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Dynamics of structures with MATLAB® applications

Book Description

This book is designed for undergraduate and graduate students taking a first course in Dynamics of Structures, Structural Dynamics or Earthquake Engineering. It includes several topics on the theory of structural dynamics and the applications of this theory to the analysis of buildings, bridges, towers and other structures subjected to dynamic and earthquake forces. This comprehensive text demonstrates the applications of numerical solution techniques to a large variety of practical, real-world problems under dynamic loads.

Table of Contents

  1. Cover
  2. Title Page
  3. Dedication
  4. Contents
  5. Preface
  6. About the Author
  7. Part 1 Single degree of Freedom Systems
    1. Chapter 1 Introduction to Structural Dynamics
      1. 1.1 Introduction
        1. 1.1.1 Why Dynamic Analysis?6
      2. 1.2 Physical and Mathematical Modelling
      3. 1.3 Discrete and Continuum Modelling
      4. 1.4 Laws of Equilibrium
        1. 1.4.1 Newton’s Law of Motion
        2. 1.4.2 D’Alembert’s Principle
        3. 1.4.3 Principle of Virtual Displacement
      5. 1.5 Types of Dynamic Loading
      6. 1.6 Solution of Equation of Motion
      7. 1.7 Illustrative Examples
      8. Problems
    2. Chapter 2 Single Degree of Freedom System: Free Vibrations
      1. 2.1 Introduction
      2. 2.2 Single Degree of Freedom System (SDOF)34
        1. 2.2.1 Undamped Free Vibrations
        2. 2.2.2 Damped Free Vibrations
      3. 2.3 MATLAB Applications
      4. 2.4 Illustrative Examples
      5. 2.5 Viscous Damping
      6. 2.6 Coulomb Damping
      7. Problems
    3. Chapter 3 Single Degree of Freedom System: Harmonic Loading
      1. 3.1 Introduction
      2. 3.2 Undamped Forced Vibrations
      3. 3.3 Damped Forced Vibrations
        1. 3.3.1 Dynamic Magnification Factor
      4. 3.4 MATLAB Applications
      5. 3.5 Resonant Response
      6. 3.6 Measurement of Viscous Damping
        1. 3.6.1 Resonant Amplification Method
        2. 3.6.2 Half Power (Bandwidth) Method
        3. 3.6.3 Energy Loss per Cycle: Resonant Testing Method
      7. 3.7 Measurement of Coulomb Damping
      8. 3.8 Illustrative Examples
      9. Problems
    4. Chapter 4 Single Degree of Freedom System: Periodic Loading
      1. 4.1 Introduction
      2. 4.2 Fourier Series
      3. 4.3 Undamped System
      4. 4.4 Damped System
      5. 4.5 Exponential form of Fourier Series Solution
      6. 4.6 Frequency Domain Analysis
      7. 4.7 Illustrative Examples
      8. 4.8 MATLAB Applications
      9. 4.9 Human-induced Vibrations in Structures
        1. 4.9.1 Forces While Walking and Running
        2. 4.9.2 Vibration Modes of a Bridge Deck
        3. 4.9.3 Fourier Representation of Running Load
        4. 4.9.4 Fourier Representation of Walking Load
      10. 4.10 Codal Provisions for Human Induced Vibrations
        1. 4.10.1 Natural Frequency of Steel Framed Floor System
        2. 4.10.2 IS : 800 – 2007 Code Provisions
        3. 4.10.3 ISO 2631 – 1997 Provisions
        4. 4.10.4 ISO 10137 2007 Provisions
        5. 4.10.5 Eurocode Provisions
      11. Problems
      12. References
    5. Chapter 5 Single Degree of Freedom System: Impulse Loading
      1. 5.1 Introduction
      2. 5.2 Duhamel Integral
      3. 5.3 Undamped System
      4. 5.4 Damped System
      5. 5.5 Shock Spectra
      6. 5.6 Illustrative Examples
      7. Problems
      8. References
    6. Chapter 6 Single Degree of Freedom System: Machine Vibrations
      1. 6.1 Introduction
      2. 6.2 Vibration Isolation Due to Base Excitation
