## 3 Damage Indexes Effectiveness
### MSA Results
Herein, only the damage indexes calculated starting from the moment-rotation values of the RC elements are represented. Similar results are obtained from the damage indexes calculated starting from the floor shear-interstory drift values. Figure 4: (**a**) Example of the computation of the damage index using the M-R approach. (**b**) Graphical representation of the dispersion (D) for a generic limit state i. (**c**) Visualization of the dispersion \(\mathrm{D_{LS,i}}\) and \(\mathrm{D_{LS,i+1}}\) for consecutive limit states. (**d**) Representation of the overlap (\(\mathrm{O_{I}}\)) between two consecutive limit states-performance levels. In order to better assess the efficiency of each damage index, specific parameters are introduced to highlight their accuracy in detecting damage while minimizing the overlap between the limit states and reducing the dispersion of the data. The dispersion (D) measures the variability of the values within a given limit state-performance level by calculating the difference between the maximum and minimum values in the interquartile range and provides an indication of the accuracy of the data. This is shown graphically in Figure 4b,c. The overlap parameter (O) evaluates the potential overlap between consecutive limit states and indicates the risk of misinterpretation of the damage levels and the uncertainty in distinguishing between them. Figure 4d graphically represents this parameter, which reflects the precision and reliability of the damage indexes in the assessment of seismic performance. Tables 10 and 11 summarize the results of damage index curves plotted in Appendix A, where the damage index values are plotted as a function of the spectral acceleration. The comparison of the individual indexes aims to provide a clear evaluation of the efficiency of the damage indicators for the different structural systems in both bare and infilled frame configurations. The results for each building configuration are reported in Appendix B. In these tables, indexes are cited as L-S for Lybas and Sozen (1977) [4], FDR for [PERSON] et al. (1977) [5], B-V for [PERSON] and [PERSON] (1982) [6], P-A for [PERSON] and Ang (1985) [8], W-S-1 for [PERSON] and Shah (first formulation (1987)) [10] and P-Al for [PERSON] and Allahabadi (1988) [11]. When analyzing the damage indexes for different building typologies (as also reported graphically in Appendix A), especially in the bare frame configuration, the indexes show strong capabilities in detecting and quantifying damage. In this configuration, the indexes exhibit remarkable uniformity in damage quantification, with overlaps O1 and O2 equal to zero for all damage indexes (except for Lybas and Sozen) and low dispersion values (D). This underlines their potential for effective \"real-time\" damage detection in BF configurations for all building types. Conversely, the performance of these indexes decreases when evaluating infilled structures. While all indexes successfully track incremental damage with increasing intensity, they exhibit greater variability, with larger dispersion values (D) and increased sensitivity to building typology. This greater heterogeneity leads to a significant overlap between the different damage states, with higher values already from O2 for LS-CP. These overlaps reduce the effectiveness of the damage indexes and limit their applicability for the reliable prediction of damage in infilled structures. In particular, in the bare-frame configuration for existing MRF and SW buildings, the L-S and P-A indexes show high efficiency for the UPD and LS limit states. They exhibit no overlap O1 and O2 and a low to medium dispersion, ranging from less than 5% for UPD to 25% for LS. However, for the CP and GC limit states, their efficiency decreases significantly due to a significant overlap (about 95%) and a larger dispersion of about 10% to 80%. Similarly, the B-V, W-S-1 and P-Al indexes show high efficiency for UPD for all building types, with a very good LS performance for frame systems.