PSI - Issue 62

Rossella Venezia et al. / Procedia Structural Integrity 62 (2024) 796–808 Rossella Venezia and Alessio Lupoi / Structural Integrity Procedia 00 (2019) 000 – 000

803

8

8-9

8

1.52 1.30 1.28 1.08 0.98

12

0 0 0 0 0

0 0 0 0 0

44 50 72 78 86

0 0 0 0 0

0 0 0 0 0

1

10

6

10-11-12-13 13

21

14 15

14 15

6 8

The dynamic response of the bridge in the transversal direction is governed by eight modes, whose periods vary from 0.73 s to 0.31 s . The modal displacements excite the pier and half-deck at the left and at the right side of the pier. The participation mass factors (PMR) of the eight modes sum up to about 91% (see Table 3).

Table 3. Modal analysis results: transversal direction. Pier no.

Mode [-] Period [s] PMR X [ % ] PMR Y [ % ] PMR Z [ % ] SUM PMR X [ % ] SUM PMR Y [ % ] SUM PMR Z [ % ]

2

16 17 20 22 28 29 30

0.73 0.65 0.61 0.56 0.45 0.41 0.33 0.31

0 0 0 0 0 0 0 0

7

0 0 0 0 0 0 0 0

86 86 86 86 86 86 86 86

8

0 0 0 0 0 0 0 0

3-4-5

18 11 11 22

25 37 48 70 77 85 91

6-7 8-9

10-11-12-13 24

1

6 8 6

14 15

4. Analysis and results The non-linear static analysis is carried out in two horizontal directions, the longitudinal direction x, and the transverse direction y, orthogonal to the longitudinal one. In each of the two horizontal directions, a static non-linear analysis is carried out until the target displacement of the reference point is reached. In longitudinal direction, the target displacement of the reference point, d T,x , is equal to d E,x , who is the displacement resulting from equivalent linear multi-mode spectrum analysis assuming q=1 due to E x +0.3E y . In transversal direction, the target displacement of the reference point, d T,y , is equal to d E,y , calculated similarly to d E,x above (see Table 4). Since the influence of the assumed reference point for displacement has been addressed, five different reference points has been chosen, one for each representative pier of the five piers groups. The spectrum analysis is carried out using cracked stiffness of ductile members, as described before.

Table 4. Deck displacements from RSA (q=1). Pier no. , [ m ] , [ m ] 1 0.18 0.04 2 0.25 0.10 6 0.22 0.08 10 0.17 0.05 14 0.15 0.03

It is well known that the displacement capacity in pushover curve is a function of the local achievement of the first element limit condition. Collapse modes, which detect collapse LS of the structure, have been checked through post processing. First possible collapse mode involves piers that can fail because either shear strength V or deformation capacity, in terms of chord rotation θ, is e ceeded . Second possible collapse mode is the unseating failure, which involves the deck and the sub-structure, and is checked at the bearing level. As described before, b earings’ failure can