Planar trusses reliability analysis based on p-boxes

The article describes the approach to steel planar trusses reliability analysis based in p-boxes (probability boxes). Modeling of stochastic parameters in the form of p-boxes is justified for structural elements due to the significant variability of climatic loads, physical and mechanical properties of structural materials, installation tolerances, and other uncertainties. The advantage of the proposed approach is that it can be used for incomplete (limited) statistical data: when it is difficult to determine the cumulative distribution function (CDF) or CDF's parameters of a random variable. The article presents the different options for p-blocks construction for various types of incomplete statistical data: for an unknown cumulative distribution function using Chebyshev's inequality, for interval estimates of CDF's parameters of random variables, etc. Information about the possibility of performing basic algebraic operations on p-boxes is provided. The failure probability of a structural element will be represented in interval form using the proposed approach. If the range of the interval is too wide (uninformative), then the quality of statistical data should be improved by conducting additional tests of control samples. The article also shows the possibility of using the proposed approach in most practical tasks in the construction industry for the safety assessment of statically determinate trusses. As a result, the special equations are given for evaluating the reliability of a truss as a conditional mechanical sequential system (in terms of reliability theory). The algorithm of reliability analysis is considered on the numerical example. The proposed approach can be used for other types of statically determinate hinge-rod systems.