PSI - Issue 64

Massimiliano Ferraioli et al. / Procedia Structural Integrity 64 (2024) 1025–1032 Ferraioli et al./ Structural Integrity Procedia 00 (2019) 000–000

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a)

b)

c)

Fig. 4. a) SMA damper (SMAD); b) Behavior under tension and compression; c) Flag-shaped hysteresis loop.

b) c) Fig. 5. a) Steel strip damper (SSD); b) Geometry of a steel strip; c) Elasto-plastic hysteresis loop.

a)

If lateral torsional buckling is prevented, the dumbbell-shaped steel strips demonstrate consistent hysteretic behavior and remarkable energy dissipation capabilities. The initiation of buckling response relies on factors such as slenderness, aspect ratio, and initial imperfection. In this study, the configuration of the strip was verified to prevent deterioration, even in the presence of an initial imperfection equivalent of 1/250. This allows modeling the damper composed of a certain number of strips through a simple kinematic elastic-plastic model (Ferraioli et al., 2023) (Fig.5c). The paper utilizes a displacement-based design approach, commonly employed in seismic design and retrofitting of buildings, following methodologies proposed by Mazza et al. (2015) and subsequent studies. In this approach, the pushover analysis of the existing building provides pushover curves (Fig. 6), forming the basis for defining an equivalent SDOF system. This system, reflecting the modal distribution of lateral load patterns, aids in determining the target design displacement and corresponding performance base shear. Idealization of capacity curves is done through ATC-40 (1996) procedures, yielding parameters for the existing structure's bilinear SDOF system (Fig.7a). Similarly, the parameters for the dissipative exoskeleton's equivalent SDOF system are determined (Fig. 7b). The stiffness and strength of the dissipative exoskeleton initially remain unknown. The retrofitted building is treated as an in-parallel system of the existing structure and the exoskeleton, with equivalent viscous damping calculated as a weighted mean over the base shear of both structures (  h (S) and  h (E) ). This damping ratio, along with other factors, aids in determining the damping reduction factor and the design displacement spectrum. The effective period of the retrofitted building is computed based on this spectrum, with the equivalent stiffness serving as a starting point for calculating parameters of the exoskeleton's bilinear equivalent SDOF system (Fig.7b). The parameters of the bilinear equivalent SDOF system of the structure ( S ) and the exoskeleton ( E ) are plotted in Tabs.2-3, respectively. The allocated design base shear is subsequently dispersed throughout the building's height, following the primary mode shape in the specified direction. This process yields the story strength and stiffness of the exoskeleton, which are then apportioned among the concentric braced frames ( n CBF ) of the orthogonal exoskeleton and the eccentrically braced frames ( n EBF ) of the parallel exoskeleton. This enables the sizing of SMADs in CBFs (Tabs. 4-5) and SSDs in EBFs (Tabs. 6-7). The layout of EBFs and CBFs in the building's plan is made to alleviate torsional effects (Fig. 8).