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Table of Contents
Intro
Structural Analysis
Brief Introduction to the Book
Preface
Contents
Notations
Introduction
Research Object and Tasks of Structural Analysis
Research Object
Tasks
Computational Models of Structures
Simplification of Structural Systems
Simplification of Members
Simplification of Joints
Simplification of the Supports
Simplification of Material Properties
Simplification of Loads
Classification of Member Structures and Loads
Classification of Member Structures
Classification of Loads
A Brief History of the Development of Structural Analysis
Energy Principles and Energy Methods
Force Method and Displacement Method
Matrix Displacement Method and Finite Element Method
A Brief Introduction to Important Figures in Structural Analysis
Kinematic Analysis of Plane Member Systems
Several Concepts of Kinematic Analysis
Degree of Freedom and Constraint
Instantaneously Changeable System and Constantly Changeable System
Instantaneous Hinge
Basic Construction Rules of Plane Geometrically Unchangeable Systems
The Rule of Pin-Joined Member System
The Rule of Two Rigid Discs
The Rule of Three Rigid Discs
Computational Degree of Freedom of Plane Member Systems
Computational Degree of Freedom of Rigid Disc System
Computational Degree of Freedom of the Hinged System
Computational Degree of Freedom of the Mixed System
Geometrical Stability and Static Determinacy of Systems
Analysis of Statically Determinate Structures
Single-Span Statically Determinate Beams
Single-Span Statically Determinate Beams and Internal Forces
Relations Between Loads and Internal Forces
Method of Segmental Superposition
Multi-Span Statically Determinate Beams
Statically Determinate Plane Trusses
Characteristics and Classification of Trusses.
Method of Joints
Method of Sections
Combined Application of the Method of Joints and the Method of Sections
Statically Determinate Plane Frames
Characteristics of Frames
Calculation of Support Reactions
Internal Force Analysis and Drawing Internal Force Diagram of Frames
Quick Drawing of Moment Diagrams of Statically Determinate Frames
Statically Determine Composite Structures
Three-Hinged Arches
Support Reactions and Internal Force Calculation of Three-Hinged Arches
Rational Axes of Three-Hinged Arches
General Properties of Statically Determinate Structures
Principle of Virtual Work and Deflection Calculation
Overview of Deflection Calculation
Concept of Structural Displacements
Purpose of Deflection Calculation
Principle of Virtual Work for Deformable Structures
Principle of Virtual Work for Rigid Body System
Application Conditions of Principle of Virtual Work for Deformable Structures
Virtual Work Equation for Deformable Structures
Principle of Virtual Forces and Principle of Virtual Displacements
Unit-Load Method for Structural Deflection Calculation
Deflection Calculation under Loads
Formula for Deflection Calculation under Loads
Deflection Formulas for Various Structures
Examples of Deflection Calculation under Loads
Graph Multiplication Method
Graph Multiplication Method and Its Application Conditions
Several Specific Problems of Applying Graph Multiplication Method
Examples of Graph Multiplication Method
Deflection Calculation under Temperature Change
Reciprocal Theorems of Linearly Elastic Structures
Theorem of Reciprocal Works
Theorem of Reciprocal Displacements
Theorem of Reciprocal Reactions
Theorem of Reciprocal Displacement-Reaction
Force Method
Determination of Degree of Static Indeterminacy.
Equilibrium and Geometric Construction Characteristics of Statically Indeterminate Structures
Determination of Degree of Indeterminacy and Number of Redundant Constraint Forces
Fundamental Concept of the Force Method
Primary Unknowns, Primary System, and Basic Equations of Force Method
Analysis of Structures with Multiple Degrees of Indeterminacy by Force Method
Canonical Equations of Force Method
Analysis of Statically Indeterminate Frames and Bent Structures
Analysis of Statically Indeterminate Trusses and Composite Structures
Analysis of Symmetric Structures and Half Structures
Selection of Symmetric Primary System
Determination of Half Structure in Terms of Symmetry
Two-Hinged and Hingeless Arches
Solving Two-Hinged Arch by the Force Method
Solving Hingeless Arch by the Force Method
Internal Force Analysis of Structures under Support Movement or Temperature Change
Support Movement
Temperature Change
Deflection Computation of Statically Indeterminate Structures
Check for Calculated Results of Statically Indeterminate Structures
Check of Equilibrium Conditions
Check of Deformation Conditions
Displacement Method
Fundamental Concept of the Displacement Method
A Simple Example of Displacement Method
Primary Unknowns and Basic Equations of Displacement Method
Basic Idea of Calculating Frame Structures by Displacement Method
Determination of Primary Unknowns of Displacement Method
Slope-Deflection Equation of Prismatic Member
Calculating Member-End Internal Forces from Member-End Displacements
Calculating Fixed-End Internal Forces from Loads
Analysis of Frames Without Sidesway
Selection of Primary Unknowns
Establishment of Basic Equations
Analysis of Frames with Sidesway
Analysis of Symmetric Structures
Primary System in the Displacement Method.
