Matrix Sturctural Analysis

by McGuire, William; Gallagher, Richard H.; Ziemian, Ronald D.

• ISBN13: 9780471129189
• ISBN10: 0471129186
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: John Wiley & Sons

Summary

Entire book and illustrative examples have been edited extensively, and several chapters repositioned. Imperial units are used instead of SI units in many of the examples and problems, particularly those of a nonlinear nature that have strong implications for design, since the SI system has not been fully assimilated in practice.

Table of Contents

Symbols	xvii
Chapter 1 Introduction	1	(8)
1.1 A Brief History of Structural Analysis	2	(1)
1.2 Computer Programs	3	(5)
1.2.1 Computational Flow and General Purpose Programs	4	(2)
1.2.2 The Program MASTAN2	6	(2)
References	8	(1)
Chapter 2 Definitions and Concepts	9	(22)
2.1 Degrees of Freedom	9	(2)
2.2 Coordinate Systems and Conditions of Analysis	11	(3)
2.3 Structure Idealization	14	(2)
2.4 Axial Force Element--Force-Displacement Relationships	16	(3)
2.4.1 Element Stiffness Equations	16	(2)
2.4.2 Element Flexibility Equations	18	(1)
2.5 Axial Force Element--Global Stiffness Equations	19	(1)
2.6 Examples	20	(6)
2.7 Problems	26	(5)
Chapter 3 Formation of the Global Analysis Equations	31	(25)
3.1 Direct Stiffness Method--The Basic Equations	31	(8)
3.2 Direct Stiffness Method--The General Procedure	39	(7)
3.3 Some Features of the Stiffness Equations	46	(1)
3.4 Indeterminacy	47	(2)
3.5 Problems	49	(6)
References	55	(1)
Chapter 4 Stiffness Analysis of Frames--I	56	(37)
4.1 Stress-Strain Relationships	56	(2)
4.2 Work and Energy	58	(2)
4.3 Reciprocity	60	(2)
4.4 Flexibility-Stiffness Transformations	62	(4)
4.4.1 Stiffness to Flexibility Transformation	62	(1)
4.4.2 Flexibility to Stiffness Transformation	63	(3)
4.5 The Framework Element Stiffness Matrix	66	(8)
4.5.1 Axial Force Member	67	(1)
4.5.2 Pure Torsional Member	67	(1)
4.5.3 Beam Bent About Its z Axis	68	(4)
4.5.4 Beam Bent About Its y Axis	72	(1)
4.5.5 Complete Element Stiffness Matrix	73	(1)
4.6 A Commentary on Deformations and Displacement Variables	74	(2)
4.6.1 Neglected Deformations	74	(1)
4.6.2 Displacement Variables	75	(1)
4.7 Examples	76	(12)
4.8 Problems	88	(4)
References	92	(1)
Chapter 5 Stiffness Analysis of Frame--II	93	(44)
5.1 Coordinate Transformations	93	(15)
5.1.1 Transformation Matrices	94	(4)
5.1.2 Transformation of Degrees of Freedom	98	(1)
5.1.3 Transformations and Energy	98	(2)
5.1.4 Rectangular Transformation Matrices	100	(8)
5.2 Loads Between Nodal Points	108	(12)
5.3 Self-Straining--Initial and Thermal Strain Conditions	120	(10)
5.3.1 Initial Strain Problems	122	(3)
5.3.2 Thermal Strain Problems	125	(5)
5.4 Problems	130	(7)
Chapter 6 Virtual Work Principles	137	(37)
6.1 Principle of Virtual Displacements--Rigid Bodies	138	(4)
6.2 Principle of Virtual Displacements--Deformable Bodies	142	(2)
6.3 Virtual Displacement Analysis Procedure and Detailed Expressions	144	(6)
6.3.1 General Procedure	144	(1)
6.3.2 Internal Virtual Work	145	(3)
6.3.3 External Virtual Work	148	(2)
6.4 Construction of Analytical Solutions by the Principal of Virtual Displacements	150	(8)
