A dimensionless analytical analysis for buckling and lateral buckling interaction of thin-walled beams with open cross sections

This paper investigates the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. First, the equilibrium equations have been transformed into dimensionless ones, and within a nonlinear stability model, various dimensionless parameters are introduced to control the interaction between buckling and lateral buckling. In comparison to a reference of literature, this work focuses on the case of arbitrary sections and includes a greater number of higher-order terms in our analysis. These additions have an impact on the coefficients of the stability formula by expanding its applicability to non- symmetric sections. Then, the effect of the different dimensionless parameters, thus introduced on the stability curve, has been studied. The proposed solutions are validated and compared to numerical solutions obtained by a general finite element package including the warping developed by the authors using Asymptotic Numerical Method (ANM) to solve the initial nonlinear equations.