Reliability analysis of a corrugated I-beam girder with ribs

The main aim of this paper is to provide a reliability analysis of a corrugated-web I girder, including the vertical ribs distributed periodically throughout its length. The generalised stochastic perturbation method and its computer implementation - the stochastic finite-element method - are both used to accomplish this goal. They are numerically implemented using the finite-element method system Abaqus with its rectangular, four-noded, structural, thin-shell finite elements and computer algebra system Maple, in which all the probabilistic procedures are programmed. The perturbation-based results are compared with those from traditional Monte Carlo simulation and, separately, an analytical solution is obtained by way of symbolic integration, carried out also in Maple. The plate girder thickness is introduced as the basic input Gaussian random variable in this study, as the most influential geometrical parameter in this structure. The reliability indices are determined according to both first-and second-order reliability methods, and correspond to the serviceability limit state of the structure. The first four basic probabilistic characteristics of the maximum deflection are also computed - expectations, coefficients of variation, skewness and kurtosis. The results obtained here and the entire methodology may be extended further towards computational modelling of the corrosion process, which is frequently mathematically modelled in steel structures using certain time series with random coefficients.