# Stress

We know that when a body is deformed, the restoring forces are developed uniformly inside the body.Stress is defined as the restoring force per unit area set up in the body, when deforming by the external force. Thus,

Stress

**=**

As the restoring force set up in the body are equal and opposite to the external deforming force (so long as no permanent deformation is produced i.e. within elastic limit), therefore, the stress may be measured as the external force acting per unit area i.e.

Stress = =

Stress is of the following two types:

**Normal stress**

The deforming force acting per unit area normal to the surface of the body is called normal stress. For example, when a force, pulls a wire with the force acting along the length of the wire, the stress is called normal stress.**Tangential stress**

The deforming force acting per unit area tangential to the surface is called tangential stress. For example, a body being sheared is under tangential stress.

In CGS system, stress is measured in**dyn cm**and it is measured in^{-2};**Newton metre**^{-}^{2}(N m^{-}in S.I. The dimensional formula of stress is^{2})**[M L**^{-1 }T^{ -2}].

# Strain

When deforming force acts on a body, it undergoes change in its dimensions and the body is said to be deformed or strained.The ratio of change in dimension of the body to the original dimension is called strain.

Since a body can have three types of deformation i.e. in length, in volume or in shape, likewise there are following three types of strains:

**Longitudinal strain**

It is defined as the increases in length per unit original length, when deformed by the external force. It is also called**linear strain or tensile strain.**

Thus, longitudinal strain =**=**

Where L is the original length and l is increase in length.**Volumetric strain**

It is defined as change in volume per unit original volume, when deformed by the external force.

Thus, volumetric strain = =

Where V is the original volume and Î” V is change in volume.**Shear strain**

When change takes place in the shape of the body, the strain is called the shear strain. It is defined as the angle Î¸ (in radian), through which a line originally perpendicular to the fixed face gets turned on applying tangential deforming force. This angle, through which the reference line turns, is called the**angle of shear.**

When force is applied parallel to the surface of a solid body, then the change takes place only in the shape of the body. Such a shear is called pure shear. It can happen only in case of a solid. If a force is applied parallel to the surface of the fluid, it will begin to flow in the direction of applied force.

All the three types of strain have**no units,**as they are ratios of the like physical quantities. Also strain is a**dimensionless**physical quantity.

**Young's Modulus (Stretching of a wire)**

It is defined as the ratio of normal stress to longitudinal strain. It is denoted by Y.

Y = (i)

Normal stress =

and longitudinal strain =

From equation (i), we have

Y =

Y = ------(ii)

If the wire has got circular cross-section of radius r, then

Y = -------(iii)

The units of Young;s modulus are

**Pascal**

**(Pa)**or

**N m**

^{-}**in S. I. and**

^{2 }**dyn cm**cgs system.

^{-2}