Primary System of the Displacement Method
Basic Equations of the Displacement Method
Process of Establishing the Basic Equations of the Displacement Method
Canonical Equations of Displacement Method
Principle of Potential Energy and Displacement Method
Principle of Stationary Potential Energy
Linear Elastic Strain Energy of Prismatic Member
Principle of Potential Energy and Equilibrium Equation of Displacement Method
Rayleigh-Ritz Method
Moment-Distribution Method and No-Shear Distribution Method
Basic Principle of the Moment-Distribution Method
Computation of Continuous Beams and Frames Without Sidesway Using the Moment-Distribution Method
No-Shear Distribution Method
Characteristics of Statically Indeterminate Structures
Influence Lines for Structures under Moving Loads
Concepts of Moving Load and Influence Line
Equilibrium Method for Constructing Influence Lines of Simply Supported Beams
Influence Lines for Girders and Trusses
Influence Lines for Internal Forces of Girders
Influence Lines for Axial Forces of Trusses
Kinematic Method for Constructing Influence Lines of Statically Determinate Structures
Applications of Influence Lines
Responses Due to Various Kinds of Loads
Most Unfavorable Position of Moving Loads
Determination of Critical Position for Polygonal Influence Line
Determination of Critical Position for Triangle Influence Line
Kinematic Method for Constructing Influence Lines of Statically Indeterminate Beams
Matrix Displacement Methods
Fundamental Principle of the Matrix Displacement Method
Elemental Stiffness Matrix
Elemental Stiffness Matrix in Local Coordinate System
Properties of Elemental Stiffness Matrix
Coordinate Transformation of Elemental Stiffness Matrix
Elemental Stiffness Matrix in the Global Coordinate System.
Elemental Stiffness Matrix of Continuous Beam
Elemental Stiffness Matrix of Axial Force Bar
Global Stiffness Matrix of Structure
Element and Node Numberings
Direct Stiffness Method for Assembling Global Stiffness Matrix
Imposing Support Conditions
Properties of Global Stiffness Matrix
Treatment of Pinned Joints
Equivalent Nodal Loads
Basic Equation of Matrix Displacement Method
Equivalent Nodal Loads of Elements
Equivalent Nodal Loads of Structure
Computational Procedures and Examples
Example of Truss Analysis
Example of Frame Structure
Example of Composite Structure
Matrix Displacement Method for Rectangular Frame Neglecting Axial Deformation
Bibliography
Appendix A1 Answers to Problems
Appendix A2 Index
Appendix A3 Matlab Program Codes of the Matrix Displacement Method for Plane Structural Analysis.
Structural Analysis
Brief Introduction to the Book
Preface
Contents
Notations
Introduction
Research Object and Tasks of Structural Analysis
Research Object
Tasks
Computational Models of Structures
Simplification of Structural Systems
Simplification of Members
Simplification of Joints
Simplification of the Supports
Simplification of Material Properties
Simplification of Loads
Classification of Member Structures and Loads
Classification of Member Structures
Classification of Loads
A Brief History of the Development of Structural Analysis
Energy Principles and Energy Methods
Force Method and Displacement Method
Matrix Displacement Method and Finite Element Method
A Brief Introduction to Important Figures in Structural Analysis
Kinematic Analysis of Plane Member Systems
Several Concepts of Kinematic Analysis
Degree of Freedom and Constraint
Instantaneously Changeable System and Constantly Changeable System
Instantaneous Hinge
Basic Construction Rules of Plane Geometrically Unchangeable Systems
The Rule of Pin-Joined Member System
The Rule of Two Rigid Discs
The Rule of Three Rigid Discs
Computational Degree of Freedom of Plane Member Systems
Computational Degree of Freedom of Rigid Disc System
Computational Degree of Freedom of the Hinged System
Computational Degree of Freedom of the Mixed System
Geometrical Stability and Static Determinacy of Systems
Analysis of Statically Determinate Structures
Single-Span Statically Determinate Beams
Single-Span Statically Determinate Beams and Internal Forces
Relations Between Loads and Internal Forces
Method of Segmental Superposition
Multi-Span Statically Determinate Beams
Statically Determinate Plane Trusses
Characteristics and Classification of Trusses.
Method of Joints
Method of Sections
Combined Application of the Method of Joints and the Method of Sections
Statically Determinate Plane Frames
Characteristics of Frames
Calculation of Support Reactions
Internal Force Analysis and Drawing Internal Force Diagram of Frames
Quick Drawing of Moment Diagrams of Statically Determinate Frames
Statically Determine Composite Structures
Three-Hinged Arches
Support Reactions and Internal Force Calculation of Three-Hinged Arches
Rational Axes of Three-Hinged Arches
General Properties of Statically Determinate Structures
Principle of Virtual Work and Deflection Calculation
Overview of Deflection Calculation
Concept of Structural Displacements
Purpose of Deflection Calculation
Principle of Virtual Work for Deformable Structures
Principle of Virtual Work for Rigid Body System
Application Conditions of Principle of Virtual Work for Deformable Structures
Virtual Work Equation for Deformable Structures
Principle of Virtual Forces and Principle of Virtual Displacements
Unit-Load Method for Structural Deflection Calculation
Deflection Calculation under Loads
Formula for Deflection Calculation under Loads
Deflection Formulas for Various Structures
Examples of Deflection Calculation under Loads
Graph Multiplication Method
Graph Multiplication Method and Its Application Conditions
Several Specific Problems of Applying Graph Multiplication Method
Examples of Graph Multiplication Method
Deflection Calculation under Temperature Change
Reciprocal Theorems of Linearly Elastic Structures
Theorem of Reciprocal Works
Theorem of Reciprocal Displacements
Theorem of Reciprocal Reactions
Theorem of Reciprocal Displacement-Reaction
Force Method
Determination of Degree of Static Indeterminacy.
