Calculation of open-frame through beams according to the A.R. Rzhanitsyn’s theoryof compound rods

Vestnik MGSU 9/2013
  • Filatov Vladimir Vladimirovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 23-31

Through beams are widely used in the construction of large-span civil and industrial buildings, bridge engineering and mechanical engineering. They include open-frame girders and castellated beams. In order to determine their stress-strain state, software systems based on the finite element method are used or approximate calculations using simplified calculation patterns of Virendel beams are performed. Recently, many projects have been completed, in which A.R. Rzhanitsyn’s theory of compound rods is applied to calculate through structures.In this model, discrete links connecting upper and lower belts of the structure are re-placed by cross ties and shift connections continuously distributed along the length of the joint. Cross links hinder the convergence or separation of belts from one another. As a rule, pliability of cross links is neglected. This assumption, which substantially facilitates the calculation, is consistent with the hypothesis that there is no lateral strain in individual rods, calculated according to the theory. Therefore, whenever a compound rod is loaded, all its layers, and in this case – belts, are deformed according to the same curve pattern. In calculations, elastically compliant shift connections are replaced by the required distribution function of shear forces distributed along the length of the beam joint. Thus, the calculation of a through-beam is reduced to the solution of three ordinary differential equations of the second order, on the basis of which the following functions should be defined: beam deflection, bending moment and shear stress in the beam joint.The author discusses development of a numerical method of calculation of through beams based on the A.R. Rzhanitsyn’s theory of compound rods. To solve the system of differential equations, difference equations of the successive approximations method are involved to take account of finite discontinuities of the desired function, its first derivative and the right-hand side of the original differential equation. They demonstrate high accuracy if compared to well-known finite difference method equations.To illustrate the algorithm, the author provides sample calculations of open-frame girders and perforated beams having openings of different shapes. The results obtained by the authors are compared with a well-known analytical solution and a numerical solution based on the finite element method.

DOI: 10.22227/1997-0935.2013.9.23-31

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