Buckling Mode Shapes of a Cold-Formed Section with pyCUFSM

What this calculation does

A buckling load on its own does not tell you what the section actually does. This calculation draws the buckled cross-section at each critical half-wavelength, so local, distortional and global buckling can be told apart by eye, and the deformation that governs the design is visible rather than inferred.

How it works

Each solution of the finite strip eigenproblem returns both a buckling load and the deformed shape that goes with it. The shape is what identifies the mode, and the three families look completely different.

• Local buckling bends the plates between the fold lines. The web bulges in and out in a single half-wave while the web-flange corners stay almost exactly where they were. The cross-section keeps its shape at the fold lines.
• Distortional buckling moves the fold lines. The flange and its lip rotate as a near-rigid unit about the web-flange junction, and the web bends to accommodate it. The cross-section changes shape.
• Global buckling moves the whole section without changing its shape at all: a rigid translation, a rigid rotation, or the two combined as flexural-torsional buckling.

Each strip node carries four degrees of freedom, two in the plane of the cross-section and two describing warping and rotation. The in-plane pair is what draws the buckled outline; the displacements are scaled to a readable size, since an eigenvector has arbitrary magnitude and only the shape carries meaning.

Under the hood

This calculation runs a real finite strip analysis in the page using pyCUFSM, so it handles arbitrary geometry entered as a table rather than a fixed standard case, and returns diagrams and contour plots alongside the numbers. The analysis is elastic, with uniform axial compression, simply supported ends, and a sharp-cornered idealisation of the section.

Limits and caveats

• A mode shape is an eigenvector, so its magnitude is arbitrary. Only the shape and the relative proportions mean anything. The exaggeration factor controls the drawing only, and nothing in the reported loads depends on it.
• The shapes drawn are the cross-section deformations. Along the member each one varies as a half sine wave over the half-wavelength quoted, so a real member of a given length displays whichever mode fits within it.
• Where two modes have similar buckling loads their shapes mix, and the eigenvector returned at a given length may be a combination rather than a pure mode. The local and distortional shapes here are extracted from constrained analyses, which forces each to be pure; the global shape comes from the unconstrained analysis at the longest half-wavelength.

Why look at the mode shape instead of just the buckling load?

The load tells you when the section buckles, not how. Two sections can share a critical load while failing in completely different ways. Drawing the buckled cross-section lets you see whether the plates are bending between the fold lines, the flange is rotating about the web, or the whole section is moving as a rigid body, so you know which limit state governs.

How do I tell local, distortional and global buckling apart?

Local buckling bends the plates while the fold lines stay put, so the cross-section keeps its shape at the corners. Distortional buckling rotates the flange and lip about the web-flange junction, so the fold lines move and the section changes shape. Global buckling translates or rotates the whole section without distorting it at all.

What does the exaggeration factor change?

Only the drawing. An eigenvector has arbitrary magnitude, so the displacements are scaled to a readable size. Changing the exaggeration factor changes how large the deformation looks, not any reported buckling load.

Why are the local and distortional shapes described as constrained?

Where two modes have similar buckling loads their shapes mix, and the raw eigenvector at a given length can be a combination rather than a pure mode. The local and distortional shapes are extracted from constrained analyses, which forces each to be pure. The global shape comes from the unconstrained analysis at the longest half-wavelength.

Can I use my own section geometry?

Yes. The calculation runs a real finite strip analysis with pyCUFSM, so you enter arbitrary geometry as a table rather than picking a fixed standard case. It returns the mode-shape diagrams and contour plots alongside the numbers.

What are the analysis assumptions?

The analysis is elastic, with uniform axial compression, simply supported ends, and a sharp-cornered idealisation of the section. Along the member each mode varies as a half sine wave over the half-wavelength quoted.