1. Analysis of Stress.
Introduction. Scope of
Treatment. Definition of Stress. Components
of Stress: Stress Tensor. Some Special Cases
of Stress. Internal Force-Resultant and
Stress Relations. Stresses on Inclined
Planes in an Axially Loaded Member.
Variation of Stress within a Body.
Two-Dimensional Stress at a Point. Principal
Stresses and Maximum Shear Stress in Two
Dimensions. Mohr's Circle for
Two-Dimensional Stress. Three-Dimensional
Stress at a Point. Principal Stresses in
Three Dimensions. Normal and Shear Stresses
on an Oblique Plane. Mohr's Circle for
Three-Dimensional Stress. Boundary
Conditions in Terms of Surface Forces.
2. Strain and Stress-Strain Relations.
Deformation. Strain Defined. Equations of
Compatibility. State of Strain at a Point.
Engineering Materials. Stress-Strain
Diagrams. Hooke's Law and Poisson's Ratio.
Generalized Hooke's Law. Measurement of
Strain: Bonded Strain Gages. Strain Energy.
Strain Energy in Common Structural Member.
Components of Strain Energy. Saint-Venant's
3. Two-Dimensional Problems in Elasticity.
Fundamental Principles of Analysis. Part
A-Formulation and Methods of Solution. Plane
Strain Problems. Plane Stress Problems.
Airy's Stress Function. Solution of
Elasticity Problems. Thermal Stresses. Basic
Relations in Polar Coordinates. Part
B-Stress Concentrations. Stresses Due to
Concentrated Loads. Stress Distribution near
Concentrated Load Acting on a Beam. Stress
Concentration Factors. NEUBER'S DIAGRAM.
4. Failure Criteria.
Failure by Yielding. Failure by Fracture.
Yield and Fracture Criteria. Maximum
Shearing Stress Theory. Maximum Distortion
Energy Theory. Octahedral Shearing Stress
Theory. Comparison of the Yielding Theories.
Maximum Principal Stress Theory. Mohr's
Theory. Coulomb-Mohr Theory. Introductory
Fracture Mechanics. Failure Criteria for
Metal Fatigue. Fatigue Life under Combined
Loading. Impact or Dynamic Loads. Dynamic
and Thermal Effects.
5. Bending of Beams.
A-Exact Solutions. Pure Bending of Beams of
Symmetrical Cross Section. Pure Bending of
Beams of Asymmetrical Cross Section. Bending
of a Cantilever of Narrow Section. Bending
of a Simply Supported, Narrow Beam. Part
B-Approximate Solutions. Elementary Theory
of Bending. Bending and Shearing Stresses.
Effect of Transverse Normal Stress.
Composite Beams. Shear Center. Statically
Indeterminate Systems. Energy Method for
Deflections. Part C-Curved Beams. Exact
Solution. Tangential Stress. Winkler's
Theory. Combined Tangential and Normal
6. Torsion of Prismatic Bars.
Elementary Theory of Torsion of Circular
Bars. General Solution of the Torsion
Problem. Prandtl's Stress Function.
Prandtl's Membrane Analogy. Torsion of
Thin-Walled Members of Open Cross Section.
Torsion of Multiply Connected Thin-Walled
Sections. Fluid Flow Analogy and Stress
Concentration. Torsion of Restrained
Thin-Walled Members of Open Cross Section.
Curved Circular Bars: Helical Springs.
7. Numerical Methods.
Differences. Finite Difference Equations.
Curved Boundaries. Boundary Conditions.
Finite Element Method. Properties of a
Finite Element. Formulation of the Finite
Element Method. Triangular Finite Element.
Use of Digital Computers.
8. Axisymmetrically Loaded Members.
Thick-Walled Cylinders. Maximum Tangential
Stress. Application of Failure Theories.
Compound Cylinders. Rotating Disks of
Constant Thickness. Rotating Disks of
Variable Thickness. Rotating Disks of
Uniform Stress. Thermal Stresses in Thin
Disks. Thermal Stress in Long Circular
Cylinders. Finite Element Solution.
Formulation of Axisymmetric Element.
9. Beams on Elastic Foundations.
Theory. Infinite Beams. Semi-Infinite Beams.
Finite Beams: Classification of Beams. Beams
Supported by Equally Spaced Elastic
Elements. Simplified Solutions for
Relatively Stiff Beams. Solution by Finite
10. Energy Methods.
Done in Deformation. Reciprocity Theorem.
Castigliano's Theorem. Unit or Dummy Load
Method. Crotti-Engesser Theorem. Statically
Indeterminate Systems. Principle of Virtual
Work. Principle of Minimum Potential Energy.
Application of Trigonometric Series.
11. Elastic Stability.
Load. Buckling of a Column. End Conditions.
Critical Stress in a Column. Allowable
Stress. Initially Curved Members
Eccentrically Loaded Columns: Secant
Formula. Energy Methods Applied to Buckling.
Solution by Finite Differences. Finite
Difference Solution for Unevenly Spaced
12. Plastic Behavior of Materials.
Introduction. Plastic Deformation. True Stress-True Strain Curve in Simple Tension. Instability in Simple Tension. Plastic Deflection of Beams. Analysis of Perfectly Plastic Beams. Collapse Load of Structures. Elastic-Plastic Torsion. Elastic-Plastic Stresses in Rotating Disks. Plastic Stress-Strain Relations. Plastic Stress-Strain Increment Relations. Stresses in Perfectly Plastic Thick-Walled Cylinders.
13. Plates and Shells.
Part A-Bending of Thin Plates.
Strain-Curvature Relations. Stress,
Curvature, and Moment Relations. Governing
Equations of Plate Deflection. Boundary
Conditions. Simply Supported Rectangular
Plates. Axisymmetrically Loaded Circular
Plates. Deflections of Rectangular Plates by
the Strain Energy Method. Finite Element
Part B-Membrane Stresses in Thin Shells.
Simple Membrane Action. Symmetrically Loaded
Shells of Revolution. Some Common Cases of
Shells of Revolution. Cylindrical Shells of
Appendix A. Indicial Notation.
Appendix B. Solution of the Stress Cubic Equation.
Principal Stresses. Direction Cosines.
Appendix C. Moments of Composite Areas.
Centroid. Moments of Inertia. Parallel-Axis Theorem. Principal Moments of Inertia.
Appendix D. Tables.
Average Properties of Common Engineering Materials. Conversion Factors: SI Units to U.S. Customary Units. SI Unit Prefixes. Deflections and Slopes of Beams.
Answers to Selected Problems.