# Types of Strain

## Types of Strain

When a deforming force is applied on a body, there is a change in the configuration of the body. The body is said to be strained or deformed. The ratio of the change in configuration to the original configuration of the body is called strain. Mathematically, strain is given as:

$$\in \,=\,\frac{Change\,\,in\,\,Configuration}{Original\,\,Configuration}$$.

Strain does not have any unit.

Types of Strain: The change in configuration can be a change either in length, volume or shape of the body. There are three types of strain.

1. Longitudinal Strain:

This type of strain is produced when the deforming force causes a change in length of the body. It is defined as the ratio of the change in length to the original length of the body. Consider a wire of length L. the wire is stretched by a force F. Let the change in length of the wire be ΔL. Then longitudinal strain:

$$\in \,=\,\frac{Change\,\,in\,\,Length}{Original\,\,Length}\,=\,\frac{\Delta L}{L}$$.

2. Volumetric Strain:

This type of strain is produced when the deforming force produces a change in volume of the body. It is defined as the ratio of the change in volume to the original volume of the body. If ΔV is change in volume and V is the original volume, then

$${{\in }_{V}}\,=\,Volume\,Strain\,=\,\frac{\Delta V}{V}$$.

3. Shear Strain:

This type of strain is produced when the deforming force causes a change in the shape of the body without changing its volume. It is defined as the angle (θ) through which a face originally perpendicular to the fixed face is turned.

$$Shear\,Strain\left( \theta \right)\,=\,\frac{\Delta L}{L}$$.

Thus, the shearing strain is also defined as the ratio of the displacement of a surface under a tangential fore to the perpendicular distance of the displaced surface from the fixed surface.