Thermal Stress Calculator

Thermal Stress in a Restrained Member

When a material is heated or cooled but fully prevented from expanding or contracting (fully restrained), internal stress builds up instead of physical strain. That stress is σ = EαΔT, where E is Young’s modulus, α is the coefficient of thermal expansion, and ΔT is the temperature change.

If restrained from expanding while heated, the member develops compressive stress; if restrained from contracting while cooled, it develops tensile stress. This is a key consideration in designing bridges, railroads, pipelines, and any structure with fixed supports across a temperature range — expansion joints exist specifically to avoid this stress buildup.