Mechanics of Structures

Contents

1. Moment of Inertia

1. Introduction

2. M.I. of Solid and Hollow Rectangular Section

Solved Examples

3. M.I. of Triangular Section

Solved Examples

4. M.I. of Solid and Hollow Circular Section

Solved Examples

5. M.I. of Semi-Circular Section

Solved Examples

6. M.I. of Quarter Circle

Solved Examples

7. Theorem of Moment of Inertia

9. Radius of Gyration (K)

10. Polar Moment of Inertia (IZZ or Ip)

11. Moment of Inertia of Composite Figures/Plane Laminas

12. Formulae of Centroid

13. Formulae of M.I.

Solved Examples

Solved Examples

2. Simple Stress and Strain

1. Introduction

2. Mechanical Properties of Materials

3. Concept of Stress and its Types

4. Concept of Strain and its Types

5. Deformation of a Body Due to Axial Load

Solved Examples

6. Stress in of Composite Sections

Solved on Bars of Composite Sections

7. Shear Stress, Shear Strain and Modulus of Rigidity

Solved on Shear Stress and Shear Strain

8. Stress Strain Curve for Mild Steel

Solved Examples

3. Elastic Constants

1. Introduction

2. Concept of Linear Strain, Lateral Strain and Poisson’s Ratio

2.1 Concept of Uniaxial Loading

2.2 Concept of Biaxial Loading

2.3 Concept of Triaxial Loading

Solved Examples on Biaxial and Triaxial Force System

Solved Examples on change in Lateral dimensions

3. Elastic Constants

4. Relation between Modulus of Elasticity and Bulk Modulus (E and K)

Solved Examples on Elastic Constants

5. Nature of Stress and Strain due to Change in Temperature

5.1 Temperature Stresses and Strain

Solved Examples on Thermal stresses

5.2 Thermal Stresses in Composite Bar

6. Hoop-Stress and Strain

Solved Example

4. Shear Force and Bending Moment

1. Introduction

2. Types of Load or Loading on a Beam

2.1 Shear Force (SF)

2.2 Bending Moment (BM)

3. Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)

4. Reaction Calculation

4.1 Reaction Calculation for Simply Supported Beam

5. Beams

5.1 Types of Beams

5.2 Types of End Supports

5.3 Classification of Loads

6. Reactions of Simply Supported Beam by Analytical Method

Solved Examples

6.1 Reaction Calculation for Cantilever

6.2 Reaction Calculation for Over Hanging Beam

Solved Examples

5. Stresses in Beams

1. Introduction

2. Theory of Simple (Pure) Bending

2.1 Stress Distribution Diagrams for Cantilever and Simply Supported Beams

2.2 Assumptions in the Theory of Bending

2.3 Flexural Formula or Equation of Bending

2.4 Moment of Resistance

2.5 Section Modulus (Z)

2.6 Bending Stresses in Beam Section

3. Application of Theory of Bending to Symmetrical and Unsymmetrical Section

4. Concept of Direct and Transverse (Vertical) Shear Stress

4.1 Direct Shear Stress

4.2 Transverse (vertical) Shear

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

Solved Examples

Solved Examples on Shear stress

6. Column

1. Introduction

1.1 Important Definitions

1.2 Equivalent Length of the Column

2. Classification of Columns

2.1 Euler’s Theory for Long Column

3. Rankine’s Formula

Solved Examples

7. Strain Energy

1. Introduction

2. Types of Loading: (Based on Way of Application)

3. Strain Energy Stored in a Body due to Different Types of Load

4. Comparison of Stresses due to Gradual Load, Sudden Load and Impact Load

4.1 ‘s’ Due to Gradually Applied Load

4.2 ‘s’ Due to Suddenly Applied Load

4.3 ‘s’ Due to Impact Load

Solved Example