Using Incremental Dynamic Analysis to Visualize the Effects of Viscous Fluid Dampers on Steel Moment Frame Drift

Transcription

1 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 Committee Member Dr. Elisa Sotelino Committee Member July 3, 7 Blacksburg, Virginia Keywords: Damping, Drift, Incremental Dynamic Analysis, Passive Energy, Seismic Design, Steel Structures, Structural Dynamics

2 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%, %, %, and 3% 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 3% 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.

3 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. iii

4 Table of Contents TABLE OF CONTENTS... IV LIST OF FIGURES... VI LIST OF TABLES... XII CHAPTER : INTRODUCTION.... BACKGROUND.... LITERATURE SURVEY OF DAMPING IN STEEL MOMENT FRAMES....3 LITERATURE SURVEY OF INCREMENTAL DYNAMIC ANALYSIS OBJECTIVE AND SCOPE... 3 CHAPTER : MODELS OVERVIEW MODEL GEOMETRY Three Story Model Geometry Nine Story Model Geometry GRAVITY LOADS AND MASSES REGIONAL PARAMETERS, DESIGN ASSUMPTIONS, AND LATERAL LOADS Seismic Design Loads Wind Design Loads P-DELTA EFFECTS JOINT MODELING STRENGTH CONTROLLED FRAME DESIGN DAMPING STIFFNESS CONTROLLED FRAME DESIGN COMPUTER AIDED STRUCTURAL MODELING USING NONLINPRO CHAPTER 3: INCREMENTAL DYNAMIC ANALYSIS DEVELOPMENT OVERVIEW GROUND MOTION SELECTION INTENSITY MEASURES ENGINEERING DEMAND PARAMETERS COMPUTER AIDED IDA DEVELOPMENT NICC Requirements NICC Collection Format and Specifications NICC Ground Acceleration Record Scaling NICC Ground Acceleration History and Response Spectra Visualization IDA DEVELOPMENT FOR THE CURRENT STUDY CHAPTER 4: INCREMENTAL DYNAMIC ANALYSIS APPLICATION OVERVIEW IDA CURVES LIMIT STATES COMPUTER AIDED IDA VISUALIZATION NIVA Requirements NIVA Main Window and *.ida Files NIVA IDA Plotting Functions NIVA Performance Objectives and Response Histories CHAPTER 5: RESULTS AND DISCUSSION OVERVIEW iv

5 5. CODE COMPLIANCE Three Story Strength Design Code Compliance Nine Story Strength Design Code Compliance Base Shear and Feasibility BENEFITS OF INCREMENTAL DYNAMIC ANALYSIS IDA Studies of Stiffness Designed Models : IDA Studies of Strength Designed Models CHAPTER 6: CONCLUSION SUMMARY LIMITATIONS AND SUGGESTIONS FOR FUTURE WORK... 9 REFERENCES APPENDIX A: USER S GUIDE TO THE NONLINPRO IDA COLLECTION CREATOR AND THE NONLINPRO IDA VISUALIZATION APPLICATION APPENDIX B: IDA STUDIES... 5 VITA v

6 List of Figures Figure.: Viscous Fluid Dampers in a Chevron Brace Configuration... 3 Figure.: Viscous Fluid Dampers Exposed in a Building... 3 Figure.3: Single IDA Curve... 7 Figure.4: Multiple Earthquake IDA Study... 9 Figure.5: Multiple Parameter IDA Study... 9 Figure.: Three Story Model Elevation... 5 Figure.: Three Story Model Floor Plan... 5 Figure.3: Nine Story Model Elevation... 7 Figure.4: Nine Story Model Floor Plan... 7 Figure.5: Design Response Spectra... 3 Figure.6: P-delta Ghost Frame... 6 Figure.7: Krawinkler Joint Model... 7 Figure.8: Elevation of the Three Story Seattle Model Designed for Strength... 9 Figure.9: Elevation of the Nine Story Seattle Model Designed for Strength... 3 Figure.: Elevation of the Three Story Boston Model Designed for Strength... 3 Figure.: Elevation of the Nine Story Boston Model Designed for Strength... 3 Figure.: Damping Ghost Frame Figure.3: Elevation of the Three Story Seattle Model Designed for Stiffness Figure.4: Elevation of the Nine Story Seattle Model Designed for Stiffness Figure 3.: NICC Main Window Figure 3.: Collection Specifications Section for a Multiple Earthquake IDA Figure 3.3: Collection Specifications Section for a Multiple Parameter IDA Figure 3.4: NICC Scaling Options Window Figure 3.5: NICC Ground Acceleration History Plot Window Figure 3.6: NICC Response Spectra Plot Window Figure 3.7: Unscaled 5% Damped Ground Acceleration Response Spectra... 5 Figure 3.8: Ground Acceleration History for Mendocino, Figure 3.9: Ground Acceleration History for Erzinican Meteorological Station, Figure 3.: Ground Acceleration History for Olympia Highway Test Lab, Figure 3.: Ground Acceleration History for Olympia Highway Test Lab, Figure 3.: Ground Acceleration History for Llolleo, Chile, Figure 3.3: Ground Acceleration History for Vina del Mar, Chile, Figure 3.4: Ground Acceleration History for Deep Interplate (simulation) Figure 3.5: Ground Acceleration History for Miyagi-oki, Figure 3.6: Ground Acceleration History for Shallow Interplate (simulation) Figure 3.7: Ground Acceleration History for Shallow Interplate (simulation) Figure 3.8: 5% Damped Ground Acceleration Response Spectra Scaled to.3g at T =.565s for Three Story Strength Design Figure 3.9: 5% Damped Ground Acceleration Response Spectra Scaled to.48g at T =.4s for Three Story Stiffness Design Figure 3.: 5% Damped Ground Acceleration Response Spectra Scaled to.7g at T =.964s for Nine Story Strength Design vi

7 Figure 3.: 5% Damped Ground Acceleration Response Spectra Scaled to.9g at T =.634s for Nine Story Stiffness Design... 6 Figure 4.: Typical IDA Curve Characteristics... 6 Figure 4.: NIVA Main Window Figure 4.3: NIVA Create New Project Group Window Figure 4.4: NIVA IDA Curve and Performance Objective Example Figure 4.5: NIVA Response History Viewing Window Figure 5.: IDA Study for nd Story Drift of Three Story Stiffness Design Figure 5.: IDA Study for 5 th Story Drift of Nine Story Stiffness Design Figure 5.3: IDA Study of nd Story Drift for Three Story Strength Design with Inherent Damping Figure 5.4: IDA Study of nd Story Drift for Three Story Strength Design with 5% Damping Figure 5.5: IDA Study of nd Story Drift for Three Story Strength Design with % Damping Figure 5.6: IDA Study of nd Story Drift for Three Story Strength Design with % Damping Figure 5.7: IDA Study of nd Story Drift for Three Story Strength Design with 3% Damping... 8 Figure 5.8: IDA Study of 5 th Story Drift for Nine Story Strength Design with Inherent Damping...8 Figure 5.9: IDA Study of 5 th Story Drift for Nine Story Strength Design with 5% Damping... 8 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with % Damping... 8 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with % Damping... 8 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with 3% Damping Figure 5.3: IDA Study of Roof Displacement for Three Story Strength Design Subject to sefp Figure 5.4: IDA Study of Roof Displacement for Nine Story Strength Design Subject to sefp Figure 5.5: IDA Study of Total Base Shear for Three Story Strength Design Subject to sefp Figure 5.6: IDA Study of Total Base Shear for Three Story Strength Design Subject to sefp Figure 5.7: IDA Study of Total Base Shear for Nine Story Strength Design Subject to sefp Figure 5.8: IDA Study of Total Base Shear for Nine Story Strength Design Subject to sefp Figure A.: NICC Main Window Figure A.: Collection Format Section Figure A.3: Collection Specifications Section for a Multiple Earthquake IDA Figure A.4: Collection Specifications Section for a Multiple Parameter IDA Figure A.5: NICC Scaling Options Window... 3 vii

