# Stress state analysis of a cylindrical tank with water of an under water sports palace

## DOI:

https://doi.org/10.32347/2410-2547.2024.112.316-326## Keywords:

analysis, stress state, cylindrical tank, sports facility, shell, calculation, moment theory## Abstract

The paper analyzes the stress state of a cylindrical tank, which is one of the main structural elements of a sports facility - an underwater sports palace. In the calculation of the cylindrical shell of the tank of constant thickness, the moment theory was used. The reservoir is, in fact, a swimming pool for conducting training sessions on underwater swimming in fins, diving, diving, is considered fixed in its base and filled with liquid (water of a special composition, homogeneous in depth, with a given specific gravity). It is known that integration of the calculation equations of the moment theory (of circular cylindrical shells), namely: a) differential equations of equilibrium; b) equations of deformations; c) equations of forces attributed to the unit length of the coordinate line (tangential forces, bending moments), is a complex mathematical problem associated with solving a system of partial differential equations with variable coefficients. Only the calculation of the curve of a cylindrical shell ultimately leads to a system of differential equations with constant coefficients. Under the assumption of significant depth of the tank compared to the thickness of its walls and the value of the radius of the cylinder base (which allows us to consider it as infinitely long), displacements and forces (tangential and transverse), bending moments are analytically found. The locations of the cylinder surface points, in which the indicated forces and moments acquire maximum values, have been determined; sketches of their diagrams, determining the character of change of these physical quantities (parameters) along the height of the tank, have been given.

The results obtained in the work can be further used to clarify and improve engineering methods of calculation of structural elements of sports facilities of this type, both at the stages of their design and in the modes of real operation in order to prevent situations associated with the loss of their strength and stability.

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