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Basic Structural Dynamics

ISBN: 978-0-470-87939-9
288 pages
July 2012
Basic Structural Dynamics (0470879394) cover image

A concise introduction to structural dynamics and earthquake engineering

Basic Structural Dynamics serves as a fundamental introduction to the topic of structural dynamics. Covering single and multiple-degree-of-freedom systems while providing an introduction to earthquake engineering, the book keeps the coverage succinct and on topic at a level that is appropriate for undergraduate and graduate students. Through dozens of worked examples based on actual structures, it also introduces readers to MATLAB, a powerful software for solving both simple and complex structural dynamics problems.

Conceptually composed of three parts, the book begins with the basic concepts and dynamic response of single-degree-of-freedom systems to various excitations. Next, it covers the linear and nonlinear response of multiple-degree-of-freedom systems to various excitations. Finally, it deals with linear and nonlinear response of structures subjected to earthquake ground motions and structural dynamics-related code provisions for assessing seismic response of structures. Chapter coverage includes:

  • Single-degree-of-freedom systems
  • Free vibration response of SDOF systems
  • Response to harmonic loading
  • Response to impulse loads
  • Response to arbitrary dynamic loading
  • Multiple-degree-of-freedom systems
  • Introduction to nonlinear response of structures
  • Seismic response of structures

If you're an undergraduate or graduate student or a practicing structural or mechanical engineer who requires some background on structural dynamics and the effects of earthquakes on structures, Basic Structural Dynamics will quickly get you up to speed on the subject without sacrificing important information.

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PREFACE xi

1 BASIC CONCEPTS OF STRUCTURAL DYNAMICS 1

1.1 The Dynamic Environment / 1

1.2 Types of Dynamic Loading / 2

1.3 Basic Principles / 3

1.4 Dynamic Equilibrium / 9

2 SINGLE-DEGREE-OF-FREEDOM SYSTEMS 13

2.1 Reduction of Degrees of Freedom / 13

2.2 Time-Dependent Force / 15

2.3 Gravitational Forces / 17

2.4 Earthquake Ground Motion / 18

2.5 Formulation of Equation of Motion / 19

2.5.1 d’Alembert’s Principle / 19

2.5.2 Virtual Work (Virtual Displacements) / 20

2.6 Generalized Coordinates / 22

2.6.1 Discrete Parameters / 23

2.6.2 Continuous Parameters / 31

2.6.3 Transformation Factors / 38

2.6.4 Axial Load Effect / 42

2.6.5 Linear Approximation / 44

3 FREE-VIBRATION RESPONSE OF SINGLE-DEGREE-OF-FREEDOM SYSTEMS 51

3.1 Undamped Free Vibration / 51

3.1.1 Alternate Solution / 53

3.1.2 Rayleigh’s Method / 58

3.1.3 Selection of Deflected Shape / 60

3.2 Damped Free Vibration / 61

3.2.1 Rotating Vector Form / 63

3.2.2 Logarithmic Decrement / 66

3.2.3 Radical Positive / 67

4 RESPONSE TO HARMONIC LOADING 77

4.1 Undamped Dynamic System / 77

4.2 Damped Dynamic System / 84

4.3 Tripartite Logarithmic Plot / 91

4.4 Evaluation of Damping / 91

4.5 Seismic Accelerometers and Displacement Meters (Seismographs) / 95

5 RESPONSE TO IMPULSE LOADS 101

5.1 Rectangular Pulse / 104

5.2 Damped Rectangular Pulse / 108

5.3 Triangular Pulse / 109

5.4 Approximate Analysis for Short-Duration Impulse Load / 112

6 RESPONSE TO ARBITRARY DYNAMIC LOADING 121

6.1 Duhamel Integral / 121

6.2 Numerical Formulation of the Equation of Motion / 123

6.3 Numerical Integration Methods / 124

6.4 Newmark’s Numerical Method / 127

7 MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 137

7.1 Elastic Properties / 137

7.1.1 Flexibility / 137

7.1.2 Stiffness / 138

7.1.3 Inertia / 139

7.1.4 Viscous Damping / 139

7.2 Undamped Free Vibration / 141

7.3 Free Vibration / 149

7.4 Betti’s Law / 153

7.5 Orthogonality Properties of Mode Shapes / 155

7.6 Changing Coordinates (Inverse Transformation) / 156

7.7 Holzer Method for Shear Buildings / 159

7.8 Axial Load Effects (Linear Approximation) / 162

7.9 Modal Equations for Undamped Time-Dependent Force Analysis / 165

7.10 Modal Equations of Damped Forced Vibration / 174

7.11 Modal Equations for Seismic Response Analysis / 179

8 NONLINEAR RESPONSE OF MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 183

8.1 Static Nonlinear Analysis / 184

8.2 Dynamic Nonlinear Analysis / 185

8.3 Gauss Reduction / 189

8.4 MATLAB Applications / 190

9 SEISMIC RESPONSE OF STRUCTURES 201

9.1 Introduction / 201

9.2 Linear Elastic Response Spectra / 203

9.3 Elastic Design Response Spectrum / 208

9.4 Earthquake Response of SDOF Systems / 215

9.5 Earthquake Response Analysis of MDOF Systems / 219

9.5.1 Time History Modal Analysis / 221

9.5.2 Modal Combinations for Spectral Analyses / 222

9.6 Structural Dynamics in the Building Code / 232

9.6.1 Equivalent Lateral Force Procedure / 234

9.6.2 Modal Response Spectrum Procedure / 237

APPENDIX—HISTORICAL DEVELOPMENT OF BUILDING CODE SEISMIC PROVISIONS 249

SELECTED REFERENCES 263

INDEX 265

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James C. Anderson is Professor of Civil Engineering at USC and is the author of, and contributor to, numerous book and journal articles.

Farzad Naeim is Vice President and General Counsel at John A. Martin & Associates, Inc., a consulting structural engineering firm headquartered in Los Angeles, California. He has received numerous awards for his contributions to earthquake engineering, including the 2007 Fazlur R. Khan Lifetime Achievement Medal by the Council on Tall Buildings and Urban Habitat.

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