Strain Equation

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Strain is the deformation caused in an object due to stress, and it is the measure of the deformation caused when compared to the original shape. Stress is the force applied per cross-sectional area and hence strain is known as the effect of stress. Strain is usually represented by the symbol ‘ε’ called as ‘epsilon’. There are different types of strain based on the type of deformation caused such as longitudinal strain, shearing strain and volumetric strain, and the equation of strain depends on the type of strain caused.

Example 1:  The length of an elastic band, originally 4cm is stretched to a length of 6cm. How much strain has been caused on the band?

Given: Original length of the elastic band, l = 4cm
After stretching, band length = 6cm
This implies, the change in length, ?l = 6cm – 4cm = 2cm
Strain, ε = (Change in length)/ Original length = ?l/ l
This gives, Strain = 2cm/4cm = 0.5

Therefore, strain caused in the elastic band = 0.5

Example 2: An object expands due to which its volume changes from 25cm3 to 40cm3. How much strain has been caused on the object?

Given: Original volume of the object, V = 25cm3
After expanding, volume = 40cm3
This implies, the change in volume, ?V = 40cm3 – 25cm3 = 15cm3
Strain, ε = (Change in volume)/ Original volume = ?V/ V
This gives, Strain = 15cm3/25cm3 = 0.6

Therefore, strain caused in the object = 0.6