8 Figure A.6: Scale to a Specified Period and Pseudo-Acceleration... 4 Figure A.7: Scale According to the NEHRP Provisions... 5 Figure A.8: NEHRP Spectrum Parameters Window... 6 Figure A.9: Scale to the Best Fit of the NEHRP Design Spectrum over a Range of Periods... 7 Figure A.: NICC Response Spectra Plot Window... 9 Figure A.: NICC Ground Acceleration History Plot Window... Figure A.: NICC File Writing Complete Message Box... Figure A.3: NIVA Main Window... 4 Figure A.4: NIVA Create New Project Group Window... 4 Figure A.5: NIVA Input File Viewing Window... 6 Figure A.6: NIVA Available Earthquakes Grid... 7 Figure A.7: NIVA Node/Element Group Selection... 8 Figure A.8: NIVA Expanded Node/Element Group Selection... 8 Figure A.9: NIVA Expanded Node Selection... 9 Figure A.: NIVA Damage Measure Selection... Figure A.: NIVA Graphing Button... Figure A.: NIVA IDA Curves... Figure A.3: NIVA Response History Plot Window... Figure A.4: NIVA Performance Objectives... 3 Figure A.5: NIVA IDA Study with Performance Objectives... 4 Figure B.: st Story Drift for Three Story Stiffness Design... 5 Figure B.: nd Story Drift for Three Story Stiffness Design... 6 Figure B.3: 3 rd Story Drift for Three Story Stiffness Design... 6 Figure B.4: Base Shear for Three Story Stiffness Design... 7 Figure B.5: st Story Drift for Three Story Strength Design with Inherent Damping... 8 Figure B.6: nd Story Drift for Three Story Strength Design with Inherent Damping.. 8 Figure B.7: 3 rd Story Drift for Three Story Strength Design with Inherent Damping... 9 Figure B.8: Base Shear for Three Story Strength Design with Inherent Damping... 9 Figure B.9: st Story Drift for Three Story Strength Design with 5% Damping... 3 Figure B.: nd Story Drift for Three Story Strength Design with 5% Damping... 3 Figure B.: 3 rd Story Drift for Three Story Strength Design with 5% Damping... 3 Figure B.: Base Shear for Three Story Strength Design with 5% Damping... 3 Figure B.3: st Story Drift for Three Story Strength Design with % Damping... 3 Figure B.4: nd Story Drift for Three Story Strength Design with % Damping... 3 Figure B.5: 3 rd Story Drift for Three Story Strength Design with % Damping Figure B.6: Base Shear for Three Story Strength Design with % Damping Figure B.7: st Story Drift for Three Story Strength Design with % Damping Figure B.8: nd Story Drift for Three Story Strength Design with % Damping Figure B.9: 3 rd Story Drift for Three Story Strength Design with % Damping Figure B.: Base Shear for Three Story Strength Design with % Damping Figure B.: st Story Drift for Three Story Strength Design with 3% Damping Figure B.: nd Story Drift for Three Story Strength Design with 3% Damping Figure B.3: 3 rd Story Drift for Three Story Strength Design with 3% Damping Figure B.4: Base Shear for Three Story Strength Design with 3% Damping viii

9 Figure B.5: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.6: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.7: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.8: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.9: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.3: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.3: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.3: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.33: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.34: Roof Displacement for Three Story Strength Design Subject to sefp Figure B.35: Base Shear for Three Story Strength Design Subject to sefp Figure B.36: Base Shear for Three Story Strength Design Subject to sefp Figure B.37: Base Shear for Three Story Strength Design Subject to sefp Figure B.38: Base Shear for Three Story Strength Design Subject to sefp Figure B.39: Base Shear for Three Story Strength Design Subject to sefp Figure B.4: Base Shear for Three Story Strength Design Subject to sefp Figure B.4: Base Shear for Three Story Strength Design Subject to sefp Figure B.4: Base Shear for Three Story Strength Design Subject to sefp Figure B.43: Base Shear for Three Story Strength Design Subject to sefp Figure B.44: Base Shear for Three Story Strength Design Subject to sefp Figure B.45: st Story Drift for Nine Story Stiffness Design Figure B.46: nd Story Drift for Nine Story Stiffness Design Figure B.47: 3 rd Story Drift for Nine Story Stiffness Design Figure B.48: 4 th Story Drift for Nine Story Stiffness Design... 5 Figure B.49: 5 th Story Drift for Nine Story Stiffness Design... 5 Figure B.5: 6 th Story Drift for Nine Story Stiffness Design... 5 ix

