Quantitative Assessment of the Reliability Index in the Safety Analysis of Spatial Truss Domes

The objective of the article is the quantitative assessment of the reliability index for a specific type of structure—trusses with node snap-through. The trends in contemporary geometric and structural design of architectural forms of rod domes are evolving towards increasing diameters and reducing rise. Therefore, it is justified to assess the safety of this type of structure. The Hasofer–Lind reliability index (β) was adopted as the reliability measure. In the reliability analysis, the FORM method was applied using the implicit form of the random variables function (combining external reliability software with the noncommercial finite-element method program) and using explicit forms of limit-state functions (neural networks were used and own original finite-element method module). In addition, the classical Monte Carlo method and the hybrid Monte Carlo method (combining with a neural network) were used. For dome loads in the range of 73–100%, the reliability index β can be estimated with reasonable accuracy (error) compared to standard methods. The obtained approximation functions allow for easy determination of the percentage of the maximum load that ensures safe operation. In addition, they allow us to indicate at what load level the reliability index reaches the standard level (at least β = 1.5 for the serviceability limit state).