1. Linear Strain
Linear strain of a deformed body is defined as the ratio of the change in length of the body due to the deformation to its original length in the direction of the force. If l is the original length and dl the change in length occurred due to the deformation, the linear strain e induced is given by e=dl/l.
2. Lateral Strain
Lateral strain of a deformed body is defined as the ratio of the change in length (breadth of a rectangular bar or diameter of a circular bar) of the body due to the deformation to its original length (breadth of a rectangular bar or diameter of a circular bar) in the direction perpendicular to the force.
A little consideration will show that due to tensile force, the length of the bar increases by an amount δl and the diameter decreases by an amount δd, as shown in Fig. 1. Similarly, if the bar is subjected to a compressive force, the length of bar will decrease which will be followed by increase in diameter.
It is thus obvious, that every direct stress is accompanied by a strain in its own direction which is known as linear strain and an opposite kind of strain in every direction, at right angles to it, is known as lateral strain.
Online Educational Resource Collection
A textbook of Machine Design by R.S.Khurmi and J.K.Gupta