A closed form procedure for the design of longitudinal bars in RC sections subjected to axial load and biaxial bending

This paper presents an analytical procedure for the design of the longitudinal reinforcement in reinforced concrete rectangular sections subjected to axial load and biaxial bending moment. The integration of the equilibrium equations is performed in analytical form for the case of uniaxial moment, including the effect of the reinforcement placed on the sides of the section and adopting code-based constitutive laws for steel and concrete. The strength domain of the section is calculated in closed form for the case of only main steel and in simplified form when including the reinforcement disposed on the side. Additionally, a formulation is proposed for the interaction domain of the two components of the bending moment for constant axial load, in which the uniaxial moment capacities are calculated including all the rebars within the section. The proposed method is adopted for setting a design procedure of the steel bars of rectangular sections subjected to biaxial bending. Comparisons with numerical results and code provisions show the reliability of the approach, which reduces computational costs and give useful indications for practitioners and designers.