Matrix Structural Analysis 2nd Revised edition [Multiple-component retail product]

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

WILLIAM MCGUIRE is Professor of Civil Engineering, Emeritus, Cornell University. He is the author of a well-known text and reference book, Steel Structures. He is a member of the National Academy of Engineering and among his awards are the T. R. Higgins Lectureship of the American Institute of Steel Construction and the Shortridge Hardesty Award of the American Society of Civil Engineers. RICHARD H. GALLAGHER, PhD, Late President, Clarkson University, was a pioneer in the development of the finite element method. He was the author of Finite Element Analysis Fundamentals. He was a member of the National Academy of Engineering and the recipient of many awards, among them the ASME Medal, the highest honor of the American Society of Mechanical Engineers, and the American Society of Engineering Education's Lamme Medal. RONALD D. ZIEMIAN, PhD, is an Associate Professor of Civil and Environmental Engineering at Bucknell University. He is engaged in the development of computer software and active as a consulting structural engineer. He is the author of the structural theory section of the Structural Steel Designer's Handbook. He is the joint recipient of the American Society of Civil Engineers' premier award, the Norman Medal, for a paper based on his doctoral research on the inelastic behavior of steel structures.