W 21X57 - Section Properties

W 21X57 has a mass of 57 lb/ft (84.8 kg/m), tabulated to AISC Shapes Database v16.0. A 12 m length therefore weighs about 1018 kg, which is the figure to use for a steel take-off or when checking a lift.

W 21X57 has a depth of 21.1 in (535.9 mm), a width of 6.56 in (166.6 mm), a web thickness of 0.405 in (10.3 mm), a flange thickness of 0.65 in (16.5 mm), with a cross-sectional area of 16.7 in² (107.7 cm²). These are the nominal dimensions from AISC Shapes Database v16.0; rolling tolerances apply to the delivered section.

The plastic section modulus about the major axis, Wpl,y, is 2,113.9 cm³, and the elastic modulus Wel,y is 1,819 cm³. Wpl,y is what sets the moment capacity of a Class 1 or 2 section: M_pl,Rd = Wpl,y x f_y / gamma_M0, so at S355 with gamma_M0 = 1.0 this section reaches about 750 kNm before any stability check.

The second moment of area about the major axis, Iy, is 48,699 cm⁴, and about the minor axis Iz is 1,274 cm⁴. Iy is the value deflection depends on - for a simply supported beam under a uniform load, the midspan deflection is 5wL⁴/384EIy - so on spans where a deflection limit governs rather than strength, this is the number that decides the section.

iy is 21.23 cm about the major axis and iz is 3.43 cm about the minor axis. Column buckling is governed by the SMALLER value: the slenderness is lambda = L_cr / i, so with iz = 3.43 cm a 0.3 m effective length already gives lambda = 100. Minor-axis buckling almost always controls unless the weak axis is restrained.

The St Venant torsion constant It is 73.67 cm⁴, and the warping constant Iw is 0.86 dm⁶. Open sections carry torsion mainly by warping rather than uniform torsion, which is why Iw appears in the lateral-torsional buckling resistance - both values feed M_b,Rd.