The strain energy stored in a solid circular shaft subjected shear stress (τ) is (where C = Modulus of rigidity the shaft material) 

Explanation:

Strain Energy:

Strain Energy of the member is defined as the internal work done in deforming the body by the action of externally applied forces.

Normal Stress:

Strain energy due to normal stress is given as

where σ = normal stress, E = young's modulus of elasticity

Shear Force:

Strain energy due to shear force is given as

where τ = shear stress due to shear force.

For solid circular shaft due to torsion strain energy is:

where τ = shear stress due to torsion, G = modulus of rigidity

For hollow shaft:

Strain energy

where τ​ = shear stress due to torsion, G = modulus of rigidity.