An Analytical Method for Tension Force Estimation of Arch Bridge Suspenders Considering Multiple Factors

Cable force estimation of the suspenders is of tremendous significance for the safety and condition evaluation of arch bridges. The modern suspender cable structure widely used nowadays calls for an efficient and robust estimation method accounting for the cable bending stiffness, complex boundary conditions, intermediate dampers, and variable suspender segments. To estimate the tension force in arch bridge suspenders, this paper proposes an exact analytical method that can simultaneously consider the aforementioned factors for the first time. Based on a generalized suspender cable model including all these factors, the transcendental equation for cable force calculation was obtained from the determinant of a 4 × 4 matrix derived using the transfer matrix method. Due to the low dimensionality of the matrix, the transcendental equation size is largely reduced. This allows rapid cable force calculation without requiring complicated numerical iteration algorithms. A dimensionless parametric analysis was conducted to investigate the impact of various factors on the frequency parameter of the suspenders. Subsequently, the efficacy of the proposed method was verified, and an extensive estimation error analysis was performed using finite elements. Moreover, the method was applied to four real-world bridges with measured vibration frequency available. The results showed that the method can accurately estimate the tension force in suspenders with flexural rigidity, arbitrary boundary conditions, and any number of intermediate dampers and nonuniform segments. The proposed method can also be used for suspender cable force estimation of other cable-supported bridges, such as suspension bridges.