story Drift for Three Story Strength Design with 20% Damping ....... 134 Figure B.18: 2nd Story Drift for Three Story Strength Design with 20% Damping ...... 134 Figure B.19: 3rd Story Drift for Three Story Strength Design with 20% Damping ....... 135 Figure B.20: Base Shear for Three Story Strength Design with 20% Damping ............ 135 Figure B.21: 1st Story Drift for Three Story Strength Design with 30% Damping ....... 136 Figure B.22: 2nd Story Drift for Three Story Strength Design with 30% Damping ...... 136 Figure B.23: 3rd Story Drift for Three Story Strength Design with 30% Damping ....... 137 Figure B.24: Base Shear for Three Story Strength Design with 30% Damping ............ 137
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Figure B.25: Roof Displacement for Three Story Strength Design Subject to se02fp0 ..................................................................................... 138
Figure B.26: Roof Displacement for Three Story Strength Design Subject to se02fp1 ..................................................................................... 138
Figure B.27: Roof Displacement for Three Story Strength Design Subject to se02fp2 ..................................................................................... 139
Figure B.28: Roof Displacement for Three Story Strength Design Subject to se02fp3 ..................................................................................... 139
Figure B.29: Roof Displacement for Three Story Strength Design Subject to se02fp4 ..................................................................................... 140
Figure B.30: Roof Displacement for Three Story Strength Design Subject to se02fp5 ..................................................................................... 140
Figure B.31: Roof Displacement for Three Story Strength Design Subject to se02fp6 ..................................................................................... 141
Figure B.32: Roof Displacement for Three Story Strength Design Subject to se02fp7 ..................................................................................... 141
Figure B.33: Roof Displacement for Three Story Strength Design Subject to se02fp8 ..................................................................................... 142
Figure B.34: Roof Displacement for Three Story Strength Design Subject to se02fp9 ..................................................................................... 142
Figure B.35: Base Shear for Three Story Strength Design Subject to se02fp0 ..................................................................................... 143
Figure B.36: Base Shear for Three Story Strength Design Subject to se02fp1 ..................................................................................... 143
Figure B.37: Base Shear for Three Story Strength Design Subject to se02fp2 ..................................................................................... 144
Figure B.38: Base Shear for Three Story Strength Design Subject to se02fp3 ..................................................................................... 144
Figure B.39: Base Shear for Three Story Strength Design Subject to se02fp4 ..................................................................................... 145
Figure B.40: Base Shear for Three Story Strength Design Subject to se02fp5 ..................................................................................... 145
Figure B.41: Base Shear for Three Story Strength Design Subject to se02fp6 ..................................................................................... 146
Figure B.42: Base Shear for Three Story Strength Design Subject to se02fp7 ..................................................................................... 146
Figure B.43: Base Shear for Three Story Strength Design Subject to se02fp8 ..................................................................................... 147
Figure B.44: Base Shear for Three Story Strength Design Subject to se02fp9 ..................................................................................... 147
Figure B.45: 1st Story Drift for Nine Story Stiffness Design ......................................... 148 Figure B.46: 2nd Story Drift for Nine Story Stiffness Design ........................................ 149 Figure B.47: 3rd Story Drift for Nine Story Stiffness Design ........................................ 149 Figure B.48: 4th Story Drift for Nine Story Stiffness Design ........................................ 150 Figure B.49: 5th Story Drift for Nine Story Stiffness Design ........................................ 150 Figure B.50: 6th Story Drift for Nine Story Stiffness Design ........................................ 151
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Figure B.51: 7th Story Drift for Nine Story Stiffness Design ........................................ 151 Figure B.52: 8th Story Drift for Nine Story Stiffness Design ........................................ 152 Figure B.53: 9th Story Drift for Nine Story Stiffness Design ........................................ 152 Figure B.54: Base Shear for Nine Story Stiffness Design ............................................. 153 Figure B.55: 1st Story Drift for Nine Story Strength Design with Inherent Damping ... 154 Figure B.56: 2nd Story Drift for Nine Story Strength Design with Inherent Damping .. 154 Figure B.57: 3rd Story Drift for Nine Story Strength Design with Inherent Damping .. 155 Figure B.58: 4th Story Drift for Nine Story Strength Design with Inherent Damping .. 155 Figure B.59: 5th Story Drift for Nine Story Strength Design with Inherent Damping .. 156 Figure B.60: 6th Story Drift for Nine Story Strength Design with Inherent Damping .. 156 Figure B.61: 7th Story Drift for Nine Story Strength Design with Inherent Damping .. 157 Figure B.62: 8th Story Drift for Nine Story Strength Design with Inherent Damping .. 157 Figure B.63: 9th Story Drift for Nine Story Strength Design with Inherent Damping .. 158 Figure B.64: Base Shear for Nine Story Strength Design with Inherent Damping ....... 158 Figure B.65: 1st Story Drift for Nine Story Strength Design with 5% Damping ........... 159 Figure B.66: 2nd Story Drift for Nine Story Strength Design with 5% Damping .......... 159 Figure B.67: 3rd Story Drift for Nine Story Strength Design with 5% Damping .......... 160 Figure B.68: 4th Story Drift for Nine Story Strength Design with 5% Damping .......... 160 Figure B.69: 5th Story Drift for Nine Story Strength Design with 5% Damping .......... 161 Figure B.70: 6th Story Drift for Nine Story Strength Design with 5% Damping .......... 161 Figure B.71: 7th Story Drift for Nine Story Strength Design with 5% Damping .......... 162 Figure B.72: 8th Story Drift for Nine Story Strength Design with 5% Damping .......... 162 Figure B.73: 9th Story Drift for Nine Story Strength Design with 5% Damping .......... 163 Figure B.74: Base Shear for Nine Story Strength Design with 5% Damping ............... 163 Figure B.75: 1st Story Drift for Nine Story Strength Design with 10% Damping ......... 164 Figure B.76: 2nd Story Drift for Nine Story Strength Design with 10% Damping ........ 164 Figure B.77: 3rd Story Drift for Nine Story Strength Design with 10% Damping ........ 165 Figure B.78: 4th Story Drift for Nine Story Strength Design with 10% Damping ........ 165 Figure B.79: 5th Story Drift for Nine Story Strength Design with 10% Damping ........ 166 Figure B.80: 6th Story Drift for Nine Story Strength Design with 10% Damping ........ 166 Figure B.81: 7th Story Drift for Nine Story Strength Design with 10% Damping ........ 167 Figure B.82: 8th Story Drift for Nine Story Strength Design with 10% Damping ........ 167 Figure B.83: 9th Story Drift for Nine Story Strength Design with 10% Damping ........ 168 Figure B.84: Base Shear for Nine Story Strength Design with 10% Damping ............. 168 Figure B.85: 1st Story Drift for Nine Story Strength Design with 20% Damping ......... 169 Figure B.86: 2nd Story Drift for Nine Story Strength Design with 20% Damping ........ 169 Figure B.87: 3rd Story Drift for Nine Story Strength Design with 20% Damping ........ 170 Figure B.88: 4th Story Drift for Nine Story Strength Design with 20% Damping ........ 170 Figure B.89: 5th Story Drift for Nine Story Strength Design with 20% Damping ........ 171 Figure B.90: 6th Story Drift for Nine Story Strength Design with 20% Damping ........ 171 Figure B.91: 7th Story Drift for Nine Story Strength Design with 20% Damping ........ 172 Figure B.92: 8th Story Drift for Nine Story Strength Design with 20% Damping ........ 172 Figure B.93: 9th Story Drift for Nine Story Strength Design with 20% Damping ........ 173 Figure B.94: Base Shear for Nine Story Strength Design with 20% Damping ............. 173 Figure B.95: 1st Story Drift for Nine Story Strength Design with 30% Damping ......... 174 Figure B.96: 2nd Story Drift for Nine Story Strength Design with 30% Damping ........ 174
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Figure B.97: 3rd Story Drift for Nine Story Strength Design with 30% Damping ........ 175 Figure B.98: 4th Story Drift for Nine Story Strength Design with 30% Damping ........ 175 Figure B.99: 5th Story Drift for Nine Story Strength Design with 30% Damping ........ 176 Figure B.100: 6th Story Drift for Nine Story Strength Design with 30% Damping ...... 176 Figure B.101: 7th Story Drift for Nine Story Strength Design with 30% Damping ...... 177 Figure B.102: 8th Story Drift for Nine Story Strength Design with 30% Damping ...... 177 Figure B.103: 9th Story Drift for Nine Story Strength Design with 30% Damping ...... 178 Figure B.104: Base Shear for Nine Story Strength Design with 30% Damping ........... 178 Figure B.105: Roof Displacement for Nine Story Strength Design
Subject to se02fp0 ..................................................................................... 179 Figure B.106: Roof Displacement for Nine Story Strength Design
Subject to se02fp1 ..................................................................................... 179 Figure B.107: Roof Displacement for Nine Story Strength Design
Subject to se02fp2 ..................................................................................... 180 Figure B.108: Roof Displacement for Nine Story Strength Design
Subject to se02fp3 ..................................................................................... 180 Figure B.109: Roof Displacement for Nine Story Strength Design
Subject to se02fp4 ..................................................................................... 181 Figure B.110: Roof Displacement for Nine Story Strength Design
Subject to se02fp5 ..................................................................................... 181 Figure B.111: Roof Displacement for Nine Story Strength Design
Subject to se02fp6 ..................................................................................... 182 Figure B.112: Roof Displacement for Nine Story Strength Design
Subject to se02fp7 ..................................................................................... 182 Figure B.113: Roof Displacement for Nine Story Strength Design
Subject to se02fp8 ..................................................................................... 183 Figure B.114: Roof Displacement for Nine Story Strength Design
Subject to se02fp9 ..................................................................................... 183 Figure B.115: Base Shear for Nine Story Strength Design Subject to se02fp0 ............. 184 Figure B.116: Base Shear for Nine Story Strength Design Subject to se02fp1 ............. 184 Figure B.117: Base Shear for Nine Story Strength Design Subject to se02fp2 ............. 185 Figure B.118: Base Shear for Nine Story Strength Design Subject to se02fp3 ............. 185 Figure B.119: Base Shear for Nine Story Strength Design Subject to se02fp4 ............. 186 Figure B.120: Base Shear for Nine Story Strength Design Subject to se02fp5 ............. 186 Figure B.121: Base Shear for Nine Story Strength Design Subject to se02fp6 ............. 187 Figure B.122: Base Shear for Nine Story Strength Design Subject to se02fp7 ............. 187 Figure B.123: Base Shear for Nine Story Strength Design Subject to se02fp8 ............. 188 Figure B.124: Base Shear for Nine Story Strength Design Subject to se02fp9 ............. 188
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List of Tables Table 2.1: Vertical Gravity Loads ................................................................................... 18 Table 2.2: Seismic Masses ............................................................................................... 18 Table 2.3: Seismic Design Parameters ............................................................................. 22 Table 2.4: Seismic Design Loads ..................................................................................... 23 Table 2.5: Wind Design Loads ........................................................................................ 25 Table 2.6: Members and Section Properties of the Three Story Seattle Model
Designed for Strength .................................................................................... 29 Table 2.7: Members and Section Properties of the Nine Story Seattle Model
Designed for Strength .................................................................................... 29 Table 2.8: Members and Section Properties of the Three Story Boston Model
Designed for Strength .................................................................................... 31 Table 2.9: Members and Section Properties of the Nine Story Boston Model
Designed for Strength .................................................................................... 31 Table 2.10: Three Story Model Stiffnesses and Damping Constants
for Inherent Damping ..................................................................................... 34 Table 2.11: Nine Story Model Stiffnesses and Damping Constants
for Inherent Damping ..................................................................................... 35 Table 2.12: Seattle Model Stiffnesses and Damping Constants
for Added Damping ....................................................................................... 36 Table 2.13: Members and Section Properties of the Three Story Seattle Model
Designed for Stiffness .................................................................................... 37 Table 2.14: Members and Section Properties of the Nine Story Seattle Model
Designed for Stiffness .................................................................................... 37 Table 3.1: Ground Acceleration Record Properties ......................................................... 50 Table 3.2: Three Story Strength Design Scaling Properties ............................................ 57 Table 3.3: Three Story Stiffness Design Scaling Properties ............................................ 58 Table 3.4: Nine Story Strength Design Scaling Properties .............................................. 59 Table 3.5: Nine Story Stiffness Design Scaling Properties ............................................. 60 Table 5.1 Interstory Drift Limits ...................................................................................... 70 Table 5.2 Interstory Drifts for 10% Damped Three Story Seattle Model ........................ 71 Table 5.3 Interstory Drifts for 10% Damped Nine Story Seattle Model ......................... 72 Table 5.4 Base Shear Tendencies for Three Story Models .............................................. 73 Table 5.5 Base Shear Tendencies for Nine Story Models ............................................... 74
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Chapter 1: Introduction 1.1 Background
The unpredictable nature of earthquakes complicates the design of structures for seismic
load effects. The probability that a structure will be subjected to notable ground
accelerations can only be estimated. The intensity and frequency content of a potential
ground motion cannot be known until after it has occurred. The inelastic response of a
structure to this unquantifiable excitation is difficult to predict accurately. Despite these
variables, structural engineers must do their best to ensure the safety of the occupants of
the buildings they design. Hence, current codes and specifications set multiple limits
restricting member selection for structures in earthquake-prone regions. Unfortunately,
designing a building to meet the most restrictive of these criteria can sometimes lead to
significant over-design with regards to the lesser limitations. A steel moment-resisting
frame is an excellent example of a structural system displaying such a disparity in seismic
requirements. A steel moment frame designed only to satisfy seismic strength
requirements will often still exceed story drift limitations. Traditionally, frame member
sizes are increased until all criteria are met. The overstrength inherent in the drift
controlled system reduces the local ductility demands, but no economic allowance is
provided because of this. The first purpose of this study is to test the inclusion of viscous
fluid dampers as an alternate method of controlling these drifts.
Designing structures to respond elastically to earthquake loads in regions of medium to
high seismic activity would be highly uneconomical. Therefore, seismic specifications in
current building codes provide guidelines for designing structures that yield when
subjected to the design basis earthquake. The primary goal of a structural engineer is to
preserve the safety of the general public. The level of allowable damage to a given
structure depends on the severity of the ground motion and the importance of that
structure. Given this philosophy, it would be logical to design structures considering
multiple ground motion intensities and the probability that an earthquake of each of these
intensities would occur. Structures should meet certain performance objectives, or limit
2
states, for each combination of probability and intensity level. They should be relatively
invulnerable to frequent, minor ground motions, and yield without collapse during less
common, critical seismic events. Current building codes governing seismic analysis and
design unfortunately do not require that engineers study the inelastic response of the
buildings they design, or examine the effects of more than one pattern of seismic loads.
In the past, this could be forgiven due to the lack of resources necessary to execute
extensive collections of complicated analyses. However, advances in computer hardware
and software have produced machines that are capable of performing complex analyses in
a fraction of the time that would previously have been required. The second purpose of
this study is to utilize present computing power to perform a new structural analysis
technique, called incremental dynamic analysis, on the aforementioned steel moment
frames in an attempt to attain a complete understanding of the effects of the viscous fluid
dampers on structural behavior.
1.2 Literature Survey of Damping in Steel Moment Frames
Adding dampers to a structure helps dissipate the energy generated during dynamic
excitation. Common passive energy dissipation systems include hysteretic damping
through the yielding of metal, friction dampers, viscoelastic damping through the
deformation of a solid, and viscous fluid dampers. This study focuses on the use of
viscous fluid dampers. These devices work through the orificing of a viscous fluid
through small passages inside an enclosed container (Constantinou et al. 1998). By
placing such a device in a bracing system in a structure, like the chevron brace shown in
Figure 1.1, motion between adjacent levels can be resisted by the damper. Figure 1.2 is a
picture displaying what dampers can actually look like in an existing building. The
contribution of viscous fluid dampers to the stiffness of a structure is negligible.
3
Fluid Viscous Dampers
Figure 1.1: Viscous Fluid Dampers in a Chevron Brace Configuration
Figure 1.2: Viscous Fluid Dampers Exposed in a Building
4
The ability of viscous fluid dampers to dissipate energy depends on the velocity of
relative motion, making them most useful during earthquakes with high frequency
content (Makris 1997). The force developed in a damper due to a given velocity is: α
dtdx
dtdxCF ⎟
⎠⎞
⎜⎝⎛= sgn (1-1)
where C is the damping coefficient, dtdx is the velocity, and α is a factor determining the
linearity of damper response. When α is unity, the device is a linear damper and
Equation 1 reduces to:
dtdxCF = (1-2)
The Northridge earthquake in 1994 caused significant damage to many moment frames
that had been designed according to the standards of the time. Brittle fractures in welded
beam to column connections were determined to be the primary cause of failure. In an
attempt to reduce the deformations that contribute to such brittle failures, researchers
have experimented with the inclusion of passive energy dissipation systems in structures
located in regions of high seismic activity. One such study investigates the ability of both
friction dampers and viscous fluid dampers to control structural deformations and
accelerations (Filiatrault et al. 2001). The building in question is a six story three bay
moment frame designed according to the pre-Northridge standards and retrofitted with
the dampers in a chevron brace configuration. Both linear (α = 1.0) and nonlinear (α =
0.5 and α = 0.3) viscous fluid dampers were used. These dampers were designed to give
the structure damping ratios ranging from 0% to 35%. At each level of damping, the
structure was subjected to six near-field earthquakes, five earthquakes scaled to have a
10% probability of exceedence in 50 years, the unscaled El Centro record from the 1940
Imperial Valley earthquake, and the unscaled Taft Lincoln Tunnel record from the 1952
Kern County earthquake. In all cases, increased damping reduced story drift and peak
floor accelerations. However, even the higher levels of damping could not prevent
structural collapse during the near-field earthquakes. Also, stronger ground motions
resulted in exceedingly high forces in the chevron braces. The nonlinear viscous fluid
5
dampers produced slightly smaller brace forces than the linear dampers, but experienced
higher velocities, which negated the desired benefit. The nonlinear dampers were also
not as effective in reducing lateral deflections. The researchers concluded that viscous
fluid dampers by themselves would not be sufficient to protect structures from extreme
seismic hazard. Their results do suggest that passive energy dissipation systems may still
be beneficial in regions of medium seismic activity or in conjunction with other structural
systems.
In this study, Filiatrault and his co-workers satisfactorily covered wide ranges of damping
exponent, damping ratio, and earthquake severity. However, their negative results
regarding viscous fluid dampers were determined without much further examination of
potential improvements to their research. Most notably, they concluded that viscous fluid
dampers were ineffective based on the results of the strongest earthquakes in the study,
the near fault earthquakes, despite the fact that their models performed admirably for all
other ground motions. They also surmised that the chevron braces that transfer the
damper forces to the structure would buckle, but did not attempt to redesign these braces
to withstand these load effects. Finally, only steel moment frames retrofitted with
viscous fluid dampers were studied. These frames were originally designed to meet both
strength and stiffness requirements. This research did not attempt to determine if passive
energy dissipaters could control interstory drift in moment frames designed solely for
strength.
A similar study involving one, five, and eleven story moment frames arrived at a slightly
different conclusion (Miyamoto and Singh 2002). These frames were retrofitted with
passive energy dissipation systems that provided 20% of critical damping. Eight ground
acceleration records were used in this study, three of which exceed recommended design
level earthquakes, representing near fault ground motions. Linear dynamic analyses were
performed with nonlinear viscous fluid dampers and nonlinear dynamic analyses were
performed with linear dampers. The models responded elastically for all records except
the three near fault motions. The one and five story models experienced interstory drifts
suggesting little to no damage would occur during the less intense earthquakes, and only
6
moderate damage would result from the near fault records. Four of the ground motions
caused the eleven story structure to exceed immediate post-earthquake occupancy drift
restrictions, but drifts in all cases were still well within the limits protecting life safety.