10 Figure B.5: 7 th Story Drift for Nine Story Stiffness Design... 5 Figure B.5: 8 th Story Drift for Nine Story Stiffness Design... 5 Figure B.53: 9 th Story Drift for Nine Story Stiffness Design... 5 Figure B.54: Base Shear for Nine Story Stiffness Design Figure B.55: st Story Drift for Nine Story Strength Design with Inherent Damping Figure B.56: nd Story Drift for Nine Story Strength Design with Inherent Damping.. 54 Figure B.57: 3 rd Story Drift for Nine Story Strength Design with Inherent Damping.. 55 Figure B.58: 4 th Story Drift for Nine Story Strength Design with Inherent Damping.. 55 Figure B.59: 5 th Story Drift for Nine Story Strength Design with Inherent Damping.. 56 Figure B.6: 6 th Story Drift for Nine Story Strength Design with Inherent Damping.. 56 Figure B.6: 7 th Story Drift for Nine Story Strength Design with Inherent Damping.. 57 Figure B.6: 8 th Story Drift for Nine Story Strength Design with Inherent Damping.. 57 Figure B.63: 9 th Story Drift for Nine Story Strength Design with Inherent Damping.. 58 Figure B.64: Base Shear for Nine Story Strength Design with Inherent Damping Figure B.65: st Story Drift for Nine Story Strength Design with 5% Damping Figure B.66: nd Story Drift for Nine Story Strength Design with 5% Damping Figure B.67: 3 rd Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.68: 4 th Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.69: 5 th Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.7: 6 th Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.7: 7 th Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.7: 8 th Story Drift for Nine Story Strength Design with 5% Damping... 6 Figure B.73: 9 th Story Drift for Nine Story Strength Design with 5% Damping Figure B.74: Base Shear for Nine Story Strength Design with 5% Damping Figure B.75: st Story Drift for Nine Story Strength Design with % Damping Figure B.76: nd Story Drift for Nine Story Strength Design with % Damping Figure B.77: 3 rd Story Drift for Nine Story Strength Design with % Damping Figure B.78: 4 th Story Drift for Nine Story Strength Design with % Damping Figure B.79: 5 th Story Drift for Nine Story Strength Design with % Damping Figure B.8: 6 th Story Drift for Nine Story Strength Design with % Damping Figure B.8: 7 th Story Drift for Nine Story Strength Design with % Damping Figure B.8: 8 th Story Drift for Nine Story Strength Design with % Damping Figure B.83: 9 th Story Drift for Nine Story Strength Design with % Damping Figure B.84: Base Shear for Nine Story Strength Design with % Damping Figure B.85: st Story Drift for Nine Story Strength Design with % Damping Figure B.86: nd Story Drift for Nine Story Strength Design with % Damping Figure B.87: 3 rd Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.88: 4 th Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.89: 5 th Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.9: 6 th Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.9: 7 th Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.9: 8 th Story Drift for Nine Story Strength Design with % Damping... 7 Figure B.93: 9 th Story Drift for Nine Story Strength Design with % Damping Figure B.94: Base Shear for Nine Story Strength Design with % Damping Figure B.95: st Story Drift for Nine Story Strength Design with 3% Damping Figure B.96: nd Story Drift for Nine Story Strength Design with 3% Damping x

11 Figure B.97: 3 rd Story Drift for Nine Story Strength Design with 3% Damping Figure B.98: 4 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.99: 5 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.: 6 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.: 7 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.: 8 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.3: 9 th Story Drift for Nine Story Strength Design with 3% Damping Figure B.4: Base Shear for Nine Story Strength Design with 3% Damping Figure B.5: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.6: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.7: Roof Displacement for Nine Story Strength Design Subject to sefp... 8 Figure B.8: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.9: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.3: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.4: Roof Displacement for Nine Story Strength Design Subject to sefp Figure B.5: Base Shear for Nine Story Strength Design Subject to sefp Figure B.6: Base Shear for Nine Story Strength Design Subject to sefp Figure B.7: Base Shear for Nine Story Strength Design Subject to sefp Figure B.8: Base Shear for Nine Story Strength Design Subject to sefp Figure B.9: Base Shear for Nine Story Strength Design Subject to sefp Figure B.: Base Shear for Nine Story Strength Design Subject to sefp Figure B.: Base Shear for Nine Story Strength Design Subject to sefp Figure B.: Base Shear for Nine Story Strength Design Subject to sefp Figure B.3: Base Shear for Nine Story Strength Design Subject to sefp Figure B.4: Base Shear for Nine Story Strength Design Subject to sefp xi

12 List of Tables Table.: Vertical Gravity Loads... 8 Table.: Seismic Masses... 8 Table.3: Seismic Design Parameters... Table.4: Seismic Design Loads... 3 Table.5: Wind Design Loads... 5 Table.6: Members and Section Properties of the Three Story Seattle Model Designed for Strength... 9 Table.7: Members and Section Properties of the Nine Story Seattle Model Designed for Strength... 9 Table.8: Members and Section Properties of the Three Story Boston Model Designed for Strength... 3 Table.9: Members and Section Properties of the Nine Story Boston Model Designed for Strength... 3 Table.: Three Story Model Stiffnesses and Damping Constants for Inherent Damping Table.: Nine Story Model Stiffnesses and Damping Constants for Inherent Damping Table.: Seattle Model Stiffnesses and Damping Constants for Added Damping Table.3: Members and Section Properties of the Three Story Seattle Model Designed for Stiffness Table.4: Members and Section Properties of the Nine Story Seattle Model Designed for Stiffness Table 3.: Ground Acceleration Record Properties... 5 Table 3.: Three Story Strength Design Scaling Properties Table 3.3: Three Story Stiffness Design Scaling Properties Table 3.4: Nine Story Strength Design Scaling Properties Table 3.5: Nine Story Stiffness Design Scaling Properties... 6 Table 5. Interstory Drift Limits... 7 Table 5. Interstory Drifts for % Damped Three Story Seattle Model... 7 Table 5.3 Interstory Drifts for % Damped Nine Story Seattle Model... 7 Table 5.4 Base Shear Tendencies for Three Story Models Table 5.5 Base Shear Tendencies for Nine Story Models xii

13 Chapter : Introduction. 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

14 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.. 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. 998). By placing such a device in a bracing system in a structure, like the chevron brace shown in Figure., motion between adjacent levels can be resisted by the damper. Figure. 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.

15 Fluid Viscous Dampers Figure.: Viscous Fluid Dampers in a Chevron Brace Configuration Figure.: Viscous Fluid Dampers Exposed in a Building 3

16 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 997). The force developed in a damper due to a given velocity is: F α dx dx = C sgn (-) dt dt dx where C is the damping coefficient, is the velocity, and α is a factor determining the dt linearity of damper response. When α is unity, the device is a linear damper and Equation reduces to: dx F = C (-) dt The Northridge earthquake in 994 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. ). 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 =.) and nonlinear (α =.5 and α =.3) viscous fluid dampers were used. These dampers were designed to give the structure damping ratios ranging from % to 35%. At each level of damping, the structure was subjected to six near-field earthquakes, five earthquakes scaled to have a % probability of exceedence in 5 years, the unscaled El Centro record from the 94 Imperial Valley earthquake, and the unscaled Taft Lincoln Tunnel record from the 95 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 4

17 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 ). These frames were retrofitted with passive energy dissipation systems that provided % 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 5

18 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 % 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 3). His research focused primarily on damper nonlinearity. The nine story five bay model being studied was fitted with dampers having an α of.5,., and.5 and damping ratios of 5%, %, 5%, and % 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 6

19 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 =.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..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.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 7

20 will begin to bend. The IDA curve in Figure.3 happens to resemble a static pushover curve, which is common. Intensity Measure Engineering Demand Parameter Figure.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.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 8

21 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. Intensity Measure A B C Engineering Demand Parameter Figure.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.5. Instead, the difference between the IDA curves will reside primarily in the degree of structural response. 9

22 Intensity Measure D E F Engineering Demand Parameter Figure.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, 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 977 and acknowledges several other succeeding scholars for being proponents of the IDA concept (Vamvatsikos and Cornell ). 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

23 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 6%, 5%, and 84% of the chosen earthquakes (Vamvatsikos and Cornell 3). 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. 6). 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 5 th percentile and 9 th 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 5 th percentile and 9 th percentile IDA

24 curves yielded the selection of three records deemed to satisfactorily represent all possible earthquakes. The record that came closest to meeting the 9 th percentile IDA curve at the DBE intensity measure was chosen to be the design basis earthquake. The record that came closest to meeting the 5 th 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 9 th percentile IDA curve did not intersect the MCE intensity measure. However, the record that most closely resembled the 9 th 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 5). 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.

