《Dynamics of structures : theory and applications to earthquake engineering》求取 ⇩

PART ⅠSINGLE-DEGREE-OF-FREEDOM SYSTEMS1

1Equations of Motion，Problem Statement，and Solution Methods3

1.1 Simple Structures3

1.2 Single-Degree-of-Freedom System7

1.3 Force-Displacement Relation8

1.4 Damping Force13

1.5 Equation of Motion：External Force14

1.6 Mass-Spring-Damper System18

1.7 Equation of Motion：Earthquake Excitation20

1.8 Problem Statement and Element Forces23

1.9 Combining Static and Dynamic Responses25

1.10 Methods of Solution of the Differential Equation25

1.11 Study of SDF Systems：Organization29

Appendix 1：Stiffness Coefficients for a Flexural Element30

2Free Vibration35

2.1 Undamped Free Vibration35

2.2 Viscously Damped Free Vibration44

2.3 Energy in Free Vibration52

2.4 Coulomb-Damped Free Vibration53

3Response to Harmonic and Periodic Excitations61

Part A：Viscously Damped Systems：Basic Results62

3.1Harmonic Vibration of Undamped Systems62

3.2 Harmonic Vibration with Viscous Damping68

Part B：Viscously Damped Systems：Applications80

3.3Response to Vibration Generator80

3.4 Natural Frequency and Damping from Harmonic Tests83

3.5 Force Transmission and Vibration Isolation85

3.6 Response to Ground Motion and Vibration Isolation87

3.7 Vibration-Measuring Instruments91

3.8 Energy Dissipated in Viscous Damping94

3.9 Equivalent Viscous Damping98

Part C：Systems with Nonviscous Damping100

3.10Harmonic Vibration with Rate-Independent Damping100

3.11 Harmonic Vibration with Coulomb Friction104

Part D：Response to Periodic Excitation108

3.12Fourier Series Representation109

3.13 Response to Periodic Force109

Appendix 3：Four-Way Logarithmic Graph Paper113

4Response to Arbitrary，Step，and Pulse Excitations119

Part A：Response to Arbitrarily Time-Varying Forces119

4.1Response to Unit Impulse120

4.2 Response to Arbitrary Force121

Part B：Response to Step and Ramp Forces123

4.3Step Force123

4.4 Ramp or Linearly Increasing Force125

4.5 Step Force with Finite Rise Time126

Part C：Response to Pulse Excitations129

4.6Solution Methods129

4.7 Rectangular Pulse Force131

4.8 Half-Cycle Sine Pulse Force137

4.9 Symmetrical Triangular Pulse Force142

4.10 Effects of Pulse Shape and Approximate Analysis for Short Pulses144

4.11 Effects of Viscous Damping147

4.12 Response to Ground Motion149

5Numerical Evaluation of Dynamic Response155

5.1 Time-Stepping Methods155

5.2 Methods Based on Interpolation of Excitation157

5.3 Central Difference Method161

5.4 Newmark’s Method164

5.5 Stability and Computational Error170

5.6 Analysis of Nonlinear Response：Central Difference Method174

5.7 Analysis of Nonlinear Response：Newmark’s Method174

6Earthquake Response of Linear Systems187

6.1 Earthquake Excitation187

6.2 Equation of Motion193

6.3 Response Quantities194

6.4 Response History195

6.5 Response Spectrum Concept197

6.6 Deformation，Pseudo-velocity，and Pseudo-acceleration Response Spectra198

6.7 Peak Structural Response from the Response Spectrum206

6.8 Response Spectrum Characteristics211

6.9 Elastic Design Spectrum217

6.10 Comparison of Design and Response Spectra225

6.11 Distinction between Design and Response Spectra227

6.12 Velocity and Acceleration Response Spectra228

Appendix 6：El Centro，1940 Ground Motion232

7Earthquake Response of Inelastic Systems241

7.1 Force-Deformation Relations242

7.2 Normalized Yield Strength，Yield Reduction Factor，and Ductility Factor248

7.3 Equation of Motion and Controlling Parameters249

7.4 Effects of Yielding250

7.5 Response Spectrum for Yield Deformation and Yield Strength257

7.6 Design Strength and Deformation from the Response Spectrum261

7.7 Design Yield Strength261

7.8 Relative Effects of Yielding and Damping263

7.9 Dissipated Energy264

7.10 Inelastic Design Spectrum269

7.11 Comparison of Design and Response Spectra274

8Generalized Single-Degree-of-Freedom Systems277

8.1 Generalized SDF Systems277

8.2 Rigid-Body Assemblages279

8.3 Systems with Distributed Mass and Elasticity281

8.4 Lumped-Mass System：Shear Building292

8.5 Natural Vibration Frequency by Rayleigh’s Method298

8.6 Selection of Shape Function302

Appendix 8：Inertia Forces for Rigid Bodies306

PART ⅡMULTI-DEGREE-OF-FREEDOM SYSTEMS311

9Equations of Motion，Problem Statement，and Solution Methods313

9.1 Simple System：Two-Story Shear Building313

9.2 General Approach for Linear Systems318

9.3 Static Condensation334

9.4 Planar or Symmetric-Plan Systems：Ground Motion337

9.5 Unsymmetric-Plan Buildings：Ground Motion342

9.6 Symmetric-Plan Buildings：Torsional Excitation350

9.7 Multiple Support Excitation351

9.8 Inelastic Systems355

9.9 Problem Statement356

9.10 Element Forces356

9.11 Methods for Solving the Equations of Motion：Overview357

10Free Vibration365

Part A：Natural Vibration Frequencies and Modes366

10.1Systems without Damping366

10.2 Natural Vibration Frequencies and Modes368

10.3 Modal and Spectral Matrices370

10.4 Orthogonality of Modes371

10.5 Interpretation of Modal Orthogonality372

10.6 Normalization of Modes372

