Structural Mechanics:Analytical and Numerical Approaches for Structural Analysis

Cover
Title Page
Copyright Page
Dedication
Preface
Table of Contents
1. Geometric Stability and Types of Structures
	1.1 Classifications of Structural Members and Connections
	1.2 Introduction to Geometrically Stable and Unstable Systems
	1.3 Rigid Degrees of Freedom and Constraints
	1.4 Rules for Constructing Geometrically Stable Systems
		1.4.1 Two-Body Rule
		1.4.2 Three-Body Rule
		1.4.3 The Dual-Link Rule
		1.4.4 The Simply-Supported Rule
	1.5 Examples of Geometric-Stability Analysis
2. Internal Forces in Statically Determinate Structures
	2.1 Analysis of Beams and Frames
		2.1.1 Properties of Moment Diagrams
		2.1.2 Constructions of Moment Diagrams by the Superposition Method in Segments
		2.1.3 Calculations of Internal Forces through Moment Diagrams
		2.1.4 Analysis of Frames
	2.2 Analysis of Trusses and Composite Structures
		2.2.1 Introduction
		2.2.2 Analysis of Statically Determinate Trusses
		2.2.3 Analysis of Statically Composite Structures
	2.3 Analysis of Statically Determinate Arches
		2.3.1 Comparison of Internal Forces in Arches and the Corresponding Beams
		2.3.2 The Ideal Axis of Parabolic Arch
3. Deflections of Statically Determinate Structures
	3.1 Virtual-Work Principle for Rigid Bodies and Its Applications
		3.1.1 Work and Virtual Work
		3.1.2 Principle of Virtual Displacements for Rigid Bodies
		3.1.3 Principle of Virtual Forces for Rigid Bodies
	3.2 Principle of Virtual Forces for Elastic Structures
	3.3 Deflections Caused by External Loads
		3.3.1 Calculation of Structural Displacements to Loads by the Unit-Load Method
		3.3.2 Graphic Multiplication and Its Applications
4. Force Method
	4.1 Statically Indeterminate Structures
	4.2 General Procedure of the Force Method
	4.3 Analysis of Statically Indeterminate Structures under Loads
	4.4 Symmetric Structures and Their Half-Structures
		4.4.1 Symmetry of Structures, Loads and Responses
		4.4.2 Half-Structures of Symmetric Structures
	4.5 Analysis of Statically Indeterminate Structures Having Thermal Changes, Fabrication Errors and Support Settlements
	4.6 Deflections of Statically Indeterminate Structures
5. Displacement Method
	5.1 Beams with Support Displacements and Slope-Deflection Equations
	5.2 Displacement Method for Analyzing Frames under Nodal Loads
		5.2.1 The Procedure Using Slope-Deflection Equations
		5.2.2 The Procedure Directly Using Primary Systems
		5.2.3 Unknown Degrees of Freedom of the Displacement Method
	5.3 The Analysis of Frames Under In-Span Loading
		5.3.1 Fixed-End Forces
		5.3.2 Processing of In-Span Loads and Nodal Equivalent Loads
	5.4 Examples of Frames with In-Span Loads
	5.5 Moment Distribution Approach
		5.5.1 Moment Distribution Approach for SDOF Structures
		5.5.2 Moment Distribution Approach for MDOF Beams
6. Influence Lines for Statically Determinate Structures
	6.1 Introduction
	6.2 Influence Lines for Beams
		6.2.1 Constructing Influence Lines by the Principle of Virtual Displacements
	6.3 Influence Lines for Trusses
	6.4 Maximum Response at a Specific Point
		6.4.1 Maximum Response at a Point under Live Loads
		6.4.2 Maximum Response at a Point under a Set of Concentrated Moving Loads
	6.5 Moment Envelopes and Absolute Maximum Moments of Members
		6.5.1 Definition of Moment Envelope
		6.5.2 Moment Envelopes of Beams under Moving Loads
7. Matrix Displacement Analysis
	7.1 An Introductory Example
		7.1.1 A Beam Element Type with Two Degree-of-Freedoms (DOFs) – Beam1
		7.1.2 Pre-processing – Discretizing and Digitizing of the Continuous Beam
		7.1.3 Calculate the Element Stiffness Matrices of the Continuous Beam
		7.1.4 Assembling Stiffness Equation of the Structure by the Direct Stiffness Method
		7.1.5 Solving and Post-processing
		7.1.6 MATLAB Codes – Beam1 Package
	7.2 Boundary Conditions and the Beam Element with Six DOFs
		7.2.1 Analyzing an Unrestrained Continuous Beam by Beam2 Element
		7.2.2 Post-Imposing of Boundary Conditions and Support Settlements
	7.3 Frames Subjected to Nodal Loading – Change of Coordinates
		7.3.1 Introduction
		7.3.2 Change of Coordinates
		7.3.3 Element Stiffness Matrices in Global Coordinates and the Assembling Rules
		7.3.4 Analysis of the Frames Subjected to Nodal Loads
	7.4 Frames Subjected to In-span Loads and Equivalent Nodal Loads
		7.4.1 The Equivalent Nodal Loads
		7.4.2 The Stiffness Equation of the Structure
		7.4.3 The End Displacement and Forces of the Structure
8. Dynamics of Structures
	8.1 Introduction to Structural Dynamics
		8.1.1 What is Structural Dynamics?
		8.1.2 Models for Dynamic Analysis
		8.1.3 Equations of Motion and Initial Conditions
		8.1.4 Free Vibrations and Dynamic Properties
		8.1.5 Dynamic Responses to External Excitations
		8.1.6 Summary
	8.2 Equations of Motion
		8.2.1 Stiffness Method: The Dynamic-Equilibrium Procedure
		8.2.2 Stiffness Method: The Virtual Constraint Approach
		8.2.3 Flexibility Method to Formulate Equations of Motion
		8.2.4 Stiffness Method: The Matrix Displacement Approach and Static Condensation
		8.2.5 Damping in Structures
	8.3 Dynamic Properties of Structures
		8.3.1 Vibrations of SDOF Systems: Natural Frequency and Damping Ratio
		8.3.2 Undamped Free Vibrations of MDOF Systems: Normal Modes
		8.3.3 Properties of Modes
		8.3.4 Rayleigh Damping Matrix
	8.4 Analysis of Dynamic Responses Using the Mode Superposition Method
		8.4.1 Transient Responses of Uncoupled MDOF Systems to Combined Excitations
		8.4.2 Steady-State Responses of Uncoupled MDOF Systems to Combined Excitations
		8.4.3 Responses of Coupled MDOF Systems: Mode Superposition Method
	8.5 Analysis of the Dynamic Response Using the MATLAB ODE Solver: “ode45”
	8.6 Steady-State Responses to Separable Excitations
		8.6.1 Response Spectra
		8.6.2 Peak Responses to Separable Excitations and Modal Combination Rules
	8.7 Appendix for Structural Dynamics
		8.7.1 Steady-State Responses to Space-time Coupled Excitations
9. Limit Loads of Structures
	9.1 Introduction
	9.2 Theorems of Plasticity
	9.3 Applications of the Upper Bound Theorem
	9.4 Limit Analysis by Linear Programing
Appendix
Index