Matrix Structural Analysis

by Felton, Lewis P.; Nelson, Richard B.

• ISBN13: 9780471123248
• ISBN10: 0471123242
• Edition: 1st
• Format: Paperback
• Copyright: 1996-12-17
• Publisher: Wiley

Summary

The field of structural analysis has experienced profound change in the past three decades. This book presents a rigorous, concise development of the concepts of modern matrix structural analysis with emphasis on techniques and methods which are the basis for the Finite Element Method. The material is presented in a traditional manner. Basic analytical tools set the groundwork for understanding more complex concepts. Meaningful examples which illustrate the underlying theories and procedures are provided throughout the text, presented in a step-by-step format to promote understanding.

Author Biography

Lewis P. Felton and Richard B. Nelson are the authors of Matrix Structural Analysis, published by Wiley.

Table of Contents

Basic Concepts	1	(71)
Introduction	1	(2)
Types of Structural Elements	3	(6)
Typical One-Dimensional Elements	4	(3)
Typical Two-Dimensional Elements	7	(2)
Three-Dimensional Elements	9	(1)
Overview of the Concepts of Structural Analysis	9	(2)
The Theorem of Virtual Work	10	(1)
Loads	11	(3)
Material Behavior	14	(2)
Review of Equilibrium Equations	16	(11)
Concentrated Forces	16	(1)
Equilibrium of Forces	17	(1)
Moment of Force	18	(2)
Equilibrium of Moments	20	(2)
Free-Body Diagrams	22	(1)
Statically Equivalent Systems of Forces	22	(1)
Treatment of Distributed Forces	23	(4)
Analytic Models	27	(27)
Connections	28	(6)
Supports	34	(20)
Determinacy and Indeterminacy	54	(9)
Stability and Instability	63	(3)
Preview	66	(6)
Statically Determinate Trusses	72	(47)
Introduction	72	(1)
Equilibrium of Axially Loaded Bars	72	(4)
Internal Forces in Statically Determinate Trusses	76	(19)
Statical Stability/Instability and Determinacy/Indeterminacy	95	(2)
Deformations of Axially Loaded Bars	97	(7)
Direct Calculation of Truss Displacements	104	(15)
Statically Determinate Frames	119	(50)
Introduction	119	(1)
Equilibrium of Beams	119	(2)
Internal Forces in Statically Determinate Frames	121	(18)
Shear and Bending Moment Diagrams	127	(10)
Alternate Representations of Bending Moment	137	(2)
Deformations of Beams	139	(5)
Direct Calculation of Beam Displacements	144	(25)
Solution of Differential Equations	145	(11)
Moment-Area Method	156	(13)
Virtual Work	169	(60)
Introduction	169	(1)
Virtual Work for Truss Joints	170	(2)
Virtual Work for Axially Loaded Bars	172	(3)
Virtual Work for Trusses	175	(17)
Virtual Work for Beams	192	(13)
Virtual Work for Frames	205	(11)
Summary	216	(13)
Introduction to Analysis of Indeterminate Structures: Force Method	229	(119)
Introduction	229	(1)
Redundant Forces	229	(3)
Trusses	232	(31)
Basic Formulation	234	(14)
Matrix Formulation	248	(13)
Matrix Formulation for Structures with General Element Flexibility	261	(2)
Frames	263	(44)
Basic Formulation	265	(12)
Flexibility Matrix for Beams	277	(7)
Matrix Formulation	284	(11)
Combined Bending and Axial Behavior	295	(5)
General Axial Behavior	300	(7)
Miscellaneous Considerations	307	(20)
Support Settlement	307	(4)
Structures Composed of Several Types of Elements	311	(7)
Initial Deformations	318	(3)
Effect of Moment-Bearing Joints on Truss Behavior	321	(6)
Computing Deflections	327	(21)
Symmetry	348	(34)
Introduction	348	(1)
Behavioral Symmetry for Beams	348	(4)
Betti's Theorem for Linearly Elastic Bernoulli-Euler Beams	349	(2)
Maxwell's Reciprocal Relationship	351	(1)
Physical Symmetry	352	(30)
Structures Symmetric With Respect to a Line	353	(19)
Structures Symmetric With Respect to a Point	372	(10)
Influence Lines	382	(26)
Introduction	382	(1)
Moving Loads and Influence Lines	383	(5)
Virtual Work and Influence Lines	388	(20)
Influence Lines for Statically Determinate Structures	388	(2)
Influence Lines for Indetermine Structures: The Muller-Breslau Principle	390	(10)
Influence Lines for Trusses	400	(8)
Introduction to the Displacement Method	408	(91)
Introduction	408	(1)
System Displacements	409	(9)
Analysis of Trusses	418	(16)
Analysis of Frames	434	(41)
Stiffness Matrix for Beams	434	(2)
Matrix Formulation	436	(7)
Equilibrium by Virtual Work	443	(25)
Fixed-End Moments From Betti's Theorem	468	(7)
Miscellaneous Considerations	475	(24)
Support Settlement	475	(3)
Structures Composed of Several Types of Elements	478	(21)
Displacement Method: Advanced Formulation	499	(73)
Introduction	499	(1)
Force-Displacement Stiffness Matrix for Beams	500	(5)
Equilibrium Equations	505	(3)
Force-Displacement Stiffness Matrix for Axially Loaded Bars	508	(1)
Combined Bending and Axial Behavior	509	(13)
Element Stiffness Matrix in Global Coordinates	522	(9)
Direct Stiffness Method	531	(15)
General Support Motions	538	(2)
Direct Stiffness Method for Trusses	540	(6)
Miscellaneous Considerations	546	(26)
Support Settlement	546	(4)
Structures Comosed of Several Types of Elements	550	(4)
Effect of Joint Dimensions	554	(6)
Releases	560	(12)
Energy Concepts and Approximations	572	(60)
Introduction	572	(1)
Basic Energy Forms	573	(17)
Strain Energy	574	(5)
Symmetry of Stiffness and Flexibility Matrices	579	(2)
Positive Definiteness of Strain Energy	581	(2)
Convexity of Strain Energy	583	(3)
Partial Derivative of Strain Energy; Castigliano's Theorem, Part I	586	(1)
Deformation Energy; Castigliano's Theorem, Part II	587	(1)
External Potential Energy	588	(1)
Total Potential Energy; Stationary and Minimum Values	588	(2)
Effects of Approximations	590	(10)
Constrained Displacements	590	(5)
Incompatible Displacements	595	(1)
Approximations in the Force Method	596	(4)
Generalized Displacements and Forces	600	(6)
Approximate Displacement Patterns	604	(2)
Applications to Structures Composed of One-Dimensional Elements	606	(26)
Strain Energy of Bars and Beams	607	(4)
Examples of Rayleigh-Ritz Method	611	(21)
Introduction to Finite Element Analysis	632	(41)
Introduction	632	(1)
Basic Reqirements	632	(3)
Stiffness Matrix and Force Vector for Assumed Displacements	635	(8)
Development Using Energy	635	(3)
Development Using Virtual Work	638	(2)
Approximate Solutions as Best Fits	640	(3)
Examples of Finite Element Analysis	643	(30)
Appendix A Fixed-End Moments and Forces	673	(8)
Appendix B Moment Distribution Method for Frame Analysis	681	(16)
Index	697