Dynamics of structures : theory and applications to earthquake engineering

著者

• Chopra, Anil K.

書誌事項

Dynamics of structures : theory and applications to earthquake engineering

Anil K. Chopra

（Prentice-Hall international series in civil engineering and engineering mechanics）

Pearson Prentice Hall, c2007

3rd ed

注記

Includes bibliographical references and index

内容説明・目次

内容説明

Designed for senior-level and graduate courses in Dynamics of Structures and Earthquake Engineering. The text includes many topics encompassing the theory of structural dynamics and the application of this theory regarding earthquake analysis, response, and design of structures. No prior knowledge of structural dynamics is assumed and the manner of presentation is sufficiently detailed and integrated, to make the book suitable for self-study by students and professional engineers.

目次

Contents Foreword xxi Preface xxiii Preface to the Second Edition xxv Preface to the First Edition xxvii Acknowledgments xxxiii PART I SINGLE-DEGREE-OF-FREEDOM SYSTEMS 1 1 Equations of Motion, Problem Statement, and Solution Methods 3 1.1 Simple Structures 3 1.2 Single-Degree-of-Freedom System 7 1.3 Force-Displacement Relation 8 1.4 Damping Force 12 1.5 Equation of Motion: External Force 14 1.6 Mass-Spring-Damper System 19 1.7 Equation of Motion: Earthquake Excitation 23 1.8 Problem Statement and Element Forces 26 1.9 Combining Static and Dynamic Responses 28 1.10 Methods of Solution of the Differential Equation 28 1.11 Study of SDF Systems: Organization 33 Appendix 1: Stiffness Coefficients for a Flexural Element 33 2 Free Vibration 39 2.1 Undamped Free Vibration 39 2.2 Viscously Damped Free Vibration 48 2.3 Energy in Free Vibration 56 2.4 Coulomb-Damped Free Vibration 57 3 Response to Harmonic and Periodic Excitations 65 Part A: Viscously Damped Systems: Basic Results 66 3.1 Harmonic Vibration of Undamped Systems 66 3.2 Harmonic Vibration with Viscous Damping 72 Part B: Viscously Damped Systems: Applications 85 3.3 Response to Vibration Generator 85 3.4 Natural Frequency and Damping from Harmonic Tests 87 3.5 Force Transmission and Vibration Isolation 90 3.6 Response to Ground Motion and Vibration Isolation 91 3.7 Vibration-Measuring Instruments 95 3.8 Energy Dissipated in Viscous Damping 99 3.9 Equivalent Viscous Damping 103 Part C: Systems with Nonviscous Damping 105 3.10 Harmonic Vibration with Rate-Independent Damping 105 3.11 Harmonic Vibration with Coulomb Friction 109 Part D: Response to Periodic Excitation 113 3.12 Fourier Series Representation 114 3.13 Response to Periodic Force 114 Appendix 3: Four-Way Logarithmic Graph Paper 118 4 Response to Arbitrary, Step, and Pulse Excitations 125 Part A: Response to Arbitrarily Time-Varying Forces 125 4.1 Response to Unit Impulse 126 4.2 Response to Arbitrary Force 127 Part B: Response to Step and Ramp Forces 129 4.3 Step Force 129 4.4 Ramp or Linearly Increasing Force 131 4.5 Step Force with Finite Rise Time 132 Part C: Response to Pulse Excitations 135 4.6 Solution Methods 135 4.7 Rectangular Pulse Force 137 4.8 Half-Cycle Sine Pulse Force 143 4.9 Symmetrical Triangular Pulse Force 148 4.10 Effects of Pulse Shape and Approximate Analysis for Short Pulses 151 4.11 Effects of Viscous Damping 154 4.12 Response to Ground Motion 155 5 Numerical Evaluation of Dynamic Response 165 5.1 Time-Stepping Methods 165 5.2 Methods Based on Interpolation of Excitation 167 5.3 Central Difference Method 171 5.4 Newmark's Method 174 5.5 Stability and Computational Error 180 5.6 Analysis of Nonlinear Response: Central Difference Method 184 5.7 Analysis of Nonlinear Response: Newmark's Method 184 6 Earthquake Response of Linear Systems 197 6.1 Earthquake Excitation 197 6.2 Equation of Motion 203 6.3 Response Quantities 204 6.4 Response History 205 6.5 Response Spectrum Concept 207 6.6 Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra 208 6.7 Peak Structural Response from the Response Spectrum 217 6.8 Response Spectrum Characteristics 222 6.9 Elastic Design Spectrum 230 6.10 Comparison of Design and Response Spectra 239 6.11 Distinction between Design