# Strain Formula

The consequence of stress is what is termed as strain. The strain is the measure of how much distortion has befallen on the body compared to its initial shape due to the action of the force. It is denoted by ϵ.

## Formula For Strain

Strain Formula is articulated as,

$Strain\,&space;\left&space;(&space;\epsilon&space;\right&space;)\,&space;=\,&space;\frac{x}{L}$

Where,

• Change in dimension is x,
• The original dimension is L.

### Types of Strain

There are three sorts of strain
The longitudinal strain is the ratio of change in length to the original length.

$Longitudinal\,&space;strain\,&space;\left&space;(&space;\epsilon&space;\right&space;)\,&space;=\,&space;\frac{\Delta&space;l&space;}{l}$

Where,

• Change in length is Δ l
• Original length is l

Shearing strain is the ratio of change in angle to which it is turned to its distance from the fixed layer.

$Shearing\,&space;strain\,&space;\left&space;(&space;\epsilon&space;\right&space;)\,&space;=\,&space;\frac{\Delta&space;l&space;}{l}$

Volumetric strain is the ratio of change in volume to the original volume.

$Volumetric\,&space;strain\,&space;\left&space;(&space;\epsilon&space;\right&space;)\,&space;=\,&space;\frac{\Delta&space;V&space;}{V}$

Where,

• ΔV is the change in volume,
• V is the original volume.

### Strain Solved Examples

Underneath are numerical founded on strain formula which might be useful for you.

Problem 1: An elastic band of length 5 cm is stretched such that its length increases by 2 mm. Compute the strain.

Known:

x (Change in length) = 2 mm,
L (Original length) = 5 cm

$Strain\,&space;is\,&space;given\,&space;by\,&space;\epsilon&space;\,&space;=\,&space;\frac{x}{L}$

= 2 x 10-3/5 x 10-2

$=\,&space;4\times&space;10^{-2}$

Problem  2: An iron bar 3 m long is heated. It stretches by 0.5 mm. Compute the strain.
$Strain\,&space;is\,&space;given\,&space;by\,&space;\epsilon&space;\,&space;=\,&space;\frac{x}{L}$
$=\,&space;\frac{5\times&space;10^{-3}}{3}$
$=\,&space;1.67\times&space;10^{-3}$