Optimization of cross-sectional dimensions of castellated beams with hexagonal openings

Abstract

The object of this study is a castellated beam, in which the web openings have the shape of a regular hexagon. The beam is examined to find optimal cross-sectional dimensions. The optimization task is stated as the task of finding the optimal profile numbers for top and bottom Tees of the beam and the optimal width of the web opening while ensuring the required load-carrying capacity of the beam. Minimization of the volume of the beam material was considered as an optimality criterion. The stated optimization problem was solved using the exhaustive search method. For an assortment of normal I-beams with parallel flanges, castellated beams were obtained with optimal cross-sectional dimensions depending on the steel grade, the beam span, and the magnitude of transverse uniformly distributed load. The optimization calculations proved that it was possible to increase the elastic section modulus of the beam to 35.48...50 % through the use of a castellated web. Castellated beams with optimal cross-sectional dimensions at the same load-carrying capacity are characterized by lower steel consumption (up to 23.19 %) compared to I-beams with a solid web. Analysis of the results has made it possible to devise recommendations for the optimal distribution of material in the cross-sections of such beams. The results are valid only for the assortment of normal I-beam profiles and only for the case of uniformly distributed load acting on the beam when the compressed beam flange is laterally restrained from the bending plane and the beam web has openings in the form of regular hexagons. It is under such conditions that the reported results can be implemented in practice both at the stage of selecting cross-sections of the studied class of structures, and at the development of effective assortments of castellated beams