Considering 3 different types of stress for solids, we have 3 different types of

elasticity modulus.

These are (a)Young’s Modulus (2) Shear Modulus (3) Bulk modulus

## Young’s Modulus

Young’s Modulus is the ratio of Longitudinal Stress and Longitudinal Strain. If it’s designated with Y then

**Y = ****Longitudinal Stress / Longitudinal Strain = (F/A)/(l/L) = (FL)/(Al)**

Its unit is N/m

^{2}or Pascal. Please note that Strain is dimensionless. [see the derivation of the longitudinal modulus formula]

Also, see the numerical problem based on Young’s modulus.

## Shear Modulus | **Modulus of Rigidity**

Shear Modulus is the ratio of Shear Stress and Shear Strain. This is also known as the

Modulus of Rigidity.If it’s designated as G then

G = (F/A)/(x/L) = (F/A)/θ = F/(Aθ).[see the derivation of the shear modulus formula]

## Bulk Modulus

Bulk Modulus (B)is the ratio of Hydraulic Stress and Volume Strain.

B = (F/A)/(Δv / V) = – P /(Δv / V)Here P is the pressure. As the change in volume is indirectly proportional to the pressure applied, that’s why the negative sign is used.

[see the derivation of the bulk modulus formula]