Erection tolerances
Thermal movement of a steel frame from the erection temperature
- where
- expansion to the highest temperature (mm)
- coefficient of linear expansion (×10⁻⁶/K)
- frame length (m)
- highest steel temperature (°C)
- temperature at erection or survey (°C)
- contraction to the lowest temperature (mm, negative)
- lowest steel temperature (°C)
- length difference from the 20 °C reference (mm)
Explain this equation
Shows how far a long steel frame will grow or shrink from the temperature it was erected at, and how its length differs from the 20 °C reference. Use it to set expansion joint gaps, slotted holes and cladding movement.
α is how much steel expands per degree, 12 millionths of its length. L is the length from a fixed point to the joint or end. T_e is the steel temperature on the day, T_max and T_min the hottest and coldest expected. ΔL₊ is the expansion, ΔL₋ the contraction (shown negative) and ΔL₂₀ the difference from 20 °C.
Thermal movement is proportional to length and to the temperature change. The 10⁻⁶ turns α into a plain number and the 1000 turns metres into millimetres, so the answer is in millimetres.
Sense check: steel moves about 0.72 mm per degree over 60 m, so a 25 °C swing is about 18 mm.
Watch out: steel in direct sun can be much hotter than the air. Set slots at the right position for the temperature on the day, not at mid-slot.
How far a steel frame or run of beams will move from the temperature it was erected at, and how far its surveyed length differs from the 20 °C reference used in the NSSS.
Enter your values to see the result.
Good to know
BS EN 1993-1-1 gives α = 12 × 10⁻⁶ per K: 0.012 mm per metre per degree, or 7.2 mm over 60 m for 10 °C. The NSSS takes 20 °C as the reference temperature for dimensions, so a long frame surveyed on a cold morning measures short. Use it to set expansion joint gaps, slotted connections and cladding movement allowances relative to the day of erection. Steel in sun can run well above air temperature.
Common mistake
Using the air temperature range only, and setting slots or joints at mid-position on a hot or cold day so the full movement one way is not available.
Limits
Free, uniform temperature change. Restrained movement, bracing and temperature gradients are the designer’s check.
Sources
- BS EN 1993-1-1 Eurocode 3: Design of steel structures – General rules (3.2.6: α = 12 × 10⁻⁶ per K, density 7850 kg/m³)
- BCSA National Structural Steelwork Specification for Building Construction, 7th edition, 1st revision (2023) – Section 9 accuracy of erected steelwork; Section 7 cambers; 8.6.2 reference temperature 20 °C
- BCSA National Structural Steelwork Specification, 5th edition (cl. 3.4.5 HD bolt holes 6 mm over bolt diameter; 8.1.6 steel packs; 9.2 foundation and HD bolt check before erection; 9.6 erected components)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Always work to the engineer’s drawings and bending schedules, BS 8666, BS EN 1992, BS EN 1090-2, BS 5531/the BCSA National Structural Steelwork Specification and manufacturers’ data. Lifting must be planned under LOLER by a competent person.