Elastic critical force of centrically loaded member with asymmetric and monosymmetric cross-sections at various boundary conditions: A parametric study

Abstract

The system of governing differential equations of stability of centrically loaded members with rigid open cross-sections was developed by Kappus in 1937 and by Vlasov in 1940. In 1941 Goľdenvejzer published a solution of this system by an approximate method. He proposed a formula for torsional-flexural critical force calculation which can take into account cases when the flexural boundary conditions of member are different to the torsional boundary conditions. This is allowed by introducing a factor α which depends on the combination of flexural and torsional boundary conditions. Goľdenvejzer investigated members with only 14 specific combinations of boundary conditions which are more frequently used in practice.The authors used Goľdenvejzer‘s approximate method for 9 different shapes of monosymmetric and 5 different shapes of asymmetric cross-sections to produce the parametric study. In the study all 100 theoretical possible combinations of boundary conditions for monosymmetric cross-sections and all 1000 theoretical combinations of boundary conditions for asymmetric cross-sections were investigated. The new α-factors were proposed to decrease the errors in the critical forces values. The finite element method with 1D elements was used for the proposition of new α-factors as well as for the verification of all results.