Two shafts A and B are made of same material. The shaft A is of diameter D and shaft 'B' is of diameter D/2. The strength of shaft B is as that of shaft A

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

Calculation:

Given:

dA = D, dB = D/2

Then, 

Since ZP ∝ d3

The polar modulus

\(\frac{{{Z_{PB}}}}{{{Z_{PA}}}} = {\left( {\frac{{0.5D}}{{D}}} \right)^3} = ({\frac {1}{2} )^3} = \frac 18\)

∴ \(Z_{PB}= \frac {Z_{PA}}{8}\)

Hence strength of shaft B is one eight of strength of shaft A.