Thermal movement
Thermal expansion of steel
- where
- change in length (mm)
- coefficient of linear expansion (×10⁻⁶ per K)
- length of member (m)
- temperature change (K)
- stress if fully restrained (N/mm²)
- Young's modulus (GPa)
Explain this equation
Works out how much a steel member grows or shrinks with temperature, and the stress that would build up if it could not move. Use it for long runs of handrail, cladding rails or pipe supports.
Steel grows about 12 millionths of its length for every degree. Multiplying by the length in millimetres and the temperature change gives the movement. If both ends are fixed, that movement is squashed back into the steel as strain, and strain times stiffness E (converted to N/mm²) gives the stress.
Linear thermal expansion, then Hooke's law for the restrained case.
Sense check: 20 m of steel warming by 40 °C grows about 9.6 mm. Fully restrained, that would be about 100 N/mm², a large part of the steel's strength.
Watch out: real restraint is rarely total, but long welded runs need expansion joints or slotted holes to avoid buckling and cracked welds.
How much a steel member grows or shrinks with temperature, and the stress that would build up if it were fully prevented from moving.
Enter your values to see the result.
Good to know
BS EN 1993-1-1 gives α = 12 × 10⁻⁶ per °C for structural steel, so steel moves about 0.012 mm per metre per degree: 1.2 mm per 10 m for a 10 °C change. Austenitic stainless steel expands about 16 × 10⁻⁶ and aluminium about 23 × 10⁻⁶. Fully restrained steel builds up about 2.5 N/mm² of stress per degree. Use it for long handrails, gantries, pipe racks and external frames, and for planning slotted holes or expansion joints.
Common mistake
Using air temperature range only: steel in direct sun can run 20–30 °C hotter than the air. Also check that slots allow movement both ways from the fixing temperature.
Limits
Linear, uniform temperature. Does not cover welding distortion, fire, or temperature gradients through the section.
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.