Achieving full equilibrium for the horizontal component force of the backstay in cable-stayed arch bridges is challenging, and the stiffness of the buckle tower has a notable influence on the overall shape of the main arch structure. Increased stiffness in the buckle tower leads to reduced construction complexity. Therefore, this study proposed a method of enhancing the longitudinal thrust stiffness of the buckle tower using the joint effect of approach bridges. A sensitivity analysis was conducted on the approach bridge–composite buckle tower structure to determine the optimal combination method, resulting in the formulation of an analytical expression for the thrust stiffness of this structure. In this study, numerical analysis was performed to explore the composition mechanism of the thrust stiffness influenced by the pier–girder connection, and we discussed the applicability of the joint effect of approach bridges during the cantilever assembly process of arch ribs. The following conclusions were obtained: 1) prior to installing the main girder of the approach bridge, when the steel buckle tower and the junction pier have already been secured, the most effective approach is to form a “T” rigid structure by firmly connecting the main girder of the approach bridge with the composite buckle tower. This configuration provides self-weight deflection and pier–girder rotation restriction effects. 2) The study presents analytical formulas for the completely rigid pier–girder connection of the approach bridge–composite buckle tower structure, partially rigid pier–girder connection, and pre-deviation. Combined with the calculation program, this can guide structural design. 3) When a large downward elevation error of the arch ribs occurs in the middle and later stages, the cable force needed to install new arch segments becomes overly large. Therefore, the joint effect of approach bridges can be utilized to substitute for a portion of the cable force, effectively reducing potential elevation errors that might arise in subsequent arch ribs in the absence of this joint effect.
