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Title: Аналітичний розв’язок задачі згину багатошарової симетричної кругової арки під дією нормальної сили у середньому перерізі. Повідомлення 2. Арки малої кривизни / Basic Stress-Strain State of a Multilayer Symmetric Circular Arch under the Action of Normal Forces in the Middle Section. Message 2. Arches of Small Curvature
Authors: Ковальчук, Станіслав Богданович
Горик, Олексій Володимирович
Keywords: багатошарова арка
ортотропний шар
зосереджена сила
многослойная арка
ортотропный слой
сосредоточенная сила
plane bending
multilayer arch
orthotropic layer
concentrated force
Issue Date: Sep-2019
Description: Circular arches are common elements of building and engineering structures. They occur as individual components as well as reinforcing elements of thin-walled shells. An important for practice case of deformation of arches is the symmetrical bending in its own plane under the action of concentrated force. The resistance of homogeneous isotropic arches is intimately examined. However, the mechanics of deformation of multilayer arches is under investigated, which creates additional barriers to the introduction of such elements in designing practice. The purpose of this work is a theoretical study of the basic stress-strain state (SSS) of a symmetrically fixed multilayer arch under the action of concentrated normal force in the middle section by developing an analytical solution of the corresponding problem. The second part of the article deals with developing a simplified solution to the problem obtained with the use of the plane section hypothesis, which eliminates the effect of share deformation and transversal compression on other components of the SSS. Considering accuracy, such a solution ranks below the obtained in the first part of the article complete solution, which takes into account the whole complex of elastic characteristics of materials of layers, but is much more simple to implement. Using the developed simplified solution, this made it possible to obtain complete ratios for unknown static and kinematic parameters (unknown constants) for solid and hinged arches in the middle section that have different types of end fixation. To test and verify the obtained theoretical ratios, the long three-layer arch of small curvature (the ratio of the midradius to the section height is 30) was calculated. The results of determining the deflection of arches with different types of end fixations, obtained with the use of the simplified and complete solutions, as well as by the finite element method, are presented. A brief analysis of accuracy of the simplified solution in the case of changes in the stiffness of outer and middle layers is made. The developed solution enables to determine the stress condition of long symmetrical composite arch elements and small curvature rings with accuracy acceptable for practice. However, the accurate determination of displacements with its application has certain limitations, the precise identification of which requires further research.
Appears in Collections:Фахові видання

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Bulletin of PDAA, Iss.94, 256-266(2019).pdf1.13 MBAdobe PDFView/Open

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