# Theory of Elasticity

425

Author: Chandramouli P N

ISBN: 9789380381633

Copy Right Year: 2017

Pages:  424

Binding: Soft Cover

Publisher:  Yes Dee Publishing

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## Description

The fundamental concepts of Theory of Elasticity have been widely used at various stages in the study of solid mechanics, fluid mechanics, geomechanics and material engineering. The basic concepts are used in their simpler form for initial analysis before preliminary design of engineering structures and the advanced principles are used for complex analysis before final design. Many of the undergraduate and postgraduate courses employ the concepts of elasticity as the basis for further development of engineering principles. Therefore, it is necessary as a first step to understand clearly the basic principles and corresponding mathematical expressions involved in theory of elasticity. Since the solutions to most of the engineering problems are obtained by solving the governing equations, it is imperative that one should learn the origin of such equations and the basis on which they have been derived. For this reason, attention has been given in this book to present the derivations of various fundamental equations in an extensive manner.

Weight .55 kg 23 × 18 × 2 cm

## Table of Content

Chapter 1 INTRODUCTION TO THEORY OF ELASTICITY
1.1 Overview of Theory of Elasticity
1.2 Differences between Elementary Theory and Theory of Elasticity
1.3 Procedure to be followed in Theory of Elasticity
1.4 Conditions Applied in Theory of Elasticity
1.5 Assumptions made in Elementary Theory and in Theory of Linear Elasticity
1.6 Classifications of Materials
1.7 Applications of Elasticity
Chapter 2 THE STRESS FIELD
2.1 Introduction
2.2 Types of Forces
2.3 Concept of Three-dimensional Stress
2.4 General State of Stress on an Element
2.4.1 Sign Conventions
2.4.2 Index Notation
2.4.3 Two-dimensional State of Stress
2.5 Differential Equation of Equilibrium in a General Three-dimensional Stress System
2.6 Stress on a General Plane
2.6.1 Direction Cosines
2.6.2 Axis Transformation
2.6.3 Stress on Oblique Plane through a Point (Cauchy’s Formula)
2.6.4 Stress Transformation
2.7 Principal Stresses and Planes
2.8 Boundary Conditions
Chapter 3 THE DISPLACEMENT FIELD AND STRAIN FIELD
3.1 Introduction
3.2 Elementary Concept of Strain
3.3 Strain Displacement Relation
3.4 Strain at a Point
3.5 Strain Components at a given Point in any Direction
3.6 Principal Strains and their Directions
3.7 Strain Rosettes
3.7.1 Rectangular Strain Rosette
3.7.2 Delta Rosette
3.8 Mohr’s Circle of Strain
Chapter 4 CONSTITUTIVE RELATIONS
4.1 Introduction
4.2 Response Model
4.3 1-D Hooke’s Law
4.4 Generalized Hooke’s Law (Anisotropic Form)
4.5 Non-isotropic Linear Elastic Behaviour
4.6 Stress-strain Relation for Isotropic Material
4.7 Stress-strain Relation for Orthotropic Material
4.8 Stress-strain Relation for Transverse Isotropic Material
Chapter 5 TWO-DIMENSIONAL PROBLEMS OF ELASTICITY
5.1 Introduction
5.1.1 Two-dimensional State of Stress
5.1.2 Two-dimensional State of Strain
5.2 Plane Stress Problems
5.3 Plane Strain Problems
5.4 Equation of Compatibility
5.5 Mathematical Conditions of Compatibility
Chapter 6 TWO-DIMENSIONAL PROBLEMS IN CARTESIAN
COORDINATE SYSTEM
6.1 Introduction
6.2 Airy’s Stress Functions
6.3 Saint-Venant’s Principle
6.4 Two-dimensional Problems in Cartesian coordinate
6.4.1 Airy’s Stress Function Method
6.4.2 Solution by Polynomials
6.5 Solution for Bending of a Cantilever Loaded at the Free End using Stress Function as
