A cylindrical torsion bar is made by bonding a solid bar made of material 1 inside a tube made of material 2, as shown below. The yield stresses of the two materials are known as tauy1 and tauy2. Both materials have the same shear modulus, G, and can be considered elastic perfectly plastic. Assume tauy2=4tauy1 and r2=3r1.
a) find the twist rate at initial yield in the bar
b) what twist rate is required to yield all of material 2. Assume tauy1=4tauy2
c) plot shear stress as a function of radius r at the state of twist calculated in part b