GATE 2017 CE (CE2) – Question 49
A hollow circular shaft has outside and inside diameters 100 and 50 mm. With allowable maximum shear stress 125 MPa, maximum torque is ______ kN m.
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Correct answer: 20 to 25
Explanation
Use $\tau_{\max}=Tc/J$, where $J=\pi(D^4-d^4)/32$ and $c=D/2$. Therefore $$T=\frac{125\pi(100^4-50^4)}{16(100)}=23.0097\times10^6\ \mathrm{N\,mm}=23.01\ \mathrm{kN\,m}.$$ The official interval is preserved.