Problem 5.12 - Axial Deformation

Problem Statement

Two forces, F1 = 15 kN and F2 = 10 kN, are applied to the system of cylinders as shown. If L1 = 5 m, L2 = 3 m, and L3 = 4 m, what is the total change in length of the system? Assume Esteel = 210 GPa and Ealuminum = 70 GPa.

Picture with two aluminum cylinders connected by a steel cylinder. The aluminum cylinder on the left is attached to the wall. The radius of the left cylinder is 0.5 m and has a length L[1]. The force F[1] is applied between the first and second cylinders. The middle cylinder has a radius of 0.3 m and a length L[2]. The force F[2] is applied between the second and third cylinder. The third cylinder has a radius 0.4 m and a length of L[3].

Figure 1: Two forces are applied to the system of cylinders.

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