The only drawback discovered during this study regarding the inclusion of viscous fluid
dampers was increased base shear. The positive results of these tests prompted the
researchers to continue their study by adding viscous fluid dampers to a five story frame
redesigned to meet strength requirements only. The larger first mode period of the new
frame led to lower base shear than that calculated in the original damped five story frame.
While interstory drifts and plastic hinge magnitudes were greater in the strength designed
frame than in the retrofitted frame, performance is still improved when compared to the
bare, undamped frame. The researchers concluded that linear viscous fluid dampers
could be used to effect compliance with codified drift limits.
While the conclusions of this study seem promising, the scope of the research was
unfortunately limited. The damping ratio was 20% of critical for all models, and no
attempt to find an optimal damping ratio was made. Also, the majority of the analyses
were performed on steel moment frames retrofitted with passive energy dissipaters. Only
the five story model was redesigned for strength to test the ability of the damping devices
to control drifts for the purpose of meeting code limits. The positive results of Miyamoto
and Singh’s research contrast heavily with the negative results determined by Filiatrault
and his co-workers. This discrepancy warrants further investigation of the true effects of
viscous fluid dampers on steel moment frame drift.
Oesterle also studied the effects of viscous fluid dampers on steel moment frame drift
(Oesterle 2003). His research focused primarily on damper nonlinearity. The nine story
five bay model being studied was fitted with dampers having an α of 0.5, 1.0, and 1.5 and
damping ratios of 5%, 10%, 15%, and 20% and subjected to both near fault and far fault
ground motions. The dampers were implemented in a chevron brace configuration. In
most of the analyses, the braces were considered to act elastically, but yielding braces
were added to some of the models to study the interaction of the elasticity of the braces
and the varying velocity exponent. It was found that the higher exponents produced the
7
most favorable results regarding the reduction of drifts and damage. Unfortunately, base
shear and brace forces increased with this reduction. Oesterle also determined that it is
important for the chevron brace members to behave elastically, especially when α = 1.5.
This is because the higher brace forces associated with this exponent value cause the
members to yield earlier than with the lower exponent values, leading to a decrease in
damper effectiveness.
Oesterle’s research strengthens the notion that viscous fluid dampers can improve the
seismic performance of steel moment frames. However, like the majority of past
research, it focuses on the retrofit of structures that have been pre-designed to meet
stiffness requirements. Considerably less work has been done regarding strength design
of steel moment frames with the inclusion of viscous fluid dampers to control drift.
1.3 Literature Survey of Incremental Dynamic Analysis
Incremental dynamic analysis (IDA) actually describes a collection of many separate
nonlinear dynamic analyses of a structural model that are organized together to provide a
comprehensive idea about how that model will react to seismic excitation. Once a
preliminary structural model has been produced, most commercial structural analysis
software is capable of testing the ability of that model to withstand ground motions. This
ground motion is usually applied to the model through the use of a ground acceleration
history file, which contains a record of the accelerations from a past earthquake. The key
to IDA is to incrementally scale a selected ground acceleration history file to effectively
create multiple earthquakes with a range of intensities and individually analyze the
structural model for each level of excitation. The maximum response of the structure is
recorded for each analysis. Once all analyses have been completed, the recorded
responses can be plotted as points on a graph versus a measure of the intensity of the
excitation that produced them. Connecting these points creates a single IDA curve. A
typical IDA curve is depicted in Figure 1.3. Provided that the ground acceleration history
has been realistically scaled, the curve should be a straight line when the ground motion
has been multiplied by lower scale factors, indicating that the structure is behaving
elastically. Once the motion is strong enough to cause the structure to yield, the curve
8
will begin to bend. The IDA curve in Figure 1.3 happens to resemble a static pushover
curve, which is common.
Engineering Demand Parameter
Inte
nsity
Mea
sure
Figure 1.3: Single IDA Curve
While plotting a single IDA curve provides a good idea about how a particular structure
would respond to varying intensities of a single earthquake, the true value of IDA lies in
plotting many curves together on the same graph. Usually, this is done by subjecting a
structure to multiple ground motions, and each ground motion is represented on the graph
by an individual IDA curve. This is called a multiple earthquake IDA study, and it is
useful because different earthquakes can elicit very different responses from the same
structure. It is virtually impossible to build a structure that will satisfactorily resist all
possible ground motions, but creating IDA curves with similar scaling parameters for
multiple earthquakes will decrease the probability of a future earthquake damaging the
structure more severely than predicted. A multiple earthquake IDA study is plotted in
Figure 1.4. The difference in structural response at equivalent levels of seismic intensity
is obvious, as is the dissimilarity of the IDA curve shapes. For example, while Curve B
behaves almost linearly at higher intensities, Curve C exhibits a much more inelastic
response, and the ground motion represented by Curve A causes complete collapse of the
9
structure. Also, while Curve A illustrates the traditional linear region, yield point, and
eventual failure of the structure, the other two curves display much less intuitive
behavior. Curve B hardens at higher intensities and Curve C weaves dramatically in a
manner known as resurrection. The eccentricities evident in this simple example
effectively demonstrate the usefulness of performing multiple nonlinear analyses.
Engineering Demand Parameter
Inte
nsity
Mea
sure
A
B
C
Figure 1.4: Multiple Earthquake IDA Study
IDA can also be used to visualize the behavior of a structure as a certain parameter or
characteristic of the structure is systematically varied. Multiple IDA curves are plotted
on the same graph, but only one ground motion is used and each curve represents a
different value of the variable parameter. This is called a multiple parameter IDA. The
shape of the curves in a multiple parameter IDA study will likely be much more similar
than those in a multiple earthquake IDA because the same earthquake is used to create
each curve. This trend is displayed in Figure 1.5. Instead, the difference between the
IDA curves will reside primarily in the degree of structural response.
10
Engineering Demand Parameter
Inte
nsity
Mea
sure
D
E
F
Figure 1.5: Multiple Parameter IDA Study
One of the most thorough investigations into the proper development and application of
IDA is the dissertation of Dimitrios Vamvatsikos in 2002, the chapters of which have
been separated and individually published by numerous engineering journals.
Vamvatsikos credits Bertero with first mention of the usefulness of incrementally scaling
seismic records in 1977 and acknowledges several other succeeding scholars for being
proponents of the IDA concept (Vamvatsikos and Cornell 2002). He clearly defines the
fundamental parameters used in creating an IDA. These parameters include scale factors,
intensity measures, and damage measures. A scale factor is a positive, constant scalar
which is multiplied by an original ground acceleration history to produce a scaled record.
An intensity measure identifies the relative strength of an earthquake. While authorities
disagree strongly on the most appropriate way to measure the magnitude of a ground
motion, it is convenient for the purposes of IDA to use a value which is proportional to
the scale factor used to obtain that record. A data point on an IDA curve will have the
intensity measure of the ground motion used to create it as its ordinate. A damage
measure, also known as an engineering demand parameter, quantifies the response of a
structure to seismic excitation. Deflections, story drifts, base shear, and member forces
and stresses are all examples of typical damage measures. The maximum value of a
11
damage measure over the duration of a nonlinear dynamic analysis becomes the abscissa
of a data point on an IDA curve. Vamvatsikos concludes his establishment of the basic
principles of IDA by noting its inherent similarities to the static pushover test. Both types
of analysis compare the response of a structure to applied forces. It may be appropriate
to describe IDA as the dynamic equivalent of a static pushover.
Appropriate application and interpretation of analysis results are important components
of the IDA process. Statistical analysis of generated IDA curves can be used to develop
new curves representing 16%, 50%, and 84% of the chosen earthquakes (Vamvatsikos
and Cornell 2003). These curves connect the mean minus one standard deviation, the
mean, and the mean plus one standard deviation, respectively, of the data gathered for
each intensity level. Comparison of these curves to pre-determined restrictions on
structural deformation, called limit states, allows analysts to judge the adequacy of a
structure to resist both frequent, small ground motions and rare, highly destructive ground
motions. Obviously, a building should take little to no damage when subjected to minor
seismic excitation with a high rate of occurrence. More extreme load effects will
typically occur at more infrequent intervals. Structural collapse should still be prevented
for these cases, but it is acceptable for the buildings to experience a larger degree of
damage. In the event of a major earthquake, repairs are assumed to be necessary (though
they may not be economical). This method of designing structures to meet damage
demands based on the probability of seismic occurrence is known as performance-based
earthquake engineering (PBEE).
IDA has been applied solely to the selection of critical ground motions (Dhakal et al.
2006). In this study, the researchers performed a multi-record IDA study using twenty
different ground acceleration history records and a simplified analytical model of a bridge
pier. The twenty IDA curves produced by this analysis were used to generate 50th
percentile and 90th percentile IDA curves. Two intensity measures were chosen to be
representative of the design basis earthquake (DBE) and the maximum considered
earthquake (MCE). Comparison of the twenty individual IDA curves to the intersections
of the DBE and MCE intensity measures with the 50th percentile and 90th percentile IDA
12
curves yielded the selection of three records deemed to satisfactorily represent all
possible earthquakes. The record that came closest to meeting the 90th percentile IDA
curve at the DBE intensity measure was chosen to be the design basis earthquake. The
record that came closest to meeting the 50th percentile IDA curve at the MCE intensity
measure was chosen to be the maximum considered earthquake. Due to the fact that
many of the twenty records caused global collapse in the analytical model when scaled to
lower intensities, the 90th percentile IDA curve did not intersect the MCE intensity
measure. However, the record that most closely resembled the 90th percentile IDA curve
for all intensity measure was selected to serve as an example of extreme seismic hazard.
Once these representative earthquakes were chosen, the researchers then used them to
perform advanced analyses on a more refined bridge pier model.
A recent examination of various nonlinear dynamic analysis methods found IDA to
satisfactorily determine seismic capacity (Mackie and Stojadinovic 2005). This study
compares the relative accuracy of the stripe method, the cloud method, and IDA. Both
the stripe and the cloud method are inherently similar to IDA. The stripe method
involves performing nonlinear dynamic analyses on a structural model using multiple
earthquakes scaled to the same intensity. Assembling a group of stripe analyses with
different intensity levels effectively creates and IDA. The cloud method also uses
multiple ground motion records to test the integrity of a structural model, but no scaling
is involved. Instead, careful selection of ground motions creates groups of earthquakes
with similar properties. The structural response of the model is determined for the
ground motions in a group to obtain data about a specific seismic hazard. After
conducting a thorough investigation of these three methods, the researchers chose the
cloud method for their reinforced concrete bridge, but noted that IDA, when
appropriately applied, would be equally acceptable. They also suggest that IDA may be
the preferred method when studying steel frame structures.
13
1.4 Objective and Scope
This study will attempt to prove that viscous fluid dampers can adequately control the
seismic response of steel moment frames so that systems designed only for strength will
meet the interstory drift limits specified in ASCE/SEI 7-05 (ASCE 2006). Both three
story and nine story steel moment frames will be tested. The added damping devices will
have a linear force-deformation relationship and provide total structural damping ratios
ranging from 5% to 30% of critical. This study will also attempt to prove the benefits of
incremental dynamic analysis. Incremental dynamic analysis will be performed on all
models to determine the complete response of the damped system when subjected to
multiple ground motions scaled to a range of intensity levels. This study will be
organized in the following manner:
• Chapter 2 will detail the design of the moment frames and state all procedures and
assumptions.
• Chapter 3 will establish the parameters for the incremental dynamic analyses and
describe the development of the computer application used to aid this effort.
• Chapter 4 will explain the application and interpretation of the incremental
dynamic analyses and describe the development of the computer application used
to aid this effort.
• Chapter 5 will discuss the results of applying incremental dynamic analysis to the
study of viscous fluid dampers as a method of controlling drift in steel moment
frames.
• Chapter 6 will summarize and conclude the study.
• Appendix A is a detailed User’s Guide for the programs described in Chapter 3
and Chapter 4.
• Appendix B contains all the IDA studies created during the course of this
research.
14
Chapter 2: Models 2.1 Overview
To aid the current research, several trial moment frames were designed to meet typical
strength demands on a lateral force resisting system in a steel frame building. These
strength designed models were fitted with devices to effect varying levels of total viscous
damping in each structure. For comparison purposes, similar moment frames were
designed to meet both strength and seismic drift requirements without the inclusion of
dampers. This chapter covers the procedures followed when designing these models and
provides details about the selected frame members.
2.2 Model Geometry
The models used in the current study were strongly influenced by the model buildings
created for the SAC Steel Project (FEMA 2000a). This project studied the design of low
rise and high rise buildings in different regions with greatly varying levels of seismic
hazard using three story, nine story, and twenty story structures. Buildings of identical
height share the same general dimensions, dead loads, and live loads regardless of
location, though the varying regional hazard will have a profound impact on member
selection. For the purposes of the current study, three and nine story models with the
same geometries as the three and nine story SAC project models were chosen to represent
low rise and high rise structures that could potentially benefit from the inclusion of
viscous fluid dampers.
2.2.1 Three Story Model Geometry
The dimensioned elevation and floor plan of a three story model are shown in Figures 2.1
and 2.2, respectively. As can be seen in these figures, each three story model is six bays
long by four bays wide. The gray rectangle on the plan view indicates the presence of a
penthouse at the roof level. A 42 in. parapet, not shown in the figures, is also assumed at
the roof level. The lateral force resisting system consists of four special steel moment
frames, two in each direction. It is assumed that each frame will resist half of the lateral
15
load in its respective direction. All columns in the moment frames are considered to be
fixed at the ground level. The current study will focus on one of the moment frames
resisting the lateral forces in the East-West direction.
4 @ 30’ = 120’
3 @
13’
= 3
9’
First Floor
Second Floor
Third Floor
Roof
Figure 2.1: Three Story Model Elevation
4 @ 30’ = 120’
6 @
30’
= 1
80’
1
2
3
4
5
6
7
BA D EC
N
Figure 2.2: Three Story Model Floor Plan
16
2.2.2 Nine Story Model Geometry
Figures 2.3 and 2.4 display the dimensioned elevation and floor plan, respectively, of a
nine story model. This model is a square five bays by five bays, and the roof level
includes a penthouse, depicted by the gray rectangle on the plan view, and a 42 in.
parapet, not shown in the figures. It has a single basement level in addition to the nine
above ground stories. Like the three story model, it has two special steel moment frames
in each direction. All columns are assumed to be pinned at the base, but the continuous
columns and the first floor lateral restraint create a condition similar to complete fixity at
the ground level. Each frame resists half of the lateral load in its respective direction, and
the current study will focus on one of the frames resisting the lateral forces in the East-
West direction.
17
12’
18’
8 @
13’
= 1
04’
5 @ 30’ = 150’
First Floor
Second Floor
Third Floor
Fourth Floor
Fifth Floor
Sixth Floor
Seventh Floor
Eighth Floor
Ninth Floor
Roof
Figure 2.3: Nine Story Model Elevation
5 @
30’
= 1
50’
5 @ 30’ = 150’
1
2
3
4
5
6
BA D EC F
N
Figure 2.4: Nine Story Model Floor Plan
18
2.3 Gravity Loads and Masses
Equivalent gravity loads were imposed on the roof and floors of each model regardless of
height or location. These loads, including floor dead load, roof dead load, penthouse
dead load, exterior wall dead load, and reduced live load, are the same as those used in
the SAC project and are listed in Table 2.1. They were applied to the models as
equivalent point loads on nodes located at midspan of each girder in the moment frames.
Seismic masses, which vary slightly depending on building height, were also taken from
the SAC project and are listed in Table 2.2. These mass values are similar but not equal
to the dead load at each level divided by gravitational acceleration. They were selected to
create representative earthquake load effects when the models are subjected to seismic
excitation. The total mass of each floor and roof level was assigned as equivalent point
masses at the end nodes of the girders in the corresponding levels of the models.
Table 2.1 Vertical Gravity Loads
Load Type Load Floor Dead Load 96 psf Roof Dead Load 83 psf
Penthouse Dead Load 116 psf Exterior Wall Dead Load 25 psf
Floor/Roof Reduced Live Load 20 psf
3 Story Effective Seismic Weight, W3 3394 k 9 Story Effective Seismic Weight, W9 10949 k
Table 2.2 Seismic Masses
Level Mass (k-s2/ft) 3 Story Structures
Roof 70.90 Floors 2 & 3 65.53
9 Story Structures Roof 73.10 Floors 3 - 9 67.86 Floor 2 69.04
19
2.4 Regional Parameters, Design Assumptions, and Lateral Loads
For the SAC Steel Project, individual designs were created for each model size in three
separate regions with varying seismic hazard to study the effects that these differences
can have on structural design. Similarly, the current study utilizes three story and nine
story models designed to meet the regional wind and seismic requirements in both
Seattle, Washington and Boston, Massachusetts. All models were assumed to be
standard office buildings located on stiff soil in a congested area. The design criteria for
these regional requirements were taken from maps included in ASCE/SEI 7-05 (ASCE
2006). This standard also contains acceptable procedures to follow when using these
criteria to calculate minimum design loads.
2.4.1 Seismic Design Loads
Appropriate seismic loads were determined using the Equivalent Lateral Force (ELF)
procedure. This method involves calculating a maximum considered total base shear and
distributes that shear vertically among the levels of the structure as lateral seismic forces.
The equation for this seismic base shear is given by:
WCV S= (2-1)
where CS is a seismic response coefficient dependent on the design response spectrum,
the natural period of the structure, the type of lateral force resisting system, and the
structural importance, and W is the effective seismic weight. The design response
spectrum is developed using acceleration parameters SS and S1 read from the maps in
ASCE/SEI 7-05 and the site class of the soil upon which the structure is located. SS and
S1 are the maximum considered 5% damped 0.2s and 1.0s spectral response accelerations
for a given seismic hazard region. These parameters are modified to suit the prevailing
soil conditions. The equations to determine the adjusted spectral response acceleration
parameters are given by:
SaMS SFS = (2-2)
and
11 SFS vM = (2-3)
20
Where Fa and Fv are the short and long period site coefficients read from tables in
ASCE/SEI 7-05. To determine the design spectral response acceleration parameters, the
following equations are utilized:
MSDS SS32
= (2-4)
and
11 32
MD SS = (2-5)
The design response spectrum is a plot of spectral response acceleration Sa versus period
T. This spectral response acceleration is given by:
DSDS
a STTS
S 4.06.00
+= for T < T0 (2-6)
DSa SS = for T0 < T < TS (2-7)
TSS D
a1= for TS < T < TL (2-8)
21
TTS
S LDa = for TL < T (2-9)
where:
T = the fundamental period of the structure (s)
DS
D
SST 1
0 2.0=
DS
DS S
ST 1=
TL = the mapped long-period transition period
The exact fundamental period of vibration of a structure cannot be known at this stage in
the design process, but an approximate period can be used to perform these calculations.
This approximate period can be estimated based on the height of the structure, the type of
lateral force resisting system, and the coefficient, Cu. Cu depends on the one second
design spectral response acceleration parameter. The seismic response coefficient can
now be determined by:
21
IRS
C Dss /= (2-10)
though this coefficient need not exceed:
( )IRTSC D
s /1= for T < TL (2-11)
( )IRTTSC LD
s /21= for T > TL (2-12)
where R is the response modification factor based on the type of lateral force resisting
system and I is the occupancy importance factor based on the Seismic Use Group.
