Question

A hollow circular shaft has the diameters 50 cm and 30 cm and is subjected to a torque. If the realized maximum shear stress is $30N/m{m}^2$, what is the applied torque to nearest units?

• A. 640884.9 Nm
• B. 610000.0 Nm
• C. 540889.5 Nm
• D. 640000.0 Nm

Answer 1

The correct option is A 640884.9 Nm

Given :

$d_o=0.5m,d_i=0.3m$

$\tau =30N/m{m}^2=30\times {10}^{6}N/m^2$

$\because \tau =\frac{T\left(\frac{d_o}{2}\right)}{\frac{\pi }{32}[d_o^4-d_i^4]}$

$\therefore T=\frac{30\times {10}^6\times \frac{\pi }{32}({0.5}^4-{0.3}^4)}{\frac{0.5}{2}}$

$=640884.9Nm$