T$\_(1)=40$kip$-$in$.,$

T$\_(2)=20$kip$-$in$.,$ and T$\_(3)=6$kip$-$in$.$x$-$coordinate $($not shown in the figure$)$ gives the location along the shaft as measured from the

fixed end.

From x$=0$ to x$=16$ in$.,$ the shaft is solid with a diameter of $3$ in$.$; from x$=16$ in$.$ to x$=48$ in$.$ the shaft

is solid with a diameter of $2$ in $.$; and from x$=48$in$.$ to x$=64$in$.$ the shaft is hollow with an outer

diameter of $2$ in $.$ and an inner diameter of $1$ in $.$ The shear modulus for the whole shaft is G$=$

$10\backslash$times $10^(6)\backslash$psi $.$

aT$=$T$($x$)$ varies throughout the shaft for $\backslash$tau $\_($max$)\backslash$phi $0$ in$.$

c

Please draw all relevant free body diagrams and show all details