Contents

Preface

About the author

1. Elementary Elasticity

1.1 Introduction

1.2 Stress Tensor

1.3 Stress at a Point

1.4 Plane Stress Condition

1.5 Strain Tensor

1.6 Plane Strain Condition

1.7 Deformations

1.8 Generalized Hooke's Law

1.9 Elastic Constants K and G

1.10 Equilibrium Equations

1.11 Second Degree Polynomial

1.12 A Beam Subjected to Pure Bending

Multiple Choice Questions

Exercise

2. Mechanical Behaviour of Materials

2.1 Introduction

2.2 Crystalline Materials

2.3 Crystal Structures of Various Elements

2.4 Atomic Bonding

2.5 Single Crystal

2.6 Polycrystalline Materials

2.7 Imperfections in Solids

2.8 Dislocations

2.9 Surface Imperfections

2.10 Volume Imperfections

2.11 Slip Systems

2.12 Mechanical Properties

2.13 Hardness

2.14 Failure Analysis

2.15 Fracture Toughness

2.16 Fatigue

2.17 Creep

2.18 Stress Relaxation

Multiple Choice Questions

Practice Problems

3. Fixed Beams

3.1 Introduction

3.2 Fixed Beam-bending Moment Diagram

3.3 Fixed Beam-support Moments

3.4 Fixed Beam with a Concentrated Load at Centre

3.5 Fixed Beam with Uniformly Distributed Load Throughout Its Length

3.6 Fixed Beam with an Eccentric Load

3.7 Effect of Sinking of a Support in a Fixed Beam

3.8 Effect of Rotation of a Support in a Fixed Beam

Multiple Choice Questions

Practice Problems

4. Continuous Beams

4.1 Introduction

4.2 Clapeyron's Theorem of Three Moments

4.3 Theorem of Three Moments—Any Type of Loading

4.4 Supports not at Same Level

4.5 Continuous Beam with Fixed End

Multiple Choice Questions

Exercise

5. Torsion of Non-circular Shafts

5.1 Introduction

5.2 Rectangular Section

5.3 Torsion of Elliptical Section Shaft

5.4 Torsion of a Shaft with Equilateral Triangular Section

5.5 Membrane Analogy

5.6 Torsion of Thin Walled Sections

5.7 Torsion of Thin Rectangular Sections

5.8 Torsion of Thin Walled Multi-cell Sections

Multiple Choice Questions

Practice Problems

6. Statically Indeterminate Structures

6.1 Introduction

6.2 Analysis of Redundant Frames with Strain Compatibility Condition

6.3 Degree of Redundancy

6.4 Analysis of Statically Indeterminate Trusses

Practice Problems

7. Rotational Stresses

7.1 Introduction

7.2 Rotating Ring

7.3 Stresses in a Thin Rotating Disc

7.4 Disc of Uniform Strength

7.5 Stresses in Rotating Long Cylinders

7.6 Temperature Stresses in a Thin Disc

Multiple Choice Questions

Practice Problems

8. Strain Gauges

8.1 Introduction

8.2 Electrical Resistance Strain Gauge

8.3 Gauge Sensitivities and Gauge Factor

8.4 Temperature Compensation

8.5 Parameters Influencing the Behaviour of Strain Gauge

8.6 Rosette Analyses

8.7 Electrical Circuits

8.8 Semiconductor Strain Gauges

8.9 Stress Gauge

Multiple Choice Questions

Practice Problems

9. Photoelasticity

9.1 Introduction

9.2 Stress Optic Law

9.3 Properties of Light

9.4 Plane Polariscope

9.5 Properties of Isoclinic Fringes

9.6 Circular Polariscope

9.7 Compensation Techniques

9.8 Fringe Sharpening by Partial Mirrors

9.9 Fringe Multiplication by Partial Mirrors

9.10 Separation Techniques

9.11 Stresses in Prototype

9.12 Three Dimensional Photoelasticity

9.13 Characteristics of a Good Photoelastic Material

Multiple Choice Questions

Practice Problems

10. Brittle Coating Technique

10.1 Introduction

10.2 Coating Stresses

10.3 Failure Theories

10.4 Crack Patterns in Brittle Coating

10.5 Refrigeration Technique

10.6 Load Relaxation Technique

10.7 Crack Detection

10.8 Types of Brittle Coating

10.9 Equipment for Brittle Coating Method

10.10 Preparation of Specimen

10.11 Testing Procedure

10.12 Calibration of Brittle Coating

Multiple Choice Questions

Practice Problems

11. Moire Fringes Technique

11.1 Introduction

11.2 Strain Analysis Through Moire Fringes

11.3 Geometrical Approach

11.4 Displacement Approach

Multiple Choice Questions

Practice Problems

12. Aircraft Structures

12.1 Introduction

12.2 Structural Components of Aircraft

12.3 Shear Centre

12.4 Shear Flow in Thin Webs

12.5 Shear Lag

12.6 Shear Load on Wing Ribs

12.7 Loads on Bulk Heads

12.8 Spanwise Taper Effect on Shear Flow in Webs

12.9 Shear Flow in Tapered Webs

12.10 Cutouts in Semimonococque Structures

Multiple Choice Questions

Exercise

13. Experiments in Material Testing and Experimental Stress Analysis

13.1 Introduction

13.2 To Plot a Graph Between Actual Stress and Actual Strain for a Sample Under Tension Using UTM

13.3 Buckling Test on Columns Using UTM

13.4 Determination of Shear Centre of a Channel Section

13.5 Creep Test

13.6 Fatigue Test

13.7 Determination of Young's Modulus and Poisson's Ratio

13.8 Determination of Shear Modulus

13.9 Calibration of a Proving Ring

13.10 Calibration of a Photoelastic Model for Stress Fringe Value