Bending and forming
Minimum inside bend radius and outer fibre strain (cold bending)
- where
- outer fibre strain (%)
- plate or bar thickness (mm)
- inside bend radius (mm)
- minimum inside radius (mm)
- minimum radius as a multiple of thickness
- radius to thickness ratio
Explain this equation
Checks how hard a cold bend stretches the outside of the plate, and compares the proposed radius with a minimum. Use it before bending thick plate or high-strength steel.
The outside fibre is stretched compared with the centre line. Its strain is the thickness divided by twice the radius to the centre line, which works out as T/(2R + T). Tighter radii and thicker plates give more strain and a greater risk of cracking. The minimum radius is set as a multiple of thickness, traditionally 2T, but the right figure depends on grade and direction of rolling.
Bending strain is distance from the neutral axis divided by its radius.
Sense check: 10 mm plate on a 20 mm radius strains the outside about 20%. Going to 3T cuts it to about 14%.
Watch out: check the cold-forming radii for the grade in BS EN 10025, and bend across the rolling direction where possible. High strain also affects toughness.
Strain on the outside of a cold bend in plate or flat bar, and a check against a minimum inside radius expressed as a multiple of thickness.
Enter your values to see the result.
Good to know
Simple bending theory gives the outer fibre strain as T/(2R + T). SCI guidance notes that cold bending to an inside radius of at least 2t (strain 20%) has a long record of use in UK bridgework without cracking. BS EN 10025-2 tabulates minimum inside radii for cold flanging by grade and thickness (for plate under 30 mm); where tighter radii are needed, specify the "C" designation (e.g. S355J2C). Bend with the burr side and flame-cut edges on the inside, and dress cut edges first.
Common mistake
Bending across a flame-cut or sheared edge that has not been dressed, or along the rolling direction at a tight radius: cracks start from edge defects.
Limits
Geometric strain only; does not account for material toughness, low temperatures, galvanising after bending (strain-age embrittlement) or the effect of cold work on properties. Follow the BS EN 1090-2 execution specification.
Sources
- SCI Guidance Note GN 5.04: Cold bending of steel (inside radius not less than 2t historically; outer fibre strain 20% at centreline radius 2.5t)
- BS EN 10025-2:2019 Hot rolled products of structural steels – Part 2: Non-alloy structural steels (S275, S355; yield strength by thickness; Table for cold flanging radii)
- BS EN 1090-2:2018 Execution of steel structures – Technical requirements (Table 11: nominal hole clearances for bolts)
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.