Section properties
I-section (UB, UC or welded plate girder): A, I, Z, r about the major axis
- where
- area (cm²)
- flange width (mm)
- flange thickness (mm)
- overall depth (mm)
- web thickness (mm)
- root radius (mm)
- second moment of area about the major axis (cm⁴)
- elastic section modulus (cm³)
- radius of gyration (cm)
Explain this equation
Works out the major-axis section properties of an I-section: a rolled UB or UC, or a welded plate girder (root radius zero).
The area is two flanges, the web between them, and the fillets at the four roots, which add (4 − π)r². For I, the section is treated as a full rectangle b × h minus the two empty rectangles beside the web; the fillet terms add the small contribution of the four root fillets, each a small area at a distance from the axis. Z divides I by half the depth in cm, and i is √(I/A).
Rectangles subtracted from a rectangle, plus standard corrections for the root fillets.
Sense check: a 203 × 133 × 25 UB comes out at about 32 cm² and 2340 cm⁴, matching the tables.
Watch out: these are elastic, major-axis properties. Lateral-torsional buckling and minor-axis properties need separate checks.
Major-axis properties of a doubly symmetric I or H section from its dimensions, including the root fillets of a rolled section. Set r = 0 for a section welded from plate.
Enter your values to see the result.
Good to know
The formula is the one the SCI uses to build the Blue Book tables: flanges and web as rectangles, plus four root fillets each of area (1 − π/4)r² placed near the flange. The fillet terms add about 2% to I for a typical UB. For a welded girder, weld throats are ignored, which is normal practice.
Common mistake
Using minor-axis properties for a beam bent about its strong axis, or the other way round. Rolled beams are far weaker about the minor axis (z–z).
Limits
Major axis (y–y) only; doubly symmetric sections only. Elastic properties; check section class and lateral-torsional buckling to BS EN 1993-1-1 before using these for design.
Sources
- 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)
- British Steel universal beams datasheet (UKB 203×133×25: h 203.2, b 133.2, tw 5.7, tf 7.8, r 7.6 mm; A 32.0 cm²; Iy 2340 cm⁴; Wel,y 230 cm³; iy 8.56 cm)
- BS EN 10365:2017 Hot rolled steel channels, I and H sections – Dimensions and masses (density 7850 kg/m³)
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.