# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 2 Methods
### Numerical Modelling and Investigation on a Reinforced Concrete Frame Structure  
The proposed methodology is applied to a 10-story, 3-bay reinforced concrete frame structure that complies with EC2 and EC8 standards [1; 2]. The designed structure is doubly symmetric and regular, both in-plan and in-elevation, to eliminate the impact of torsional effects that could potentially skew the results. This building type is widespread in regions with high seismicity (e.g., in Greece). Using a two-dimensional model allows for accurate investigation of the ductile behavior of regular R/C buildings without the performance overhead of three-dimensional analyses. On the other hand, a 2D structural model neglects torsional and directionality effects. However, the present study focuses not on the effects previously mentioned but on the interrelation between seismic intensity parameters and overall structural Damage Indices. The loads considered in the analysis were self-weight, live, snow, wind, seismic excitation, and geometric imperfections. Regarding environment, soil, and seismicity conditions, exposure class XC3 and soil type B were considered, and a design acceleration of 0.24 g was achieved. The structure was designed for the medium ductility class (DCM) and importance class II. The beam and column dimensions (in cm) are illustrated in Figure 1. The slab thickness was 0.20 m, and the T-beam effective flange widths were calculated according to Eurocode standards. The fundamental period of the test frame was computed as T\({}_{1}\) = 1.25 s.  
Figure 1: Schematic representation of the examined reinforced concrete frame structure. \begin{table}
\begin{tabular}{c c c c} \hline
**Damage Grade** & **MISDR** & \
\begin{tabular}{c} **Modified** \\ **Park–Ang** \\ \end{tabular} &
\begin{tabular}{c} **Maximum** \\ **Softening** \\ \end{tabular} \\ \hline Minor & \(\leq\)0.5\% & \(\leq\)0.30 & \(\leq\)0.30 \\ Moderate & 0.5–1.5\% & 0.30–0.60 & 0.30–0.60 \\ Severe & 1.5–2.5\% & 0.60–0.80 & 0.60–0.80 \\ Partial or Total Collapse & \(\geq\)2.5\% & \(\geq\)0.80 & \(\geq\)0.80 \\ \hline \end{tabular}
\end{table} 
Table 3: Classification limits for various Damage Indices. Upon design and detailing completion, the test frame was modeled in the computer program IDARC-2D [7] and was subjected to a series of non-linear time history analyses for all the selected ground motions to obtain all the necessary data (MISDR, DIPA, Fundamental Period). The test frame was initially subjected to all 180 unscaled accelerograms. Then, a scale factor was adopted for each accelerogram. It was determined in such a way that, using the MISDR as the target parameter, the scale factor of each accelerogram was adjusted until a uniform set of the damage grades was achieved, i.e., 60 cases of minor, 60 cases of moderate, and 60 cases of severe damage sustained to the structure, respectively. IDARC-2D features distributed and concentrated plasticity elements with uniform and linear flexibility distributions for their rigid ends. The program incorporates a polygonal hysteretic model with stiffness degradation, strength deterioration, and pinching behavior to simulate the hysteretic response of reinforced concrete members. In this study, distributed plasticity elements with linear flexibility distribution were selected, as the calibration of the hysteretic response parameter set with experimental data has been conducted on this type of element, given that prior releases of the program did not contain all of the above options. Nominal values without slip effects corresponding to structures designed according to the Eurocodes mentioned above were adopted in the current study. The hysteretic parameters have been calibrated with experimental data, as found in the case studies section of [7] for various reinforced concrete structures. Furthermore, a Rayleigh damping model was assigned to the structure, with 5% critical damping.