Analysis of Linear Surfaces of Building Structures

Abstract

Purpose of reseach is to analyze the practice in the application of surfaces formed by the movement of a straight line. It is known that among the second-order surfaces cones, cylinders, hyperboloids of one sheet and hyperbolic paraboloids, as well as lines represented in the polar coordinate system in the form of intricate shapes that can be represented in space by the above-mentioned surfaces, adding a third dimension, have rectilinear generators. The strength resulting from covering each point of the listed surfaces with straight lines from different families does not make the structure heavier but strengthens it and makes it light compared to monoliths without reinforcements made of other materials, in which stability is not based on Shukhov calculation formulas. Methods Finding families of rectilinear generators for second-order surfaces calculation of which is based on the separation of equations that represent a second-order surface as a difference of squares in one part of the equation and as a product with an arbitrary parameter in the other part. Results. Analyzing second-order surfaces, we came to the conclusion that cones, cylinders are prone to this method of Shukhov calculations; equation of the form F (x,y)=0 in space defines a cylindrical surface whose generators are parallel to axis oz. Similarly, F (x, z)=0 defines a cylindrical surface with generators parallel to axis oy and F (y;z)=0 is a cylindrical surface with generators parallel to axis ox. A hyperboloid of one sheet, hyperbolic paraboloid, i.e. 10 surfaces out of 14, make up more than 70%. Conclusion. As a result of applying these formulas for calculating reinforced building structures, city buildings will acquire a new appearance, which will create a comfortable environment for residents, as well as lead to saving construction material resources.