**Contents**

**1. Mechanical Properties of Material & Simple Stresses & Strains**

1.1 Introduction

1.2MechanicalProperties of Materials3

Types of Loads4

1.3Concept of Stress and its Types6

Types of Stress6

1.4Concept of Strain and its Types7

Types of Strain8

Elastic Limit and Hooke’s Law9

Change in length of body due to force acting on it10

Numericals on Simple Formulae11

Numericals on Change in Length of Bar Subjected to External and Internal Forces16

Numericals on Change in Length of Stepped Bars22

Change in Length of Rectangular Bar of Uniformly Varying Section Subjected to Axial Loading30

Change in Length of Circular Bar of Uniformly Varying Section, Subjected to Axial Loading32

Numericals on Change in Length, Stresses and Strains in the Bar of Uniformly varying Section Subjected to Axial Load Only34

Bars of Composite Sections35

Numericals on Bars of Composite Sections36

Numericals on Shear Stress and Shear Strain44

Behaviour of Ductile Material under Load49

Behaviour of Brittle Material under Load51

Some Important Concepts /Terms52

Numericals on Stress-Strain Curve53

Concept of Linear Strain, Lateral Strain and Poisson’s Ratio54

1.5Concept of Uniaxial Loading55

1.6Concept of Biaxial Loading56

1.7Concept of Triaxial Loading58

Numericals on Biaxial and Triaxial Force System59

1.8Elastic Constants65

Relation between Modulus of Elasticity and Bulk Modulus (E and K)66

Relation between Modulus of Elasticity and Modulus of Rigidity66

Relation between Three Elastic Constants (E, G and K)67

Numericals on Elastic Constants68

1.9Temperature stresses and Strain71

Numericals on Thermal stresses72

1.10Hoop-stress and Strain76

2.Bending Moment and Shear Force

2.1Introduction3

Types of Load or Loading on a Beam3

Shear Force (SF)4

Relation between Loading Shear force and Bending Moment5

2.2Shear force diagram (SFD) and Bending moment diagram (BMD)6

2.3Reaction Calculation7

Reaction Calculation for Simply Supported Beam7

Reaction Calculation for Cantilever10

Reaction Calculation for Over Hanging Beam11

Tips to draw SFD13

3.Moment of Inertia

3.1Introduction3

3.2Polar Moment of Inertia (IZZ or Ip)4

3.3Radius of Gyration (K)4

Centroidal Axes, Reference Axes and Axis of Symmetry5

3.4Theorem of Moment of Inertia6

Figure 3.5 ii. Perpendicular axis theorem6

3.5M.I. of Solid and Hollow Rectangular Section7

Hollow Rectangular Section7

3.6M.I. of Solid and Hollow Circular Section13

3.7M.I. of Semi-Circular Section16

3.8M.I. of Quarter Circle18

3.9M.I. of Triangular Section20

3.10Moment of Inertia of Composite Figures/Plane Laminas22

3.11Formulae of Centroid23

3.12Formulae of M.I.26

4.Bending Stresses

4.1Introduction3

Theory of Simple (Pure) Bending3

Stress Distribution Diagrams for Cantilever and Simply Supported Beams4

Assumptions in the Theory of Bending5

Flexural Formula or Equation of Bending5

Moment of Resistance6

Section Modulus for Rectangular Section8

Bending Stress Distribution Diagram for Symmetrical Section8

Bending Stress Distribution Diagram for Unsymmetrical Sections9

4.2Concept of direct and transverse (vertical) shear stress10

Direct Shear Stress10

Transverse (vertical) Shear10

4.3Shear Stress equation12

4.4shear stress distribution for a rectangular section12

4.5Shear stress distribution for a circular section13

4.6Shear stress distribution for hollow rectangular section13

5.Direct and Bending Stresses

5.1Introduction3

Direct Load (Arial Load)3

Eccentric Load4

Direct Stresses4

Bending Stresses4

Maximum and Minimum stresses (Resultant stresses)5

5.2Stress Distribution Diagram5

5.3condition for no tension in the section7

Middle Third Rule7

6.Torsion

6.1Introduction3

6.2Concept of Pure Torsion3

6.3Assumptions in Theory of Pure Torsion4

6.4Torsional Equation for Solid Circular Shaft4

Torsional Formula and its Meaning7

6.5Power Transmitted by Rotating Shaft7

Polar Modulus (ZP)8

Strength of the Shaft or Torque Transmitted by Shaft9

Strength of Hollow Shaft9

Torsional Rigidity of Shaft9

6.6Parameters /comparison of Solid & Hollow Shaft10

1.2 Mechanical Properties of Materials

1.3 Concept of Stress and its Types

1.4 Concept of Strain and its Types

1.5 Concept of Uniaxial Loading

1.6 Concept of Biaxial Loading

1.7 Concept of Triaxial Loading

1.8 Elastic Constants

1.9 Temperature stresses and Strain

1.10 Hoop-stress and Strain

**2. Bending Moment and Shear Force**

2.1 Introduction

2.2 Shear force diagram (SFD) and Bending moment diagram (BMD)

2.3 Reaction Calculation

**3. Moment of Inertia**

3.1 Introduction

3.2 Polar Moment of Inertia (IZZ or Ip)

3.3 Radius of Gyration (K)

3.4 Theorem of Moment of Inertia

3.5 M.I. of Solid and Hollow Rectangular Section

3.6 M.I. of Solid and Hollow Circular Section

3.7 M.I. of Semi-Circular Section

3.8 M.I. of Quarter Circle

3.9 M.I. of Triangular Section

3.10 Moment of Inertia of Composite Figures/Plane Laminas

3.11 Formulae of Centroid

3.12 Formulae of M.I.

**4. Bending Stresses**

4.1 Introduction

4.2 Concept of direct and transverse (vertical) shear stress

4.3 Shear Stress equation

4.4 Shear stress distribution for a rectangular section

4.5 Shear stress distribution for a circular section

4.6 Shear stress distribution for hollow rectangular section

**5. Direct and Bending Stresses**

5.1 Introduction

5.2 Stress Distribution Diagram

5.3 Condition for no tension in the section

**6. Torsion**

6.1 Introduction

6.2 Concept of Pure Torsion

6.3 Assumptions in Theory of Pure Torsion

6.4 Torsional Equation for Solid Circular Shaft

6.5 Power Transmitted by Rotating Shaft

6.6 Parameters /comparison of Solid & Hollow Shaft