Generalization of the Vlasov theory for lateral torsional buckling analysis of built-up monosymmetric assemblies

Abstract

The present study provides a formal generalization of the elastic lateral torsional buckling solution based on the Vlasov theory, initially intended for monolithic sections, to extend its applicability to any number of cross-sections connected together to form a monosymmetric assembly. The theory applies the well-known Vlasov kinematic assumptions to each of the components and augments them by assuming no relative slip between the components, as would be the case when components are bolted or welded. The formulation naturally leads to general expressions for effective sectional properties for the assembly (e.g., location of the shear centre, warping constant, monosymmetry parameter, and the Saint-Venant torsional constant). By adopting the effective sectional property definitions arising from the theory, the resulting lateral torsional buckling variational principle for the assembly is cast in a form analogous to that of monolithic sections. Alternative techniques are proposed to estimate the effective warping constant and monosymmetry parameter for assemblies. The solution shows that assemblies of sections connected through plug welds have lower critical moments than those continuously welded at the edges, while assemblies with intermittent welds have intermediate critical moment values. It is shown that treating the assembly as a monolithic section yields higher critical moments than assemblies with plug welds. The theory is used to quantify the critical moments in a number of built-up applications. Comparisons with the predictions of shell finite element model in Abaqus and S-Frame demonstrate the validity of the formulation.