Once these coefficients and the total seismic base shear have been calculated, the
equivalent lateral force, Fx, at each level can be determined from the following equations:
VCF vxx = (2-13)
and
∑=
= n
i
kii
kxx
vx
hw
hwC
1
(2-14)
where Cvx is the vertical distribution factor, V is the calculated total base shear, wi and wx
are the portions of the total gravity load assigned to level i or x, h is the height from the
base of the structure to level i or x, and k is an exponent related to the natural period of
vibration of the structure. If the period is less than 0.5, then k = 1. If the period is greater
than 2.5, then k = 2. For periods in between these values, k shall be determined using
linear interpolation.
Based on the provided assumptions about the structural, situational, and soil
characteristics, Seismic Use Group I and Site Class D were used for the current study.
Buildings in Seismic Use Group I have an importance factor, I, equal to 1.0. Special
steel moment frames have a response modification factor, R, equal to 8 and a deflection
amplification factor, Cd, equal to 5.5. The calculated seismic design parameters for both
Seattle and Boston are listed in Table 2.3. The design response spectra for both regions
are plotted together in Figure 2.5 and the calculated lateral forces for the models are listed
22
in Table 2.4. As would be expected, the seismic design forces in Seattle are considerably
greater than those in Boston. The Seattle models are in Seismic Design Category D and
the Boston models are in Seismic Design Category B.
Table 2.3 Seismic Design Parameters
Seattle Boston Regional Parameters
SS = 1.25 0.25 S1 = 0.50 0.08 Fa = 1.00 1.60 Fv = 1.50 2.40
SMS = 1.25 0.40 SM1 = 0.75 0.18 SDS = 0.83 0.27 SD1 = 0.50 0.12 Cu = 1.40 1.66
3 Story Parameters T (approximate) = 0.73s 0.87s
Cs = 0.09 0.02 k = 1.12 1.19 V = 288.70k 58.44k
9 Story Parameters T (approximate) = 1.83s 2.17s
Cs = 0.03 0.01 k = 1.66 1.83 V = 374.01k 109.49k
23
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5
Period (s)
Pseu
do-A
ccel
erat
ion
(g)
SeattleBoston
Figure 2.5: Design Response Spectra
Table 2.4 Seismic Design Loads
Level Seattle ELF (k) Boston ELF (k) 3 Story Structures
Roof 137.1 28.4 3rd Floor 103.8 20.9 2nd Floor 47.8 9.2
9 Story Structures Roof 81.2 25.1 9th Floor 80.1 24.3 8th Floor 64.8 19.2 7th Floor 50.9 14.7 6th Floor 38.3 10.8 5th Floor 27.2 7.4 4th Floor 17.7 4.6 3rd Floor 9.9 2.4 2nd Floor 4.0 0.9
24
2.4.2 Wind Design Loads
In regions with medium to high seismic hazard, seismic lateral load effects will generally
control the design of structures over lateral wind loads. However, these wind loads are
essential to the proper execution of this study for two reasons. First, while Seattle sits on
the earthquake-prone west coast of North America, Boston is located in a region of low
seismic hazard and high wind speeds. It is quite likely that the design of structures in this
situation will be controlled by wind load requirements. Second, wind drift cannot be
effectively controlled by dampers. Wind is essentially a static force, and dampers need a
relatively high level of velocity to produce drift-reducing forces. Therefore, all models in
this study which are designed to meet the strength requirements of lateral load effects
must still also meet wind drift limitations before the inclusion of the viscous fluid
dampers.
Different methods were used to perform the wind load calculations for the three story and
nine story models. ASCE/SEI 7-05 allows a simplified procedure to be followed for
regularly shaped low rise buildings with no unusual characteristics. This method, which
involves reading simplified design wind pressures out of a chart and modifying them
based on height, exposure, and importance, was used to calculate the horizontal wind
loads for the three story models. The nine story models, however, do not meet the
requirements for the simplified method. A more computationally intensive analytical
procedure which calculates wind pressures that vary along the height of the building had
to be performed. This method also takes into account exposure and importance, as well
as building geometry and natural frequency.
Based on the provided assumption about the congested area around the model structures,
the wind exposure in all cases is Category B. The structural importance factor, I, is equal
to 1. No terrain abnormalities were assumed in the immediate vicinity of the models. All
roofs were assumed to be without slope. The mapped regional wind speeds taken from
ASCE/SEI 7-05 were 85mph for Seattle and 110mph for Boston. The wind design loads
calculated based on these assumptions are listed in Table 2.5.
25
Table 2.5 Wind Design Loads
Level Seattle Wind (k) Boston Wind (k) 3 Story Models
Roof 9.0 14.2 3rd Floor 11.7 18.4 2nd Floor 11.7 18.4
9 Story Models Roof 18.2 32.5 9th Floor 13.6 27.9 8th Floor 14.3 27.3 7th Floor 14.9 26.6 6th Floor 15.4 25.8 5th Floor 15.9 24.9 4th Floor 16.3 23.9 3rd Floor 16.7 22.8 2nd Floor 19.4 30.5
2.5 P-delta Effects
All structures were designed taking P-delta effects into account. However, the tributary
area for the gravity loads associated with P-delta effects is not the same as the tributary
area for the gravity loads that affect the model moment frames directly. Each frame
supports the gravity load of half of a single bay, but resists half of the total lateral load in
its respective direction. Therefore, it must also withstand the P-delta effects associated
with the gravity loads imposed upon half of the entire structure. To account for these P-
delta effects without adding unnecessary vertical loads to the moment frame, a “ghost
frame” was modeled in the plane of the frame. An example of this ghost frame is
displayed in Figure 2.6. It consists of an infinitely rigid vertical truss member spanning
each story of the structure. All gravity loads which are not directly supported by the
moment frame, but which contribute to the P-delta forces it must endure, are imposed on
the ghost frame. Because the truss members have no horizontal components, it is
unstable by itself when subjected to any horizontal force. This is why the horizontal
displacements at each node along its height are slaved to those of the corresponding
levels in the moment frame. The axially rigid truss members bear the weight of the extra
gravity load, and the slaving transfers the P-delta forces to the moment frame as the
model deforms horizontally.
26
Gravity
Pin
Axially Rigid Truss Member
Horizontal Slaving
Figure 2.6: P-delta “Ghost Frame”
2.6 Joint Modeling
The joints for all structures were modeled using the revised Krawinkler model with
revised force-deformation behavior (Charney and Marshall 2006). This model allows for
more accurate approximation of joint deformations than the simpler centerline model.
From an elevation view, it consists of four rigid links, four frictionless hinges, and two
rotational springs as shown in Figure 2.7. The rigid links are located at approximately
the same position as the column flanges and girder continuity plates in the actual
structure. The rotational spring in the upper left corner represents the shear stiffness of
the joint panel zone. The stiffness and yield moment of this shear spring depend on the
material properties of the steel and are proportional to the volume of the panel zone. The
rotational spring in the lower right corner represents the contribution of the column
flanges to the resistance of rotation in the joint. The stiffness and yield moment of this
flange spring also depend on the material properties of the steel, but are calculated using
the dimensions of the column flange. The other two corners are hinged with no rotational
stiffness.
27
Rotational SpringRepresentingShear Panel
Rotational SpringRepresenting
Column Flange
Hinge(no rotational stiffness)
Hinge(no rotational stiffness)
Rigid Link
Figure 2.7: Krawinkler Joint Model
2.7 Strength Controlled Frame Design
A steel moment frame designed to meet all strength and section property requirements
will still probably exceed standard limits on interstory drift. The frame member sizes can
be increased until the frame is stiff enough to meet these restrictions, with the unfortunate
result of a heavier, more expensive frame than would be necessary if the drifts could be
controlled by some other agent. Viscous fluid dampers have proven themselves to be
effective in reducing seismic drifts, so it is possible that they could be used in steel
moment frames to effect compliance with the drift limits set by current design standards.
To test this, three story and nine story steel frame models were created for both Seattle
and Boston according to Load and Resistance Factor Design (LRFD) to meet the strength
requirements determined by the load combinations provided in ASCE/SEI 7-05. Models
with preliminary member selections based on rough calculations were created and tested
for adequacy. Members were reselected and models were updated and analyzed in an
28
iterative fashion until all strength requirements were met. Spreadsheets were created to
facilitate the calculations performed for each iteration. In addition, all section properties,
panel zones, and beam to column ratios were checked for compliance with the
requirements set by ANSI/AISC 341-05 (AISC 2005). Finally, all models were designed
to meet a maximum interstory wind drift of h/700, where h is the story height. This drift
ratio was chosen to represent an acceptable interstory drift under a wind load with a 50
year mean recurrence interval (MRI). The final member selections are detailed in the
following figures and tables. Table 2.6 lists the chosen members and section properties
for the three story Seattle model, and Figure 2.8 displays a labeled elevation view. The
fundamental period of vibration of the three story Seattle strength design is 1.565s. Table
2.7 lists the chosen members and section properties for the nine story Seattle model, and
Figure 2.9 displays a labeled elevation view. The fundamental period of vibration of the
nine story Seattle strength design is 2.964s. Table 2.8 lists the chosen members and
section properties for the three story Boston model, and Figure 2.10 displays a labeled
elevation view. The fundamental period of vibration of the three story Boston strength
design is 1.672s. Table 2.9 lists the chosen members and section properties for the nine
story Boston model, and Figure 2.11 displays a labeled elevation view. The fundamental
period of vibration of the nine story Boston strength design is 2.386s. No doubler plates
were required to meet ANSI/AISC 341-05 requirements. For all four strength designed
models, the fundamental period is significantly larger than was approximated using the
method allowed by ASCE/SEI 7-05. This is expected, because the ASCE/SEI 7-05
assumes that the structures would have been designed to meet stiffness requirements,
which would have reduced the fundamental period.
29
Table 2.6 Members and Section Properties of the Three Story Seattle Model
Designed for Strength
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Columns W14x132 38.8 1530 14.7 14.7 1.03 0.645 234 Interior Columns W14x145 42.7 1710 14.8 15.5 1.09 0.68 260
Floor Girders W18x86 25.3 1530 18.4 11.1 0.77 0.48 186 Roof Girders W18x60 17.6 984 18.2 7.56 0.695 0.415 123
W14
x132
W14
x132
W14
x145
W14
x145
W14
x145
W18x60 W18x60 W18x60 W18x60
W18x86
W18x86
W18x86
W18x86
W18x86
W18x86
W18x86
W18x86
Figure 2.8: Elevation of the Three Story Seattle Model Designed for Strength
Table 2.7 Members and Section Properties of the Nine Story Seattle Model Designed
for Strength
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Column B-2 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Interior Column B-2 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Exterior Column 2-4 W18x258 75.9 5510 21.5 11.8 2.30 1.28 611 Interior Column 2-4 W18x258 75.9 5510 21.5 11.8 2.30 1.28 611 Exterior Column 4-6 W18x192 56.4 3870 20.4 11.5 1.75 0.96 442 Interior Column 4-6 W18x211 62.1 4330 20.7 11.6 1.91 1.06 490 Exterior Column 6-8 W18x130 38.2 2460 19.3 11.2 1.20 0.67 290 Interior Column 6-8 W18x143 42.1 2750 19.5 11.2 1.32 0.73 322 Exterior Column 8-R W18x86 25.3 1530 18.4 11.1 0.77 0.48 186 Interior Column 8-R W18x86 25.3 1530 18.4 11.1 0.77 0.48 186
Girder 1 & 2 W21x201 59.2 5310 23.0 12.6 1.63 0.91 530 Girder 3 & 4 W21x166 48.8 4280 22.5 12.4 1.36 0.75 432 Girder 5 & 6 W21x132 38.8 3220 21.8 12.4 1.04 0.65 333 Girder 7 & 8 W18x106 31.1 1910 18.7 11.2 0.94 0.59 230 Girder 9 & R W18x65 19.1 1070 18.4 7.6 0.75 0.45 133
30
W18
x311
W18
x258
W18
x258
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x258
W18
x258
W18
x258
W18
x258
W18
x192
W18
x192
W18
x211
W18
x211
W18
x211
W18
x211
W18
x130
W18
x130
W18
x143
W18
x143
W18
x143
W18
x143
W18
x86
W18
x86
W18
x86
W18
x86
W18
x86
W18
x86
W21x201 W21x201 W21x201 W21x201 W21x201
W21x201 W21x201 W21x201 W21x201W21x201
W21x166 W21x166 W21x166 W21x166 W21x166
W21x166 W21x166 W21x166 W21x166 W21x166
W21x132 W21x132 W21x132 W21x132 W21x132
W21x132 W21x132 W21x132 W21x132 W21x132
W18x106 W18x106 W18x106 W18x106 W18x106
W18x65
W18x106 W18x106 W18x106 W18x106
W18x65
W18x106
W18x65 W18x65 W18x65
W18x65 W18x65 W18x65 W18x65 W18x65
Figure 2.9: Elevation of the Nine Story Seattle Model Designed for Strength
31
Table 2.8 Members and Section Properties of the Three Story Boston Model
Designed for Strength
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Columns W14x132 38.8 1530 14.7 14.7 1.03 0.645 234 Interior Columns W14x132 38.8 1530 14.7 14.7 1.03 0.645 234
Floor Girders W18x71 20.8 1170 18.5 7.64 0.81 0.495 146 Roof Girders W18x65 19.1 1070 18.4 7.59 0.75 0.45 133
W14
x132
W14
x132
W14
x132
W14
x132
W14
x132
W18x65 W18x65 W18x65 W18x65
W18x71
W18x71
W18x71
W18x71
W18x71
W18x71
W18x71
W18x71
Figure 2.10: Elevation of the Three Story Boston Model Designed for Strength
Table 2.9 Members and Section Properties of the Nine Story Boston Model Designed
for Strength
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Column B-2 W14x550 162 9430 20.2 17.2 3.82 2.38 1180 Interior Column B-2 W14x550 162 9430 20.2 17.2 3.82 2.38 1180 Exterior Column 2-4 W14x398 117 6000 18.3 16.6 2.85 1.77 801 Interior Column 2-4 W14x426 125 6600 18.7 16.7 3.04 1.88 869 Exterior Column 4-6 W14x342 101 4900 17.5 16.4 2.47 1.54 672 Interior Column 4-6 W14x370 109 5440 17.9 16.5 2.66 1.66 736 Exterior Column 6-8 W14x257 75.6 3400 16.4 16.0 1.89 1.18 487 Interior Column 6-8 W14x283 83.3 3840 16.7 16.1 2.07 1.29 542 Exterior Column 8-R W14x132 38.8 1530 14.7 14.7 1.03 0.645 234 Interior Column 8-R W14x145 42.7 1710 14.8 15.5 1.09 0.68 260
Girder 1 & 2 W24x306 89.8 10700 27.1 13.4 2.28 1.26 922 Girder 3 & 4 W24x229 67.2 7650 26.0 13.1 1.73 0.96 675 Girder 5 & 6 W21x201 59.2 5310 23.0 12.6 1.63 0.91 530 Girder 7 & 8 W18x175 51.3 3450 20.0 11.4 1.59 0.89 398 Girder 9 & R W18x65 19.1 1070 18.4 7.59 0.75 0.45 133
32
W14
x550
W14
x398
W14
x426
W14
x550
W14
x550
W14
x550
W14
x550
W14
x550
W14
x426
W14
x426
W14
x426
W14
x398
W14
x342
W14
x342
W14
x370
W14
x370
W14
x370
W14
x370
W14
x257
W14
x257
W14
x283
W14
x283
W14
x283
W14
x283
W14
x132
W14
x145
W14
x145
W14
x145
W14
x132
W14
x145
W24x306 W24x306 W24x306 W24x306 W24x306
W24x306 W24x306 W24x306 W24x306W24x306
W24x229 W24x229 W24x229 W24x229 W24x229
W24x229 W24x229 W24x229 W24x229 W24x229
W21x201 W21x201 W21x201 W21x201 W21x201
W21x201 W21x201 W21x201 W21x201 W21x201
W18x175 W18x175 W18x175 W18x175 W18x175
W18x65
W18x175 W18x175 W18x175 W18x175
W18x65
W18x175
W18x65 W18x65 W18x65
W18x65 W18x65 W18x65 W18x65 W18x65
Figure 2.11: Elevation of the Nine Story Boston Model Designed for Strength
33
2.8 Damping
Inherent damping in all structures was calculated using Rayleigh damping. As with the
buildings in the SAC Steel Project, the total damping in each structure was determined by
setting the critical damping ratio to 2% at the natural period of the structure and at a
period of 0.2s. To model this inherent damping, a “ghost frame” similar to that used for
P-delta effects was placed in the plane of the frame. An example of this ghost frame is
displayed in Figure 2.12. The ghost frame is composed of special truss members
representing stiffness proportional and mass proportional damping and infinitely rigid
truss members which support the dampers. To achieve the desired level of inherent
damping in the structure, first the Rayleigh damping mass proportionality constant, α, and
stiffness proportionality constant, β, were determined for the entire structure. The
damping constant, c, for the mass and stiffness damper in each story was then calculated
using the equations:
αxMc = (2.15)
βxKc = (2.16)
where x is the story level, Kx is the story stiffness, and Mx is the story mass. The product
of the horizontal stiffness of each damper and its individual stiffness proportionality
constant must equal this damping constant to produce the desired level of inherent
damping in the structure. Because these damping elements must be exceedingly flexible
to avoid adding false stiffness to the rest of the model, the stiffness of each damping
element was set to a very small value and the individual stiffness proportionality constant
of each element was set to a very large value. The individual numbers do not matter as
long as their product equals c. The values calculated for the stiffnesses and damping
constants for the three story and nine story structures are listed in Tables 2.10 and 2.11.
34
Stiffness Proportional DamperMass Proportional Damper
Horizontal SlavingPin
Axially Rigid Truss Member
Figure 2.12: Damping “Ghost Frame”
Table 2.10 Three Story Model Stiffnesses and Damping Constants for
Inherent Damping
Seattle Boston
Structure: α = 0.1424 0.1343 β = 0.0011 0.0011 Mass Damper Stiffness Damper Mass Damper Stiffness Damper 1st Story: β = 70.0 376.0 66.0 348.6 kx (k/in) = 0.0056 0.0022 0.0056 0.0022 2nd Story: β = 70.0 422.3 66.0 400.1 kx (k/in) = 0.0056 0.0022 0.0056 0.0022 3rd Story: β = 75.7 166.2 71.4 161.0 kx (k/in) = 0.0056 0.0022 0.0056 0.0022
35
Table 2.11 Nine Story Model Stiffnesses and Damping Constants for
Inherent Damping
Seattle Boston
Structure: α = 0.0794 0.0972 β = 0.0012 0.0012 Mass Damper Stiffness Damper Mass Damper Stiffness Damper 1st Story: β = 40 750 50 1250 kx (k/in) = 0.0057 0.0017 0.0056 0.0014 2nd Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0041 0.0055 0.0035 3rd Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0039 0.0055 0.0029 4th Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0035 0.0055 0.0026 5th Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0029 0.0055 0.0022 6th Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0025 0.0055 0.0020 7th Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0017 0.0055 0.0015 8th Story: β = 40 750 50 1250 kx (k/in) = 0.0056 0.0016 0.0055 0.0011 9th Story: β = 40 750 50 1250 kx (k/in) = 0.0060 0.0006 0.0059 0.0003
To test the effectiveness of viscous fluid dampers at controlling interstory drift, each
strength designed model was equipped with devices which raised the total damping to
5%, 10%, 20%, and 30%. These damping ratios were accomplished by adding truss
elements with equal damping constants to every story in a chevron brace configuration.
