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When a rod is clamped between rigid walls and temperature changes, expansion is prevented and stress develops: $\sigma = Y\alpha\Delta T$, $F = YA\alpha\Delta T$. Thermal stress is independent of rod length (strain $= \alpha\Delta T$ is independent of $L$).

Magnitude: for steel ($Y = 200$ GPa, $\alpha = 12 \times 10^{-6}$), a 50 K rise gives $\sigma = 120$ MPa — nearly half the yield stress. This explains why expansion joints are essential in railway tracks, bridges, concrete roads, and pipelines.

Applications: shrink-fitting (heat a ring, slip over shaft, cool to grip), bimetallic thermostats, thermal compensation in clock pendulums (combining materials to cancel net expansion). If a rod is only partially constrained (one end free), it expands freely with no stress. Full constraint from both ends is needed for thermal stress to develop.