# Notation and calculation method

> Source page: [https://steelinfo.au/notation/](https://steelinfo.au/notation/)

How every value on this site is calculated, and what the symbols mean. Where the input data comes from and how it was checked: [data sources & verification](https://steelinfo.au/sources/).

## Section properties

- **Geometry.** Each section is modelled from nominal dimensions as an exact outline, including root radii (r_1), toe radii (r_2), the 8° taper of TFB flanges and the corner radii of hollow sections.
- **A, I, Z.** Area and second moments of area are integrated numerically over the outline (Green's theorem, arcs subdivided to better than 0.01% accuracy). Elastic moduli Z = I / y_max.
- **S.** Plastic moduli are found by locating the equal-area axis and summing the first moments of area of each half.
- **J.** Rolled I-sections use the El Darwish & Johnston expression including the root fillets. Welded sections, channels, angles and tees use Σbt³/3, which is slightly conservative. Hollow sections use the thin-walled closed-section formula J = t³h/3 + 2KA_h.
- **I_w.** I-sections: I_w = I_y(d − t_f)²/4. Channels use the thin-walled expression with centreline dimensions.
- **Hollow section corner radius.** External radius r_o = 2.0t for t ≤ 3 mm and 2.5t for t > 3 mm; internal radius r_o − t.
- **Mass.** Nominal catalogue mass is shown. Calculated mass uses a density of 7850 kg/m³.
- **Surface area.** The external perimeter (including radii), for estimating paint and galvanizing quantities to AS/NZS 2312.

## AS 4100 design capacities

- **Section classification (Cl. 5.2).** Plate element slenderness λ_e = (b/t)√(f_y/250) compared with the limits of Table 5.2. The governing element has the largest λ_e/λ_ey. Flange outstands use b = (b_f − t_w)/2 for I-sections; hollow section flats use b − 2t.
- **Effective section modulus.** Compact: Z_e = min(S, 1.5Z). Non-compact: linear interpolation between Z and Z_c. Slender: Z(λ_sy/λ_s), or the CHS expressions of Cl. 5.2.5.
- **Form factor k_f (Cl. 6.2).** Effective width method with λ_ey from Table 6.2.4. CHS use the effective diameter expression.
- **Member moment capacity (Cl. 5.6.1.1).** M_o = √[(π²EI_y/L_e ²)(GJ + π²EI_w/L_e ²)], α_s = 0.6[√((M_s/M_o)² + 3) − M_s/M_o], φM_b = φα_m α_s M_s ≤ φM_s, with E = 200 000 MPa and G = 80 000 MPa.
- **Compression (Cl. 6.3.3).** Modified slenderness λ_n = (L_e/r)√k_f√(f_y/250), with the column curve constants α_a, α_b, η and ξ of Cl. 6.3.3.
- **Shear (Cl. 5.11).** φV_v = φ0.6f_y A_w, reduced for slender webs (λ_w > 82). A_w = d·t_w for rolled sections and d_1·t_w for welded sections. CHS use 0.36f_y A_e.
- **Capacity factor.** φ = 0.9 throughout.

## Symbols

| Symbol | Meaning |
|---|---|
| d, b_f, t_f, t_w | Depth, flange width, flange thickness, web thickness |
| r_1, r_2, r_o | Root radius, toe radius, external corner radius |
| A_g | Gross area of cross-section |
| I_x, I_y; I_u, I_v | Second moments of area about the geometric and principal axes |
| Z, S, Z_e | Elastic, plastic and effective section modulus |
| r | Radius of gyration √(I/A) |
| J, I_w, C | Torsion constant, warping constant, torsion modulus |
| k_f, α_b | Form factor, compression member section constant |
| φM_s, φM_b | Design section and member moment capacity |
| φN_s, φN_c, φN_t | Design section compression, member compression and tension capacity |
| φV_v | Design shear capacity |
| L_e, α_m | Effective length, moment modification factor |

## Axes

x-x is the major (strong) axis and y-y the minor axis for symmetric sections. For angles, x and y are parallel to the legs, and u-u and v-v are the principal axes. For flat bar, x is parallel to the wide face, so I_x is the weak-axis value.

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From SteelInfo (https://steelinfo.au/notation/), 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.