## 4 Conclusions
Among the five different IDA procedures compared in this paper, the standard procedure that refers to the elastic fundamental period produces IDA curves with the most dispersion. The coefficient of the collapse interstory drift ratio is COV = 0.76 in both the \(x\)- and the \(y\)-directions, while COV = 0.98 and COV = 0.73 are found for the collapse spectral acceleration in the \(x\)- and \(y\)-directions, respectively. 2. On the other hand, referring to approximate values of the inelastic period may not lead to significant improvements in the effectiveness of the IDA procedure. In the present study, the methods proposed by [PERSON] et al. and [PERSON] are unable to reduce the COVs of the collapse interstory drift ratio in either of the two directions, while they reduced the COV of the collapse spectral acceleration only in the \(x\)-direction. 3. When the IDA procedure is applied by considering the calculated values of the inelastic period \(T_{inP}\) and \(T_{inSP}\), the dispersion of the results can be significantly reduced, although different impacts of the two values of the inelastic period are detected. 4. The most remarkable improvement is achieved in reference to the inelastic smooth peak period \(T_{inSP}\). Calculating the IDA curves through this value of the elongated period is found to always reduce the COV of both the _DM_ indicator and the _IM_ parameter in any direction with respect to all the other methods. The COV values are halved or even reduced to one-third of those obtained with respect to the standard procedure that refers to the elastic period. It is not surprising that smoothing the spectra decreases the coefficient of variation of the results. However, the adoption of a smooth Fourier spectrum allows to fix issues regarding the dispersion of the results and the inconsistencies in the values of the \"inelastic\" period, which may occur when applying the IDA procedure. On one hand, it is widely recognized that referring to the elastic period usually leads to highly dispersed IDA curves. Much lower dispersed IDA curves are obtained when a reference to the inelastic smooth peak period \(T_{inSP}\) is made instead. On the other hand, it is found in this paper that inconsistent values of period can be taken from the unsmoothed Fourier spectrum. In fact, the higher the scale factor of the seismic record, the more the Fourier amplitude spectrum can exhibit peaks in the range where the predominant frequency falls, makes it rather hard to determine its correct value with confidence. This may lead to obtaining lower inelastic periods for higher scale factors of the input record (that is for higher levels of damage in the structure). This inconsistency can be avoided when reference to the inelastic smooth peak period \(T_{inSP}\) is made. Of course, the fact that the IDA curves are less dispersed and that the values of period are more consistent may be considered merely as an index of more reliable results. Further investigation, however, is needed to assert this fact with certainty. It should also be stressed that the above findings are relevant to the building and to the set of earthquakes considered in this study. Therefore, the effectiveness of the proposed IDA procedure should be assessed in future studies by also considering other types of structures and different sets of earthquakes. Future studies can be also directed to determine the intensity measure (IM) by using \"inelastic\" response spectra relevant to equivalent single degree of freedom systems with elastic-plastic behavior. This would allow a more moderate growth of the intensity measurement. Finally, it is to note that, although most of the works that have sought to reduce the variability of IDA curves have focused almost exclusively on intensity measurements, it is of special importance to reduce the scatter in the _DM_ parameter since determining the collapse value of the building is crucial to carry out the performance-based design. Research design, M.C.P. and J.C.V. ; methodology, M.C.P. and J.C.V. ; earthquake selection, M.C.P.