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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 196

The Use of Ramp Superposition to Analyse the Influence of Road Irregularities on Maximum Beam Stresses due to a Moving Load

D. Cantero1, A. González1 and E.J. O'Brien2

1School of Architecture, Landscape and Civil Engineering,
2Institute for Sustainable Development,
University College Dublin, Richview, Ireland

Full Bibliographic Reference for this paper
, "The Use of Ramp Superposition to Analyse the Influence of Road Irregularities on Maximum Beam Stresses due to a Moving Load", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 196, 2007. doi:10.4203/ccp.86.196
Keywords: bridge, dynamics, vehicle, interaction, bending moment, ramp, superposition, ISO profile.

The road profile is a key parameter in the dynamic amplification that a bridge experiences as result of a vehicle traversing it. The road profile can be classified according to different guidelines (ISO, IRI) from 'very good' to 'very poor'. However, these classifications do not keep a relationship with the level of dynamics that the bridge will be excited with. The crossing of a vehicle over a 'good' profile could produce a wide range of bridge responses depending on the location and magnitude of its irregularities.

Li et al. [1,2] developed the principle of ramp superposition to gather a better understanding of the influence of each road segment on the mid-span stresses. It consists of discretizeing the road profile into a series of ramps. Then, the contribution of each ramp is evaluated individually and mid-span stresses are obtained for every possible ramp location. The total effect due to a road profile can be obtained from multiplying the effect of each unit ramp by the magnitude of the measured ramp and adding together the effect of all ramps. In this paper, the concept is extended to the full length of the beam, since maximum total stresses do not necessarily take place at mid-span.

In order to illustrate how this method can be employed to analyse a profile, the bridge has been modelled as a simply supported beam and the vehicle as a quarter-car model. Then, the critical road and bridge section locations are identified for three road profiles. An envelope of maximum bending moments for any section of the bridge can be obtained for a given road profile or a given unit ramp location. From this envelope, it is possible to extract the maximum moment and the critical section where it takes place.

This paper has shown that the consideration of all sections across the full beam length is necessary when dealing with dynamics effects, and an envelope of maximum bending stresses have been obtained to evaluate the significance of these stresses for a given road profile or a specified road singularity (i.e. a damaged joint).

Y. Li, E.J. O'Brien, A. González, "The Development of a Dynamic Amplification Estimator for Bridges with Good Road Profiles", Journal of Sound and Vibration, Vol. 293, 125-137, 2006. doi:10.1016/j.jsv.2005.09.015
E.J. O'Brien, Y. Li, A. González, "Bridge Roughness Index as an Indicator of Bridge Dynamic Amplification", Computers & Structures, Vol. 84, 759-769, 2006. doi:10.1016/j.compstruc.2006.02.008

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