Introduction to the Second Edition |
|
xix | |
Introduction to the First Edition |
|
xxi | |
|
List of Repeated Engineering Symbols |
|
|
xxv | |
Acknowledgments |
|
xxxiii | |
|
Part I The Fundamentals of Structural Analysis |
|
|
|
|
1 | (1) |
|
Summary of Taylor's Series |
|
|
2 | (1) |
|
Summary of Newton's Method for Finding Roots |
|
|
2 | (1) |
|
|
3 | (1) |
|
The Chain Rule for Partial Differentiation |
|
|
4 | (1) |
|
|
5 | (33) |
|
|
5 | (7) |
|
The General Interior Equilibrium Equations |
|
|
12 | (7) |
|
Equilibrium at the Outer or Inner Boundary |
|
|
19 | (4) |
|
|
23 | (4) |
|
|
27 | (11) |
|
|
29 | (9) |
|
Stresses and Coordinate Axis Rotations |
|
|
38 | (30) |
|
|
38 | (1) |
|
Stress Values in Other Cartesian Coordinate Systems |
|
|
38 | (5) |
|
The Determination of Maximum Stress Values |
|
|
43 | (4) |
|
|
47 | (5) |
|
A Three-Dimensional View of Plane Stress |
|
|
52 | (1) |
|
**Principal Stresses in the General Three-Dimensional Case** |
|
|
53 | (6) |
|
|
59 | (1) |
|
Octahedral (von Mises) Shearing Stresses |
|
|
59 | (3) |
|
**The Mathematical Description of Stresses** |
|
|
62 | (6) |
|
|
63 | (4) |
|
Endnote (1) Solution for the Planes of Principal Stress |
|
|
67 | (1) |
|
Displacements and Strains |
|
|
68 | (27) |
|
|
68 | (1) |
|
|
68 | (1) |
|
|
69 | (8) |
|
|
77 | (2) |
|
|
79 | (1) |
|
The Strain--Displacement Equations |
|
|
80 | (1) |
|
The Compatibility Equations |
|
|
81 | (4) |
|
|
85 | (1) |
|
|
86 | (9) |
|
|
87 | (2) |
|
Endnote (1) The Derivation of the Strain--Displacement Equations for Cylindrical Coordinates |
|
|
89 | (1) |
|
Endnote (2) A Third Derivation of the Compatibility Equations |
|
|
90 | (5) |
|
Strains in Rotated Coordinate Systems |
|
|
95 | (14) |
|
|
95 | (1) |
|
Strains in Other Cartesian Coordinate Systems |
|
|
95 | (3) |
|
|
98 | (4) |
|
The Mathematical Properties of Strains |
|
|
102 | (1) |
|
|
102 | (7) |
|
|
105 | (4) |
|
The Mechanical Behavior of Engineering Materials |
|
|
109 | (37) |
|
|
109 | (7) |
|
|
116 | (8) |
|
Compression and Shear Tests |
|
|
124 | (1) |
|
|
125 | (2) |
|
Factors Other than Stress That Affect Material Behavior |
|
|
127 | (9) |
|
**Biaxial and Triaxial Loadings** |
|
|
136 | (2) |
|
Simplifications of Material Behavior |
|
|
138 | (8) |
|
|
140 | (3) |
|
Endnote (1) Residual Stress Example Problem |
|
|
143 | (1) |
|
Endnote (2) Crack Growth Example |
|
|
144 | (2) |
|
Linearly Elastic Materials |
|
|
146 | (21) |
|
|
146 | (2) |
|
|
148 | (5) |
|
Isotropic and Other Linearly Elastic Materials |
|
|
153 | (4) |
|
The Plane Stress Constitutive Equations |
|
|
157 | (1) |
|
**Applications to Fiber Composites** |
|
|
157 | (2) |
|
|
159 | (6) |
|
|
160 | (3) |
|
Endnote (1) Negative Poisson Ratios |
|
|
163 | (2) |
|
Part II **Introduction to the Theory of Elasticity** |
|
|
|
|
165 | (2) |
|
|
167 | (25) |
|
|
167 | (1) |
|
A Theory of Elasticity Solution Using Stresses |
|
|
168 | (5) |
|
A Theory of Elasticity Solution Using Displacements |
|
|
173 | (4) |
|
|
177 | (4) |
|
|
181 | (11) |
|
|
181 | (6) |
|
Endnote (1) General Problem Formulations |
|
|
187 | (3) |
|
Endnote (2) Another Solution to the Disk Displacement Equation |
|
|
190 | (1) |
|
Endnote (3) Example 7.1 Compatibility Equation |
|
|
190 | (2) |
|
Plane Stress Theory of Elasticity Solutions |
|
|
192 | (33) |
|
|
