The article considers the work of a reinforced concrete beam lying on an elastic half-plane. The strength of concrete is considered as a random variable, while the initial modulus of elasticity of concrete and, accordingly, the initial stiffness of the beam are taken as functions of the random cubic strength of concrete. The base of the beam is considered as an elastic stochastically inhomogeneous half-plane. Using the method of canonical expansions of random functions, the probabilistic parameters of the probability distribution densities of beam deflections, as well as bending moments and transverse forces in a reinforced concrete beam, which are non-stationary random functions, are obtained. This makes it possible to further determine the probability of occurrence of limit states in a reinforced concrete beam.

Keywords: reinforced concrete beam, initial stiffness, cubic strength, inhomogeneous half-plane, distribution density, beam deflection, random function