Upper Bound Plastic Interaction Relations for Elliptical Hollow Sections

Abstract

A family of interaction expressions are developed for steel elliptical hollow sections (EHSs) subjected to combinations of axial force, biaxial bending moments, torsion, and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. The interaction expressions developed consist of a set of elliptical integrals which are cast in a dimensionless form applicable for EHS of general geometries. An iterative solution technique is developed to solve the resulting nonlinear relations. The applicability of the resulting interaction relations for conducting the cross-sectional check is illustrated through examples. A comparison with shell finite-element analysis results illustrates the validity of the interaction relations derived.