## 1 Introduction
### Background  
The unified procedure usually adopted to carry out IDA was originally formulated by [PERSON] and [PERSON] in [19]. Their approach is based on a simple transformation of the amplitude of a reference \"as-recorded\" accelerogram \(a_{1}(t)\) that is uniformly scaled up or down by a scale factor (SF), denoted \(\lambda\), so that \(\lambda\in[0,+\infty]:\;a_{\lambda}=\lambda\;a_{1}\). In the elastic range, scaling the accelerogram corresponds to scaling the elastic response spectrum or, equivalently, scaling the Fourier amplitude spectrum while keeping the phase information intact. By successively integrating the non-linear motion equations under a given earthquake, which is scaled at each iteration with a different SF, the progressive performance of a structure can be assessed from the elastic to the inelastic range until collapse. To characterize the intensity of the scaled ground motion, a parameter is adopted, namely, the intensity measure (_IM_), which depends on the unscaled accelerogram \(a_{1}\) and increases with the SF \(\lambda\), that is, \(IM=f_{a_{1}}(\lambda)\)[19]. On the other hand, an engineering demand parameter, namely, the damage measure (_DM_) should be chosen to assess the structural responses at different seismic intensity levels. For each given accelerogram, a curve plotting the values of _DM_ as a function of _IM_ can be built. However, a single-record IDA study cannot fully capture the seismic capacity of a building. Therefore, a consistent set of records should be considered to perform a complete multi-record IDA analysis. FEMA (Federal Emergency Management Agency) codes [6; 7] recommend the use of a group of earthquakes registered in the Pacific Earthquake Engineering Research Center (PEER) database. A group of curves can thus be obtained for multi-record IDA analysis, which is expected to give a thorough understanding of the structural demand for different intensity levels of seismic action. Although different _DM_ values can be chosen to assess the seismic demand under earthquakes of different intensities, the maximum interstory drift ratio is widely adopted as one of the most significant parameters. In contrast, the choice of the most appropriate _IM_ value is still much debated (see, e.g., [17; 18; 19; 20; 21; 22; 23; 24; 25]). The reason for this debate is that a suitable choice of _IM_ should account for both the seismological characteristics of the ground motion (which are typically related to the statistical properties of seismic hazard analysis) and the structural response features of the considered building (which can be estimated through the maximum values of the given target engineering parameters). However, due to record-to-record variability, comparatively high scatter in the structural responses under different reference accelerograms may affect the efficiency (the ability to predict the structural capacity independent of the selected record), the sufficiency (no other ground motion information is needed) and the scaling robustness (the ability of the SF to predict the structural response) of _IM_[20; 21; 22; 23; 24; 25] and, consequently, the effectiveness of the whole IDA procedure. Several _IM_ parameters have been proposed in the literature with the aim of meeting the above requirements and reducing the dispersion of the results under different ground motions. Such parameters refer, for instance, to the peak ground acceleration (PGA), peak ground velocity, peak ground displacement, effects of the spectral shape and ground motion duration, Arias intensity, Housner intensity, spectral response, and yield reduction R-factor [17; 18; 19; 20; 21; 22; 23]. Nevertheless, a common choice for _IM_ is the spectral acceleration taken at the structure's first-mode period; for a damping factor \(\xi=5\%\), the spectral acceleration is \(S_{a}(T_{1},\xi)\). The elastic response spectrum is broadly recognized as an excellent tool to link the seismological characteristics of an earthquake to the seismic demand in single-degree-of-freedom systems.