## 7 Short-Length Energy-Saving Accelerograms for Numerical Analyses

Table 10: Duration and Arias Intensity for IBC-C-X-E5 (from SeismoSignal). Figure 10: Procedure to obtain a suitable time-window for time-history analyses. (**a**) Full-length X and Y accelerations; (**b**) Arias Intensity of the two components of the earthquake, where the range from 5% to 95% is highlighted in green; (**c**) time windows corresponding to 5–95% of \(I_{A}\) in green; (**d**) final chosen time-window for the two components, in red; (**e**) cut earthquake components for the numerical analyses. Additionally, the beams have symmetrical longitudinal reinforcements for the upper and lower layers, consisting of 4 bars of 20 mm. The applied loads correspond to those of a building with solid reinforced concrete slabs measuring 15 cm in thickness, with a tributary width of the slabs of 3 m. The applied live loads correspond to those of a residential building (2 kPa). The archetype with gravity loads and the accelerations imposed on the supports in the \(X\) direction is shown in Figure 11.  
NLTHAs were conducted by assuming that the reinforcing steel and the concrete follow the constitutive relationships proposed by [PERSON] and [PERSON] [55] and by [PERSON] et al. [56], respectively. The analyses were conducted considering only the accelerograms consistent with the EC8 spectra (the suites plotted in Figure 8). NLTHAs were carried out under full-length and short length accelerograms. To validate the procedure, two variables of the seismic response of the archetype have been investigated as target parameters: the horizontal displacement of the center of gravity of the roof level (defined by the connection of the central column and the beam at this level) and the total shear force at the base. For each analysis, the maximum values of roof displacement and total shear at the base were obtained. The absolute difference between the values of such parameters calculated under full-length and short length accelerograms was obtained. This difference (in %) and the mean value over the seven earthquakes are provided in Table 11. It can be noted that EC8, like other codes, advocates working with mean values instead of considering maximum values whenever more than three accelerograms are considered for the analysis. The results indicate that the differences between the values obtained with full-length and short length accelerograms are relatively small. The maximum difference between the roof displacements is 10.5% (reached for accelerogram 2 and soil type C). The maximum difference between the shear forces is 12.8% (reached for accelerogram 4 and soil type E). However, it is worth noting the arithmetic mean of the calculated differences does not exceed 5% either for displacements or for base shear (see \"Mean\" columns of Table 11). This validates the effectiveness of the procedure, at least for the kind of structure and the earthquakes considered here. All the accelerograms given in Figures 7 and 9 have been processed according to the above suggested procedure and the corresponding short length accelerograms have been obtained. They can be freely downloaded from a repository hosting them, as indicated at the end of the paper. It is worth noting that, on average, the short-length EC8 and IBC  
Figure 11: Elevation view of the structural archetype considered to validate the procedure. consistent accelerograms are found to be, respectively, about 1/5 and 1/4 of the full-length ones, although much stronger reductions are achieved for some of the accelerograms. This time-length shortening can drastically reduce the computational time, particularly when non-linear analyses of three-dimensional structures are involved. Some of the short-length IBC-spectrum-consistent earthquakes were successfully used to carry out NLTHAs on a Lebanese historical hammam and predict its post-elastic seismic behavior [57].