Strain in a body

Strain in a body

Strain in a body – When a body is subjected to some deforming force, the configuration of the body changes (i.e. length or volume or the shape of the body changes and the body is said to be strained by the force. The strain produced in a body is measured as the ratio of the change in configuration to the original configuration of the body. As the strain is the ratio of two identical quantities, hence it has no units and no dimensions.

Types of strain

Strain is of three types.
a) Tensile or longitudinal strain: If the deforming force produces a change in length alone, the strain, the strain is said to be longitudinal strain. Within elastic limit, it is defined as the ratio of the change in length (ΔL) of the body to its original length(L)
Hence, longitudinal strain = ΔL/L.
b) Bulk or volumetric strain: If the deforming force produces a change in volume alone, the strain is said to be volumetric strain. Within elastic limit, it is defined as the ratio of the change in volume (ΔV) of the body to its original (V)
Hence, volumetric strain = ΔV/V.
The volumetric strain may be expansive or compressive depending upon the volume is increased or decreased.
c) Shearing strain: If the deforming force acting on the body produces a change only in the shape but not change in volume, then the body is said to be suffer a shearing strain. Within elastic limit, it is measured by the ratio of the relative displacements of one plane to its distance from the fixed plane. It can also be expressed through the angle through which a line originally perpendicular to the fixed plane is rotated. The angle is called as angle of shear.
Hence, shearing strain=θ=tanθ=ΔL/L.
(Within elastic limit, θ is small)
If L=1, then shearing strain =ΔL.
Hence, shearing strain may also be defined as the relative displacement between two parallel separated from each other by a unit distance.

Figure showing strain in a body after stressing.

strain in a body
strain in a body