It frequently arises that a torque is transmitted by a hollow circular shaft. Suppose a1 and a2 are the internal and external radii, respectively, of such a shaft.
We make the same general assumptions as in the torsion of a solid circular shaft. If r is the shearing stress at radius r, the total torque on the shaft is
If we assume, as before, that radii remain straight during twisting, and that the material is elastic, we have
Here, J is the polar second moment of area or, more generally, the torsion constant of the crosssection about an axis through the centre; J has the value