The torsional instability of a cruciform column in the plastic range: Analysis of an old conundrum

Over the years a large number of works have shown that for many buckling problems of plates and shells in the plastic range the flow theory of plasticity seems to lead to a significant overestimation of the critical stress while the deformation theory seems to provide much more accurate predictions and therefore the latter has been generally recommended for use in practical applications. This fact is generally known in literature as the “plastic buckling paradox”. Possibly the simplest examples of such a circumstance is given by the torsional instability of a cruciform column. The present study examines the problem from its roots and shows that in order to overcome this apparent conundrum it is not only necessary to consider an imperfect column, as generally suggested in the past, but principally to account correctly for the effects of the imperfection up to the point where the limit load is attained. In such manner a very good agreement between the results from the flow theory of plasticity and other analytical and experimental results can be obtained on the basis of classic formulae only.