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Nowadays there are various calculation methods for solving a wide range of problems in construction, hydrodynamics, thermal conductivity, aerospace research and many other areas of industry. Analytical methods that make up one class for solving problems, and numerical calculation methods that make up another class, including those implemented in computing complexes, are used for the design and construction of various thin-walled structures such as shells. Due to the fact that thin-walled spatial structures in the form of various shells are widely used in many areas of human activity it is useful to understand and know the capabilities of different calculation methods. Research works on the study of the stress-strain state of the torse shell of equal slope with an ellipse at the base are not widely available at the moment. For the first time the derivation of the differential equations of equilibrium of momentless theory of shells to determine the normal force Nu from the action of uniformly distributed load tangentially directed along rectilinear generatrixes to the middle surface of the torse of equal slope with a directrix ellipse is presented in this article. The parameters of the stress state of the studied torse are also obtained by the finite element method and the variational-difference method. The SCAD software based on the finite element method and the program SHELLVRM written on the basis of the variational-difference method are used. The numerical results of the parameters of the stress state of the studied torse are analyzed, and the advantages and disadvantages of the analytical method and two numerical calculation methods are determined.

Thin-walled shell-type structures today constitute an extensive class in architecture, civil and industrial construction, mechanical engineering, ship- building, etc. Each surface has certain advantages over others. Torso surfaces can be expanded to the plane by all its points without folds and breaks, while the lengths of curves and angles between any curves that are appropriate for the sur- face do not change. The study of the stress-strain state of shells of equal slope with a director ellipse at the base is presented today in a small volume. The purpose of the article is to obtain new data when studying the stress-strain state of torso shells of equal slope with a director ellipse at the base. To assess the stress-strain state, the SCAD Office computer system is used, which is an integrated system for strength analysis and design of structures based on the finite element method. In the article, a new design of the awning over the entrance to the building in the form of a surface of equal slope is proposed, the stress-strain state of this structure is numerically studied.