Fast Reliability Evaluation of Existing Building Spatial Structures via the Intersection Area Method

In the reliability assessment of existing spatial structures, the steel yield strength, steel tube wall thickness, and load effect are the primary random variables. Targeting two cases—one with two variables (yield strength and load effect) and another with three variables (additionally including steel tube wall thickness)—this paper proposes the intersection area method (IA method). The method exploits two features: the probability density curves of resistance and load effect have a unique intersection within the mean-value region, and the reliability index varies approximately linearly with the steel tube wall thickness. By confining the double-nonlinear stability ultimate bearing capacity analysis to the vicinity of this intersection, the number of analyses is substantially reduced. Theoretical derivation shows that the ratio of the reliability indices obtained by the IA method to those by the checking point method (JC method) lies between 1.0 and √2. A tensile bar example verifies that the IA method requires only 40 analyses to obtain the reliability index, far fewer than the probability density evolution method and the Monte Carlo method, and the ratio falls within the theoretical interval. In an existing double-arch latticed shell engineering example, under the three-variable condition, the IA method reduces the number of double-nonlinear analyses to 47; the ratio of the reliability index from the IA method to that from the probability density evolution method also falls within the theoretical interval, with acceptable error. The results demonstrate that the IA method significantly improves computational efficiency while maintaining accuracy, providing a fast algorithm for the reliability assessment of existing spatial structures that is both theoretically grounded and practically applicable.