Load-Sharing Ratio in Variable-Depth Beam–Arch Composite Bridges: Analytical Formulation, Numerical Verification, and Construction-Monitoring Assessment

Beam–arch composite bridges resist external loads through the interaction of the main girder, arch ribs, and hangers. This study develops an analytical method for evaluating the arch-rib load-sharing ratio of variable-depth, three-span continuous beam–arch composite bridges. The variable-depth main girder is represented by two piecewise energy-equivalent stiffness regions and closed-form expressions are derived using the force method and deformation compatibility conditions. A three-dimensional finite element model of a prototype bridge with a span arrangement of 80 + 152 + 80 m is established for numerical verification, while construction-monitoring data obtained during hanger tensioning are used to assess the predicted stress-redistribution behavior. The global and piecewise analytical solutions are 0.276 and 0.359, respectively, compared with the complete finite element result of 0.320. By representing the nonuniform membrane-tension distribution using a sixth-degree polynomial, the refined analytical result is improved to 0.303, reducing the relative error of the piecewise solution from 12.2% to 5.3%. Construction-monitoring data obtained during hanger tensioning further showed that the FE model reproduced the measured stress development and redistribution trends, thereby providing an indirect assessment of the model’s ability to characterize girder–arch interaction during hanger-tensioning-related structural evolution. Within the investigated parameter ranges, the girder-to-arch flexural rigidity ratios and the arch-rib–hanger equivalent-stiffness ratio exert the greatest influence on the load-sharing behavior. The proposed method provides a mechanically transparent and computationally efficient tool for the preliminary design and mechanical assessment of variable-depth beam–arch composite bridges, subject to the stated assumptions and parameter ranges.