Notation and calculation method

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.

Section properties

Geometry. Each section is modelled from nominal dimensions as an exact outline, including root radii (r₁), toe radii (r₂), 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_e²)(GJ + π²EI_w/L_e²)], α_s = 0.6[√((M_s/M_o)² + 3) − M_s/M_o], φM_b = φα_mα_sM_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_yA_w, reduced for slender webs (λ_w > 82). A_w = d·t_w for rolled sections and d₁·t_w for welded sections. CHS use 0.36f_yA_e.
Capacity factor. φ = 0.9 throughout.

Symbols

Symbol	Meaning
d, b_f, t_f, t_w	Depth, flange width, flange thickness, web thickness
r₁, r₂, 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.