SOLVING THE PROBLEM OF ANALYZING THE STATE FUNCTION BASED ON THE APPROXIMATION OF THE TAIL PARTS OF THE DISTRIBUTIONS OF RANDOM VARIABLES LOADS AND RESISTANCES

Abstract

The semi-probabilistic calculation method does not provide an adequate design of structures in terms of a reasonable choice of a “design” (calculated) point.

The proposed way to overcome this problem is to solve the problem of analyzing the state function not in the entire domain of its definition, but only for the condition X=R-E<0, which corresponds to the interval of overlapping of the probabilistic functions of load g(E) and resistance distribution g(R). An enlarged fragment of differential probability distributions of load and resistance random variables is considered. Additionally, the conditional probability distribution is considered g(R|X<0), which corresponds to the failure condition.

The position of the maximum (mode) of the probability distribution function g(R|X<0) uniquely determines the most probable combination of random variables E and R, such that R<E, and its position in the best way corresponds to the meaning of the calculated design point.