Strength of Materials

1 Simple Stress And Strain

1.1 Introduction

1.2 Tensile and Compressive Stress and Strain

1.3 Shear Stress and Strain

1.4 Hooke's Law

1.5 Factor of Safety

1.6 Stresses in Thin Cylindrical Shells

1.7 Stress in Thin Spherical Shells

1.8 Stress in Thin Rotating Rims

1.9 Stresses in Composite Bars

1.10 Strain Energy

1.11 Shear Strain Energy

Worked Examples 1-10

Unworked Examples 11-36


2 Shearing Force And Bending Moment

2.1 Shearing Force and Bending Moment

2.2 Shearing Force and Bending Moment Diagrams

2.3 Relation Between Intensity of Loading, Shearing Force and Bending Moment

2.4 Graphical Construction of S.F. and B.M. Diagrams

Worked Examples 1-8

Unworked Examples 9-30


3 Bending Stresses

3.1 Pure Bending

3.2 Second Moment of Area

3.3 Theorem of Parallel Axes

3.4 Theorem of Perpendicular Axes

3.5 Equimomental System

3.6 Stress Due to Bending

3.7 Modulus of Section

3.8 Position of Neutral Axis

3.9 Radius of Curvature

3.10 Composite Beams

3.11 Combined Bending and Direct Stresses

3.12 Short Column with Eccentric Load

3.13 Bending Beyond the Limit of Proportionality

Worked Examples 1-14

Unworked Examples 15-49


4 Torsion

4.1 Stress Due to Twisting

4.2 Modulus of Section

4.3 Angle of Twist

4.4 Strain Energy

4.5 Composite Shafts

4.6 Twisting Beyond the Limit of Proportionality

Worked Examples 1-7

Unworked Examples 8-27


5 Deflection Of Beams

5.1 Integration Method

5.2 Standard Cases of Beam Deflections

5.3 Single Concentrated Load Not at Centre—Macaulay's Method

5.4 Distributed Loads

5.5 Couple Applied at a Point

5.6 Area-Moment Method

5.7 Maxwell's Reciprocal Rule

5.8 Deflection Due to Impact

Worked Examples 1-15

Unworked Examples 16-56


6 Built-In And Continuous Beams

6.1 Built-In Beams

6.2 Built-In Beam with Central Concentrated Load

6.3 Built-In Beam with Uniformly Distributed Load

6.4 Built-In Beam with Concentrated Load Not at Centre

6.5 Supports at Different Levels

6.6 Continuous Beams—Three Moments Theorem

Worked Examples 1-8

Unworked Examples 9-30


7 Struts

7.1 Introduction

7.2 Euler's Theory

7.3 Validity Limit for Euler's Theory

7.4 Rankine's Theory

7.5 Strut with Eccentric Load

7.6 Strut with Initial Curvature

7.7 Laterally Loaded Struts

7.8 Alternative Method for Determining Bending Moment

7.9 Eccentrically and Transversely Loaded Tie-Bars

Worked Examples 1-7

Unworked Examples 8-30


8 Thin Curved Bars

8.1 Strain Energy Due to Bending

8.2 Castigliano's Theorem

8.3 Application of Castigliano's Theorem to Deflection of Curved Bars

8.4 Strain Energy Due to Twisting

Worked Examples 1-10

Unworked Examples 11-35


9 Springs

9.1 Close-Coiled Helical Spring with Axial Load

9.2 Close-Coiled Helical Spring with Axial Couple

9.3 Open-Coiled Helical Springs

9.4 Composite Action of Axial Load and Couple

9.5 Flat Spiral Springs

9.6 Leaf, Laminated or Carriage Springs

9.7 Vibration of Springs

Worked Examples 1-11

Unworked Examples 12-44


10 Shear Stress In Beams

10.1 Shear Stress Distribution

10.2 Built-Up Girders

10.3 Deflection Due to Shear

10.4 Total Deflection

Worked Examples 1-8

Unworked Examples 9-30


11 Unsymmetrical Bending

11.1 Principal Axes and Principal Moments of Inertia

11.2 Determination of Principal Axes and Principal Moments of Inertia

11.3 Momental Ellipse

11.4 Theorem of Perpendicular Axes for Product of Inertia

11.5 Beam with Unsymmetrical Bending Moment

11.6 Short Column with Unsymmetrical Load

Worked Examples 1-7

Unworked Examples 8-18


12 Complex Stress And Strain

12.1 Stresses on an Oblique Section

12.2 Material Subjected to Two Perpendicular Stresses

12.3 Material Subjected to Shear Stress

12.4 Material Subjected to Direct and Shear Stresses

12.5 Alternative Derivation of Principal Stresses and Planes

12.6 Mohr's Stress Circle

12.7 Combined Bending and Twisting

12.8 Principal Strains

12.9 Strains on an Oblique Section

12.10 Electric Resistance Strain Gauges

12.11 Determination of Principal Strains

Worked Examples 1-12

Unworked Examples 13-42


13 Elastic Constants: Volumetric Strain

13.1 Relation Between E, G and v

13.2 Three-Dimensional Strain

13.3 Volumetric Strain

13.4 Bulk Modulus

13.5 Relation Between E, K and v

13.6 Relation Between E, G and K

13.7 Volumetric Strain Due to Unequal Stresses

Worked Examples 1-9

Unworked Examples 10-31


14 Thick Cylinders

14.1 Lamé's Theory

14.2 Comparison with Thin-Cylinder Theory

14.3 Longitudinal and Shear Stresses

14.4 The Lamé Line

14.5 Compound Cylinders

14.6 Solid Shaft Subjected to External Pressure

14.7 Shrinkage Allowance

Worked Examples 1-9

Unworked Examples 10-33


15 Strain Energy: Theories Of Failure

15.1 Strain Energy Due to Three Principal Stresses

15.2 Volumetric and Shear Strain Energy

15.3 Theories of Elastic Failure

15.4 Two-Dimensional Cases

Worked Examples 1-6

Unworked Examples 7-28