Q$3.[0\mathrm{.}6\backslash \%]$

An electric motor at A exerts a total torque of $800$ Nm on the steel shaft $\backslash ($ A B C D $\backslash ).$ If $300$ Nm is used to rotate gear $\backslash ($ B $\backslash )$ and $500$ Nm is used to rotate gear C $,$ and the shaft at support $\backslash ($ D $\backslash )$ is free to rotate, calculate $($a$)$ the torque at shaft $\backslash ($ C D $\backslash ),($b$)$ the torque at shaft $\backslash ($ B C $\backslash ),$ and $($c$)$ the torque at shaft $\backslash ($ A B $\backslash ).$ Design specifications require that the diameter of the shaft be uniform from $\backslash ($ A $\backslash )$ to $\backslash ($ D $\backslash )$ and that the angle of twist between $\backslash ($ A $\backslash )$ to $\backslash ($ D $\backslash )$ not to exceed $1\mathrm{.}5$ degrees.

Knowing that allowable shearing stress is $60$ MPa and G $\backslash (=77\backslash$mathrm$\{$GPa$\}\backslash ),$ determine $($d$)$ the minimum diameter solid shaft that can be used.

$($Hint: First design the shaft based on the allowable shear stress, then design the shaft based on the max angle of twist. Finally, use the larger diameter as the answer.$)$