Dynamics of Structures : Theory and Applications to Earthquake Engineering

by Chopra, Anil K.

• ISBN13: 9780131561748
• ISBN10: 013156174X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: Prentice Hall

Summary

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.

Table of Contents

Foreword	p. xxi
Preface	p. xxiii
Preface to the Second Edition	p. xxv
Preface to the First Edition	p. xvii
Acknowledgments	p. xxxiii
Single-Degree-of-Freedom Systems	p. 1
Equations of Motion, Problem Statement, and Solution Methods	p. 3
Simple Structures	p. 3
Single-Degree-of-Freedom System	p. 7
Force-Displacement Relation	p. 8
Damping Force	p. 12
Equation of Motion: External Force	p. 14
Mass-Spring-Damper System	p. 19
Equation of Motion: Earthquake Excitation	p. 23
Problem Statement and Element Forces	p. 26
Combining Static and Dynamic Responses	p. 28
Methods of Solution of the Differential Equation	p. 28
Study of SDF Systems: Organization	p. 33
Stiffness Coefficients for a Flexural Element	p. 33
Free Vibration	p. 39
Undamped Free Vibration	p. 39
Viscously Damped Free Vibration	p. 48
Energy in Free Vibration	p. 56
Coulomb-Damped Free Vibration	p. 57
Response to Harmonic and Periodic Excitations	p. 65
Viscously Damped Systems: Basic Results	p. 66
Harmonic Vibration of Undamped Systems	p. 66
Harmonic Vibration with Viscous Damping	p. 72
Viscously Damped Systems: Applications	p. 85
Response to Vibration Generator	p. 85
Natural Frequency and Damping from Harmonic Tests	p. 87
Force Transmission and Vibration Isolation	p. 90
Response to Ground Motion and Vibration Isolation	p. 91
Vibration-Measuring Instruments	p. 95
Energy Dissipated in Viscous Damping	p. 99
Equivalent Viscous Damping	p. 103
Systems with Nonviscous Damping	p. 105
Harmonic Vibration with Rate-Independent Damping	p. 105
Harmonic Vibration with Coulomb Friction	p. 109
Response to Periodic Excitation	p. 113
Fourier Series Representation	p. 114
Response to Periodic Force	p. 114
Four-Way Logarithmic Graph Paper	p. 118
Response to Arbitrary, Step, and Pulse Excitations	p. 125
Response to Arbitrarily Time-Varying Forces	p. 125
Response to Unit Impulse	p. 126
Response to Arbitrary Force	p. 127
Response to Step and Ramp Forces	p. 129
Step Force	p. 129
Ramp or Linearly Increasing Force	p. 131
Step Force with Finite Rise Time	p. 132
Response to Pulse Excitations	p. 135
Solution Methods	p. 135
Rectangular Pulse Force	p. 137
Half-Cycle Sine Pulse Force	p. 143
Symmetrical Triangular Pulse Force	p. 148
Effects of Pulse Shape and Approximate Analysis for Short Pulses	p. 151
Effects of Viscous Damping	p. 154
Response to Ground Motion	p. 155
Numerical Evaluation of Dynamic Response	p. 165
Time-Stepping Methods	p. 165
Methods Based on Interpolation of Excitation	p. 167
Central Difference Method	p. 171
Newmark's Method	p. 174
Stability and Computational Error	p. 180
Analysis of Nonlinear Response: Central Difference Method	p. 184
Analysis of Nonlinear Response: Newmark's Method	p. 184
Earthquake Response of Linear Systems	p. 197
Earthquake Excitation	p. 197
Equation of Motion	p. 203
Response Quantities	p. 204
Response History	p. 205
Response Spectrum Concept	p. 207
Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra	p. 208
Peak Structural Response from the Response Spectrum	p. 217
Response Spectrum Characteristics	p. 222
Elastic Design Spectrum	p. 230
Comparison of Design and Response Spectra	p. 239
Distinction between Design and Response Spectra	p. 241
Velocity and Acceleration Response Spectra	p. 242
El Centro, 1940 Ground Motion	p. 246
Earthquake Response of Inelastic Systems	p. 257
Force-Deformation Relations	p. 258
Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor	p. 264
