## 2 Strategies to Model Behaviour of FPS and of Masonry Infills in RC Framed Structures
### Modelling Mechanical Behaviour of Masonry Infills for Seismic Assessment  
The principal role of infills in framed buildings derives from the need to confine the external environment from the internal one or to separate the internal compartments. As widely recognized, the masonry panels are able to interact with the surrounding RC structural frame in the presence of significant lateral actions [32; 33]. This interaction produces both positive and negative effects on the overall response of the structure, as can be deduced from the post-earthquake observed damage scenarios [34]. In fact, although the overall stiffness of the structural system turns out to be increased, the presence of infills leads to a reduction in the natural period with the related increase in the seismic spectral acceleration. Moreover, with particular reference to partially infilled panels, their presence provides additional stiffness locally, increasing the shear demand on columns that can collapse with brittle mechanisms (e.g., captive and short column effects) [35]. For instance, despite the inevitable modeling issues, neglecting such elements in the refined non-linear analysis of RC frames may not allow to properly estimate the actual stiffness, resistance, and ductility of the structure system [33; 36; 37]. The scientific literature proposes different approaches to account for masonry infills within the definition of numerical models of RC frames. These ones can be classified primarily as micro-modeling and macro-modeling [37]. In the present investigation, the macro-modeling approach is adopted according to [37] for the fully infilled masonry panels to consider the effects deriving from the interaction between the infills and RC members. Specifically, they are reproduced by means of a single-strut model able to take into account the masonry mechanical non-linearities. According to [37], the strut can be defined by adopting a fiber-modeling approach with fibers characterized by the appropriate constitutive law able to reproduce the macro-behavior of the masonry panel [37]. As suggested in [37; 38], the above-mentioned constitutive law can be defined similarly to the one used for concrete, in which the peak strength \(f_{mld}\), the corresponding deformation \(\varepsilon_{mld}\), the ultimate resistance \(f_{mld}\), and the related deformation \(\varepsilon_{mld}\) are assigned depending on the mechanical and geometric properties of the masonry, which are introduced in the next. With reference to the macro-modeling of the partially infilled masonry panels, approaches able to take into account their non-linear behavior, without large uncertainties, are scarce in the scientific literature. For instance, they have been reproduced by means of a single-strut model with elastic behavior in order to take into account unfavorable effects related to shear demand on columns [35]. In order to characterize the geometrical configuration of the macro-model with a single strut for each partial infill under examination, a micro-model using shell elements has been defined using the SAP200 software platform [25] according to Figure 2. The thickness of the shell elements used for micro-modeling has been defined in accordance with the geometry of the masonry panel, while the interface between the shells and the surrounding RC frame has been reproduced using spring elements [25] able to take into account the friction between concrete and masonry (using a friction coefficient equal to 0.45 [37]). In order to define an equivalent macro-model, the width of the single strut was determined by a trial-and-error process until the same displacements, monitored at the top of the panel in the presence of horizontal force, were obtained for the macro-models with respect to the micro-models. The evaluation mentioned above has been performed for all the different geometrical configurations of the partial infills of the RC frame.