ESTIMATION OF THE PROBABILISTIC CHARACTERISTICS OF THE PROBABILITY DENSITY OF THE ULTIMATE TRANSVERSE FORCE IN BENDING CONCRETE ELEMENTS

Abstract

Strength parameters that determine the ultimate load-bearing of a bent reinforced concrete element along an oblique section from the action of a transverse force are clearly random. In order to construct the probability density distribution of the ultimate transverse force, it is necessary to find the parameters of this distribution. If we assume that the distribution of the ultimate transverse force is close to the Gaussian law, then it suffices to know the mathematical expectation and variance of this probability density distribution. The probabilistic characteristics of the ultimate transverse force in a reinforced concrete bending element are constructed. The ultimate transverse force is a nonlinear function of the strength of concrete and reinforcement, which are considered as random, normally distributed quantities. It is shown that the nonlinear function of the ultimate transverse force can be linearized by expanding in a Taylor series near the mathematical expectations of the tensile strength of concrete and the yield strength of the reinforcement with sufficient accuracy for practical calculations. The distribution density of the ultimate transverse force in this case can be considered obeying the normal law.