Plastic interaction relations for elliptical hollow sections

Abstract

Interaction expressions are developed for steel elliptical hollow sections (EHS) subjected to combinations of axial force, biaxial bending moments and torsion. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. The interaction expressions developed consist of a set of elliptical integrals which are cast in a dimensionless form and numerically evaluated to obtain a grid of internal force combinations lying on the yield surface sought. A series of trial functions are fitted to the grid of internal force combinations and a simplified and conservative interaction equation is selected. The interaction relation relates axial force, biaxial bending and twisting moment combinations for EHS sections of common geometries. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example.