Strain (ε)

When a single force or a system force acts on a body, it undergoes some deformation. This deformation per unit length is known as strain. Strain is a dimensionless unit since it is the ratio of two lengths. But it also a common practice to state it as the ratio of two length units like m/m or mm/mm etc. Strain is represented by 'ε' (Greek lowercase alphabet Epsilon).

No material is perfectly rigid. Under the action of forces it undergoes changes in shape and size. All materials including steel, cast iron, brass, concrete etc. undergo deformation when loaded. But the deformations are very small and hence we cannot see them with naked eye. There are instruments like extensometer and electric strain gauges which can measure this extension. Strain may be of linear strain or lateral strain.

The bars extend under tensile force and shorten under compressive forces along axial direction. The change in length per unit length is known as linear strain/longitudinal strain. Thus, 

When there is a changes in longitudinal direction takes place change in lateral direction also take place. The nature of these changes in lateral direction are exactly opposite to that of changes in longitudinal direction i.e., if extension is taking place in longitudinal direction, the shortening of lateral dimension takes place and if shortening is taking place in longitudinal direction extension takes place in lateral directions. The lateral strain may be defined as changes in the lateral dimension per unit lateral dimension. Thus,

Consider a square bar of length ‘L’ and breadth ‘b’. The linear dimension (length) changes by ‘Δ’ due to the application of tensile or compressive force. The lateral dimension (breadth) changes by b’ due to the application of tensile or compressive force as shown in the figure.

Fig.1 Deformation of a square bar due to axial tensile/compressive force

Shear Strain (ϕ)

This type of strain is produced when the deforming force causes change in the shape of the body. The distortion produced by shear stress on an element or rectangular block is shown in the figure. The shear strain is expressed by angle ‘ϕ’ and it can be defined as the change in the right angle. It is measured in radians and is dimensionless in nature.

Shearing stress has a tendency to distort the element to position AB′C′D from the original position ABCD as shown in figure. This deformation is expressed in terms of angular displacement and is called shear strain. 

Fig.2 Deformation of a rectangular body fixed at bottom due to shear force