25 .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 7-5 (ASCE 6). 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 3% 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 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. 3

26 Chapter : Models. 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.. Model Geometry The models used in the current study were strongly influenced by the model buildings created for the SAC Steel Project (FEMA a). 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... Three Story Model Geometry The dimensioned elevation and floor plan of a three story model are shown in Figures. and., 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 4 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 4

27 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. Roof 3 = 39 Third Floor Second Floor First Floor 3 = Figure.: Three Story Model Elevation A B C D E 3 3 = N 7 3 = Figure.: Three Story Model Floor Plan 5

28 .. Nine Story Model Geometry Figures.3 and.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 4 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. 6

29 Roof Ninth Floor Eighth Floor 8 3 = 4 Seventh Floor Sixth Floor Fifth Floor Fourth Floor Third Floor Second Floor First Floor 3 = 5 Figure.3: Nine Story Model Elevation A B C D E F 3 = N 6 3 = 5 Figure.4: Nine Story Model Floor Plan 7

30 .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.. 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.. 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. Vertical Gravity Loads Load Type Floor Dead Load Roof Dead Load Penthouse Dead Load Exterior Wall Dead Load Floor/Roof Reduced Live Load Load 96 psf 83 psf 6 psf 5 psf psf 3 Story Effective Seismic Weight, W k 9 Story Effective Seismic Weight, W k Table. Seismic Masses Level Mass (k-s /ft) 3 Story Structures Roof 7.9 Floors & Story Structures Roof 73. Floors Floor

31 .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 7-5 (ASCE 6). This standard also contains acceptable procedures to follow when using these criteria to calculate minimum design loads..4. 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: V = C W (-) S where C S 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 S S and S read from the maps in ASCE/SEI 7-5 and the site class of the soil upon which the structure is located. S S and S are the maximum considered 5% damped.s and.s 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: S = F S (-) MS a S and S F = M vs (-3) 9

32 Where F a and F v are the short and long period site coefficients read from tables in ASCE/SEI 7-5. To determine the design spectral response acceleration parameters, the following equations are utilized: and S DS = S MS (-4) 3 S D = S M (-5) 3 The design response spectrum is a plot of spectral response acceleration S a versus period T. This spectral response acceleration is given by: S = T + S for T < T (-6) DS S a.6. 4 T DS S a = S DS for T < T < T S (-7) S a S D = for T S < T < T L (-8) T where: S DTL S a = for T L < T (-9) T T = the fundamental period of the structure (s) T =. S S D DS T S S = S D DS T L = 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, C u. C u depends on the one second design spectral response acceleration parameter. The seismic response coefficient can now be determined by:

33 though this coefficient need not exceed: C C C s s s S Ds = (-) R / I S D = for T < T L (-) T ( R / I ) S DTL = for T > T L (-) T ( R / I ) 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, F x, at each level can be determined from the following equations: Fx = CvxV (-3) and C vx = n w i= x h i k x w h k i (-4) where C vx is the vertical distribution factor, V is the calculated total base shear, w i and w x 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.5, then k =. If the period is greater than.5, then k =. 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.. Special steel moment frames have a response modification factor, R, equal to 8 and a deflection amplification factor, C d, equal to 5.5. The calculated seismic design parameters for both Seattle and Boston are listed in Table.3. The design response spectra for both regions are plotted together in Figure.5 and the calculated lateral forces for the models are listed

34 in Table.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.3 Seismic Design Parameters Regional Parameters Seattle Boston S S =.5.5 S =.5.8 F a =..6 F v =.5.4 S MS =.5.4 S M =.75.8 S DS =.83.7 S D =.5. C u = Story Parameters T (approximate) =.73s.87s Cs =.9. k =..9 V = 88.7k 58.44k 9 Story Parameters T (approximate) =.83s.7s Cs =.3. k = V = 374.k 9.49k

35 Pseudo-Acceleration (g) Period (s) Seattle Boston Figure.5: Design Response Spectra Table.4 Seismic Design Loads Level Seattle ELF (k) Boston ELF (k) 3 Story Structures Roof rd Floor nd Floor Story Structures Roof th Floor th Floor th Floor th Floor th Floor th Floor rd Floor nd Floor

36 .4. 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 7-5 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. 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 7-5 were 85mph for Seattle and mph for Boston. The wind design loads calculated based on these assumptions are listed in Table.5. 4

37 Table.5 Wind Design Loads Level Seattle Wind (k) Boston Wind (k) 3 Story Models Roof rd Floor nd Floor Story Models Roof th Floor th Floor th Floor th Floor th Floor th Floor rd Floor nd Floor 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.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. 5

38 Horizontal Slaving Gravity Pin Axially Rigid Truss Member Figure.6: P-delta Ghost Frame.6 Joint Modeling The joints for all structures were modeled using the revised Krawinkler model with revised force-deformation behavior (Charney and Marshall 6). 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.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. 6

39 Rotational Spring Representing Shear Panel Hinge (no rotational stiffness) Rigid Link Hinge (no rotational stiffness) Rotational Spring Representing Column Flange Figure.7: Krawinkler Joint Model.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 7-5. 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 7

40 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 34-5 (AISC 5). Finally, all models were designed to meet a maximum interstory wind drift of h/7, where h is the story height. This drift ratio was chosen to represent an acceptable interstory drift under a wind load with a 5 year mean recurrence interval (MRI). The final member selections are detailed in the following figures and tables. Table.6 lists the chosen members and section properties for the three story Seattle model, and Figure.8 displays a labeled elevation view. The fundamental period of vibration of the three story Seattle strength design is.565s. Table.7 lists the chosen members and section properties for the nine story Seattle model, and Figure.9 displays a labeled elevation view. The fundamental period of vibration of the nine story Seattle strength design is.964s. Table.8 lists the chosen members and section properties for the three story Boston model, and Figure. displays a labeled elevation view. The fundamental period of vibration of the three story Boston strength design is.67s. Table.9 lists the chosen members and section properties for the nine story Boston model, and Figure. displays a labeled elevation view. The fundamental period of vibration of the nine story Boston strength design is.386s. No doubler plates were required to meet ANSI/AISC 34-5 requirements. For all four strength designed models, the fundamental period is significantly larger than was approximated using the method allowed by ASCE/SEI 7-5. This is expected, because the ASCE/SEI 7-5 assumes that the structures would have been designed to meet stiffness requirements, which would have reduced the fundamental period. 8

41 Table.6 Members and Section Properties of the Three Story Seattle Model Designed for Strength Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Columns W4x Interior Columns W4x Floor Girders W8x Roof Girders W8x W8x6 W8x6 W8x6 W8x6 W8x86 W8x86 W8x86 W8x86 W4x3 W8x86 W4x45 W8x86 W4x45 W8x86 W4x45 W8x86 W4x3 Figure.8: Elevation of the Three Story Seattle Model Designed for Strength Table.7 Members and Section Properties of the Nine Story Seattle Model Designed for Strength Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Column B- W8x Interior Column B- W8x Exterior Column -4 W8x Interior Column -4 W8x Exterior Column 4-6 W8x Interior Column 4-6 W8x Exterior Column 6-8 W8x Interior Column 6-8 W8x Exterior Column 8-R W8x Interior Column 8-R W8x Girder & Wx Girder 3 & 4 Wx Girder 5 & 6 Wx Girder 7 & 8 W8x Girder 9 & R W8x