192 | (1) |
|
|
192 | (6) |
|
|
198 | (1) |
|
|
199 | (3) |
|
|
202 | (1) |
|
**The Airy Stress Function** |
|
|
202 | (17) |
|
|
204 | (5) |
|
Endnote (1) An Example of Calculating Displacements from a Stress Solution |
|
|
209 | (2) |
|
Parts I and II Review Questions |
|
|
211 | (8) |
|
Part III Engineering Theory for Straight, Long Beams |
|
|
|
Aircraft and Other Vehicular Structures |
|
|
219 | (2) |
|
The Method of Undetermined Coefficients |
|
|
221 | (2) |
|
|
223 | (1) |
|
|
224 | (1) |
|
Bending and Extensional Stresses in Beams |
|
|
225 | (46) |
|
|
225 | (1) |
|
An Elaboration on the Scope of Strength of Materials |
|
|
226 | (1) |
|
|
227 | (3) |
|
The Approximate Pattern for Beam Displacements |
|
|
230 | (8) |
|
The Accuracy of the Beam Stress Equation |
|
|
238 | (3) |
|
Calculation of the Area Properties of the Nonhomogeneous Cross-Section |
|
|
241 | (8) |
|
Calculation of Equivalent Thermal Loads |
|
|
249 | (3) |
|
Principal Axes for the Beam Cross-Section |
|
|
252 | (2) |
|
|
254 | (17) |
|
|
259 | (9) |
|
Endnote (1) The Predominance of the Normal Axial Stress |
|
|
268 | (2) |
|
Endnote (2) Schwartz's Inequality |
|
|
270 | (1) |
|
Beam Bending and Extensional Deflections |
|
|
271 | (39) |
|
|
271 | (1) |
|
The Small Deflection Beam Equilibrium Equations |
|
|
272 | (2) |
|
Nonlinear Beam Equilibrium Equations |
|
|
274 | (8) |
|
Boundary Conditions and the Boundary Value Problem |
|
|
282 | (3) |
|
Uncoupled Forms of the GDEs and the BCs |
|
|
285 | (1) |
|
Solutions for Beam Deflection Problems |
|
|
286 | (10) |
|
|
296 | (14) |
|
|
300 | (5) |
|
Endnote (1) Different BCs in Different Planes at the Same Beam End |
|
|
305 | (1) |
|
Endnote (2) The Nonlinear Form of the Axial Deflection Equation |
|
|
306 | (1) |
|
Endnote (3) The Presence of the Moment per Unit Length Terms in the Shear Force Boundary Condition Expressions |
|
|
307 | (1) |
|
Endnote (4) Exact Integrations for a Nonuniform Beam |
|
|
307 | (3) |
|
Additional Beam Bending Topics |
|
|
310 | (58) |
|
|
310 | (1) |
|
The Concept of Elastic Boundary Conditions |
|
|
310 | (2) |
|
Elastic Support Boundary Conditions |
|
|
312 | (4) |
|
Concentrated and Partial Span Loads |
|
|
316 | (4) |
|
Partial Span and Concentrated Load Example Problems |
|
|
320 | (9) |
|
Introduction to Beam Buckling |
|
|
329 | (5) |
|
**Additional Comments on Beam Buckling** |
|
|
334 | (2) |
|
|
336 | (32) |
|
|
346 | (13) |
|
Endnote (1) The Bending Slope Sign Convention |
|
|
359 | (1) |
|
Endnote (2) Combined Beam Axial and Lateral Loadings |
|
|
359 | (4) |
|
Endnote (3) Heaviside Step Function Additional Comments |
|
|
363 | (1) |
|
Endnote (4) Combined Bending and Torsional Loadings |
|
|
364 | (2) |
|
Endnote (5) Beams Continuous over Several Supports |
|
|
366 | (2) |
|
|
368 | (35) |
|
|
368 | (1) |
|
The Stress Formulation for Uniform Torsion |
|
|
369 | (7) |
|
Further Properties of the Prandtl Stress Function |
|
|
376 | (2) |
|
|
378 | (4) |
|
Closed Form Beam Torsion Analytical Solutions |
|
|
382 | (5) |
|
Open Form Uniform Beam Torsion Solutions |
|
|
387 | (4) |
|
|
391 | (12) |
|
|
396 | (4) |
|
Endnote (1) A Comment on the Solution for a Circular Shaft with a Keyway |
|
|
400 | (1) |
|
Endnote (2) Orthogonality |
|
|
400 | (1) |
|
Endnote (3) A Separation of Variables Approach to Example 12.1 |
|
|
401 | (2) |
|
Beam Torsion Approximate Solutions |
|
|
403 | (41) |
|
|
403 | (1) |
|
Open Cross-Section Beam Torsion |
|
|
404 | (6) |
|
Closed Section Beam Torsion |
|
|
410 | (10) |
|
Accuracy of the Uniform Torsion Theory |
|
|
420 | (1) |
|
Beams Subjected to a Variable Torque |
|
|
421 | (3) |
|
|
424 | (20) |
|
|
426 | (4) |
|
Endnote (1) Torsion Constants for Rolled and Extruded Beams |
|
|
430 | (3) |
|
Endnote (2) Warping Constraint Due to Varying Torque |
|
|
433 | (1) |
|
Beam Bending and Torsion Review Questions |
|
|
434 | (10) |
|
Beam Shearing Stresses Due to Shearing Forces |
|
|
444 | (35) |
|
|
444 | (1) |
|
Thin-Walled Open Cross-Sections |
|
|
444 | (4) |
|
Thin-Walled Open Cross-Section Example Problems |
|
|
448 | (9) |
|
The Open Section Shear Center |
|
|
457 | (2) |
|
Shear Flows in Thin-Walled Closed Cross-Sections |
|
|
459 | (5) |
|
|
464 | (11) |
|
|
469 | (4) |
|
Endnote (1) The Shear Center as the Center of Twist |
|
|
473 | (2) |
|
Part IV Work and Energy Principles |
|
|
|
|
475 | (1) |
|
|
475 | (4) |
|
Work and Potential Energy Principles |
|
|
479 | (44) |
|
|
479 | (2) |
|
Work and Potential Energy |
|
|
481 | (2) |
|
Virtual Work and Virtual Potential Energy |
|
|
483 | (3) |
|
|
486 | (4) |
|
The Principle of Virtual Work |
|
|
490 | (5) |
|
|
495 | (2) |
|
Complementary Virtual Work |
|
|
497 | (5) |
|
**Energy and Other Principles** |
|
|
502 | (2) |
|
**Modifications for Temperature Changes** |
|
|
504 | (2) |
|
|
506 | (15) |
|
|
507 | (3) |
|
Endnote (1) Further Explanation of the Variational Operator |
|
|
510 | (4) |
|
Endnote (2) Proof That the Principle of Virtual Work Is a Sufficient Condition for Equilibrium |
|
|
514 | (2) |
|
Endnote (3) Proof of the Pairing of BCs for the Beam Fourth Order Bending Equations and the Second Order Extension Equations |
|
|
516 | (2) |
|
Endnote (4) Derivation of the Uniform Torsion Beam Equations Using the Principle of Complementary Virtual Work |
|
|
518 | (3) |
|
Part V Energy-Based Numerical Solutions |
|
|
|
|
521 | (2) |
|
**Precursor Numerical Analyses** |
|
|
523 | (22) |
|
|
523 | (1) |
|
Numerical Methods of Note |
|
|
523 | (17) |
|
|
540 | (5) |
|
|
542 | (3) |
|
Introduction to the Finite Element Method |
|
|
545 | (57) |
|
|
545 | (1) |
|
|
546 | (5) |
|
The Beam Bending Finite Element |
|
|
551 | (5) |
|
The Bar and Spring Element Stiffness Matrix Equations |
|
|
556 | (2) |
|
Assembling the System Matrix Equation |
|
|
558 | (7) |
|
Solving the System Matrix Equation |
|
|
565 | (2) |
|
Example Beam Frame and Grid Problems |
|
|
567 | (7) |
|
More Extensive Example Problems |
|
|
574 | (7) |
|
|
581 | (21) |
|
|
592 | (6) |
|
Endnote (1) Distributed Coordinates |
|
|
598 | (1) |
|
Endnote (2) Accuracy of the Concentrated Load Approximation |
|
|
599 | (1) |
|
Endnote (3) The Reason for the Name ``Generalized Coordinates'' |
|
|
600 | (2) |
|
Finite Element Truss Problems |
|
|
602 | (21) |
|
|
602 | (1) |
|
|
602 | (5) |
|
|
607 | (3) |
|
|
610 | (1) |
|
|
611 | (1) |
|
|
612 | (11) |
|
|
617 | (3) |
|
Endnote (1) Substructuring in Static Analyses |
|
|
620 | (3) |
|
Basic Aspects of Multidimensional Finite Elements |
|
|
623 | (32) |
|
|
623 | (1) |
|
A Rectangular Plane Stress Finite Element |
|
|
623 | (12) |
|
A Triangular Plane Stress Element in Brief |
|
|
635 | (1) |
|
Three-Dimensional Finite Elements |
|
|
636 | (1) |
|
Refined Finite Elements of Simple Shapes |
|
|
637 | (5) |
|
**The Finite Element Method with Time-Varying Loads** |
|
|
642 | (7) |
|
|
649 | (6) |
|
|
650 | (3) |
|
Endnote (1) An Explanation for Rigid Body Motion-Induced False Strains |
|
|
653 | (1) |
|
Endnote (2) Reducing the Number of DOF in a Dynamic Analysis |
|
|
653 | (2) |
|
The Unit Load Method for Determinate Structures |
|
|
655 | (45) |
|
|
655 | (1) |
|
External Complementary Virtual Work in the Unit Load Method |
|
|
656 | (2) |
|
Internal CVW for Beam Bending and Extension |
|
|
658 | (9) |
|
Internal Complementary Virtual Work for Beam Torsion |
|
|
667 | (2) |
|
**Internal CVW for Beam Shearing** |
|
|
669 | (1) |
|
Additional Illustrative Examples |
|
|
670 | (7) |
|
**Examples of Using the ULM for Design Purposes** |
|
|
677 | (5) |
|
**General Deflection Solutions** |
|
|
682 | (1) |
|
**Large Radius Curved Beams** |
|
|
683 | (5) |
|
|
688 | (1) |
|
Maxwell's Reciprocity Theorem |
|
|
689 | (11) |
|
|
693 | (5) |
|
Endnote (1) ULM Limitations |
|
|
698 | (1) |
|
Endnote (2) Internal Complementary Virtual Work |
|
|
699 | (1) |
|
The Unit Load Method for Indeterminate Structures |
|
|
700 | (59) |
|
|
700 | (1) |
|
Identifying Redundant Forces and Moments |
|
|
700 | (4) |
|
The Coiled Spring Structural Elements |
|
|
704 | (3) |
|
The Strategy of Releases and Reattachments |
|
|
707 | (4) |
|
|
711 | (13) |
|
**Further Example Problems** |
|
|
724 | (5) |
|
|
729 | (28) |
|
|
737 | (10) |
|
Parts IV and V Review Questions |
|
|
747 | (10) |
|
Part VI Thin Plate Theory and Structural Stability |
|
|
|
|
757 | (2) |
|
|
759 | (33) |
|
|
759 | (1) |
|
|
760 | (1) |
|
The Plate Stress Resultants |
|
|
761 | (2) |
|
The Approximate Pattern for Plate Displacements |
|
|
763 | (3) |
|
The Small Deflection Thin Plate Bending Equation |
|
|
766 | (4) |
|
Thin Plate Boundary Conditions |
|
|
770 | (3) |
|
**Classical Small Deflection Plate Bending Solutions** |
|
|
773 | (4) |
|
**Plate Buckling and Its Uses** |
|
|
777 | (4) |
|
A Simple Plate Bending Finite Element |
|
|
781 | (7) |
|
|
788 | (4) |
|
|
788 | (3) |
|
Endnote (1) The Second Finite Deflection Plate Equation |
|
|
791 | (1) |
|
Elastic and Aeroelastic Instabilities |
|
|
792 | (47) |
|
|
792 | (1) |
|
An Energy Formulation of the Beam Buckling Problem |
|
|
792 | (3) |
|
A Beam Buckling Finite Element |
|
|
795 | (5) |
|
Further Aspects of the Energy Formulation |
|
|
800 | (6) |
|
Types of Fluid--Structure Interaction Instabilities |
|
|
806 | (2) |
|
|
808 | (6) |
|
|
814 | (6) |
|
Matrix Iteration for Symmetric Matrices |
|
|
820 | (19) |
|
|
829 | (2) |
|
|
831 | (2) |
|
Endnote (2) Diagonalization and Functions of Matrices |
|
|
833 | (6) |
|
Appendix A: Additional Topics |
|
|
839 | (12) |
|
Integration of the Strains to Obtain Displacements |
|
|
839 | (2) |
|
Proof of the Symmetry of the Compliance Matrix |
|
|
841 | (5) |
|
Uniform Torsion Stress Resultants for Multiply Connected Cross-Sections |
|
|
846 | (2) |
|
The Uniform Torsion GDE for Multiply Connected Cross-Sections |
|
|
848 | (2) |
|
Calculation of the Twist per Unit Length of a Single Cell of an N-Cell Cross-Section |
|
|
850 | (1) |
|
Appendix B: Selected Answers to Exercises |
|
|
851 | (74) |
References |
|
925 | (4) |
Index |
|
929 | |