## 4 Recommendation on Improving the Efficiency of Intensity Measures
### EDP-IM Relationship
#### 4.2.1 Period Dependence  
In this section, we investigate the structural period dependence of the estimated correlations by classifying frames by their natural period. Figure 6 illustrates the variation of correlations of peak measures, spectral measures, and energy measures with fundamental period of the structure. We observe that correlations of peak measures show significant variations with fundamental period (Figure 6a). \(PGA\) exhibits strong correlations for short-period structures (T < 0.4 s), and \(PGV\) shows strong correlations for intermediate-period (0.4 < T < 0.8 s) and long-period structures (0.8 < T < 1.2 s). Although the correlations with \(PGD\) reveal an increasing trend with period, \(PGD\) does not saturate to a constant value \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Parameter** & **Value** \\ \hline \multirow{8}{*}{Concrete} & \(f_{pc}\) & 25 MPa \\  & \(c\) & 0.002 \\  & \(\mathrm{p}\mathrm{s}\mathrm{o}\) & \\  & \(f_{pcu}\) & 2 MPa \\  & \(c\) & 0.0035 \\  & \(\mathrm{p}\mathrm{s}\mathrm{u}\) & \\  & \(E_{o}\) & 29/00 MPa \\  & \(\lambda\) & 0.1 \\  & \(f_{t}\) & 3.5 MPa \\  & \(E_{ts}\) & 1750 MPa \\ \hline \multirow{3}{*}{Steel} & \(f_{y}\) & 500 MPa \\  & \(E_{o}\) & 200/00 MPa \\ \cline{1-1}  & \(b\) & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Material properties for concrete and steel models used for modeling frames. for the structural periods considered. Therefore, we conclude that \(PGD\) is not a good IM indicator for building frames for this range of natural periods. Figure 5: Correlation between inter-story drift ratio and six intensity measures. Bold numbers denote the correlation coefficient, efficiency, practicality, and proficiency of IMs with respect to equation \(log\ (\Delta)=a+b*log\ (IM)\) (red line). Variability (sigma) is computed as the mean of residual (\(\delta\)) from equation \(log(\Delta)=a+b*log\ (IM)+\delta\). (**a,b**) correspond to peak measures (\(PGA\), \(PGV\)) and (**d,e**) correspond to spectral measures (\(ASI\), \(VSI\)). (**c,f**) are for significant duration (\(T_{sig}\)) and Arias intensity (\(I_{A}\)). Figure 6b depicts the variation of correlations between spectral parameters and ISD with the fundamental period of structures, as well as the correlations between significant durations and _Sa(T)_. _Sa(T)_ seems to be an applicable IM over the entire range of natural period. Since _ASI_ and _VSI_ are influenced by high-frequency and intermediate-frequency contributions of the pseudo-spectral acceleration and velocity response, they exhibit strong correlations at the corresponding natural periods. The good performance of spectral measures over peak measures to predict building response is consistent with previous studies [10; 11; 12; 98]. This can be attributed to the fact that spectral shape of ground motion affects the building response and that peak measures are not representative of the shape of the spectra. Figure 6c shows the period-dependent correlations of energy measures. _A_RMS and _I_A exhibit correlations of around 0.9 for short period structures and decrease with period. For _CAV_, correlations are around 0.8 and remain almost invariant with the natural period. For the building frames modeled in our study, we do not observe any correlation of ISD with ground motion duration, _Tsig_. Several studies have shown that longer ground motion durations impart a larger number of cycles of earthquake loading on the structure,  
Figure 6: Correlations between IMs and EDPs as a function of structural period. (**a**-**c**) are for peak, spectral and energy measures, respectively. _PGA_ and _PGV_ exhibit good correlation; _PGA_ decreases with period. The correlation with _PGV_ increases with period, with a slight decrease beyond 1.2 s; the correlation with _PGD_ is moderate and increases with period. Among the spectral measures, the correlation for _ASI_ is similar to that of _PGA_, and _VSI_ is similar to that of _PGV_. For long period structures, correlation with _VSI_ remains almost constant.