Equation of Motion and Controlling Parameters	p. 265
Effects of Yielding	p. 266
Response Spectrum for Yield Deformation and Yield Strength	p. 273
Yield Strength and Deformation from the Response Spectrum	p. 277
Yield Strength-Ductility Relation	p. 277
Relative Effects of Yielding and Damping	p. 279
Dissipated Energy	p. 280
Energy Dissipation Devices	p. 283
Inelastic Design Spectrum	p. 288
Applications of the Design Spectrum	p. 295
Comparison of Design and Response Spectra	p. 301
Generalized Single-Degree-of-Freedom Systems	p. 305
Generalized SDF Systems	p. 305
Rigid-Body Assemblages	p. 307
Systems with Distributed Mass and Elasticity	p. 309
Lumped-Mass System: Shear Building	p. 321
Natural Vibration Frequency by Rayleigh's Method	p. 328
Selection of Shape Function	p. 332
Inertia Forces for Rigid Bodies	p. 336
Multi-Degree-of-Freedom Systems	p. 343
Equations of Motion, Problem Statement, and Solution Methods	p. 345
Simple System: Two-Story Shear Building	p. 345
General Approach for Linear Systems	p. 350
Static Condensation	p. 367
Planar or Symmetric-Plan Systems: Ground Motion	p. 370
Unsymmetric-Plan Buildings: Ground Motion	p. 375
Symmetric-Plan Buildings: Torsional Excitation	p. 383
Multiple Support Excitation	p. 384
Inelastic Systems	p. 389
Problem Statement	p. 389
Element Forces	p. 390
Methods for Solving the Equations of Motion: Overview	p. 390
Free Vibration	p. 401
Natural Vibration Frequencies and Modes	p. 402
Systems without Damping	p. 402
Natural Vibration Frequencies and Modes	p. 404
Modal and Spectral Matrices	p. 406
Orthogonality of Modes	p. 407
Interpretation of Modal Orthogonality	p. 408
Normalization of Modes	p. 408
Modal Expansion of Displacements	p. 418
Free Vibration Response	p. 419
Solution of Free Vibration Equations: Undamped Systems	p. 419
Free Vibration of Systems with Damping	p. 422
Solution of Free Vibration Equations: Classically Damped Systems	p. 426
Computation of Vibration Properties	p. 428
Solution Methods for the Eigenvalue Problem	p. 428
Rayleigh's Quotient	p. 430
Inverse Vector Iteration Method	p. 430
Vector Iteration with Shifts: Preferred Procedure	p. 435
Transformation of k[phi] = [omega superscript 2]m[phi] to the Standard Form	p. 440
Damping in Structures	p. 447
Experimental Data and Recommended Modal Damping Ratios	p. 447
Vibration Properties of Millikan Library Building	p. 447
Estimating Modal Damping Ratios	p. 452
Construction of Damping Matrix	p. 454
Damping Matrix	p. 454
Classical Damping Matrix	p. 455
Nonclassical Damping Matrix	p. 463
Dynamic Analysis and Response of Linear Systems	p. 467
Two-Degree-of-Freedom Systems	p. 467
Analysis of Two-DOF Systems without Damping	p. 467
Vibration Absorber or Tuned Mass Damper	p. 470
Modal Analysis	p. 472
Modal Equations for Undamped Systems	p. 472
Modal Equations for Damped Systems	p. 475
Displacement Response	p. 476
Element Forces	p. 477
Modal Analysis: Summary	p. 477
Modal Response Contributions	p. 482
Modal Expansion of Excitation Vector p(t) = sp(t)	p. 482
Modal Analysis for p(t) = sp(t)	p. 486
Modal Contribution Factors	p. 487
Modal Responses and Required Number of Modes	p. 489
Special Analysis Procedures	p. 496
Static Correction Method	p. 496
Mode Acceleration Superposition Method	p. 499
Analysis of Nonclassically Damped Systems	p. 500
Earthquake Analysis of Linear Systems	p. 507
Response History Analysis	p. 508
Modal Analysis	p. 508
Multistory Buildings with Symmetric Plan	p. 514
Multistory Buildings with Unsymmetric Plan	p. 533
Torsional Response of Symmetric-Plan Buildings	p. 544
Response Analysis for Multiple Support Excitation	p. 548
Structural Idealization and Earthquake Response	p. 554
Response Spectrum Analysis	p. 555
