Volume 17, Issue 5 (September 1989)
Applicability of the Southwell Plot to Shear Deformable Columns
This paper examines the applicability of the Southwell method to predict the buckling load of columns where the shear deformation cannot be neglected. It is shown by mode superposition that the convergence of the series solution to the buckling mode is slow, since there are two critical loads of the same order associated with the first mode shape for rotation of the cross section. More important, the Southwell plot is not linear even when only one mode shape (corresponding to the lowest critical load in compression) is considered. An example of numerical simulation demonstrates that linearly fitting the Southwell plot can lead to significant errors in the prediction of the buckling load. The accuracy of buckling load determined by the Southwell method for typical elastomeric isolation bearings is also discussed.