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.

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Laws of Equilibrium

A body is said to be in equilibrium if the system of forces acting on the body tends to keep the body at rest, in other words, there is no translation motion or net torque on the body. Under such conditions, the equilibrium conditions are to be applied to analyze the condition. The branch of mechanics that deals with this condition is known as 'statics'. Under equilibrium, there are no net forces on the body.