Book Contents

PART (1):DIFFERENTIAL EQUATIONS AND STRUCTURAL DYNAMICS (SDOF)

CHAPTER 1: REVISION OF DIFFERENTIAL EQUATIONS
1. Introduction to Differential Equations
1.1 Definitions
1.2 Types of Solutions of a DE
1.3 Initial-Value Problem
1.4 Linear Differential Equations: Theory of Solutions Linear
1.4.1 Linear Differential Equations
1.4.2 Second-order linear homogeneous differential equation with constant coefficients
1.4.3 Initial-value problems for linear differential equation
1.5 Steps of solution of the initial value problem for ordinary second order linear differential equations with constant coefficients

CHAPTER 2: STRUCTURAL DYNAMICS INTRODUCTION
2.1 Book Objective
2.2 Book outlines
2.3 Objective of structural dynamic analysis
2.4 Types of dynamic loading
2.5 Dynamic problem vs static problem
2.6 Newton’s First Law
2.7 Newton’s Second Law
2.8 Basic definition related structural dynamics
2.9 Components of Basic Dynamic System
2.10 Equations of Motion for SDOF
2.10.1 The Degree of Freedom, DOF
2.10.2 Equations of Motion for SDOF Using Newton’s 2nd Law
2.10.3 Equations of Motion for SDOF Using D’Alembert’s Principle
2.10.4 Equations of Motion for SDOF Using Mass-Spring damper system
2.11 Solved Examples
2.11.1 Example 1
2.11.2 Example 2
2.11.3 Example 3
2.12 Equation of Motion for Earthquake excitation

CHAPTER 3: FREE VIBRATION RESPONSE
3.1 Undamped Free Response
3.2 Examples on Equation of Motion, Problem Statement,and Solution Methods
3.2.1 Example 1
3.2.2 Example 2
3.3 Case # 1: Critically Damped Free Vibration
3.4 Case 2: Underdamped Systems of Free Vibrations
3.4.1 Free Vibration Test
3.4.1.1 Solved Example 1 on Free Vibration Test
3.4.1.2 Solved Example 2 on Free Vibration Test
3.4.1.3 Solved Example 3 on Free Vibration Test
3.5 Summary of Types of Damped Free Vibration Systems

CHAPTER 4: FORCED VIBRATION
4.1 Response to harmonic motion
4.1.1 Introduction
4.1.2 Undamped systems
4.2 Response to Arbitrary General Dynamic Loading
4.2.1 Response to Unit Impulse
4.2.2 Effect of Viscous Damping on Pulse Excitation
4.2.3 Type of Numerical Methods
4.2.3.1 Types of time-stepping
4.2.3.2 Note about time-Stepping method
4.3 Triangular Load

PART (2):STRUCTURAL DYNAMICS (MDOF) AND SEISMIC DESIGN

CHAPTER 5: MULTI-DEGREE OF FREEDOM SYSTEMS (MDOF)
5.1 Introduction
5.2 General Equation of Motion, EOM
5.2.1 General EOM (matrix form)
5.3 Undamped free vibration
5.3.1 Dynamic characteristics of MDOF systems
5.3.2 Examples on Natural Frequencies and Mode Shapes
5.3.3 SAP Verification
5.3.3 The orthogonality of modes
5.3.4 Normalization of mode shapes
5.3.5 Solution of the EOM for Undamped Systems
5.3.6 Example on modal expansion of displacement

CHAPTER 6: MODAL SUPERPOSITION
6.1 Response Spectrum Curves
6.1.1 Elastic Response Spectrum Curves
6.2 Modal Superposition & Modal Expansion Theorem
6.3 Example

CHAPTER 7: DYNAMIC ANALYSIS FUNDAMENTALS FOR SEISMIC
DESIGN RESPONSE SPECTRUM CONCEPT
7.1 Equation of Motion for Linear Elastic SDOF
7.2 Response History
7.3 Response spectrum concept
7.3.1 Response Spectrum Definition
7.3.2 Concept of Response Spectrum
7.4 Example
7.5 Response Spectrum Concept Displacement-Velocity-Acceleration
Response Spectra
7.5.1 Deformation Response Spectrum
7.5.2 Pseudo-Velocity Response Spectrum
7.5.3 Pseudo-Acceleration Response Spectrum
7.5.4 Tripartite Response Spectrum: Combined Displacement-VelocityAcceleration Spectra
7.5.4.1 Combined D-V-A response spectrum for EI Centroground motion;
7.5.5 Maximum Elastic Displacement for SDOF and MDOF Structures
7.5.5.1 Calculation of the maximum displacement for SDF Structure
7.5.5.2 Calculation of the maximum displacement for MDOF Structure
7.5.5.3 Pseudo Vs True Values for Velocity and Acceleration
7.5.5.4 Characteristics of Response Spectrum
7.5.5.5 Difference between Design and Actual Response Spectra
7.6 Solved Examples
7.6.1 Example (1)
7.6.2 Example (2)
7.6.3 Example (3)
7.6.4 Example (4)

CHAPTER 8: SEISMIC PROVISIONS
8.1 Introduction
8.2 ASCE provisions
8.3 Seismic forces on a structure
8.4 Equivalent lateral force procedure
8.5 Philosophy of design and detailing
8.6 Mapped Acceleration Parameters, SS and S1
8.7 Why 0.2s and 1.0 s
8.8 Risk – Targeted MCE
8.9 Why ASCE7-05 approach is not used
8.10 Site Coefficients and
8.11 Maximum Spectral Acceleration
8.12 Design spectral acceleration parameters
8.13 The Rationale of the 2/3 Factor