Question

What is the diameter d of a solid circular shaft when subjected to a torque T with a corresponding maximum shear stress of magnitude $f_s$?

• A. $\frac{16T}{\pi f_s}$
• B. $\frac{\pi f_s}{16T}$
• C. $\sqrt{\frac{16T}{\pi f_s}}$
• D. $3\sqrt{\frac{16T}{\pi f_s}}$

Answer 1

The correct option is D $3\sqrt{\frac{16T}{\pi f_s}}$

Form torsion formula

$\frac{\tau }{r}=\frac{T}{J}=\frac{G\theta }{L}$

$So{\tau }_{max}=\frac{Tr}{J}$

$\Rightarrow f_s=\frac{T\frac{d}{2}}{\pi d^4/32}$

$f_s=\frac{16T}{\pi d^3}$

$d=\sqrt{\frac{16T}{\pi f_s}}$