INTRODUCTION

1. Introduction to Strength of Material

Strength of Materials, also known as Mechanics of Materials, is a branch of applied mechanics that analyzes the behavior of solid objects under stress and strain caused by external forces. It’s crucial for engineering design, ensuring components can withstand applied loads without failure. This field studies how materials deform and react to various loads like tension, compression, shear, and torsion.

Strength of Materials, also known as Mechanics of Solids, is a fundamental subject in mechanical, civil, and structural engineering. It deals with the behavior of solid materials when they are subjected to external forces, loads, or moments.

Do you remember Newton’s third law of motion,” Each and every action has its equal and opposite reaction”. When an external force applied on a body to deform, the body also resist its deformation with equal and opposite force.

2. What is Stress? :

In strength of material stress can be defined as ”The force of resistance per unit area, offered by a body against its deformation is known as stress”.

Types of Stress

2.1 Tensile Stress

Tensile stress is the internal resistance or intensity of force per unit area acting within a material subjected to axial pulling forces. causing it to elongate. Tensile stress measures the tensile load per unit area.

Tensile stress formula as follows and SI unit of tensile stress is Pascal.

2.2 Compressive Stress

Compressive stress is the internal pressure acting within a material subjected to an external, inward-pushing force that reduces its volume and causing shortening or buckling. Compressive stress can be calculated by the total applied force on the cross-sectional area the material. Formula of calculating compressive stress as mentioned in above figure.

Tensile and compressive strength has the only difference in the direction of force or nature of the force.

Compressive stress formula as follows and SI unit of tensile stress is Pascal.

2.3 Shear Stress

Shear Stress (τ) can be calculated by the following formula. $$\tau = \frac{F}{A}$$

3. What is Strain ?

Strain is a measure of the deformation or change in size/ Shape of a material relative to its original dimensions, When subjected to external force. Strain can be defined as the deformation per unit original length.

$$Strain = \frac{Change\ in\ length}{Original\ length}$$

Strain is dimensionless.

Types of Strain

1. Longitudinal Strain (ε)

Occurs when the length of a body changes due to tensile or compressive stress. $$\varepsilon = \frac{\Delta L}{L}$$

• ΔL = Change in length
• L = Original length

2. Lateral Strain

compressive strain is a measure of the deformation or elongation of a material under compressive load.$$\varepsilon = \frac{\Delta L}{L}$$

• L = Original length
• ΔL = Change in length

3. Shear Strain

Angular deformation caused by shear stress.

4. Volumetric Strain

Change in volume divided by original volume.

4. Hooke’s Law

Hooke’s law states:

“Within elastic limit, stress is directly proportional to strain.”

$$Stress \propto Strain$$$$\sigma = E \epsilon$$Where

• $E$ = Modulus of elasticity (Young’s modulus)

5. Stress–Strain Curve

The stress–strain curve represents the relationship between stress and strain when a material is subjected to loading.

Important points in the curve:

1. Proportional Limit

Stress is directly proportional to strain.

2. Elastic Limit

Maximum stress at which the material returns to original shape after unloading.

3. Yield Point

Point at which plastic deformation begins.

4. Ultimate Stress

Maximum stress the material can withstand.

5. Breaking Point

Point where material fractures.

6. Elasticity and Plasticity

Elasticity

Elasticity is the property of a material to regain its original shape after removal of load.

Example:
Steel

Plasticity

Plasticity is the ability of a material to undergo permanent deformation without breaking.

Example:
Clay

7. Important Mechanical Properties

1. Strength

Ability of material to resist applied loads.

2. Elasticity

Ability to regain original shape.

3. Plasticity

Ability to undergo permanent deformation.

4. Ductility

Ability to be stretched into wires.

Example:
Copper, aluminum.

5. Malleability

Ability to be hammered into thin sheets.

Example:
Gold.

6. Toughness

Ability to absorb energy before fracture.

7. Hardness

Resistance to scratching or indentation.

8. Brittleness

Ability to fracture without significant deformation.

Example:
Cast iron.

8. Factor of Safety

Factor of Safety (FOS) is used to ensure safe design.$$FOS = \frac{Ultimate\ Stress}{Working\ Stress}$$It provides a margin of safety in design.

Typical values:

• Steel structures: 1.5 – 2
• Bridges: 3 – 5

9. Applications of Strength of Materials

Strength of materials is applied in:

1. Structural engineering
2. Mechanical design
3. Aircraft structures
4. Automobile components
5. Pressure vessels
6. Machine parts

Access for NPTEL course on Strength of Materials

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Continue Your Reading With Next Chapter Below

Chapter 1 : Elastic Constant

Chapter 2 : Principal Stress and Strain

Chapter 3 : Strain Energy and Impact Loading

Chapter 4 : Center of Gravity

Chapter 5 : Moment of Inertia

Chapter 6 : Shear Force and Bending Moment

Chapter 7 : Bending Stress

Chapter 8 : Deflection of Beams

Chapter 9 : Columns and Struts

Chapter 10 : Thin Cylinders and Spherical Shells

Chapter 11 : Thick Cylinders