The work primarily examines the engineering features of earthquake including its amplitude, duration, and spectrum. A main-aftershock evolutionary power spectrum density (EPSD) model has established via utilizing the relationship in terms of peak acceleration, duration, and site predominant frequency of them. Then, the main-aftershock ground motion process may be accurately simulated at the probability level with just three elementary random variables using the spectral representation-dimension reduction method (SR-DRM). An office building's refined dynamic response analysis and reliability evaluation are performed at the probability density level using the probability density evolution method (PDEM) and the extreme reliability theory based on the first passage failure. It is clear reveal from the numerical example that the DRM could be used to produce a small number of representative sample sets which are accurate enough for engineering purposes, and that the information about the set's probability is comprehensive. In addition, it can be used in tandem with the PDEM to yield a wealth of probabilistic information at varying thresholds. This opens a new avenue for studying the seismic response and reliability of frame buildings under main-aftershocks.