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Optimized reinforcement distribution in reinforced concrete structures under plane stress state

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The strut-and-tie model is widely used for analysis and design of reinforced concrete structures. To apply this model, it is necessary to define strut-and-tie systems that represent the flow of stresses generated in the analyzed structure. In many situations, this strut-and-tie model is defined through an evolutionary structural optimization (ESO) considering linear isotropic material. The results obtained from this model are not always satisfactory Query ID="Q1" Text="Please confirm the inserted city name and country name in affiliations 1 and 2 are correct and amend if necessary." because of the nonlinear behavior of the concrete, mainly because of the great difference in the behavior under tension and compression. Because of this, an evolutionary algorithm is developed in this article to define the optimized reinforcement distribution in reinforced concrete structures under plane stress state, considering the nonlinearity of the materials. This algorithm adopts the same principle as the ESO algorithm; however, it does not eliminate the mesh element that discretizes the analyzed domain, but it eliminates the reinforcement of the elements that do not meet an efficiency criterion. A three-node triangular finite element is used for nonlinear analysis of the reinforced concrete structure under plane stress state. The structure domain is discretized by this element, which can be of four types: with reinforcement in two fixed orthogonal directions, only in one direction, or without reinforcement. During the evolutionary process of the algorithm using a rejection criterion based on the level of reinforcement strain, the elements with reinforcement are changed to elements without reinforcement or with reinforcement in only one direction. Three practical applications were evaluated to verify the efficiency of the algorithm proposed in this article. Two of them had their results compared with results provided in the literature, verifying the efficiency of the proposed algorithm.

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The authors would like to thank the Federal University of Ouro Preto (UFOP/PROPEC), FAPEMIG ,and CNPq for collaboration.

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Correspondence to Amilton Rodrigues da Silva.

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da Silva, A.R., Ladeira, A.H. Optimized reinforcement distribution in reinforced concrete structures under plane stress state. Struct Multidisc Optim 65, 205 (2022).

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