Lateral buckling of tapered thin walled bi-symmetric beams under combined axial and bending loads with shear deformations allowed

•New nonlinear kinematical model for tapered beams is proposed.•New geometrical parameters associated to the shear deformations are considered.•Nonlinear analysis procedure by Ritz method is developed.•New lateral buckling resistance results for box and I beams are provided. In this paper, the effect of shear deformations on elastic lateral buckling of tapered thin-walled open and closed bi-symmetric section beams under combined bending and axial forces is investigated. For the purpose, a geometrical non-linear beam theory is presented according to a new kinematic model that incorporates shear flexibility components. Ritz method is applied to obtain the governing equilibrium equations, then the buckling loads are computed by solving the eigenvalue problem basing on the singularity of the tangential stiffness matrix. The elastic lateral buckling resistances given by the proposed method are generally in good agreement with the finite element simulation using Abaqus software. The numerical results for cantilevers and simply supported thin walled beams with open and box sections reveal that the classical stability solution tends to overestimate the real lateral buckling resistance of short tapered box cantilever beams.