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

807

12

Modal shape X (-)_P6 Modal shape X (-)_P10 Modal shape X (-)_P14

0.09 0.10 0.06

0.22 0.20 0.16

0.41 0.47 0.38

The N2 method accuracy has been investigated by comparing the displacement enveloples of superstructure, i.e. the displacement demand obtained assuming different reference points, with those from the inelastic time-history analysis (ITHA). The result of the N2 method and the ITHA are presented in Table 9.

Table 9. Comparison of displacement demand obtained by the N2 method with different reference point and the ITHA. Pier no. Reference point Uniform shape X (+) [ m ] Uniform shape X (-) [ m ] Modal shape X (+) [ m ] Modal shape X (-) [ m ]

N2 (envelope) [ m ]

ITHA [ m ]

1 2 6

P1 P2 P6

0.19 0.23 0.26 0.20 0.18

0.21 0.25 0.25 0.21 0.15

0.22 0.21 0.23 0.20 0.19

0.20 0.23 0.22 0.20 0.16

0.22 0.25 0.26 0.21 0.19

0.14 0.18 0.22 0.19 0.10

10 14

P10 P14

The match between displacement demand envelopes obtained by the N2 method and by the ITHA is clearly much better in the case of the reference point at the top of no. 10 pier. In the plastic hinge at the bottom of the no. 10 pier, the first limit condition is reached. Hence, to obtain good correlation with the ITHA, an appropriate choice of the reference point needs to be made. A good option for the reference point seems to be the point at the deck level where the first collapse mode occurred in the analysis. Hence, the N2 method, assuming a reasonable reference point, can estimate the response surprisinlgy well, even in a irregular bridge structure (Fig. 15).

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

IT

niform shape (+) 0 odal shape (+) 0

niform shape ( ) 0 odal shape ( ) 0

isplacement m

2

0

0 0 00 02002000 000 000 000 000

tation m

Fig. 15. The response of the bridge obtained by the N2 method with reference point P10 and the ITHA.

5. Conclusions It is acknowledged that explicit consideration of structural inelastic behaviour is necessary in seismic evaluation of existing structures. Although non-linear time history analysis (NTHA) appears to be the most appropriate choice, non linear static (pushover) single-mode methods are preferred for their alleged simplicity. However, it is important to understand their limitations and/or approximations in comparison to NTHA. The extension of the applicability of the N2 method, a nonlinear static method developed for buildings, to bridges, has been discussed in this paper. The specific problem considered is related the choice and influence of the control point for the displacement response in the construction of the pushover curve. The case study was an asymmetric reinforced viaduct with a large number of simply-supported spans. It resulted, for this case-study that - however - represent a large population of existing structures in Italy, that the displacement at the deck level of a particular column, where the first collapse mode occurs, could be used to construct the pushover curve in the N2 method.