This work presents an algorithm for calculating the bending plates of medium thickness according to the Reissner’. To obtain numerical results, the method of successive approximations (MSA) is used. This method has high accuracy and fast convergence, which was confirmed by the solution of a range of tasks. Publication of the results of the calculation of plates of medium thickness with the boundary conditions revised here is supposed to be in the following articles.

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In the article, a verification proposal of the composite rods theory on the structural analysis of skeletons for high-rise buildings. A testing design model been formed on which horizontal elements been represented by a multilayer cantilever beam operates on transverse bending on which slabs are connected with a moment-non-transferring connections and a multilayer columns represents the vertical elements. Those connections are sufficiently enough to form a shearing action can be approximated by a certain shear forces function, the thing which significantly reduces the overall static indeterminacy degree of the structural model. A system of differential equations describe the operation mechanism of the multilayer rods that solved using the numerical approach of successive approximations method. The proposed methodology to be used while preliminary calculations for the sake of determining the rigidity characteristics of the structure; are needed. In addition, for a qualitative assessment of the results obtained by other methods when performing calculations with the verification aims.