a Polynomial
6.6 Bending of a Beam by Uniform Load using the Stress Function as a Polynomial
Chapter 7 TWO-DIMENSIONAL PROBLEMS IN POLAR COORDINATES
SYSTEM
7.1 Introduction
7.2 Two-dimensional Differential Equation of Equilibrium in Polar Coordinates.
7.3 Derivations of Airy’s Stress Function in Polar Coordinates
7.4 Stress-strain Relationship in Polar Coordinates
7.5 Strain−displacement Relations
7.6 Compatibility Equation
7.7 Stresses due to Concentrated Loads
7.8 Bending of a Curved Bar by a Force at the End
7.9 Semi-infinite Medium Loaded with a Concentrated Force at the Boundary
Chapter 8 AXI-SYMMETRIC STRESS DISTRIBUTION
8.1 Introduction
8.2 Plane Stress and Plane Strain
8.3 Compatibility Equation for Axi-symmetric Case
8.4 Rotating Circular Disc
8.5 Thick Cylinder Subjected to Internal and External Radial Pressure or Lame’s Problem 199
8.6 Pure Bending of Curved Bars
Chapter 9 TORSIONON PRISMATIC BARS
9.1 Introduction
9.2 Saint-Venant’s Theory
9.3 Torsion of Elliptical Cross Section
9.4 Torsion of Equilateral Triangle Cross Section Bar
Chapter 10 THEOREMS OF ELASTICITY
10.1 Introduction
10.2 Uniqueness Theorem
10.3 Principle of Superposition
10.4 Method of Virtual Work and Minimum Potential Energy Principle of Elasticity
10.5 Complimentary Strain Energy
10.6 The Crotti-Engesser Theorem
10.7 Castigliano’s Theorem
10.8 Maxwell Reciprocal Theorem
10.9 Clapeyron’s  Theorem in Linear Elastic Theory
Chapter 11 STRESS CONCENTRATION
11.1 Introduction
11.2 Stresses Concentration around Circular Hole
Chapter 12 STRESSES DUE TO ROTATION
12.1 Introduction
12.2 Rotational Stresses in Thin Cylinder or Rotating Ring
12.3 Expression for Stresses in a Rotating Thin Disc
12.3.1 Expression for Radial and Circumferential Stresses in a Solid Disc 12.3.2 Expression for Radial and Circumferential Stresses for Disc with Central Hole
12.4 Disc of Uniform Strength
12.5 Long Cylinders
Chapter 13 CURVED BEAMS
13.1 Introduction
13.2 Assumptions made in the Derivation of Stresses in a Curved Bar
13.3 Expression for Stresses in a Curved Bar
13.3.1 To Find the Position of Neutral Axis
13.4 Determination of Factor K for Various Sections
13.4.1 Rectangular Section
13.4.2 Triangular Section
13.4.3 Trapezoidal Section
13.4.4 Circular Section
13.4.5 T-section
13.4.6 I-section
13.5 Resultant Stress in a Curved Bar Subjected to Direct Stresses and Bending Stresses
13.5.1 Resultant Stress in a Hook
13.5.2 Stresses in Circular Ring
13.5.3 Stresses in a Chain Link
Chapter 14 SHEAR CENTER
14.1 Introduction
14.2 Shear Flow
14.3 Principle Involved in Finding the Shear Centre
14.3.1 Shear Centre for a Channel Section
14.3.2 Shear Centre for Unequal I-section
14.3.3 Shear Centre for an Angle Section
14.3.4 T-section
14.3.5 I-section
14.3.6 Half Thin Walled Cylindrical Section
Chapter 15 UNSYMMETRICAL BENDING
15.1 Introduction
15.2 Product of Inertia for an Area
15.3 Parallel-axis Theorem
15.4 Moment of Inertia of an Area about Inclined Axes
15.5 Principal Moments of Inertia
15.6 Shear Centre (Unsymmetrical Sections)
15.7 Unsymmetrical Bending
15.8 Determination of Bending Stress through Product of Inertia

P N Chandramouli is Professor, Department of Civil Engineering, The National Institute of Engineering, Mysore. He received his B.E in Civil Engineering from University of Mysore, M.E from Indian Institute of Science, Bangalore and Ph.D from Indian Institute of Technology, Roorkee. He has over 30 years of teaching experience at The National Institute of Engineering. He is a life member of ISTE and ACCE.

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