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CivilComp Proceedings
ISSN 17593433 CCP: 77
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 82
Influence of the Second Flexural Mode on the Response of HighSpeed Bridges P. Museros+ and E. Alarcón*
+Department of Structural Mechanics, Superior School of Civil Engineering, University of Granada, Spain
P. Museros, E. Alarcón, "Influence of the Second Flexural Mode on the Response of HighSpeed Bridges", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 82, 2003. doi:10.4203/ccp.77.82
Keywords: resonance in railway bridges, highspeed bridge, second mode contribution,.
Summary
This paper deals with the assessment of the contribution of the second flexural mode
to the dynamic behaviour of simply supported railway bridges. Alluding to the
works of other authors, it is suggested in some references [1,2] that the dynamic
behaviour of simply supported bridges could be adequately represented taking into
account only the contribution of the fundamental flexural mode. On the other hand,
the European Rail Research Institute (ERRI) proposes that the second mode should
also be included whenever the associated natural frequency is lower than 30 Hz [1].
This investigation endeavours to clarify the question as much as possible by
establishing whether the maximum response of the bridge, in terms of
displacements, accelerations and bending moments, can be computed accurately not
taking account of the contribution of the second mode.
To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed =VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed highspeed bridges, a parametric analysis is conducted over realistic ranges of values of and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the socalled Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twentyone different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode. The most important conclusions obtained from the investigation are the following:
References
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