Keywords: brake attempt, equations of motion, rail interaction, resonance, stability, ultimate dynamics, updated Lagrangian formulation, wave propagation.

The problem of distribution of braking forces into structural components of railway viaducts and their supporting systems appears in reconstructions of old railway bridges for loads and velocities for present railway transport. The braking forces for which the bridges were designed have been distinctly increased in the facilities of modern trains. The interaction between rail and bridge in the propagation of braking forces appears as a significant item in the assessment. The braking forces are transmitted to rails, bridges and supporting systems of the railway viaducts studied.

The theory was adopted in scope of a braking test on the Railway Bridge in Rendsburg, Germany. This bridge crossing the Kiel Canal was launched in 1911 and is in full railway transport use until now [1,2,3,4,5]. The bridge consists of two viaduct bridges on northern and southern sides of the Kiel Canal with total lengths of 1260 and 908 m, respectively, and of the central Canal Bridge with a total length 294 m. In order to obtain the assessment of the problem a train braking test was made on the bridge. The experimental train adopted in the braking test consisted of two Diesel locomotives of type 218, five E-locomotives of type E 143 as well as two E-locomotives of type 140. The total weight of the experimental train was 741 t. The maximal braking force was 852 kN.

In order to find the actual distribution of braking forces other data measured included the stress in the rails of the Canal Bridge, the forces in the contacts of the Canal Bridge between the end pylons, the horizontal and vertical displacements of the Canal Bridge and the frequency spectrum, response and damping of the Canal Bridge. A maximum stress of 16 N/mm2 was initiated in the rail. In the gaps between the Canal Bridge and end pylons a pressure force of 150 kN was registered. The stress in the rail was measured at intervals of ±16 MPa.

The continually welded rail contributes significantly to the propagation of horizontal braking forces into structural components of viaduct bridges. The calculations made with use of standards for the design of railway bridges resulted in 40% participation of the end pylons in the distribution of the braking forces on the railway viaduct and 60% of the braking forces were transmitted the Canal Bridge and rails.

The evaluation of the results has led to some new considerations dealing with applicability and accuracy of present standards for treatment of the above problems as well as some new assessments of the rail interaction in the distribution of the horizontal braking forces in railway viaducts.

1

A. Tesar, H. Helms, B. Meyer, H. Fuchs, H. Nöller, "Die Ankerbolzen- messungen an der Eisenbahnhochbrücke Rendsburg", Der Stahlbau, 4, 1997.

2

A. Tesar, H. Helms, H.J. Schröder, "Die Brücken über den Nord-Ostsee-Kanal - Faszination der Brückenbaukunst im Laufe der Zeit", Nieswand Verlag, Kiel, 1995.

3

"Schlussbericht zur Auswertung des kleinen Bremsversuchs an der Eisenbahnhochbrücke Rendsburg", Ing.-Büro Böger und Jäckle, Henstedt-Ulzburg, November 1995.

4

"Rendsburger Hochbrücke - Kleiner Bremsversuch", Meßergebnisse, Ing.-Büro Tscheslog und Beck, Stipsdorf, September 1995.

5

DS 804, "Vorschrift für Eisenbahnbrücken und sonstige Ingenieurbauwerke (VEI)", January 1983.

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