Q$3(10$ points$)$ Bonus.

The solid rod $AB$ has a diameter $d_{AB}=80mm$ and is made of steel, for which the shear $G$ modulus is $85$GPa. The solid rod $CD$ has a diameter of $120mm$ and is made of aluminum, for which the shear modulus is $30$GPa. For the torque $T=15kN.$m$.$

Determine:

a$)$ the largest sheer stress in the rods.

b$)$ the angle of twist of point $A$ in degrees $(.$