Abstract
The article is devoted to the development of methods for assessing the reliability of elastic systems with random parameters of structural elements based on static models. At present, probabilistic methods are increasingly replacing traditional approaches based on allowable stresses and limit states, becoming the foundation of modern building codes and standards. Within this framework, structural failure is considered a random event, while reliability and stability are defined by the probability of failure-free operation. For systems subjected to time-invariant loads and possessing constant material properties, static reliability models provide an effective analytical tool. Despite advances in construction science and engineering, the assessment of structural reliability under random actions remains a highly relevant issue due to increasingly complex operating conditions and growing safety requirements for engineering structures. The scientific novelty of the study lies in the fact that approximate analytical relationships have been obtained for the first time for determining the reliability and service life of elastic structural systems, taking into account the random nature of both variable stress amplitudes and the fatigue limit of mаterials. A new engineering methodology for the probabilistic analysis and design of multielement mechanical systems has been proposed, incorporating the effect of dependent failures of structural elements. Furthermore, analytical relationships between static reliability models and multifactor random parameters of structures have been established for the first time. The developed methods and analytical relationships have been transformed into engineering algorithms, providing a practical basis for the reliable design of complex load-bearing systems.