Abstract
The results of the evaluation of the reliability of reinforced concrete beams lying on an elastic foundation are presented. The load on the beam is considered as a non-stationary random function, the elastic properties of the foundation are described as a stationary random function. Beam stiffness is considered as a random variable depending on the cubic strength of concrete. To solve the beam bending equation on an elastic foundation with random properties and a loaded non-stationary random load, the small parameter method and the method of spectral representations are used. The obtained probability characteristics of the probability density distribution of bending moments allow us to find the probability of failure of a reinforced concrete beam on an elastic stochastically inhomogeneous foundation.
Highlights
The results of the evaluation of the reliability of reinforced concrete beams lying on an elastic foundation are presented
In [7] the parameters of the distribution of deflections and bending moments in a reinforced concrete beam lying on an elastic foundation were constructed
(29) into the expression for the probability of failure of a reinforced concrete beam over a normal cross section (2) and considering that all the above calculations were made for a concrete implementation of the concrete cube strength R, which is a random variable with a Gaussian distribution pR(R) with parameters: expectation < R > and variance DR and on which the beam stiffness and the probability characteristics of bending moments depend, find the probability of jelly destruction reinforced concrete beams of normal cross section
Summary
The results of the evaluation of the reliability of reinforced concrete beams lying on an elastic foundation are presented. Mult(R,σт) where pR(R), pσт(σт), pq(q), pC(C) - probability density functions of cubic concrete strength R and the yield strength of reinforcement σт, random non-stationary load q(x) and random function of coefficient of the foundation (bed ratio) C(x); pM(M, R, q, C) - probability density function of bending moments in the beam.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
