AbstractContinuous rigid-frame bridge (CRFB), a type of bridge adopting the unique form of pier-girder consolidation, combines a T-shaped rigid frame with a continuous girder. CRFBs located in western China are likely to suffer destructive earthquakes, which may result in serious damage to bridges. To study the longitudinal seismic responses and damage control of different structure types of the CRFB under strong ground motions, this work develops three nonlinear dynamic analysis models considering the initial internal force state and longitudinal girder-pier pounding effect based on the OpenSEES (version 3.3.0) platform. Moreover, the present study comparatively analyzes the displacement responses, internal force of piers, pounding force and times, and damage condition of the three models and investigates the effectiveness of tuned inerter-based dampers (TIBDs) in controlling seismic responses of the CRFB. The numerical results show that the longitudinal seismic responses of the main piers in the three models are obviously different, especially when subjected to near-fault ground motions. The peak pounding force at the abutments is much larger than at the transition piers, while the pounding times are the opposite. Under near-fault ground motions with a peak ground acceleration (PGA) of 0.4g, the main piers may be damaged moderately or even more seriously, and the bearings are completely destructive. The TIBDs can effectively control the maximum seismic responses and damage degree of the CRFB under pulse-like near-fault ground motions. Among them, both the tuned viscous mass damper and tuned inerter damper are ideal and useful devices. This study can provide useful references for the seismic design and performance analysis of CRFBs.