Stress and Strain

When an external force acts on a body, the body tends to undergo some deformation. due to cohesion between the molecules, the body resists the deformation. the resistance by which material of the body opposes the deformation is known as strength of material.

Stress

The force of resistance per unit area, offered by a body against deformation is known as stress. The external force acting on the body is called the load or force. A loaded member remains in equilibrium when the resistance offered by the member against the deformation and applied load are equal.

Mathematically stress is written as, σ =P/A

σ = stress (N/m², Pa)

P = force (N)

A = original cross-sectional area (m²)

Strain

When a body is subjected to some external force, there is some change of dimension of the body. The ratio of change of dimension of the body to the original dimension is known as strain. Strain is dimensionless.

Strain may be;

1. Tensile strain

2. Compressive strain

3. Volumetric strain

4. Shear strain

If there is some increase in length of a body due to external force, then the ratio of increase of length to the original length of the body is known as tensile strain. But if there is some decrease in length of the body, then the ratio of decrease of the length of the body to the original length is known as compressive strain. The ratio of change of volume of the body to the original volume is known as volumetric strain. The strain produced by shear stress is known as shear strain.

Types of Stress

• Tensile Stress - The stress induced in a body, when it is subjected to two equal and opposite pulls, as a result of which there is an increase in length, is known as tensile stress. It acts normal to the area.

Mathematically tensile stress, σt = P/A

• Compressive Stress - The stress induced in a body, when it is subjected to two equal and opposite pushes, as a result of which there is a decrease in length, is known as compressive stress. It acts normal to the area.

Mathematically compressive stress, σc = P/A

• Shear Stress - The stress induced in a body, when subjected to two equal and opposite forces which are acting tangentially across the resisting area, as a result of which body tends to shear off across the section, is known as shear stress.

Mathematically shear stress, τ = shear resistance / area