COLD-FORMED SECTIONS — STABILITY

What this calculator checks

The calculator analyses the stability of thin-walled cold-formed sections (C, Z, U sections) by the Finite Strip Method, using the pyCUFSM engine. Unlike rolled profiles, where a single buckling mode dominates, cold-formed sections can fail in several instability modes, and the analysis brings all of them out.

Why cold-formed sections are different

Hot-rolled profiles have relatively thick walls, and EN 1993-1-1 treats them with the four-class classification and the buckling curves. Cold-formed sections have very thin walls and often edge stiffeners (lipped returns), which introduce an extra failure mode absent in thick profiles: distortional buckling. That is why they are covered by a separate code, EN 1993-1-3.

The three buckling modes

The analysis produces the signature curve — the critical buckling stress as a function of the half-wavelength — on which three families of modes appear, in order of increasing length:

1. Local — the flat walls ripple over short lengths, with the section corners staying straight. Similar to the local buckling of rolled profiles.
2. Distortional — the edge stiffener, together with the flange, rotates relative to the web; the section changes shape. This is the mode characteristic of cold-formed sections and often the governing one.
3. Global — flexural, torsional or flexural-torsional buckling of the member as a whole, over long lengths — the same as the buckling of ordinary compression members.

The local minima of the signature curve give the critical stresses for the local and distortional modes; the descending branch toward long lengths gives the global mode.

The constrained finite strip method (cFSM)

The engine runs both the classical analysis (the full signature, where modes can mix) and the constrained analysis (cFSM), which isolates each pure mode — local, distortional, global — separately. The separation matters because design codes (the Direct Strength Method, DSM) require the critical stress of each mode taken individually.

Input data

• Section geometry — the type (C, Z, U), depth, flange width, stiffener length, thickness.
• Steel grade — \(f_y\), \(E\), \(\nu\).
• Loading — compression and/or bending, which defines the analysed stress distribution.
• The range of half-wavelengths over which the signature curve is traced.

Assumptions and limitations

• The finite strip model assumes a prismatic, simply supported member, with stresses constant along the length. Real supports and diaphragms change the result.
• The analysis gives the critical stresses (elastic bifurcation); the step to design resistance is made with the Direct Strength Method (EN 1993-1-3 / DSM), outside this calculation.
• It requires the computation agent connected (the pyCUFSM engine runs externally); without it, the analysis cannot run.
• It does not treat large geometric imperfections or post-buckling behaviour through nonlinear analysis.

Related calculations

• Local plate buckling — the local mode, for a single flat wall
• Flexural buckling — the global mode, for rolled profiles
• Cross-section class — the classification applicable to rolled profiles