PSI - Issue 78

Parvane Rezaei Ranjbar et al. / Procedia Structural Integrity 78 (2026) 615–622

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frames are used for seismic retrofit (Fig. 2a-c). This double-frame configuration offers several advantages: a) energy dissipation is enhanced, as fuses placed along the height of the frame experience larger modal deformations; b) the design allows greater flexibility since the fuse plates are positioned away from the post-tensioning tendons; c) it eliminates the need for hinged connections between the fuses and the frame, thereby avoiding complications related to hole alignment and tolerances; d) the post-tensioning system is split into two independent sets, simplifying the structural detailing; e) lower self-centering ratios can be adopted if desired. Despite their benefits, such as improved reparability and minimized residual drift, designing rocking systems presents challenges, including complex detailing, managing P-Delta effects, and higher implementation costs. The complex structural behavior can be interpreted as the combined action of two main components: the post-tensioned cables and the energy-dissipating devices. To achieve a fully self-centering, flag-shaped load – deformation response, the restoring moment must exceed the opposing moments generated by the energy-dissipating fuses. Critical design parameters influencing this behavior include: a) the geometric ratio A / B (Fig. 2b); b) the strength ratio OT , defined as the ratio of overturning resistance to the design overturning moment; c) the self-centering ratio SC , representing the ratio between the post-tensioning force and the fuse resistance. These parameters collectively govern the balance between restoring and resisting actions, ensuring proper re-centering after seismic events. In this paper, a displacement-based design procedure is used to determine all major structural components, including: the cross-sectional area and prestressing level of the stainless steel cables; the energy dissipation devices; and the steel members, which are designed to remain elastic under seismic loading. Details of this design methodology are provided in Ferraioli et al. (2025c). The energy dissipation devices, which function as structural fuses, consist of dumbbell-shaped steel strips. Their geometry is specifically tailored to avoid stress concentrations, limit plastic strain accumulation, and prevent buckling failures (Ferraioli et al. , 2025d).

(a)

(b) Fig. 1. (a) External rendering view; b) Plan view.

(a) (c) Fig. 2. (a) Geometry of self-centering dual-frame rocking system; (b) Rocking behavior under lateral loads; (c) 3D Model of retrofitted building. 4. Seismic fragility assessment For the Incremental Dynamic Analysis (IDA), seven earthquake records were selected and scaled using the REXEL software (Iervolino et al. , 2010), following the spectrum-compatibility criteria of Eurocode 8 (2004). Fig. 3 presents the seismic parameters of the selected ground motions, along with spectrum-compatibility verification for those used to evaluate the Collapse Prevention (CP) limit state. Both components of the earthquake ground motions were applied (b)