Plastic interaction relations for semi-elliptical hollow sections

General plastic interaction relationships are developed for semi-elliptical hollow structural sections subjected to general combinations of normal force, twisting moments and biaxial bending moments. The lower bound theorem of plasticity is employed to obtain the fully plastic resistance of the section in conjunction with the maximum distortional energy density criterion.The developments are expressed as universal, non-dimensional relationships suitable for limit state design. An iterative scheme to solve the parametric form of the interaction relations is developed and a grid of admissible stress resultant combination is generated. A series of trial functions are fitted to the grid of internal force combinations and two simplified and conservative interaction equations are proposed. The interaction relations relate axial force, biaxial bending and twisting moment combinations for semi-elliptical hollow sections of common geometries. The applicability of the newly proposed interaction equations for conducting the cross-sectional interaction check is illustrated through practical examples.