Dynamics of Structures : Theory and Applications to Earthquake Engineering

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2007-01-01
  • Publisher: Prentice Hall
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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

Forewordp. xxi
Prefacep. xxiii
Preface to the Second Editionp. xxv
Preface to the First Editionp. xvii
Acknowledgmentsp. xxxiii
Single-Degree-of-Freedom Systemsp. 1
Equations of Motion, Problem Statement, and Solution Methodsp. 3
Simple Structuresp. 3
Single-Degree-of-Freedom Systemp. 7
Force-Displacement Relationp. 8
Damping Forcep. 12
Equation of Motion: External Forcep. 14
Mass-Spring-Damper Systemp. 19
Equation of Motion: Earthquake Excitationp. 23
Problem Statement and Element Forcesp. 26
Combining Static and Dynamic Responsesp. 28
Methods of Solution of the Differential Equationp. 28
Study of SDF Systems: Organizationp. 33
Stiffness Coefficients for a Flexural Elementp. 33
Free Vibrationp. 39
Undamped Free Vibrationp. 39
Viscously Damped Free Vibrationp. 48
Energy in Free Vibrationp. 56
Coulomb-Damped Free Vibrationp. 57
Response to Harmonic and Periodic Excitationsp. 65
Viscously Damped Systems: Basic Resultsp. 66
Harmonic Vibration of Undamped Systemsp. 66
Harmonic Vibration with Viscous Dampingp. 72
Viscously Damped Systems: Applicationsp. 85
Response to Vibration Generatorp. 85
Natural Frequency and Damping from Harmonic Testsp. 87
Force Transmission and Vibration Isolationp. 90
Response to Ground Motion and Vibration Isolationp. 91
Vibration-Measuring Instrumentsp. 95
Energy Dissipated in Viscous Dampingp. 99
Equivalent Viscous Dampingp. 103
Systems with Nonviscous Dampingp. 105
Harmonic Vibration with Rate-Independent Dampingp. 105
Harmonic Vibration with Coulomb Frictionp. 109
Response to Periodic Excitationp. 113
Fourier Series Representationp. 114
Response to Periodic Forcep. 114
Four-Way Logarithmic Graph Paperp. 118
Response to Arbitrary, Step, and Pulse Excitationsp. 125
Response to Arbitrarily Time-Varying Forcesp. 125
Response to Unit Impulsep. 126
Response to Arbitrary Forcep. 127
Response to Step and Ramp Forcesp. 129
Step Forcep. 129
Ramp or Linearly Increasing Forcep. 131
Step Force with Finite Rise Timep. 132
Response to Pulse Excitationsp. 135
Solution Methodsp. 135
Rectangular Pulse Forcep. 137
Half-Cycle Sine Pulse Forcep. 143
Symmetrical Triangular Pulse Forcep. 148
Effects of Pulse Shape and Approximate Analysis for Short Pulsesp. 151
Effects of Viscous Dampingp. 154
Response to Ground Motionp. 155
Numerical Evaluation of Dynamic Responsep. 165
Time-Stepping Methodsp. 165
Methods Based on Interpolation of Excitationp. 167
Central Difference Methodp. 171
Newmark's Methodp. 174
Stability and Computational Errorp. 180
Analysis of Nonlinear Response: Central Difference Methodp. 184
Analysis of Nonlinear Response: Newmark's Methodp. 184
Earthquake Response of Linear Systemsp. 197
Earthquake Excitationp. 197
Equation of Motionp. 203
Response Quantitiesp. 204
Response Historyp. 205
Response Spectrum Conceptp. 207
Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectrap. 208
Peak Structural Response from the Response Spectrump. 217
Response Spectrum Characteristicsp. 222
Elastic Design Spectrump. 230
Comparison of Design and Response Spectrap. 239
Distinction between Design and Response Spectrap. 241
Velocity and Acceleration Response Spectrap. 242
El Centro, 1940 Ground Motionp. 246
Earthquake Response of Inelastic Systemsp. 257
Force-Deformation Relationsp. 258
Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factorp. 264
