Keywords: stress

Three Bimoments Equation of V.I. Slivker’s Semi-Shear Theory for the Calculation of Multi-Span Thin-Walled Beams

https://doi.org/10.58224/2618-7183-2023-6-3-31-46
Abstract
This article discusses the method of static calculation of multi-span thin-walled beams with bending torsion in the framework of the semi-shear theory of V.I.Slivker. The main advantage of the semi-shear theory is that it is suitable for rods of both open and closed (as well as open-closed and multi-contour) profiles due to the similarity of differential equations according to the theories of V.I. Slivker and A.A. Umansky, and also increases the accuracy of the calculation due to taking into account part of the shear deformation. The analytical solution of the problem is obtained based on three bimoments equations system of, including values of correlating functions for cases of application of torsional loads in the span and on the cantilever of thin-walled multi-span continuous beams. Bimoment func-tions for a number of simple beams are obtained within the framework of the semi-shear theory. It is shown that the values of the parameter of the influence of the shape of the cross-section of the semi-shear theory ranges from 1.000086 to 1.0014 for channel profiles, while the presence of shelf bends (C-profile) in comparison with the channel profile reduces the value of this parameter by 10%, which indicates a lower contribution of part of the shear deformations to the stress strain state at the torsion of the C-profile. It is shown that, despite the convergence of the calculation results by the proposed method, due to the proximity of the values of the shape influence parameter to 1.0 with the similar one according to the theory of V.Z. Vlasov, the area of application of the proposed method are significant-ly wider (both open and closed profiles).
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NUMERICAL ANALYSIS OF EARTH DAM STRESS-STRAIN STATE UNDER SEISMIC IMPACT CONSIDERING THE WAVE DYNAMICS

https://doi.org/10.34031/2618-7183-2020-3-3-5-20
Abstract
The design, construction and operation of high-rise earth dams in seismic regions, such as the territory of the Republic of Uzbekistan, requires constant improvement of the methods to calculate them under various loads, both of a static nature (gravitational forces, hydrostatic, etc.), and of a dynamic nature, including seismic effects. Emergency situations at such facilities or their partial destruction under any impact can lead to disastrous aftermath. The aim of this study is to develop a mathematical statement and an algorithm for numerical solution to an unsteady-state problem for an earth dam in a plane elastic statement. To verify the proposed methodology and the corresponding complex of applied programs, a solution to the test problem was given (the Lamb’s problem). According to the developed methodology and algorithm based on numerical method of finite differences, the problem of studying the stress-strain state was solved under shear stress on the foundation (in the form of a seismogram) on the example of the high-rise Charvak earth dam located near Tashkent city. The solution is presented in the form of distribution lines of equal displacements, stresses along the dam body, depending on time. The most vulnerable zones of the earth dam under consideration were identified.
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