Maximum value of shear stress for a hollow shaft of outer and inner diameter $D$ and $d$ will be: [where $T$ = Applied torque]

Question

Question

This question was previously asked in

SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

Considering the rigidity of shaft,

The maximum shear stress induced in the solid shaft of diameter d, to transmit twisting moment T is given by,

$\tau_{max}\;=\frac{{16T}}{{\pi d^3 }}$

The maximum shear stress induced in the hollow shaft of outer diametr do and inner diameter di to transmit the twisting moment T.

.$\tau_{max}\;=\frac{{16T}}{{\pi d_o^3 (1-K^4)}}$, where K is the ratio of outer and inner diameter, $K =\frac{{d_i}}{{d_o}}$

Explanation:

Given:

do = D, di = d

⇒ τmax = $\frac{16TD}{\pi(D^4 - d^4)}$