Stability of centrically loaded members with monosymmetric cross-section at various boundary conditions

Abstract

The system of governing differential equations of stability of centrically loaded members with rigid open cross-sections was presented by Kappus in 1937 and by Vlasov in 1940. In 1941 Goľdenvejzer published a solution of this system by Bubnov-Galerkin's variational method using eigenfunctions of flexural vibration modes as fundamental functions. The result is a formula for torsional-flexural critical force calculation.The simplified formula for torsional-flexural critical force calculation is in EN 1993-1-3 as formula (6.35). This formula gives exact values of elastic critical force for torsional-flexural buckling of centrically loaded members with monosymmetric cross-section only if the flexural boundary conditions are the same as the torsional boundary conditions at both member ends. The Goľdenvejzer's formula differs from (6.35) by allowing different flexural boundary conditions to the torsional ones. Goľdenvejzer takes this into account by introducing factor α.The purpose of this paper is to verify whether the factor α can correctly include the influence of combinations of flexural and torsional boundary conditions which Goľdenvejzer did not investigate, and to verify if the simplified formula (6.35) may be used for any boundary conditions. The authors used Goľdenvejzer's method for 8 different shapes of monosymmetric cross-sections for all 100 theoretical possible combinations of boundary conditions, and for two different fundamental functions: a) eigenfunctions of flexural vibration modes (which were also used by Goľdenvejzer) and b) eigenfunctions of buckling modes (which is a more natural choice). All results are verified by the finite element method with 1D member elements. Research fieldStability of metal members under axial compression.