## Strain Formula

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

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

Where,
Change in dimension = x,
Original dimension = L.
There are three sorts of strain
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 = Δ l
Original length = l
Shearing strain is the ratio of change in angle to which it is turned to its distance from 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 Δ V = Change in Volume,
V = 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 5cm is stretched such that its length increases by 2mm. Compute the strain.

Known:

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

$Strain\,&space;is\,&space;given\,&space;by\,&space;\epsilon&space;\,&space;=\,&space;\frac{x}{L}$
$=\,&space;\frac{2\times&space;10^{-3}m}{5\times&space;10^{-2}}$
$=\,&space;4\times&space;10^{-2}$

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