A solid $45-$mm$-$diameter cold$-$rolled brass $[G=40\mathrm{.}4$GPa $]$ shaft that is $1\mathrm{.}17$ m long extends through and is completely bonded to a hollow aluminum $[G=26\mathrm{.}4$GPa $]$ tube. Aluminum tube $(1)$ has an outside diameter of $76$ mm $,$ an inside diameter of $45$ mm $,$ and a length of $0\mathrm{.}73$ m $.$ Both the brass shaft and the aluminum tube are securely attached to the wall support at $A.$ Assume $L_1=L_2=0\mathrm{.}73m,L_3=0\mathrm{.}44m,T_B=25kN-m,$ and $T_C=7kN-m.$ When the two torques shown are applied to the composite shaft, determine:

$($a$)$ the maximum shear stress magnitude ${}_1$ in aluminum tube $(1).$

$($b$)$ the maximum shear stress magnitude ${}_2$ in brass shaft segment $(2).$

$($c$)$ the maximum shear stress magnitude ${}_3$ in brass shaft segment $(3).$

$($d$)$ the rotation angle ${}_B$ of joint $B.$

$($e$)$ the rotation angle ${}_C$ of joint $C.$