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9781577661436

Matrix Analysis of Structures

by
  • ISBN13:

    9781577661436

  • ISBN10:

    1577661435

  • Format: Paperback
  • Copyright: 2000-05-01
  • Publisher: Waveland Pr Inc

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Table of Contents

Preface xi
Analysis of One-Dimensional Bars
1(30)
Introduction
1(3)
Nodes and Degrees of Freedom
4(1)
Stiffness Definition
4(4)
Individual Element Stiffness
8(1)
Combination of Element Stiffness
9(6)
Structures with Specified Non-Zero Displacements
15(2)
Non-Nodal Forces
17(4)
Thermal Effects
21(1)
Computer Formulation
22(4)
Summary
26(5)
Problems
26(5)
Analysis of Two-Dimensional Trusses
31(26)
Introduction
32(1)
Coordinate Transformations
33(2)
Global Stiffness Matrix
35(6)
Support Movements
41(5)
Temperature Changes and Fabrication Errors
46(4)
Computer Formulation for the Truss
50(2)
Summary
52(5)
Problems
52(5)
Analysis of Two-Dimensional Beams and Frames
57(29)
Introduction
58(1)
The Beam Elemental Stiffness Matrix
59(2)
Stiffness Matrix for the Two-Dimensional Frame Element
61(1)
The Transformation Matrix for the Frame Element
62(1)
Example Beam and Frame Problems
63(5)
Non-Nodal Loads
68(6)
Thermal Effects in Beams and Frames
74(2)
Support Movement for Beams and Frames
76(1)
Computer Formulation for the Frame
77(2)
Summary
79(7)
Problems
80(6)
Analysis of Grids
86(12)
Introduction
87(1)
Development of the Grid Elemental Stiffness Matrix
88(2)
Coordinate Transformation
90(1)
Non-Nodal Loads
91(1)
Example Grid Problems
91(4)
Computer Formulation
95(1)
Summary
95(3)
Problems
95(3)
Three-Dimensional Trusses
98(11)
Introduction
99(1)
Elemental Stiffness Matrix
100(1)
Coordinate Transformation
100(3)
Examples of Three-Dimensional Truss Problems
103(3)
Computer Formulation for the Three-Dimensional Truss
106(1)
Summary
106(3)
Problems
106(3)
Analysis of Three-Dimensional Frames
109(16)
Introduction
110(1)
Development of the Elemental Stiffness Matrix
110(1)
Transformation of Coordinates
111(2)
Example of a Three-Dimensional Frame Problem
113(7)
Computer Formulation
120(1)
Summary
121(4)
Problems
122(3)
Additional Topics in the Stiffness Method
125(32)
Discussion of Bandwidth
126(3)
Combining Different Elements to Model a Structure
129(2)
Elastic Supports
131(2)
Inclined Supports
133(3)
Hinges in Beam and Frame Elements
136(5)
Static Condensation
141(3)
Axial Deformation in Frames
144(3)
Substructuring
147(3)
Non-Uniform Members
150(4)
Linearly Tapered Bar
150(1)
Stepped Bar
151(1)
Linearly Tapered Beam
152(2)
Summary
154(3)
Problems
154(3)
Virtual Work and the Principle of Minimum Potential Energy
157(31)
Introduction
158(1)
The Principle of Virtual Work
159(8)
Rigid Bodies
159(3)
Deformable Bodies
162(2)
Expressions for Internal Virtual Work
164(3)
Elemental Stiffness Using the Principle of Virtual Work
167(7)
Shape Functions and Elemental Stiffness for an Axially Loaded Bar
167(3)
Shape Functions and Elemental Stiffness for a Beam Element
170(3)
Shape Functions and Elemental Stiffness for a Three-Node Axial Element
173(1)
Non-Nodal Forces Using the Concept of Equivalent Work
174(2)
Strain Energy and Force Potential
176(4)
Strain Energy
176(2)
Force Potential
178(2)
The Principle of Minimum Potential Energy
180(1)
Approximate Solutions Using Minimum Potential Energy
181(3)
Determination of the Structural Stiffness Equation Using Minimum Potential Energy
184(1)
Summary
184(4)
Problems
186(2)
A Brief Introduction to the Finite Element Method
188(13)
Introduction
189(1)
Plane Stress and Plane Strain
190(1)
Shape Functions for the Three-Node Triangular Element
191(2)
Strain-Displacement Relationships and Strain Energy
193(1)
Force Potential
194(1)
Application of the Principle of Minimum Potential Energy
195(1)
Example Plane Stress Problem
196(3)
Summary
199(2)
Problems
199(2)
A Review of Matrix Algebra 201(5)
B Matrix Inversion Routines 206(5)
C Derivation of the Slope-Deflection Equations 211(5)
Selected References 216(1)
Answers to Selected Problems 217(9)
Index 226

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