and Response Spectra 241 6.12 Velocity and Acceleration Response Spectra 242 Appendix 6: ElCentro, 1940 Ground Motion 246 7 Earthquake Response of Inelastic Systems 257 7.1 Force-Deformation Relations 258 7.2 Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor 264 7.3 Equation of Motion and Controlling Parameters 265 7.4 Effects of Yielding 266 7.5 Response Spectrum for Yield Deformation and Yield Strength 273 7.6 Yield Strength and Deformation from the Response Spectrum 277 7.7 Yield Strength-Ductility Relation 277 7.8 Relative Effects of Yielding and Damping 279 7.9 Dissipated Energy 280 7.10 Energy Dissipation Devices 283 7.11 Inelastic Design Spectrum 288 7.12 Applications of the Design Spectrum 295 7.13 Comparison of Design and Response Spectra 301 8 Generalized Single-Degree-of-Freedom Systems 305 8.1 Generalized SDF Systems 305 8.2 Rigid-Body Assemblages 307 8.3 Systems with Distributed Mass and Elasticity 309 8.4 Lumped-Mass System: Shear Building 321 8.5 Natural Vibration Frequency by Rayleigh's Method 328 8.6 Selection of Shape Function 332 Appendix 8: Inertia Forces for Rigid Bodies 336 PART II MULTI-DEGREE-OF-FREEDOM SYSTEMS 343 9 Equations of Motion, Problem Statement, and Solution Methods 345 9.1 Simple System: Two-Story Shear Building 345 9.2 General Approach for Linear Systems 350 9.3 Static Condensation 367 9.4 Planar or Symmetric-Plan Systems: Ground Motion 370 9.5 Unsymmetric-Plan Buildings: Ground Motion 375 9.6 Symmetric-Plan Buildings: Torsional Excitation 383 9.7 Multiple Support Excitation 384 9.8 Inelastic Systems 389 9.9 Problem Statement 389 9.10 Element Forces 390 9.11 Methods for Solving the Equations of Motion: Overview 390 10 Free Vibration 401 Part A: Natural Vibration Frequencies and Modes 402 10.1 Systems without Damping 402 10.2 Natural Vibration Frequencies and Modes 404 10.3 Modal and Spectral Matrices 406 10.4 Orthogonality of Modes 407 10.5 Interpretation of Modal Orthogonality 408 10.6 Normalization of Modes 408 10.7 Modal Expansion of Displacements 418 Part B: Free Vibration Response 419 10.8 Solution of Free Vibration Equations: Undamped Systems 419 10.9 Free Vibration of Systems with Damping 422 10.10 Solution of Free Vibration Equations: Classically Damped Systems 426 Part C: Computation of Vibration Properties 428 10.11 Solution Methods for the Eigenvalue Problem 428 10.12 Rayleigh's Quotient 430 10.13 Inverse Vector Iteration Method 430 10.14 Vector Iteration with Shifts: Preferred Procedure 435 10.15 Transformation of k = 2m to the StandardForm 440 11 Damping in Structures 447 Part A: Experimental Data and Recommended Modal Damping Ratios 447 11.1 Vibration Properties of Millikan Library Building 447 11.2 Estimating Modal Damping Ratios 452 Part B: Construction of Damping Matrix 454 11.3 Damping Matrix 454 11.4 Classical Damping Matrix 455 11.5 Nonclassical Damping Matrix 463 12 Dynamic Analysis and Response of Linear Systems 467 Part A: Two-Degree-of-Freedom Systems 467 12.1 Analysis of Two-DOF Systems without Damping 467 12.2 Vibration Absorber or Tuned Mass Damper 470 Part B: Modal Analysis 472 12.3 Modal Equations for Undamped Systems 472 12.4 Modal Equations for Damped Systems 475 12.5 Displacement Response 476 12.6 Element Forces 477 12.7 Modal Analysis: Summary 477 Part C: Modal Response Contributions 482 12.8 Modal Expansion of Excitation Vectorp(t) = sp(t) 482 12.9 Modal Analysis for p(t) = sp(t) 486 12.10 Modal Contribution Factors 487 12.11 Modal Responses and Required Number of Modes 489 Part D: Special Analysis Procedures 496 12.12 Static Correction Method 496 12.13 Mode Acceleration Superposition Method 499 12.14 Analysis of Nonclassically Damped Systems 500 13 Earthquake Analysis of Linear Systems 507 Part A: Response History Analysis 508 13.1 Modal Analysis 508 13.2 Multistory Buildings with Symmetric Plan 514 13.3 Multistory Buildings with Unsymmetric Plan 533 13.4 Torsional Response of Symmetric-Plan Buildings 544 13.5 Response Analysis for Multiple Support Excitation 548 13.6 Structural Idealization and Earthquake Response 554 Part B: Response Spectrum Analysis 555 13.7 Peak