PSI - Issue 44

Massimiliano Ferraioli et al. / Procedia Structural Integrity 44 (2023) 974–981 Massimiliano Ferraioli et al./ Structural Integrity Procedia 00 (2022) 000–000

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Table 2. Modal properties

Before Retrofit

After Retrofit

N. Description

Frequency (Hz)

Period (s)

Period (s) 0.732 0.677 0.626 0.354

Frequency (Hz)

X- Modal mass ratio

Y- Modal mass ratio

X- Modal mass ratio

Y- Modal mass ratio

1 Flexural X - Torsional 1.216 0.823

0.73 0.06 0.00 0.12

0.00 0.17 0.07 0.00

1.366 1.477 1.599 2.829

0.43 0.04 0.00 0.08

0.00 0.12 0.42 0.00

2 Flexural Y 3 Torsional 4 Flexural X

1.019 0.982 0.968 1.033 0.502 1.994

Fig. 3. (a) External view of the residential building; (b) Fem model of the retrofitted building.

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Fig. 4. Models of the frame system.

The procedure is based on two equivalent SDOF systems, one for the main structure, and the other for the SC-SMA brace system (Ferraioli et al. 2018). The first SDOF system (Fig. 4) is defined from the pushover analysis of the main structure. To this aim, the story pushover curves (Fig. 5a) are first idealized using the well-known Takeda model (1970) (Fig.5b), and then simplified considering the same yield drift and the same target drift for all the stories (Fig. 5c). The optimal stiffness ratio between damped braces and RC frame is defined using the closed-form expression originally proposed Kasai et al. (2004) and then applied by Ferraioli et al. (2020, 2021, 2022) for the seismic retrofit of RC buildings. This gives the equivalent SDOF system of the SC-SMA damped braces (Fig. 6a). An optimal distribution rule is applied to the lateral stiffness (Sutcu et al. 2014; Ferraioli et al. 2021) (Fig. 6b) that aims for a uniform distribution of drift and ductility over the height of the building.