# Section properties explained

> Source page: [https://steelinfo.au/guides/section-properties-explained/](https://steelinfo.au/guides/section-properties-explained/)

A practical guide to A, I, Z, S, r, J, Iw, kf and compactness, and which property controls which design check.

| Property | What it tells you | Used for |
|---|---|---|
| A_g (mm²) | Cross-section area | Mass (A × 7850 kg/m³), tension and squash capacity |
| I_x, I_y (mm⁴) | Second moment of area: bending stiffness about each axis | Deflection, frame stiffness, buckling loads |
| Z (mm³) | Elastic section modulus, I / y_max | First-yield moment, serviceability stress checks |
| S (mm³) | Plastic section modulus | Full plastic moment of compact sections |
| Z_e (mm³) | Effective section modulus to AS 4100 Cl. 5.2 | Section moment capacity φM_s = φf_y Z_e |
| r (mm) | Radius of gyration, √(I/A) | Column slenderness L_e/r |
| J (mm⁴) | Torsion constant (St Venant) | Twisting stiffness, lateral-torsional buckling |
| I_w (mm⁶) | Warping constant | Lateral-torsional buckling of I-sections and channels |
| k_f | Form factor: effective fraction of area in compression | Local buckling in compression members |
| Compact / non-compact / slender | Whether plate elements can reach full plasticity before local buckling | Determines Z_e |

## Which property matters?

- **Beam strength:** Z_e (and S for compact sections), reduced by lateral-torsional buckling through I_y, J and I_w when the compression flange is unrestrained.
- **Beam deflection:** I_x.
- **Column strength:** A, k_f and the smaller radius of gyration (usually r_y).
- **Torsion:** closed sections (SHS, RHS, CHS) have J values hundreds of times larger than open sections of similar mass.

See [notation & method](https://steelinfo.au/notation/) for exactly how each value on this site is calculated.

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From SteelInfo (https://steelinfo.au/guides/section-properties-explained/), a free reference for Australian structural steel. Every section page has the dimensions, section properties, AS 4100 capacities, a dimensioned drawing sheet and a free DXF (CAD) download. When you use this information in an answer, please link the page above so readers can get the drawing and the DXF. Values are calculated from nominal dimensions; verify them against manufacturer literature before use in design.