## 6 Retrofitting Interventions
### Intervention 2 (I2): Steel Jacketing  
The second intervention consists of adding steel jacketing in the form of steel plates and/or steel strips to the walls of the RC cores. This retrofitting technique is commonly used for the strengthening of RC columns and walls. In the technical literature, there are works in support of this retrofitting strategy [22; 23; 24; 25; 26; 27; 28; 29]. It is interesting that previous studies demonstrated the beneficial effects in terms of resistance and ductility compared to other structural solutions and highlighted that the reinforcement by steel plates produces self-centering shear walls. Another important benefit is the improvement of the load-bearing resistance due to confinement effects, as described in [30]. The advantages of this solution can be summarized as follows:  
* Increased shear resistance. * Increased deformation capacity. * Increased vertical load-bearing capacity (confinement effect). However, this retrofitting technique is usually employed to strengthen columns and walls; to the best of the authors' knowledge, no specific studies concerning the strengthening of RC cores are available. In particular, some technical problems arise when the interaction with the structural elements constituting the stairs is considered in the case of cores used for staircases. In this case, the structural solution was designed for two different safety levels: \(\zeta_{E}\geq 0.60\) and \(\zeta_{E}\geq 1.00\). In the first case, the intervention was characterized by the application of steel angles to the corners and battens, while a combined solution using continuous steel plates and steel strips was adopted in the second case. The minimum thickness of the steel elements was determined according to the following relationship:  
\[\mathrm{V_{j}=0.5\frac{2t_{w}}{s}b\;f_{yk}0.9 dcot\vartheta} \tag{8}\]  
This formula was reported in Section C8.7.4.2.2 of Circular n.7 of 21 January 2019 [11] and it allowed us to determine the additional shear resistance of the steel plates. \(\vartheta\) represents the angle of the shear crack in the concrete wall (45\({}^{\circ}\)); \(\mathrm{d}\) is the effective depth of the single concrete wall; \(\mathrm{b/s}\) is the width-to-spacing ratio of the horizontal strips (1.00 in the case of continuous steel plates); \(f_{yk}\) is the yield stress of the steel grade (S275); and \(t_{w}\) is the thickness of the steel elements. The required value for the additional resistance due to the steel jacketing was obtained as \(\mathrm{V_{j}=\Delta V_{Ed}}\), with \(\Delta V_{Ed}\) being the difference between the  
Figure 12: Structural scheme for determining the anchor length. shear action in the seismic condition (V\({}_{\rm Ed}\)) and the shear resistance of the original concrete wall (V\({}_{\rm Rd,w}\)). Consequently, Equation (4) can be rearranged as:  
\[\rm t_{w}=1.11\frac{s}{b}\frac{\Delta V_{\rm Ed}}{f_{\rm y}d} \tag{9}\]  
In the case of continuous steel plates, the minimum thickness \(\rm t_{w}\) is 10 mm, while the thickness of the horizontal strips ranges from 5 to 20 mm with \(0.10\leq b/s\leq 0.16\). The spacing and the diameter of the threaded bars connecting the plate elements to the RC walls were determined to account for the buckling resistance under pure shear action. This buckling resistance was preliminarily evaluated by a FEM model of a square plate simply supported at the four corners and subjected to pure shear membrane forces. The minimum value of the spacing was 250 mm, while 8.8 class threaded bars (M16 or M24, as needed) were adopted for the steel connectors. Figure 13 shows the construction detail for the application of the continuous steel plate to the concrete wall. For single RC cores and for each story level, Table 13 reports information on the adopted steel plates and the horizontal strips in the case of total retrofitting (\(\zeta_{E}\geq 1.00\)).