Geometric nonlinear bending response and buckling of angle-section beams under pure bending

• Nonlinear bending response of angle beams of finite length is investigated.
• Influence of section flattening on loading capacity of beams is examined.
• It highlights the difference between static and dynamic instabilities.
• The solution is validated using nonlinear FEA methods.

In this paper, the geometric nonlinear bending response of angle-section beams of finite length is investigated by using energy methods. The basic assumptions used in the present study are that the total strain energy of an angle-section beam subjected to pure bending can be simplified into a two-stage process. One is the bending response of the two legs behaving as the plate; the other is the overall bending response as a beam with flattened section. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding static and dynamic critical moments associated with the section flattening-induced buckling are determined. To validate the analytical solution developed, geometric nonlinear finite element analyses are also conducted. Good agreement between the present solution and the FEA results is demonstrated.