Analytical integration of stress field and tangent material moduli over concrete cross-sections

This paper presents a novel stress field and tangent material moduli integration procedure over a cross-section of a biaxially loaded concrete beam. The procedure assumes a sufficiently simple analytical form of the constitutive law of concrete, the polygonal shape of the boundary of the simply- or multi-connected cross-section and the monotonically increasing loading. The area integrals are transformed into the boundary integrals and then integrated analytically. The computational efficiency of the procedure is analyzed by comparing it with respect to the number of floating-point operations needed in various numerical integration-based methods. It is found that the procedure is not only exact, but also computationally effective.