Biaxial Moment–Thrust–Curvature for Metal Cross Sections

The strength of cross section of different metals subjected to axial load and biaxial bending has been a problem of great interest for decades. Due to its complexity, this topic is addressed in short chapters in classical texts and codes. This research is the extension of a previously published work applied to concrete and metal cross sections. The M-P-φ curves are very useful to obtain the interaction diagrams of sections and to calculate the deflections and rotations of elements, but this second topic is not discussed in this paper; a simple numerical method to obtain theses curves for metal cross sections subjected to axial load and bending moment (axial or biaxial) is presented. The effects of bending residual stresses, strain hardening, and local buckling are included. Channel, box, tubular, I, and other shapes made of steel, aluminum, or other metals can be analyzed by dividing the cross section in discrete areas. The effects of shear or torsion stresses and strains are not taken into account. The sections can be subject to proportional or nonproportional loads producing biaxial bending. The model is presented in complete form with all the necessary equations to be programmed by readers. Three examples taken from the literature that show theoretical and experimental results are presented to verify the validity of the proposed model.