DETERMINATION OF THE OPTIMAL DISTRIBUTION OF SUPPORTS IN THE FLOOR SLABS OF IN-DUSTRIAL BUILDINGS USING STOCHASTIC METHODS

Abstract

Abstract. Aim. The purpose of the study is to determine the optimal location of supports used in the floor slab of an industrial building.Method. In order to determine the optimal arrangement of the columns, a Monte Carlo algorithm was used in combination with the finite element method. The calculation was carried out on the basis of the theory of elastic thin plates.Results. The article presents a solution to the problem of determining the optimal location of a given number of point-supports of a floor slab n from the condition of minimum objective function. For the objective function, the maximum deflection of the slab, the potential energy of deformation and the flow rate of reinforcement were selected as variables. The selection of reinforcement was carried out in accordance with current generally-accepted standards for the design of reinforced concrete structures. The calcu-lations were performed using a program developed by the authors in the MATLAB computing environment. The results are given for n = 3,4,5. The algorithm, which has been modified for a large num-ber of supports n, is presented alongside a comparison of the basic and modified algorithm with n = 25. The possibility of a significant reduction in plate deformations with an irregular arrangement of supports compared to a regular distribution is shown.Conclusion. A method is proposed for finding the rational locations of point supports for a floor slab for a given quantity from the condition of min-imum deflection, potential strain energy and consumption of reinforcement materials based on the Monte Carlo method. This technique is suitable for arbitrary slab configurations and arbitrary loads. A modification of the algorithm is presented that is suitable for a large number of supports. The test example shows that the maximum deflection can be reduced by 42% when using an irregular support configuration compared to regular column spacing. In the considered examples, the position of all the supports was previously considered unknown, but the developed algorithm easily allows for stationary supports, whose position does not change.