Live load response assessment for suspension bridges with the main cable’s self-balanced system: an analytical method

As the span of the suspension bridge becomes increasingly long, the tower tops are subject to enormous unbalanced horizontal forces under the live load. A novel type of cable-tower restraint system, known as the main cable’s self-balanced system, has been proposed to mitigate the above problem. In this restraint system, the main saddle is designed with self-balanced rollers to adjust the geometrical shape of the main cable on the two sides through the limited slip of the main saddle. Thus, the rollers maintain the self-balance between the unbalanced horizontal forces in the main cable, the longitudinal component of support forces imposed by the towers on the main saddle, and the longitudinal component of rolling friction on the saddle under the load. This study proposes an analytical method for solving the internal forces and deformations of the suspension bridge with a self-balanced system of the main cable under any uniformly distributed live load. The proposed algorithm considers various factors, which makes the estimation of structural deformation more reasonable, including the slip and friction between the saddle and tower top, stiffness contribution of the stiffening girder, compression and bending deformation of the tower (the second-order effect included), hanger inclination and elongation, and longitudinal displacement of the stiffening girder. With the parameters already known under the dead load, the force states and deformations of the main cable, stiffening girder, and towers are studied. Next, equations are built based on conditions such as the conservation of unstressed lengths of main cable segments and the closure of span length between the main cables in different spans, which are converted into one objective function. Solutions are found by programming, and the structure’s live load response is estimated. Finally, the proposed analytical method is validated against finite element method (FEM) results for a suspension bridge with a 2300 m main span and a self-balanced main cable system. The comparison demonstrates excellent agreement, with a maximum relative error within 3%, confirming the high accuracy and wide applicability of the method.