$4.)$ A solid $2\mathrm{.}5$ in$.$ diameter cold$-$rolled brass $G=6,400$ksi shaft that is $L1+L3=123in.$ long extends

through and is completely bonded to a hollow aluminum $[$G$=3,800$ ksi $]$ tube, as shown in the

figure. Aluminum tube $(1)$ has an outside diameter of $3\mathrm{.}750$ in $.,$ an inside diameter of $2\mathrm{.}500$ in $.,$ and

a length of $L1=64in.$ Both the brass shaft and the aluminum tube are securely attached to the wall

support at $A.$ External torques in the directions shown are applied at $B$ and $C.$ The torque

magnitudes are $TB=5\mathrm{.}0$kip$*ft$ and $TC=1\mathrm{.}5$kip$*ft,$ respectively. After $TB$ and TC are applied to the

composite shaft, determine:

$($a$)$ the maximum shear stress magnitude in aluminum tube $(1).[$Answer: $3\mathrm{.}58$ ksi $]$

$($b$)$ the maximum shear stress magnitude in brass shaft segment $(2).[$Answer: $3\mathrm{.}99$ ksi $]$

$($c$)$ the maximum shear stress magnitude in brass shaft segment $(3).[$Answer: $5\mathrm{.}87$ ksi $]$

$($d$)$ the rotation angle of joint B$.[.0321$ rad$]$

$($e$)$ the rotation angle of end $C.[-0\mathrm{.}0112$ rad$]$

Hint: In this problem, shaft $(3)$ can be treated as a normal shaft since it is just a single shaft, not bonded

to anything. On the other hand, Shafts $(1)$ and $(2)$ and are bonded and comprise a composite shaft, so

they deform as a unit.