Principles of Solid Mechanics: 1st Edition (Hardback) book cover

Principles of Solid Mechanics

1st Edition

By Rowland Richards, Jr.

CRC Press

456 pages

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pub: 2000-12-12
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Description

Evolving from more than 30 years of research and teaching experience, Principles of Solid Mechanics offers an in-depth treatment of the application of the full-range theory of deformable solids for analysis and design. Unlike other texts, it is not either a civil or mechanical engineering text, but both. It treats not only analysis but incorporates design along with experimental observation. Principles of Solid Mechanics serves as a core course textbook for advanced seniors and first-year graduate students.

The author focuses on basic concepts and applications, simple yet unsolved problems, inverse strategies for optimum design, unanswered questions, and unresolved paradoxes to intrigue students and encourage further study. He includes plastic as well as elastic behavior in terms of a unified field theory and discusses the properties of field equations and requirements on boundary conditions crucial for understanding the limits of numerical modeling.

Designed to help guide students with little experimental experience and no exposure to drawing and graphic analysis, the text presents carefully selected worked examples. The author makes liberal use of footnotes and includes over 150 figures and 200 problems. This, along with his approach, allows students to see the full range, non-linear response of structures.

Table of Contents

PREFACE

INTRODUCTION

Types of Linearity

Displacements-Vectors and Tensors

Finite Linear Transformation

Symmetric and Asymmetric Components

Principal or Eigenvalue Representation

Field Theory

STRAIN AND STRESS

Deformation (Relative Displacement)

The Strain Tensor

The Stress Tensor

Components at an Arbitrary Orientation (Tensor Transformation)

Isotropic and Deviatoric Components

Principal Space and Octahedral Representation

Two-Dimensional Stress or Strain

Mohr's Circle for a Plane Tensor

Mohr's Circle in Three Dimensions

Equilibrium of a Differential Element

Other Orthogonal Coordinate Systems

Summary

STRESS-STRAIN RELATIONSHIPS (RHEOLOGY)

Linear Elastic Behavior

Linear Viscous Behavior

Simple Viscoelastic Behavior

Fitting Laboratory Data with Viscoelastic Models

Elastic-Viscoelastic Analogy

Elasticity and Plasticity

Yield of Ductile Materials

Yield (Slip) of Brittle Materials

STRATEGIES FOR ELASTIC ANALYSIS AND DESIGN

Rational Mechanics

Boundary Conditions

Tactics for Analysis

St. Venant's Principle

Two-Dimensional Stress Formulation

Types of Partial Differential Field Equations

Properties of Elliptic Equations

The Conjugate Relationship between Mean Stress and Rotation

The Deviatoric Field and Photoelasticity

Solutions by Potentials

LINEAR FREE FIELDS

Isotropic Stress

Uniform Stress

Geostatic Fields

Uniform Acceleration of the Half-Space

Pure Bending of Prismatic Bars

Pure Bending of Plates

TWO-DIMENSIONAL SOLUTIONS FOR STRAIGHT AND CIRCULAR BEAMS

The Classic Stress-Function Approach

Airy's Stress Function in Cartesian Coordinates

Polynomial Solutions and Straight Beams

Polar Coordinates and Airy's Stress Function

Simplified Analysis of Curved Beams

Circular Beams with End Loads

Concluding Remarks

RING, HOLES AND INVERSE PROBLEMS

Lames Solution for Rings under Pressure

Small Circular Holes in Plates, Tunnels, and Inclusions

Harmonic Holes and the Inverse Problem

Harmonic Holes for Free Fields

Neutral Holes

Solution Tactics for Neutral Holes-Examples

Rotating Disks and Rings

WEDGES AND THE HALF-SPACE

Concentrated Loadings at the Apex

Uniform Loading Cases

Uniform Loading over a Finite Width

Nonuniform Loadings on the Half-Space

Line Loads within the Half-Space

Diametric Loadings of a Circular Disk

Wedges with Constant Body Forces

Corner Effects-Eigenfunction Strategy

TORSION

Elementary (Linear) Solution

St. Venant's Formulation (Noncircular Cross-Sections)

Prandtl's Stress Function

Membrane Analogy

Thin-Walled Tubes of Arbitrary Shape

Hydrodynamic Analogy and Stress Concentration

CONCEPTS OF PLASTICITY

Plastic Material Behavior

Plastic Structural Behavior

Plastic Field Equations

Example-Thick Ring

Limit Load by a "Work" Calculation

Theorems of Limit Analysis

The Lower-Bound Theorem

The Upper-Bound Theorem

Example-The Bearing Capacity (Indentation) Problem

ONE-DIMENSIONAL PLASTICITY FOR DESIGN

Plastic Bending

Plastic "Hinges"

Limit Load (Collapse) of Beams

Limit Analysis of Frames and Arches

Limit Analysis of Plates

Plastic Torsion

Combined Torsion with Tension and/or Bending

SLIP-LINE ANALYSIS

Mohr-Coulomb Criterion (Revisited)

Lateral "Pressures" and the Retaining Wall Problem

Graphic Analysis and Minimization

Slip-Line Theory

Purely Cohesive Materials (f = 0)

Weightless Materials (g = 0)

Retaining Wall Solution for f = 0 (EPS Material)

Comparison to the Coulomb Solution (f = 0)

Other Special Cases: Slopes and Footings (f = 0)

Solutions for Weightless Mohr-Coulomb Materials

The General Case

An Approximate "Coulomb Mechanism"

Note: Each chapter also contains a section of Problems and Questions

About the Series

Mechanical and Aerospace Engineering Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCI041000
SCIENCE / Mechanics / General
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical