Keywords: riveted bridge, train-bridge interaction, fatigue, rainflow counting.

The structure investigated in this paper is a railway bridge that was built between 1905 and 1907 and reconditioned in 1965. It is a riveted truss bridge with a span of 40 metres. The bridge's construction material is a form of alkaline low carbon steel called "basisches Martin-Flusseisen". The bridge came under scrutiny as it has developed well visible cracks on five out of the eleven cross-girders. The intention is to qualify this damage and assess whether it could have been caused by fatigue or rather by inappropriate detailing.

At first a test programme was conducted to allow for the extraction of experimental modal parameters. A global numerical model was created in the ANSYS software and tuned until the modes showed good agreement. For the interaction analysis a spatial model of an ICE3 train with suspensions and couplings was developed. The contact of the wheel and the rail was modelled using a Hertzian spring [1]. The assumed train velocity was 120km/h. Time steps of 0.002s and 0.005s were used. In the closed system of ANSYS two approaches to the interaction solution were taken. The first was to couple the two systems by constraint equations. This bond is active for the solution of one given time step, is then removed, the train shifts forward and new constraint equations are defined in the updated position. The aforementioned procedure is valid only until no loss of contact occurs. For verification an uncoupled, iterative solver was developed. The two systems influence each other by transmission of interaction forces on the wheels and the resulting displacements of the rails. The two approaches matched well.

For evaluating the fatigue the detailed stress histories were extracted. The rainflow algorithm [2] was used for counting the number of stress cycles. The smaller time step of 0.002s gives more low level perturbations, which can be filtered out, as these are not critical. Finally, for a fatigue assessment of this type a time step of 0.005s is sufficient.

Comparing the numerical results to the normative curve the one year cycles lies below it. The number of trains using the bridge per day could be estimated at 53. By assuming a life expectancy of one hundred years the final curve reaches the normative one for class 80. This leads us to believe that fatigue could have caused cracking of the element at the joint.

1

C. Esveld, A.W.M. Kok, "Interaction between moving vehicles and railway track at high speed", Rail Engineering International, 27(3), 14-16, 1998.

2

D. Ribeiro, R. Calçada, R. Delgado, "Fatigue on metallic railway bridges: Methodology of analysis and application to Alcácer do Sal Bridge", IABMAS, Porto, Portugal, 2006.

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