Structural reliability analysis based on limit state functions and the first-order second-moment (FOSM) method

Abstract

This paper presents the theoretical framework of reliability-based structural design, focusing on the concepts of limit states and limit state functions. The relationship between resistance and load effects is modeled using random variables, enabling evaluation of the probability of failure. Due to the complexity of directly calculating failure probability, the reliability index β is adopted as a practical measure of structural safety. The First-Order Second-Moment (FOSM) method is introduced as an efficient approach for evaluating the reliability index. For linear limit state functions, β can be directly determined from the mean values and standard deviations of the random variables. For nonlinear cases, the limit state function is linearized using a first-order Taylor series expansion at the mean values, allowing an approximate evaluation of β. Illustrative examples demonstrate the method's applicability to both steel and reinforced concrete structures. The results indicate that the FOSM method is a simple and effective tool for reliability analysis in structural engineering, and it provides a fundamental basis for more advanced reliability-based design methods.