The Southwell Method for Predicting Plastic Buckling Loads for Elbows

Abstract

The Southwell method for the prediction of buckling loads is applied to results obtained from tests of two 16-in-dia Type 304 stainless steel elbows loaded by an in-plane closing bending moment M. The basis of the method is discussed, and it is shown that proper application of the method requires that the nonlinear component of the deformation, δnl, be used in the Southwell plot. Predicted buckling loads determined from four experimental M-δnl curves for each test are found to be consistent and accurate, with an average value that is only slightly above the experimental plastic buckling load. The major conclusion of this paper is that the Southwell method based on δnl is valid for elbows loaded by an in-plane closing bending moment, and for a certain broader class of elastic or plastic nonlinear buckling (geometric collapse) problems for imperfection-insensitive structures. Consequently, tests and analyses of such structures need not be carried out to buckling to determine buckling loads. Practical advantages of such nonbuckling tests and analyses are discussed.