6.4.1 Exact Solutions	150	(3)
6.4.2 Approximate Solutions and the Significance of the Chosen Virtual Displacements	153	(1)
6.4.3 Examples	154	(4)
6.5 Principle of Virtual Forces	158	(12)
6.5.1 Equations of Equilibrium	158	(3)
6.5.2 Characteristics of Virtual Force Systems	161	(1)
6.5.3 Formulation of the Virtual Forces Principle	162	(2)
6.5.4 Construction of Analytical Solutions by the Virtual Forces Principle	164	(6)
6.6 Problems	170	(3)
References	173	(1)
Chapter 7 Virtual Work Principles in Framework Analysis	174	(42)
7.1 Description of the Displaced State of Elements	175	(6)
7.1.1 Definition of the Shape Function Mode of Description	175	(1)
7.1.2 Formulation of Shape Functions	176	(4)
7.1.3 Characteristics of Shape Functions	180	(1)
7.2 Virtual Displacements in the Formulation of Element Stiffness Equations	181	(3)
7.2.1 Construction of Expressions for Real and Virtual Displacements	181	(1)
7.2.2 Virtual Displacements Formula for an Element Stiffness Matrix	182	(1)
7.2.3 Application to Standard Axial, Torsional, and Flexural Elements	183	(1)
7.3 Nonuniform Elements	184	(2)
7.4 Nonuniform Torsion	186	(8)
7.4.1 An Element Stiffness Matrix	187	(3)
7.4.2 Application and Examples	190	(4)
7.5 Loads Between Nodal Points and Initial Strain Effect--A General Approach	194	(5)
7.6 Virtual Forces in the Formulation of Element Force-Displacement Equations	199	(10)
7.6.1 Construction of Element Equations by the Principle of Virtual Forces	199	(4)
7.6.2 Further Applications--Shearing Deformations and Curved Elements	203	(6)
7.7 Problems	209	(5)
References	214	(2)
Chapter 8 Nonlinear Analysis of Frames--An Introduction	216	(26)
8.1 Nonlinear Behavior, Analysis, and Design	216	(18)
8.1.1 Sources of Nonlinearity	217	(1)
8.1.2 Levels of Analysis	218	(2)
8.1.3 Examples from Established Theory	220	(10)
8.1.4 A Commentary on Stability	230	(4)
8.2 A Matrix Approach	234	(1)
8.3 The Equations of Analysis and Their Solution	235	(4)
8.3.1 Equation Solution--The Options	236	(1)
8.3.2 A Fundamental Problem	237	(2)
8.4 Problems	239	(2)
References	241	(1)
Chapter 9 Geometric Nonlinear and Elastic Critical Load Analysis	242	(27)
9.1 Geometric Stiffness Matrices for Planar Elements	243	(11)
9.1.1 Axial Force Member	243	(2)
9.1.2 Combined Bending and Axial Force	245	(1)
9.1.3 Examples of Plane Structure Analysis	246	(8)
9.2 Combined Torsion and Axial Force	254	(3)
9.3 Three Dimensional Geometric Nonlinear Analysis--An Overview	257	(2)
9.4 Examples of Three Dimensional Structure Analysis	259	(4)
9.5 Problems	263	(5)
References	268	(1)
Chapter 10 Material Nonlinear Analysis	269	(32)
10.1 Nonlinear Material Behavior	269	(5)
10.1.1 Plasticity Theory	270	(2)
10.1.2 Plastic Analysis	272	(1)
10.1.3 Further Considerations	273	(1)
10.2 A Plastic Hinge Method For Ductile Frames	274	(4)
10.2.1 The Yield Surface and a Plastic Reduction Matrix	274	(3)
10.2.2 Definition of the Yield Surface	277	(1)
10.3 Inelastic Critical Load Theory	278	(1)
10.4 Examples	279	(1)
10.5 The Yield Surface Concept--A Brief Survey of Further Applications	290	(4)