Equilibrium and Geometric Construction Characteristics of Statically Indeterminate Structures
Determination of Degree of Indeterminacy and Number of Redundant Constraint Forces
Fundamental Concept of the Force Method
Primary Unknowns, Primary System, and Basic Equations of Force Method
Analysis of Structures with Multiple Degrees of Indeterminacy by Force Method
Canonical Equations of Force Method
Analysis of Statically Indeterminate Frames and Bent Structures
Analysis of Statically Indeterminate Trusses and Composite Structures
Analysis of Symmetric Structures and Half Structures
Selection of Symmetric Primary System
Determination of Half Structure in Terms of Symmetry
Two-Hinged and Hingeless Arches
Solving Two-Hinged Arch by the Force Method
Solving Hingeless Arch by the Force Method
Internal Force Analysis of Structures under Support Movement or Temperature Change
Support Movement
Temperature Change
Deflection Computation of Statically Indeterminate Structures
Check for Calculated Results of Statically Indeterminate Structures
Check of Equilibrium Conditions
Check of Deformation Conditions
Displacement Method
Fundamental Concept of the Displacement Method
A Simple Example of Displacement Method
Primary Unknowns and Basic Equations of Displacement Method
Basic Idea of Calculating Frame Structures by Displacement Method
Determination of Primary Unknowns of Displacement Method
Slope-Deflection Equation of Prismatic Member
Calculating Member-End Internal Forces from Member-End Displacements
Calculating Fixed-End Internal Forces from Loads
Analysis of Frames Without Sidesway
Selection of Primary Unknowns
Establishment of Basic Equations
Analysis of Frames with Sidesway
Analysis of Symmetric Structures
Primary System in the Displacement Method.
Primary System of the Displacement Method
Basic Equations of the Displacement Method
Process of Establishing the Basic Equations of the Displacement Method
Canonical Equations of Displacement Method
Principle of Potential Energy and Displacement Method
Principle of Stationary Potential Energy
Linear Elastic Strain Energy of Prismatic Member
Principle of Potential Energy and Equilibrium Equation of Displacement Method
Rayleigh-Ritz Method
Moment-Distribution Method and No-Shear Distribution Method
Basic Principle of the Moment-Distribution Method
Computation of Continuous Beams and Frames Without Sidesway Using the Moment-Distribution Method
No-Shear Distribution Method
Characteristics of Statically Indeterminate Structures
Influence Lines for Structures under Moving Loads
Concepts of Moving Load and Influence Line
Equilibrium Method for Constructing Influence Lines of Simply Supported Beams
Influence Lines for Girders and Trusses
Influence Lines for Internal Forces of Girders
Influence Lines for Axial Forces of Trusses
Kinematic Method for Constructing Influence Lines of Statically Determinate Structures
Applications of Influence Lines
Responses Due to Various Kinds of Loads
Most Unfavorable Position of Moving Loads
Determination of Critical Position for Polygonal Influence Line
Determination of Critical Position for Triangle Influence Line
Kinematic Method for Constructing Influence Lines of Statically Indeterminate Beams
Matrix Displacement Methods
Fundamental Principle of the Matrix Displacement Method
Elemental Stiffness Matrix
Elemental Stiffness Matrix in Local Coordinate System
Properties of Elemental Stiffness Matrix
Coordinate Transformation of Elemental Stiffness Matrix
Elemental Stiffness Matrix in the Global Coordinate System.
Elemental Stiffness Matrix of Continuous Beam
Elemental Stiffness Matrix of Axial Force Bar
Global Stiffness Matrix of Structure
Element and Node Numberings
Direct Stiffness Method for Assembling Global Stiffness Matrix
Imposing Support Conditions
Properties of Global Stiffness Matrix
Treatment of Pinned Joints
Equivalent Nodal Loads
Basic Equation of Matrix Displacement Method
Equivalent Nodal Loads of Elements
Equivalent Nodal Loads of Structure
Computational Procedures and Examples
Example of Truss Analysis
Example of Frame Structure
Example of Composite Structure
Matrix Displacement Method for Rectangular Frame Neglecting Axial Deformation
Bibliography
Appendix A1 Answers to Problems
Appendix A2 Index
Appendix A3 Matlab Program Codes of the Matrix Displacement Method for Plane Structural Analysis.