Interaction yield hypersurfaces for the plastic behaviour of beams. I: Combining bending, tension and shear. II: Combining bending, tension, shear and torsion (Q1804417)

A variational method has been used to construct envelopes of the interaction yield surfaces for elastic, perfectly plastic beams subjected to combined bending moment, axial tension and transverse shear force. A lower bound of the envelope for the interaction yield curves relating bending moment and transverse shear force is obtained using a numerical scheme for beams having rectangular-shaped cross-sections. The result is recast into a simple equation with the aid of the least-squares method. A good upper bound of the envelope for the interaction yield curves which combine transverse shear force and axial tension is also derived. A formula for the interaction yield surfaces for combined bending moment, axial tension and transverse shear force is suggested.