Computational Modeling Applied to the Study of Thermal Buckling of Columns

Abstract

Buckling is an instability phenomenon that can happen in slender structural components when subjected to a compressive axial load. This phenomenon can occur due to an externally applied force, which when exceed a certain limit, called critical load, will promote the mechanical buckling on the structural member. Another buckling possibility happens to statically indeterminate structural elements when submitted to a positive temperature variation. As the axial displacements are restricted, if the temperature gradient is larger than the critical temperature variation, it will be generated a compressive axial load higher than the critical load of the structural component and the thermal buckling will occur. In this context, the present work presents a computational model to solve the thermal buckling problem of columns. A thin shell finite element, called SHELL93, was adopted for the computational domain discretization. It was employed a solution involving homogeneous algebraic equations, where the critical temperature variation is determined by the smallest eigenvalue and the buckled configuration is defined by its associated eigenvector. A case study was performed considering a steel column with three different support conditions at its ends: fixed-fixed, fixed-pinned, and pinned-pinned. The numerical results obtained for the critical temperature variation showed a maximum absolute difference around 2% when compared to the analytical solutions. Moreover, the buckled shape of the column, for each case, was defined in agreement with the configurations found in literature. Therefore, the computational model was verified, i.e., it is able to satisfactorily predict the mechanical behavior of the thermal buckling of columns. So, it is possible to use this numerical model in practical situations that do not have an analytical solution, as is the case of the thermal buckling of columns with cutouts.