PSI - Issue 78

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

402

Table 3. Critical scale factor for the three cases and each of the five independently reinforced floors.

(The

values of the optimal configuration are highlighted in bold). Configurations (a)

(b)

(c)

1 st

4.68 4.68 4.68 4.68 4.68

6.82 8.13 7.27 4.55 4.17

9.76

13.93 11.52

2 nd 3 rd 4 th 5 th

4.90 4.31

8. Effectiveness of local modifications It is intuitive to assume that structural strengthening increases resistance to instability. However, this study demonstrates that a targeted intervention in the most vulnerable areas, where plasticization most significantly reduces stiffness, can be more effective. Specifically, it was previously observed that to achieve a critical intensity factor I c =8.13, it would be sufficient to increase the flexural strength of only three beams by 200%. To obtain the same result through uniform strengthening of all 60 beams, an increase of 82% in their strength would be required. Similarly, to reach a value of I c =13.93, achieved with a 500% increase in the strength of three beams, all beams would need to be strengthened by 248%. These findings demonstrate that a localized intervention can represent a more efficient solution both technically and economically, as it enhances stability without modifying the entire frame, thereby avoiding material waste and excessive costs. 9. Conclusions During a seismic event, accurately predicting the areas of the structure where plasticization will occur is extremely complex. Consequently, it is not straightforward to determine whether the seismic excitation will drive the structure toward an unstable configuration or whether such a condition will persist long enough to cause collapse. This consideration leads to one of the central concepts of the paper: the analysis of the potential to positively influence the distribution of plasticity through targeted local modifications, to mitigate the risk of structural instability. The study focuses on the effectiveness of localized reinforcement. It is demonstrated that selectively strengthening specific beams involved in unstable mechanisms can delay the onset of structural instability, allowing the structure to develop additional plastic hinges and, consequently, to increase its overall load-bearing capacity. Furthermore, the results indicate the existence of an optimal reinforcement configuration, in which the maximum stability enhancement is achieved for a given level of intervention. Finally, dynamic analyses conducted on a real structural case confirm that such targeted interventions can produce benefits comparable to those achieved through global strengthening of the entire frame. This highlights the potential of localized reinforcement as a technically and economically efficient engineering strategy. References Bernal, D. 'P-delta effects and instability in the seismic response of buildings', Report no. CE-90-14, Northeastern University, Boston, MA, 1990 Bernal, D. 'Instability of buildings subjected to earthquakes', J. Struct. Engng, ASCE, 1992, 18 (8), 2239-2260 Bernal, D. 'Dynamic instability in buildings subjected to earthquakes', Report no. CE-92-14, Northeastern University, Boston, MA, 1992 Bernal, D. 'Instability of buildings during seismic response. Engineering Structures', 20(4-6):496 – 502, 1998. El Kordi, E. and Bernal, D. 'Instability in buildings subjected to earthquakes', Report no. CE-91-15, Northeastern University, Boston, MA, 1991 Husid, R. Gravity effects on the earthquake response of yielding structures, Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, CA, 1967 Jennings, P. C. and Husid, R. 'Collapse of yielding structures under earthquakes', J Engng Mech., ASCE 1968, 94 (5), 1045-1065