Nonlinear analysis and elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures with warping constraints

An analysis of the elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures is presented. It is based on a beam theory valid for large displacements and rotations, which admits arbitrary cross‐sections, curved axes, initial imperfections, a general material description, and which fully accounts for the influence of warping constraints as well as the stress‐history dependence of the elastic–plastic shear moduli. An incremental updated Lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle, and in the numerical solution procedure the displacement–finite element approach is followed. The associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle. Applications of the theory are given in which the influence of the loading configuration, material parameters, geometric nonlinearities and warping constraints on the load‐carrying behaviour and on the bifurcation and ultimate loads of thin‐walled beam structures is explored.