Thermal stress

Materials expand when heated and contract when cooled. A free bar of length L that warms by ΔT grows by α L ΔT, where α is the coefficient of thermal expansion, about 12 × 10⁻⁶ per °C for steel and around 10 × 10⁻⁶ per °C for typical concrete. If the bar is free to move, no stress develops. Stress appears only when the movement is prevented.

If both ends are fully fixed, the supports must push back enough to cancel the free expansion, so the restrained strain equals α ΔT and the stress equals E α ΔT, independent of length. For steel and a 40 °C rise that is roughly 200 000 × 12 × 10⁻⁶ × 40 = 96 MPa in compression, a large fraction of the yield stress. If there is a gap that partly closes first, only the remaining expansion is restrained.

Composite bars of two materials heated together, such as a steel bolt through an aluminium sleeve, develop equal and opposite forces because the material that wants to expand more is held back by the other. Two conditions solve them: the forces balance, and the final lengths are equal.

Thermal effects shape real structures. Long buildings need expansion joints; bridge decks sit on bearings and expansion joints that allow movement; continuous welded rail is laid at a chosen stress-free temperature so it does not buckle in summer; and mass concrete in dams and rafts cracks if the core heats up from hydration while the surface cools. Codes give temperature ranges and coefficients for design.