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

\(U= \frac{{{σ ^2}}}{{2E}}\times volume~of~shaft\)

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

Shear Force:

Strain energy due to shear force is given as

\(\frac{τ^2}{2G}\times volume~of\ shaft\)

where τ = shear stress due to shear force.

For solid circular shaft due to torsion strain energy is:

\(U = \frac{{{τ ^2}}}{{4G}} \times Volume~of~shaft\)

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

For hollow shaft:

Strain energy

\(U = \frac{{{τ ^2}}}{{4G}}\times\frac{{{D^2} + {d^2}}}{{{D^2}}} \times Volume~of~shaft\)

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