Structural Dynamics

I Structures Modeled as a Single Degree-of-Freedom System.- 1 Undamped Single Degree-of-Freedom Systems.- 1.1 Degrees of Freedom.- 1.2 Undamped System.- 1.3 Springs in Parallel or in Series.- 1.4 Newton's Law of Motion.- 1.5 Free Body Diagram.- 1.6 D'Alembert's Principle.- 1.7 Solution of the Differential Equation of Motion.- 1.8 Frequency and Period.- 1.9 Amplitude of Motion.- 2 Damped Single Degree-of-Freedom System.- 2.1 Viscous Damping.- 2.2 Equation of Motion.- 2.3 Critically Damped System.- 2.4 Overdamped System.- 2.5 Underdamped System.- 2.6 Logarithmic Decrement.- 3 Response of One-Degree-of-Freedom System to Harmonic Loading.- 3.1 Undamped Harmonic Excitation.- 3.2 Damped Harmonic Excitation.- 3.3 Evaluation of Damping at Resonance.- 3.4 Bandwidth Method (Half-Power) to Evaluate Damping.- 3.5 Response to Support Motion.- 3.6 Force Transmitted to the Foundation.- 3.7 Seismic Instruments.- 4 Response to General Dynamic Loading.- 4.1 Impulsive Loading and Duhamel's Integral.- 4.2 Numerical Evaluation of Duhamel's Integral-Undamped System.- 4.3 Numerical Evaluation of Duhamel's Integral-Damped System.- 4.4 Response by Direct Integration.- 4.5 Program 2-Response by Direct Integration.- 4.6 Program 3-Response to Impulsive Excitation.- 5 Fourier Analysis and Response in the Frequency Domain.- 5.1 Fourier Analysis.- 5.2 Response to a Loading Represented by Fourier Series.- 5.3 Fourier Coefficients for Piecewise Linear Functions.- 5.4 Exponential Form of Fourier Series.- 5.5 Discrete Fourier Analysis.- 5.6 Fast Fourier Transform.- 5.7 Program 4-Response in the Frequency Domain.- 6 Generalized Coordinates and Rayleigh's Method.- 6.1 Principle of Virtual Work.- 6.2 Generalized Single Degree-of-Freedom System-Rigid Body.- 6.3 Generalized Single Degree-of-Freedom System-Distributed Elasticity.- 6.4 Rayleigh's Method.- 6.5 Improved Rayleigh's Method.- 6.6 Shear Walls.- 7 Nonlinear Structural Response.- 7.1 Nonlinear Single Degree-of-Freedom Model.- 7.2 Integration of the Nonlinear Equation of Motion.- 7.3 Linear Acceleration Step-by-Step Method.- 7.4 Elastoplastic Behavior.- 7.5 Algorithm for the Step-by-Step Solution for Elastoplastic Single Degree-of-Freedom System.- 7.6 Program 5-Response for Elastoplastic Behavior System.- 8 Response Spectra.- 8.1 Construction of Response Spectrum.- 8.2 Response Spectrum for Support Excitation.- 8.3 Tripartite Response Spectra.- 8.4 Response Spectra for Elastic Design.- 8.5 Response Spectra for Inelastic Systems.- 8.6 Response Spectra for Inelastic Design.- 8.7 Program 6-Seismic Response Spectra.- II Structures Modeled as Shear Buildings.- 9 The Multistory Shear Building.- 9.1 Stiffness Equations for the Shear Building.- 9.2 Flexibility Equations for the Shear Building.- 9.3 Relationship Between Stiffness and Flexibility Matrices.- 9.4 Program 7-Modeling Structures as Shear Buildings.- 10 Free Vibration of a Shear Building.- 10.1 Natural Frequencies and Normal Modes.- 10.2 Orthogonality Property of the Normal Modes.- 10.3 Program 8-Natural Frequencies and Normal Modes.- 11 Forced Motion of Shear Buildings.- 11.1 Modal Superposition Method.- 11.2 Response of a Shear Building to Base Motion.- 11.3 Program 9-Response by Modal Superposition.- 11.4 Harmonic Forced Excitation.- 11.5 Program 10-Harmonic Response.- 11.6 Combining Maximum Values of Modal Response.- 12 Damped Motion of Shear Buildings.- 12.1 Equations for Damped Shear Building.- 12.2 Uncoupled Damped Equations.- 12.3 Conditions for Damping Uncoupling.- 12.4 Program 11-Absolute Damping From Damping Ratios.- 13 Reduction of Dynamic Matrices.- 13.1 Static Condensation.- 13.2 Static Condensation Applied to Dynamic Problems.- 13.3 Dynamic Condensation.- 13.4 Modified Dynamic Condensation.- 13.5 Program 12-Reduction of the Dynamic Problem.- III Framed Structures Modeled as Discrete Multidegree-of-Freedom Systems.- 14 Dynamic Analysis of Beams.- 14.1 Static Properties for a Beam Segment.- 14.2 System Stiffness Matrix.- 14.3 Inertial Properties-Lumped Mass.- 14.4 Inertial Properties-Consistent Mass.- 14.5 Damping Properties.- 14.6 External Loads.- 14.7 Geometric Stiffness.