Question

In a circular shaft of diameter d, subjected to a torque T, the maximum shear stress inducted is

• A. proportional to $d^3$
• B. proportional to $d^4$
• C. inversely proportional to $d^3$
• D. inversely proportional to $d^4$

Answer 1

The correct option is C inversely proportional to $d^3$

For a circular shaft

$\frac{T}{J}=\frac{f_s}{r}$

$\Rightarrow f_s=\frac{T}{J}r=\frac{T}{\frac{\pi d^4}{32}}\times \frac{d}{2}=\frac{16T}{\pi d^3}$

$\therefore f_s\propto \frac{1}{d^3}$