(Solved): 3) A 20-mm-diameter solid steel shaft is to be used as a torsion spring. If the torsional stress i ...

3) A 20-mm-diameter solid steel shaft is to be used as a torsion spring. If the torsional stress in the shaft is not to exceed $110\mathrm{MPa}$ when one end is twisted through an angle of $15^{?}$, a) what must be the length of the solid shaft? $J_{\text{solid }}=1.57\times 10^{?8}{\mathrm{m}}^4$. b) if the solid shaft is replaced by a tube of the same weight and an outer diameter of $40$ $\mathrm{mm}$, what is the maximum torque that can be obtained from the tube, provided that the maximum torsional shear stress in the tube cannot exceed $110\mathrm{MPa}$ ? Assume the shear modulus, $\mathbf{G}$, is $79.3\times 10^9\mathrm{Pa}$. (30 points)