# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 2 Methods
### Damage Indices
Since it is closely related to the maximum attained member rotations, inter-story drift is an easily calculated quantity that many building codes and guidelines use as the preferred indicator to limit damage formation on structures. Reference [16] presents inter-story drift limits for various structural damage degrees, with a 2.5% threshold inter-story drift \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**RSN** & **Seismic Event** & **Station** & **Magnitude** & \begin{tabular}{c} **Hypocenter** \\ **Depth** \\ **(km)** \\ \end{tabular} & \
\begin{tabular}{c} **Epicentral** \\ **Distance** \\ **(km)** \\ \end{tabular} &
\begin{tabular}{c} **V\({}_{\text{s30}}\)** \\ **(m/s)** \\ \end{tabular} & **Components** \\ \hline
3764 & Northridge-02 & LA—UCLA Grounds & 6.05 & 6.00 & 23.53 & 398.42 & 0, 90 \\
3779 & Northridge-06 & Glendale—Las Palmas & 5.28 & 13.09 & 22.72 & 371.07 & 177, 267 \\  & Chi-Chi & & & & & & \\
3845 & (aftershock 2), Taiwan & CHY006 & 6.20 & 7.80 & 39.60 & 438.19 & 0, 270 \\  & Chi-Chi & & & & & & \\
3865 & (aftershock 5), Taiwan & CHY006 & 6.30 & 16.00 & 56.64 & 438.19 & 0, 270 \\
4031 & San Simeon, CA & Templeton—1-story & & & & & \\
4040 & Bam, Iran & Bam & 6.6 & 6.00 & 12.59 & 487.40 & 8, 278 \\  & Parkfield-02, CA & Slack Canyon & 6.00 & 8.10 & 31.53 & 648.09 & 0, 90 \\
4114 & Parkfield-02, CA & Parkfield—Fault Zone & 6.00 & 8.10 & 9.28 & 541.73 & 0, 90 \\
4284 & Basso Tirreno, Italy & & & & & & \\
4456 & Yugo. & Petrovac—Hotel Olivia & 7.10 & 7.00 & 28.30 & 543.26 & 0, 90 \\
4861 & Chuetsu-oki & Nakanoshima Nagaoka & 6.80 & 9.00 & 23.28 & 319.00 & 0, 90 \\
5663 & Iwate & MYG004 & 6.90 & 6.50 & 35.40 & 479.37 & 0, 90 \\
5819 & Iwate & Ichinoseki Maikawa & 6.90 & 6.50 & 30.72 & 640.14 & 0, 90 \\
5823 & Cucapah & Chihauhua & 7.20 & 5.45 & 20.63 & 242.05 & 0, 90 \\
6059 & Big Bear-01 & Morongo Valley Fire & & & & & \\
6952 & Darfield, New Zealand & & & & & & \\
8157 & Christchurch, New Zealand & & & & & & \\
8169 & San Juan & Geophysical Obs., Hollister, CA, USA & & & & & \\
9071 & 14151344 & Pinson Flats Observatory, CA, USA & & & & & \\
11133 & 21530368 & Sonoma Mountain & 4.50 & 6.99 & 2.19 & 664.57 & 0, 90 \\
12261 & 40199209 & Oakland—Hwys 13 and & & & & & \\
20125 & 40204628 & Coe Ranch & 5.45 & 7.49 & 21.25 & 400.00 & 0, 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._corresponding to collapse. Dividing the MISDR with the threshold value allows direct comparison with other DIs. The Modified Park-Ang Damage Index [7] is one of the most widely used Damage Indices that incorporates ductility and hysteretic energy dissipation in a single expression, effectively capturing damage induced by both monotonic and cyclic loading effects:  
\[\text{DI}_{\text{PA,local}}=\frac{\theta_{\text{m}}-\theta_{\text{r}}}{\theta_{ \text{u}}-\theta_{\text{r}}}+\frac{\beta}{\text{M}_{\text{y}}\cdot\theta_{ \text{u}}}\cdot\text{E}_{\text{T}} \tag{2}\]  
where \(\theta_{\text{m}}\) is the maximum attained rotation during load history, \(\theta_{\text{u}}\) is the cross-sectional ultimate rotation capacity, \(\theta_{\text{r}}\) is the recoverable rotation at unloading, \(\text{M}_{\text{y}}\) is the section yield moment, \(\text{E}_{\text{T}}\) is the dissipated hysteretic energy, and \(\beta\) is a strength deterioration control parameter that is related to the degree of section detailing, with a higher value indicating a poorly detailed cross-section. The global value of the Modified Park-Ang DI (\(\text{DI}_{\text{PA}}\)) is calculated with a weighted average procedure, with the dissipated hysteretic energies acting as the weights of their respective sections:  
\[\text{DI}_{\text{PA}}=\frac{\sum_{i=1}^{\text{n}}\text{DI}_{\text{PA,local}_{i} }\cdot\text{E}_{i}}{\sum_{i=1}^{\text{n}}\text{E}_{i}} \tag{3}\]  
where n is the number of locations of the computed local Damage Indices.