PSI - Issue 78

Francesco Nigro et al. / Procedia Structural Integrity 78 (2026) 1537–1544

1540

Table 1. Minimum safety indexes for the as-built structural models

Bare Frame (BF) structure

Infilled Frame (IF) structure

 E, DL

 E, SD, ductile

 E, SD, shear columns

 E, SD, shear joints

 E, DL

 E, SD, ductile

 E, SD, shear columns

 E, SD, shear joints

1.06 0.70

0.15

0.09

1.34 0.71

0.46

0.18

3. Design of the retrofitting exterior steel bracing 3.1. Overview of the design approach

A force-based approach was selected to design the steel exoskeletons, because it is likely the approach followed by design professionals in Italy. However, unfortunately the current seismic design codes do not provide explicit design rules for the hybrid structural system comprising RC frames and steel braces. This lack of design rules is actually also characteristic of the scientific literature, except for some conceptual considerations developed by Faella et al. (2008) and Caterino et al. (2009). Nigro et al. (2023; 2024) have recently outlined a parametric study aimed at comparing different seismic retrofit scenarios, combining different types of intervention techniques (i.e., both local and global strengthening) as well as discussing the resulting performance from both economic and environmental viewpoints. Similarly, in the present work two design scenarios were investigated: • in the first scenario it was assumed that the CBFs are the sole structural system resisting seismic forces; • in the second scenario, the intensity of the base shear force utilized to design the CBFs was obtained as half of the one corresponding to the first scenario. In other words, in the first scenario it is implicitly assumed that the designer would calculate the total base shear force of the system comprising both the older building and the new steel structure, while designing the new steel structure to resist this entire value of the lateral force. Consequently, in the case of “Scenario 1”, the exoskeletons were designed assuming that the fundamental period of the upgraded structure is short enough to correspond to the plateau branch of the design spectra provided by the Italian technical code (D.M. 2018) for the considered construction site. Therefore, the corresponding design value of the base shear force is provided by Eq. (1): where symbols have the following meaning: •  accounts for the ratio among the effective modal mass of the fundamental mode and the total mass; • m tot is the total mass of the structure in the seismic load combination; •  is an amplification coefficient representing the effect of accidental torsional effects, equal to 1.30; • F 0 is a site amplification factor, equal to 2.29; •  is a damping factor, assumed equal to unity for an equivalent elastic viscous damping ratio of 5%; • S considers the type of soil and is equal to 1.34 for the SD Limit State; • PGA SD is the Peak Ground Acceleration for SD limit state; • q CBFs is the behaviour factor, which is equal to 4 in case of CBFs. Instead, i n the case of “Scenario 2”, the design base shear was computed as shown by Eq. (2): 0 b d, Scenario1 ( )     tot m     F S PGA = SD CBFs V q (1)

(2)

b d, Scenario1 0.50 =  V

V

b d, Scenario2

The approach pursued with the second design scenario, Eq. (2), allowed considering roughly the contribution of the existing structure in resisting seismic actions. The scope of this approach was simply that of modulating the stiffness and resistance of the new steel structure relative to the existing RC frame structure in order to have a parametric design (and analysis) of the possible upgrading configurations. Clearly, more refined displacement-based