Problem 5.52 - Thermal Deformation

Problem Statement

Two cylindrical rods are heated until they expand, just closing the gap of d = 0.01 in. The coefficient of thermal expansion, α, for material A and B is 6 x 10-6/°F and 10 x 10-6/°F, respectively. The radius of A rA = 0.5 in and the length is L1 = 10 in. The radius of B is rB = 0.8 in and the length is L2 = 6 in. What is the change in temperature?

Two cylindrical rods are connected and heated until they expand to close the gap to the wall on the right hand side. The left hand side is fixed. Rod A is attached to the wall on the left hand side. Rod B is attached to Rod A.

Figure 1: Two cylindrical rods are connected and heated until they expand to close a gap.

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