Steel Beam Preliminary Sizing

How is a steel beam sized?

Preliminary sizing of a steel beam looks for three things: the section must carry the bending moment, the web must carry the shear force, and the beam must not deflect more than allowed under service load. Shear tends to govern short heavily loaded beams and deflection usually governs long spans. This tool checks all three together and shows which one governs.

Formulas

For a simply supported beam under uniform load the maximum moment is M = w L² / 8 and the maximum shear V = w L / 2. Bending resistance is M_c,Rd = W × f_y / γ_M0 and shear resistance V_pl,Rd = A_v × f_y / (√3 × γ_M0). Deflection is δ = 5 w L⁴ / (384 E I), worked out with the unfactored service load.

Read backwards, the three conditions give the required section properties: a section modulus of at least M / f_y, a shear area of at least V √3 / f_y and a second moment of area large enough to meet the deflection limit.

Example

A simply supported beam spans 6 m with a design load of 10 kN/m and a service load of 7 kN/m in S235 steel. The moment is 10 × 6² / 8 = 45 kN·m and the shear 30 kN. An IPE 300 has an elastic modulus of 557 cm³, so its bending resistance is 557 × 235 / 1000 = 131 kN·m and the utilisation 0.34. Shear resistance is 348 kN. Deflection comes to 6.7 mm against an L / 300 limit of 20 mm. All three conditions are met. Searching for the lightest section under the same load, the tool suggests a smaller IPE.

How to use the tool

Pick the load case: uniform load, a point load at midspan, or moment and shear entered directly. Check a section tests the section you choose. Find the lightest section lists the lightest adequate sections in the IPE, HEA, HEB and HEM series. Manual section is for shapes that are not in the table. The self weight of the beam is added to the load if you ask for it.

The key limit: lateral torsional buckling

This calculation assumes the compression flange cannot move sideways. That holds for beams carrying a concrete slab or held by closely spaced bracing. A beam with a free flange can have a far lower resistance than found here and needs a separate check. Continuous beams, cantilevers and connection design are also outside this tool.