PSI - Issue 64

Massimiliano Ferraioli et al. / Procedia Structural Integrity 64 (2024) 1017–1024 Ferraioli et al./ Structural Integrity Procedia 00 (2019) 000–000

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7

5. Seismic performance assessment The seismic assessment utilizes nonlinear time-history analysis, incorporating two simultaneous accelerograms representing distinct horizontal earthquake ground motion components. Seven real ground motions are selected and scaled following spectrum-compatibility criteria. Fig. 8a illustrates both the target and average spectrum, alongside scaling factors ensuring spectrum compatibility. Fig. 8b illustrates the variation in the peak Inter-story Drift Ratio (IDR) response of four points in plan (namely A, B, C, and D in Fig.4b) across the building height for the CP Limit State. The IDR response exhibits a certain variability as the column analyzed varies due to residual torsional effects. Notably, the peak IDR response remains below the maximum transient drift limit of 2%, aligning with the collapse prevention objective. Tab.7 shows that all the HBF dampers yield dissipating seismic energy. The chord rotation capacity, calculated according to the Italian Code (2018), is compared to the chord rotation demand at each time step of the analysis. The chord rotation capacity of the column in uniaxial bending determines the corresponding inter story drift capacity. For bi-axial bending, the inter-story drift capacity is established under the assumption that the interaction diagram forms a circle when the chord rotation components in bi-axial bending are normalized to those in uniaxial loading. As an example, Fig.9 compares the demand and capacity for a beam and a column. The demand slightly exceeds the capacity for the DL limit state, while it remains below the capacity for the LS limit state.

Table 7. Mean value of the displacement demand in HBF dampers (cm). HBF1X HBF2X  HBF3X HBF4X HBF5Y HBF6Y HBF7Y HBF8Y

Floor

2 3 4

1.917 2.052 1.657

1.093 1.916 1.936

1.623 1.761 1.467

1.124 1.740 1.906

1.156 1.443 0.480

1.235 1.439 0.545

1.132 1.412 0.456

1.160 1.402 0.490

5

5

X-Direction

Y-Direction

A B C D

A B C D

2.00

Average

S. Target

Upper

Lower

230x SF=3.4884 600x SF=2.4267 334x SF=1.4409 414x SF=1.7374 133x SF=3.8269 1703x SF=1.1056 196x SF=0.9184

230y SF=1.5585 600y SF=3.9299 334y SF=0.8121 414y SF=1.5314 133y SF=4.3861 1703y SF=0.8121 196y SF=1.3633

1.50

4

4

1.00

Story level

Story level

0.50

Spectral Acceleration (g)

3

3

0.00

0.00% 0.50% 1.00% 1.50% 2.00%

0.00% 0.50% 1.00% 1.50% 2.00%

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

b) Fig. 8. a) Earthquake records spectrum compatibilità; b)Variation of peak inter-story drift response (IDR) over the height. Period [sec] Peak IDR (%) Peak IDR (%)

a)

0.05

0.040

DL

LS

TH133 TH334 TH1703

TH196 TH414

TH230 TH600

0.03

0.020

0.01

0.000

-0.01

IDR-Y

TH196 TH414 TH230

TH1703 TH230

-0.03 Rotation (rad)

TH230

TH414

-0.020

LS

DL

-0.05

-0.040

0

10

20

30

40

50

-0.040 -0.020 0.000

0.020

0.040

Time (s)

a) b) Fig. 9. a) Time history chord rotation demand vs chord rotation capacity (Beam 112); b) IDR demand v s IDR capacity (Column C - 3 rd story). 6. Conclusions This study addresses the limitations of current nonlinear static procedures in the seismic retrofit of irregular and high-rise buildings, particularly those that fail to account for torsional effects and higher mode contributions. A "two IDR-X