Curved-girder bridge systems, owing to the bending–torsion coupling effect, tend to rotate out of plane under vertical loading. Compared with straight girder bridges, curved-girder bridges face greater difficulties during construction, particularly in regard to cross-frame installation. Three types of cross-frame detailing methods are employed, where the cross-section achieves the desired fit on the basis of the load type: no load fit (NLF), steel dead load fit (SDLF), and total dead load fit (TDLF). One of these methods determines the bridge’s final shape and workability; thus, in this study, curved multiple-girder bridges with different curvatures are studied numerically to examine the effects of different cross-frame detailing methods on the internal forces, deformations, and load-bearing capacities of curved-girder bridges. This study focuses on the construction stage, so only the steel dead load and weight of the concrete slab are considered. The analysis results reveal that for bridges with small curvature radii, the use of an SDLF or a TDLF reduces bridge deformation (vertical deflection and rotation) but increases internal forces relative to the NLF. When the curvature radius increases, the influence of the SDLF and TDLF on the bridge’s response diminishes. The study findings can be helpful for choosing proper detailing methods to use in the construction of composite curved I-girder bridges with various curvature radii.