The stiffnesses and damping constants for the added dampers are listed in Table 2.12.
Only the values determined for the Seattle models are listed in this table, for reasons
described in the following section.
36
Table 2.12: Seattle Model Stiffnesses and Damping Constants for Added Damping
Damping 3 Story Model 9 Story Model 5%: β = 480 1002
kx (k/in) = 0.0056 0.0104 10%: β = 715 2730
kx (k/in) = 0.0111 0.0111 20%: β = 1700 6275
kx (k/in) = 0.0108 0.0111 30%: β = 2730 9825
kx (k/in) = 0.0106 0.0111
2.9 Stiffness Controlled Frame Design
To achieve a thorough comparison between drift reduction methods, traditional stiffness
designed moment frames had to be developed and subjected to the same analyses as the
strength designed models. These stiffness designs were given the same inherent Rayleigh
damping as the strength designs through the use of ghost frames, but additional viscous
fluid dampers were not added. Seismic drift limits were met by increasing member sizes
until the desired stiffness was reached. During this process, it was discovered that both
the three story and nine story Boston strength designs were compliant with ASCE/SEI 7-
05 seismic drift limits. This is due to the design wind loads in New England being
considerably larger than the seismic design loads. Increasing the member sizes in the
Boston models to meet the wind drift requirements effectively created buildings with no
need for devices to control seismic drift. Therefore, it can be concluded at an early stage
in this study that viscous fluid dampers are not overly useful in regions with high average
wind speeds or low seismic activity. However, the Seattle strength designs exceeded the
standard seismic drift limits, making them perfect candidates for testing the damping
devices. Both three story and nine story control models were designed for Seattle,
meeting interstory drift restrictions by increased stiffness. The members and section
properties of the drift designed three story model are provided in Table 2.13 and a
corresponding elevation is displayed in Figure 2.13. The fundamental period of vibration
of the three story Seattle stiffness design is 1.042s. The members and section properties
of the drift designed nine story model are provided in Table 2.14 and a corresponding
elevation is displayed in Figure 2.14. The fundamental period of vibration of the nine
story Seattle stiffness design is 2.634s.
37
Table 2.13 Members and Section Properties of the Three Story Seattle Model
Designed for Stiffness
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Columns W14x283 83.3 3840 16.7 16.1 2.07 1.29 542 Interior Columns W14x311 91.4 4330 17.1 16.2 2.26 1.41 603
Floor Girders W18x175 51.3 3450 20.0 11.4 1.59 0.89 398 Roof Girders W18x60 17.6 984 18.2 7.56 0.695 0.415 123
W14
x283
W14
x283
W14
x311
W14
x311
W14
x311
W18x60 W18x60 W18x60 W18x60
W18x175
W18x175
W18x175
W18x175
W18x175
W18x175
W18x175
W18x175
Figure 2.13: Elevation of the Three Story Seattle Model Designed for Stiffness
Table 2.14 Members and Section Properties of the Nine Story Seattle Model
Designed for Stiffness
Shape A (in2) Ix (in4) d (in) bf (in) tf (in) tw (in) Zx (in3) Exterior Column B-2 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Interior Column B-2 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Exterior Column 2-4 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Interior Column 2-4 W18x311 91.6 6970 22.3 12.0 2.74 1.52 754 Exterior Column 4-6 W18x258 75.9 5510 21.5 11.8 2.30 1.28 611 Interior Column 4-6 W18x258 75.9 5510 21.5 11.8 2.30 1.28 611 Exterior Column 6-8 W18x211 62.1 4330 20.7 11.6 1.91 1.06 490 Interior Column 6-8 W18x234 68.8 4900 21.1 11.7 2.11 1.16 549 Exterior Column 8-R W18x86 25.3 1530 18.4 11.1 0.77 0.48 186 Interior Column 8-R W18x86 25.3 1530 18.4 11.1 0.77 0.48 186
Girder 1 & 2 W21x201 59.2 5310 23.0 12.6 1.63 0.91 530 Girder 3 & 4 W21x201 59.2 5310 23.0 12.6 1.63 0.91 530 Girder 5 & 6 W21x182 53.6 4730 22.7 12.5 1.48 0.83 476 Girder 7 & 8 W18x175 51.3 3450 20.0 11.4 1.59 0.89 398 Girder 9 & R W18x65 19.1 1070 18.4 7.59 0.75 0.45 133
38
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x311
W18
x258
W18
x258
W18
x258
W18
x258
W18
x258
W18
x258
W18
x211
W18
x211
W18
x234
W18
x234
W18
x234
W18
x234
W18
x86
W18
x86
W18
x86
W18
x86
W18
x86
W18
x86
W21x201 W21x201 W21x201 W21x201 W21x201
W21x201 W21x201 W21x201 W21x201W21x201
W21x201 W21x201 W21x201 W21x201 W21x201
W21x201 W21x201 W21x201 W21x201 W21x201
W21x182 W21x182 W21x182 W21x182 W21x182
W21x182 W21x182 W21x182 W21x182 W21x182
W18x175 W18x175 W18x175 W18x175 W18x175
W18x65
W18x175 W18x175 W18x175 W18x175
W18x65
W18x175
W18x65 W18x65 W18x65
W18x65 W18x65 W18x65 W18x65 W18x65
Figure 2.14: Elevation of the Nine Story Seattle Model Designed for Strength
2.10 Computer Aided Structural Modeling Using NonlinPro
All structural modeling and analyses necessary for these design processes were
performed with the structural analysis program NonlinPro (Charney and Barngrover
2006), which is a graphical user interface for the structural analysis engine DRAIN-2DX
(Prakash et al. 1993). NonlinPro is powerful enough to take second order effects and P-
delta effects into account, and it is capable of running nonlinear dynamic analyses, which
will be necessary for the continuation of this study.
39
Chapter 3: Incremental Dynamic Analysis Development 3.1 Overview
Proper development of incremental dynamic analysis (IDA) is essential to achieve
meaningful results. For a multiple earthquake IDA, the analyst must select ground
motions, intensity measures, and engineering demand parameters appropriate for the
modeled structure. For a multiple parameter IDA, only one ground motion is necessary,
but a variable parameter, such as the critical damping ratio, must be defined. Selected
ground motions must be correctly scaled for proper comparison of results. This chapter
reviews the IDA development process as performed for this study, notes important
factors to be considered when choosing the necessary parameters, and explains how this
process is aided by current computer software.
3.2 Ground Motion Selection
A multiple earthquake IDA needs a comprehensive group of past earthquake records to
render results that will adequately portray the ability of a structure to resist seismic
excitation. Using more diverse ground motion collections will provide a more complete
idea about the potential damage a structure could suffer due to future earthquakes. For
this reason, at least eight records should be included in a collection (Mackie and
Stojadinovic 2005). Only one ground acceleration record is used in a multiple parameter
IDA study, but this record is subject to the same following restrictions as the ground
motions in a multiple earthquake IDA study. In any case, each ground motion must
resemble an earthquake that could realistically affect the structure being analyzed.
Structural response depends on seismic magnitude and frequency content, which is
influenced by the location of the structure. For example, shear wave velocity is much
greater through hard rock than through less dense soils. Hence, a design response
spectrum as defined by ASCE/SEI 7-05 is contingent upon the soil classification of the
location in question (ASCE 2006). Likewise, care should be taken when selecting
ground motions for use in an IDA to ensure that each earthquake was recorded in an area
with site conditions similar to those of the site being studied. Selecting a record or suite
40
of records from the same geological region will usually satisfy this requirement. The
distance to the source of seismic excitation also has an impact on structural response. An
earthquake will tend to cause large, low frequency pulses near its epicenter that diminish
in both strength and natural period as the waves travel away from the source (Kunnath
and Kalkan 2005). This causes near-fault earthquakes to be more destructive than far-
fault earthquakes of the same moment magnitude. For all ground motions used in a
single IDA study, the distance between the epicenter of the earthquake and the location at
which it was recorded should be approximately the same. The effects of near-fault
earthquakes can still be compared to those of far-fault earthquakes by creating a separate
IDA study for each relative distance.
3.3 Intensity Measures
“Intensity” usually refers to subjective earthquake measures, like the Richter Scale or the
Modified Mercalli Scale, which describe the human perception of earthquake effects.
This type of measure does not lend itself to precise ground motion scaling. “Magnitude”
more aptly describes the instrumental measure of ground motion strength that is
necessary for IDA. However, most people are more familiar with the term “intensity”,
therefore, this will be the term used to describe objective measures of strength for the
purposes of this study. It is desirable to select an intensity measure which varies linearly
with the scale factor when performing an IDA. In almost all previous work with IDA, the
first mode spectral acceleration of the elastic structure is the chosen to describe the
severity of each record. The five percent damped first mode spectral acceleration is
particularly popular. The peak ground accelerations of the records provide another
reasonable basis for comparison, but using spectral values tends to produce more
consistent results (Dhakal et al. 2006).
Once the intensity measure is selected for an IDA, the ground motion or collection of
ground motions can be scaled. Each record is subjected to two separate scaling
processes. The first scaling ensures that all records have approximately the same
reasonable strength. There are many methods to accomplish this. One method involves
matching the response spectrum of each earthquake to a predetermined pseudo-
41
acceleration at the first-mode period of the structure. Other methods attempt to fit all
response spectra to a design spectrum. ASCE/SEI 7-05 currently requires that all records
in a suite “…be scaled such that the average value of the 5 percent damped response
spectra for the suite of motions is not less than the design response spectrum for the site
for periods ranging from 0.2T to 1.5T where T is the natural period of the structure in the
fundamental mode…” when using a nonlinear response history procedure for design
purposes (ASCE 2006). The second scaling creates multiple ground acceleration records
with incrementally increasing intensities from each original record. Mathematically, the
simplest way to perform this scaling is to choose a constant scale factor increment and
create multiples of that increment up to a maximum desired scale factor. While this
allows all scaling to be completed before beginning any analyses, it has the disadvantage
of being more computationally exhausting than advanced algorithms like the hunt and fill
method. This method, which involves systematically selecting scale factors based on the
results of previous analyses, minimizes required computing power (Vamvatsikos and
Cornell 2002).
3.4 Engineering Demand Parameters
Engineering demand parameters, sometimes referred to as damage measures, can be any
measure of structural response to load effects. Appropriate parameters are chosen based
on the scope of the analysis. Usually, lateral deflections and story drift ratios are the
most desired results of seismic analysis, but ductility, base shear, and internal forces are
also relatively common. IDA curves representing only one damage measure can be
plotted on a single graph. However, if more than one measure of structural response is to
be studied, the maximum value of many different engineering demand parameters can be
recorded during the analysis process, to be separated and plotted individually during the
review process.
3.5 Computer Aided IDA Development
To facilitate the formulation of IDA, the NonlinPro IDA Collection Creator (NICC)
computer application was developed as a part of this study. NICC works in conjunction
with the preexisting program NonlinPro (Charney and Barngrover 2006) to define the
42
variable parameters of an IDA. NonlinPro is capable of sequentially performing
numerous analyses using a collection of input files. NICC aids the IDA process by
writing the necessary input files and organizing them into a format which NonlinPro can
read. Subsections 3.5.1 through 3.5.4 of this chapter outline the basic functions of NICC.
A detailed guide explaining the use of NICC is included in Appendix A.
3.5.1 NICC Requirements
NICC can only be used to detail the ground acceleration histories applied to a structure; it
cannot define the structure itself. Therefore, a pre-existing NonlinPro input file
containing the geometry, physical properties, static loads, and constant analysis
parameters of the desired model is needed. NICC generates the collection of new input
files by systematically replicating this original file and editing the sections that define the
dynamic excitation. The original file should be subjected to a modal analysis before the
IDA collection is created, both to check the file for errors and to determine the
fundamental period of vibration of the structure, which is an important factor in the
ground motion scaling process.
NICC also needs a suite of ground acceleration history records to apply to the structure.
The required file format of these records is described in the DRAIN-2DX User’s Manual
(Prakash et al. 1993). It is the responsibility of the user to select appropriate ground
motions, following the guidelines provided in Section 3.2 of this chapter.
3.5.2 NICC Collection Format and Specifications
The main NICC window is shown in Figure 3.1. In the upper portion of the window,
labeled Collection Format, the user selects an IDA type, the original input file to be
replicated, and enters a name for the collection. The lower portion of the window,
labeled Collection Specifications, will appear differently depending on the IDA type
selected in the Collection Format section. If the user decides to create a multiple
earthquake IDAs, the Collection Specifications section will look like Figure 3.2, with a grid
for entering multiple ground acceleration records. If a multiple parameter IDA is desired,
a text box for selecting a single ground acceleration record will appear along with
43
controls for selecting which parameter is to be varied and to what degree. Figure 3.3
displays these controls. In both cases, information detailing the dynamic excitation and
scaling must be provided. The duration, the number of steps, and the size of the time step
to be used for each ground acceleration record are all input via text boxes on the right
side of the window. The first scaling process is handled in the Scaling Options window,
summoned by clicking the Scale Ground Acceleration Records button on the left side of the
main window. The second, incremental scaling process, which utilizes the
mathematically simple constant step algorithm, is defined by entering the maximum scale
factor and the number of increments to achieve that scale factor in the text boxes located
at the bottom left portion of the window.
44
Figure 3.1: NICC Main Window
45
Figure 3.2: Collection Specifications Section for a Multiple Earthquake IDA
Figure 3.3: Collection Specifications Section for a Multiple Parameter IDA
46
3.5.3 NICC Ground Acceleration Record Scaling
The Scaling Options window, displayed in Figure 3.4, provides three scaling options. The
option selected in the Scaling Options frame determines the parameters that must be
entered in the Scaling Parameters frame. All three options depend on the response spectra
of the chosen earthquakes for the critical damping ratio of the structure. The first option
scales the records such that all spectra equal a specified pseudo-acceleration at a specified
period, presumably the natural period of vibration of the structure. The second option
scales the records to meet the guidelines provided in ASCE/SEI 7-05 (ASCE 2006). The
third option scales the records to minimize the square root of the sum of the squares
difference between each response spectrum and the design spectrum defined in
ASCE/SEI 7-05 within a specified period range. When the records are scaled, the new
response spectra are plotted in the graph on the right side of the window and the
calculated scale factors are listed in the graph legend.
3.5.4 NICC Ground Acceleration History and Response Spectra Visualization
On the main window above the Scale Ground Acceleration Records button are two buttons,
labeled View Acceleration History and View Response Spectra, which summon windows
summarizing the characteristics of the chosen ground records. The Ground Acceleration
History Plot window, displayed in Figure 3.5, plots the scaled acceleration history for an
individual earthquake file and lists pertinent information including the title, duration,
time step, number of steps, original peak ground acceleration, and scaled peak ground for
that file. The Response Spectra Plot window, displayed in Figure 3.6, plots the scaled
response spectra for all chosen earthquakes together and provides more advanced plotting
options than the Scaling Options window. Pseudo-acceleration, pseudo-velocity, and
displacement spectra can be plotted versus either period or frequency, or all three spectra
can be seen together on a tripartite plot. The user can also plot an average spectrum and
the ASCE/SEI 7-05 design spectrum, choose between logarithmic and arithmetic scales,
and determine the number of points on each spectrum to calculate and plot. However,
both the Ground Acceleration History Plot window and the Response Spectra Plot window are
for visualization purposes only and have no direct effect on the IDA collection creation
process.
47
Figure 3.4: NICC Scaling Options Window
48
Figure 3.5: NICC Ground Acceleration History Plot Window
49
Figure 3.6: NICC Response Spectra Plot Window
3.6 IDA Development for the Current Study
The current research consists primarily of earthquake IDA studies in which the structural
models described in Chapter 2 are subjected to a suite of appropriate ground acceleration
records. These earthquakes were taken from the SAC Steel Project (FEMA 2000a),
which includes both near-fault and far-fault records from Los Angeles, California;
Seattle, Washington; and Boston, Massachusetts. Ten far-fault, fault parallel recordings
determined to be representative of ground motions through stiff soil with a 2% in 50 year
probable return interval in Seattle were selected for the current study. These ground
acceleration records are listed in Table 3.1 along with their characteristic properties.
Figure 3.7 shows the unscaled response spectra for the records, plotted with the Seattle
design response spectrum. Figures 3.8 to 3.17 display the ground acceleration histories
for the unscaled records.
50
Table 3.1 Ground Acceleration Record Properties
File Name Duration (s) Time Step (s) PGA (g)
se02fp0.acn Mendocino, 1992 60.00 0.020 0.486 se02fp1.acn Erzinican Meteorological Station, 1992 20.78 0.005 0.539 se02fp2.acn Olympia Highway Test Lab, 1949 80.00 0.020 0.822 se02fp3.acn Olympia Highway Test Lab, 1965 81.84 0.020 1.392 se02fp4.acn Llolleo, Chile, 1985 100.00 0.025 1.574 se02fp5.acn Vina del Mar, Chile, 1985 100.00 0.025 0.902 se02fp6.acn Deep Interplate (simulation) 80.00 0.020 0.647 se02fp7.acn Miyagi-oki, 1978 80.00 0.020 0.784 se02fp8.acn Shallow Interplate 1 (simulation) 80.00 0.020 0.535 se02fp9.acn Shallow Interplate 2 (simulation) 80.00 0.020 0.750
0
1
2
3
4
5
6
7
0 1 2 3 4 5
Natural Period of Vibration (s)
Pseu
do-A
ccel
erat
ion
(g)
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Design Spectrum
Figure 3.7: Unscaled 5% Damped Ground Acceleration Response Spectra
51
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60
Time (s)
Acc
eler
atio
n (g
)
Figure 3.8: Ground Acceleration History for Mendocino, 1992
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10 12 14 16 18 20
Time (s)
Acc
eler
atio
n (g
)
Figure 3.9: Ground Acceleration History for Erzinican Meteorological Station, 1992
52
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.10: Ground Acceleration History for Olympia Highway Test Lab, 1949
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.11: Ground Acceleration History for Olympia Highway Test Lab, 1965
53
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80 90 100
Time (s)
Acc
eler
atio
n (g
)
Figure 3.12: Ground Acceleration History for Llolleo, Chile, 1985
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80 90 100
Time (s)
Acc
eler
atio
n (g
)
Figure 3.13: Ground Acceleration History for Vina del Mar, Chile, 1985
54
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.14: Ground Acceleration History for Deep Interplate (simulation)
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.15: Ground Acceleration History for Miyagi-oki, 1976
55
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.16: Ground Acceleration History for Shallow Interplate 1 (simulation)
-1.5
-1
-0.5
0
0.5
1
1.5
0 10 20 30 40 50 60 70 80
Time (s)
Acc
eler
atio
n (g
)
Figure 3.17: Ground Acceleration History for Shallow Interplate 2 (simulation)
56
For each IDA, the ten earthquakes were scaled to meet the 5% damped ASCE/SEI 7-05
design spectrum at the natural period of vibration of the model being analyzed. Tables
3.2 through 3.5 list the scale factors and corresponding peak ground accelerations for the
three story strength design, the three story stiffness design, the nine story strength design,
and the nine story stiffness design, respectively. Figures 3.18 through 3.21 display the
scaled response spectra associated with these models.
