Long, thin, open section beams and corrugated panels undergo a cross section flattening when bent longitudinally. This leads to a “soft” nonlinear moment-curvature response and geometrical instability. The problem is analyzed by means of a closed, convergent sequence of algebraic and integral equations which are tractable on modern microcomputers. The shape of the cross section is unrestricted, save that it be thin, symmetrical, and not self-penetrating. Results for circular section and angle section beams are obtained and compared with the existing literature. Example results for a wide, corrugated panel are also obtained. Bifurcations in the deformed cross section are found to occur.

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