Keywords: railway bridge, dynamic, fatigue, assessment, Miner hypothesis, rain-flow.

The objective of this project is to develop a methodology for assessing and evaluating the effects of dynamic loading on metal railway bridges. Accurate assessments of bridges must be made in order to avoid unnecessary and untimely expensive repairs and replacements, while at the same time maintaining an adequate margin of safety. Safely extending the life and maximizing load ratings of such railway bridges, while maintaining ongoing, uninterrupted train operations, is of both concern and great economic benefit to the bridge owner. Achieving such goals depends to a large extent on developing and maintaining an effective bridge inspection program.

The case study bridge used is the Thomastown Railway Viaduct (UB 87) which carries single line traffic and is located approximately 100 miles south of Dublin on the Cherryville - Waterford line. The structure is a through arch bridge and is approximately 65m long and comprises mild steel plate girder and lattice members. The loading from the rolling stock is transferred to the deck by means of waybeams.

The phenomenon of metal fatigue was discovered during the expansion of railroads. Fatigue causes steel to fracture at stresses well below its ultimate stress when subject to repeated/cyclic loading. Approximately 80-90% of failures in metallic structures are related to fatigue and fracture [1]. Fatigue only occurs in situations when the cyclic stresses are above the fatigue limit. The fatigue or endurance limit for most steels ranges between 35% and 50% of the tensile strength of the material [2]. The Wöhler () curve is used to describe the relationship between the level of stress and the number of cycles to failure at that stress for a particular material [3]. In steels, the fatigue life/number of cycles to failure steadily increases as the stress decreases until the stress level of the fatigue limit is reached. Fatigue failures occur very suddenly. However, the initial phase of the development of fatigue cracks give the bridge owner an opportunity to perform non-destructive testing on the bridge.

Railway loading by nature is of variable amplitude. When a fatigue analysis of a bridge is being carried out the critical members in the bridge structure need to be identified. The cross beams and longitudinal beams at the entry and exit to the Thomastown Railway Viaduct were identified as being critical. If the live loading and corresponding stresses on a bridge member are below the fatigue limit, then the fatigue effects will not manifest themselves and can be neglected. However, at locations on the bridge that experience high stresses then fatigue can be important. The fatigue damage per cycle is principally determined by the stress range.

It is extremely difficult to accurately recreate the loading history for an old bridge. There are a large number of elements that contribute to this, such as; the variability in the suspension of the rolling stock, the condition of the bridge and track and the variable speed of the train as it crosses the bridge. Thus, as this work develops, the currently used deterministic model will be phased out and the statistical approach will be adopted. In order to consider the fatigue loading of railway bridges certain computer models need to be developed. The computer models generated include bridge, rolling stock and track models and are coded in Fortran. In the computer program developed, the bridge, track and rolling stock are modelled separately and their interactions are considered explicitly. This enables the interaction between the wheels and the track to be modelled non-linearly. The bridge model developed is tree dimensional, whereas the rolling stock and track models are two dimensional. A direct time stepping method was used in the dynamic analyses it was desired to pick up the vibrations of every degree of freedom of each member in the bridge. In order to attempt to evaluate the cumulative damage undergone by a bridge, several steps must be followed:

1. An estimate of the frequency and axle weights of the trains.
2. Properties of the bridge material, particularly tensile and fatigue strength.
3. Accurate survey carried out of the bridge.
4. Generate loading data from old timetables.
5. Generate computer models of bridge, track and rolling stock for the dynamic analyses.
6. Measure the dynamic response of the bridge to validate the computer models.

1

Committee on Structural Safety and Reliability of the Structural Division, "Fatigue Reliability: Introduction", in "Journal of the Structural Division, Proc. ASCE", 108 (ST1), 3-23, 1982.

2

Suresh S., "Fatigue of Materials", University Press, Cambridge, 1998.

3

Sandor B.I., "Fundamentals of Cyclic Stress and Strain", University of Wisconsin Press, Wisconsin, 1972.

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