Structural Dynamics: Theory and Computation - Brossura

Paz, Mario

Brossura

ISBN 10: 1461579201 ISBN 13: 9781461579205

Casa editrice: Springer, 2012

Riassunto

solution, are provided for calculation of the responses to forces or motions exciting the structure. The new chapters in earthquake-resistant design of buildings describe the provisions of both the 1985 and 1988 versions of the UBC (Uniform Building Code) for the static lateral force method and for the dynamic lateral force method. Other revisions of the book include the presentation of the New­ mark beta method to obtain the time history response of dynamic systems, and the direct integration method in which the response is found assuming that the excitation function is linear for a specified time interval. A modifi­ cation of the dynamic condensation method, which has been developed re­ cently by the author for the reduction of eigenproblems, is presented in Chap­ ter 13. The proposed modification substantially reduces the numerical operation required in the implementation of the dynamic condensation method. The subjects in this new edition are organized in six parts. Part I deals with structures modeled as single degree-of-freedom systems. It introduces basic concepts and presents important methods for the solution of such dynamic systems. Part II introduces important concepts and methodology for multi­ degree-of-freedom systems through the use of structures modeled as shear buildings. Part III describes methods for the dynamic analysis of framed struc­ tures modeled as discrete systems with many degrees of freedom.

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Contenuti

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.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461579201
• ISBN 13: 9781461579205
• Rilegatura: Copertina flessibile
• Numero di pagine: 648
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com