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 distribution, Φ i is equal to 1 for the deck, while it is equal to z i z P ⁄ for the piers connected to the deck. The z i term is the height of point i above the foundation of the individual pier and the z P term is the total height of pier P (distance from the ground to the centre line of the deck). Second load distribution is proportional to the first mode shape. In this distribution, Φ i is proportional to the component, in the considered horizontal direction, of the modal displacement at point i , of the first mode, in the same direction. In this regard, the latest Italian technical provisions (NTC2018) indicate that at least two distributions of lateral loads should be considered, one within the main distributions (Group 1) and the other in the secondary distributions (Group 2). One of the secondary distributions is a uniform pattern, based on lateral forces that are proportional to mass regardless of elevation (uniform response acceleration). This is the previous constant along the deck distribution. While among the main distributions there is one that refers to cases in which first mode has a modal participation mass unless of 75%, and another one, compatible with each case, that is a “modal” pattern, proportional to lateral forces consistent with the lateral force distribution determined by an elastic response spectrum analysis, including in the considered direction a number of modes with overall mass participation at least of 85%. Hence, in the presence of multiple modes with comparable participation masses, the second load distribution is one that considers the contribution of the modes according to the response spectrum analysis. This is the typical situation, for example, of bridges with simply supported decks, in which each pier represents a separate dynamic system with its own "vibration mode". 2.2. Target displacement and reference point Eurocode 8 Part 2 (EC8-2, CEN 2005) prescribes that, in each of the two horizontal directions x and y, the horizontal loads should be increased until a target displacement is reached at a reference point. Moreover, it refers that in longitudinal direction x, the target displacement of the reference point, d T,x , should be 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 y, the target displacement of the reference point, d T,y , is equal to d E,y , calculated similarly to d E,x above. The spectrum analysis should be carried out using effective stiffness of ductile members (cracked stiffness). Eurocode 8 Part 2 (EC8-2, CEN 2005) refers that the reference point should be the centre of mass of the deformed deck. A suitable option for the reference point could be the point at the deck level where the greatest lateral displacement is expected (Fajfar et al. 1997). 3. Description of the case study 3.1. Bridge description The bridge over the Tagliamento II river is in the Italian highway A23 (Palmanova-Tarvisio). The simply supported beams bridge is composed by two structurally separated roadways with a curvilinear trend of R=3000m. In this study the attention is focused on the Nord roadway. The deck is about 706m long and consists of 16 spans all having equal length of 43m (41.20m calculation span). The longitudinal profile is shown in Fig. 2. The simple deck is made of four reinforced concrete beams pre-thesis, spaced of 3.55m, which are connected by two span transoms and those at the head, all in reinforced concrete post-thesis. The beams have a double T section with a height of 2.60m, and the slab has a thickness of 0.20m. The deck is about 13m wide, except for the two spans near the junction (no.15 and no.16), which have a width of about 16.50m being made up of five beams having the same geometric characteristics as the other spans. The piers from the first till the thirteenth consist of triple stem RC frames, with a trapezoidal horizontal cross beam, 2m tall, 4m wide and 12m long. They have a circular cross section with a diameter equal to 1.6m. After the 1976 earthquake, the first pier was reinforced and has a diameter equal to 2.1m. The fourteenth and fifteenth piers consist of quadruple stem RC frames, with a trapezoidal horizontal cross beam, 2m tall, 4m wide and 15.55m long. They have a circular cross section of 1.6m diameter. Piers have been divided into five groups, according to their heights and longitudinal rebars (see Table 1). Transversal profile of typical four beams deck with triple stem frames pier (left) and five beams deck with quadruple stem frames pier (right) are shown in Fig. 3. 799 4