The shaft shown consists of a steel tube (1) bonded to a brass core (2). The shear modulus of steel is 11,400 ksi and the shear modulus of brass is 5,200 ksi. A torque is applied at A. The radius of the brass core is 0.5 in. The outer radius of the steel tube is 1 in. a) Write the equilibrium and compatibility equation(s) needed to solve the problem along with supporting sketches. b) Find a symbolic relationship between the applied torque, T, and the internal torques. c) Assume the allowable shear stress in the steel tube is 2,000 psi. Calculate the maximum torque you could apply to the system in k-in.

Question

The shaft shown consists of a steel tube (1) bonded to a brass core (2). The shear modulus of steel is 11,400 ksi and the shear modulus of brass is 5,200 ksi. A torque is applied at A. The radius of the brass core is 0.5 in. The outer radius of the steel tube is 1 in.
a) Write the equilibrium and compatibility equation(s) needed to solve the problem along with supporting sketches.
b) Find a symbolic relationship between the applied torque, T, and the internal torques.
c) Assume the allowable shear stress in the steel tube is 2,000 psi. Calculate the maximum torque you could apply to the system in k-in.