PSI - Issue 44

Paola Sorrentino et al. / Procedia Structural Integrity 44 (2023) 1308–1315 Paola Sorrentino et al. / Structural Integrity Procedia 00 (2022) 000–000

1314

7

To compare the capacity of the structure with the seismic demand, defined through response spectra, it has been considered an equivalent SDOF system, whose mass, displacement and force are defined as follow: ∗ = A / / (3) ∗ = D (4) ∗ = (5) where / is the story mass, is the displacement shape, D is the time-dependent top displacement, is the base shear of the MDOF model and is the modal participation factor. The force-displacement relation of the equivalent SDOF system has been idealized into an elasto-plastic form. It has been determined with graphical procedure: nonlinear force-displacement curve of the equivalent SDOF system and elasto-plastic curve cross at a force equal to 60 per cent of the yield strength and the areas of the original and idealized curve are approximately equal. The resulting curves exhibit yield forces F ∗ and displacements F∗ equal to 441.8t and 2.50cm and 59.40t and 7.60cm, and maximum displacements <∗ => of 4.29cm and 8.91cm, respectively in y and x direction. The elastic periods in two orthogonal directions have been defined as follows: ∗ = 2 H ∗ F∗ F ∗ (6) In Table 3 the values of mass, stiffness and periods of the equivalent SDOF system in direction x and y are listed.

∗

∗

∗ [s]

Table 3. Equivalent SDOF system.

Direction

[-]

[kNs 2 /m]

[kN/m] 7,450 162,611

x y

1,771 1,771

2.87 0.65

The evaluation of demand in x and y direction is shown graphically by using Acceleration-Displacement Response Spectrum (ADRS) (Figure 5). In terms of displacement, the demand is equal to 7.30 cm and 2.35 cm and the capacity is 9.30 cm and 3.13 cm in x and y direction, respectively.

Spettro ADRS Villaggio Olimpico, Roma

Spettro ADRS Villaggio Olimpico, Roma

S e /g

S e /g

Longitudinal direction Mode X+ SLV-Elastic Demand

Transversal direction Mode Y+ SLV-Elastic Demand

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Equivalent S-DOF d*e,max - demand d*ult - capacity d*max - demand TS

Equivalent S-DOF d*e,max - demand d*ult - capacity d*max - demand TS

PGA D =0.12

PGA D =0.12

d* max = 7.30

d* max = 2.35

d* ult =9.30

d* ult =3.13

S De (cm)

S De (cm)

0

2

4

6

8

10

0

1

2

3

4

5

6

7

8

Figure 5. (a) N2 method: evaluation of demand and capacity in (a) x direction and (b) y direction. The Ϛ 6 ratios between capacity and demand in y direction and in x direction are equal to 1.33 and 1.27, considering only the flexural failure mechanism. (a) (b)