Design and optimization of skew reinforcement in concrete shells

Nowadays, it is more and more often necessary to design two‐dimensional reinforced concrete elements to satisfy both architectural demands and to comply with traffic safety requirements in the design of road and railway infrastructures. In fact, the demand for non‐regular structural geometry is increasing in both cases. As a consequence, the use of finite element analyses to model structures and calculate internal actions is constantly growing because closed‐form solutions are generally unavailable for irregular shapes. Therefore, the problem of reinforcement design needs our attention because steel bars, in general, should be placed in non‐orthogonal directions and can vary over the structure. Consequently, there are two different kinds of design problem: choice of reinforcement direction and evaluation of the reinforcement ratio between the chosen directions, with the aim of minimizing the total amount. Such problems can be easily overcome by generalizing a mechanical model consolidated in the literature for orthogonal reinforcement for skew directions. The model is set up according to the ultimate plastic behaviour of the elements. An optimization technique based on genetic algorithms is then applied to the new model to reduce the amount of reinforcement. This paper describes both the ultimate resisting mechanism with generic reinforcement directions and the way genetic algorithms are employed to optimize the amount of reinforcement.