Stress & Strain

Deforming force - An applied external force which changes shape & size of the body; known as deforming force.

The change of shape & size of the body after application of deforming force is called deformation.

Restoring force - When a body is subjected to deforming force a restoring force is developed in the body. This restoring force is equal in magnitude but opposite in direction of deforming force. 

Elastic body - If a body regains its original size & shape after removable of deforming force then the body is called elastic body.

E.g.  spring, rubber, balloons, Jelly, tennis ball etc.

Elasticity - It is defined as a property of a body through which body tends to regain its original size & shape on removal of deforming force.

Plastic body - If a body does not regain its original size & shape after removable of deforming force then the body is called plastic body.

E.g. wax, putty, toys made of clay etc.

Plasticity - It is defined as a property of a body because of which body does not regain its original size & shape on removal of deforming force.

Stress - The internal restoring force per unit area of the body is called stress.

  i.e., 

  Unit- N/m²

Strain - It is defined as the ratio of change in dimension to the original dimension of the body.

             i.e.;

                                    

   It is a unit less quantity.

Types of stress & strain

Longitudinal stress

Tensile stress

If a wire suspended from a rigid support having length "L" and mass "m" is attached to its free end then the downward force "mg" acts on a wire and wire elongates by "l". If "r" is radius of wire then its cross sectional area is πr². 

        
             Unit- N/m²

Compressive stress

If the body is compressed after application of deforming force then the stress is called Compressive stress.
            Tensile stress & Compressive stress are also termed as longitudinal stress.

Longitudinal strain

Tensile strain- It is defined as the ratio of increase in length of wire to the original length of wire.

Compressive strain- It is defined as the ratio of decrease in length of wire to the original length of wire.

                      Tensile strain & Compressive strain are also termed as longitudinal strain.

Volume stress

If a balloon has volume "V" at atmospheric pressure "P" & it is compressed with additional pressure "dp" then its volume decreases as shown in figure.                    

Volume strain - It is defined as the ratio of change in volume to the original volume.

Shearing stress or tangential stress

If two equal and opposite deforming forces are applied parallel to the cross sectional area of cylinder as shown in figure below then there is a relative displacement between the opposite faces of cylinder. 

The restoring force per unit area developed due to applied tangential force is called as 

Shearing stress or tangential stress.

Shearing strain

It is defined as the ratio of relative displacement between two layers under the action of force to the distance between the two layers.         

It is a unit less quantity.