PSI - Issue 64

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

1021

5

lateral-torsional mode shapes unchanged. To overcome these limitations and drawbacks, a “two-step” design procedure is implemented in this paper. The first step involves the insertion of non-dissipative steel braces (Fig. 4) that are designed to balance the lateral stiffness of the underground concrete walls. Their effectiveness in mitigating the torsional effects is highlighted by the modal properties of the retrofitted building (Step 1) (Tab. 1b). Once the torsional effects have been mitigated, the procedure proposed by Mazza et al. (2015) may be applied. The seismic retrofit is carried out using an endoskeleton composed of braces equipped with steel hysteretic dampers (type HBF). Initially, the analysis defines the equivalent SDOF system based on the pushover curves of the retrofitted building (Step 1) under the first mode distribution of the lateral forces (Fig. 5). ATC-40 procedure is applied to define the bilinear idealization of the capacity curve corresponding to the target design displacement ( d P ) (Fig. 6a, Table 3). The equivalent SDOF system's parameters are then scaled by the participation factor ( Γ ) of the fundamental mode. The dissipative exoskeleton is idealized using an elastoplastic model (Fig. 6b). The retrofitted building (Step 2) is a parallel system including the as-built structure ( S ) and the dissipative endoskeleton ( E ). Its equivalent viscous damping ( (SE) ) is given by averaging the base shear-weighted equivalent viscous damping ratios (S) and (E) and adding a 5% viscous damping. The effective period ( T e ) is computed using the (SE) -damped displacement spectrum. An iterative process is used since (SE) is unknown. The design parameters of the endoskeleton are shown in Tab. 4. The design base shear is distributed over the height according to the first mode shape (Tab. 5). The story stiffness ( K i ) on the endoskeleton is distributed all the damped braces (brace and HBF arranged in series) (Tab. 6) and distributed in plan (Fig. 4b). Each brace is designed from the HBF strength to avoid buckling.

Table 3. Parameters of the bilinear equivalent SDOF system of the retrofitted building (Step 1) ( S )

d p

V p

V y

d y

K e

T e

m e

 d p

*

*

(S)

(S)

(S)

(S)

(S)

(S)

(S)

 h

 v

Direction

r (S)  (S)

[kN ꞏ s 2 /mm]

[mm]

[mm]

[kN]

[kN]

[mm]

[kN/mm]

[s]

[%]

[%]

X Y

0.596 0.665

1.36 100 73.53 1603.32 1431.88 100 15.45

1.234 1 1.00 5 0.966 1 1.00 5

5 5

1.32 75

56.82 2289.43 1410.76 75

28.11

a)

b) Fig. 4. Layout of the elastic steel braces (ELBs) (Retrofit Step 1). a) 3D view; b) Plan view.

300000

350000

300000

250000

250000

200000

200000

150000

150000

100000

As Built Building Retofitted Building - Step 1 Retrofitted Building - Step 2

As Built Building Retrofitted Building - Step 1 Retrofitted Building - Step 2

100000

50000 Base Shear (daN)

50000 Base Shear (daN)

0

0

0

5

10

15

20

25

0

5

10

15

20

25

30

35

40

45

Roof Displacement (cm)

Roof Displacement (cm)

a)

b) Fig. 5. Pushover curves. a) X-Direction; b) Y-Direction.