Optimization of building structure design using probability distributions

Abstract

The article examines the application of probabilistic models for optimizing the design of building structures under operational uncertainty, a challenge of increasing importance in modern engineering. Unlike traditional deterministic methods, the probabilistic approach enables more realistic predictions of structural degradation by accounting for variable loads, material heterogeneity, environmental fluctuations, and stochastic wear processes. Using open-source materials science datasets and numerical simulations conducted in Python, the study analyzes the behavior of steel, concrete, and partially timber structures through the Weibull distribution and the exponential distribution. The Weibull model proved highly effective for representing fatigue failures in steel elements across different load levels, allowing early assessment of failure risks. The exponential distribution accurately reflected long-term deterioration trends in concrete structures, particularly under temperature extremes and elevated humidity. Additional reliability indicators – including hazard function, reliability function, and probability density of performance characteristics – were employed to evaluate long-term durability and determine optimal material usage boundaries. A comparative analysis of steel, concrete, and timber confirmed that steel remains the most reliable option for heavily loaded and safety-critical structures, while concrete offers a cost-effective solution for medium-load applications, and timber performs adequately only in stable environmental conditions. The findings demonstrate that integrating probabilistic methods into structural design significantly improves prediction accuracy, reduces the likelihood of operational failures, and supports more informed material selection aligned with expected service conditions.