A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending

This paper deals with the implementation of two integration procedures for arbitrary geometry reinforced concrete cross-sections with axial forces and biaxial bending, from service load to ultimate load. Two methods are proposed: the first method is suitable for a general stress field, and the second method is applicable in sections in which the stress field is uniform at least in one direction. Both methods decompose the integration area into thick layers parallel to the most tensile stressed fiber, whose definition depends on the constitutive equation of the concrete. The integration of the stress field of each thick layer is transformed into a double integral or a path integral over the perimeter of this layer. They are evaluated by a Gauss quadrature. The methods have been tested in different section types by modifying the depth and the inclination angle of the neutral axis. The results obtained for the different alternatives are compared in accuracy and in speed with the results obtained from the classical fiber decomposition method and also with those from an alternative method proposed by a different author.