OPTIMIZATION OF SELECTION OF ECCENTRICALLY COMPRESSED CONTINUOUS STEEL COLUMNS ACCORDING TO THE CRITERION OF MINIMIZING STEEL CONSUMPTION USING COMPUTER PROGRAMS

Abstract

The article presents the results of a theoretical study devoted to improving the selection of the cross-sectional dimensions of an eccentrically compressed steel column in the form of a welded symmetric I-beam based on ensuring general and local stability while meeting the requirements of building codes and minimizing steel consumption. The analysis of the standard conditions for the stability of the column showed that it is advisable to take the width and thickness of the shelves as unknown cross-sectional dimensions. It is assumed that the dimensions of the wall are known and are determined during the layout of the building as a whole. The possibility of designing a column with an unstable wall is considered. The conditions of local and general stability in two main planes are considered as functional dependences of the shelve thickness on its width, given implicitly. It is shown that the graphs of such implicit functions on the coordinate plane limit certain areas in which the corresponding condition of general or local stability is ensured. It is proposed to solve the problem using a computer program in the MathCAD environment, since obtaining analytical formulas that would explicitly express a function through an argument is associated with significant mathematical difficulties. The method has been developed for establishing a correspondence between the numerical values of the thickness and width of the shelves by using the tools of the MathCAD environment. Based on the analysis of the constructed graphs of the functional dependences of the shelve thickness on its width, a method for optimizing the cross section of the column was developed according to the criterion of minimum steel costs. This technique is substantiated by a theoretical analysis of the obtained dependencies, which was aimed at proving the effectiveness of the proposed solution to the problem of selecting a rational column cross-section.