PSI - Issue 78

Filippo Dringoli et al. / Procedia Structural Integrity 78 (2026) 395–403

401

• (a). Design configuration (assumption of elastic columns). • (b). Increasing by 200% the bending resistance on the beams in the first level. • (c). Increasing by 500% the bending resistance on the beams in the first level.

The hypothesis underlying the study is that the structure exhibits plasticity first in the beams and subsequently in the columns, in accordance with the ideal behavior intended by the design based on strength hierarchies. The following table shows how the critical scale factor increases as the configurations vary for the three seismic records used in the analyses. The configurations of the plastic hinges and the deformation shapes of the structure at the moment of collapse due to dynamic instability are shown for the three configurations analyzed using the Northridge earthquake, as reported in Figure 8.

Table 2. Critical Intensity factor I c . Earthquakes

(a)

(b)

(c)

Northridge Loma Prieta

4.68 5.68 6.20

6.82 6.65 8.95

9.76 9.30

Amatrice

10.60

Fig. 8. Comparison between the three configurations

As observed in Figure 8, the initial configuration collapses involving the plasticization of the beams up to the first seven stories, with a critical scale factor equal to 4.68. By increasing the flexural strength of the first-story beams by 200%, the critical scale factor rises to 6.82, indicating greater plasticization of the structure alongside an enhanced resistance to instability. However, at the moment of collapse, the configuration remains similar to the original design, as the applied strengthening is still insufficient to keep the first-story beams within the elastic range. To achieve this outcome, it is necessary to increase the flexural strength of these beams by 500%. In this case, the critical scale factor increases significantly, and the structure collapses, showing more extensive plasticization in the upper stories, while the first-story beams remain entirely elastic. This change highlights an evolution in the collapse mechanism, consistent with the observations made in the previous paragraph concerning the eigenvalue-based static analyses. 7. Optimal local modifications Another key finding of this study is that the resistance to instability varies depending on the elevation at which the beam reinforcement is applied. While it is expected that strengthening is effective only when it involves members participating in the collapse mechanism, it is noteworthy that an optimal reinforcement configuration exists. In the case study considered, the most effective reinforcement location corresponds to the second story of the structure. Table 3 illustrates how the critical intensity factor (Ic) changes as a function of the level at which the previously described reinforcement is applied.