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

979

6

Fig. 7. Layout in plan of the damped braces.

The story lateral stiffness ( K d,i ) is distributed in-plan (Fig. 7) according to different issues: torsional stiffness, architectural impact, and full operationally during the retrofit implementation. This gives the lateral stiffness and, then, the axial stiffness of each damped brace (Fig. 6c). Finally, the buckling resistance of the brace is designed higher than the strength of the RSMAD according to the capacity design rule. 5. Seismic performance assessment The effectiveness of both the retrofit strategy and the design procedure is finally evaluated using the nonlinear response history analysis. Seven earthquakes are selected and scaled using Rexel computer code (Iervolino et al., 2010) by applying the spectrum-compatibility rules of Eurocode 8 (2004). Tab. 5 shows the seismic parameters of the selected earthquakes for the Life Safety (LS) and Collapse Prevention (CP) limit states. Fig.8 plots the corresponding acceleration spectra highlighting their spectrum compatibility. The two components of the earthquake ground motions are simultaneously applied to the building during the time history analysis. Both the Life Safety verification of the building and the Collapse Prevention verification of the SC-SMA dampers are checked. Fig. 9 shows the hysteresis loops of the SC-SMA dampers for the CP limit state. The results show the effectiveness of the design procedure to obtain very uniform yielding in all dampers. The Life Safety verification is satisfied when the chord rotation demand of structural members is greater than the corresponding chord rotation capacity. For columns, the chord rotation capacity in uniaxial bending is directly related to the inter-story drift. Moreover, the chord rotation capacity in bi axial bending is calculated under the hypothesis that the corresponding interaction diagram is circular if the components of chord rotation in X- and Y-direction are divided by the corresponding chord rotation capacity in uniaxial bending. Fig. 10 shows the comparison between the inter-story drift capacity and demand for the Limit State of Life Safety (LSD). The seismic demand never exceeds the structural capacity thus meaning that the Life Safety verification is satisfied. Moreover, only in limited cases the seismic demand marginally exceeds the Damage Limitation (DL) limit state thus meaning that columns yielding is rather limited. The residual inter-story drift is at most 0.34%, thus, never exceeding the repairable limit of 0.5% that has been considered acceptable.

1.40

1.00

E1 X-dir. (SF=1.058) E2 X-dir. (SF=2.811) E3 X-dir. (SF=1.693) E4 X-dir. (SF=5.856) E5 X-dir. (SF=15.06) E6 X-dir. (SF=2.562) E7 X-dir. (SF=1.969)

E1 Y-dir. (SF=1.798) E2 Y-dir. (SF=3.221) E3 Y-dir. (SF=1.366) E4 Y-dir. (SF=7.780) E5 Y-dir. (SF=10.95) E6 Y-dir. (SF=1.145) E7 Y-dir. (SF=1.741)

E1 X-dir. (SF=0.8502) E2 X-dir. (SF=1.145) E3 X-dir. (SF=5.494) E4 X-dir. (SF=2.258) E5 X-dir. (SF=1.360) E6 X-dir. (SF=12.10) E7 X-dir. (SF=0.6557)

E1 Y dir. (SF=1.444) E2 Y dir. (SF=0.8293) E3 Y dir. (SF=6.658) E4 Y-dir. (SF=2.588) E5 Y dir. (SF=1.097) E6 Y dir. (SF=8.796) E7 Y dir. (SF=0.6783)

1.20

0.20 Spectral Acceleration (g ) 0.40 0.60 0.80 1.00

0.20 Spectral Acceleration (g ) 0.40 0.60 0.80

Average

S. Target

Average

S. Target

Upper

Lower

Upper

Lower

0.00

0.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

(b)

(a)

Period (sec)

Period (sec)

Fig. 8. Acceleration spectra. a) Life Safety limit state; b) Collapse Prevention limit state.