## 2 Materials and Methods
### Finite Element Modeling and Analysis  
The seismic analysis was conducted using Pro_Sap, which is software developed by the Italian company 2S.I. Software e Servizi per L'Ingegneria S.r.l. (Ferrara, Italy). The case study building was modeled in the software both before and after the installation of the Resisto 5.9 Tube system to assess its contribution to the seismic upgrading of the existing RC structure. The structure was evaluated through nonlinear static analyses, and the seismic safety factor was calculated in accordance with the Italian code. Pushover analysis is the most common method used to investigate the seismic behavior of existing buildings, considering that nonlinear dynamic analyses are more complex procedures that are unknown to many designers. Only mechanical non-linearities were considered. RC members were modeled as bidimensional beam elements with nonlinear properties using a concentrated plasticity model with assigned values for the plastic hinges' capacities, while steel X-bracings were modeled as non-linear trusses. The values of plastic moments to be considered in the non-linear analysis were automatically assessed by the Pro_Sap software thanks to a linear calculation model called source model. The elastic-plastic behavior of non-linear trusses for X-bracings was considered by assigning tension and compression limits in terms of strength. Notably, the infill walls were not included in the structural model; instead, they were represented as a uniform load distributed along the perimeter beams. Vertical loads were applied to the floors at each level, as specified in Table 5. The permanent loads on the top floor also included the weight of the roof, which was not directly incorporated into the calculation software. The floors were modeled as rigid slabs with a membrane thickness of 4 cm. Figure 6: Schematic configuration of the reinforcement: longitudinal (**a**) and transversal (**b**) facades of the retrofitted building. Seismic loads for the nonlinear static analyses were computed using the foundation soil category (C) and topographic category (T1). A standard damping of 5% was applied, while the soil-structure interactions were neglected, as the reinforced concrete and steel vertical elements at ground level were assumed to be fixed at the base. The type of action was calculated at the ultimate limit state (ULS) with different accidental eccentricities (positive, negative and none) for each principal direction (longitudinal X and transverse Y). Two force distributions were considered: a triangular distribution, similar to that used in linear static analysis, and a mass-proportional distribution. The solid view of the existing structure model, as implemented in the Pro_Sap software, is shown in Figure 7.  
The same loading conditions were applied to the retrofitted model, which was equivalent to the unreinforced structure, but equipped with the cold-formed exoskeleton. The steel elements were incorporated into the structural model as closely as possible to their actual configuration, with some necessary simplifications. Horizontal and vertical profiles were modeled as beam elements with moment releases, which accurately represented the system's constraint conditions. The diagonal bracings were modeled as nonlinear trusses, which were capable of sustaining only tensile stresses. The connections between the horizontal and vertical members and the RC structure were represented by rigid links, which simulated the presence of the chemical anchors. The solid view of the retrofitted structure model, as implemented in the Pro_Sap software, is shown in Figure 8.