Abstract
In the article it was investigated deflections of the castellated beams using the theory of composite bars. Differential equation of the flexure axis of composed beam was integrated with Fourier series. Reliable expression for deflection was obtained due to good choice of the rigidity coefficient of elastic lay formed with web-posts. Analytical solution for deflection is applicable for wide range of perforations: ; ; . An accuracy of obtained relation was estimated with calculations by the finite element method. Divergence of results does not exceed 3%. DOI: https://dx.doi.org/10.5755/j01.mech.21.5.12181
Highlights
In Russian structural Norms SN&R [1], as in Eurocode 3 [2], one of the basic demand to castellated beams is securing of necessary rigidity, i.e. restriction of relative deflection f / l
For today there are three different methods of calculation of the castellated beams deflections: method based on the theory of composed bars (TCB) [3]; method using the theory of Vierendeel truss [4] and the finite element method (FEM) [5]
It’s seems the best of all to use FEM for calculation of deflections, but application of FEM demands of existence of rather expensive program complex for modeling of calculated structure and beside of this a researcher is to be qualified in using ANSYS, so as even small deviations in adopted boundary conditions or description of model can bring to significant distortions in results
Summary
In Russian structural Norms SN&R [1], as in Eurocode 3 [2], one of the basic demand to castellated beams is securing of necessary rigidity, i.e. restriction of relative deflection f / l. In SN&R [1] the relative height of openings in castellated beams is restricted by value h / H 0.667 , as more useful in structural practice. For today there are three different methods of calculation of the castellated beams deflections: method based on the theory of composed bars (TCB) [3]; method using the theory of Vierendeel truss [4] and the finite element method (FEM) [5]. In Russian practice the method of the theory of composed bars, elaborated by А.R. Rzanizyn [3] is more popular and in abroad Vierendeel method is widespread, application of which to calculation of castellated beams was even included in one of the previous variants of Eurocode 3 [4]. Calculation of deformations of perforated beams deflections with the theory of composed bars was modified by author with integration of differential equation in Fourier series [6]
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