10.7 Modal Expansion of Displacements382

Part B：Free Vibration Response383

10.8Solution of Free Vibration Equations：Undamped Systems383

10.9 Free Vibration of Systems with Damping386

10.10 Solution of Free Vibration Equations：Classically Damped Systems390

Part C：Computation of Vibration Properties392

10.11Solution Methods for the Eigenvalue Problem392

10.12 Rayleigh’s Quotient394

10.13 Inverse Vector Iteration Method394

10.14 Vector Iteration with Shifts：Preferred Procedure399

10.15 Transformation of kφ=ω2mφ to the Standard Form404

11Damping in Structures409

Part A：Experimental Data and Recommended Modal Damping Ratios409

11.1Vibration Properties of Millikan Library Building409

11.2 Estimating Modal Damping Ratios414

Part B：Construction of Damping Matrix416

11.3Damping Matrix416

11.4 Classical Damping Matrix417

11.5 Nonclassical Damping Matrix425

12Dynamic Analysis and Response of Linear Systems429

Part A：Two-Degree-of-Freedom Systems429

12.1Analysis of Two-DOF Systems without Damping429

12.2 Vibration Absorber or Tuned Mass Damper432

Part B：Modal Analysis434

12.3Modal Equations for Undamped Systems434

12.4 Modal Equations for Damped Systems436

12.5 Displacement Response438

12.6 Element Forces438

12.7 Modal Analysis：Summary439

Part C：Modal Response Contributions444

12.8Modal Expansion of Excitation Vector p（t） = sp（t）444

12.9 Modal Analysis for p（t） = sp（t）447

12.10 Modal Contribution Factors448

12.11 Modal Contributions to Response449

Part D：Special Analysis Procedures455

12.12Static Correction Method455

12.13 Mode Acceleration Superposition Method458

12.14 Analysis of Nonclassically Damped Systems459

13Earthquake Analysis of Linear Systems467

Part A：Response History Analysis468

13.1Modal Analysis468

13.2 Multistory Buildings with Symmetric Plan474

13.3 Multistory Buildings with Unsymmetric Plan492

13.4 Torsional Response of Symmetric-Plan Buildings503

13.5 Response Analysis for Multiple Support Excitation508

13.6 Structural Idealization and Earthquake Response513

Part B：Response Spectrum Analysis514

13.7Peak Response from Earthquake Response Spectrum514

13.8 Multistory Buildings with Symmetric Plan519

13.9 Multistory Buildings with Unsymmetric Plan532

14Reduction of Degrees of Freedom549

14.1 Kinematic Constraints550

14.2 Static Condensation551

14.3 Rayleigh-Ritz Method551

14.4 Selection of Ritz Vectors554

14.5 Dynamic Analysis Using Ritz Vectors560

15Numerical Evaluation of Dynamic Response565

15.1 Time-Stepping Methods565

15.2 Analysis of Linear Systems with Nonclassical Damping567

15.3 Analysis of Nonlinear Systems574

16Systems with Distributed Mass and Elasticity585

16.1 Equation of Undamped Motion：Applied Forces586

16.2 Equation of Undamped Motion：Support Excitation587

16.3 Natural Vibration Frequencies and Modes588

16.4 Modal Orthogonality595

16.5 Modal Analysis of Forced Dynamic Response596

16.6 Earthquake Response History Analysis600

16.7 Earthquake Response Spectrum Andlysis604

16.8 Difficulty in Analyzing Practical Systems607

17Introduction to the Finite Element Method613

Part A：Rayleigh-Ritz Method613

17.1Formulation Using Conservation of Energy613

17.2 Formulation Using Virtual Work617

17.3 Disadvantages of Rayleigh-Ritz Method618

Part B：Finite Element Method619

17.4Finite Element Approximation619

17.5 Analysis Procedure621

17.6 Element Degrees of Freedom and Interpolation Functions622

17.7 Element Stiffness Matrix624

17.8 Element Mass Matrix625

17.9 Element（Applied） Force Vector626

17.10 Comparison of Finite Element and Exact Solutions630

17.11 Dynamic Analysis of Structural Continua632

PART ⅢEARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS639

18 Earthquake Response of Linearly Elastic Buildings641

18.1Systems Analyzed，Design Spectrum，and Response Quantities641

18.2 Influence of T1 and p on Response646

18.3 Modal Contribution Factors647

18.4 Influence of T1 on Higher-Mode Response649

18.5 Influence of p on Higher-Mode Response652

18.6 Heightwise Variation of Higher-Mode Response653

18.7 How Many Modes to Include655

19Earthquake Response of Inelastic Buildings659

19.1 Allowable Ductility and Ductility Demand660

19.2 Buildings with “Weak” or “Soft” First Story665

19.3 Buildings Designed for Code Force Distribution670

19.4 Limited Scope680

20Earthquake Dynamics of Base-Isolated Buildings683

20.1 Isolation Systems683

20.2 Base-Isolated One-Story Buildings686

20.3 Effectiveness of Base Isolation691

20.4 Base-Isolated Multistory Buildings695

20.5 Applications of Base Isolation701

21Structural Dynamics in Building Codes703

Part A：Building Codes and Structural Dynamics704

21.1Uniform Building Code（United States），1994704

21.2 National Building Code of Canada，1995707

21.3 Mexico Federal District Code，1987711

21.4 Structural Dynamics in Building Codes713

Part B：Evaluation of Building Codes720

21.5Base Shear720

21.6 Story Shears and Equivalent Static Forces723

21.7 Overturning Moments726

21.8 Concluding Remarks728

ANotation731

BAnswers to Selected Problems743

Index753