Thesis ETD

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 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.35: Base Shear for Three Story Strength Design Subject to se02fp0 ..................................................................................... 143










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 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

1

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.


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


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



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


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



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


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


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


0

1

2

3

4

5

6

7

0 1 2 3 4 5


Pseu

do-A

ccel

erat

ion

(g)

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9

Design Spectrum


T = 1.042s for Three Story Stiffness Design

59

Table 3.4 Nine Story Strength Design Scaling Properties


0

1

2

3

4

5

6

7

0 1 2 3 4 5


Pseu

do-A

ccel

erat

ion

(g)

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9

Design Spectrum


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


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


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


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% 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


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


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


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


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.

92

• 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.

93

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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.

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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

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95

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.

96

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.

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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.

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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.

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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

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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

0

0.2

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1

1.2

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1.6

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0 4 8 12 16

1st Story Drift (in)

Scal

e Fa

ctor

se02fp0

se02fp1

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Figure B.1: 1st Story Drift for Three Story Stiffness Design

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

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0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

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se02fp4

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Figure B.2: 2nd Story Drift for Three Story Stiffness Design

0

0.2

0.4

0.6

0.8

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1.2

1.4

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0 4 8 12 16

3rd Story Drift (in)

Scal

e Fa

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se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

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Figure B.3: 3rd Story Drift for Three Story Stiffness Design

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0

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0 500 1000 1500 2000

Base Shear (k)

Scal

e Fa

ctor

se02fp0

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Figure B.4: Base Shear for Three Story Stiffness Design

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B.1.2 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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9

Figure B.5: 1st 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


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

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


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

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.8: Base Shear for Three Story Strength Design with Inherent Damping

130

B.1.3 Three 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 4 8 12 16


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

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


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

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


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

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.12: Base Shear for Three Story Strength Design with 5% Damping

132


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


133

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


134


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


136


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


137

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


138

B.1.7 Three Story Strength Design Parameter IDA Studies

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping


Figure B.25: 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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



139

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



140

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



141

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



142

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



143

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


Figure B.35: Base Shear 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

0 500 1000 1500

Base Shear (k)

Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



144

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



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



145

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



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



146

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



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



147

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



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



148

B.2 Nine Story Models

B.2.1 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


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

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10


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


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


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


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


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


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


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


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


169


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


174


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


Scal

e Fa

ctor

se02fp0

se02fp1

se02fp2

se02fp3

se02fp4

se02fp5

se02fp6

se02fp7

se02fp8

se02fp9


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


179

B.2.7 Nine Story Strength Design Parameter IDA Studies

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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% 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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


Scal

e Fa

ctor

Inherent Damping

5% Damping

10% Damping



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


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



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



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



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



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



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



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



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



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



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.

Thesis ETD

Documents

vina del mar

erzinican

1st story

5th story

2nd story

4th story

9th story

6th story