A Generalized Nonlinear Beam Element for Slender RC Members Using a Polygonization Section Approach—Part I: Theoretical Formulation

A mathematical model for RC beam elements is presented that falls into the category of distributed inelasticity models discretizing the cross-section in polygons (trapezoids, triangles). The models falling into these categories are considered to be able to describe in the best manner the inelastic behavior of the element across its whole clear length, since its response results from the numerical integration of the stiffnesses of its cross-sections, while presenting an ideal combination of accuracy, simplicity, and computational cost. The behavior of the cross-section is described through the constitutive relationships σ–ε of its materials for cyclic loading. The main objectives for the development of the proposed mathematical model are as follows: (a) the increased accuracy of the results compared to existing experimental ones; (b) the limitless generalization of its application, regarding of the cross-section shape; and (c) the elimination of the numerical problems presented by the application of other related models, a fact that leads to their impractical use in real three-dimensional structures. The proposed model falls under the category of distributed inelasticity models. This paper focuses on its initial version, which targets slender beam elements with negligible shear and bond-slip effects (i.e., with ribbed bars, sufficiently anchored). Thus, it is applicable to 2D and 3D framed structures that fulfill these conditions, while its modular structure allows for future adjustments for the inclusion of other effects.