Stress and Strain

STRESS AND STRAIN

A body is said to be a rigid body, if the distance between any two points in a body is unaltered due to application of force. In practice, no body is perfectly rigid. When a body is subjected to some external forces, the body will offer some resistance to the deforming forces, as a result, some work is done on the body and this work is stored as the elastic potential energy. Now, if the deforming forces are removed, the energy stored brings back the body to its original condition.

Stress: Stress is defined as the restoring force per unit area which brings back the body to its original state from the deformed state. As long as no permanent change is produced in the body, the restoring force is equal to the force applied. Unit of stress is N/m².

TYPES OF STRESS

(i) Normal Stress: When the force is applied perpendicular to the surface of the body, then the stress applied is called as normal stress.

(ii) Tangential Stress: When the force is applied along the surface of the body, then the stress applied is called as tangential stress. The tangential stress is also called as SHEARING STRESS.

In general, depending on the stress applied it can be classified into compressive stress which produces compression and tensile stress which produces tension.

Strain: Strain is defined as the change in dimension (fractional deformation) produced by the external force on the body. In other way, it can also be defined as the ratio of the change in dimension to the original dimension.

(i.e) Strain = Change in dimension / Original dimension

TYPES OF STRAIN

(I) LONGITUDINAL (OR) TENSILE STRAIN

Definition: It is defined as the ratio between the change in length to the original length, without any change in its shape, after the removal of the external forces.

Explanation: When a force is applied along the original length (L) of the body, due to this applied force, if the change in length is l, then

Longitudinal strain = l/L

(II) SHEARING STRAIN

Definition: It is defined as the angular deformation produced on the body, due to the application of external tangential forces on it.

Explanation: Let ABCD be a body with its side CD fixed as shown in Fig. 1.1. A tangential force is applied on the upper surface AB of the body. Therefore the body is sheared to an angle 'ϕ' and it goes to a new position A'B'CD. Then this angle 'ϕ' measured in radians is called as shearing strain.

(III) VOLUMETRIC STRAIN

Definition: It is defined as the ratio between the change in volume to the original volume, without any change in its shape.

Explanation: When forces are applied normal to the surface of the body of volume 'V', it undergoes a change in volume (v), then

Volumetric Strain = v/V