This article presents an analytical procedure for determining the magnitudes of the buckling loads of homogeneous elastic columns. The novelty of the proposed procedure lies in its ability to perform buckling analysis also for columns with supports not aligned with the principal axes of inertia of the cross-section. The Simo–Reissner spatial beam model is used as the mathematical model of the column. In addition to bending deformations, the influence of axial and shear deformations is therefore also taken into account when determining the buckling loads of the columns. The procedure for determining the buckling loads is based on Keller’s findings, which state that the critical points of a nonlinear system of ordinary differential equations are identical those of the corresponding linearized system. Since the critical points of the Simo–Reissner mathematical model correspond to the buckling loads of the column, the presented analytical procedure enables the exact determination of the buckling loads of elastic columns. The applicability of the proposed procedure is demonstrated by a parametric study of how the orientation of boundary conditions affects the magnitudes of the buckling loads of homogeneous elastic columns. It was found that the orientation of the boundary conditions significantly affects the magnitudes of the column buckling loads. However, these loads are always greater than the well-known Euler buckling loads of columns.
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