PSI - Issue 64

E. Michelini et al. / Procedia Structural Integrity 64 (2024) 1967–1974 1971 Elena Michelini, S ł awomir Dudziak, Simone Ravasini, Beatrice Belletti / Structural Integrity Procedia 00 (2019) 000–000 5 or θ 2 ) are monitored, as indicated in Figures 4(c), (d). In the following part of the paper, these angles are expressed through values of their tangents in percent, according to the relation reported in Figure 4(c).

60 60

610 635

60 60

499 496

60 60

ϕ 6/10

ϕ 6/10

ϕ 6/19

ϕ 6/19

ϕ 6/10

ϕ 6/10

2 ϕ 12

2 ϕ 14

5 ϕ 20+2 ϕ 14

4 ϕ 14+2 ϕ 12+3 ϕ 20

2 ϕ 12+2 ϕ 14+3 ϕ 20+3 ϕ 16

5 ϕ 20+2 ϕ 12

2 ϕ 8 2 ϕ 8

2 ϕ 16 2 ϕ 8 2 ϕ 8

5 ϕ 16 2 ϕ 8 2 ϕ 8

2 ϕ 16 2 ϕ 8 2 ϕ 8

2 ϕ 14 2 ϕ 8 2 ϕ 8

2 ϕ 16 2 ϕ 8 2 ϕ 8

LV 5

16.10

3 ϕ 14+ 1 ϕ 12

66 cm

66 cm

66 cm

66 cm

66 cm

66 cm

30 cm

LV 4

30 cm

13.60

30 cm

30 cm

30 cm

30 cm

LV 3

5 ϕ 14 + 2 ϕ 20

10.30

3.7 3.3 3.3 3.3 2.5

3.5 3.5 3.5 3.5 3.5 3.5

ϕ 6/12

5 ϕ 14 + 2 ϕ 20

45 cm

C

32 cm

LV 2

7.00

16

15

17

18

19

20 21

5 ϕ 14 + 2 ϕ 20

ϕ 6/12

Z

6.95 5.56

5 ϕ 14 + 2 ϕ 20

50 cm

B

LV 1

3.70

32 cm

8

9

10

11

12

13 14

5 ϕ 16 + 2 ϕ 20

ϕ 6/10

Y

LV 0

55 cm

5 ϕ 16 + 2 ϕ 20

5

6 7

1

2

3

4

32 cm

A

Y

ϕ 6/8

5 ϕ 16 + 2 ϕ 20

1

2

3

4

7

5

6

6.95

5.56

X

5 ϕ 16 + 2 ϕ 20

60 cm

32 cm

Fig. 3. In plan and elevation view of the case-study building; typical cross-section dimensions and reinforcement layout for beams and columns.

(a) (d) Fig. 4. Model of the Norcia school’s structure: (a) FE mesh in Seismostruct (model with roof beams); (b) FE mesh in ABAQUS (model without roof); (c), (d) assumed settlement scenarios and monitored variables. The results of preliminary analyses, which are referred to settlement scenario No.1, are plotted in terms of sum of the reactions under the fixed external columns vs. central column settlement in Figure 5(a), and in terms of diagrams of normal forces corresponding to a settlement of 90 mm in Figure 5(b). In the case of the model with roof beams, an alternative load-bearing scheme develops, in which roof-beams act like an arch subjected to significant compressive forces, and the beam above the last level behaves like a tie. Consequently, the corresponding initial stiffness and load bearing capacity are much greater than those obtained for the model without roof. It is worth noting that such force redistribution is possible only in the case of a structure with properly designed reinforcement at beam-column joints (i.e., ensuring proper continuation of the main reinforcement, and preventing the nodes from shear failures). For the analyzed building, such reinforcement layout within the beam-column joints is not provided, so the model without roof is selected for more detailed analysis. For the latter model, Figure 5(a) provides a further comparison between the numerical results obtained from two different FE software (Seismostruct and ABAQUS), to verify the effectiveness of the adopted modelling choices. The achievement of the LS summarized in Table 1 is plotted on the (b) (c)