PSI - Issue 78

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

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Fig. 3. (a) Local kinematic mechanism; (b) Lowest Eigenvalue due to distribution of plastic hinges for a 20-story; (c) Global kinematic mechanism 3. Importance of the position of plastic hinges This section examines the influence of plastic hinge placement on the overall stability of the structure. It will be demonstrated that, beyond a greater number of plastic hinges, their distribution within the frame plays a decisive role. It is evident that when plastic hinges develop in the columns, the structure may exhibit a localized kinematic mechanism. However, this section specifically aims to illustrate how the eigenvalues of the effective stiffness matrix change under different configurations of plastic hinges localized in the beams of a structure subjected to significant axial loads, such as the previously analyzed twenty-story example. Two cases will be presented. In the first, the objective is to highlight the effect of the elevation at which plasticization occurs. Notably, the higher the plastic hinges form in the beams at the upper part of the structure, the less detrimental their impact on the overall structural behavior. In other words, the minimum eigenvalue decreases only slightly when plasticization is concentrated in the upper region of the frame. Conversely, an unstable configuration can be reached with a smaller number of plastic hinges when they develop in the lower part of the structure. This behavior is closely linked to the magnitude of axial loads present in the columns. Intuitively, instability tends to develop earlier in the lower part of the frame due to the higher axial forces. Figure 4 provides a clearer visualization of how the minimum eigenvalue varies as the same number of plastic hinges is introduced at different positions.

Fig. 4. (a) Lower configuration; (b) Lowest Eigenvalue due to the development of plastic hinges at different heights, (c) Higher configuration

In the second case, the analysis aims to compare the previously identified unstable configuration (Figure 4a) with an alternative configuration in which plasticization initially develops in all the beams connected to the left node and subsequently progresses toward the right node, as illustrated in Figure 5c. The comparison reveals that in the second configuration, the structure remains stable until 20 hinges have formed on the left side. However, instability manifests