The effect of stress is what we call as strain. The strain is the measure of how much deformation has occurred in the body compared to its original shape due to the action of force. It is denoted by **$\epsilon$**.

**Strain Formula** is given by

Where,

x = Change in dimension,

L = Original dimension.

There are three types of strain

Longitudinal strain is the ratio of change in length to the original length.

Where,**$\Delta$ $l$ **= Change in length,

**$l$** = Original length.

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

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

Where**$\Delta$ V** = Change in Volume,

**V** = Original volume.

x = Change in dimension,

L = Original dimension.

There are three types of strain

Longitudinal strain is the ratio of change in length to the original length.

Where,

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

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

Where

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Below are problems based on strain formula which may be helpful to you.

### Solved Examples

**Question 1: **A rubber band of length 5cm is stretched such that its length increases by 2mm. Calculate the strain.

** Solution: **

Given: Change in length x = 2mm,

Original length L = 5 cm

Strain is given by $\epsilon$ = $\frac{x}{L}$

= $\frac{2 \times 10^{-3} m}{5 \times 10^{-2}}$

= 4 $\times$ 10^{-2}.

**Question 2: **A iron bar of 3m long is heated. It stretches by 0.5 mm. Calculate the strain.

** Solution: **

Given: Change in length x = 0.5 mm,

Original length L = 3m.

Strain is given by $\epsilon$ = $\frac{x}{L}$

= $\frac{5 \times 10^{-3}}{3}$

= 1.67 $\times$ 10^{-3}.

Given: Change in length x = 2mm,

Original length L = 5 cm

Strain is given by $\epsilon$ = $\frac{x}{L}$

= $\frac{2 \times 10^{-3} m}{5 \times 10^{-2}}$

= 4 $\times$ 10

Given: Change in length x = 0.5 mm,

Original length L = 3m.

Strain is given by $\epsilon$ = $\frac{x}{L}$

= $\frac{5 \times 10^{-3}}{3}$

= 1.67 $\times$ 10

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