Analytical Derivation and Simplified Application of In-Plane Equivalent Static Wind Loads for Cantilever Arch Rings during Construction

This study focuses on deriving a general formula for calculating the in-plane equivalent static wind load (ESWL) of an unclosed cantilever arch ring during the cantilever construction stage, enabling rapid estimation of extreme dynamic responses without performing time-domain analysis. Using the Euler–Bernoulli beam model, we derive the in-plane vibration differential equation for the cable-arch system, specific to the cable-stayed fastening-hanging cantilever construction state of arch rings. By assuming the first-order radial and tangential mode functions of the arch ring, the natural frequency of the cable-arch system was determined by the Galerkin method. Subsequently, analytical solutions for both the wind-induced vibration background and the resonant wind loads on the cable-arch system were derived, employing the load–response correlation method and the inertial wind load method, respectively. Additionally, by introducing the equivalent calculation length and a simplified formula for the multiobjective equivalent influence line function, this study proposes a straightforward solution for the background ESWL while achieving multiobjective equivalence. A concrete arch bridge erected using the cable-stayed fastening-hanging cantilever construction method was used to verify the proposed analytical ESWL formula, and a simplified ESWL formula was subsequently proposed based on a parametric analysis. The results indicate that buckle cable tension has a significant influence on structural frequency and must be considered in the calculation of fundamental frequency; the effect of longitudinal fluctuating wind speed u ( t ) has a minimal impact on the final in-plane ESWL and can be omitted; the influence line function does not significantly affect the calculation of in-plane ESWL and can be approximated for computational convenience. The static analysis results obtained using the simplified ESWL exhibit strong concordance with those from finite-element time-domain analysis, demonstrating that the proposed formula provides a theoretical basis for the rapid assessment of extreme buffeting responses.