PSI - Issue 78

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

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immediately upon the addition of the first three hinges on the right side, as illustrated in Figure 5. The analyzed phenomenon is particularly significant as it demonstrates that the instability of the frame is primarily governed by the plasticization of specific points, rather than merely by the total number of plastic hinges. It is evident that while the quantity of plastic hinges has a marginal effect on overall stability, their positioning is the primary determining factor. The analysis suggests that the frame remains stable when plastic hinges form exclusively on one side of the structure. This observation highlights that stability is preserved as long as each beam undergoes plasticization at only one end, confirming the crucial role of plasticization at both ends of a beam in leading to unstable system configurations.

Fig. 5. (a) Lower configuration; (b) Lowest Eigenvalues due to the development of plastic hinges on different sides, (c) Left side configuration

4. Local modification It has been observed that enforcing the elasticity of one of the beams involved in the unstable mechanism compels the structure to develop a new instability pattern, which requires a greater number of plastic hinges to form. Figure 5 aims to compare how the smallest eigenvalue changes by contrasting the previously identified worst-case configuration (Figure 5a) with the configuration in which the second beam is constrained to remain elastic (Figure 5b). It is evident that, when arranging the plastic hinges from the bottom upward, an additional twelve hinges are required before the structure reaches an unstable configuration.

Fig. 6. (a) Lower configuration; (b) Lowest Eigenvalues due to the development of plastic hinges in different configurations, (c) Elastic beam on second floor configuration

From a seismic perspective, considering only the plasticization of beams and not of columns (as prescribed by seismic design codes as the ideal structural behaviour), it is observed that a localized structural strengthening aimed at preserving the elasticity of a highly stressed beam may contribute to enhancing the overall stability capacity of the structure under dynamic loading.