PSI - Issue 78

Giada Frappa et al. / Procedia Structural Integrity 78 (2026) 17–24

23

of steel under cyclic axial loading. In particular, at ground level, BRAD 21/40-b devices are installed, whereas BRAD 14/40-b devices are used at the first floor. The devices are implemented in SAP2000 through non-linear link elements having bilinear elastic-hardening constitutive law. The stiffness values of the first and second branches, yield displacement and force, as well as the equivalent elastic stiffness and damping, are provided by the device manufacturer, FIP-MEC, for the Collapse Limit State (CLS). Since the analysis method employed, FNA, is based on the decoupling of the equations of motion and is developed as an extension of the modal superposition method to nonlinear systems, it is essential to define as accurately as possible the values of equivalent elastic stiffness and damping of the devices used in the modal analysis for the limit state considered. The parameter values provided by the manufacturer for the CLS are suitable for device-level verifications. Instead, for the verification of the structural elements carried out at the life safety limit state, the displacements experienced by the BRAD devices under this limit state are iteratively evaluated, and the equivalent elastic stiffness and damping are calibrated accordingly. The external bracing elements are subjected to vertical loads only due to their self-weight. As for horizontal actions, they experience forces proportional to their stiffness. Since they carry limited axial loads, but are significantly stressed in the horizontal direction, high tensile forces develop in the steel frame columns. For this reason, the foundations of the frames, constructed parallel to those of the main building, are designed with two foundation micropiles, each with a diameter of 200 mm and a length of 6 m, placed at the base of each steel column. The effects of the installation of the steel braced frames along the perimeter of the building are initially observed in the results of the modal analysis. Following the retrofitting intervention, the first mode of vibration remains purely translational along the X direction, with a period T 1 = 0.441 s , slightly lower than that of the as-built configuration due to the introduction of the dissipating bracing system. This mode accounts for a participating mass of 80.3%. The next two most significant modes are the 35 th , with a period T 35 =0.097 s , contributing 61.7% of the participating mass along the Y direction and 1.8% around the Z axis, and the 36 th , with T 36 =0.094 s , contributing 3.7% along Y and 72.2% around Z. These results clearly demonstrate that the translational motion along the Y direction has been effectively decoupled from the rotational motion about the Z axis thanks to the bracing system. Following the intervention, the Fast Nonlinear Analysis (FNA) provides internal force demands under which all columns are verified for shear in the Y direction, while only 4 columns do not satisfy the shear requirements in the X direction. As for the walls, the only verifications still not satisfied are those related to shear–tension interaction at the base of all walls, and sliding shear at the base of all walls and elevator core. Finally, the intervention with external steel bracing frames is not effective in reducing the internal forces in the beams, as these are subjected only to vertical loads and not to seismic actions, being simply supported on the columns. Based on the reported results, the value of ζ V remains constant at 0.74. Regarding ζ E , initially equal to 0.34, even some verifications are still not satisfied, its value increases to 0.84, exceeding 0.6. Hence, the target value for ζ E is achieved, whereas reaching the target value of 1 for ζ V requires additional local strengthening interventions. 4.2. Local strengthening interventions The local strengthening interventions regard the beams in the regions where they are not verified under shear. The proposed strengthening technique involves the use of the Active Confinement Method (CAM), which consists in the application of high-strength steel straps wrapped around the cross-sections of the structural elements to be reinforced. Each strap is subjected to a pre-tensioning process, in order to activate the strengthening intervention from the outset, thereby ensuring its effectiveness under service load conditions. In order to wrap the beams, it will be necessary to drill through the floor slabs in proximity to the beam itself, taking care not to compromise the slab ribs. Consequently, the required demolitions will be limited to the top and bottom layers of the hollow portion of the slab. To avoid excessively weakening the slab-to-beam connection section, it is preferable to work with a wider spacing, applying multiple overlapping steel straps for each tie, until the required strengthening target is achieved. Additional proposed local strengthening interventions concern the slab-to-beam and beam-to-column connections. These joints currently rely solely on friction for their load transfer. To enhance their seismic performance and prevent loss of support of the connected elements during seismic shaking, the installation of mechanical shear connectors is proposed.