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

802

7

00 00 00 00 00

00 00 00 00 00

Base shear k

Base shear k

0 00 200

0 00 200

Fi ed support ongitudinally fi ed support

ongitudinally sliding support Free sliding support

0.00 0.0 0. 0 0. 0.20 0.2 0. 0 0. 0. 0 0. 0. 0 0. 0. 0

0.00 0.0 0. 0 0. 0.20 0.2 0. 0 0. 0. 0 0. 0. 0 0. 0. 0

ong. isp m

ong. isp m

Fig. 6. Constitutive laws of bearings in longitudinal direction: fixed type alignment (left) and movable type alignment (right).

00 00 00 00 00

00 00 00 00 00

Base shear k

0 00 200

Base shear k

0 00 200

Transversally fi ed support Free sliding support

Fi ed support Transversally sliding support

0.00 0.0 0. 0 0. 0.20 0.2 0. 0 0. 0. 0 0. 0. 0 0. 0. 0 0. 0. 0

0.00 0.0 0. 0 0. 0.20 0.2 0. 0 0. 0. 0 0. 0. 0 0. 0. 0 0. 0. 0

ong. isp m

ong. isp m

Fig. 7. Constitutive laws of bearings in transversal direction: fixed type alignment (left) and movable type alignment (right).

Constitutive laws for expansion joints consider the existence of the gap. For practical purpose, the one assumed for expansion joints located between adjacent decks is infinitely rigid and resistant once the gap is closed. While constitutive law assumed for expansion joints located between deck and abutment considers the activation of the contrast of the soil behind the backwall. In accordance with the Caltrans guidelines, the interaction between the deck and the backwall plus soil system is modelled with a bond where the limit force F (passive thrust) and the stiffness of the elastic part K are functions of the width of the backwall w, and its height h. Assumed constitutive laws for expansion joints are shown in Fig. 8.

000 000 000

000 000 000

0000 2000

0000 2000

000 000 000

000 000 000

ial Force k

ial Force k

eft side abutment ight side abutment

0 2000

0 2000

0.2 0.20 0. 0. 2 0.0 0.0 0.00 0.0 0.0 0. 2 0. 0.20 0.2

0.2 0.20 0. 0. 2 0.0 0.0 0.00 0.0 0.0 0. 2 0. 0.20 0.2

isp m

isp m

Fig. 8. Constitutive laws of expansion joints: adjacent decks (left) and deck-abutment (right).

The dynamic response of the bridge in the longitudinal direction is governed by eight modes, whose periods vary from 1.93 s to 0.98 s . The modal displacements excite the pier and the deck at the right-side of the pier. The participation mass factors (PMR) of the eight modes sum up to about 86% (see Table 2).

Table 2. Modal analysis results: longitudinal direction. Pier no.

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

2

1 4 6

1.93 1.70 1.63

5

0 0 0

0 0 0

5

0 0 0

0 0 0

3-4-5

15 12

21 33

6-7