• id: JME-08-N12
• title: Thermal Stress in Constrained Bodies
• tags: thermal-stress, expansion, clamped-rod

When a rod is clamped at both ends and temperature changes by $\Delta T$, it cannot expand/contract freely. The prevented thermal strain equals $\alpha \Delta T$, producing stress: $\sigma_{\text{thermal}} = Y \alpha \Delta T$ $F_{\text{thermal}} = Y A \alpha \Delta T$

This is independent of the length of the rod. Railway tracks use expansion gaps to prevent buckling from thermal stress. For a steel rail ($Y = 200$ GPa, $\alpha = 12 \times 10^{-6}$ K$^{-1}$): a mere 30 K rise produces 72 MPa stress — significant enough to buckle the track.