Basic Structural Dynamics – James C. Anderson, Farzad Naeim (EHCS0009)

Basic Structural Dynamics – James C. Anderson, Farzad Naeim

1. Basic concepts of structural dynamics

1.1 The Dynamic Environment

1.2 Types of Dynamic Loading

1.3 Basic Principles

1.4 Dynamic Equilibrium

2. Single-degree-of-freedom systems

2.1 Reduction of Degrees of Freedom

2.2 Time – Dependent Force

2.3 Gravitational Forces

2.4 Earthquake Ground Motion

2.5 Formulation of Equation of Motion

2.5.1 d’Alembert’s Principle

2.5.2 Virtual Work (Virtual Displacements)

2.6 Generalized Coordinates

2.6.1 Discrete Parameters

2.6.2 Continuous Parameters

2.6.3 Transformation Factors

2.6.4 Axial Load Effect

2.6.5 Linear Approximation

3. Free – vibration response of single-degree-of-freedom systems

3.1 Undamped Free Vibration

3.1.1 Alternate Solution

3.1.2 Rayleigh’s Method

3.1.3 Selection of Deflected Shape

3.2 Damped Free Vibration

3.2.1 Rotating Vector Form

3.2.2 Logarithmic Decrement

3.2.3 Radical Positive

4. Response to harmonic loading

4.1 Undamped Dynamic System

4.2 Damped Dynamic System

4.3 Tripartite Logarithmic Plot

4.4 Evaluation of Damping

4.5 Seismic Accelerometers and Displacement Meters (Seismographs)

5. Response to impulse loads

5.1 Rectangular Pulse

5.2 Damped Rectangular Pulse

5.3 Triangular Pulse

5.4 Approximate Analysis for Short-Duration Impulse Load

6. Response to arbitrary dynamic loading

6.1 Duhamel Integral

6.2 Numerical Formulation of the Equation of Motion

6.3 Numerical Integration Methods

6.4 Newmark’s Numerical Method

7. Multiple-degree-of-freedom systems

7.1 Elastic Properties

7.1.1 Flexibility

7.1.2 Stiffness

7.1.3 Inertia

7.1.4 Viscous Damping

7.2 Undamped Free Vibration

7.3 Free Vibration

7.4 Betti’s Law

7.5 Orthogonality Properties of Mode Shapes

7.6 Changing Coordinates (Inverse Transformation)

7.7 Holzer Method for Shear Buildings

7.8 Axial Load Effects (Linear Approximation)

7.9 Modal Equations for Undamped Time-Dependent Force Analysis

7.10 Modal Equations of Damped Forced Vibration

7.11 Modal Equations for Seismic Response Analysis

8. Nonlinear response of multiple-degree-of-freedom systems

8.1 Static Nonlinear Analysis

8.2 Dynamic Nonlinear Analysis

8.3 Gauss Reduction

8.4 MATLAB Applications

9. Seismic response of structures

9.1 Introduction

9.2 Linear Elastic Response Spectra

9.3 Elastic Design Response Spectrum

9.4 Earthquake Response of SDOF Systems

9.5 Earthquake Response Analysis of MDOF Systems

9.5.1 Time History Modal Analysis

9.5.2 Modal Combinations for Spectral Analyses

9.6 Structural Dynamics in the Building Code

9.6.1 Equivalent Lateral Force Procedure

9.6.2 Modal Response Spectrum Procedure