Torsional Shear Stresses

When a machine member is twisted, shear stress is developed. Because it is developed due to torsion, the stress is called torsional shear stress. Its value is zero at neutral axis and increases as its distance from its neutral axis increases. Thus, the stress is the maximum at the outer surface (Figure 7.1).

If a rod is fixed at one end to take the reaction torque, as shown in Figure 7.1, it gets twisted by an angle q due to torque at the other end. The torque and the shear stress are related as:

Design for Rigidity

A shaft is not only designed for strength to bear the torsional shear stresses, but it has to be rigid enough as well, such that it does not twist beyond a certain twist angle. Rigidity can be calculated using the following equation:

The term (G × J) is called the torsional rigidity of a shaft.

Design of a Hollow Shaft

For a hollow shaft having outside diameter D and inside diameter d, the design procedure is same as that for solid shaft, but the polar moment of inertia is calculated as under:

From the given allowable stress t and assuming a suitable ratio of inside to outside diameter k (about 0.5), outside shaft diameter D can be calculated for the required torque.

Torsion of Non-Circular Shafts

Some machine components are not circular, but are subjected to torsion.