City Guilds Model Questions Vol1 2025 Engineering Question 1

A composite rod consists of two sections in series. Section A is steel, length \(1.2\ \text{m}\), coefficient of thermal expansion \(\alpha_1 = 12\times10^{-6}\ \text{°C}^{-1}\) and Young's modulus \(E_1 = 200\ \text{GPa}\). Section B is aluminium, length \(0.8\ \text{m}\), coefficient \(\alpha_2 = 23\times10^{-6}\ \text{°C}^{-1}\) and Young's modulus \(E_2 = 70\ \text{GPa}\). Both sections have the same circular cross‑section of area \(20\ \text{mm}^2\). The left end of the rod is fixed, and a linear spring of stiffness \(k = 5.0\times10^{5}\ \text{N\,m}^{-1}\) is attached to the free right end, resisting extension. The whole assembly is uniformly heated by \(\Delta T = 60\ \text{°C}\). Determine the compressive force in the spring after heating (assume static equilibrium).