In this study, a computational platform is developed for fragility assessment of reinforced concrete (RC) bridges using a damage index (DI)-based approach. The platform integrates a reliability analysis in conjunction with sophisticated nonlinear finite element (FE) analysis. In this process, the first-order reliability method enables efficient probabilistic evaluation, while the FE analysis provides DI values that directly quantify bridge damage condition. The platform was applied to a hollow RC bridge pier under cyclic loading, and fragility curves were derived for multiple damage levels calibrated by experimental thresholds. Compared with Monte Carlo simulation, the proposed platform achieved similar accuracy with far fewer analyses, requiring only 80 runs instead of 2,711. A parametric study further investigated the effect of threshold uncertainty on fragility curves. These results demonstrate the potential of the proposed platform as an efficient tool for reliability-based vulnerability assessment and the derivation of seismic fragility curves.