Response from Earthquake Response Spectrum 555 13.8 Multistory Buildings with Symmetric Plan 560 13.9 Multistory Buildings with Unsymmetric Plan 572 14 Reduction of Degrees of Freedom 593 14.1 Kinematic Constraints 594 14.2 Mass Lumping in Selected DOFs 595 14.3 Rayleigh-Ritz Method 595 14.4 Selection of Ritz Vectors 599 14.5 Dynamic Analysis Using Ritz Vectors 604 15 Numerical Evaluation of Dynamic Response 609 15.1 Time-Stepping Methods 609 15.2 Analysis of Linear Systems with Nonclassical Damping 611 15.3 Analysis of Nonlinear Systems 618 16 Systems with Distributed Mass and Elasticity 629 16.1 Equation of Undamped Motion: Applied Forces 630 16.2 Equation of Undamped Motion: Support Excitation 631 16.3 Natural Vibration Frequencies and Modes 632 16.4 Modal Orthogonality 639 16.5 Modal Analysis of Forced Dynamic Response 641 16.6 Earthquake Response History Analysis 648 16.7 Earthquake Response Spectrum Analysis 653 16.8 Difficulty in Analyzing Practical Systems 656 17 Introduction to the Finite Element Method 661 Part A: Rayleigh-Ritz Method 661 17.1 Formulation Using Conservation of Energy 661 17.2 Formulation Using Virtual Work 665 17.3 Disadvantages of Rayleigh-Ritz Method 667 Part B: Finite Element Method 667 17.4 Finite Element Approximation 667 17.5 Analysis Procedure 669 17.6 Element Degrees of Freedom and InterpolationFunctions 671 17.7 Element Stiffness Matrix 672 17.8 Element Mass Matrix 673 17.9 Element (Applied) Force Vector 675 17.10 Comparison of Finite Element and ExactSolutions 679 17.11 Dynamic Analysis of Structural Continua 680 PART III EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS 687 18 Earthquake Response of Linearly Elastic Buildings 689 18.1 Systems Analyzed, Design Spectrum, and Response Quantities 689 18.2 Influence of T1 and ? on Response 694 18.3 Modal Contribution Factors 695 18.4 Influence of T1 on Higher-Mode Response 697 18.5 Influence of ? on Higher-Mode Response 700 18.6 Heightwise Variation of Higher-Mode Response 701 18.7 How Many Modes to Include 703 19 Earthquake Analysis and Response of Inelastic Buildings 707 Part A: Nonlinear Response History Analysis 708 19.1 Equations of Motion: Formulation and Solution 708 19.2 Computing Seismic Demands: Factors To Be Considered 709 19.3 Story Drift Demands 713 19.4 Strength Demands for SDF and MDF Systems 719 Part B: Approximate Analysis Procedures 720 19.5 Motivation and Basic Concept 720 19.6 Uncoupled Modal Response History Analysis 722 19.7 Modal Pushover Analysis 729 19.8 Evaluation of Modal Pushover Analysis 734 19.9 Simplified Modal Pushover Analysis for Practical Application 739 20 Earthquake Dynamics of Base-Isolated Buildings 741 20.1 Isolation Systems 741 20.2 Base-Isolated One-Story Buildings 744 20.3 Effectiveness of Base Isolation 750 20.4 Base-Isolated Multistory Buildings 754 20.5 Applications of Base Isolation 760 21 Structural Dynamics in Building Codes 767 Part A: Building Codes and Structural Dynamics 768 21.1 International Building Code (United States), 2006 768 21.2 National Building Code of Canada, 2005 771 21.3 Mexico Federal District Code, 2004 773 21.4 Eurocode 8, 2004 775 21.5 Structural Dynamics in Building Codes 778 Part B: Evaluation of Building Codes 784 21.6 Base Shear 784 21.7 Story Shears and Equivalent Static Forces 788 21.8 Overturning Moments 790 21.9 Concluding Remarks 793 22 Structural Dynamics in Building Evaluation Guidelines 795 22.1 Nonlinear Dynamic Procedure: Current Practice 796 22.2 SDF-System Estimate of Roof Displacement 797 22.3 Estimating Deformation of Inelastic SDF Systems 799 22.4 Nonlinear Static Procedure 806 22.5 Concluding Remarks 812 A Frequency-Domain Method of Response Analysis 815 B Notation 837 C Answers to Selected Problems 849 Index 865

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詳細情報

• NII書誌ID(NCID): BA78859657
• ISBN:
  • 013156174X
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Upper Saddle River, N.J.
• ページ数/冊数: xxxiv, 876 p.
• 大きさ: 25 cm
• 分類:
  • LCC : TA654.6
  • DC21 : 624.1/762
• 件名:
  • LCSH : Earthquake engineering
  • LCSH : Structural dynamics
• 親書誌ID:
  • BA00215532