# The Influence of Vertical Ground Motion on the Design of Common R/C Frames
## 3 Evaluation of Frames for Vertical Ground Motion
### Evaluation Through Time History Analysis  
Eurocode 8 specifies that time history analysis should be conducted, utilizing three accelerograms as a minimum. In compliance with this code provision, the six frames under consideration were subjected to three ground motions obtained from a free database [32]. In particular, one horizontal component and the vertical component of each record were considered. All records corresponded to near-field earthquakes and experienced significant vertical accelerations. Some relevant information is provided in Table 7. The application of more records (at least seven, according to the codes) in order to obtain the mean values of response quantities which are considered more representative for design purposes was not considered necessary. The objective of the non-linear time history analysis was not the estimation of the exact values of response quantities or the design of the frames, but the demonstration that the fundamental requirements of the conventional design might not be achieved due to the omission of the vertical seismic component. The scaling procedure applied to the accelerograms complied with the specifications of Eurocode 8. Initially, each horizontal accelerogram was multiplied by a scale factor, sf1, in order to equalize its PGA to the design acceleration for zone I of the Greek earthquake hazard map (Table 8). Thus, the Eurocode 8, Part 1 requirement that the mean of the zero-period spectral response acceleration values (calculated from the individual time histories) should not be smaller than the value of a\({}_{\text{g}}\cdot\)S was satisfied. Then, the three elastic response spectra along with the mean elastic response spectrum were plotted, and the ratios, r\({}_{\text{i}}\), of the mean spectral accelerations to the corresponding Eurocode 8 elastic spectrum ordinates were determined. A second scale factor, sf2, common to the three accelerograms, was calculated so that not a single ordinate of the mean spectrum was less than 90 percent of the corresponding ordinate of the Eurocode 8 elastic response spectrum in a period ranging from 0.2T\({}_{\text{1 min}}\) to 2T\({}_{\text{1 max}}\), where T\({}_{\text{1 min}}\) = 1.091 s and T\({}_{\text{1 max}}\) = 1.317 s (Table 4). Namely, the value of sf2 was equal to 0.9/minr\({}_{\text{i}}\). As a consequence, the relevant Eurocode 8, Part 1 requirement was satisfied. Finally, a third scale factor, sf3, was applied to adapt the excitations to the three seismic hazard level zones. sf3 was equal to the ratio of the design ground acceleration, a\({}_{\text{gr}}\), of each zone to the a\({}_{\text{gr}}\) of zone I (Table 1). The product of sf1, sf2 and sf3 was applied to both the horizontal and vertical components of each excitation (Table 8). Indicatively, the horizontal elastic response spectra after the scaling, along with Eurocode 8 and 90% of the Eurocode 8 elastic spectrum for seismic hazard level zone I, are shown in Figure 13. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Earthquake** & **PGA\({}_{\text{H}}\) (g)** & **PGA\({}_{\text{V}}\) (g)** \\ \hline
01 & Imperial Valley & 0.29 & 0.47 \\ \hline
02 & Landers & 0.79 & 0.82 \\ \hline
03 & N. Palm Springs & 0.22 & 0.36 \\ \hline \end{tabular}
\end{table} 
Table 7: Ground motions. In general, the scaling methodology should ensure spectral compatibility in a way that avoids unrealistically high seismic demands inconsistent with the site hazard levels. For example, it is suggested that the spectral ratios, \(\rm r_{i}\), should have an upper limit of 1.1-1.2 [33; 34]. Similarly, the draft of the forthcoming new version of Eurocode 8 specifies an upper limit of \(\rm r_{i}\) equal to 1.3 for the period range 0.2T\({}_{1}\)-1.5T\({}_{1}\). The present study was conducted according to the current version of the Eurocode, which does not specify an upper limit. This enabled the possibility of extremely high \(\rm r_{i}\) values for some periods.