42 W8x65 W8x65 W8x65 W8x65 W8x65 W8x86 W8x65 W8x86 W8x86 W8x86 W8x65 W8x65 W8x65 W8x65 W8x86 W8x86 W8x6 W8x6 W8x6 W8x6 W8x6 W8x3 W8x43 W8x43 W8x6 W8x6 W8x6 W8x6 W8x6 W8x43 W8x43 W8x3 Wx3 Wx3 Wx3 Wx3 Wx3 W8x9 W8x W8x Wx3 Wx3 Wx3 Wx3 Wx3 W8x W8x W8x9 Wx66 Wx66 Wx66 Wx66 Wx66 W8x3 W8x58 W8x58 W8x3 W8x58 Wx66 Wx66 Wx66 Wx66 Wx66 Wx Wx Wx Wx Wx W8x3 Wx Wx Wx Wx Wx W8x58 W8x3 W8x58 W8x3 W8x58 W8x3 Figure.9: Elevation of the Nine Story Seattle Model Designed for Strength 3

43 Table.8 Members and Section Properties of the Three Story Boston Model Designed for Strength Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Columns W4x Interior Columns W4x Floor Girders W8x Roof Girders W8x W8x65 W8x65 W8x65 W8x65 W8x7 W8x7 W8x7 W8x7 W4x3 W8x7 W4x3 W8x7 W4x3 W8x7 W4x3 W8x7 W4x3 Figure.: Elevation of the Three Story Boston Model Designed for Strength Table.9 Members and Section Properties of the Nine Story Boston Model Designed for Strength Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Column B- W4x Interior Column B- W4x Exterior Column -4 W4x Interior Column -4 W4x Exterior Column 4-6 W4x Interior Column 4-6 W4x Exterior Column 6-8 W4x Interior Column 6-8 W4x Exterior Column 8-R W4x Interior Column 8-R W4x Girder & W4x Girder 3 & 4 W4x Girder 5 & 6 Wx Girder 7 & 8 W8x Girder 9 & R W8x

44 W8x65 W8x65 W8x65 W8x65 W8x65 W4x3 W8x65 W4x45 W4x45 W4x45 W8x65 W8x65 W8x65 W8x65 W4x45 W4x3 W8x75 W8x75 W8x75 W8x75 W8x75 W4x57 W4x83 W4x83 W8x75 W8x75 W8x75 W8x75 W8x75 W4x83 W4x83 W4x57 Wx Wx Wx Wx Wx W4x34 W4x37 W4x37 Wx Wx Wx Wx Wx W4x37 W4x37 W4x34 W4x9 W4x9 W4x9 W4x9 W4x9 W4x55 W4x398 W4x46 W4x55 W4x46 W4x9 W4x9 W4x9 W4x9 W4x9 W4x36 W4x36 W4x36 W4x36 W4x36 W4x55 W4x36 W4x36 W4x36 W4x36 W4x36 W4x46 W4x55 W4x46 W4x55 W4x398 W4x55 Figure.: Elevation of the Nine Story Boston Model Designed for Strength 3

45 .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 % at the natural period of the structure and at a period of.s. 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.. 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: c = M x α (.5) c = K x β (.6) where x is the story level, K x is the story stiffness, and M x 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. and.. 33

46 Axially Rigid Truss Member Pin Horizontal Slaving Mass Proportional Damper Stiffness Proportional Damper Figure.: Damping Ghost Frame Table. Three Story Model Stiffnesses and Damping Constants for Inherent Damping Seattle Boston Structure: α = β =.. Mass Damper Stiffness Damper Mass Damper Stiffness Damper st Story: β = k x (k/in) = nd Story: β = k x (k/in) = rd Story: β = k x (k/in) =

47 Table. Nine Story Model Stiffnesses and Damping Constants for Inherent Damping Seattle Boston Structure: α = β =.. Mass Damper Stiffness Damper Mass Damper Stiffness Damper st Story: β = k x (k/in) = nd Story: β = k x (k/in) = rd Story: β = k x (k/in) = th Story: β = k x (k/in) = th Story: β = k x (k/in) = th Story: β = k x (k/in) = th Story: β = k x (k/in) = th Story: β = k x (k/in) = th Story: β = k x (k/in) = 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%, %, %, and 3%. 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.. Only the values determined for the Seattle models are listed in this table, for reasons described in the following section. 35

48 Table.: Seattle Model Stiffnesses and Damping Constants for Added Damping Damping 3 Story Model 9 Story Model 5%: β = 48 k x (k/in) =.56.4 %: β = k x (k/in) =.. %: β = k x (k/in) =.8. 3%: β = k x (k/in) =.6..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 7-5 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.3 and a corresponding elevation is displayed in Figure.3. The fundamental period of vibration of the three story Seattle stiffness design is.4s. The members and section properties of the drift designed nine story model are provided in Table.4 and a corresponding elevation is displayed in Figure.4. The fundamental period of vibration of the nine story Seattle stiffness design is.634s. 36

49 Table.3 Members and Section Properties of the Three Story Seattle Model Designed for Stiffness Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Columns W4x Interior Columns W4x Floor Girders W8x Roof Girders W8x W8x6 W8x6 W8x6 W8x6 W8x75 W8x75 W8x75 W8x75 W4x83 W8x75 W4x3 W8x75 W4x3 W8x75 W4x3 W8x75 W4x83 Figure.3: Elevation of the Three Story Seattle Model Designed for Stiffness Table.4 Members and Section Properties of the Nine Story Seattle Model Designed for Stiffness Shape A (in ) I x (in 4 ) d (in) b f (in) t f (in) t w (in) Z x (in 3 ) Exterior Column B- W8x Interior Column B- W8x Exterior Column -4 W8x Interior Column -4 W8x Exterior Column 4-6 W8x Interior Column 4-6 W8x Exterior Column 6-8 W8x Interior Column 6-8 W8x Exterior Column 8-R W8x Interior Column 8-R W8x Girder & Wx Girder 3 & 4 Wx Girder 5 & 6 Wx Girder 7 & 8 W8x Girder 9 & R W8x

