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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 77
Edited by: B.H.V. Topping
Paper 76

Stress Ranges in Bridges under High Speed Trains

L. Frýba+, C. Fischer+ and J.-D. Yau*

+Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, Prague
*Tamkang University, Taipei, Taiwan

Full Bibliographic Reference for this paper
, "Stress Ranges in Bridges under High Speed Trains", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 76, 2003. doi:10.4203/ccp.77.76
Keywords: dynamics of bridges, classification of stress ranges, parametric study.

The trains have attained the speed of 200 to 350 km/h in most countries and may cause the intensive vibration of railway bridges. The French and German maintenance services remarked the destabilization of ballast on bridges of small and medium spans and the ballast has reflected by a white colour in that cases. It is caused by milling of ballast grains during the resonant vibration of bridges. The phenomenon affects the safety of the railway traffic, the passenger comfort and the maintenance economy.

The problem was tackled in [1,2,3,4] and the resonant vibration was studied in [3,5] together with the estimation of the maximum amplitudes. A simple theoretical model provided the deflection-, bending moment- and vertical acceleration-time histories which were analysed with respect to their amplitudes. The vertical acclerations have appeared as a limit case.

The submitted paper shows the classification of the bending moment-time history using the rain-flow counting method and presents the stress spectra that are important for the fatigue analysis, calculation of inspection intervals and for the estimation of residual life of bridges.

According to the design standards (e.g. Eurocodes 1, 2, 3), the dynamic stresses are covered by the dynamic impact factor


where $ \sigma_{dyn}$ and $ \sigma_{stat}$ are the maximum dynamic and static stresses, respectively. The dynamic impact factors are prescribed by Eurocodes for various cases and speeds.

On the other hand, the fatigue is substantially affected by the stress range defined as the difference


between the local maximum $ \sigma_{max}$ and local minimum $ \sigma_{min}$. The Equations (76.1) and (76.2) clearly show the important difference between $ \varphi$ and $ \Delta \sigma$.

The fatigue calculations prescribed in Eurocodes 1, 2 and 3 are based on the stress spectra received at speeds up to 200 km/h, while the present study extends their knowledge up to the speed of 500 km/h.

The paper defines the stress ranges that appear in bridges subjected to high speed trains and they were calculated for both the concrete and steel bridges of spans 5 to 50 m under three types of high speed trains, ICE 2, Eurostar/TGV and Talgo AV 2, at speeds 5 to 500 km/h.

The travelling speed substantially affects the form of the stress spectra and the values of stress ranges. The stress spectra are weak at low speeds and filled in at higher speeds. The maximum stress ranges increase with increasing speed, of course, with several local maxima depending on the dynamic system bridge + train. On the other hand, the total number of stress cycles approximately remains constant when changing the speed.

The stress spectra depend on the bridge span and on the applied train. The ICE 2 train generally provides an agreable effect on the stress ranges in comparison to the other assumed trains. As the concrete bridges have greater mass and damping and lower natural frequencies than the steel bridges, their stress spectra are favourable with respect to fatigue.


The supports of the grants GA CR 103/01/0243, 103/03/P080, GA AS CR A 207 1103 and of the project KONTAKT ME 503 in the Czech Republic as well as of the grant NSC 91-2211-E-032-018 in the Republic of China are gratefully acknowledged.

Matsuura, A., "Dynamic behaviour of bridge girder for high speed railway bridge", Quarterly Reports, Tokyo, Railway Technical Research Institute, 20, No. 2, 70-76, 1979.
Yang, Y.-B., Yau, J.-D., Hsu, L.-C., "Vibration of simple beams due to trains moving at high speeds". Engineering Structures, 19, No. 11, 936-944, 1997. doi:10.1016/S0141-0296(97)00001-1
Frýba, L., Náprstek, J., "Appearance of resonance vibration on railway bridges", in "Advances in civil and structural engineering computing practice", B.H.V. Topping (editor), Civil-Comp Press, Edinburgh, 377-382, 1998. doi:10.4203/ccp.56.10.2
ERRI D 214 "Rail bridges for speeds higher than 200 km/h", Research report of the European Rail Research Institute, Utrecht, 1999.
Frýba, L., "A rough assessment of railway bridges for high speed trains", Engineering Structures, 23, No. 5, 548-556, 2001. doi:10.1016/S0141-0296(00)00057-2

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