**Introduction:**

If one end of the shaft is assumed to be fixed, then the work done in twisting the other end through an angle θ is the area under the T-θ relationship,

**Description:**

The torque-twist relationship for a circular shaft has the form

This shows that the angle of twist, θ, of one end relative to the other, increases linearly with T. If one end of the shaft is assumed to be fEed, then the work done in twisting the other end through an angle θ is the area under the T-θ relationship.

This work is conserved in the shaft as strain energy, which has the value

**Figure : Linear torque-twist relationship and strain energy of elastic torsion.**

we may eliminate either θ or T, a d we have