The influence of shaping on the behavior of a mesh shell shaped as a one-sheeted hyperboloid

Abstract

Introduction. The stress-strain state (SSS) of mesh shells that have the shape of a one-sheeted hyperboloid, consisting of one, two and three sections and subjected to vertical and wind loads coupled with their own weight is studied. The feature of these shells is the use of the Fibonacci number in their geometry, or in the ratio of their diameters and heights.
 Materials and methods. The position of rectilinear generatrices of shell depends on the angle of inclination of generatrices, which is determined by the mutual rotation of the upper and lower bases, and it determines various shapes of the structure. The stress-stain state of shells is found numerically using the LIRA–SAPR software package. The largest forces arising in the generatrices and the largest horizontal displacements of the upper edge of the shell, caused by wind loading, are compared.
 Results. Equations are obtained to identify the position of the generatrix and the size of the real semi-axis of the hyperboloid. Analytical models of shells with different inclinations of generatrices are provided. As a result of the data analysis, the shapes of shells, having different heights and numbers of storeys, are proposed to ensure their optimal strength and stiffness. If the structure is subjected to vertical loads and self-weight, the mutual rotation of upper and lower bases does not affect the SSS of e shells. When the wind load is applied, the situation is completely different. Hence, for single-section shells of medium height and high shells with optimal parameters of internal forces and displacements, the size of the real semi-axis coincides with the size corresponding to the “golden section”. At the same time, shells with a small angle of mutual rotation of the bases barely resist lateral loading. In two- and three-sectional shells, the value of the real half-axis is slightly greater.
 Conclusions. The use of mesh shells, having the shape of a one-sheeted hyperboloid that has the “golden section” ratio, allows obtaining more expressive structural solutions. Analytical models of such structures are presented.