GATE 2018 ME (ME2) – Question 30
A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m acts as a torsional spring. Its shear modulus is 150 GPa. Find torsional stiffness in kN·m/rad, to two decimal places.
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Correct answer: 35.24 to 35.44
Explanation
Torsional stiffness is $k_\theta=GJ/L$, with $J=\pi(r_o^4-r_i^4)/2$. Using metres, $$k_\theta=150\times10^9\frac\pi2(0.02^4-0.01^4)=35342.92\ \mathrm{N\,m/rad}.$$ Divide by 1000: **35.34 kN·m/rad**.