Problem 6.12 - Torsional Deformation

Problem Statement

A bar with a shear modulus G = 11 x 10⁶ psi is subjected to torques T₁ = 1,500 lb-ft at its center and T₂ at its free end. The inner diameter is 1 in and the outer diameter is 2 in and the total length of the bar is 10 in. If the rotation of the rod at its free end is Φ = 2° clockwise, what is the magnitude of torque T₂?

Figure 1: A bar is attached to a wall. {fig-alt=” A bar is attached to a wall. The bar has an inner diameter of 1 in and outer diameter of 2 in. Torque, T[1] is applied halfway down the bar. The bar length is 10 in total.”}