        1. 6.2.1 Isolation of Ground Acceleration
      3. 6.3 Vibration Isolation Due to Rotating Unbalance
      4. 6.4 Application to Earthquake Engineering
      5. 6.5 I.S. Code on Machine Foundations
        1. 6.5.1 General Requirements
      6. 6.6 Illustrative Examples
      7. Problems
      8. References
      9. Further Reading
    7. Chapter 7 Direct Integration of Equation of Motion
      1. 7.1 Introduction
      2. 7.2 Algorithms
      3. 7.3 Constant Acceleration Method
      4. 7.4 Central Difference Method
      5. 7.5 Incremental Equation of Motion
      6. 7.6 Linear Acceleration Method
        1. 7.6.1 Selection of the Time Increment h
      7. 7.7 Newmark β Method
        1. 7.7.1 Stability of the Newmark Method
        2. 7.7.2 Newmark Method in Incremental Form
      8. 7.8 Wilson θ Method
      9. 7.9 Nonlinear Problems
      10. Problems
    8. Chapter 8 Elastic Response Spectra
      1. 8.1 Introduction
      2. 8.2 Mathematical Background
      3. 8.3 Elastic Response Spectra
        1. 8.3.1 Displacement Response Spectra
        2. 8.3.2 Velocity Response Spectra
        3. 8.3.3 Acceleration Response Spectra
      4. 8.4 Fourier Amplitude Spectra
      5. 8.5 Design Response Spectra
      6. 8.6 Housner’s Average Spectra
      7. 8.7 Tripartite Graph
        1. 8.7.1 MATLAB Code
      8. 8.8 Elastic Design Tripartite Spectra
      9. 8.9 Indian Code:1893 Part 1-2002253
        1. 8.9.1 Eurocode: EC8-part 1-2004255
        2. 8.9.2 Design Spectrum
      10. Problems
      11. References
  8. Part 2 Multi-degree of Freedom Systems
    1. Chapter 9 Two-degree of Freedom Systems
      1. 9.1 Introduction
      2. 9.2 Undamped Free Vibrations
      3. 9.3 Undamped Forced Vibrations
      4. 9.4 Damped Forced Vibrations
      5. 9.5 Undamped Vibration Absorber
      6. 9.6 Tuned Vibration Absorber
        1. 9.6.1 Effect of Mass Ratio on the Amplitude of Primary Mass
        2. 9.6.2 Secondary Mass with Viscous Damping
        3. 9.6.3 Applications
      7. 9.7 Illustrative Examples
      8. Problems
    2. Chapter 10 Multi-degree of Freedom Systems
      1. 10.1 Introduction
      2. 10.2 Spring Mass Model: Mdof System
      3. 10.3 Holtzer Method
      4. 10.4 Dynamic Equilibrium Condition: Mdof System
        1. 10.4.1 Elastic Force (Spring Force)311
        2. 10.4.2 Damping Force
        3. 10.4.3 Inertia Force
      5. 10.5 Undamped Free Vibration Analysis
        1. 10.5.1 Solution of Eigenvalue Problem
        2. 10.5.2 Rayleigh’s Quotient
        3. 10.5.3 Orthogonality Condition of Modes
        4. 10.5.4 Normalization of Modes
      6. 10.6 Transformation of Eigenvalue Problem to Standard Form
      7. 10.7 Normal Coordinates
      8. 10.8 Uncoupled Equations of Motion
      9. 10.9 Solution of Undamped Free Vibration Analysis
      10. 10.10 Response Spectrum Analysis
        1. 10.10.1 Member Forces
        2. 10.10.2 Modal Mass
        3. 10.10.3 Mode Superposition
        4. 10.10.4 Closely Spaced Modes
        5. 10.10.5 Minimum Number of Modes
      11. 10.11 Illustrative Examples
      12. 10.12 Rayleigh Damping
      13. Problems
    3. Chapter 11 Systems with Distributed Mass and Elasticity
      1. 11.1 Introduction
      2. 11.2 Distributed Mass and Stiffness Systems
      3. 11.3 Simply Supported Beam
      4. 11.4 Cantilever Beam
      5. 11.5 Rayleigh’s Principle: Conservation of Energy
      6. 11.6 Multi-degree of Freedom System
      7. 11.7 Improved Rayleigh Method
      8. 11.8 Generalized Sdof Systems
      9. 11.9 Illustrative Examples
      10. 11.10 Lumped Mass System: Shear Buildings
      11. Problems
      12. References
