STOCHASTIC CALCULATION OF THE CRITICAL FACTOR COEFFICIENT FOR CENTRALLY CMPRESSED ELEMENTS

Abstract

This paper deals with the problem of determining a generalized critical factor. It is the ratio of the generalized efforts to the strength. These values are random. Besides, the study is about the stochastic calculation of the steel constructions’ central-compressed elements. There is a complexity in using stochastic methods of calculation, because the coefficient of longitudinal bending is the function of the element’s flexibility, the yield strength and the type of stability curve. For obtaining the final solution it is necessary to perform complex multi-stage mathematical operations. Therefore, the function’s approximation of the coefficient of longitudinal bending was made by using exponential dependence. Exponential dependence was used for this purpose. The stability curves’ parameters, which depend on the type of the transverse section, were calculated. A graphical comparison of the normative expression for the coefficient of longitudinal bending with the proposed dependence was made. The convergence of the results is sufficient in the values’ range of elements flexibility from 0-100. The differences increase with values of flexibility greater than 100. However, the coefficient values of the longitudinal bending of more than 0.3 are seldom achieved. The expressions are obtained for determining the random value of the critical factor of the central-compressed element in a simple analytical form. It has been numerically proved that the values of an exponent in the formula of a critical factor could be equated to one. It simplifies the calculation greatly. The distribution density of the critical factor’s random value of the central compressed element at the two coordinate planes, the classical and critical probability scale, is presented graphically. Distribution histograms were made for two variants on the basis of numerical simulation using the formulas of the State Construction Standards [1] and, respectively, statistical processing of the simulation results according to the obtained dependencies. The data analysis showed clear correspondence of the element’s critical factor to the reference curve in the area of probability values.