50 W8x65 W8x65 W8x65 W8x65 W8x65 W8x86 W8x65 W8x86 W8x86 W8x86 W8x65 W8x65 W8x65 W8x65 W8x86 W8x86 W8x75 W8x75 W8x75 W8x75 W8x75 W8x W8x34 W8x34 W8x75 W8x75 W8x75 W8x75 W8x75 W8x34 W8x34 W8x Wx8 Wx8 Wx8 Wx8 Wx8 W8x58 W8x58 W8x58 Wx8 Wx8 Wx8 Wx8 Wx8 W8x58 W8x58 W8x58 Wx Wx Wx Wx Wx W8x3 W8x3 W8x3 W8x3 W8x3 Wx Wx Wx Wx Wx Wx Wx Wx Wx Wx W8x3 Wx Wx Wx Wx Wx W8x3 W8x3 W8x3 W8x3 W8x3 W8x3 Figure.4: Elevation of the Nine Story Seattle Model Designed for Strength. 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 6), which is a graphical user interface for the structural analysis engine DRAIN-DX (Prakash et al. 993). 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. 38

51 Chapter 3: Incremental Dynamic Analysis Development 3. 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. 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 5). 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 7-5 is contingent upon the soil classification of the location in question (ASCE 6). 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 39

52 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 5). This causes near-fault earthquakes to be more destructive than farfault 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. 6). 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- 4

53 acceleration at the first-mode period of the structure. Other methods attempt to fit all response spectra to a design spectrum. ASCE/SEI 7-5 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.t to.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 6). 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 ). 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 6) to define the 4

54 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. through of this chapter outline the basic functions of NICC. A detailed guide explaining the use of NICC is included in Appendix A 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-DX User s Manual (Prakash et al. 993). It is the responsibility of the user to select appropriate ground motions, following the guidelines provided in Section 3. of this chapter NICC Collection Format and Specifications The main NICC window is shown in Figure 3.. 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., 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 4

55 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. 43

56 Figure 3.: NICC Main Window 44

57 Figure 3.: Collection Specifications Section for a Multiple Earthquake IDA Figure 3.3: Collection Specifications Section for a Multiple Parameter IDA 45

58 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 7-5 (ASCE 6). 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 7-5 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 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 7-5 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. 46

59 Figure 3.4: NICC Scaling Options Window 47

60 Figure 3.5: NICC Ground Acceleration History Plot Window 48

61 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 are subjected to a suite of appropriate ground acceleration records. These earthquakes were taken from the SAC Steel Project (FEMA a), 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 % in 5 year probable return interval in Seattle were selected for the current study. These ground acceleration records are listed in Table 3. 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 3.7 display the ground acceleration histories for the unscaled records. 49

62 Table 3. Ground Acceleration Record Properties File Name Duration (s) Time Step (s) PGA (g) sefp.acn Mendocino, sefp.acn Erzinican Meteorological Station, sefp.acn Olympia Highway Test Lab, sefp3.acn Olympia Highway Test Lab, sefp4.acn Llolleo, Chile, sefp5.acn Vina del Mar, Chile, sefp6.acn Deep Interplate (simulation) sefp7.acn Miyagi-oki, sefp8.acn Shallow Interplate (simulation) sefp9.acn Shallow Interplate (simulation) Pseudo-Acceleration (g) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Design Spectrum Natural Period of Vibration (s) Figure 3.7: Unscaled 5% Damped Ground Acceleration Response Spectra 5

63 .5 Acceleration (g) Time (s) Figure 3.8: Ground Acceleration History for Mendocino, 99.5 Acceleration (g) Time (s) Figure 3.9: Ground Acceleration History for Erzinican Meteorological Station, 99 5

64 .5 Acceleration (g) Time (s) Figure 3.: Ground Acceleration History for Olympia Highway Test Lab, Acceleration (g) Time (s) Figure 3.: Ground Acceleration History for Olympia Highway Test Lab, 965 5

65 .5 Acceleration (g) Time (s) Figure 3.: Ground Acceleration History for Llolleo, Chile, Acceleration (g) Time (s) Figure 3.3: Ground Acceleration History for Vina del Mar, Chile,

66 .5 Acceleration (g) Time (s) Figure 3.4: Ground Acceleration History for Deep Interplate (simulation).5 Acceleration (g) Time (s) Figure 3.5: Ground Acceleration History for Miyagi-oki,

67 .5 Acceleration (g) Time (s) Figure 3.6: Ground Acceleration History for Shallow Interplate (simulation).5 Acceleration (g) Time (s) Figure 3.7: Ground Acceleration History for Shallow Interplate (simulation) 55

68 For each IDA, the ten earthquakes were scaled to meet the 5% damped ASCE/SEI 7-5 design spectrum at the natural period of vibration of the model being analyzed. Tables 3. 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 3.8 through 3. display the scaled response spectra associated with these models. For all earthquakes, the scale factors used in the second scaling ranged from. to. with an increment size of.. 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.s 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. 56

69 Table 3. Three Story Strength Design Scaling Properties File Scale Factor Scaled PGA (g) sefp.acn sefp.acn sefp.acn sefp3.acn sefp4.acn sefp5.acn sefp6.acn sefp7.acn.7. sefp8.acn.34.8 sefp9.acn Pseudo-Acceleration (g) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Design Spectrum Natural Period of Vibration (s) Figure 3.8: 5% Damped Ground Acceleration Response Spectra Scaled to.3g at T =.565s for Three Story Strength Design 57

70 Table 3.3 Three Story Stiffness Design Scaling Properties File Scale Factor Scaled PGA (g) sefp.acn sefp.acn.5.8 sefp.acn sefp3.acn sefp4.acn sefp5.acn sefp6.acn sefp7.acn.9.5 sefp8.acn sefp9.acn Pseudo-Acceleration (g) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Design Spectrum Natural Period of Vibration (s) Figure 3.9: 5% Damped Ground Acceleration Response Spectra Scaled to.48g at T =.4s for Three Story Stiffness Design 58

71 Table 3.4 Nine Story Strength Design Scaling Properties File Scale Factor Scaled PGA (g) sefp.acn sefp.acn sefp.acn sefp3.acn sefp4.acn.776. sefp5.acn sefp6.acn sefp7.acn sefp8.acn sefp9.acn Pseudo-Acceleration (g) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Design Spectrum Natural Period of Vibration (s) Figure 3.: 5% Damped Ground Acceleration Response Spectra Scaled to.7g at T =.964 for Nine Story Strength Design 59

72 Table 3.5 Nine Story Stiffness Design Scaling Properties File Scale Factor Scaled PGA (g) sefp.acn sefp.acn.4. sefp.acn sefp3.acn sefp4.acn sefp5.acn.4.9 sefp6.acn sefp7.acn sefp8.acn sefp9.acn Pseudo-Acceleration (g) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Design Spectrum Natural Period of Vibration (s) Figure 3.: 5% Damped Ground Acceleration Response Spectra Scaled to.9 at T =.634 for Nine Story Stiffness Design 6

73 Chapter 4: Incremental Dynamic Analysis Application 4. 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. 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.. 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 prescaled 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.. When the structure begins to yield, the curves 6

74 Scale Factor Engineering Demand Parameter A B C D E Figure 4.: 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 6

75 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 b). 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 5% chance of occurrence in a 5 year 63

76 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 % 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 4). 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 6). NonlinPro uses the analysis engine DRAIN-DX (Prakash et al. 993) 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. through of this chapter outline the basic functions of NICC. A detailed guide explaining the use of NIVA is included in Appendix A 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 *.dz input files written by NICC and the *.rxx output files written by NonlinPro NIVA Main Window and *.ida Files The main NIVA window, displayed in Figure 4., 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 64

