Otimização do dimensionamento de vigas em concreto armado

Abstract

Software currently used in engineering offices, even the most modern ones, require pre-sizing, which is done manually by the designer, through trial and error based on his experiences. This software makes all the necessary adjustments to ensure security, but the solution found is rarely the most economical, since the possible results are diverse. Mathematical optimization then emerges as an aid tool for engineers looking for savings, not only in the cost of construction, but also in the time of project design. In this context, the present work aimed to develop a computational routine to optimize the design of reinforced concrete beams based on material and labor cost criteria. This problem starts from an objective cost function for the cross section of a beam, subject to constraints that guarantee its safety conditions and other limitations, which is to be minimized through an iterative exact method that initially receives some user supplied data. Through the algorithm created, the solutions can be found, by which it was noticed that most of the costs of concrete beams, when compared shapes, concrete and steel, is due to the shapes for smaller moments and from a certain point the armor stands out. Thus, the lowest cost occurs when there is no use of negative reinforcement to resist compressive forces, being used only when the concrete area is restricted by other factors, such as architectural. It is evident that the cost of shapes can be significantly reduced with their reuse, pointing out the predominance of steel in this composition.