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A compound shaft supports several pulleys. Segments $(1)$ and $(4)$ are solid $22-$mm$-$diameter steel $[$G $=89$ GPa$]$

shafts. Segments $(2)$ and $(3)$ are solid $52-$mm$-$diameter steel shafts. The bearings shown allow the shaft to

turn freely. Assume $L_1=700mm,L_2=545mm,L_3=715mm,L_4=545mm,T_A=160N-m,T_B=1975N-m,T_C=1435$

$N-m,T_D=585N-m,T_E=205N-m.$

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