To further study the global seismic behaviour and post-earthquake reparability of RC building frames with the proposed self-centring columns with low-bond high-strength reinforcements (LBHSRs), incremental dynamic analysis (IDA) of five-floor and ten-floor frame archetypes under excitation by twenty ground motions (GMs) was performed. First, the pushover results indicated that the use of LBHSR could substantially improve the yield and ultimate lateral drift of both the archetypes, although the archetype had a smaller longitudinal reinforcement ratio (LR) of the LBHSR and similar seismic resistance. The dynamic response results indicated that the archetype with LBHSRs exhibited a smaller residual story lateral drift although the effectiveness of the use of LBHSR to reduce seismic response was not apparent for the archetype subjected to a low-intensity earthquake. The seismic fragility results showed that LBHSR was more effective for preventing seismic collapse than for attaining the immediate occupancy (IO), life safety (LS), and collapse prevention (CP) limit states. Furthermore, the higher the LR, the lower was the likelihood of seismic collapse. The fragility curves of the residual story lateral drifts indicate that the use of LBHSR can significantly mitigate the residual deformation in the DS1, DS2, and DS3 damage states. Moreover, the effectiveness increases with the increase in the LR and earthquake intensity. Comparisons of residual story lateral drifts between the predicted results and IDA results indicated that the present calculation models are not suitable for predicting residual deformation. The model needs to be studied further.