This paper concerns the safety of a simply supported prestressed concrete beam subject only to bending and shear loads: so the probability of failure Pf is calculated. This is achieved firstly at the so-called third probabilistic level that requires the knowledge of the probability density functions (p.d.f.) of both the stress S and the resistance R: attention is firstly focused on the construction of the latter. In order to do this the Monte Carlo Techniques have been chosen: they are based on the extraction of random numbers and are thus very suitable for simulating random events and quantities. Samples are obtained of the values of the moment capacity MR of the beam; the histograms of the samples are plotted and the statistical function that gives the best fitting is chosen as p.d.f. of MR. The p.d.f. of the stress is obtained from the p.d.f. of the loads provided in the literature: the cases of a single and of many repetitions are considered in calculating Pf.Pf is also found through the MFOSM level 2 Method evaluating the safety index β with an iterative procedure: a comparison is made between the two methods.
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