77 Figure 4.: NIVA Main Window Figure 4.3: NIVA Create New Project Group Window 65

78 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 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 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 66

79 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 67

80 Figure 4.5: NIVA Response History Viewing Window 68

81 Chapter 5: Results and Discussion 5. Overview An Incremental Dynamic Analysis (IDA) was performed on both the three story and nine story Seattle strength designs with inherent, 5%, %, %, and 3% 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.s. 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. 69

82 5. Code Compliance According to ASCE/SEI 7-5 (ASCE 6), interstory drift in any story of a linear model should not exceed % 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 5% 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.. In order for a structure to be code compliant, the drift experienced by every story must meet these limits. Table 5. 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.. 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 sefp and sefp caused all three stories to exceed their interstory drift limits, and sefp and sefp5 caused at least one story to exceed its limit. The limit was also surpassed in the second and third stories due to sefp and sefp5 when the total structural damping was increased to 5%. The lowest added damping level to effect code compliance in the three 7

83 story strength design was %. Table 5. lists the maximum interstory drifts experienced by all stories in the % damped model for all earthquakes. It can be seen that all values are comfortably within the provided limits. The three story models with % damping and 3% damping also meet these criteria, but are more conservative than necessary. Table 5. Interstory Drifts for % Damped Three Story Seattle Strength Design Story sefp sefp sefp sefp3 sefp Story sefp5 sefp6 sefp7 sefp8 sefp 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 sefp5 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 % damped model. The maximum interstory drifts calculated in all stories of the % damped nine story model for all ground motions are displayed in Table 5.3. The % damped and 3% damped nine story models also met the codified restrictions, but were overly conservative. 7

84 Table 5.3 Interstory Drifts for % Damped Nine Story Seattle Strength Design Story sefp sefp sefp sefp3 sefp Story sefp5 sefp6 sefp7 sefp8 sefp 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 % damping, and the three story model designed to meet drift requirements without dampers. Surprisingly, the base shears in the % 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 % of critical damping does not 7

85 produce the high damper forces that are present in the % damped and 3% damped models. It is also interesting to note that the base shears calculated for the % 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) % Damped Strength Design Base Shear (k) % Difference Drift Design Base Shear (k) sefp sefp sefp sefp sefp sefp sefp sefp sefp sefp The corresponding base shear values for the nine story models are listed in Table 5.5. In every case, the base shear in the % 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 % damped model is.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 % and 3% 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 % 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 73

86 with current standards, collapses when subjected to sefp4, 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) % Damped Strength Design Base Shear (k) % Difference Drift Design Base Shear (k) sefp sefp sefp sefp sefp collapse sefp5 collapse collapse sefp sefp sefp sefp 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 7-5, 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 74

87 dampers, provides a more complete understanding of the effect of the damping devices on structural behavior than other traditional methods 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. displays the IDA study for drift in the nd story of the three story model and Figure 5. displays the IDA study for drift in the 5 th 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 sefp4 and sefp5 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 sefp6 curve at a scale factor of.3. 75

88 Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.: IDA Study for nd Story Drift of Three Story Stiffness Design Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.: IDA Study for 5 th Story Drift of Nine Story Stiffness Design 76

89 5.3.: 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 nd story drift in the three story strength design as the structural damping ranges from inherent only to 3%. Figures 5.8 through 5. display the multiple earthquake IDA studies for the 5 th story drift in the nine story strength design as the structural damping ranges from inherent only to 3%. 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 sefp and sefp5 before reaching the maximum considered earthquake. This yielding is obviously reduced in the 5% damped model, and only sefp5 experiences complete failure. There is some reduction in drift and weaving behavior between 5% and % damping, and by the time the damping has reached % 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 3% of critical, drifts have reduced drastically and visible yielding is minimal. 77

90 Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.3: IDA Study of nd Story Drift for Three Story Strength Design with Inherent Damping Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.4: IDA Study of nd Story Drift for Three Story Strength Design with 5% Damping 78

91 Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.5: IDA Study of nd Story Drift for Three Story Strength Design with % Damping Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.6: IDA Study of nd Story Drift for Three Story Strength Design with % Damping 79

92 Scale Factor nd Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.7: IDA Study of nd Story Drift for Three Story Strength Design with 3% 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 sefp5 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.4 is reached. Only one earthquake causes collapse when the damping ratio is increased to % of critical, and the structure still survives until a scale factor of.9. The % damped model displays complete dynamic stability, and the response of the 3% model is almost completely linear for all records. 8

93 Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.8: IDA Study of 5 th Story Drift for Nine Story Strength Design with Inherent Damping Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.9: IDA Study of 5 th Story Drift for Nine Story Strength Design with 5% Damping 8

94 Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with % Damping Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with % Damping 8

95 Scale Factor th Story Drift (in) sefp sefp sefp sefp3 sefp4 sefp5 sefp6 sefp7 sefp8 sefp9 Figure 5.: IDA Study of 5 th Story Drift for Nine Story Strength Design with 3% Damping Multiple parameter IDA studies more clearly depict the correlation between structural damping ratio and seismic response. Figures 5.3 and 5.4 are examples of parameter IDA studies which display the roof displacements of the three story model for the sefp ground motion and nine story model for the sefp6 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 3% 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. 83

96 Scale Factor Roof Displacement (in) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.3: IDA Study of Roof Displacement for Three Story Strength Design Subject to sefp.8.6 Scale Factor Roof Displacement (in) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.4: IDA Study of Roof Displacement for Nine Story Strength Design Subject to sefp6 84

97 Multiple parameter IDA studies can also be used to examine total base shear. Figures 5.5 and 5.6 contain the base shear plots for the three story strength design subjected to the sefp and sefp9 ground motions, respectively. The IDA curves on both plots exhibit the same typical shape progression as the structural damping is increased from inherent to 3% 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 sefp IDA study, this point occurs somewhere between scale factors of.8 and.9. The sefp9 plot depicts convergence closer to a scale factor of.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 % or less will not inflate base shear to an alarming degree. The % and 3% damped IDA curves do demonstrate noticeably higher base shears in the nonlinear region, but the inherent, 5%, and % damped curves follow paths that are almost identical, all the way up to the maximum considered intensity. 85

98 Scale Factor Base Shear (k) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.5: IDA Study of Total Base Shear for Three Story Strength Design Subject to sefp.8.6 Scale Factor Base Shear (k) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.6: IDA Study of Total Base Shear for Three Story Strength Design Subject to sefp9 86

99 The nine story model IDA studies illustrate similar trends. The nine story model plots for base shear due to sefp and sefp9 are displayed in Figures 5.7 and 5.8, 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 % damping tend to be more distinct from one another than those generated for the three story models..8.6 Scale Factor Base Shear (k) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.7: IDA Study of Total Base Shear for Nine Story Strength Design Subject to sefp 87

