A solid constant$-$diameter shaft is subjected to the torques shown in Figure. The bearings shown allow the shaft to turn freely.

D

$($a$)$ Plot a torque diagram showing the internal torque in segments $1,2$ and $3$ of the shaft. Use the sign convention.

$($b$)$ If a solid $1\mathrm{.}905$ cm diameter shaft is subjected to that particular torque.

Determine the maximum shear stress magnitude in the shaft.

$($c$)$ If the allowable shear stress in the shaft is $80$ MPa $,$ determine the minimum acceptable diameter for the shaft.