What is the formula for Shearing (or) Rigidity modulus ‘n’?

The ratio of tangential force per unit area to angular deformation occurred in body is known as Shearing (or) Rigidity modulus ‘n’ . It can also be defined as the ratio of shearing stress to shearing strain within elastic limit is Modulus of Rigidity ‘n’.
Rigidity modulus = T / θ   —- where T = the tangential force/unit area and θ is the angle of shear measured in radian,

Rigidity modulus = Force /Area  θ

It can also be  Rigidity modulus = Shear Stress / Shear Strain

Shear Stress = Force (F) /Area (A)

Shear Strain = Δ x / h  —— where Δ x is displacement and h is the separation between the top and bottom surfaces.

using the above formula we get,

Rigidity modulus = F h /A Δx

The unit for rigidity modulus is ‘newton metre-2 radian-1’ with symbol N m-2 rad-1.
The other unit which is widely used for rigidity modulus is pascal radian-1(Pa rad-1).