Reliability Analysis of Footbridge Serviceability Considering Crowd Loading

Abstract

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: