Preface .
About the Authors
1 Fundamental Notions
1.1 Introduction
1.2 Fundamental Concepts
1.3 Vectors and Tensors
1.4 Force Distributions
1.5 A Note on Force and Mass
1.6 Closure
1.7 A Look Back
2 Stress
2.1 Introduction
2.2 Stress
2.3 Stress Notation
2.4 Complementary Property of Shear
2.5 A Comment on the Complementary Property of Shear
2.6 Equations of Equilibrium in Differential Form
2.7 Closure
2.8 A Look Ahead: Hydrostatics Highlights (2)
3 strain
3.1 Introduction
3.2 The Displacement Field
3.3 Strain Components
3.4 Strains in Terms of the Displacement Field
3.5 Compatibility Considerations
3.6 Closure 69
3.7 A Look Ahead; Fluid Mechanics I Highlights (3)
4 Introduction to Mechanical Properties of Solids
4.1 Introduction
4.2 The Tensile Test
4.3 Strain Hardening and Other Properties
4.4 Idealized One-Dimensional, Time-Independent, Stress-Strain Laws
4.5 A Look Ahead; Viscoelasticity and Creep
4.6 Fatigue
4.7 Stress Concentration
4.8 One-Dimensional Thermal Stress
4.9 Closure
4.10 A Look Back
4.11 A Look Ahead; Composite Materials
Highlights (4)
5 One-Dimensional Problems
5.1 Introduction
5.2 Basic Considerations
5.3 Statically Determinate Problems
5.4 Statically Indeterminate Problems
5.5 Residual Stress Problem
5.6 Design Problem
5.7 Thermoelastic Problems
5.8 Closure
5.9 A Look Ahead; Basic Laws of Continua
Highlights (5)
6 Generalized HoOke's Law and Introduction to Energy Methods
6.1 Introduction
Part A: Simple Constitutive Relations
6.2 Three-Dimensional Hooke's Law for Isotropic Materials
6.3 Relation Between the Three Material Constants
6.4 Nonisothermal Hooke's Law
6.5 Nonisotropic, Linear, Elastic Behavior:Generalized Hooke's Law
6.6 A Look Ahead; Fluid Mechanics II
Part B: Introduction to Energy Methods
6.7 Strain Energy
6.8 Castigliano's Second Theorem (Energy Methods I)
6.9 Basic Equations of Elasticity
6.10 Closure
6.11 A Look Ahead; Variational Methods
6.12 Highlights (6)
7 Plane Stress
7.1 Introduction
7.2 Stress Variations at a Point for Plane Stress
7.3 A Pause and a Comment
7.4 Principal Stresses and Principal Axes
7.5 Mohr's Circle
7.6 Closure
Highlights (7)
8 Plane strain
8.1 Introduction
8.2 A Look Back; Taylor Series and Directional Derivatives
8.3 Transformation Equations for Plane Strain
8.4 Properties of Plane Strain
8.5 A Pertinent Comment 24
8.6 Strain Gages
8.7 Closure
Highlights (8)
9 Failure Criteria
9.1 Introduction
9.2 Yield Criteria for Isotropic Ductile Materials
9.3 Yield Surfaces
9.4 Maximum Normal Stress Theory for Brittle Fracture
9.5 Comparison of the Theories
9.6 Closure
Highlights (9)
9.7 A Look Back; Equivalent Force Systems
10 Section Forces in Beams
10.1 Introduction
10.2 Shear Force, Axial Force,and Bending Moment
10.3 Direct Formulations of Shear and Bending-Moment Equations
10.4 Differential Relations for Bending Moment, Shear Force, and Load
10.5 Sketching Shear-Force and Bending-Moment Diagrams ..
10.6 Problems Requiring Equations and Diagrams
10.7 Additional Considerations
10.8 Closure
10.9 A Look Back
Highlights (10)
11 Stresses in Beams
11.1 Introduction
Part A: Basic Considerations
11.2 Pure Bending of Symmetric Beams
11.3 Bending of Symmetric Beams with Shear: Normal Stress
11.4 Bending of Symmetric Beams with Shear: Shear Stress
11.5 Determination of the Sign of the Shear Stress
11.6 Consideration of General Cuts
Part B: Special Topics
11.7 Composite Beams
11.8 Case of Unsymmetric Beams
11.9 Shear Stress in Beams of Narrow Open Cross Section
11.10 A Note on the Shear Center for Thin-Walled Open Members
11.11 Inelastic Behavior of Beams:The Elastic, Perfectly Plastic Case
11.12 A Note on the Failure of a Structure:Limit Design
11.13 Inelastic Behavior of Beams:Generalized Stress-Strain Relation
11.14 Stress Concentrations for Bending
11.15 Bending of Curved Beams
11.16 Closure
Highlights for Part A (11 )
12 Deflection of Beams
12.1 Introduction
12.2 Differential Equations for Deflection of Symmetric Beams
12.3 Additional Problems
12.4 Statically Indeterminate Beams
12.5 Superposition Methods
12.6 Shear Deflection of Beams
12.7 Energy Methods for Beams
12.8 Closure
A Look Ahead: A Closer Look at Beam Deflection and Highlights (12)
13 *Singularity Functions
13.1 Introduction
13.2 Delta Functions and Step Functions
13.3 Deflection Computations Using Singularity Functions
13.4 The Doublet Function
13.5 Closure
14 Torsion
14.1 Introduction
14.2 Circular Shafts
14.3 Torsion Problems Involving Circular Shafts
14.4 Stress Concentrations
14.5 Torsion of Thin-Walled Noncircular Closed Shahs
14.6 Elastic, Perfectly Plastic Torsion
14.7 Noncircular Cross Sections
14.8 Strain Energy Computations for Twisting
14.9 Closure
Highlights (14)
15 Three-Dimensional Stress Properties at a Point
15.1 Introduction
15.2 Three-Dimensional Transformation Formulations for Stress
15.3 Principal Stresses for a General State of Stress
15.4 Tensor Invariants
15.5 A Look Ahead: Tensor Notation
15.6 Closure 593
Highlights (15)
16 Three-Dimensional Strain Relations at a Point
16.1 Introduction
16.2 Transformation Equations for Strain
16.3 Properties of Strain
16.4 Closure
Highlights (16)
17 Introduction to Elastic Stability
17.1 Introduction
17.2 Definition of Critical Load
17.3 A Note on Types of Elastic Instabilities
17.4 Beam-Column Equations
17.5 The Column: Buckling Loads
17.6 Looking Back as Well as Ahead
17.7 Solution of Beam-Column Problems
17.8 Initially Bent Member 631
17.9 Eccentrically Loaded Columns
17.10 General Considerations
17.11 Inelastic Column Theory
17.12 A Note on Column Formulas
17.13 Closure 642
17.14 A Look Ahead: Finite Elements
Highlights (17)
18 *ENERGY METHODS
18.1 Introduction
Part A: Displacement Methods
18.2 Principal of Virtual Work
18.3 Method of Total Potential Energy
18.4 A Comment on the Total Potential Energy Method
18.5 The First Castigliano Theorem
Part B: Force Methods
18.6 Principal of Complementary Virtual Work
18.7 Complementary Potential Energy Principal
18.8 Use of the Total Complementary Energy Principal
18.9 The Second Castigliano Theorem
18.10 Closure
19 *Introduction to Finite Elements
19.1 A Comment
Part A: Finite Elements for Trusses
19.2 Introduction
19.3 The Stiffness Matrix for an Element: Definition
19.4 Finite Elements and Trusses
19.5 Stiffness Matrix for an Element
19.6 The Global Stiffness Matrix
19.7 Solution of a Truss Problem
Part B: Some Preliminary General Considerations
19.8 Basic Considerations for Finite Elements
19.9 General Theory for the Displacement Method
19.10 Closure
APPENDICES
I. Deformation of Isotroplc Materials
II. Proof Using Tensor Notation that Strain Is a Second-Order Tensor
III. A Note on the MaxwelI-Betti Theorem
IV. Tables
Wide-flange Beams
Standard Channels
Standard Angles
Standard Pipes
Property of Areas
Mechanical Properties of Materials
V. Answers to Problems
Index ...
