Nonlinear instability analyses of channel-section beams subjected to minor-axis pure bending

• It presents an analytical solution of nonlinear instability of channel section beams under pure bending.
• It highlights the influence of section flattening on the loading capacity of channel section beams.
• It highlights the difference between static and dynamic instabilities.
• The analytical solution is validated using nonlinear finite element analysis methods.

This paper presents the analytical solutions of nonlinear instability of channel-section beams subjected to pure bending about its minor axis. The solutions are derived using energy methods by taking into account the cross-section flattening. The present results show that, the section flattening is very important during the bending, which can induce the nonlinear snap-through instability of the beam. It is also shown that the dynamic instability of channel-section beams under the action of a sudden step moment occurs at a moment about 71% of the corresponding critical static moment, but the deformations of the longitudinal curvature and flattening at the critical dynamic state are almost twice of those corresponding to the static instability case. To validate the analytical solutions, nonlinear finite element analyses using ANSYS are also conducted. Good agreement between the analytical solutions and FEA results is found.