## 3 Numerical Applications  
In order to test and verify the performance of the upgraded Curvature Evolution Method (CEM), the method has been applied to several nonlinear numerical models representative of realistic reinforced concrete framed structures characterized by 3, 5 and 8 floors, with regular and irregular geometric plans designed by considering only gravity loads (Figures 2 and 3). The inter-story height is constant and equal to 3 m, resulting in a total height of the buildings equal to 9 m, 15 m and 24 m, respectively. With reference to the mechanical properties of the materials adopted in the numerical models, the concrete is characterized by a compressive strength equal to 25 MPa, whereas the steel by a yield stress equal to 380 MPa. Reinforced concrete floors with a thickness of 25 cm have been considered. The dead load was set as 5 kN/m\({}^{2}\), while the live load was 2 kN/m\({}^{2}\). Nonlinear numerical analyses have been carried out using a software tool based on nonlinear finite elements (SAP2000 non-linear [47]). A kinematic constraint has been added to each floor to simulate the slab as rigid diaphragms. Structural elements, such as beams and columns, were modeled with type elements \"FRAME\", while the non-linear characteristics have been applied using the \"LINK\" elements. Link elements and plastic hinges were introduced at the ends of both beam and column elements to simulate the structural nonlinear behavior during a strong ground motion. Link elements have a Pivot hysteretic behavior, while plastic hinges have an axial load-dependent one. Rigid offsets at beam-column joints have been considered. Figure 4 shows the Force-Deformation relationship of the link elements used for the nonlinear numerical analyses. The masses were considered distributed on the structural elements. Figure 3: Numerical model of a building that has an irregular plan with 5 floors. Figure 2: Numerical models of structures that are regular in plan: (**a**) 3 floors, (**b**) 5 floors, (**c**) 8 floors. In order to define the damage threshold of even the non-structural component, the numerical simulations have been carried out by modeling the effects caused by the presence of infill panels within the structural R/C framed models (Figure 5). Both the masonry strength and stiffness contribution have been considered by introducing two equivalent structural elements in the models. The mechanical characteristics of these elements were evaluated considering the Mainstone model, through the Equation (4) [48]:  
\[b_{w}=d_{w}.0.20\cdot sin\ sin\ 2\theta\cdot\left(\frac{E_{w}\cdot t_{w}\cdot h_{w} ^{3}\cdot sinsin\ 2\theta}{E_{c}\cdot I_{p}}\right)^{-0.1}\cong\frac{1}{10}d_{w} \tag{4}\]  
where \(b_{w}\) is the equivalent width, \(h_{w}\) is the panel height, \(d_{w}\) is the strut length, \(t_{w}\) is the panel thickness, \(\theta\) is the angle that the strut forms with the horizontal line, \(E_{w}\) is the elastic modulus of the panel, chosen as 2000 N/mm\({}^{2}\), \(E_{c}\) is the elastic modulus of the concrete and \(I_{p}\) is the moment of inertia of the columns. In the simulation, a 12 cm + 8 cm thick panel has been considered. Using the SAP2000 finite elements program, these elements were modeled using multi-linear plastic links. The Force-Displacement behavior of the Mainstone model is depicted in Figure 6a. Concentric connection of the equivalent diagonal struts has been considered in the modelling strategy (Figure 6b). This sees a fundamental period of vibration of the 5-story infilled numerical model to be 0.51 s. Table 1 reports the value of the fundamental periods of vibration of the numerical models. Figure 4: Multilinear plastic link with Pivot hysteretic model used for the nonlinear numerical analyses in SAP2000. Figure 5: Numerical model of the infilled framed structure.