S 4X7.7 - Section Properties

S 4X7.7 has a mass of 7.7 lb/ft (11.5 kg/m), tabulated to AISC Shapes Database v16.0. A 12 m length therefore weighs about 138 kg, which is the figure to use for a steel take-off or when checking a lift.

S 4X7.7 has a depth of 4 in (101.6 mm), a width of 2.66 in (67.6 mm), a web thickness of 0.193 in (4.9 mm), a flange thickness of 0.293 in (7.4 mm), with a cross-sectional area of 2.26 in² (14.6 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 57.355 cm³, and the elastic modulus Wel,y is 49.653 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 20 kNm before any stability check.

The second moment of area about the major axis, Iy, is 251.8 cm⁴, and about the minor axis Iz is 31.13 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 4.17 cm about the major axis and iz is 1.46 cm about the minor axis. Column buckling is governed by the SMALLER value: the slenderness is lambda = L_cr / i, so with iz = 1.46 cm a 0.1 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 3.05 cm⁴. Closed sections carry torsion in a shear flow around the perimeter, which makes them far stiffer in torsion than an open section of the same weight and is usually why one is specified.