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).