Modelling of an imperfect column having variable cross-sections and non-symmetric responses in tension and compression

The behavior of a column having variable rectangular cross-sections has been modelled assuming that the column material has non-symmetric responses both in tension and compression. For this purpose, a powerful numerical scheme, based on the finite difference technique, has been devised and used to trace the load-deflection curves (equilibrium configuration paths) of a column that has highly non-linear stress-strain curves which are non-symmetric both in tension and compression. The appearance of the critical load, that causes enormous deflections with an infinitesimall increase in the loading parameters, is determined from those load-deflection curves. The devised method can be used to calculate buckling loads of any column with material and geometric nonlinearities. To make the study realistic an initial shape imperfection has been included and its effect on the column's response has also been discussed in detail. A comparison shows a good agreement between results based on the devised numerical scheme and those obtained from experiments for a specific case and other available studies.