Problem $2.$ A compound shaft $($Figure P$6\mathrm{.}9)$ consists of

bronze segment $(1)$ and aluminum alloy segment $(2).$

Segment $(1)$ is a solid bronze $[G=45$GPa $]$ shaft with an

outside diameter of $80$ mm $,$ a length of $L_1=780mm,$

and an allowable shear stress of $65$ MPa $.$ Segment $(2)$ is

a solid aluminum alloy $[G=26$GPa ksi$]$ shaft with an

outside diameter of $95$ mm $,$ a length of $L_2=620mm,$

and an allowable shear stress of $40$ MPa $.$ The maximum

rotation angle at the free end of the compound shaft must

be limited to ${}_{A}2\mathrm{.}5.$ Determine the magnitude of the

largest torque $T_A$ that may be applied at $A.$

FIGURE P$6\mathrm{.}6/7$