Structural Engineering & Statics
where the load goes
Series

Distortional buckling — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. Three minima, and only two of them get a check. Elastic buckling stress against half-wavelength for a 200 × 65 × 15 × 1.5 mm lipped channel in uniform compression. The local minimum is at 200 mm and 41 N/mm²; the distortional at 689 mm and 287; the global curve falls away to the right and reaches 489 at the 1.5 m member. The distortional branch is a strut on an elastic foundation — the flange and lip rotating about the web junction, restrained by the web's own bending at 627 N·mm per radian per millimetre — so its minimum is at π(EC_w/k_φ)^¼ and its value is (2√(EC_wk_φ) + GJ)/I₀, the same closed form a continuously braced strut has. The elastic stresses are in the order local, distortional, global, and the mode that governs the strength is not the lowest of them, because they have very different amounts of post-buckling reserve.

    The mode between the two that get checked

    A thin-walled strut has three ways of buckling and two of them have design rules. The third has a half-wavelength several times the section depth, a shape in which the fold lines themselves move, and an elastic stress that no effective-width calculation can produce.

    part 1 · stability

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