Torsional stress is the shear stress developed in a component due to torsion. Figure 1 shows the shear stress distribution in a circular bar in torsion, T.

Shear stress varies linearly from the center of the bar to the extreme fiber. The maximum shear stress in a bar undergoing torsion is:

Where Ip is the polar moment or Inertia. For a circular cross section, the torsion formula simplifies to:

[1] Mechanics of Materials 7th Ed, James Gere
This page is part of The Encyclopedia of Stresses in Solids