- 14.8 Equations of Motion.- 14.9 Element Forces at Nodal Coordinates.- 14.10 Program 13-Modeling Structures as Beams.- 15 Dynamic Analysis of Plane Frames.- 15.1 Element Stiffness Matrix for Axial Effects.- 15.2 Element Mass Matrix for Axial Effects.- 15.3 Coordinate Transformation.- 15.4 Program 14-Modeling Structures as Plane Frames.- 16 Dynamic Analysis of Grids.- 16.1 Local and Global Coordinate Systems.- 16.2 Torsional Effects.- 16.3 Stiffness Matrix for a Grid Element.- 16.4 Consistent Mass Matrix for a Grid Element.- 16.5 Lumped Mass Matrix for a Grid Element.- 16.6 Transformation of Coordinates.- 16.7 Program 15-Modeling Structures as Grid Frames.- 17 Three-Dimensional Frames.- 17.1 Element Stiffness Matrix.- 17.2 Element Mass Matrix.- 17.3 Element Damping Matrix.- 17.4 Transformation of Coordinates.- 17.5 Differential Equation of Motion.- 17.6 Dynamic Response.- 17.7 Program 16-Modeling Structures as Space Frames.- 18 Dynamic Analysis of Trusses.- 18.1 Stiffness and Mass Matrices for the Plane Truss.- 18.2 Transformation of Coordinates.- 18.3 Program 17-Modeling Structures as Plane Trusses.- 18.4 Stiffness and Mass Matrices for Space Trusses.- 18.5 Equation of Motion for Space Trusses.- 18.6 Program 18-Modeling Structures as Space Trusses.- 19 Time History Response of Multidegree-of-Freedom Systems.- 19.1 Incremental Equations of Motion.- 19.2 The Wilson-? Method.- 19.3 Algorithm for Step-by-Step Solution of a Linear System Using the Wilson-? Method.- 19.4 Program 19-Response by Step Integration.- 19.5 Newmark Beta Method.- 19.6 Elastoplastic Behavior of Framed Structures.- 19.7 Member Stiffness Matrix.- 19.8 Member Mass Matrix.- 19.9 Rotation of Plastic Hinges.- 19.10 Calculation of Member Ductility Ratio.- IV Structures Modeled with Distributed Properties.- 20 Dynamic Analysis of Systems with Distributed Properties.- 20.1 Flexural Vibration of Uniform Beams.- 20.2 Solution of the Equation of Motion in Free Vibration.- 20.3 Natural Frequencies and Mode Shapes for Uniform Beams.- 20.4 Orthogonality Condition Between Normal Modes.- 20.5 Forced Vibration of Beams.- 20.6 Dynamic Stresses in Beams.- 21 Discretization of Continuous Systems.- 21.1 Dynamic Matrix for Flexural Effects.- 21.2 Dynamic Matrix for Axial Effects.- 21.3 Dynamic Matrix for Torsional Effects.- 21.4 Beam Flexure Including Axial-Force Effect.- 21.5 Power Series Expansion of the Dynamic Matrix for Flexural Effects.- 21.6 Power Series Expansion of the Dynamic Matrix for Axial and for Torsional Effects.- 21.7 Power Series Expansion of the Dynamic Matrix Including the Effect of Axial Forces.- V Random Vibration.- 22 Random Vibration.- 22.1 Statistical Description of Random Functions.- 22.2 The Normal Distribution.- 22.3 The Rayleigh Distribution.- 22.4 Correlation.- 22.5 The Fourier Transform.- 22.6 Spectral Analysis.- 22.7 Spectral Density Function.- 22.8 Narrow-Band and Wide-Band Random Processes.- 22.9 Response to Random Excitation.- VI Earthquake Engineering.- 23 Equivalent Static Lateral Force Method: Uniform Building Code 1985.- 23.1 Earthquake Ground Motion.- 23.2 Equivalent Seismic Lateral Force.- 23.3 Distribution of the Lateral Seismic Force.- 23.4 Horizontal Torsional Moment.- 23.5 Overturning Moments and Story Shear.- 23.6 Story Drift.- 23.7 Diaphragm Forces.- 23.8 Program 22-UBC 85.- 23.9 Design Process.- 24 Equivalent Static Lateral Force Method: Uniform Building Code-1988.- 24.1 Earthquake-Resistant Design Methods.- 24.2 Static Lateral Force Method.- 24.3 Distribution of Lateral Forces.- 24.4 Story Shear Force.- 24.5 Horizontal Torsional Moment.- 24.6 Overturning Moment.- 24.7 Story Drift Limitation.- 24.8 P-Delta Effects (P-A).- 24.9 Diaphragm Design Force.- 24.10 Program 23 UBC-1988: Equivalent Static Lateral Force Method.- 25 Dynamic Method: Uniform Bulding Code-1988.- 25.1 Modal Seismic Response of Buildings.- 25.2 Total Design Values.- 25.3 Provision of UBC-88: Dynamic Method.- 25.4 Scaling Results.- 25.5 Program 24 UBC-1988: Dynamic Lateral Force Method.- Appendix I: Answers to Problems in Part I.- Appendix II: Computer Programs.- Appendix III: Organizations and Their Acronyms.- Selected Bibliography.