Comparative study of computational methods of structural reliability assessment

Safety is an essential requirement of a structural system. Reliability is an additional tool of growing importance in engineering, as it allows us to quantify uncertainties in the design. Thus, reliability assists us in making more suitable decisions regarding the safety of a structure. The present work compares and analyzes structural reliability methods applied to various examples of limit state functions. These methods are essential tools for this analysis because they identify and quantify uncertainties in random variables, allowing the evaluation of the probability of failure of the structure. Structural reliability methods were programmed and simulated in the Python language. The performance of these methods was analyzed through examples of linear, nonlinear, implicit, and explicit limit state functions. The results indicate that the simulation of Monte de Carlo brute force (MCBF) and importance sampling (MCAI) proved to be quite efficient for the examples studied in this work, with values equal to or very close to the reference values from the literature. The First Order and Second Moment Method (FOSM) presented limitations in some examples when the basic random variables do not have a normal distribution and the limit state function is nonlinear. The first-order reliability method (FORM) employs a failure surface linearization, which does not work well for highly nonlinear problems. The second-order reliability method (SORM) has improved the FORM results by including additional information about the curvature of the limit state function.