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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

:ompletely bonded to a hollow aluminum $[G=26\mathrm{.}4$GPa tube. Aluminum tube $(1)$ has an outside diameter

ff $76$ 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 $T_C=7$

N $-$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 $C.$

Answers: $$

$($a$){}_1=$

i

MPa.

$($b$){}_2=$

i

MPa.

$($c$){}_3=$

MPa $.$

$($d$){}_B=$

$($e$){}_C=$