Steel optimization for reinforced concrete using an equilibrium-based formulation

This article introduces an innovative approach to optimize steel reinforcement in reinforced concrete structures using the equilibrium-based formulation described in Ferradi et al. (Comput Struct 286:107095, 2023). The objective is to enhance structural performance and cost-effectiveness by efficiently distributing steel reinforcement within an arbitrary volume representing the concrete, while ensuring external loading equilibrium. To achieve this goal, two approaches are proposed: the first approach focuses on optimizing the cross section of 1D rebars that are already defined in the concrete volume as curves, while the second approach optimizes the steel bulk densities throughout the entire volume, with or without assuming predetermined principal directions for the reinforcement, represented by a steel stress tensor. The latter approach does not rely on any prior knowledge of the geometric distribution of rebars and can be seen as an automated strut and tie method for three-dimensional problems , where the struts are derived from the compression flow, and the ties originate from the tensile flow. Both approaches are formulated as optimization problems, enabling the utilization of the interior point method for effective problem-solving. Numerical examples and comparisons with existing results vividly illustrate the flexibility and potential efficiency gains achievable through the proposed approaches.