Abstract: The inelastic lengthening rule of the fundamental period of a structure due to its softening under the enlarging of earthquake forces is derived by SPO. The structural asymptotical softening and damage along the IM increasing in IDA are analyzed. An asymptotical IM function for IDA was presented. The comparison between the elastic spectrum and Cordova’s two-parameter models show that the asymptotical IM function can improve the convergence of IDA curves. All the improvements and results from these researches are available for the aseismic performance evaluation of a building, which was based on nonlinear seismic response analysis.