Analysis of bridge reliability based on normal and asymmetric distribution laws.

In modern calculations of structural reliability, it is traditionally assumed that the distribution laws of random variables, such as material resistance and load effects, obey the normal law (Gauss’ law). This approach is convenient and well-known due to the symmetric nature of the distribution and its mathematical simplicity. However, the results of experimental studies show that in real conditions the distributions of such variables often have an asymmetric nature. In modern calculations of structural reliability, traditionally, the asymmetry of the distribution of material resistance in most cases has a negligible effect and can be ignored. At the same time, ignoring the asymmetry in load distributions can lead to significant errors in assessing the reliability of structures. In the paper, the lognormal law was used to model asymmetric distributions, which is universal and widely used to describe physical quantities such as material strength, load, river flow, etc. The results of the study are presented in the form of tables and graphs, reflecting the dependence of the reliability of structures on the safety factor. The results for symmetric (PNN) and asymmetric (PLL, PNL) distribution laws are compared. All calculations were performed using the Mathcad software package, which provides high accuracy and convenience in performing complex mathematical calculations. The paper also discusses the selection of distribution parameters, which should be based on statistical data for a specific design, materials, and operating mode. It is concluded that the need to consider asymmetry depends on the value of the asymmetry coefficient and the safety factor. The purpose of the study is to determine the conditions under which taking into consideration the asymmetry of the distribution of random variables is necessary to ensure the accuracy of calculations of the reliability of structures, as well as to justify the cases when the use of symmetric models is acceptable.