Influence of the Second Bending Mode on the Response of High-Speed Bridges at Resonance
Publication: Journal of Structural Engineering
Volume 131, Issue 3
Abstract
This paper deals with the assessment of the contribution of the second bending mode to the dynamic behavior of simply supported railway bridges. Traditionally the contributions of modes higher than the fundamental have been considered of little importance for the computation of the magnitudes of interest to structural engineers (vertical deflections, bending moments, etc.). Starting from the dimensionless equations of motion of a simply supported beam subjected to moving loads, the key parameters governing the dynamic behavior are identified. Then, a parametric study over realistic ranges of values of those parameters is conducted, and the influence of the second mode examined in detail. The main purpose is to decide whether the second mode should be taken into account for the determination of the maximum displacement and acceleration in high-speed bridges. In addition, the reasons that cause the contribution of the second bending mode to be relevant in some situations are highlighted, particularly with regard to the computation of the maximum acceleration.
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Acknowledgment
The writers wish to express their gratitude to Mr. Jorge Nasarre, from the Spanish National Railways (RENFE), also a member of the ERRI D-214 Committee, for his help and encouragement during the development of this investigation.
References
Biggs, J. M. (1964). Introduction to structural dynamics, McGraw–Hill, New York.
European Committee for Standardization (CEN. (2002a). “Actions on structures. Part 2: General actions—Traffic loads on bridges. Final Draft prEN 1991-2,” Eurocode 1, Brussels, Belgium.
European Committee for Standardization (CEN. (2002b). “Basis of Structural Design. Annex A2: Application for bridges. Final PT Draft EN 1990-prAnnex A2.” Brussels, Belgium.
European Rail Research Institute, D-214 Committee (ERRI D-214. (2001). “Ponts-Rails pour vitesses . Rapport Final.” Rep. No. 9, Utretch, France (in French).
Frýba, L. (1996). Dynamics of railway bridges, Thomas Telford, London.
Frýba, L. (1999). Dynamics of solids and structures under moving loads, 3rd Ed., Thomas Telford, London.
Frýba, L. (2001). “A rough assessment of railway bridges for high speed trains.” Eng. Struct., 23, 548–556.
Klasztorny, M., and Langer, J. (1990). “Dynamic response of single-span beam bridges to a series of moving loads.” Earthquake Eng. Struct. Dyn., 19, 1107–1124.
Li, J., and Su, M. (1999). “The resonant vibration for a simply supported girder bridge under high-speed trains.” J. Sound Vib., 224(5), 897–915.
Museros, P. (2002). “Vehicle-bridge interaction and resonance effects in simply supported bridges for high speed lines.” PhD thesis, Superior School of Industrial Engineering, Technical Univ. of Madrid, Madrid, Spain (in Spanish).
Museros, P., and Alarcón, E. (2002). “An investigation on the importance of train-bridge interaction at resonance.” Proc., 6th Int. Conf. on Computational Structures Technology, Civil-Comp Press, Stirling, Scotland, 335–336.
Museros, P., Romero, M., Poy, A., and Alarcón, E. (2002). “Advances in the analysis of short span railway bridges for high speed lines.” Comput. Struct., 80(27–30), 2121–2132.
Museros, P., Vivero, G., and Alarcón, E. (1999). “Moving loads on railway bridges: the Spanish Code approach.” Proc., 4th European Conf. on Structural Dynamics (Eurodyn ’99), A.A. Balkema, Rotterdam, The Netherlands, 675–680.
Olsson, M. (1991). “On the fundamental moving load problem.” J. Sound Vib., 145(2), 299–307.
Smith, J. W. (1988). Vibration of structures: Applications in civil engineering design, Chapman & Hall, London.
Yang, Y. B., Lin, C. L., Yau, J. D., and Chang, D. W. (2004). “Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings.” J. Sound Vib., 269(1–2), 345–360.
Yang, Y. B., Yau, J. D., and Hsu, L. C. (1997). “Vibration of simple beams due to trains moving at high speeds.” Eng. Struct., 19(11), 936–944.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 131 • Issue 3 • March 2005
Pages: 405 - 415
Copyright
© 2005 ASCE.
History
Received: Dec 8, 2003
Accepted: May 27, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
Notes
Note. Associate Editor: Barry Thomas Rosson
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