Optimal Performance-based

Transcription

1 BUILDING CONTROL WITH PASSIVE DAMPERS Optimal Performance-based Design for Earthquakes Izuru Takewaki Kyoto University, Japan TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER \ / John Wiley & Sons (Asia) Pte. Ltd.

2 Contents Preface xi 1 Introduction Background and Review Fundamentals of Passive-damper Installation Viscous Dampers Visco-elastic Dampers Organization of This Book 6 References 9 2 Optimality Criteria-based Design: Single Criterion in Terms of Transfer Function Introduction Incremental Inverse Problem: Simple Example Incremental Inverse Problem: General Formulation Numerical Examples I Viscous Damping Model 21 Model Hysteretic Damping Six-DOF Models with Various Possibilities of Damper Placement Optimality Criteria-based Design of Dampers: Simple Example Optimality Criteria Solution Algorithm Optimality Criteria-based Design of Dampers: General Formulation Numerical Examples II Example 1: Model with a Uniform Distribution of Story Stiffnesses Example 2: Model with a Uniform Distribution of Amplitudes of Transfer Functions Comparison with Other Methods Method of Lopez Garcia Method of Trombetti and Silvestri Summary 44 Appendix 2.A 46 References 48 3 Optimality Criteria-based Design: Multiple Criteria in Terms of Seismic Responses Introduction Illustrative Example General Problem Optimality Criteria Solution Algorithm Numerical Examples Multicriteria Plot 73

3 vi Contents 3.7 Summary References / Optimal Sensitivity-based Design ofdampers in Moment-resisting Frames Introduction 4.2 Viscous-type Modeling of Damper Systems 4.3 Problem of Optimal Damper Placement and Optimality Criteria 78 (Viscous-type Modeling) Optimality Criteria Solution Algorithm (Viscous-type Modeling) Numerical Examples I (Viscous-type Modeling) Maxwell-type Modeling of Damper Systems Modeling of a Main Frame Modeling of a Damper-Support-member System Effects of Support-Member Stiffnesses on Performance of Dampers Problem of Optimal Damper Placement and Optimality Criteria (Maxwell-type Modeling) Optimality Criteria Solution Algorithm (Maxwell-type Modeling) Numerical Examples II (Maxwell-type Modeling) Nonmonotonic Sensitivity Case Summary 106 Appendix 4.A 108 References Optimal Sensitivity-based Design of Dampers in Three-dimensional Buildings Introduction Problem of Optimal Damper Placement Modeling of Structure Mass, Stiffness, and Damping Matrices Relation of Element-end Displacements with Displacements at Center of Mass Relation of Forces at Center ofmass due to Stiffness Element K(i, j) with Element-end Forces Relation of Element-end Forces with Element-end Displacements Relation of Forces at Center of Mass due to Stiffness Element K(i,j) with Displacements at Center of Mass Equations of Motion and Transfer Function Amplitude Problem of Optimal Damper Positioning Optimality Criteria and Solution Algorithm Nonmonotonic Path with Respect to Damper Level Numerical Examples Summary 129 References Optimal Sensitivity-based Design of Dampers in Shear Buildings on Surface Ground under Earthquake Loading Introduction ] Building and Ground Model 132

4 Contents vii 6.3 ScismicRespon.se Problem of Optimal Damper Placement anil Optimality Criteria Optimality Conditions Solution Algorithm Numerical Examples Summary 147 Appendix 6.A 149 Appendix 6.B 150 References Optimal Sensitivity-based Design of Dampers in Bending-shear Buildings on Surface Ground under Earthquake Loading Introduction Building and Ground Model Ground Model Building Model Equations of Motion in Ground Equations of Motion in Building and Seismic Response I5'J 7.5 Problem of Optimal Damper Placement and Optimality Criteria Optimality Conditions Solution Algorithm Numerical Examples Summary 171 Appendix 7.A 175 Appendix 7.B 175 References Optimal Sensitivity-based Design of Dampers in Shear Buildings with TMDs on Surface Ground under Earthquake Loading Introduction Building with a TMD and Ground Model Equations of Motion and Seismic Response Problem of Optimal Damper Placement and Optimality Criteria Optimality Conditions Solution Algorithm Numerical Examples Whole Model and Decomposed Model 1% 8.8 Summary 199 Appendix 8.A 199 Appendix 8.B 201 Appendix 8.C 202 References Design of Dampers in Shear Buildings with Uncertainties Introduction liquations of Motion and Mean-square Response Critical Excitation Conservativeness of Bounds (Recorded Ground Motions) Design of Dampers in Shear Buildings under Uncertain Ground Motions Optimality Conditions 218

5 viii Contents Solution Algorithm Numerical Examples I Approach Based on Info-gap Uncertainty Analysis Info-gap Robustness Function Earthquake Input Energy to an SDOF System Earthquake Input Energy to an MDOF System Critical Excitation Problem for Acceleration Power Evaluation of Robustness of Shear Buildings with Uncertain Damper Properties under Uncertain Ground Motions Load Uncertainty Representation in Terms of Info-gap Models Info-gap Robustness Function for Load and Structural Uncertainties Numerical Examples II Summary 243 Appendix 9.A 244 Appendix 9.B 245 References Theoretical Background of Effectiveness of Passive Control System Introduction Earthquake Input Energy to SDOF model Constant Earthquake Input Energy Criterion in Time Domain Constant Earthquake Input Energy Criterion to MDOF Model in Frequency Domain Earthquake Input Energy as Sum of Input Energies to Subassemblages Effectiveness of Passive Dampers in Terms of Earthquake Input Energy Advantageous Feature of Frequency-domain 10.8 Numerical Examples for Tall Buildings with Supplemental Viscous Method 261 Dampers and Base-isolated Tall Buildings Tall Buildings with Supplemental Viscous Dampers Base-isolated Tall Buildings Energy Spectra for Recorded Ground Motions Summary 271 References Inelastic Dynamic Critical Response of Building Structures with Passive Dampers Introduction Input Ground Motion Acceleration Power and Velocity Power of Sinusoidal Motion Pulse-like Wave and Long-period Ground Motion Structural Model Main Frame Building Model with Hysteretie Dampers Building Model with Viscous Dampers Dynamic Response Evaluation Response Properties of Buildings with Hysteretie or Viscous Dampers Two-dimensional Sweeping Performance Curves Two-dimensional Sweeping Performance Curves with Respect to Various Normalization Indices of Ground Motion Upper Bound of Total Input Energy to Passively Controlled Inelastic Structures Subjected to Resonant Sinusoidal Motion 288

6 Contents Structure with Supplemental Viscous Dampers Structure with Supplemental Hysteretic Dampers Relationship of Maximum Interstory Drift of Uncontrolled Structures with Maximum Velocity of Ground Motion Relationship of Total Input Energy to Uncontrolled Structures with Velocity Power of Ground Motion Summary 296 Appendix 11.A 297 Appendix 11.B 298 Appendix 11.C 300 References 301 Index 303