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

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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

shearing strain

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).

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