Paul Archbold

Characteristic vertical response of a footbridge due to crowd loading

The characteristic vertical vibration of a flexible footbridge subject to crowd loading is examined in this paper. Typically, bridge vibrations produced from a crowd of pedestrians are estimated by using an enhancement factor applied to the effect caused by a single pedestrian. In this paper, a single pedestrian model, represented by a spring mass damper, which incorporates variables such as pedestrian mass and body stiffness, is used to calibrate a computationally efficient moving force model. This calibrated moving force model is further used in Monte Carlo simulations of non-homogenous crowds to estimate characteristic vertical vibration levels. Enhancement factors, which could be applied to simple single pedestrian moving force models in estimating the response due to a crowd are thus derived. Such enhancement factors are then compared to previously published values. It is found that the greatest difference between the spring mass damper and moving force models respectively occurs when the bridge frequency is at the mean crowd pacing frequency. For bridges with frequencies even slightly removed from this mean, moving force models appear adequate.

Lateral loads applied by pedestrians at normal walking velocities

The issue of horizontal loading from pedestrians has received increased attention from bridge designers and researchers in the past decade, primarily due to notable instances of excessive vibration of structures subjected to this form of excitation. Nonetheless, there is a scarcity of reliable information on the magnitude and nature of this type of loading. The authors have carried out over 100 walking trials on 27 healthy adult participants walking at normal velocities on a rigid walkway mounted with a force plate. Subject data, pertinent tempro-spacial parameters of gait, walking velocity and pacing frequency are presented for each participant. Additionally, the lateral forces recorded during these tests are presented and analysed. A simplistic force function, based on the fundamental frequency of the applied excitation force, which may approximate the actual load applied by individual pedestrians is proposed. Further, this function is improved by consideration of the lateral force contribution at higher order harmonics of the fundamental frequency, and relevant dynamic load factors and phase angles associated with the individual force functions are derived and optimised.

A Study on the Effect Slope Walking Has on Vertical Pedestrian Loading in Terms of Footbridge Design

This paper reviews current literature in terms of the effect of slope walking on vertical pedestrian loading. In this review the gait style, gait parameters, and vertical pedestrian loading is reviewed. The reason why such a study was conducted is explained; and the force profiles from the authors own experimental studies are presented. From that study, two contrasting vertical force profiles exist; one for rigid walking and one for flexible walking; here possible reasons for such differences are explored.

The Effect of Clusters within Crowds of Pedestrians on the Vertical Response of a Flexible Footbridge

The issue of excessive vibrations of footbridges due to the passage of pedestrians has been well documented in the past decade. Despite this there still remains great uncertainty as to how to predict the acceleration response of a footbridge due to crowd loading. This paper investigates the vibration response of a flexible footbridge subjected to crowd loading. Using a statistical model which caters for the variability of pedestrians, the vibration response of the footbridge is obtained. In this work, the effect of social groups or clusters of pedestrians in a crowd is investigated. Herein a cluster is defined as two or more pedestrians walking together with the same velocity. The predictions of this model are compared to a model which uses only lone pedestrians walking within a crowd. None of the current design codes or guidelines considers the possibility of pedestrians walking together. The size of the clusters is found in literature to follow a Poisson distribution. In this paper variations of the probability of clusters appearing in the crowd are assessed. It is found that the response of a crowd with clusters present is similar to the predictions of the UK National Annex to Eurocode 1.

Reliability analysis of footbridge serviceability considering crowd loading

The characteristic vertical response of flexible footbridges subjected to single pedestrian and crowd loading is examined in this paper. Typically, bridge vibrations produced from a crowd of pedestrians are estimated by using an enhancement factor applied to the effect caused by a single pedestrian. In this paper a moving force model is used in Monte Carlo simulations of a non-homogeneous sample of single pedestrians and crowds to estimate characteristic vertical vibration levels. Also in this work, statistical distributions of the bridge parameters are considered, these include flexural rigidity, mass and rotational stiffness at the supports. It was previously proven by the authors that the statistical range of pedestrian parameters, most notably the pacing frequency, has a significant effect on the bridge deck vibration. In this paper, probability of failure is calculated for ranges of pedestrian and bridge input parameters and it is found that the addition of statistical ranges for bridge parameters has only a small effect on the vertical acceleration response of the bridge deck. It reduced the probability of serviceability failure for a bridge with a natural frequency of 1.96 Hz and 2.2 Hz subjected to the loading of a characteristic single pedestrian. sign codes, such as BS 5400 (2006) and Eurocode 5 (2004), use deterministic load models to determine the vertical acceleration response to a single pedestrian. These models are commonly unable to accurately predict the response due to a single pedestrian and usually overestimate it significantly (Zivanovic, 2006). Archbold (2008) reported that a moving force model, such as that used in BS 5400 (2006) does not allow for the interaction between the pedestrian and the moving structure, thus its predictions may be conservative. 1.2 Approach of this work In this work pedestrians and the bridge are modelled using statistical distributions of their respective input parameters. The bridge used in the model is chosen to be susceptible to excitation from typical pedestrian pacing rates. The beam is modelled as a simplysupported beam with some rotational stiffness allowed for at the supports. A time-varying harmonic force, proposed by Fanning et al (2005), is used to represent the pedestrian force imparted to the bridge. Input parameters for the model include pedestrian mass, step length and pacing frequency, bridge mass, flexural stiffness, damping ratio and rotational stiffness at the supports. The aim of the work herein is to assess the effect of introducing statistical ranges of the bridge and pedestrian parameters on the reliability and probability of serviceability failure of bridges assessed using currently available design guideline. 2 HUMAN RESPONSE TO BRIDGE VIBARATION 2.1 Overview of phenomenon Zivanovic et al (2005) give a thorough literature review of human perception of surface vibrations, consequently only a brief overview is given here. In the case of loading on pedestrian bridges, the pedestrian is both the source and the receiver. Therefore if the vibrations are intolerable, the pedestrian will stop walking and the vibrations will dampen out. This is a simple solution to bridge vibrations but an unacceptable one, as users may choose an alternative route in future, obviating the bridge function. Standing and walking pedestrians are known to experience bridge vibrations differently, with standing pedestrians being more susceptible. Zivanovic et al (2005) reports on Leonard (1966) which rightfully stated that it was not economically justifiable to design a footbridge so that a standing person would not feel vibrations, as users of the bridge will most likely be walking. It is acknowledged by Pedersen & Frier (2010) that individual humans perceive vibrations differently and that the acceptance level of vibrations is thus a random variable in itself. As a result, human perception of vibrations is difficult to predict due to the many variables: each person reacts differently to the same vibrations, and even an individual exposed to the same vibrations on different days is likely to react differently. The current vibration acceptability guidelines generally do not consider such variables. 2.2 Serviceability limits Eurocode 5 (2004) is a recent design code for the design of timber structures and includes recommendations for vibration of footbridges. However, the response model defined is not material dependent, and so can be used to check the vibration serviceability of a footbridge constructed of any material (Pavic 2011). The code specifies use of the comfort criteria of EN1990:2002/A1 which states that if the natural frequency of a bridge is below 5 Hz it should be assessed for vibrations due to pedestrian loading. Using Eurocode 5 (2004) for a bridge with a natural frequency less than or equal to 2.5 Hz, the bridge deck acceleration for a single pedestrian is: