In this paper, expressions for the critical axial–torsional loads are derived for the buckling of an elastic rod embedded in an elastic medium. The derivation is based on the assumption that the deforming rod encounters a response force from the surrounding medium, and a first-order perturbation analysis of the governing equilibrium equations. It is shown that a dimensionless universal buckling relationship, independent of material and geometry, exists between the critical axial load, both in compression and tension, and the critical torsional load. A reducing axial compression, or an increasing axial tension, enhances the critical torsional load. In addition, two different mode shapes are predicted for the same critical combined loads, and the buckled shapes are generally three-dimensional.
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