Lateral-torsional buckling of beams and the Southwell plot

The Southwell plot is a well-known technique for determining experimentally the elastic critical load of a structure, without having to subject the structure to loading in the vicinity of critical. But several authors have suggested that when the structure is a beam which undergoes lateral-torsional buckling, a modified version of the Southwell plot is called for. In this paper we demonstrate that the modified form of the Southwell plot is not needed, and that the standard version is indeed satisfactory. We do this by plotting and re-plotting some experimental data; by drawing attention to some very clear work by Meck; and by explaining the practical coupling between the variables describing the lateral deflection and the rotation when lateral-torsional buckling occurs. Finally, we examine an argument based on symmetry which appears to support the idea that a modification of the standard Southwell plot is needed in the case of lateral-torsional buckling: but we show that a correct deployment of the argument from symmetry leads to the conclusion that the modified form of the Southwell plot is valid only for special, unrealistic cases.