It is desired to transmit torque through a solid circular bar with a constant cross$-$section, an elasticity modulus of $40$ GPa, a Poisson's ratio of $0\mathrm{.}4,$ and a maximum allowable shear stress of $40$ MPa. The length of each section is $40$ cm$.$ Considering the torques: T$1=3000$ kNm$,$ T$2=5000$ kNm$,$ T$3=1500$ kNm$,$ and T$4=500$ kNm$.$

Shaft

Determine the minimum required radius of the bar. Report your answer in millimeters.

Determine the strain energy of section BC$.$ Report your answer in Joules.