Comparative study of analytical and numerical algorithms for designing reinforced concrete sections under biaxial bending

This paper presents a comparative study of different integration methods of stresses (both analytical and numerical) for concrete sections subjected to axial loads and biaxial bending. Such methods are applied to circular and rectangular sections. The constitutive equation used is a parabola-rectangle from the Eurocode-2. The comparison was performed with regard to the accuracy and the computational speed of each method. The objective of the paper is to determine which of the integration methods compared is more efficient in computing the interaction surfaces for rectangular and circular sections. The analytical method proposed by Barros et al. [Barros MHFM, Barros A, Ferreira C. Closed form solution of optimal design of rectangular reinforced concrete sections. Eng Comput 2004;21(7):761–76] for rectangular sections is compared with the numerical method termed “modified thick layer integration” proposed by Bonet et al. [Bonet JL, Romero ML, Miguel PF, Fernandez MA. A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending. Comput Struct 2004;82(2–3):213–25] and with the well-known fiber method. Furthermore, two new methods are proposed for circular sections: one analytical and one numerical based on the Gauss–Legendre quadrature. The results of both methods are compared with the classical layer decomposition method.