Stochastic Load Models and Footbridge Response

Abstract

Pedestrians may cause vibrations in footbridges and these vibrations may potentially be annoying. This calls for predictions of footbridge vibration levels and the paper considers a stochastic approach to modeling the action of pedestrians assuming walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. to be random variables. By this approach a probability distribution function of bridge response is calculated. The paper explores how sensitive estimates of probability distribution functions of bridge response are to some of the decisions to be made when modelling the footbridge and when describing the action of the pedestrians (such as for instance the number of load harmonics). Focus is on estimating vertical structural response to single person loading.

Vibration reduction of footbridges subjected to walking, running, and jumping pedestrian

“…Since the vertical component produced by a person is predominantly higher than the longitudinal and transversal components, this study has considered the vertical component (Shahabpoor et al, 2016; Casciati et al, 2017; Rezende et al, 2020). The vertical force produced by the pedestrian’s feet is usually of the same magnitude and can be approximated by a sine function (Zivanovic, 2006; Kala et al, 2009; Pedersen and Frier, 2010; Caprani and Ahmadi, 2016; Fujino and Siringoringo, 2016), which is present by equation (1)where W=mpg is the weight of the pedestrian; fp is pedestrian pacing rate (pedestrian frequency), which is a function of pedestrian velocity and stride length, fp=vlp (Pedersen and Frier, 2015); ηk represents the coefficient of Fourier series named as "dynamic load factor (DLF)"; φk is the harmonic phase angle, which can be taken uniformly random in the range of [−π,π] (Racic and Pavic, 2010; Racic and Brownjohn, 2011).…”

“…where W ¼ m p g is the weight of the pedestrian; f p is pedestrian pacing rate (pedestrian frequency), which is a function of pedestrian velocity and stride length, f p ¼ v l p (Pedersen and Frier, 2015); η k represents the coefficient of Fourier series named as }dynamic load factor ðDLFÞ}; φ k is the harmonic phase angle, which can be taken uniformly random in the range of ½Àπ,π (Racic and Pavic, 2010;Racic and Brownjohn, 2011). For a walking pedestrian, Young (2001) proposed DLFs for the first four harmonics as a function of the walking rate assumed to be in the range from 1 to 2.8 Hz, which is shown in equation ( 2) in the present study…”