This paper is a continuation of a previous one, Sanz-Andr! es, Santiago-Prowald, Baker and Quinn (J. Wind Eng. Ind. Aerodyn. 91 (2003) 925) concerning the loads generated on a structural panel (traffic sign) by vehicle running along the road, although obviously, the results are also applicable to the effects of other moving vehicles such as trains. The structural panel was modelized as a large plate whose largest dimension is perpendicular to the vehicle motion direction. In this paper a similar approach is used to develop a mathematical model for the vehicle-induced load on pedestrian barriers, modelized as a large plate whose largest dimension is parallel to the vehicle motion direction. The purpose of the work is to develop a model simple enough to give analytical results, although with the physical phenomena correctly accounted for, such as to be able to explain, at least qualitatively, the main characteristics of the phenomenon, as observed in the experiments performed by Quinn et al. (J. Wind Eng. Ind. Aerodyn. 89 (2001) 831).Actually, in spite of the model simplicity, results of the theoretical model show a reasonable good quantitative agreement with the experimental results. The aim of this and previous publications is to provide to the transport infrastructure community with some simple tools that can help to explain, and in some cases also to compute, the unsteady loading produced by moving vehicles on persons and installations placed close to the roads or tracks. r Nomenclature b barrier half-height (m) c F net force coefficient c F 2S force coefficient in the case of two sources c F 2Sm maximum value of the force coefficient in the case of two sources c F m extreme value of the force coefficient c F c p pressure coefficient c l ðyÞ point force coefficient c N dummy variable c s configuration parameter d distance from the barrier to the body middle plane (m) d q distance between sources (m) f ðtÞ complex potential ðm 2 =sÞ h b barrier distance to ground (m) k ratio of source intensities p static pressure (Pa) t time (s) t p characteristic time of vehicle pass t v viscous time scale x barrier section position considered (m) x 0 source position in ground-fixed reference frame (m) x 0 ; r vehicle fixed reference system (m) x; y; z ground fixed reference system (m) A b twice the vehicle cross-sectional area, body cross-sectional area far downstream ðm 2 Þ B sign half-span (m) F net force, per unit length (N/m) L characteristic length N symmetry of the flow, N ¼ 1 two-dimensional, N ¼ 2 axisymmetric three-dimensional flow Q; Q 1 ; Q 2 volumetric source intensity ðm 3 =sÞ Re Reynolds number T dimensionless time U N vehicle speed (m/s) V velocity modulus (m/s) V N incident speed modulus (m/s) ðV N Þ y projection of V N along y ðV N Þ xz projection of V N in the plane xz X r dimensionless relative coordinate X rm dimensionless relative position of the force extremes y position across the barrier in trigonometric variable (rad) r fluid density ðkg=m 3 Þ a speed orientation angle (rad) A. Sanz-Andr! es et al. /...
The main object of this study is to contribute to the study of the train-induced force on pedestrians with a theoretical model based on unsteady potential flow. The same method can be applied to other bodies and other kind of moving vehicles.The outcome of this theoretical model is that the force coefficient (referred to the vehicle speed and the pedestrian cross-section diameter) acting on the pedestrian are proportional to a single parameter which involves the pedestrian cross-section diameter, the vehicle cross-section area and the distance between the pedestrian and the vehicle.The results of the present model concerning the change in modulus and orientation experienced by the pedestrian, as the vehicles pass by, has a similar appearance to that considered in the European standards.The results obtained are mainly qualitative because of the simplifying assumptions needed to obtain a simple formulation leading to analytical results, except in the case of a vehicle with streamlined front shapes, where quantitative results can be expected.
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