This paper presents a probabilistic reliability analysis of a cantilever beam subjected to uncertaintyin Young’s modulus and applied load. The structural response is described using the classical elasticdeflection model, and failure is defined as the exceedance of a prescribed allowable displacement.Several probabilistic techniques are applied to evaluate the probability of failure, including Monte Carlosimulation, the First Order Reliability Method (FORM), and variance-reduction techniques such asimportance sampling and adaptive importance sampling. In addition, Sobol sensitivity analysis is used toidentify dominant uncertainty sources, and reliability-based design is employed to determine the beamgeometry satisfying a target reliability requirement.The results show very good agreement between Monte Carlo simulation and FORM, with a differencein estimated failure probability below 2×10−4. Sensitivity analysis indicates that load variability is thedominant contributor to structural reliability. The reliability-based design procedure identifies an optimalbeam height of hopt = 0.120 m required to satisfy the target reliability index β = 3.Overall, the study demonstrates how uncertainty quantification, reliability analysis, and reliability-baseddesign can be integrated within a unified framework for structural engineering applications.The results are further illustrated using reliability maps and reliability atlases that visualize how differentuncertainty regimes influence structural safety and the applicability of approximation-based reliabilitymethods.
Sobański et al. (Sat,) studied this question.