Problem 6.30 - Statically Indeterminate Problems

Problem Statement

A shaft is fixed between two walls. One portion is made from nickel (Gnickel = 11.4 x 106 psi) with a diameter of d1 = 2 in. The other portion is aluminum (Galuminum = 4 x 106 psi) with a diameter of d2 = 4 in. A torque T = 1,000 lb-ft is applied at the point where the two materials meet. If lengths L1 = 8 ft and L2 = 4 ft, what is the maximum shear stress in the shaft?

A shaft made of two different materials is fixed between two walls. The portion of the shaft made of nickel has diameter d[1] and length L[1]. The portion of the shaft made of aluminum has diameter d[2] and length L[2]. The torque is applied where the two metals meet.

Figure 1: A shaft made of two different materials is fixed between two walls.

[Problem adapted from © Kurt Gramoll CC BY NC-SA 4.0]