For all earthquakes, the scale factors used in the second scaling ranged from 0.1 to 2.0
with an increment size of 0.1. Duration was selected so that each record reached its peak
ground acceleration. The time step selected for each analysis was chosen on a trial basis.
All analyses were originally performed using the interval between recorded acceleration
values as the analysis time step. However, it was found that this was insufficiently large
for some analyses, causing intolerable unbalanced moment to accumulate and resulting in
a false collapse of the model. In these cases, the time step was systematically reduced to
a minimum of 0.001s until a correct response was attained. Time scale factors were not
applied to any ground motions in an attempt to preserve the inherent natural frequencies.
57
Table 3.2 Three Story Strength Design Scaling Properties
File Scale Factor Scaled PGA (g) se02fp0.acn 0.898 0.436 se02fp1.acn 0.396 0.213 se02fp2.acn 0.775 0.637 se02fp3.acn 0.386 0.537 se02fp4.acn 0.365 0.574 se02fp5.acn 0.759 0.684 se02fp6.acn 0.539 0.348 se02fp7.acn 0.270 0.211 se02fp8.acn 0.340 0.182 se02fp9.acn 0.456 0.342
0
1
2
3
4
5
6
7
0 1 2 3 4 5
Natural Period of Vibration (s)
Pseu
do-A
ccel
erat
ion
(g)
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Design Spectrum
Figure 3.18: 5% Damped Ground Acceleration Response Spectra Scaled to 0.32g at
T = 1.565s for Three Story Strength Design
58
Table 3.3 Three Story Stiffness Design Scaling Properties
File Scale Factor Scaled PGA (g) se02fp0.acn 0.171 0.348 se02fp1.acn 0.522 0.282 se02fp2.acn 0.644 0.529 se02fp3.acn 0.426 0.592 se02fp4.acn 0.373 0.587 se02fp5.acn 0.285 0.257 se02fp6.acn 0.673 0.435 se02fp7.acn 0.192 0.150 se02fp8.acn 0.441 0.236 se02fp9.acn 0.439 0.329
0
1
2
3
4
5
6
7
0 1 2 3 4 5
Natural Period of Vibration (s)
Pseu
do-A
ccel
erat
ion
(g)
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Design Spectrum
Figure 3.19: 5% Damped Ground Acceleration Response Spectra Scaled to 0.48g at
T = 1.042s for Three Story Stiffness Design
59
Table 3.4 Nine Story Strength Design Scaling Properties
File Scale Factor Scaled PGA (g) se02fp0.acn 1.199 0.582 se02fp1.acn 0.507 0.274 se02fp2.acn 0.435 0.357 se02fp3.acn 1.139 1.585 se02fp4.acn 0.776 1.221 se02fp5.acn 1.515 1.366 se02fp6.acn 1.753 1.134 se02fp7.acn 0.673 0.527 se02fp8.acn 0.744 0.398 se02fp9.acn 1.158 0.868
0
1
2
3
4
5
6
7
0 1 2 3 4 5
Natural Period of Vibration (s)
Pseu
do-A
ccel
erat
ion
(g)
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Design Spectrum
Figure 3.20: 5% Damped Ground Acceleration Response Spectra Scaled to 0.17g at
T = 2.964 for Nine Story Strength Design
60
Table 3.5 Nine Story Stiffness Design Scaling Properties
File Scale Factor Scaled PGA (g) se02fp0.acn 0.723 0.351se02fp1.acn 0.411 0.222se02fp2.acn 0.557 0.458se02fp3.acn 0.767 1.067se02fp4.acn 1.083 1.704se02fp5.acn 1.241 1.119se02fp6.acn 1.555 1.006se02fp7.acn 0.684 0.536se02fp8.acn 0.661 0.354se02fp9.acn 0.572 0.429
0
1
2
3
4
5
6
7
0 1 2 3 4 5
Natural Period of Vibration (s)
Pseu
do-A
ccel
erat
ion
(g)
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Design Spectrum
Figure 3.21: 5% Damped Ground Acceleration Response Spectra Scaled to 0.19 at
T = 2.634 for Nine Story Stiffness Design
61
Chapter 4: Incremental Dynamic Analysis Application 4.1 Overview
Once an incremental dynamic analysis (IDA) has been properly developed and all its
analyses have been performed, the results can be organized and interpreted. This
involves the creation of graphs to facilitate the comparison of the data to desired
standards, or limit states. This chapter discusses standard limit states and typical IDA
curve characteristics and explains how this process is aided by current software.
4.2 IDA Curves
An IDA produces a large quantity of data that must be properly organized to be easily
understood. A separate graph will be created for each engineering demand parameter
chosen during the development process. The maximum value of that engineering
demand parameter over the course of an individual analysis will become a data point on
the appropriate graph. For a multiple earthquake IDA, all data points corresponding to a
particular ground motion will be connected from the smallest scale factor to the largest
scale factor, creating an IDA curve representing that ground motion. For a multiple
parameter IDA, all data points corresponding to a particular parameter value will be
connected from the smallest scale factor to the largest scale factor, creating an IDA curve
representing that parameter value. The plotting of multiple IDA curves on one graph is
often referred to as an IDA study.
IDA curves tend to exhibit certain common characteristics. Examples of five typical IDA
curves are displayed in Figure 4.1. The first common property, shared by all five curves,
is the linear region created by the data points corresponding to the lower scale factors.
The ground motions with these scale factors do not force the structure into the nonlinear
region, so the seismic response is reasonably predictable. If all ground motions were pre-
scaled so that their response spectra meet the same pseudo-acceleration at the natural
period of vibration of the structure using the correct damping ratio, these linear regions
will coincide, as they do in Figure 4.1. When the structure begins to yield, the curves
62
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1 2 3 4 5
Engineering Demand Parameter
Scal
e Fa
ctor
A
B
C
DE
Figure 4.1: Typical IDA Curve Characteristics
diverge, and their shapes are less certain. Curve A begins to bend slightly as the intensity
increases, resembling a static pushover curve. Curve B also has a simple pushover shape,
but experiences global collapse when the ground motion is scaled to higher levels. Curve
C exhibits hardening behavior. After wavering slightly during early yielding, the slope of
this curve actually increases for the higher intensities. Curve D starts to bend in the same
manner of curves A and B, but suddenly returns to a lower response range before
continuing to push over. Curve E has a shape very similar to curve D, except that E
experiences global collapse before reappearing as a stable structure for higher excitation
levels. This behavior illustrated by both curve D and curve E is known as resurrection.
4.3 Limit States
It is obvious that, in general, higher scale factors produce stronger ground motions that
cause more damage to affected structures. Ideally, a building will sustain no structural
damage during minor earthquakes, repairable damage during moderate earthquakes, and
remain standing after the rare strong ground motion. Standard objectives for structural
performance at various levels of earthquake intensity, or limit states, help engineers
design structures to be both adequate and economical. An IDA study is an excellent
63
method of comparing a design to these limit states due to its ability to instantaneously
portray the response of a model to motions of all desired strengths.
A minimum of two performance objectives for different intensity levels are necessary to
truly conform to performance-based design standards. In many cases, however, the
behavior of a model is studied with regards to three or even four limit states to check for
complete compliance with design objectives. These checks account for the effects of
both structural and nonstructural damage on public safety (FEMA 2000b). Three
commonly considered limit states are Immediate Occupancy Level, Life Safety Level,
and Collapse Prevention Level. The Immediate Occupancy Level indicates that a
building has sustained no structural damage, though minor repair to nonstructural
components may be necessary. It could be mostly functional immediately following the
seismic event, as it should be safe for use during the repair process. A building meeting
the Life Safety Level will probably show both structural and nonstructural damage, but
this damage would not present a serious safety hazard to its occupants during the
earthquake. Members may yield, but not rupture. Repairs would be possible, though
perhaps not economically so. The goal of the Collapse Prevention Level is to ensure that
the building remains standing after the seismic activity has passed. The building will
sustain extensive damage, its occupants could potentially be injured by nonstructural
failures, but the main gravity resisting system would remain intact, though wrecked
beyond repair. While the building itself may be a loss, the hope is that preventing
complete global collapse will minimize fatalities.
Because computer generated models typically focus on structural members and do not
provide details on the behavior of the nonstructural components, approximate numerical
limits must be determined for comparison between the response of the model and the
desired performance objectives. Current codified non-incremental design standards
applied to ground motions with an incremental scale factor of unity can be considered
equivalent to the Life Safety Level. The Immediate Occupancy Level, which includes
response values somewhat less than the Life Safety Level and preferably remaining in the
linear region, corresponds to an earthquake with a 50% chance of occurrence in a 50 year
64
return interval. The Collapse Prevention Level technically includes any response short of
dynamic instability, indicated by the flatlining of an IDA curve, caused by the maximum
considered earthquake. While the point on an IDA curve where the slope of the local
tangent equals 20% of the elastic slope can be used to represent the onset of instability,
caution must be exercised when determining this point due to the weaving behavior and
resurrection potential of many curves (Vamvatsikos and Cornell 2004).
4.4 Computer Aided IDA Visualization
The NonlinPro IDA Visualization Application (NIVA) was developed to supplement the
IDA capabilities of the program NonlinPro (Charney and Barngrover 2006). NonlinPro
uses the analysis engine DRAIN-2DX (Prakash et al. 1993) to produce all necessary
response data, and NIVA massages this data so that in can be easily understood in the
context of an IDA. Subsections 4.4.1 through 4.4.4 of this chapter outline the basic
functions of NICC. A detailed guide explaining the use of NIVA is included in Appendix
A.
4.4.1 NIVA Requirements
Before NIVA can be used to visualize IDA studies, NonlinPro must perform all analyses
included in the desired IDA collection. Specifically, NIVA needs the *.wzm file and
*.2dz input files written by NICC and the *.rxx output files written by NonlinPro.
4.4.2 NIVA Main Window and *.ida Files
The main NIVA window, displayed in Figure 4.2, appears upon initialization of the
program. IDA studies are plotted on the graph on the right side of the window. The
upper left corner of the window contains the graph legend, where IDA curves can be
added or removed in the form of *.ida files. The first time a particular IDA collection is
loaded into NIVA, its *.ida files must be compiled using the Create New Project Group
window, accessed via the Create -> New Project Group -> From NonlinPro menu option.
This window is displayed in Figure 4.3. The user selects the *.wzm file from the current
collection and provides a name for the new project group. NIVA will accept both
earthquake IDA and parameter IDA collections. It calculates the maximum values of
65
Figure 4.2: NIVA Main Window
Figure 4.3: NIVA Create New Project Group Window
66
each engineering demand parameter recorded by NonlinPro and writes them into *.ida
files. Each *.ida file contains all IDA curve data for either a specific earthquake or a
specific parameter value, depending on the IDA collection type. NIVA then loads all
files in the new project group into the visualization utility. Once a project group has been
created in this manner, the *.ida files can be individually unloaded from the utility, or
reloaded at a later date for easy reference using the Add and Remove buttons on the main
window. Loaded files can also be viewed in text format by selecting the View -> Input
File menu option.
4.4.3 NIVA IDA Plotting Functions
A loaded project group can be used to plot the IDA study of any engineering demand
parameter recorded by NonlinPro during the analysis process. The two drop down list
boxes in the top center of the main window allow the user to determine the individual
node or element for which data is desired, and the drop down list box in the bottom right
corner selects the engineering demand parameter associated with that node or element.
Clicking the Graph button plots the IDA study. Alternatively, NIVA can plot a
combination IDA study. Instead of selecting a single node or element, the user will select
two, and NIVA will plot the IDA study of the difference between those two nodes or
elements. This capability is useful for plotting interstory drift data.
4.4.4 NIVA Performance Objectives and Response Histories
NIVA includes features which aid the user in developing a complete understanding of
structural response and adequacy. Because performance objectives are such an important
aspect of studying IDA curves, NIVA is capable of marking up to three limit states on the
plot with the curves. They can be either drawn on the graph using the mouse or entered
manually in the text boxes in the lower left corner of the main window. An example of
plotted performance objectives is shown in Figure 4.4. NIVA can also display response
history data from any analysis in the IDA. As mentioned earlier, each data point on the
graph is actually the maximum value of a response history from one of the analyses, and
clicking on an intensity level will summon a new window displaying the corresponding
67
response histories from ground motions of that intensity. An example of this window is
shown in Figure 4.5.
Figure 4.4: NIVA IDA Curve and Performance Objective Example
68
Figure 4.5: NIVA Response History Viewing Window
69
Chapter 5: Results and Discussion 5.1 Overview
An Incremental Dynamic Analysis (IDA) was performed on both the three story and nine
story Seattle strength designs with inherent, 5%, 10%, 20%, and 30% damping. For
comparison, IDAs were also performed on the three story and nine story Seattle drift
designs. After each set of analyses, multiple earthquake IDA studies were created for the
interstory drift in every story and the total base shear of the model. In addition, multiple
parameter IDA studies were compiled from the results of all analyses with percent critical
damping as the variable parameter. All IDA study plots can be found in Appendix B.
The current chapter reviews the results of these analyses by comparing the response of
the damped strength designs to codified limits and discussing how IDA provides a more
complete understanding of the benefits of including viscous fluid dampers in steel
moment frame design than other analysis procedures.
Great care was taken to ensure the dynamic time step of each analysis was sufficiently
small. Whenever collapses or resurrections characteristic of time step error occurred, the
time step for each offending analysis was reduced, to a minimum of 0.001s. This
minimum step size was chosen because further time step refinement had little to no effect
on structural response, but exacted a high price in terms of computational time. The nine
story inherently damped strength design and the nine story stiffness design still exhibited
suspicious behavior at high intensity levels, even when the minimum considered time
step was used. To discern whether these failures were true representations of structural
response, energy plots were created and studied for these analyses, and no discrepancies
indicating time step error were found. While these results are not necessarily conclusive,
there is no evidence to indicate that these collapses and resurrections were not due to the
true dynamic instability of the models. Therefore, this study assumes that all data
collected from these analyses is correct.
70
5.2 Code Compliance
According to ASCE/SEI 7-05 (ASCE 2006), interstory drift in any story of a linear model
should not exceed 2% of the story height during a design level earthquake, which
corresponds to the Life Safety performance objective. For nonlinear dynamic analyses,
these interstory drift limits are allowed to be increased to 125% of the linear limits.
Given that IDA incorporates nonlinear dynamic analyses, these amplified limits were
used in the current study. The calculated drift restrictions are provided in Table 5.1. In
order for a structure to be code compliant, the drift experienced by every story must meet
these limits.
Table 5.1 Interstory Drift Limits
Story Drift Limit (in) Three Story Models
All Stories 3.9 Nine Story Models
Bottom Story 5.4 All Other Stories 3.9
While the primary advantage of IDA is to instantaneously examine the effects of multiple
ground motion intensities on structural response, it can also be dissected so that each
individual analysis can be studied separately. For each IDA collection, the analysis with
an incremental scale factor of unity for every earthquake in the collection was used to
determine code compliance. In each case, the maximum drift experienced by every story
for strength designs with each level of damping was compared to the provided limits.
5.2.1 Three Story Strength Design Code Compliance
As anticipated, the three story structure met the code restrictions when higher levels of
damping were included. When only inherent damping was utilized, many interstory drift
levels exceeded the maximum allowable values. Ground motions se02fp0 and se02fp2
caused all three stories to exceed their interstory drift limits, and se02fp1 and se02fp5
caused at least one story to exceed its limit. The limit was also surpassed in the second
and third stories due to se02fp2 and se02fp5 when the total structural damping was
increased to 5%. The lowest added damping level to effect code compliance in the three
71
story strength design was 10%. Table 5.2 lists the maximum interstory drifts experienced
by all stories in the 10% damped model for all earthquakes. It can be seen that all values
are comfortably within the provided limits. The three story models with 20% damping
and 30% damping also meet these criteria, but are more conservative than necessary.
Table 5.2 Interstory Drifts for 10% Damped Three Story Seattle Strength Design
Story se02fp0 se02fp1 se02fp2 se02fp3 se02fp4 3 3.16 2.51 3.02 2.04 2.54 2 3.40 3.37 3.72 2.05 2.69 1 2.82 2.88 3.46 1.68 1.52
Story se02fp5 se02fp6 se02fp7 se02fp8 se02fp9 3 3.57 2.08 2.82 2.16 1.98 2 3.79 2.38 3.08 2.68 2.34 1 2.92 1.43 1.93 1.91 1.55
5.2.2 Nine Story Strength Design Code Compliance
The nine story models followed the same trend as the three story models, but with
slightly exaggerated values. The se02fp5 ground motion caused the global collapse of
the inherently damped model, and eight of the other nine ground motions caused at least
one of the top four stories to exceed the allowable drift limit. When total structural
damping was increased to 5% of critical, the model remained dynamically stable for all
earthquakes, but the interstory drifts were still greater than the maximum allowable
values in many instances, especially the top four stories. As with the three story models,
the nine story model with lowest level of damping that still met the provided drift
restrictions was the 10% damped model. The maximum interstory drifts calculated in all
stories of the 10% damped nine story model for all ground motions are displayed in Table
5.3. The 20% damped and 30% damped nine story models also met the codified
restrictions, but were overly conservative.
72
Table 5.3 Interstory Drifts for 10% Damped Nine Story Seattle Strength Design
Story se02fp0 se02fp1 se02fp2 se02fp3 se02fp4 9 1.61 1.48 1.13 2.03 1.65 8 2.30 2.13 1.62 2.90 2.26 7 2.38 2.40 1.92 3.16 2.37 6 2.03 2.24 1.91 2.83 2.02 5 1.98 1.93 1.78 2.37 1.72 4 2.00 1.76 1.71 2.21 1.66 3 1.97 1.69 1.62 2.14 1.64 2 1.91 1.63 1.56 2.11 1.66 1 2.40 2.07 1.98 2.67 2.16
Story se02fp5 se02fp6 se02fp7 se02fp8 se02fp9 9 1.72 1.80 1.87 1.94 1.73 8 2.45 2.58 2.78 2.80 2.58 7 2.59 2.82 3.22 3.09 2.94 6 2.35 2.56 3.18 2.77 2.74 5 2.14 2.42 2.93 2.32 2.35 4 2.24 2.50 2.77 1.99 2.03 3 2.40 2.49 2.63 1.78 1.78 2 2.49 2.43 2.46 1.65 1.65 1 3.15 3.11 2.92 2.15 2.15
5.2.3 Base Shear and Feasibility
It is generally accepted the one of the biggest problems with linear viscous fluid dampers
is their tendency to experience large damper forces, increasing total base shear during
earthquakes that cause significant nonlinear behavior. Their benefits involving the
reduction of interstory drift mean little if the member sizes required to prevent buckling
in the chevron braces are uneconomical. Therefore, base shear plots were created to
study the extent of the effect of the damping devices on base shear.
Table 5.4 contains the maximum total base shears experienced by the three story strength
designs with inherent damping and 10% damping, and the three story model designed to
meet drift requirements without dampers. Surprisingly, the base shears in the 10%
damped structure are very comparable to those in the inherently damped structure. The
average base shear actually decreases slightly for the higher level of damping, though this
decrease is not the result of a true trend due to the high degree of scatter. This is
probably due to a low occurrence of inelastic behavior in the three story structure for the
design intensity ground motion, and that fact that 10% of critical damping does not
73
produce the high damper forces that are present in the 20% damped and 30% damped
models. It is also interesting to note that the base shears calculated for the 10% damped
strength design are roughly half of those found in the drift designed model. These results
suggest that any changes in total base shear for low rise buildings with viscous fluid
dampers should be economically manageable.
