Joint Distribution of Wind Speed, Wind Direction, and Air Temperature Actions on Long-Span Bridges Derived via Trivariate Metaelliptical and Plackett Copulas

Abstract

Comprehensive bridge design should consider simultaneous actions of wind and temperature. The current load combination method of directly superposing extreme wind and temperature actions ignores the correlation between wind and temperature, resulting in too conservative bridge load estimates, and limiting the further development of the bridge span. Therefore, this paper proposes a method to determine the joint distribution of wind speed, wind direction, and air temperature actions on long-span bridges based on trivariate metaelliptical and Plackett copulas. First, the technique of establishing the trivariate joint distribution via trivariate metaelliptical and Plackett copulas is introduced. Next, the conditional joint distributions of wind speed and air temperature under the specific wind directions are derived from these. Using the concept of conditional bivariate Kendall return period (KRP) proposed in this paper, the conditional KRP isolines of wind speed and air temperature for specific wind directions are constructed. Then, conditional joint estimates of wind speed and air temperature actions for several specific wind directions are obtained using the following principle: the conditional bivariate design return period should be equal to the conditional univariate one. The method feasibility is verified by the case study of the Changtai Yangtze River Bridge in China, which is currently under construction and will be the largest cable-stayed bridge in the world. The results show that the joint actions of wind and temperature on the bridge greatly reduce as compared with the simple superposition of extreme wind and temperature actions specified in the design code. Moreover, a significant contribution of wind direction in the above joint distribution on the large-span bridge load is proved.