Stress-Based Method for Concrete Solids’ Reinforcement Design
Résumé
The development of computing capacities in finite element modelling has led to the possibility of modelling complex three-dimensional concrete structures, such as those in nuclear or hydraulic projects, using solid elements. These models with solid elements give only internal stresses in elements and not force results. For reinforcement design, in order to apply the traditional force-based method, the method of equivalent shells is ommonly used in practice, but its applicability is limited to only uniform geometries. Therefore, a reinforcement calculation method that allows directly exploiting the stress results is reviewed and its implementation in industrial projects is studied in this paper. The study presented here was
carried out for reinforcement design at the Ultimate Limit State. With the reinforced concrete considered as a homogeneous three-dimensional
medium in this method, the stresses in the structure can be decomposed as the sum of the stresses in the concrete and those in the steel. The problem is defined by using the element principal stresses, but the directions of the reinforcing bars are imposed to follow any three
orthogonal directions as usually seen in practice. The Mohr-Coulomb yield criterium is applied to restrict the concrete stresses. The minimum reinforcement amount at each element is achieved by using convex optimisation. In the present work, the algorithm was implemented with Python programming language and takes as input the internal stresses provided by a finite element software. Reinforcement calculations were then run on some simple test cases as well as on a complex industrial project, and the results were compared with those obtained by other methods such
as the method of equivalent shells or the strut-and-tie one. The analyses are discussed and some recommendations when using this stress-based method are made in this paper.
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