## 3 Damage Indexes Effectiveness
### Numerical Modeling  
For the numerical analyses, two finite element models have been developed. For the design phase, elastic models were developed with the software Midas GEN v.1.1 [19] and response spectrum analyses were conducted. For the performance assessment phase, non-linear models were developed with the software Opensees [20] and non-linear response history analyses were conducted.  
For the response spectrum analyses, RC elements were modeled as _beam_-type elements with flexural stiffness scale factors equal to 0.7 and 0.5 for columns and beams, respectively. As for the shear walls, a stiffness scale factor equal to 0.7 was considered and the beam-to  
Figure 2: Reference plan and frontal view of the perimetral frame for (**a**) the existing structure (EX_MRF), (**b**) code-conforming moment-resisting frame (CC_MRF) and (**c**) code-conforming wall (CC_W).  
After completing the design phase, the final cross-section, the amount of longitudinal and transverse reinforcement, and the axial load in seismic condition were used to define the non-linear behavior of the structure. Two non-linear models were defined for each building configuration: the bare frame (BF) model, where only the infill mass is considered, and the infill frame (IF) model, which considers the contribution of the infills with an equivalent compression-only strut. Lumped plastic hinges were introduced to capture the non-linear behavior with the PeakOriented hysteretic model developed by [PERSON] (IMK) [21] (Figure 3a). Such hinges were applied by means of _zeroLength_ elements in the end sections of the elements, while the inner part of the member was modeled with _ElasticBeamColumn_ elastic frame elements.  
The infill panels were modeled as compression-only diagonal struts whose backbone curve values were derived from [PERSON] et al. [22] and adapted according to available experimental tests [23; 24] and on the masonry properties defined by [PERSON] et al. [25]. An example of the backbone curve is represented in Figure 3b whose values for a typical 30 cm thick infill panel with 2.65 m \(\times\) 4.15 m dimensions are \(\Delta_{\rm y}\), F\({}_{\rm y}\) (0.30%, 388 kN), \(\Delta_{\rm m}\), F\({}_{\rm m}\) (0.50%, 485 kN) and \(\Delta_{\rm m}\), F\({}_{\rm m}\) (1.86%, 0 kN).  
For the non-linear assessment, Multi-Stripe Analyses (MSA) were conducted. MSA is a method that enables the evaluation of the seismic behavior of structures under earthquake scenarios with increasing intensity measures (IM) of ground motion. This method stems from the work of [PERSON] et al. [26] and aims to calculate the distributions of one or more Engineering Demand Parameter for several scenarios of ground motion records represented by an intensity measure, herein represented by the elastic spectral acceleration, S\({}_{\rm a}\)(T\({}_{\rm j}\)), at the fundamental period of vibration of the building, T\({}_{\rm j}\).  
Ten intensity measure levels (IMLs) were considered for each building type and configuration (i.e., BF, IF) corresponding to return periods of 10, 50, 100, 250, 500, 1000, 2500, 5000, 10,000 and 100,000 years for the site of L'Aquila (high seismicity area in Italy), with a soil category C [27]. For each intensity level, 20 different ground motions were selected from the DPC-ReLUIS project and were used to evaluate the Engineering Demand Parameters (EDP) [28; 29] adopting the conditional mean spectrum approach [30]. The conditioning periods at which the various spectra of the chosen ground motion converge to the spectral acceleration at each intensity level are reported in Table 8.  
Figure 3: (**a**) Modified Ibarra–Medina–Krawinkler deterioration model (image from [20]) and (**b**) masonry infills backbone curve.