Table 5.4 Base Shear Tendencies for Three Story Models
Inherently Damped Strength Design Base
Shear (k)
10% Damped Strength Design Base Shear (k) % Difference
Drift Design Base Shear (k)
se02fp0 526.24 562.41 6.87 966.18 se02fp1 442.86 467.23 5.50 1151.34 se02fp2 616.48 622.38 0.96 1505.49 se02fp3 577.32 456.46 -20.94 1366.69 se02fp4 640.02 433.06 -32.34 1329.18 se02fp5 671.99 591.04 -12.05 945.61 se02fp6 505.31 466.00 -7.78 1412.38 se02fp7 389.97 484.56 24.26 1036.07 se02fp8 461.44 468.75 1.58 1198.40 se02fp9 505.97 449.55 -11.15 1245.64
The corresponding base shear values for the nine story models are listed in Table 5.5. In
every case, the base shear in the 10% damped model is strikingly similar to the base shear
in both the inherently damped model and the drift design. The average increase in Base
shear from the inherently damped model to the 10% damped model is 2.4%, though this
is not a true trend due to the high degree of scatter. The base shear does decrease for four
of the ten ground motions. As with the three story models, the limited increase in base
shear can probably be explained by the relatively low level of added damping. This
theory is supported by the larger base shear values in the 20% and 30% damped nine
story models. The only significant difference in trends between the three story and nine
story models lies in the ratio of the base shear in the 10% damped strength design to that
in the drift design. This difference is not alarming considering the greater occurrence of
inelastic behavior in the nine story model caused by higher overturning moments.
Therefore, it can be inferred that the increase in total base shear due to the inclusion of
viscous fluid dampers in high rise structures should not be uneconomical to
accommodate. It is also interesting to note that stiffness design, which is fully compliant
74
with current standards, collapses when subjected to se02fp4, while the weaker inherently
damped strength design remains dynamically stable. This is yet another example of how
nonlinear structural response to dynamic excitation is not always intuitive.
Table 5.5 Base Shear Tendencies for Nine Story Models
Inherently Damped Strength Design Base
Shear (k)
10% Damped Strength Design Base Shear (k) % Difference
Drift Design Base Shear (k)
se02fp0 1156.77 1294.66 11.92 1143.17 se02fp1 967.44 1024.86 5.94 1071.63 se02fp2 998.41 1011.47 1.31 1395.65 se02fp3 1544.87 1493.05 -3.35 1381.28 se02fp4 1355.44 1234.55 -8.92 collapse se02fp5 collapse 1664.75 - collapse se02fp6 1503.74 1802.04 19.84 1433.61 se02fp7 1187.13 1376.61 15.96 1320.86 se02fp8 1174.78 1116.60 -4.95 1285.76 se02fp9 1469.18 1272.15 -13.41 1090.64
5.3 Benefits of Incremental Dynamic Analysis
The equivalent lateral force (ELF) method for designing structures to resist seismic load
effects is computationally simple, but it has its disadvantages. Take, for example, the
traditional drift controlled designs. Ideally, a structure deemed adequate using one
analysis procedure should also meet the general requirements of other standard methods.
However, these models, which are completely compliant with all ELF requirements as
stated by ASCE/SEI 7-05, are sometimes less than satisfactory when subjected to a
nonlinear response history procedure. The three story stiffness model faired rather well,
with only one ground motion causing interstory drift limits to be exceeded, but the nine
story models were less reliable. It collapsed during two of the chosen earthquakes at the
design level of intensity. Also, while the bottom seven stories performed well under the
remaining eight ground motions, the top two stories exceeded drift restrictions during
five of those motions. It is difficult to predict how well a structure will perform under a
variety of loading conditions without thoroughly testing an analytical model and
examining its behavior. A notable advantage of IDA is that it defines a logical system
both for selecting a range of loading conditions to study and for visualizing the results.
This procedure, when applied to steel moment frames fitted with linear viscous fluid
75
dampers, provides a more complete understanding of the effect of the damping devices
on structural behavior than other traditional methods.
5.3.1 IDA Studies of Stiffness Designed Models
Multiple earthquake IDA studies of the maximum interstory drifts experienced by the
drift controlled designs show how these structures perform when subjected to the chosen
suite of ground motions. Figure 5.1 displays the IDA study for drift in the 2nd story of the
three story model and Figure 5.2 displays the IDA study for drift in the 5th story of the
nine story model. The middle story of each model was chosen to represent structural
response because the corresponding IDA studies are typical of all drift plots generated for
the respective structures. The three story model performs very well. It does not collapse
under any loading of any intensity. This model is a good example of a structure that will
be affordable to repair after a minor earthquake and preserve the safety of its occupants
during a serious seismic event. The nine story model does not behave as well. The
ground motions se02fp4 and se02fp5 both cause global collapse at intensities less than
those associated with the Life Safety performance objective. Both of these IDA curves
resurrect temporarily, but are joined in failure by the se02fp6 curve at a scale factor of
1.3.
76
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.1: IDA Study for 2nd Story Drift of Three Story Stiffness Design
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.2: IDA Study for 5th Story Drift of Nine Story Stiffness Design
77
5.3.2: IDA Studies of Strength Designed Models
IDA studies are especially useful for visualizing the results from all analyses of the
strength designed models. Figures 5.3 through 5.7 display the multiple earthquake IDA
studies for the 2nd story drift in the three story strength design as the structural damping
ranges from inherent only to 30%. Figures 5.8 through 5.12 display the multiple
earthquake IDA studies for the 5th story drift in the nine story strength design as the
structural damping ranges from inherent only to 30%. The middle story of each model
was chosen to represent structural response because the corresponding IDA studies are
typical of all drift plots generated for the respective structures.
Inspection of Figures 5.3 though 5.7 reveals that added damping, in addition to reducing
interstory drifts, has a significant impact on dynamic stability and predictability of
seismic response in low rise structures. The inherently damped model yields
substantially during four of the earthquakes at higher intensities, and collapse for se02fp0
and se02fp5 before reaching the maximum considered earthquake. This yielding is
obviously reduced in the 5% damped model, and only se02fp5 experiences complete
failure. There is some reduction in drift and weaving behavior between 5% and 10%
damping, and by the time the damping has reached 20% of critical, the structure remains
dynamically stable for all ground motions. As interstory drifts diminish, all IDA curves
begin to converge, creating a set of IDA curves with similar, roughly linear shapes. Once
the damping ratio has reached 30% of critical, drifts have reduced drastically and visible
yielding is minimal.
78
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.3: IDA Study of 2nd Story Drift for Three Story Strength Design with
Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.4: IDA Study of 2nd Story Drift for Three Story Strength Design with 5%
Damping
79
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.5: IDA Study of 2nd Story Drift for Three Story Strength Design with 10%
Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.6: IDA Study of 2nd Story Drift for Three Story Strength Design with 20%
Damping
80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.7: IDA Study of 2nd Story Drift for Three Story Strength Design with 30%
Damping
The effects of the damping devices are even more dramatic in the nine story models.
Only three earthquakes allow the inherently damped model to remain standing at the
maximum considered intensity. The record se02fp5 causes collapse before the design
basis intensity is reached. Failure does not occur until higher scale factors for the other
six offending motions and two curves experience temporary resurrections, but it is still
obvious that inherent damping alone is unsatisfactory. The 5% damped model shows a
vast improvement over the inherently damped model. Three of the ground motions incite
global collapse, but the first failure does not occur until a scale factor of 1.4 is reached.
Only one earthquake causes collapse when the damping ratio is increased to 10% of
critical, and the structure still survives until a scale factor of 1.9. The 20% damped
model displays complete dynamic stability, and the response of the 30% model is almost
completely linear for all records.
81
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.8: IDA Study of 5th Story Drift for Nine Story Strength Design with
Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.9: IDA Study of 5th Story Drift for Nine Story Strength Design with 5%
Damping
82
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.10: IDA Study of 5th Story Drift for Nine Story Strength Design with 10%
Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.11: IDA Study of 5th Story Drift for Nine Story Strength Design with 20%
Damping
83
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure 5.12: IDA Study of 5th Story Drift for Nine Story Strength Design with 30%
Damping
Multiple parameter IDA studies more clearly depict the correlation between structural
damping ratio and seismic response. Figures 5.13 and 5.14 are examples of parameter
IDA studies which display the roof displacements of the three story model for the
se02fp0 ground motion and nine story model for the se02fp6 ground motion. The three
story model graph illustrates the tendency of models with higher added damping values
to have increasingly linear IDA curves. The nine story model graph shows the
progression from early global collapse to complete dynamic stability as the damping ratio
increases to 30% of critical. Both plots demonstrate the ability of the viscous fluid
dampers to reduce interstory drift and their increased effectiveness at higher levels of
intensity.
84
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.13: IDA Study of Roof Displacement for Three Story Strength Design
Subject to se02fp0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.14: IDA Study of Roof Displacement for Nine Story Strength Design
Subject to se02fp6
85
Multiple parameter IDA studies can also be used to examine total base shear. Figures
5.15 and 5.16 contain the base shear plots for the three story strength design subjected to
the se02fp1 and se02fp9 ground motions, respectively. The IDA curves on both plots
exhibit the same typical shape progression as the structural damping is increased from
inherent to 30% of critical. At the lowest intensity levels, while the structure behaves in a
linear elastic manner, added damping decreases total base shear. As intensity increases
and yielding becomes more substantial, this trend reverses. The IDA curves converge
briefly before displaying an increase in base shear corresponding to added damping for
greater scale factors. The operative difference between these two plots is the particular
intensity level at the point of convergence. In the se02fp1 IDA study, this point occurs
somewhere between scale factors of 0.8 and 0.9. The se02fp9 plot depicts convergence
closer to a scale factor of 1.3. This results in perceived ambiguity regarding the
relationship between damping and base shear for the design level earthquake, as
experienced when determining code compliance earlier in this chapter. In actuality, the
trends are consistent, but significant nonlinear behavior at the Life Safety Level will
indicate that the added dampers increase base shear, while primarily elastic behavior
suggests the opposite. These IDA studies also give evidence to the theory that total
damping ratios of 10% or less will not inflate base shear to an alarming degree. The 20%
and 30% damped IDA curves do demonstrate noticeably higher base shears in the
nonlinear region, but the inherent, 5%, and 10% damped curves follow paths that are
almost identical, all the way up to the maximum considered intensity.
86
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 500 1000 1500
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.15: IDA Study of Total Base Shear for Three Story Strength Design
Subject to se02fp1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 500 1000 1500
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.16: IDA Study of Total Base Shear for Three Story Strength Design
Subject to se02fp9
87
The nine story model IDA studies illustrate similar trends. The nine story model plots for
base shear due to se02fp1 and se02fp9 are displayed in Figures 5.17 and 5.18,
respectively. They are slightly more difficult to read due to the higher occurrence of
collapse in the models with low levels of damping, but the curves have the same general
shape. Base shear decreases as damping increases in the linear region, the curves cross
around the design basis intensity, and base shear increases with damping in the nonlinear
region. However, the IDA curves for inherent (if stable), 5%, and 10% damping tend to
be more distinct from one another than those generated for the three story models.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.17: IDA Study of Total Base Shear for Nine Story Strength Design Subject
to se02fp1
88
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure 5.18: IDA Study of Total Base Shear for Nine Story Strength Design Subject
to se02fp9
89
Chapter 6: Conclusion 6.1 Summary
The first goal of this study was to determine if strength designed steel moment frames
could me made to meet codified interstory drift limitations through the use of viscous
fluid dampers. The second goal of this study was to use incremental dynamic analysis
(IDA) to gain a complete understanding of the effects of these dampers when the steel
moment frames were subjected to multiple earthquakes of varying intensities.
Two steel moment frames, one three stories tall and one nine stories tall, were designed
to meet the gravitational and lateral strength requirements for buildings in Seismic Use
Group I, Seismic Site Class D, and Wind Exposure B in Seattle, Washington. A three
story and a nine story steel moment frame were also designed to meet the gravitational
and lateral strength requirements for buildings under the same conditions in Boston,
Massachusetts. All four frames were designed using the Equivalent Lateral Force
method. Using Rayleigh Damping, these structures were given an inherent structural
damping ratio of 2% in their first mode period of vibration and at a period of 0.2s. The
frames were also made to comply with wind drift limitations considering the prevailing
wind speeds in their respective locations. The final strength designs were tested for
seismic interstory drift limit compliance. The Seattle three story and nine story steel
moment frames were not compliant, but the Boston three story and nine story steel
moment frames were compliant. This is because Seattle is in a region of high seismic
hazard and low wind speeds, and Boston is in a region of low seismic hazard and high
wind speeds. In Boston, the structures that were stiff enough to satisfactorily resist wind
drift were so stiff that seismic drift was irrelevant.
The study continued using only the Seattle models. Both strength designs were fitted
with linear viscous fluid dampers in each story which raised total structural damping to
5%, 10%, 20%, and 30% of critical. For comparison purposes, a three story and a nine
90
story moment frame were also designed to meet stiffness requirements in Seattle without
dampers.
Incremental dynamic analysis is a relatively new concept, and current readily available
commercial software was insufficient to meet the needs of this study. Therefore, the
NonlinPro IDA Collection Creator (NICC) and the NonlinPro IDA Visualization
Application (NIVA) were created to work in conjunction with the structural analysis
program NonlinPro. NICC creates a collection of input files that NonlinPro can use to
perform an IDA. NIVA accepts the results of a NonlinPro IDA and organizes them in a
clear and concise manner. NICC, NonlinPro, and NIVA were used to perform an IDA on
each of the twelve Seattle models using ten ground acceleration records deemed
acceptable for use in the Seattle area. These records were prescaled to meet the
ASCE/SEI 7-05 design response spectrum at the natural period of vibration of the
structure being analyzed. The interstory drifts and total base shears of the structures
when subjected to these motions are of particular interest.
It was found that both the three story and the nine story strength designs were compliant
with codified interstory drift limitations for all ten ground motions at the design basis
intensity when 10% damping was added. There was no clear evidence associating the
dampers with increase in total base shear at this level of damping. In the damped three
story models, the base shears calculated with 10% damping were very comparable to
those calculated for the model with only inherent damping. Also, the 10% damped base
shears were approximately half of those calculated for the three story model designed for
stiffness without dampers. In the nine story models, the base shears of the inherently
damped strength design, the 10% damped strength design, and the stiffness design were
all very comparable, though there was a noticeable increase in base shear from these
models to the 20% and 30% damped strength designs. These results suggest that
structures using strength designed steel moment frames as their lateral force resisting
systems can be compliant with interstory drift restrictions when viscous fluid dampers
raise the structural damping ratio at least 10% of critical. Furthermore, 10% damped
steel moment frames should not be in danger of excessive total base shears that would
91
buckle properly designed damping system braces. These braces should not be
uneconomical to design properly.
Incremental dynamic analysis was found to be useful in gathering important information
about the behavior of these structures. Its ability to simultaneously display the responses
of a multitude of separate analyses gives it a clear advantage over less versatile methods
of analysis. The following conclusions can be drawn from the IDA studies created for
this research:
• Linear viscous fluid dampers can be used in the design of new steel moment
frames to control interstory drift without adding unnecessary stiffness to the
system.
• Added damping in steel moment frames increases the dynamic stability of the
frames.
• Fitting steel moment frames with damping devices reduces the normal dispersion
of the IDA curves at higher intensity levels, making the structural seismic
response more predictable despite the unpredictable nature of earthquakes.
• Linear viscous fluid dampers can increase the base shear of steel moment frames
during seismic activity.
• Base shear increase due to the inclusion of dampers is limited to higher intensity
ground motions that cause inelastic behavior.
• Base shear increase due to the inclusion of dampers is more of a concern when
total structural damping ratios are 20% of critical or higher.
• Base shear increase due to the inclusion of dampers is easily manageable when
total structural damping ratios are approximately 10% of critical, provided the
chevron braces in the damping frame are designed with damper forces in mind.
6.2 Limitations and Suggestions for Future Work
The following are the primary limitations of this study:
• Only two different regions of seismic hazard were studied.
• Only two different building heights were studied.
• Only one method of initial ground motion scaling was utilized.
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• Only linear viscous fluid dampers were fitted in the steel moment frames.
• Only a chevron brace configuration was used to support the dampers.
• The dampers in every story of each model were assigned the same damping
constant. No other damper configurations were studied.
Further research on viscous fluid dampers should continue to test strength designed steel
moment frames for adequate reduction of drift. However, more effort should be put into
experimenting with nonlinear viscous fluid dampers that have exponents both greater
than and less than unity. This research should attempt to find an optimal configuration of
dampers in a structure. More variety with regards to seismic hazard and building
geometry should be utilized to ensure that the results are applicable to most structures.
Also, because the buckling of damper braces is a constant concern, future researchers
should attempt to find out if different types of bracing systems would be better suited for
use with viscous fluid dampers. Buckling restrained braces would be an obvious first
choice for such studies.
As advances in computer hardware and software continue to improve structural analysis
capabilities and reduce computational time, dynamic analyses should be performed with
smaller and smaller time steps to reduce the possibility of false collapse. The suspicious
failures and resurrections of the inherently damped nine story Seattle strength design and
the nine story Seattle stiffness design should be further studied to ensure the validity of
the results of the current research.
Finally, the computer applications NICC and NIVA are currently limited in scope, but
have the potential to become powerful analysis tools with more work and as IDA
becomes a more accepted method of structural analysis. These programs should be
modified and improved to make them more versatile so that they may continue to aid
research in the future.
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References American Institute of Steel Construction, Inc. (2005). “Seismic Provisions for Structural
Steel Buildings.” Standard No. ANSI/AISC 341-05, AISC, Chicago, IL. American Society of Civil Engineers (ASCE). (2006). “Minimum Design Loads for
Buildings and Other Structures.” Standard No. ASCE/SEI 7-05, ASCE, Reston, VA. Charney, F. A. and Barngrover, B. (2006). NonlinPro Base Program Description and
User Guide. Advanced Structural Concepts, Blacksburg, VA. Charney, F. A. and Marshall, J. D. (2006). “A comparison of the Krawinkler and scissors
models for including beam-column joint deformations in the analysis of moment-resisting steel frames.” Engineering Journal, 43(1), 31-48.
Constantinou, M. C., Soong, T. T., and Dargush, G. F. (1998). Passive Energy
Dissipation Systems for Structural Design and Retrofit, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.
Dhakal, R. P., Mander, J. B., and Mashiko, N. (2006). “Identification of critical ground
motions for seismic performance assessment of structures.” Earthquake Eng. Struct. Dyn., 35(8), 989-1008.
Federal Emergency Management Agency (FEMA). (2000a). “State of the art report on
systems performance of steel moment frames subject to earthquake ground shaking.” Rep. No. FEMA-355C, SAC Joint Venture, Washington, D.C.
Federal Emergency Management Agency (FEMA). (2000b). “State of the art report on
performance prediction and evaluation of steel moment-frame buildings.” Rep. No. FEMA-355F, SAC Joint Venture, Washington, D.C.
Federal Emergency Management Agency (FEMA). (2003). “NEHRP Recommended
Provisions for Seismic Regulations for New Buildings and Other Structures.” Rep. No. FEMA-450, Washington, D.C.
Filiatrault, A., Tremblay, R., and Wanitkorkul, A. (2001). “Performance evaluation of
passive damping systems for the seismic retrofit of steel moment-resisting frames subjected to near-field ground motions.” Earthquake Spectra, 17(3), 427-456.