100 Scale Factor Base Shear (k) Inherent Damping 5% Damping % Damping % Damping 3% Damping Figure 5.8: IDA Study of Total Base Shear for Nine Story Strength Design Subject to sefp9 88

101 Chapter 6: Conclusion 6. 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 % in their first mode period of vibration and at a period of.s. 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%, %, %, and 3% of critical. For comparison purposes, a three story and a nine 89

102 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 7-5 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 % 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 % damping were very comparable to those calculated for the model with only inherent damping. Also, the % 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 % 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 % and 3% 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 % of critical. Furthermore, % damped steel moment frames should not be in danger of excessive total base shears that would 9

103 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 % of critical or higher. Base shear increase due to the inclusion of dampers is easily manageable when total structural damping ratios are approximately % of critical, provided the chevron braces in the damping frame are designed with damper forces in mind. 6. 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. 9

104 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. 9

105 References American Institute of Steel Construction, Inc. (5). Seismic Provisions for Structural Steel Buildings. Standard No. ANSI/AISC 34-5, AISC, Chicago, IL. American Society of Civil Engineers (ASCE). (6). Minimum Design Loads for Buildings and Other Structures. Standard No. ASCE/SEI 7-5, ASCE, Reston, VA. Charney, F. A. and Barngrover, B. (6). NonlinPro Base Program Description and User Guide. Advanced Structural Concepts, Blacksburg, VA. Charney, F. A. and Marshall, J. D. (6). A comparison of the Krawinkler and scissors models for including beam-column joint deformations in the analysis of momentresisting steel frames. Engineering Journal, 43(), Constantinou, M. C., Soong, T. T., and Dargush, G. F. (998). 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. (6). Identification of critical ground motions for seismic performance assessment of structures. Earthquake Eng. Struct. Dyn., 35(8), Federal Emergency Management Agency (FEMA). (a). 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). (b). 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). (3). NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures. Rep. No. FEMA-45, Washington, D.C. Filiatrault, A., Tremblay, R., and Wanitkorkul, A. (). Performance evaluation of passive damping systems for the seismic retrofit of steel moment-resisting frames subjected to near-field ground motions. Earthquake Spectra, 7(3), Kunnath, S. K. and Kalkan, E. (5). IDA capacity curves: the need for alternative intensity factors. Proc., Structures Congress and Exposition, ASCE, Reston, VA,

106 Mackie, K. R. and Stojadinovic, B. (5). Comparison of incremental dynamic, cloud, and stripe methods for computing probabilistic demand models. Proc., Structures Congress and Exposition, ASCE, Reston, VA, Makris, N. (997). Vibration control of structures during urban earthquakes. Proc., American Control Conference, AACC, Albuquerque, NM, Miyamoto, H. K. and Singh, J. P. (). Performance of structures with passive energy dissipators. Earthquake Spectra, 8(), 5-9. Oesterle, M. G. (3). Use of incremental dynamic analysis to assess the performance of steel moment-resisting frames with fluid viscous dampers. Master of Science Thesis, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA. Prakash, V., Powell, G. H., and Campbell, S. (993). DRAIN-DX Base Program Description and User Guide: Version.. Dept. of Civil Engineering, Univ. of California at Berkley. Vamvatsikos, D. and Cornell, C. A. (). Incremental dynamic analysis. Earthquake Eng. Struct. Dyn., 3(3), Vamvatsikos, D. and Cornell, C. A. (4). Applied incremental dynamic analysis. Earthquake Spectra, (),

107 Appendix A: User s Guide to the NonlinPro IDA Collection Creator and the NonlinPro IDA Visualization Application A. 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 6) 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-DX analysis engine (Prakash and Powell 993), the NonlinPro environment, and ASCE/SEI 7-5 building code (ASCE 6). All questions regarding the use of DRAIN-DX, NonlinPro, and the ASCE/SEI 7-5 provisions are referred to the DRAIN-DX user s Guide, the NonlinPro User s Guide, and ASCE/SEI 7-5, respectively. 95

108 A. NonlinPro IDA Collection Creator (NICC) A.. Before Using NICC NICC accepts NonlinPro analysis definition files as input. These files have the extension *.dx or *.dz. Files with the extension *.dx are traditional individual NonlinPro input files. Files with the extension *.dz are identical to *.dx 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 *.dz 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 *.dz 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.. NICC Main Window Upon startup of NICC, the main window, shown in Figure A., is displayed. 96

109 Figure A.: NICC Main Window A... Collection Format The topmost section of the window is labeled Collection Format. A focused view of this section is displayed in Figure A.. This is where the user determines very basic information about the collection by entering the following information. 97

110 Figure A.: 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 *.dx or the extension *.dz 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... 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. 98

111 Figure A.3: Collection Specifications Section for a Multiple Earthquake IDA Figure A.4: Collection Specifications Section for a Multiple Parameter IDA 99

112 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.

113 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-DX, and the DRAIN-DX 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.

114 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..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.

115 Figure A.5 NICC Scaling Options Window 3

116 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 and 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 4

117 Scale according to the NEHRP Provisions: ASCE/SEI 7-5, which provides essentially the same seismic design guidelines as the NEHRP Provisions (FEMA 3), specifies that for two-dimensional analyses: The ground motions shall be scaled such that for each period between.t and.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 or 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 5

118 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 7-5. o Site Class: ACSE/SEI 7-5 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, S, are the five-percent damped spectral accelerations at periods of.s and.s, respectively. These values can be determined from maps in ASCE/SEI 7-5. 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 /3 factor. 6

119 Checking the box includes the factor and leaving the box unchecked, which indicates a return probability of % in 5 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 7

120 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..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.. 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.. 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 pseudoacceleration, 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. 8

121 Figure A.: 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 7-5 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 9

122 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..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.. 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.

123 Figure A.: NICC Ground Acceleration History Plot Window A..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..

124 Figure A.: 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-DX. The following file names listed in the message box are the individual analysis definition files with the extension *.dz 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

125 user can direct NonlinPro to perform any of these analyses individually by opening the desired *.dz file in NonlinPro. A.3 NonlinPro IDA Visualization Application (NIVA) A.3. 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 *.dz 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. NIVA Main Window Upon startup of NIVA, the main window, shown in Figure A.3, 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.4. 3

126 Figure A.3: NIVA Main Window Figure A.4: NIVA Create New Project Group Window 4

127 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.5. 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 *.dz 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. 5

128 Figure A.5: 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. 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.6. 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 6

129 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.6: 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.7 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.8. 7

130 Figure A.7: NIVA Node/Element Group Selection FigureA.8: 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.9. This is where the user selects the individual element for which the IDA curves will be plotted. 8

131 Figure A.9: 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., 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. 9

132 Figure A.: 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. provides a close up view of this corner. Figure A.: NIVA Graphing Button

133 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.. Figure A.: 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

134 clicked point. This window is displayed in Figure A.3. This feature will only work if the graph is up to date. Figure A.3: 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

135 Performance Objectives frame in the bottom left corner of the main window, which is displayed in Figure A.4. Figure A.4: 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 3

136 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.5. Figure A.5: NIVA IDA Study with Performance Objectives 4