The use of COSMOS for the analysis and solution of structural dynamics problems is introduced in this new edition. The COSMOS program was selected from among the various professional programs available because it has the capability of solving complex problems in structures, as well as in other engin­ eering fields such as Heat Transfer, Fluid Flow, and Electromagnetic Phenom­ ena. COSMOS includes routines for Structural Analysis, Static, or Dynamics with linear or nonlinear behavior (material nonlinearity or large displacements), and can be used most efficiently in the microcomputer. The larger version of COSMOS has the capacity for the analysis of structures modeled up to 64,000 nodes. This fourth edition uses an introductory version that has a capability limited to 50 nodes or 50 elements. This version is included in the supplement, STRUCTURAL DYNAMICS USING COSMOS 1. The sets of educational programs in Structural Dynamics and Earthquake Engineering that accompanied the third edition have now been extended and updated. These sets include programs to determine the response in the time or frequency domain using the FFf (Fast Fourier Transform) of structures modeled as a single oscillator. Also included is a program to determine the response of an inelastic system with elastoplastic behavior and a program for the development of seismic response spectral charts. A set of seven computer programs is included for modeling structures as two-dimensional and three­ dimensional frames and trusses.

I Structures Modeled as a Single-Degree-of-Freedom System.- 1 Undamped Single-Degree-of-Freedom System.- 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.- 1.10 Undamped Single-Degree-of-Freedom Systems Using COSMOS.- 1.11 Summary.- Problems.- 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.- 2.7 Summary.- Problems.- 3 Response of One-Degree-of-Freedom System to Harmonic Loading.- 3.1 Undamped System: Harmonic Excitation.- 3.2 Damped System: Harmonic Excitation.- 3.3 Evaluation of Damping at Resonance.- 3.4 Bandwidth Method (Half-Power) to Evaluate Damping.- 3.5 Energy Dissipated by Viscous Damping.- 3.6 Equivalent Viscous Damping.- 3.7 Response to Support Motion.- 3.8 Force Transmitted to the Foundation.- 3.9 Seismic Instruments.- 3.10 Response of One-Degree-of-Freedom System to Harmonic Loading Using COSMOS.- 3.11 Summary.- Problems.- 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.- 4.7 Response to General Dynamic Loading Using COSMOS.- 4.8 Summary.- Problems.- 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.- 5.8 Summary.- Problems.- 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 Shear Forces and Bending Moments.- 6.5 Generalized Equation of Motion for a Multistory Building.- 6.6 Shape Function.- 6.7 Rayleigh's Method.- 6.8 Improved Rayleigh's Method.- 6.9 Shear Walls.- 6.10 Summary.- Problems.- 7 Nonlinear Structural Response.- 7.1 Nonlinear Single Degree-of-Freedom Model.- 7.2 Integration of the Nonlinear Equation of Motion.- 7.3 Constant Acceleration Method.- 7.4 Linear Acceleration Step-by-Step Method.- 7.5 The Newmark Beta Method.- 7.6 Elastoplastic Behavior.- 7.7 Algorithm for the Step-by-Step Solution for Elastoplastic Single-Degree-of-Freedom System.- 7.8 Program 5-Response for Elastoplastic Behavioar System.- 7.9 Nonlinear Structural Response Using COSMOS.- 7.10 Summary.- Problems.- 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 Influence of Local Soil Conditions.- 8.6 Response Spectra for Inelastic Systems.- 8.7 Response Spectra for Inelastic Design.- 8.8 Program 6-Seismic Response Spectra.- 8.9 Response Spectra Using COSMOS.- 8.10 Summary.- Problems.- II Structures Modeled as Shear Buildings.- 9 The Multistory Shear Building.- 9.1 Stiffness Equations for the Shear Building.- 9.2 P-? Effect on a Plane Shear Building.- 9.3 Flexibility Equations for the Shear Building.- 9.4 Relationship Between Stiffness and Flexibility Matrices.- 9.5 Program 7-Modeling Structures as Shear Buildings.- 9.6 Summary.- Problems.- 10 Free Vibration of a Shear Building.- 10.1 Natural Frequencies and Normal Modes.- 10.2 Orthogonality Property of the Normal Modes.- 10.3 Rayleigh's Quotient.- 10.4 Program 8-Natural Frequencies and Normal Modes.- 10.5 Free Vibration of a Shear Building Using COSMOS.- 10.6 Summary 304 Problems.- 11 Forced Motion of Shear Building.- 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.- 11.7 Forced Motion of a Shear Building Using COSMOS.- 11.8 Summary.- Problems.- 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.- 12.5 Summary.- Problems.- 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.- 13.6 Summary.- Problems.- III 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.- 14.11 Dynamic Analysis of Beams Using COSMOS.- 14.12 Summary.- Problems.- 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.- 15.5 Dynamic Analysis of Frames Using COSMOS.- 15.6 Summary.- Problems.- 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.- 16.8 Dynamic Analysis of Grids Using COSMOS.- 16.9 Summary.- Problems.- 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.- 17.8 Dynamic Response of Three-Dimensional Frame…