The polar modulus for a solid shaft of diameter D is

Concept:

A shaft is subjected to torsional shear stress during its functionality. For a shaft, the polar modulus is the measure of strength in resisting torsion. 

Polar modulus is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as torsional section modulus. It is denoted by Zp.

For solid shaft

\({I_p} = \frac{\pi }{{32}}{d^4};{Z_p} = \frac{\pi }{{16}}{d^3}\)

where d = diameter of shaft