The location of supports under the monolithic reinforced concrete slabs optimization

We consider the problem of finding the optimal location of point supports under a monolithic reinforced concrete floor slab, which provides the minimum of the objective function. The maximum deflection, potential strain energy, and reinforcement consumption are selected as the objective function. The load and plate configuration can be arbitrary. A restriction on the number of supports is introduced. The solution is performed using stochastic and deterministic optimization methods in combination with the finite element method to determine the objective functions An assessment of the proposed methods for a different number of supports n is made. Particular solutions are presented for n = 3, 4, 5.The optimal relations between the marginal and middle spans are established for buildings with a rectangular grid of columns with large n. It is shown that only the pitch of the columns of the marginal rows can act as a variable parameter, and the steps of the middle rows at the optimal arrangement are equal to each other. The developed methods were tested for the real object. It is established that of the three criteria used, the criterion of the minimum potential strain energy is preferable. It was also revealed that in most of the considered problems, the selected criteria give very close results. The plate thickness and material characteristics do not affect the optimal arrangement of columns.