CROSS-SECTION CLASS

What this calculator checks

The calculator determines the class of a steel cross-section according to EN 1993-1-1 §5.5.2, Table 5.2. The class tells whether the section can develop its full plastic capacity or whether local buckling limits it first — and it decides which calculation method applies to all subsequent resistance and stability checks.

The four classes

The classification ranks sections by their rotation capacity before a compressed wall buckles locally:

• Class 1 — plastic: develops the plastic moment \(M_{pl}\) and has enough rotation capacity for plastic analysis (plastic hinges).
• Class 2 — compact: reaches \(M_{pl}\), but with limited rotation.
• Class 3 — semi-compact: reaches only the elastic moment \(M_{el}\) (first-fibre yield); buckling occurs before full plastification.
• Class 4 — slender: buckles locally before reaching yield; reduced effective properties are used.

The consequence is direct: in bending, classes 1–2 use \(W_{pl}\), class 3 uses \(W_{el}\) (about 10–15% smaller), and class 4 uses \(W_{eff}\).

How each wall is classified

Each flat wall of the section is classified separately, by its slenderness \(c/t\) compared with limits that depend on:

• the support type — an outstand wall (the flange of an I-profile, supported on one edge) or an internal wall (the web, supported on both). Outstands buckle more easily, so they have smaller limits: \(9/10/14\,\varepsilon\) against \(33/38/42\,\varepsilon\) in compression.
• the stress distribution — uniform compression, pure bending, or combined (N+M). For a web under N+M, the limit is adjusted through the parameter \(\alpha\) (the plastic neutral axis position) for classes 1–2, or \(\psi\) (the elastic stress ratio) for class 3.

The factor \(\varepsilon = \sqrt{235/f_y}\) ties the limits to the steel grade: a stronger steel is more prone to buckling.

The section class = the most unfavourable class among the compressed walls.

Families covered

• Rolled I/H (HEA, HEB, HEM, IPE) — outstand flange + internal web
• UPN — outstand flange (a single outstand) + internal web
• RHS/SHS — both walls internal (no outstand)
• CHS — a single check \(d/t\) against \(50/70/90\,\varepsilon^2\)

Assumptions and limitations

• Classification in major-axis (y-y) bending and in compression. The N+M interaction is covered for I/H and UPN (a single web); for RHS/SHS, compression and pure bending are given.
• The geometry of hollow-section walls uses \(c = \text{side} - 3t\) (the note in Table 5.2).
• Minor-axis bending (an outstand with a stress gradient) is not treated in the current version.

Related calculations

• Bending moment — uses \(W_{pl}\) or \(W_{el}\) by class
• Compression — class 4 works with the effective area
• Local plate buckling — the mechanism behind the \(c/t\) limits
• Bending and axial force — where the class decides the interaction criterion