To investigate the influence of mainshock-aftershock sequences on displacement responses, failure mode, global damage evolution, etc of structures, the sequences are generated by combining the next generation attenuation (NGA) relationship for earthquakes with the relationship between main shock and strong aftershock. The modified section damage ratio model is applied to analyze additional damage of an example structure under strong aftershocks, as well as probabilistic accumulative damage. The investigation indicates that additional damage incurred by strong aftershocks tends to increase as their probabilities of exceedance (POE) decrease. Approximate negative correlation could be observed between the damage ratios of main shocks and those added by strong aftershocks. When structures experience substantial damage under main shocks, probabilistic accumulative damage of structures would change significantly even coupled with damage induced by low-level aftershocks. Additional damage would be aggravated by so-called analogous resonance phenomenon when the predominant periods of the response spectra of these aftershocks are close to the vibration periods of damaged structures under main shocks.