PSI - Issue 44

Michele Angiolilli et al. / Procedia Structural Integrity 44 (2023) 2074–2081 M. Angiolilli et al./ Structural Integrity Procedia 00 (2022) 000 – 000

2078

5

to that associated to the aggregated condition, since the walls of neighboring buildings sharing the same mid-walls have double thickness (see Tab. 2).

Table 2. Mechanical properties (*for spandrels; **for piers; ***isolated; ****aggregated)

Site

f m (MPa)

τ 0 (MPa) 0.09-0.12

E [MPa]

G [MPa]

W [kN/m

3 ]

SU’s w eight [kN]

Catania

4.6-5.8

1740

580

21.4 21.4

25,071*** – 22,420**** 5,528 *** – 5,528**** (SU1) 5,762*** – 4,155**** (SU3)

Visso

4.49*-6.42**

0.062*;0.127**

2078*;2968**

693*;991**

Note: fm: compressive strength; τ 0 shear strength, E: Young Module; G: Shear Module; W: density;

Table 3. Parameters adopted for the four NLBEAM-EF models (P and S stand for piers and spandrels, respectively).

Shear behaviour

Flexural behaviour

Residual. Str. [%]

Residual Str. [%]

Site

Drift [%]

Hyst. Resp.

Drift [%]

Hyst. Resp.

DL3 0.45

DL4 0.75

DL5

DL3

DL4

c1

c2

c3

DL3

DL4

DL5

DL4

c1

c2

c3

c4

P S P S

1

60 40 60 70

20 40 20 70

0.8 0.2 0.8 0.2

0.8

0

0.6 0.6 0.6 0.5

1 1

1.5 1.5

80 95 85 70

0.9 0.2 0.9 0.2

0.8

0.6 0.3 0.6 0.3

0.5 0.8 0.5 0.8

Cat ania

0

1

1.5

0

0.3

0

0.45 0.50

0.7 1.5

1.48

0.8

0

0.8 1.5

1.81

0.8

Vis so

2.0

0

0.3

2.0

0

Note: c1, …, c4 define the slope of unloading and loading branches of the hysteretic response

2.2. Pushover analyses Figure 2 shows the capacity curves, expressed in terms of base shear over weight ratio versus roof drift, for the two investigated case studies and obtained by considering uniform load pattern distributions proportional to the mass. For each direction (x or y as well as positive or negative) a comparison between isolated or aggregated behavior is reported. First of all, when compared to isolated SUs, all SUs in aggregate have higher stiffness along the direction where interaction with adjacent structures occurs. For the SU of Catania’s aggregate, the aggregate -effect led to a negative contribution, in terms of both strength and drift capacity, along X+ direction (one direction in which the interaction between the SUs takes place) and a positive contribution along the other three directions of the pushover analyses, especially in terms of strength. In detail, along X +, one can observe a slightly higher maximum shear capacity coefficient for the isolated case with respect to the aggregated case. However, the same trend cannot be observed for the other direction in which the interaction between the adjacent SUs takes place (Y-). This result can be justified by the fact that the building connected to the reference SU along y direction was much vulnerable than the building connected to the reference SU along X direction, mainly depending on both the disposition and cross-section of the walls. For the SU1 of the Visso’s aggregate, the capacity curves show a negative influence of the aggregate -effect in terms of strength (about 5%) only along X+ (where the interaction with the adjacent SU takes place), whereas a positive effect along the Y direction (both negative and positive directions). Instead, SU1 is positively influenced by the aggregate-affect in both strength and drift capacity along the Y direction (both negative and positive directions). On the other hand, for SU3, the aggregate-effect negatively affected the Y direction in terms of strength (about 5%) and especially in terms drift capacity. In X direction, the result is a bit ambiguous since the base shear increased (about 50% in the positive and negative directions) but, at the same time, the global ductility decreased. Definitively, when comparing only the capacity curves obtained by NSA, it is challenging to determine with clarity whether the aggregate-effect is positive or negative in terms of global seismic performance of each SU because a combination of resistance, stiffness, and ductility must be considered within seismic verifications. Moreover, note that it is not possible to include OOP effect within NSAs.