  9. Part 3 Application to Earthquake Engineering
    1. Chapter 12 Analysis of Buildings for Earthquake Force
      1. 12.1 Introduction
      2. 12.2 What is a Building?390
      3. 12.3 Structural Systems
      4. 12.4 Concrete Frame and Shear Walls
      5. 12.5 Member Proportions
      6. 12.6 Irregularity in Configurations of Buildings
      7. 12.7 Modelling of a Building
      8. 12.8 Base Shear in a Building
      9. 12.9 Fundamental Period of Vibration
      10. 12.10 Earthquake Force
        1. 12.10.1 Seismic Coefficient Method
        2. 12.10.2 Response Spectrum Method
      11. 12.11 Response Reduction Factor
      12. 12.12 Building on Stilts
      13. 12.13 Deflection and Separation of Buildings
      14. 12.14 Illustrative Examples
      15. 12.15 Special Devices
        1. 12.15.1 Passive Control Systems
        2. 12.15.2 Active Control Systems
      16. Problems
      17. References
    2. Chapter 13 Nonlinear Analysis of Structures
      1. 13.1 Introduction
      2. 13.2 Overview of Nonlinearity
        1. 13.2.1 Measure of Nonlinearity: Ductility
      3. 13.3 Modeling for Nonlinear Analysis
        1. 13.3.1 Steel Brace
        2. 13.3.2 Steel Beam
        3. 13.3.3 Steel Column
        4. 13.3.4 Concrete Beam
        5. 13.3.5 Concrete Column
        6. 13.3.6 Nonlinear Behaviour of Frames
      4. 13.4 Nonlinear Analysis
        1. 13.4.1 Newmark β Method: With Iterations
        2. 13.4.2 Newmark β Method: Without Iterations
      5. 13.5 Illustrative Examples
      6. 13.6 Inelastic Response Spectra
      7. 13.7 Smoothened Inelastic Response Spectra
        1. 13.7.1 New Zealand Code NZS 1170.5:2004491
        2. 13.7.2 Eurocode EC8-part 1:2004491
      8. 13.8 Illustrative Examples
      9. 13.9 Energy Dissipation Systems
        1. 13.9.1 Viscoelasticity
        2. 13.9.2 Hysteresis Behaviour of Dampers
        3. 13.9.3 ADAS Energy Dissipating System
      10. 13.10 Modeling of Expansion Gap in Bridges
      11. 13.11 Illustrative Examples
      12. Problems
      13. References – Further Reading
    3. Chapter 14 Performance-based Seismic Design of Structures
      1. 14.1 Introduction
      2. 14.2 Performance-based Seismic Design
      3. 14.3 Acceptable Risk in an Earthquake
      4. 14.4 Requirements for Seismic Rehabilitation
        1. 14.4.1 Seismic Design Category
        2. 14.4.2 Building Performance Objectives
        3. 14.4.3 Rehabilitation Objectives
      5. 14.5 Nonlinear Procedures
        1. 14.5.1 Performance Point
      6. 14.6 Stress–strain Curve for Concrete Section
      7. 14.7 Moment-curvature Curve for Concrete Section
      8. 14.8 Axial Force–moment Interaction Curves for Concrete
      9. 14.9 Acceleration-displacement Response Spectra (ADRS)545
        1. 14.9.1 Elastic A–D Response Spectra
        2. 14.9.2 Inelastic A–D Response Spectra
        3. 14.9.3 Acceptance Criteria for Nonlinear Procedures
      10. 14.10 Illustrative Examples
      11. Problems
      12. References – Further Reading
  10. Part 4 Wind Load
    1. Chapter 15 Wind Load
      1. 15.1 Introduction
      2. 15.2 Terminology
      3. 15.3 Wind Load
      4. 15.4 Static Wind Pressure
        1. 15.4.1 Change of Terrain
        2. 15.4.2 Design Wind Pressure
      5. 15.5 Illustrative Examples
      6. 15.6 Dynamic Wind Pressure
      7. 15.7 Illustrative Examples
      8. 15.8 Wind Load on a Truss Bridge
      9. 15.9 Response of Structures to Wind Load
      10. Problems
      11. References – Further Reading
  11. Appendix 1 Measuring Earthquakes: Magnitude and Intensity
  12. Appendix 2 MATLAB Basics
  13. Answers to Selected Problems