Use of optimization for automatic grouping of beam cross-section dimensions in reinforced concrete building structures

• Formulation to minimize the cost of reinforced concrete structures was implemented.
• Beam sections were used as design variables.
• Simulated annealing optimization method was adopted.
• The grouping of elements was automated by means of cardinality constraints.
• The procedure can reduce costs even for a small group of different cross-sections.

In the development of structural designs, in general, designers avoid varying the size of structural elements, seeking to group them as much as possible. These groupings produce aesthetic effects and facilitate formwork design for reinforced concrete frames, checks, and implementation. Therefore, the elements are pre-grouped into a smaller number of different cross-sections to provide an interesting and practical solution. However, the outcome is highly dependent on this grouping because the dimension of each element and, consequently, the overall cost, will be determined by the element that is the most stressed in each group. This paper minimizes the costs of the beams in reinforced concrete buildings using a grid model. The sizing is performed according to the Brazilian NBR 6118 standard [1], taking into account the flexural, shearing, torsional, and web reinforcements, in addition to checks on the service limit states (deflection and maximum crack opening). In addition to determining the beam height that leads to the lowest global cost, an automatic determination of the optimized group is performed, taking into account the required maximum number of groups. Several numerical analyses were performed using the computational implementation of the developed formulation. This paper presents the results obtained from an analysis of two floors. These results provide evidence that the chosen procedure may provide a significant reduction in the cost of a structure, even for a small number of different cross-sections. Thus, the determination of the optimum dimensions of the elements is less dependent on the designer’s experience and sensitivity. The proposed procedure is easy to implement and may generate a significant reduction in the consumption of structural material when incorporated into the daily routine of project offices.