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

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3.2. Bridge F.E. model A three-dimensional finite element model of the bridge is set up in SAP2000 framework (see Fig. 4). The deck is modelled by linear-elastic beam frames, one for each span of the bridge. These elements are geometrically located at the slab level. Piers frames and cross-beam frames are modelled at their centre of gravity.

Fig. 4. Bridge Finite Element Model.

Piers frames are modelled as elastic beams with Plastic Hinges concentrated at the top and the bottom of each frame. Plastic Hinges are P-M2-M3 Fiber Hinges that can represent nonlinear moment-curvature relationship in both directions, longitudinal and transversal, as the axial stress varies. Yield and ultimate curvatures are determined automatically from section moment-curvature analysis to deal with general cross-section shapes and reinforcement layouts. Material constitutive model has been assigned to each concrete and steel Fiber. The stress-strain diagrams for both concrete and reinforcement steel reflects the probable post-yield behaviour. Concrete is governed by the parabola rectangle constitutive law, while steel by a trilinear hardening constitutive law (see Fig. 5).

00 00 00 00 00 00

0

0

20 2 0

pa

pa

0 00 200

0

0

0.0000 0.000 0.00 0 0.00 0.0020 0.002 0.00 0 0.00 0.00 0

0.0000

0.0200

0.0 00

0.0 00

0.0 00

0. 000

0. 200

Fig. 5. Constitutive laws of concrete (left) and steel (right) material.

The stiffness of the element elastic part is reduced according to the cracking level produced by seismic action. The deck-pier connection is made through two rigid-link elements, whose orientation is orthogonal to the deck (i.e. in the frames plane); one rigid-link is located on the right-side of the desk, the other one on the left-side. Piers are fully restrained at the foundation level. The structural bearings are modelled with non-linear constitutive law that consider their post-failure behaviour. Bearings’ failure can lead to the full loss of support from the pier head. This condition detects a possible collapse LS of the structure. Displacement capacity of bearings is derived from the pier cap and bearing seats geometry and considered as deterministically known. This modelling is carried out using multi-linear link elements. The fixed bearings alignment is modelled by one fixed support and four longitudinally fixed and transversally sliding supports. The movable bearings alignment is modelled by four free sliding supports and one that is transversally fixed and longitudinally sliding. Assumed constitutive laws for bearings in longitudinal and transversal directions are shown in Fig. 6 and in Fig. 7, respectively.