Assessment of the Probability of Occurrence of Normal Cracks in a Reinforced Concrete Beam with Probabilistic Parameters Lying on a Stochastic Half-Plane

Abstract

The work of a reinforced concrete beam resting on an elastic foundation is considered. The strength characteristics of the beam materials - concrete and reinforcement - are considered as random normally distributed quantities. The parameters of the distribution of the probability density of the initial stiffness of the beam, the moment of crack resistance of the beam under the control of the strength of concrete in compression and tension are obtained. The beam base is considered as statistically inhomogeneous elastic half-plane with the soil elasticity modulus taken as a quasi-stationary random function of depth. The load on the beam, its geometric parameters and the modulus of elasticity of the foundation soil are taken as deterministic values. The parameters of the density distribution of the probability of bending moments in a reinforced concrete beam lying on a stochastic half-plane, and the probability of the formation of normal cracks in it, are obtained for the case of controlling the strength of concrete only in compression and for the case of controlling the strength of concrete both in compression and in tension.