Comparative Study of Vlasov and Euler Instabilities of Axially Compressed Thin-Walled Box Columns

Abstract

Through experimental studies, Vlasov showed that Euler’s critical load formula cannot be directly applied to the buckling analysis of thin-walled closed columns. In this study, Vlasov’s displacement model with modification by Varbanov and Euler’s elastica model were used in a comparative study to determine the flexural buckling strength of single-cell doubly symmetric thin-walled box columns with different boundary conditions. The study involved a theoretical formulation based on Vlasov’s theory as modified by Varbanov and implemented the associated displacement model in analyzing flexural buckling modes. Euler’s critical load formula was used to solve the same set of problems and the results thereof were compared with those obtained from Vlasov’s model. The flexural behaviour showed that for all three sets of boundary conditions considered, the critical load due to flexure about the oz-axis will control design in both models. Comparison with the Euler critical load results showed that Euler’s model underestimated the critical buckling load by 67.53% for hinged-hinged, 67.11% for clamped-hinged and 66.11% for clamped-clamped boundary conditions respectively. For bending about the oy-axis, the underestimation ranged from 51.14% for hinged-hinged, 50.33% for clamped-hinged to 48.52% for clamed-clamped boundary conditions. The results show that for single-cell doubly symmetric box columns, the Euler buckling strength should be increased by about 100% to 200% to obtain the Vlasov buckling strength. The actual percentage depends on the axis of symmetry and the boundary conditions under consideration.