Equation of Motion and Controlling Parametersp. 265
Effects of Yieldingp. 266
Response Spectrum for Yield Deformation and Yield Strengthp. 273
Yield Strength and Deformation from the Response Spectrump. 277
Yield Strength-Ductility Relationp. 277
Relative Effects of Yielding and Dampingp. 279
Dissipated Energyp. 280
Energy Dissipation Devicesp. 283
Inelastic Design Spectrump. 288
Applications of the Design Spectrump. 295
Comparison of Design and Response Spectrap. 301
Generalized Single-Degree-of-Freedom Systemsp. 305
Generalized SDF Systemsp. 305
Rigid-Body Assemblagesp. 307
Systems with Distributed Mass and Elasticityp. 309
Lumped-Mass System: Shear Buildingp. 321
Natural Vibration Frequency by Rayleigh's Methodp. 328
Selection of Shape Functionp. 332
Inertia Forces for Rigid Bodiesp. 336
Multi-Degree-of-Freedom Systemsp. 343
Equations of Motion, Problem Statement, and Solution Methodsp. 345
Simple System: Two-Story Shear Buildingp. 345
General Approach for Linear Systemsp. 350
Static Condensationp. 367
Planar or Symmetric-Plan Systems: Ground Motionp. 370
Unsymmetric-Plan Buildings: Ground Motionp. 375
Symmetric-Plan Buildings: Torsional Excitationp. 383
Multiple Support Excitationp. 384
Inelastic Systemsp. 389
Problem Statementp. 389
Element Forcesp. 390
Methods for Solving the Equations of Motion: Overviewp. 390
Free Vibrationp. 401
Natural Vibration Frequencies and Modesp. 402
Systems without Dampingp. 402
Natural Vibration Frequencies and Modesp. 404
Modal and Spectral Matricesp. 406
Orthogonality of Modesp. 407
Interpretation of Modal Orthogonalityp. 408
Normalization of Modesp. 408
Modal Expansion of Displacementsp. 418
Free Vibration Responsep. 419
Solution of Free Vibration Equations: Undamped Systemsp. 419
Free Vibration of Systems with Dampingp. 422
Solution of Free Vibration Equations: Classically Damped Systemsp. 426
Computation of Vibration Propertiesp. 428
Solution Methods for the Eigenvalue Problemp. 428
Rayleigh's Quotientp. 430
Inverse Vector Iteration Methodp. 430
Vector Iteration with Shifts: Preferred Procedurep. 435
Transformation of k[phi] = [omega superscript 2]m[phi] to the Standard Formp. 440
Damping in Structuresp. 447
Experimental Data and Recommended Modal Damping Ratiosp. 447
Vibration Properties of Millikan Library Buildingp. 447
Estimating Modal Damping Ratiosp. 452
Construction of Damping Matrixp. 454
Damping Matrixp. 454
Classical Damping Matrixp. 455
Nonclassical Damping Matrixp. 463
Dynamic Analysis and Response of Linear Systemsp. 467
Two-Degree-of-Freedom Systemsp. 467
Analysis of Two-DOF Systems without Dampingp. 467
Vibration Absorber or Tuned Mass Damperp. 470
Modal Analysisp. 472
Modal Equations for Undamped Systemsp. 472
Modal Equations for Damped Systemsp. 475
Displacement Responsep. 476
Element Forcesp. 477
Modal Analysis: Summaryp. 477
Modal Response Contributionsp. 482
Modal Expansion of Excitation Vector p(t) = sp(t)p. 482
Modal Analysis for p(t) = sp(t)p. 486
Modal Contribution Factorsp. 487
Modal Responses and Required Number of Modesp. 489
Special Analysis Proceduresp. 496
Static Correction Methodp. 496
Mode Acceleration Superposition Methodp. 499
Analysis of Nonclassically Damped Systemsp. 500
Earthquake Analysis of Linear Systemsp. 507
Response History Analysisp. 508
Modal Analysisp. 508
Multistory Buildings with Symmetric Planp. 514
Multistory Buildings with Unsymmetric Planp. 533
Torsional Response of Symmetric-Plan Buildingsp. 544
Response Analysis for Multiple Support Excitationp. 548
Structural Idealization and Earthquake Responsep. 554
Response Spectrum Analysisp. 555
