PSI - Issue 22

Stéphane Sire et al. / Procedia Structural Integrity 22 (2019) 64–69 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4.1. Calculation data and hypothesis

We consider the 3 type trains described in Fig. 2. The 1891 train includes 14 axles and 1915 and 1927 type trains include 20 and 24 axles respectively. The speed of 40km/h is considered for theses historical trains. The following modeling simplifications have been employed (Plu et al., 2016): • the connection between cross-beam and stringer is modelled as a semi-rigid connection transferring 10% of the isostatic bending moment of the stringer • the general bending of the deck is neglected • the dynamic amplification for tracks in mediocre state proposed in ORE (1985) is considered. The stress range calculated in the stringer, determined from a beam model, is assumed to be purely normal. In order to compare the aggressiveness of the type train on the mechanical behaviour of the stringers, we define: , ( , ) the damage caused by train i on the stringer j and , ( , ) the damage caused by reference train (1927 at 100km/h, considered at the current speed of trains) on the stringer j The aggressiveness index (AI) has been established as follows: if ∆ ≥ ∆ then = , , . 100 if ∆ < ∆ then = 0 4.2. Results and analysis The stress calculation in the stringers shows a maximum value of 61 MPa, a minimum value of 21 MPa and an average of 40.6 MPa; the standard deviation is 11.2 MPa. Among the 37 selected stringers, 7 of them have a calculated stress higher than 43 MPa. In other words, seven stringers were likely to be sensitive to fatigue. The analysis of the SNCF inventory of repairs shows that these seven bridges have indeed been subject to fatigue and have been repaired or reinforced (flange continuity, added riveted parts and gussets, replacement of stringers). This result shows that the choice of the SIA fatigue curve (fatigue limit at 58 MPa) coupled with the partial factor for fatigue strength  Mf =1.35 is relevant to identify the stringers whose design made them sensitive to fatigue. For the 37 studied stringers, the aggressiveness index for each train is as follows: • AI 1891 = 0 These index show that the 1891 train is not damaging for the studied stringers. The damage begins indeed with the 1915 train. The reference (1927, 100km/h) train is 64% more damaging than the 1915 train at 40km/h and is 57% more damaging that the 1917 train at 40km/h. Among the 7 bridges identified as likely to be subject to fatigue, one was built in wrought iron in 1869. The calculation of the stringers for this bridge gives a stress of 62 MPa. After observing the mediocre state of the bridge track, a 30 km/h slowdown was imposed in 1958 for the bridge crossing u ntil it’s repaired . In 1998, gussets were added to strengthen the stringer-to-cross-beam connection. Considering only the damage from 1915 onwards, the bridge was slowed down in 1958 to about 3E6 cycles (assuming 8 trains per day) and reinforced in 1998 after about 6E6 cycles. These data are compatible with the calculation model presented in this study. They nevertheless require further works, particularly to determine a more accurate number of cycles to failure. • AI 1915 = 36 • AI 1927 = 43