Nonlinear Analysis of Cross Sections under Axial Load and Biaxial Bending

The paper presents a method and an integration procedure specifically targeting the analysis of cross sections under biaxial bending and axial load, whatever the shape—including internal voids—and made of different materials (for example, concrete) internally or externally reinforced by mild steel, prestressing tendons, and fiber-reinforced polymers. Surface integration of meshed cross sections allows moment-curvature relationships to be computed using nonlinear constitutive relationships (also with softening) and three-dimensional (3D) interaction domains P-Mx-My to be drawn. Iteration procedures and convergence criteria are herein proposed to rapidly solve the highly nonlinear problem. Numerical tests showed fast convergence of the algorithm and good agreement with experimental results elsewhere; comparisons between the numerical outcomes and the simplified expressions available in the literature have been performed to point out the current limits of the available codes’ formulas.