A simplified version of the method of calculation of multilayer composite rods according to the theory of A.R. Rzhanitsyn

Introduction. A modification of the theory of composite rods (TCR) by A.R. Rzhanitsyn is proposed. It is one of the most common methods for calculating multilayer building structures. The stress-strain state of multilayer composite beams is determined by the functions of deflections, bending moments and forces in continuously distributed interlayer connections that prevent mutual shear of the layers. The forces in the shear connections are determined by solving a system of n ordinary differential equations of the second order, where n is the number of interlayer seams. The proposed method is based on the hypothesis of a functional relationship between the shear forces in the beam seams. This assumption allows us to reduce the problem of determining the functions of shear forces to solving one ordinary differential equation of the second order. Thus, the number of simultaneously solved differential equations describing the problem is reduced from n + 2 to three for any number of layers.

Materials and methods. To solve the system of differential equations, both in Rzhanitsyn’s formulation and in a simplified formulation, difference equations of the method of successive approximations (MSA) are used.

Results. The results of calculation of a six-layer beam using three models are obtained: in the formulation of A.R. Rzhanitsyn, with the involvement of the simplified method of R.F. Gabbasov and V.V. Filatov, in the formulation of the authors of the paper. The results of calculation by simplified methods with TCR are compared. The influence of various parameters (geometric and mechanical characteristics of layers, shear stiffness of seams) on the operation of simplified models is studied. Diagrams of maximum longitudinal and tangential stresses are constructed for different options for the layout of the cross section of a composite beam

Conclusions. Recommendations are presented and limitations on the possibilities of using the proposed calculation method for multilayer beams under static loads are described. The method can be recommended for use in the practice of design organizations and in the educational process of specialized higher education institutions.

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