Peak Response from Earthquake Response Spectrum	p. 555
Multistory Buildings with Symmetric Plan	p. 560
Multistory Buildings with Unsymmetric Plan	p. 572
Reduction of Degrees of Freedom	p. 593
Kinematic Constraints	p. 594
Mass Lumping in Selected DOFs	p. 595
Rayleigh-Ritz Method	p. 595
Selection of Ritz Vectors	p. 599
Dynamic Analysis Using Ritz Vectors	p. 604
Numerical Evaluation of Dynamic Response	p. 609
Time-Stepping Methods	p. 609
Analysis of Linear Systems with Nonclassical Damping	p. 611
Analysis of Nonlinear Systems	p. 618
Systems with Distributed Mass and Elasticity	p. 629
Equation of Undamped Motion: Applied Forces	p. 630
Equation of Undamped Motion: Support Excitation	p. 631
Natural Vibration Frequencies and Modes	p. 632
Modal Orthogonality	p. 639
Modal Analysis of Forced Dynamic Response	p. 641
Earthquake Response History Analysis	p. 648
Earthquake Response Spectrum Analysis	p. 653
Difficulty in Analyzing Practical Systems	p. 656
Introduction to the Finite Element Method	p. 661
Rayleigh-Ritz Method	p. 661
Formulation Using Conservation of Energy	p. 661
Formulation Using Virtual Work	p. 665
Disadvantages of Rayleigh-Ritz Method	p. 667
Finite Element Method	p. 667
Finite Element Approximation	p. 667
Analysis Procedure	p. 669
Element Degrees of Freedom and Interpolation Functions	p. 671
Element Stiffness Matrix	p. 672
Element Mass Matrix	p. 673
Element (Applied) Force Vector	p. 675
Comparison of Finite Element and Exact Solutions	p. 679
Dynamic Analysis of Structural Continua	p. 680
Earthquake Response and Design of Multistory Buildings	p. 687
Earthquake Response of Linearly Elastic Buildings	p. 689
Systems Analyzed, Design Spectrum, and Response Quantities	p. 689
Influence of T[subscript 1] and [rho] on Response	p. 694
Modal Contribution Factors	p. 695
Influence of T[subscript 1] on Higher-Mode Response	p. 697
Influence of [rho] on Higher-Mode Response	p. 700
Heightwise Variation of Higher-Mode Response	p. 701
How Many Modes to Include	p. 703
Earthquake Analysis and Response of Inelastic Buildings	p. 707
Nonlinear Response History Analysis	p. 708
Equations of Motion: Formulation and Solution	p. 708
Computing Seismic Demands: Factors To Be Considered	p. 709
Story Drift Demands	p. 713
Strength Demands for SDF and MDF Systems	p. 719
Approximate Analysis Procedures	p. 720
Motivation and Basic Concept	p. 720
Uncoupled Modal Response History Analysis	p. 722
Modal Pushover Analysis	p. 729
Evaluation of Modal Pushover Analysis	p. 734
Simplified Modal Pushover Analysis for Practical Application	p. 739
Earthquake Dynamics of Base-Isolated Buildings	p. 741
Isolation Systems	p. 741
Base-Isolated One-Story Buildings	p. 744
Effectiveness of Base Isolation	p. 750
Base-Isolated Multistory Buildings	p. 754
Applications of Base Isolation	p. 760
Structural Dynamics in Building Codes	p. 767
Building Codes and Structural Dynamics	p. 768
International Building Code (United States), 2006	p. 768
National Building Code of Canada, 2005	p. 771
Mexico Federal District Code, 2004	p. 773
Eurocode 8, 2004	p. 775
Structural Dynamics in Building Codes	p. 778
Evaluation of Building Codes	p. 784
Base Shear	p. 784
Story Shears and Equivalent Static Forces	p. 788
Overturning Moments	p. 790
Concluding Remarks	p. 793
Structural Dynamics in Building Evaluation Guidelines	p. 795
Nonlinear Dynamic Procedure: Current Practice	p. 796
SDF-System Estimate of Roof Displacement	p. 797
Estimating Deformation of Inelastic SDF Systems	p. 799
Nonlinear Static Procedure	p. 806
Concluding Remarks	p. 812
Frequency-Domain Method of Response Analysis	p. 815
Notation	p. 837
Answers to Selected Problems	p. 849
Index	p. 865
Table of Contents provided by Ingram. All Rights Reserved.