## 5 Discussion
### Summary of the Discussions  
In this section, the discussions are focused on the four points that are important to discuss the accuracy of MABPA. The summary of the discussions are as follows.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Ground**} & **First Mode** & **Second** & **Third Mode** & & \\  & \(V_{\Delta E}\)(\(T_{1 eff}\)) & **Mode** & \(V_{\Delta E}\)(\(T_{2 eff}\)) & **Ratio** & **Ratio** (2 nd/1 st) & **Ratio** (3 rd/1 st)** \\ \hline UTO0414 & 0.4108 & 0.4232 & 0.7151 & 1.030 & 1.741 \\ TCU & 0.7575 & 0.7319 & 0.2519 & 0.9662 & 0.3325 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Equivalent velocities of the maximum momentary input energy predicted from the bidirectional \(V_{\Delta E}\) spectrum (\(\beta\) = 0.100).  
Figure 42: Comparisons of the modal responses at the edge of level 0 (structural model: Model-T34, ground motion: TCU, angle of incidence of seismic input: \(\psi\) = 60\({}^{\circ}\)): (a) \(X_{1A}\) and (b) \(X_{6A}\).  
The relationship between the maximum momentary input energy and the peak equivalent displacement of the first modal response was discussed in Section 5.2. The results confirmed that the \(V_{\Delta E\mu 1U}{}^{*}\)-\(D_{1U}{}^{*}\) curve obtained from pushover analysis results fit the plots obtained from the time-history analysis results very well. This is because the contribution of the first modal response to the whole response may be large in both Models Tf34 and Tf44.  
Then, the predictability of the maximum momentary input energy of the first modal response was discussed in Section 5.3. The results confirmed that bidirectional \(V_{\Delta E}\) spectrum can approximate the upper bound of the equivalent velocity of the maximum momentary input energy of the first mode \(V_{\Delta E1U}{}^{*}\). This is because that the maximum momentary input energy of the first mode was calculated from the unidirectional input in U-axis, while the effect of simultaneous bidirectional input was included in the calculation of bidirectional \(V_{\Delta E}\) spectrum automatically.  
Since (a) the \(V_{\Delta E\mu 1U}{}^{*}\)-\(D_{1U}{}^{*}\) curve can be properly predicted from the pushover analysis results, and (b) the upper bound of the equivalent velocity of the maximum momentary input energy can be predicted via the bidirectional \(V_{\Delta E}\) spectrum, the largest peak equivalent displacement should be predicted accurately. The accuracy of the predicted equivalent displacements of the first and second modal responses was discussed in Section 5.4. The results confirmed that the upper bound of the peak equivalent displacement of the first and second modal responses can be predicted accurately.  
Although the upper bound of the peak equivalent displacement of the first and second modal responses can be predicted accurately, the accuracy of the predicted horizontal distributions of the peak displacement at level 0 depends on the ground motion dataset. Section 5.5 discussed the contribution of the higher mode to the displacement response at the edge of level 0. The results showed that higher modal responses may not be negligible for the prediction of the peak displacement at the edge of level 0. In the MABPA prediction, only the contributions of the first and second modal responses were considered. Therefore, a discrepancy of the predicted results from the time-history analysis may occur because of the lack of a contribution from the higher modal responses.