Kunnath, S. K. and Kalkan, E. (2005). “IDA capacity curves: the need for alternative
intensity factors.” Proc., Structures Congress and Exposition, ASCE, Reston, VA, 1869-1877.
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Mackie, K. R. and Stojadinovic, B. (2005). “Comparison of incremental dynamic, cloud, and stripe methods for computing probabilistic demand models.” Proc., Structures Congress and Exposition, ASCE, Reston, VA, 1835-1845.
Makris, N. (1997). “Vibration control of structures during urban earthquakes.” Proc.,
American Control Conference, AACC, Albuquerque, NM, 3957-3961. Miyamoto, H. K. and Singh, J. P. (2002). “Performance of structures with passive energy
dissipators.” Earthquake Spectra, 18(1), 105-119. Oesterle, M. G. (2003). “Use of incremental dynamic analysis to assess the performance
of steel moment-resisting frames with fluid viscous dampers.” Master of Science Thesis, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA.
Prakash, V., Powell, G. H., and Campbell, S. (1993). DRAIN-2DX Base Program
Description and User Guide: Version 1.10. Dept. of Civil Engineering, Univ. of California at Berkley.
Vamvatsikos, D. and Cornell, C. A. (2002). “Incremental dynamic analysis.” Earthquake
Eng. Struct. Dyn., 31(3), 491-514. Vamvatsikos, D. and Cornell, C. A. (2004). “Applied incremental dynamic analysis.”
Earthquake Spectra, 20(2), 523-553.
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Appendix A: User’s Guide to the NonlinPro IDA Collection Creator and the NonlinPro IDA Visualization Application A.1 Introduction
The NonlinPro IDA Collection Creator (NICC) and NonlinPro IDA Visualization
Application (NIVA) are computer applications designed to work in conjunction with the
structural analysis program NonlinPro (Charney and Barngrover 2006) to create and
visualize a complete incremental dynamic analysis. NICC allows the user to subject a
selected structure to an assortment of different ground motions, each scaled to a range of
incrementally increasing intensity levels, by taking an existing NonlinPro analysis
definition file and creating copies of the file with the correct ground motion data and
scale factors. These new files can then be input together as a single unit in NonlinPro.
Once all analyses have been performed, NIVA displays the results of these analyses in a
clear and concise manner.
This User’s Guide explains how to use both NICC and NIVA. It enumerates the
capabilities of both applications and describes them in detail. Screenshots from both
applications are included where appropriate to illustrate certain concepts. This User’s
Guide assumes that the user has a basic understanding of the DRAIN-2DX analysis
engine (Prakash and Powell 1993), the NonlinPro environment, and ASCE/SEI 7-05
building code (ASCE 2006). All questions regarding the use of DRAIN-2DX,
NonlinPro, and the ASCE/SEI 7-05 provisions are referred to the DRAIN-2DX user’s
Guide, the NonlinPro User’s Guide, and ASCE/SEI 7-05, respectively.
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A.2 NonlinPro IDA Collection Creator (NICC)
A.2.1 Before Using NICC
NICC accepts NonlinPro analysis definition files as input. These files have the extension
*.2dx or *.2dz. Files with the extension *.2dx are traditional individual NonlinPro input
files. Files with the extension *.2dz are identical to *.2dx files in format and function,
but are members in a file collection for ease of performing multiple analyses. Both file
types include all data necessary to define a stable structure including nodal and elemental
geometry, member types, and member properties. They also contain details about the
static and dynamic loads applied to the structure and the types of analyses which are to be
performed. Before using NICC, the user must create one of these files by using either the
NonlinPro preprocessor or a standard text editor. Once this is done, NICC can be used to
create a collection of *.2dz files which NonlinPro can read to perform an incremental
dynamic analysis (IDA).
NICC can generate two types of IDA collections, multiple earthquake IDAs and multiple
parameter IDAs. For a multiple earthquake IDA, NICC will copy all data segments
outlining the geometry and properties of the structural elements into each *.2dz file. No
other data segments are necessary, but if static gravity loads and analysis parameters are
included in the original file, they will also be copied into every new input file in the
collection. NICC will then write a unique ground motion definition and dynamic analysis
segment into each new file according to the specifications of the user. For a multiple
parameter IDA, NICC will copy all data segments detailing structural geometry and
properties except those regarding the chosen variable parameter. The variable parameter
in each file and the dynamic analysis segment in each new input file will be uniquely
written according to the specifications of the user. NICC will not copy modal analysis
segments, static pushover analysis segments, pre-existing ground motion definition
segments, or pre-existing dynamic analysis segments.
A.2.2 NICC Main Window
Upon startup of NICC, the main window, shown in Figure A.1, is displayed.
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Figure A.1: NICC Main Window
A.2.2.1 Collection Format
The topmost section of the window is labeled Collection Format. A focused view of this
section is displayed in Figure A.2. This is where the user determines very basic
information about the collection by entering the following information.
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Figure A.2: Collection Format Section
• Analysis Program: NICC is intended to be compatible with multiple structural
analysis programs. This capability is still in development, and this User’s Manual
will focus only on NonlinPro.
• IDA Type: In a multiple earthquake IDA, a structure is subjected to an
assortment of different ground motions, each scaled to a range of intensity levels.
In a multiple parameter IDA, a certain aspect of the structure, such as damping, is
given a range of specific values. For each of these values, the structure is
subjected to a single ground motion which is scaled to a range of intensity levels.
The user must select which type of IDA collection is to be created.
• Original NonlinPro Input File: NICC needs an original file containing all
details regarding structural geometry and member properties to replicate. Click
the Browse button to select this file. A file with either the extension *.2dx or the
extension *.2dz can be selected.
• New Collection Identifier: NICC will be writing many new files and needs to
know what name to give them. The first four characters of every new file will be
the identifier which is entered here. NICC will allow less than four characters to
be entered, but will truncate any identifier which contains greater than four
characters.
A.2.2.2 Collection Specifications
The large section below the Collection Format section on the main window is the Collection
Specification section. Focused views of this section are displayed in Figures A.3 and A.4.
Figure A.3 is the Collection Specifications section for a multiple earthquake IDA and Figure
A.4 is the Collection Specifications section for a multiple parameter IDA. This is where
the user defines the variable data that will be written into each new input file.
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Figure A.3: Collection Specifications Section for a Multiple Earthquake IDA
Figure A.4: Collection Specifications Section for a Multiple Parameter IDA
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For a multiple earthquake IDA, the following information must be provided.
• Ground Acceleration Files: NICC needs ground acceleration history files to
apply to the structure. Click the Add button to select these files. Only files with
the extension *.acn that meet the format followed by NonlinPro can be used.
Each selected file is added to the grid. The file pathname is displayed in the first
column. The number of data points contained in the record is displayed in the
second column. The constant time step between data points is displayed in the
third column. Adding an acceleration file that does not have a constant time step
will generate an error message upon file creation. The peak ground acceleration,
which NICC converts to gravity units, is displayed in the fourth column. The
factor by which the original record will be scaled is displayed in the fifth and final
column. This scale factor is initially set to equal unity, though the user will have
the opportunity to modify it later. Highlighting a row in the grid and clicking the
Remove button will remove that ground motion from the grid. Once one or more
records have been added to the grid, the records can be scaled and the ground
acceleration history plots can be viewed. These options will be discussed in more
detail later in the User’s Guide.
For a multiple parameter IDA, the following information must be provided.
• Parameter Scope: This is where the user selects the element group for which a
parameter will be modified. NICC will read the original input file and provide
options which can be selected using the drop-down list box.
• Variable Parameter: This is where the user selects the parameter which is to be
varied. NICC will read the original input file and provide options which can be
selected using the drop-down list box.
• Minimum Parameter Value: This is the smallest value which will be entered for
the variable parameter. Any positive number can be entered.
• Parameter Value Increment Size: The parameter value will be incrementally
increased by a constant step size. This is where the user selects what that step
size will be. Any positive number can be entered.
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• Number of Parameter Values: This positive integer determines the number
of times the variable parameter will be incremented.
• Ground Acceleration File: The Ground Acceleration File works the same way for
both multiple earthquake and multiple parameter IDAs. The only difference is
that only one file can be selected for a multiple parameter IDA.
The follow information must be provided for both multiple earthquake and multiple
parameter IDAs. With the exception of the Target Multiplier and the Number of
Increments, all of the following information is data required by DRAIN-2DX, and the
DRAIN-2DX User’s Guide can be referenced for more details.
• Target Multiplier: After each original ground acceleration record is multiplied
by the scale factor listed in the last column of its row in the grid, it is multiplied
by incrementally increasing factors to create sets of ground motions with the same
acceleration pattern but a range of different intensity levels. The Target Multiplier
is the largest incremental scale factor by which the original scaled ground
acceleration records will be multiplied.
• Number of Increments: This positive integer determines the number of
incremental scale factors by which each original scaled ground acceleration
record will be multiplied. The Target Multiplier divided by the Number of Increments
equals the value of the step size between incremental scale factors.
• Time Step Option: This option selects whether the structure will be analyzed
with a constant or variable time step.
• Acceleration Direction Code: Checking a direction code box will apply the
ground accelerations in the corresponding direction. The default is accelerations
applied in the X translational direction only.
• Time Increment: This is the duration of each record, in seconds, that will be
used in the analyses.
• Max. Time Steps: This is the maximum number of time steps that will be
considered during each analysis. This positive integer must be greater than the
Time Increment divided by the Optional Time Step.
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• Optional Time Step: For a constant time step, this is the size of the time step
during analyses. This value should be no greater than the record time step in a
ground acceleration file. For a variable time step, this is the size of the first step.
• X Center of Rotation: For the Z rotational direction, this is the X coordinate of the
center of rotation. The default value is zero.
• Y Center of Rotation: For the Z rotational direction, this is the Y coordinate of the
center of rotation. The default value is zero.
• Time Scale: This is the time scale factor. The default value is unity, and in
most cases this will not change due to the fact that a time scale factor can alter the
inherent frequencies in a ground acceleration record.
A.2.3 Ground Motion Scaling
Once one or more ground acceleration records have been added to the grid on the main
window, they can be scaled so that each record has the desired original intensity.
Clicking the Scale Ground Acceleration Records button on the main window will summon
the Scaling Options window. This window is displayed in Figure A.5. With this window,
the user can scale all the selected ground motions and view the scaled response spectrum
for each.
The legend is in the top left corner. Each ground acceleration file from the grid on the
main window is copied into the first column of the legend grid. The current scale factor
for each record is listed in the second column of the legend grid, and the color of the third
column corresponds to the scaled response spectrum of the that record on the graph.
The user has a choice of three scaling options in the section immediately below the
legend.
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Figure A.5 NICC Scaling Options Window
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• Scale to a specified period and pseudo-acceleration: This option scales
each ground motion so that the maximum pseudo-acceleration at the specified
period is equal to the specified pseudo-acceleration. The specified period is
usually the fundamental period of the structure, though any period between 0 and
10 seconds can be entered. The user inputs the pseudo-acceleration, the period,
and the damping of the structure, as shown in Figure A.6.
Figure A.6: Scale to a Specified Period and Pseudo-Acceleration
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• Scale according to the NEHRP Provisions: ASCE/SEI 7-05, which provides
essentially the same seismic design guidelines as the NEHRP Provisions (FEMA
2003), specifies that for two-dimensional analyses:
“The ground motions shall be scaled such that for each period between 0.2T and
1.5T (where T is the natural period of the structure in the fundamental mode for
the direction of response being analyzed) the average of the five-percent-damped
response spectra for the suite of motions is not less than the corresponding
ordinate of the design response spectrum, determined in accordance with Sec.
3.3.4 or 3.4.4.”
The user inputs the natural period of the structure and the site parameters to
calculate the design response spectrum, as shown in Figure A.7. To modify these
parameters, click the NEHRP Parameters button to bring up the NEHRP Spectrum
Parameters window, which is displayed in Figure A.8. The same scale factor is
calculated for all records using this option.
Figure A.7: Scale According to the NEHRP Provisions
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Figure A.8: NEHRP Spectrum Parameters Window
In this window, the user is asked to provide parameters for calculating design
response spectrum as per ASCE/SEI 7-05.
o Site Class: ACSE/SEI 7-05 defines a site class as “A classification
assigned to a site based on the types of soils present and their properties”.
The user is referred to the Provisions for further aid in selecting a site
class.
o Mapped Accelerations: The short period acceleration, Ss, and the one
second acceleration, S1, are the five-percent damped spectral accelerations
at periods of 0.2s and 1.0s, respectively. These values can be determined
from maps in ASCE/SEI 7-05.
o Total Damping: The design response spectrum assumes a structural
damping ratio of 5% of critical. This value cannot currently be modified.
o Miscellaneous: The user is given the option of calculating the design
spectral response acceleration parameter with or without a 2/3 factor.
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Checking the box includes the factor and leaving the box unchecked,
which indicates a return probability of 2% in 50 years, excludes the factor.
• Scale to the best fit of the NEHRP design spectrum over a range of periods: This
option scales the ground motions so that the square root of the sum of the squares
of the difference between the response spectrum of each ground motion and the
design response spectrum is minimized. The best fit is determined by trial and
error. The user inputs the lower and upper bounds of the period range, the
damping of the structure, the lower and upper bounds of the trial scale factors, the
increment by which the scale factor is increased for each trial, and the site
parameters to calculate the design response spectrum, as shown in Figure A.9. To
modify the NEHRP parameters, click the NEHRP Parameters button to bring up
the NEHRP Spectrum Parameters window.
Figure A.9: Scale to the Best Fit of the NEHRP Design Spectrum over a Range of
Periods
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Clicking the Scale button, which can be seen on the Scaling Options window in Figure A.5,
will use the selected scaling option to calculate the scaled response spectra for the ground
acceleration records and plot them together on the graph. If either of the second two
options is selected, the design response spectrum will also be plotted on the graph. The
scale factor used for each record will be displayed in the legend. Any plot generated
using this window can be printed using the File -> Print Plot menu option, or it can be sent
to a spreadsheet file using the File -> Create File menu option. To save the calculated
scale factors and return to the main window, click the OK button. To close the Scaling
Options window and return to the main window without saving the scale factors, click the
Cancel button.
A.2.4 Response Spectra Plot
Response spectra can be plotted for all ground acceleration records in the grid on the
main window, displayed in Figure A.1. Once at least one record has been added to the
grid, click the Response Spectra Plot button to summon the Response Spectra Plot window,
displayed in Figure A.10. The legend is to the left of the graph. Each ground
acceleration file from the grid on the main window is copied into the first column of the
legend grid. The current scale factor for each record is listed in the second column of the
legend grid, and the color of the third column corresponds to the scaled response
spectrum of the that record on the graph. Unlike the scaling window, this window cannot
be used to modify the ground motion records used in the analyses in any way. Its
purpose is solely to let the user view the response spectra of the selected ground motions.
However, the response spectra plot window has more advanced options regarding the
manner in which the response spectra are plotted.
• Plot Style: The user can choose to plot the response spectra for the peak pseudo-
acceleration, peak pseudo-velocity, or peak displacement of the linear structure.
In addition, all three response measures can be viewed on the same graph using a
tripartite plot. Checking the Plot Average Spectrum box will plot a white dashed
line representing the average of all selected spectra for any plot style.
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Figure A.10: NICC Response Spectra Plot Window
• Plot versus…: The user can change the X-axis to plot the response spectra versus
either the natural period or the natural frequency of a structure.
• Points per decade: This option determines the number of points plotted in the
spectra. Choosing lower numbers allows for faster calculation times, while
choosing higher numbers creates more complete curves.
• Damping: The default value is 5% of critical damping. If the ground
acceleration records have already been scaled, the damping ratio used to scale
them will be copied into this box. Damping cannot be modified using this
window.
• NEHRP Spectrum: Checking the Overlay NEHRP Spectrum box plots the 5%
damped design response spectrum as per ASCE/SEI 7-05 as a bold white line on
the graph for ease of comparison with the ground motion response spectra. To
modify the design spectrum parameters, click the NEHRP Parameters button to
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summon the NEHRP Spectrum Parameters window. This is the same window
associated with the design response spectrum on the Scaling Options window.
Once all of the viewing parameters have been set, the corresponding response spectra are
plotted on the graph at the right side of the window. Moving the mouse over the graph
causes the pseudo-acceleration, pseudo-velocity, displacement, period, and frequency to
be calculated for the cursor location. These values are displayed in the Spectral
Coordinates section in the center of the window. Any plot generated using this window
can be printed using the File -> Print Plot menu option, or it can be sent to a spreadsheet
file using the File -> Create File menu option.
A.2.5 Ground Acceleration History Plot
The ground acceleration history plot can be displayed for any ground motion by
highlighting that ground motion in the grid on the main form and clicking the Acceleration
History Plot button. This summons the Ground Acceleration History Plot window, displayed
in Figure A.11. NICCA copies all ground acceleration records selected on the main
window into the drop-down list box in the top left corner of the Ground Acceleration History
Plot window. When the user selects a ground acceleration record in this list box, the
record title will appear at the top of the window, and characteristic information including
the original peak ground acceleration, the scaled peak ground acceleration, the scale
factor, the number of data points, the time step, and the record duration are displayed at
the bottom of the form. The scaled acceleration history is plotted in the center graph. As
with the Response Spectra Plot window, this window is solely for viewing the ground
acceleration histories and cannot be used to modify ground motions for the analyses in
any way.
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Figure A.11: NICC Ground Acceleration History Plot Window
A.2.6 Creating an IDA Collection
Once the collection format has been determined and ground motions have been added,
scaled, and parameterized, then the new IDA collection of files can be generated. Click
the Create button at the bottom of the main window to begin the creation process. This
process may take a few seconds. If NICC is missing any information necessary for the
creation of an IDA collection, it will prompt the user to enter the appropriate data. All
files will be written to the directory in which the original input file is located. Once the
IDA file collection has been successfully created, a message box will appear to inform
the user and identify the new files. An example of this message box is displayed in
Figure A.12.
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Figure A.12: NICC File Writing Complete Message Box
The first file name listed in the message box is simply the new collection identifier with
the file extension *.wzm. This very important file is a record of all analysis definition
files written by the program during the creation process. This is the file NonlinPro will
read to perform an IDA on the collection that NICC just generated. To accomplish this,
simply open this file in NonlinPro, check the Options -> Run All menu option, then run
DRAIN-2DX.
The following file names listed in the message box are the individual analysis definition
files with the extension *.2dz that are read by NonlinPro. As mentioned earlier in this
User’s Guide, each file name begins with the new collection identifier. The last four
characters in each file name are digits identifying the ground motion or parameter value
and the incremental scale factor that were written to that file. For a multiple earthquake
IDA, the first two digits correspond to one of the ground motions in the grid on the main
window. For a multiple parameter IDA, the first two digits correspond to a specific
parameter value. For either IDA type, the second two digits distinguish which scale
factor increment is being applied to that ground motion. The lower digits correspond to
the smaller scale factors and the higher digits correspond to the larger scale factors. The
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user can direct NonlinPro to perform any of these analyses individually by opening the
desired *.2dz file in NonlinPro.
A.3 NonlinPro IDA Visualization Application (NIVA)
A.3.1 Before Using NIVA
The NonlinPro IDA Graphing Utility requires certain files created by NonlinPro as a
result of IDA process. This program assumes that these files exist in the same directory
as the *.wzm file and the *.2dz files created by NICC. Before using this program, the
user must create an IDA file collection using NICC and perform the analyses with
NonlinPro. Once all analyses have been run, the NIVA can be used to graphically
display the results of the IDA.
