Topology Optimization of Reinforced Concrete Plane Frames

The definition of the number of columns, as well as their positions in the structure, is one of the tasks of the designer, and has a significant impact on both cost and structural behavior. This work presents a study developed in order to obtain the spacing of reinforced concrete columns of building structures corresponding to the smallest global cost (concrete, steel, and formworks). To achieve this objective, the plane frame was modeled as beam elements supported by springs with rotational rigidity. The optimization design variables are the height of beams and the length of columns. At the beginning of the process, columns were closely positioned, with small spacing among them, being the cost of the whole structure minimized. The less stressed column were removed from the structure, generating a redistribution of efforts. The optimization process was repeated, with the columns being successively removed from the structure. The optimal spacing corresponds to the configuration of minimum cost. The present work presents some examples of structures analyzed by the proposed procedure. It was observed that the optimum column spacing is similar to those suggested by practice.