## 4 Conclusions  
A new IDA procedure is presented in this paper with the aim of reducing the high record-to-record variability of the curves representing the maximum demand on a given building at different scaled seismic intensities. Here, the seismic intensity is measured through the \(\xi=5\%\) damped spectral acceleration at the structure's first-mode period, where the first-mode period is assumed to be the elongated inelastic period exhibited by the system when it deforms in the plastic range. Two different methods are adopted to obtain the value of the inelastic fundamental period: the first one obtains the inelastic peak period \(T_{inP}\) from the fundamental frequency taken at the maximum peak of the Fourier amplitude spectrum of the acceleration of a building's reference point; the second method calculates the inelastic smooth peak period \(T_{inSP}\) from a smooth Fourier spectrum derived from the original spectrum by means of a suitable filtering technique. The efficacy of adopting a smooth elongated period is expected to still be valid regardless of the approach adopted to smooth the Fourier spectrum in the range where the elongated period of the considered structure falls. An investigation is presented in the paper to assess the effectiveness of the proposed new IDA procedure. By referring to a R/C building and to a set of 10 earthquakes, consistent with the design response spectrum relevant to a high-seismicity zone of Italy, multi-record IDA is carried out by considering a 3D finite element model of the building with non-linear behavior (distributed plasticity model). The first part of the present study analyzed the variation in the inelastic period as a function of the seismic intensity, the latter being evaluated in terms of PGA. The following results were found in this preliminary analysis. 1. The value of the elongated \"inelastic\" period calculated as the peak period \(T_{inP}\) or as the smooth peak period \(T_{inSP}\) can be much higher than (even more than twice) the elastic fundamental period of the structure and increases as the earthquake intensity level increases. 2. Some approximation methods proposed in the literature to estimate the elongated inelastic period are found to often deviate from the rigorous values (given by \(T_{inP}\) or by \(T_{inSP}\)). 3. The values of the elongated period obtained through time-history analysis (\(T_{inP}\) or \(T_{inSP}\)) are found to depend on the PGA of the given accelerogram. As expected, however, this dependence is far from monotonic and predictable since the PGA is not able to unequivocally define the violence of an earthquake. Of course, higher PGA values typically imply that the structure reaches higher levels of damage, which directly affects the value of the elongated period. However, further studies on the variation in the elongated period with respect to the characteristics of the structure and of the earthquakes are still required. 4. Much more gradual growth of \(T_{inSP}\) with increasing PGA values is found with respect to \(T_{inP}\). In fact, \(T_{inSP}\) is obtained from the smooth Fourier spectrum, which avoids abrupt changes in the period values while guaranteeing that the predominant frequency is found in the frequency band containing the highest Fourier amplitudes. This generally leads to a more suitable relationship between the elongated structural period and the intensity measure of the earthquake. The second part of the study investigated the effectiveness of the proposed IDA procedure based on calculating the earthquake _IM_ as the spectral acceleration taken at either the peak period \(T_{inP}\) or the smooth peak period \(T_{inSP}\). A comparison is performed among the IDA curves derived through the new procedure, those obtained with the standard procedure that refers to the elastic fundamental period, and those obtained with the procedure that refers to the approximate values of the inelastic period proposed in the literature. The following conclusions can be drawn from the results. 1.