Question

A circular shaft which has a diameter of 100 mm is subjected to torque of 5 kN-m. The shear stress in $N/m{m}^2$, induced in the shaft would be

• A. $\frac{160}{\pi }$
• B. $\frac{120}{\pi }$
• C. $\frac{125}{\pi }$
• D. $\frac{80}{\pi }$

Answer 1

The correct option is D $\frac{80}{\pi }$

From torsion formula, we have

$\frac{{\tau }_{max}}{R}=\frac{T}{I_p}$

$\Rightarrow \frac{{\tau }_{max}}{D/2}=\frac{T}{\frac{\pi }{32}\times D^4}$

$\Rightarrow {\tau }_{max}=\frac{16T}{\pi D^3}$

$\Rightarrow {\tau }_{max}=\frac{16\times 5\times {10}^6}{\pi \times (100{)}^3}$

$\Rightarrow {\tau }_{max}=\frac{80}{\pi }$