A parametric subdomain discretization for the analysis of the multiaxial response of reinforced concrete sections

• An improved discretization strategy for arbitrary shaped R.C. sections is presented.
• The integration process uses parametric and nested parametric transformations.
• The algorithm provides also a direct treatment of circular or hollow circular sections.
• The widely used fiber approach is simply a particular case of the proposed approach.
• A general and compact procedure to build 3D interaction domains is presented.

The paper presents an improved sectional discretization method for evaluating the response of reinforced concrete sections. The section is subdivided into parametric subdomains that allow the modelization of any complex geometry while taking advantage of the Gauss quadrature techniques. In particular, curved boundaries are dealt with two nested parametric transformations, reducing the modeling approximation. It is shown how the so-called fiber approach is simply a particular case of the present more general method. Many benchmarks are presented in order to assess the accuracy of the results. The influence of the discretization into subdomains and of the quadrature rules, chosen for integration, is discussed. The numerical tests highlight also the effects of spurious stress distributions in the tensile concrete zone, due the interpolation functions adopted for the Gauss integration. It is shown how balancing the number of subdomains and the number of sampling points such spurious effects vanish. The method shows to be accurate, very flexible in the discretization process and robust in analyzing any sectional state. Moreover, it converges faster than the fiber method, reducing the computational demand. All these properties are of great importance when the computations are iteratively repeated, as for the case of the sectional analysis within a computational procedure for a R.C. frame analysis.