Steel weights
Square or rectangular hollow section (SHS/RHS) weight per metre
- where
- cross-sectional area (mm²)
- wall thickness (mm)
- section width (mm)
- section depth (mm)
- outside corner radius (mm)
- inside corner radius (mm); if left at 0, taken as r_o − t
- mass per metre (kg/m)
- steel density (kg/m³)
- total mass (kg)
- total length (m)
Explain this equation
Works out the cross-section area and weight per metre of a square or rectangular hollow section, allowing for its rounded corners.
With square corners the steel is four walls of thickness t, totalling 2t(B + H − 2t). Rounded corners remove a little steel: each corner loses a square of side r minus a quarter circle, so four corners lose (4 − π)r². The outside corners lose r_o worth and the inside corners give back r_i worth, hence (4 − π)(r_o² − r_i²).
Square-cornered box area, corrected for the corner radii.
Sense check: 100 × 50 × 5 cold-formed RHS with r_o = 10 mm gives about 1336 mm², about 10.5 kg/m, which matches published tables.
Watch out: cold-formed and hot-finished sections of the same size have different corner radii and slightly different weights. Use the right radii.
Mass per metre of box section (SHS or RHS), allowing for the rounded corners as the product standards do.
Enter your values to see the result.
Good to know
BS EN 10219-2 (cold-formed) gives the outside corner radius as 2t for walls up to 6 mm, 2.5t for 6–10 mm and 3t above 10 mm; BS EN 10210-2 (hot-finished) uses 1.5t outside and 1.0t inside. For cold-formed sections the inside radius is the outside radius less t (leave the inside radius at 0); for hot-finished enter it as t, otherwise the area comes out about 1% low. Set the corner radius to 0 for a sharp-cornered box fabricated from plate.
Common mistake
Using the sharp-corner area 2t(B + H − 2t) for cold-formed tube. For thin walls the difference is small but for heavier walls it overstates the weight by a few per cent.
Limits
Nominal mass from the standard's simplified corner geometry. Actual radii vary between mills and thickness tolerances apply.
Sources
- BS EN 10219-2:2019 Cold formed welded steel structural hollow sections – Part 2: Tolerances, dimensions and sectional properties (mass from density 7.85 kg/dm³; corner radius rules and area formula)
- BS EN 10210-2:2019 Hot finished steel structural hollow sections – Part 2: Tolerances, dimensions and sectional properties (density 7.85 kg/dm³)
- SCI / Steel for Life Blue Book: Steel building design – design data (section property formulas and tables for UKB, UKC, hot-finished and cold-formed hollow sections)
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.