Problem 5.34 - Statically Indeterminate Problems

Problem Statement

A copper circular rod of radius r = 4 cm is inserted into an aluminum tube with inner radius ri = 5 cm and outer radius ro = 6 cm as shown. Load P is applied to the rigid top plate. If length L = 15 cm, what load P will cause the plate to deflect dL = 0.23 mm downward? Assume Ecopper = 110 GPa and Ealuminum = 70 GPa.

Picture with an circular copper rod inserted into an aluminum tube. A load is applied at the top of the tube. The radius of the copper rod is r. The inner radius of the aluminum tube is r[i] and the outer radius is r[o]

Figure 1: A copper circular rod is inserted into an aluminum tube as shown.

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