# Types of modulus of elasticity

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/m2 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.