Using the stress strain relations you developed in part: 1. derive the theoretical torque versus angle of twist relationship for the cast iron and for the steel. a. for every angle of twist recorded in the lab, determine which part of the shaft cross section is in the linear elastic range, which part is in perfectly plastic range (if any) and which part is in strain hardening (if any). b. given the shearing stress-strain models you developed, derive the equations for the torque for each of the parts identified above.