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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Thus, the fatigue design of the stringers, which are cyclically loaded in tension between 0 and  max , the allowable limit stress for wrought iron stringers was 6 kg/mm² (60 MPa) according to the 1891 regulation. 3. Definition of an acceptable fatigue range To describe the fatigue behaviour of materials and assemblies, a classification by constructive details is implemented in norms, such as the Eurocodes (Afnor, 2005). The fatigue curves of the Eurocodes show a slope m=3 up to 5E6 cycles (the corresponding stress range is called the constant amplitude fatigue limit), then a slope m=5 up to 1E8 cycles. From 1E8 cycles, it is the cut-off limit, without any evolution of the stress range with the number of cycles. This approach, although useful in the conservative determination of the remaining life of assemblies, shows limitations, as shown in Taras and Greiner, 2010 (Gallegos Mayorga et al., 2017). The latters propose indeed another classification with a single slope (m=5), up to the cut-off at 1E8 cycles. In this study, we consider the SIA fatigue curve (SIA, 2011), which has the same slope as Taras and Greiner proposal, and which includes the determination of the constant amplitude fatigue limit at 1E7 cycles. We therefore propose a fatigue limit at 1E7 cycles of 58 MPa and a cut-off limit of 37 MPa. This fatigue limit of 58 MPa is in accordance with the 60MPa limit determined for wrought iron stringers dimensioned by the 1891 regulation. In a self-life method, we also consider a partial factor for fatigue strength  Mf = 1.35 (high consequence of failure). This enables us to define an acceptable fatigue zone for the study of the stringers of old bridges, as shown in the following Fig. 3.

Fig. 3. Definition of an acceptable fatigue range considering the constant amplitude fatigue limit at 1E7 cycles defined in the SIA norm.

4. Comparison of the aggressiveness of trains on a bridge For these calculations, a set of 37 real stringers was selected, including different periods of construction (from 1860 to 1915), different spans and inertias. 26 different spans are studied ; these vary from 1.77 to 4.68 meters, with an average value of 2.75 meters. These stringers are not currently subject to fatigue; they have already been repaired or reinforced. These repairs or reinforcements are registred in the inventory compiled by SNCF. It is therefore possible to compare the stresses calculated in the stringers with the acceptable limit previously defined and then to validate or not the relevance of this value.