Steel Column Preliminary Sizing

How is a steel column sized?

A steel column in compression usually loses its capacity by buckling before the material yields. Choosing a column therefore depends not just on the cross section area but on the length of the column, how its ends are held and the radius of gyration about the weak axis. Eurocode 3 covers this with one factor, the buckling reduction factor χ: N_b,Rd = χ × A × f_y / γ_M1.

Calculation steps

First find the buckling length, L_cr = K × L. Then the Euler critical load N_cr = π² E I / L_cr² and the relative slenderness λ̄ = √(A f_y / N_cr). The reduction factor uses the imperfection factor α of the buckling curve, which depends on how the section is made: Φ = 0.5 [1 + α (λ̄ − 0.2) + λ̄²] and χ = 1 / (Φ + √(Φ² − λ̄²)). The calculation is done for both axes and the smaller resistance governs. For I and H sections that is usually the weak axis.

Example

An HEB 360 column in S235 with a buckling length of 6.5 m about both axes carries a design load of 2000 kN. About the weak axis N_cr = 4974 kN and λ̄ = 0.924. Curve c gives Φ = 1.104 and χ = 0.585. With a yield strength of 235 MPa the buckling resistance is 0.585 × 180.6 cm² × 235 MPa = 2483 kN and the utilisation is 0.81. These figures match a published Eurocode example.

How to use the tool

There are three tabs. In Check a section you pick the series and the size, and the tool gives the slenderness and χ about both axes, the resistance and the utilisation. Find the lightest section searches the IPE, HEA, HEB and HEM series and lists the lightest section in each that carries the load. In Manual section you enter the area and second moments of area yourself, for built up sections and shapes outside the table.

Buckling length factor

The factor K describes the end conditions. The theoretical values are 1.0 for a column pinned at both ends, 0.5 for fixed at both ends, 0.7 for fixed at one end and pinned at the other, and 2.0 for a cantilever. If side rails restrain the column about its weak axis, the factor for that axis is smaller. In sway frames the factor rises above 1.0 and comes from a frame analysis.

Limits

The tool deals with concentric compression only. If the column also carries moment an interaction check is needed and the chosen section may not be enough. Class 4 sections, torsional buckling and connection design are outside the scope. The result is for preliminary sizing.