A compound shaft supports several pulleys. Segments $(1)$ and $(4)$ are solid $20-$mm$-$diameter steel $[G=66$GPa shafts. Segments $(2)$ and

$(3)$ are solid $47-$mm$-$diameter steel shafts. The bearings shown allow the shaft to turn freely. Assume $L_1=745mm,L_2=475mm,L_3=655$

$mm,L_4=465mm,T_A=190N-m,T_B=2140N-m,T_C=1515N-m,T_D=690N-m,T_E=255N-m.$

$($a$)$ Determine the maximum absolute value of the shear stress ${}_{\text{m}\text{a}\text{x}}$ in the compound shaft.

$($b$)$ Determine the rotation angle ${}_{\frac{D}{B}}$ of pulley $D$ with respect to pulley $B.$

$($c$)$ Determine the rotation angle ${}_{\frac{E}{A}}$ of pulley $E$ with respect to pulley $A.$

Answers:

$($a$){}_{\text{m}\text{a}\text{x}}=$

MPa.

$($b$){}_{\frac{D}{B}}=$

$($c$){}_{\frac{E}{A}}=$

$$

$.$