Peak Response from Earthquake Response Spectrump. 555
Multistory Buildings with Symmetric Planp. 560
Multistory Buildings with Unsymmetric Planp. 572
Reduction of Degrees of Freedomp. 593
Kinematic Constraintsp. 594
Mass Lumping in Selected DOFsp. 595
Rayleigh-Ritz Methodp. 595
Selection of Ritz Vectorsp. 599
Dynamic Analysis Using Ritz Vectorsp. 604
Numerical Evaluation of Dynamic Responsep. 609
Time-Stepping Methodsp. 609
Analysis of Linear Systems with Nonclassical Dampingp. 611
Analysis of Nonlinear Systemsp. 618
Systems with Distributed Mass and Elasticityp. 629
Equation of Undamped Motion: Applied Forcesp. 630
Equation of Undamped Motion: Support Excitationp. 631
Natural Vibration Frequencies and Modesp. 632
Modal Orthogonalityp. 639
Modal Analysis of Forced Dynamic Responsep. 641
Earthquake Response History Analysisp. 648
Earthquake Response Spectrum Analysisp. 653
Difficulty in Analyzing Practical Systemsp. 656
Introduction to the Finite Element Methodp. 661
Rayleigh-Ritz Methodp. 661
Formulation Using Conservation of Energyp. 661
Formulation Using Virtual Workp. 665
Disadvantages of Rayleigh-Ritz Methodp. 667
Finite Element Methodp. 667
Finite Element Approximationp. 667
Analysis Procedurep. 669
Element Degrees of Freedom and Interpolation Functionsp. 671
Element Stiffness Matrixp. 672
Element Mass Matrixp. 673
Element (Applied) Force Vectorp. 675
Comparison of Finite Element and Exact Solutionsp. 679
Dynamic Analysis of Structural Continuap. 680
Earthquake Response and Design of Multistory Buildingsp. 687
Earthquake Response of Linearly Elastic Buildingsp. 689
Systems Analyzed, Design Spectrum, and Response Quantitiesp. 689
Influence of T[subscript 1] and [rho] on Responsep. 694
Modal Contribution Factorsp. 695
Influence of T[subscript 1] on Higher-Mode Responsep. 697
Influence of [rho] on Higher-Mode Responsep. 700
Heightwise Variation of Higher-Mode Responsep. 701
How Many Modes to Includep. 703
Earthquake Analysis and Response of Inelastic Buildingsp. 707
Nonlinear Response History Analysisp. 708
Equations of Motion: Formulation and Solutionp. 708
Computing Seismic Demands: Factors To Be Consideredp. 709
Story Drift Demandsp. 713
Strength Demands for SDF and MDF Systemsp. 719
Approximate Analysis Proceduresp. 720
Motivation and Basic Conceptp. 720
Uncoupled Modal Response History Analysisp. 722
Modal Pushover Analysisp. 729
Evaluation of Modal Pushover Analysisp. 734
Simplified Modal Pushover Analysis for Practical Applicationp. 739
Earthquake Dynamics of Base-Isolated Buildingsp. 741
Isolation Systemsp. 741
Base-Isolated One-Story Buildingsp. 744
Effectiveness of Base Isolationp. 750
Base-Isolated Multistory Buildingsp. 754
Applications of Base Isolationp. 760
Structural Dynamics in Building Codesp. 767
Building Codes and Structural Dynamicsp. 768
International Building Code (United States), 2006p. 768
National Building Code of Canada, 2005p. 771
Mexico Federal District Code, 2004p. 773
Eurocode 8, 2004p. 775
Structural Dynamics in Building Codesp. 778
Evaluation of Building Codesp. 784
Base Shearp. 784
Story Shears and Equivalent Static Forcesp. 788
Overturning Momentsp. 790
Concluding Remarksp. 793
Structural Dynamics in Building Evaluation Guidelinesp. 795
Nonlinear Dynamic Procedure: Current Practicep. 796
SDF-System Estimate of Roof Displacementp. 797
Estimating Deformation of Inelastic SDF Systemsp. 799
Nonlinear Static Procedurep. 806
Concluding Remarksp. 812
Frequency-Domain Method of Response Analysisp. 815
Notationp. 837
Answers to Selected Problemsp. 849
Indexp. 865
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