10.5.1 Spread of Plasticity	290	(2)
10.5.2 Multiple Yield Surfaces	292	(1)
10.5.3 Reinforced Concrete Members	293	(1)
10.6 Problems	294	(5)
References	299	(2)
Chapter 11 Solution of Linear Algebraic Equations	301	(38)
11.1 The Basic Choice--Direct Inversion versus Elimination or Iteration	302	(1)
11.2 Direct Elimination Methods	302	(8)
11.2.1 Gauss Elimination	304	(3)
11.2.2 Cholesky Method	307	(3)
11.3 Iterative Methods	310	(6)
11.3.1 Gauss-Seidel and Jacobi Iterations	310	(2)
11.3.2 Conjugate Gradient Method	312	(4)
11.4 Sparseness and Bandedness	316	(1)
11.5 Frontal Solvers	317	(5)
11.6 Errors	322	(3)
11.6.1 The Condition Number	326	(1)
11.6.2 Estimate of Condition Number	327	(2)
11.6.3 Error Estimates and Preconditioning	329	(4)
11.6.4 Detecting, Controlling, and Correcting Error	333
11.7 Problems	325
References	337	(2)
Chapter 12 Solution of Nonlinear Equilibrium Equations	339	(36)
12.1 Incremental Analysis	339	(1)
12.2 Incremental Single-Step Methods	340	(5)
12.2.1 Euler Method	341	(1)
12.2.2 Second-Order Runge-Kutta Methods	341	(4)
12.3 Incremental-Iterative Methods	345	(6)
12.3.1 Load Control Method	347	(1)
12.3.2 Displacement Control Methods	348	(1)
12.3.3 Work Control Method	349	(1)
12.3.4 Constant Arc Length Methods	349	(1)
12.3.5 Modified Iterative Technique	349	(1)
12.3.6 Convergence Criteria	350	(1)
12.4 Automatic Load Incrementation	351	(1)
12.4.1 Change in Stiffness	351	(1)
12.4.2 Number of Iterations	352	(1)
12.5 Element Result Calculations	352	(3)
12.5.1 Updating Deformed Geometry	352	(1)
12.5.2 Force Recovery	352	(3)
12.6 Plastic Hinge Constraints	355	(3)
12.7 Limit Point and Post-Limit Analysis	358	(2)
12.8 Critical Load Analysis--An Eigenproblem	360	(10)
12.8.1 Reduction to Standard Form	361	(2)
12.8.2 Polynomial Expansion	363	(1)
12.8.3 Power Method	364	(3)
12.8.4 Inverse Iteration	367	(3)
12.9 Problems	370	(3)
References	373	(2)
Chapter 13 Special Analysis Procedures	375	(44)
13.1 Condensation	376	(1)
13.2 Substructuring	377	(8)
13.3 Constraints	385	(3)
13.4 Joint Coordinates	388	(5)
13.5 Connections and Joints	393	(10)
13.5.1 Flexible Connections	393	(5)
13.5.2 Finite Joint Size	398	(5)
13.6 Symmetry and Antisymmetry	403	(5)
13.7 Reanalysis Techniques	408	(5)
13.8 Problems	413	(5)
References	418	(1)
Appendix A Nonlinear Analysis--A Further Look	419	(25)
A.1 Virtual Displacement Principles in Lagrangian Formulations	420	(5)
A.2 An Updated Lagrangian Formulation and Its Linearization	425	(1)
A.3 Application to the Framework Element	426	(5)
A.4 Finite Rotations and Equilibrium in the Deformed Configuration	431	(6)
A.4.1 The Finite Rotation Equation	432	(1)
A.4.2 Application of the Finite Rotation Equation to the Framework Element	433	(4)
A.5 Nonuniform Torsion	437	(4)
References	441	(3)
Appendix B On Rigid Body Motion and Natural Deformation	444	(7)
B.1 The Nature of the Problem	444	(1)
B.2 Distinguishing Between Rigid Body Motion and Natural Deformation	445	(2)
B.3 Critique of Force Recovery Methods	447	(3)
B.3.1 The Natural Deformation Approach	447	(1)
B.3.2 The Elementary Approach	448	(2)
References	450	(1)
Author Index	451	(2)
Subject Index	453