A.3.2 NIVA Main Window
Upon startup of NIVA, the main window, shown in Figure A.13, is displayed. The first
step to viewing IDA curves is to begin a new project. To clear all old data and start a
new project, click the File -> New -> Earthquake IDA menu option, or the File -> New ->
Parameter IDA menu option, depending on the type of IDA desired.
A.3.3 Creating a New Project Group
Before IDA curves can be plotted on the graph, the results from a collection of analyses
must be organized into files that can be read by NIVA. Clicking the Create -> New Project
Group -> From NonlinPro menu option brings up the Create New Project Group window.
This window is displayed in Figure A.14.
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Figure A.13: NIVA Main Window
Figure A.14: NIVA Create New Project Group Window
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The title entered into the upper box will be written into each input file, as well as
displayed at the top of the main window when the project group is loaded. Clicking the
Browse button allows the user to select a *.wzm file to use to create the new project
group. The results of the analyses from all files included in this *.wzm file will be
compiled into IDA input files with the extension *.ida. Clicking the Create and Load
Project button will write these *.ida files. This process may take a few minutes. Once all
files are written, they are loaded into NIVA and the Create New Project Group window
closes.
The user can view the contents of any loaded *.ida file by highlighting that file in the grid
on the main window, then selecting the View -> Input File menu option. This summons the
input file viewing window, displayed in Figure A.15. The title of the selected *.ida file is
displayed in the drop-down list box at the top of the window, and the contents of that file
are displayed below the title. As can be seen in the figure, The header of a *.ida file
includes the type of IDA, the analysis program, the project group title, the earthquake
title (or parameter value), the number of increments, and all *.2dz files used in the
creation of the *.ida file. The information following the header is the data used to create
the IDA curves on the main window. The user can choose to view other input files
without closing the input file viewing window by selecting the title of another file in the
drop-down list box.
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Figure A.15: NIVA Input File Viewing Window
A.3.4 Adding and Removing Files
There are two methods of loading *.ida files into NIVA. The first method was described
in the previous section. When a project group is created, all IDA input files are
automatically loaded and each file is listed in the grid on the main window. The user can
also add previously created IDA input files manually by clicking the Add button located
above the grid and selecting the desired file. All files added in this manner must be part
of the same project group. Attempting to add files from separate project groups will
generate an error message. The maximum number of files that can be loaded is 21.
The title of each loaded IDA input file is listed in the first column of the grid on the main
window. The second column of the grid is a checkbox surrounded by a unique color. An
example of this is illustrated in Figure A.16. This figure is an example of a multiple
earthquake IDA grid. A multiple parameter IDA grid would be labeled Available
Parameters, and the parameter value for each file would be listed in the first column of the
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grid. Checking the box next to a file title tells the program to include that file when
plotting the IDA curves on the graph. The IDA curve for that file will be drawn in the
same color that surrounds the checkbox. The program will temporarily ignore the file
corresponding to any unchecked box, but that file will not be unloaded. Loaded files can
be unloaded from the program by highlighting the file the user wishes to unload and
clicking the Remove button. Files can be individually unloaded whether they were
automatically loaded during the project group creation process or manually loaded by the
user. Files can be reloaded by clicking the Add button.
Figure A.16: NIVA Available Earthquakes Grid
A.3.5 Plotting IDA Curves
Once *.ida files have been loaded into the program, IDA curves can be plotted on the
graph. The user has many options when plotting these curves. The drop-down list boxes
above the graph allow the user to select a structural element on which to focus. Figure
A.17 provides a close up view of these list boxes. The topmost list box, determines the
current element group. This list box is expanded in Figure A.18.
118
Figure A.17: NIVA Node/Element Group Selection
FigureA.18: NIVA Expanded Node/Element Group Selection
For a NonlinPro IDA, the first option in this list box will always be Nodes and contain all
the nodes of the structure. This option is followed by the user-defined elements groups,
identified by number and type. Making a selection in this list box will fill the two drop
down list boxes directly below it with names of all nodes or elements in that group. The
leftmost of these two list boxes is expanded in Figure A.19. This is where the user
selects the individual element for which the IDA curves will be plotted.
119
Figure A.19: NIVA Expanded Node Selection
The rightmost of the two list boxes under the group selection list box is disabled by
default. Checking the Plot combination checkbox will cause it to become enabled. When
this box is unchecked, IDA curves will be drawn only for the node or element selected in
the left list box. When the box is checked, IDA curves will be drawn for the difference
between the two nodes or elements selected in the left and right list boxes. This feature is
useful in calculating IDA curves for interstory drifts.
Using the group selection list box to choose a node or element group also fills the drop
down list box in the bottom right corner of the window with the potential damage
measures for that node or element group. This list box is expanded in Figure A.20,
displaying the damage measure options for the Nodes group. The damage measure
selected in this list box will become the X-axis value for the IDA curves.
120
Figure A.20: NIVA Damage Measure Selection
Once the desired node or element and a corresponding damage meter have been selected
in these list boxes, IDA curves can be plotted. Clicking the Graph button in the top right
corner of the main window plots the IDA curves on the graph. Figure A.21 provides a
close up view of this corner.
Figure A.21: NIVA Graphing Button
121
If the Plot Data Points check box underneath the Graph button is left unchecked, the
program will plot smooth IDA curves. If it is checked, small circles will be drawn at the
individual data points along each IDA curve. The small colored picture box to the right
of the Graph button is a signal informing the user if the graph is up to date. If the box is
red, modifications have been made to the IDA graphing parameters since the last time the
curves were plotted. If the box is green, the graph is current. This is good to know
because some features of the program only operate when the graph is up to date. An
example of a plotted set of IDA curves is displayed in Figure A.22.
Figure A.22: NIVA IDA Curves
A.3.6 Response History Plots
Each point on an IDA curve is the maximum value of a specific damage measure from a
time history analysis for a particular ground motion intensity. Clicking on any of these
points on the graph will bring up a new window, displaying the response history plots for
the current damage meter from all selected ground motions scaled to the intensity of the
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clicked point. This window is displayed in Figure A.23. This feature will only work if
the graph is up to date.
Figure A.23: NIVA Response History Plot Window
The selected node or element and damage meter are listed in the title bar of the window.
The selected scale factor is listed in the drop down list box in the top left corner of the
window. Selecting a different scale factor in this list box will plot the response histories
of the structure for the ground motions at that intensity.
A.3.7 Performance Objectives
NIVA is capable of plotting three difference levels of performance objectives on the
graph along with the IDA curves. This can be done in two ways using the tools in the
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Performance Objectives frame in the bottom left corner of the main window, which is
displayed in Figure A.24.
Figure A.24: NIVA Performance Objectives
The first method of plotting performance objectives is to manually enter the scale factor
and response restrictions into the text boxes in the Performance Objectives section before
plotting the graph. Any values entered into these text boxes will be plotted on the graph
with the IDA curves when the Graph button is clicked. The second method is to plot the
desired IDA curves and draw the performance objectives graphically. Once the graph is
up to date, the three buttons labeled Draw will become active. Clicking any of these Draw
buttons will enable Draw Mode for the corresponding performance objective. While in
draw mode, the mouse cursor becomes a crosshair when positioned over the graph.
Clicking and dragging a rectangle on the graph will assign the boundaries of that
rectangle to the range restrictions of the selected performance objective and draw those
restrictions on the graph. Once performance objective boundaries have been drawn, they
can be manually fine-tuned using the text boxes in the Performance Objective section. As
long as the graph is current, these manual modifications will be drawn immediately.
Clicking one of the Draw buttons while in Draw Mode will exit Draw Mode. Clicking
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one of the Reset buttons will clear the current range restrictions for the corresponding
performance objective and update the graph. A complete IDA plot with performance
objectives is displayed in Figure A.25.
Figure A.25: NIVA IDA Study with Performance Objectives
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Appendix B: IDA Studies B.1 Three Story Models
B.1.1 Three Story Stiffness Design
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1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.1: 1st Story Drift for Three Story Stiffness Design
126
0
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2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.2: 2nd Story Drift for Three Story Stiffness Design
0
0.2
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0.6
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0 4 8 12 16
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.3: 3rd Story Drift for Three Story Stiffness Design
127
0
0.2
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1.2
1.4
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2
0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.4: Base Shear for Three Story Stiffness Design
128
B.1.2 Three Story Strength Design with Inherent Damping
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0 4 8 12 16
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
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Figure B.5: 1st Story Drift for Three Story Strength Design with Inherent Damping
0
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0.6
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0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.6: 2nd Story Drift for Three Story Strength Design with Inherent Damping
129
0
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0 4 8 12 16
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.7: 3rd Story Drift for Three Story Strength Design with Inherent Damping
0
0.2
0.4
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0.8
1
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1.6
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2
0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.8: Base Shear for Three Story Strength Design with Inherent Damping
130
B.1.3 Three Story Strength Design with 5% Damping
0
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0 4 8 12 16
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.9: 1st Story Drift for Three Story Strength Design with 5% Damping
0
0.2
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0.6
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1.8
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0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.10: 2nd Story Drift for Three Story Strength Design with 5% Damping
131
0
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3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.11: 3rd Story Drift for Three Story Strength Design with 5% Damping
0
0.2
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0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.12: Base Shear for Three Story Strength Design with 5% Damping
132
B.1.4 Three Story Strength Design with 10% Damping
0
0.2
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0 4 8 12 16
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.13: 1st Story Drift for Three Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
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1.2
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1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.14: 2nd Story Drift for Three Story Strength Design with 10% Damping
133
0
0.2
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1.2
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1.6
1.8
2
0 4 8 12 16
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.15: 3rd Story Drift for Three Story Strength Design with 10% Damping
0
0.2
0.4
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1
1.2
1.4
1.6
1.8
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0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.16: Base Shear for Three Story Strength Design with 10% Damping
134
B.1.5 Three Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.17: 1st Story Drift for Three Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.18: 2nd Story Drift for Three Story Strength Design with 20% Damping
135
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.19: 3rd Story Drift for Three Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.20: Base Shear for Three Story Strength Design with 20% Damping
136
B.1.6 Three Story Strength Design with 30% Damping
0
0.2
0.4
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0.8
1
1.2
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1.6
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2
0 4 8 12 16
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.21: 1st Story Drift for Three Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 4 8 12 16
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.22: 2nd Story Drift for Three Story Strength Design with 30% Damping
137
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
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2
0 4 8 12 16
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.23: 3rd Story Drift for Three Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 500 1000 1500 2000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.24: Base Shear for Three Story Strength Design with 30% Damping
138
B.1.7 Three Story Strength Design Parameter IDA Studies
0
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2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.25: Roof Displacement for Three Story Strength Design Subject to se02fp0
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Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.26: Roof Displacement for Three Story Strength Design Subject to se02fp1
139
0
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Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.27: Roof Displacement for Three Story Strength Design Subject to se02fp2
0
0.2
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0.8
1
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1.4
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0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.28: Roof Displacement for Three Story Strength Design Subject to se02fp3
140
0
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1
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2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.29: Roof Displacement for Three Story Strength Design Subject to se02fp4
0
0.2
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0.8
1
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1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.30: Roof Displacement for Three Story Strength Design Subject to se02fp5
141
0
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1
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2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.31: Roof Displacement for Three Story Strength Design Subject to se02fp6
0
0.2
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0.6
0.8
1
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1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.32: Roof Displacement for Three Story Strength Design Subject to se02fp7
142
0
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1
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2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.33: Roof Displacement for Three Story Strength Design Subject to se02fp8
0
0.2
0.4
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0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.34: Roof Displacement for Three Story Strength Design Subject to se02fp9
143
0
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1
1.2
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1.6
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2
0 500 1000 1500
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.35: Base Shear for Three Story Strength Design Subject to se02fp0
0
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1
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1.4
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2
0 500 1000 1500
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.36: Base Shear for Three Story Strength Design Subject to se02fp1
144
0
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1
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.37: Base Shear for Three Story Strength Design Subject to se02fp2
0
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1
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2
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
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Figure B.38: Base Shear for Three Story Strength Design Subject to se02fp3
145
0
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.39: Base Shear for Three Story Strength Design Subject to se02fp4
0
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1
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2
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
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Figure B.40: Base Shear for Three Story Strength Design Subject to se02fp5
146
0
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.41: Base Shear for Three Story Strength Design Subject to se02fp6
0
0.2
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1
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1.8
2
0 500 1000 1500
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
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Figure B.42: Base Shear for Three Story Strength Design Subject to se02fp7
147
0
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Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
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20% Damping30% Damping
Figure B.43: Base Shear for Three Story Strength Design Subject to se02fp8
0
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Base Shear (k)
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e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.44: Base Shear for Three Story Strength Design Subject to se02fp9
148
B.2 Nine Story Models
B.2.1 Nine Story Stiffness Design
0
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0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.45: 1st Story Drift for Nine Story Stiffness Design
149
0
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Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.46: 2nd Story Drift for Nine Story Stiffness Design
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.47: 3rd Story Drift for Nine Story Stiffness Design
150
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.48: 4th Story Drift for Nine Story Stiffness Design
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.49: 5th Story Drift for Nine Story Stiffness Design
151
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.50: 6th Story Drift for Nine Story Stiffness Design
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.51: 7th Story Drift for Nine Story Stiffness Design
152
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.52: 8th Story Drift for Nine Story Stiffness Design
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.53: 9th Story Drift for Nine Story Stiffness Design
153
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.54: Base Shear for Nine Story Stiffness Design
154
B.2.2 Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.55: 1st Story Drift for Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.56: 2nd Story Drift for Nine Story Strength Design with Inherent Damping
155
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.57: 3rd Story Drift for Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.58: 4th Story Drift for Nine Story Strength Design with Inherent Damping
156
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.59: 5th Story Drift for Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.60: 6th Story Drift for Nine Story Strength Design with Inherent Damping
157
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.61: 7th Story Drift for Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.62: 8th Story Drift for Nine Story Strength Design with Inherent Damping
158
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.63: 9th Story Drift for Nine Story Strength Design with Inherent Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.64: Base Shear for Nine Story Strength Design with Inherent Damping
159
B.2.3 Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.65: 1st Story Drift for Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.66: 2nd Story Drift for Nine Story Strength Design with 5% Damping
160
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.67: 3rd Story Drift for Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.68: 4th Story Drift for Nine Story Strength Design with 5% Damping
161
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.69: 5th Story Drift for Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.70: 6th Story Drift for Nine Story Strength Design with 5% Damping
162
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.71: 7th Story Drift for Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.72: 8th Story Drift for Nine Story Strength Design with 5% Damping
163
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.73: 9th Story Drift for Nine Story Strength Design with 5% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.74: Base Shear for Nine Story Strength Design with 5% Damping
164
B.2.4 Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.75: 1st Story Drift for Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.76: 2nd Story Drift for Nine Story Strength Design with 10% Damping
165
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.77: 3rd Story Drift for Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.78: 4th Story Drift for Nine Story Strength Design with 10% Damping
166
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.79: 5th Story Drift for Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.80: 6th Story Drift for Nine Story Strength Design with 10% Damping
167
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.81: 7th Story Drift for Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.82: 8th Story Drift for Nine Story Strength Design with 10% Damping
168
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.83: 9th Story Drift for Nine Story Strength Design with 10% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.84: Base Shear for Nine Story Strength Design with 10% Damping
169
B.2.5 Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.85: 1st Story Drift for Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.86: 2nd Story Drift for Nine Story Strength Design with 20% Damping
170
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.87: 3rd Story Drift for Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.88: 4th Story Drift for Nine Story Strength Design with 20% Damping
171
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.89: 5th Story Drift for Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.90: 6th Story Drift for Nine Story Strength Design with 20% Damping
172
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.91: 7th Story Drift for Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.92: 8th Story Drift for Nine Story Strength Design with 20% Damping
173
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.93: 9th Story Drift for Nine Story Strength Design with 20% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.94: Base Shear for Nine Story Strength Design with 20% Damping
174
B.2.6 Nine Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
1st Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.95: 1st Story Drift for Nine Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
2nd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.96: 2nd Story Drift for Nine Story Strength Design with 30% Damping
175
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
3rd Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.97: 3rd Story Drift for Nine Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
4th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.98: 4th Story Drift for Nine Story Strength Design with 30% Damping
176
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
5th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.99: 5th Story Drift for Nine Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
6th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.100: 6th Story Drift for Nine Story Strength Design with 30% Damping
177
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
7th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.101: 7th Story Drift for Nine Story Strength Design with 30% Damping
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
8th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.102: 8th Story Drift for Nine Story Strength Design with 30% Damping
178
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 2 4 6 8 10
9th Story Drift (in)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.103: 9th Story Drift for Nine Story Strength Design with 30% Damping
0
0.2
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0.6
0.8
1
1.2
1.4
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1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
se02fp0
se02fp1
se02fp2
se02fp3
se02fp4
se02fp5
se02fp6
se02fp7
se02fp8
se02fp9
Figure B.104: Base Shear for Nine Story Strength Design with 30% Damping
179
B.2.7 Nine Story Strength Design Parameter IDA Studies
0
0.2
0.4
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0.8
1
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1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.105: Roof Displacement for Nine Story Strength Design Subject to se02fp0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.106: Roof Displacement for Nine Story Strength Design Subject to se02fp1
180
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.107: Roof Displacement for Nine Story Strength Design Subject to se02fp2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.108: Roof Displacement for Nine Story Strength Design Subject to se02fp3
181
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.109: Roof Displacement for Nine Story Strength Design Subject to se02fp4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.110: Roof Displacement for Nine Story Strength Design Subject to se02fp5
182
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.111: Roof Displacement for Nine Story Strength Design Subject to se02fp6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.112: Roof Displacement for Nine Story Strength Design Subject to se02fp7
183
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.113: Roof Displacement for Nine Story Strength Design Subject to se02fp8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50
Roof Displacement (in)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.114: Roof Displacement for Nine Story Strength Design Subject to se02fp9
184
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.115: Base Shear for Nine Story Strength Design Subject to se02fp0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.116: Base Shear for Nine Story Strength Design Subject to se02fp1
185
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.117: Base Shear for Nine Story Strength Design Subject to se02fp2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.118: Base Shear for Nine Story Strength Design Subject to se02fp3
186
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.119: Base Shear for Nine Story Strength Design Subject to se02fp4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.120: Base Shear for Nine Story Strength Design Subject to se02fp5
187
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.121: Base Shear for Nine Story Strength Design Subject to se02fp6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.122: Base Shear for Nine Story Strength Design Subject to se02fp7
188
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.123: Base Shear for Nine Story Strength Design Subject to se02fp8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1000 2000 3000 4000 5000
Base Shear (k)
Scal
e Fa
ctor
Inherent Damping
5% Damping
10% Damping
20% Damping30% Damping
Figure B.124: Base Shear for Nine Story Strength Design Subject to se02fp9
189
VITA Stephanie Jean Kruep graduated as a salutatorian of the Northwest High School Class of
2000 in Greensboro, North Carolina, after which she enrolled in the engineering program
at North Carolina State University in Raleigh. There, she was a charter member of the
University Honors Program, a drummer in the Power Sound of the South Marching Band,
a Brother of Mu Beta Psi, a Toni Christine Masini Memorial Scholarship recipient, and
an inductee of both Tau Beta Pi and Chi Epsilon. She graduated in Spring of 2005 with a
Bachelor of Science degree in Civil Engineering and a minor in percussion performance,
but not before being accepted into the Structural Engineering and Materials Program at
the Virginia Polytechnic Institute and State University. Stephanie began her studies at
Virginia Tech in Fall of 2005 and is currently completing the requirements for a Master
of Science degree in Civil Engineering, to graduate in Summer of 2007.