Probabilistic response analysis of steel-concrete composite structures

Loading conditions, material properties, geometry and several other parameters often show considerable variability, since they are stochastic quantities in nature. The rational treatment of uncertainties in computational mechanics, based on statistical and probabilistic methods, is object of increasing attention, particularly in recent years. Modern design codes often directly account, with approximate procedures, for parameter and model uncertainties and stress out the importance of assessing such uncertainties to ensure satisfactory designs. Thus, in addition to accurate deterministic models, a methodology is necessary to propagate uncertainties from the parameters defining the finite element models of structures in terms of geometry and constitutive materials to the structural response quantities of interest to engineers. In this paper, the First-Order Second-Moment (FOSM) approximation is extended to steel-concrete composite structures to compute the first- and second-order statistical moments (means, variances and covariances) of structural response quantities when the parameters describing the constitutive models for steel, concrete and shear connection, are modeled as random quantities. The FOSM approximation has been found sufficiently accurate for engineering applications in estimating mean and standard deviation of response quantities of random structural and soil-foundation-structure interaction systems subjected to quasi-static non-linear pushover analysis when structural response non-linearities are in the low-to-moderate range. FOSM analysis is combined with the Direct Differentiation Method (DDM) for computing the response sensitivities required by FOSM. The combination of FOSM and DDM provides an extremely efficient yet accurate methodology for estimating first- and second-order statistical moments of response quantities of steel-concrete composite structures subjected to quasi-static probabilistic pushover analysis. A non-symmetric, two-span continuous beam subjected to monotonic loading, for which experimental results are available in the literature, is considered as benchmark example. First and second statistical moments of response quantities are computed and compared with the corresponding estimates obtained via Monte Carlo simulation (MCS). The relative importance of the material parameters describing the structure is studied in both the deterministic (response sensitivities scaled with the nominal/mean values of the considered parameters) and probabilistic (response sensitivities scaled with the standard deviations of the considered parameters) sense. Conclusions are drawn on the limits of applicability of the FOSM by comparison with the corresponding MCS results.