$5.)$ A compound steel $[G=67GP]$ shaft consists of a solid $51$ mm diameter segment $(1)$ and a

solid $35$ mm diameter segment $(2).$ The allowable shear stress of the steel is $77$ MPa $,$ and the

maximum rotation angle at the free end of the compound shaft must be limited to $c3\mathrm{.}4.$

Assume $L_1=0\mathrm{.}9m$ and $L_2=2\mathrm{.}0m.$ Determine the magnitude of the largest torque $T_c$ that may be

applied at $C$

$[$Answer: The shear stress condition gives $T_c=648Nm($shaft $2)$ and $T_c=2006Nm($shaft $1).$

The twist angle condition gives $T_c=266Nm.$ Choose the one that will ensure that all conditions

are met$]$