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Probabilistic and statistical modeling of loads and forces

Introduction. At present, numerical methods enjoy widespread use in construction practice. They enable performing and analyzing complex non-linear, multi-factor models without excessive analytical procedures. However, as a rule, the most complex tasks, performed in a three-dimensional setting with account taken of physical, geometric and other nonlinearities, are performed in deterministic formulations without the analysis of the stochastic nature of physical processes. This seems particularly strange, given that numerical methods are well-suited for modeling stochastic processes. Numerical probabilistic and statistical approaches (PSA) can be applied to simulate and take into consideration various spatiotemporal aspects of the probabilistic nature of loads and forces, structural system resistances, materials and geological terrains. Even the most advanced numerical models of deterministic physical systems are merely a specific case of probabilistic and statistical modeling: they enable obtaining only one value (point) on the whole field of possible implementations, being unable to demonstrate an objective and exhaustive variety of probable outcomes. This article presents a case study of numerical probabilistic and statistical analyses of loads and forces. 
Methods of research. Materials from different sources, such as reference books, regulatory documents, laboratory test results, as well as available experimental data, were used as input parameters. The principal calculation and analysis of the integral function of loads was performed using the Monte Carlo numerical method of probabilistic and statistical modeling and various theoretical (statistical) and empirical distributions, followed by the quantitative assessment of design loads at various confidence probability values. 
Results. This study provides an example of the probabilistic and statistical calculation (determination) of the integral function of loads and forces with account taken of different origins of loads and varied input parameter distribution patterns, including empirical distributions. It has proven great importance of accurate description of initial distributions of a random value for the determination of reliable design load values. 
Conclusions. Probabilistic and statistical approaches have the ability to objectively assess the performance of structural systems based on the quantitative assessment of the probabilistic nature of load factors. These approaches have huge potential for increasing the reliability of buildings and structures and the cost effectiveness of construction projects.