Section builder
Type a shape and get its properties from first principles: area, second moments, elastic and plastic moduli, radii of gyration, torsion and warping constants, and the mass per metre. Any depth is as valid as a catalogue size, which is the point of a builder.
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Area | A | 9080 | mm² |
| Second moment, strong axis | Ix | 145.23 | ×10⁶ mm⁴ |
| Second moment, weak axis | Iy | 21.36 | ×10⁶ mm⁴ |
| Elastic modulus, strong axis | Sx | 968.2 | ×10³ mm³ |
| Elastic modulus, weak axis | Sy | 213.6 | ×10³ mm³ |
| Plastic modulus | Zx | 1088.4 | ×10³ mm³ |
| Torsion constant | J | 635.5 | ×10³ mm⁴ |
| Warping constant | Cw | 430.17 | ×10⁹ mm⁶ |
| Radius of gyration | rx / ry | 126.5 / 48.5 | mm |
| Mass | m | 71.3 | kg/m |
J and Cw use the thin-walled approximation; they are accurate for rolled sections and conservative for stocky plates.
Ix = (b·h³ − (b − tw)·hw³)/12 · Subtract the missing web rectangle from the bounding rectangle.
Sx = Ix / (h/2) · Outer fibre distance to the extreme fibre.
rx = √(Ix/A) · Used directly in the buckling length.
A clear path from inputs to results.
Every member check starts with the section. This builder derives the properties from the geometry rather than looking them up, so a 317 mm deep beam is as valid as a 310 catalogue size — and the numbers can be checked by hand.
How to use
- Pick the shape family and enter depth, width and thicknesses.
- Read Ix, Sx and rx for the strong axis and Iy, Sy, ry for the weak axis.
- Check the shape factor and the plate class before using the section in a member check.
The formula
Reference: Parallel-axis theorem applied to the rectangles that make up the shape.
Worked example
300 × 200 × 16 × 10 I-section
- Depth 300 mm, width 200 mm, flange 16 mm, web 10 mm.
- 1
Area 9,080 mm². Ix = (200·300³ − 190·268³)/12 = 145.2 × 10⁶ mm⁴. Sx = Ix/150 = 968 × 10³ mm³. rx = √(Ix/A) = 126.5 mm.
145.2 × 10⁶ mm⁴, Sx 968 × 10³ mm³, 71.3 kg/m.
Interpreting the result
Depth buys strong-axis stiffness as the cube; width buys weak-axis stiffness. A shape factor near 1.12 means the section has about 12% reserve between first yield and a full plastic hinge.
Assumptions & limitations
- Sharp corners: fillets and root radii are ignored.
- Uniform thickness within each plate.
- J and Cw use thin-walled approximations.
- Mass assumes 7850 kg/m³ steel.
Frequently asked questions
Why is my J lower than the catalogue?
The thin-walled formula ignores the fillets, which contribute a surprising amount of torsional stiffness to a rolled section.
What is the plastic modulus for?
It gives the plastic moment Z·fy, which is what a compact section can reach before local buckling.
Can I build an asymmetric section?
Not yet — the seven families here are symmetric or singly symmetric. A general polygon builder is the next step.
Does the plate class matter?
Yes: a slender flange buckles before yield, so the plastic modulus is not available.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.