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• W46785428 abstract "Footbridge vibration has received much attention in recent years. However, stochastic models for crowd loading are not common, and estimation of crowd-induced vibration is typically done through enhancement factors applied to single pedestrian loading models. This work compares two such models, a moving force model and a spring-mass-damper model (SMD). Typical ranges for various pedestrian parameters are examined, and it is found that the pacing frequency has by far the greatest influence on bridge vibration response. It is also found that the magnitude of the response for pacing frequencies near the bridge natural frequency is lower for the SMD model, but otherwise the results prove similar. This suggests that moving SMD models may be more suitable than moving force models when the bridge natural frequency is in the critical frequency range. 2 EVACES 2011 – Experimental Vibration Analysis for Civil Engineering Structures (2011) noted that several recently published design guidelines, while adopting a similar general approach, all differed in the input parameters used even for these moving force models and that the results derived from applying each of the guides to a benchmark structure varied by a factor of approximately four. It has further been acknowledged for a long time that there is a need for a probabilistic approach to pedestrian loading (Matsumoto et al, 1978; Wheeler, 1982). Despite this, design codes such as BS 5400 (1978, 2006) and Eurocode 5 (EN 1995-2:2004) use deterministic moving force models to predict the response of a single pedestrian. Zivanovic (2006) stated that these models are commonly unable to accurately predict the response of a bridge due to a single pedestrian and usually overestimate it significantly. This inevitably leads to overestimation of the crowd response if enhancement factors are used in conjunction with moving force models. Archbold (2008) also found the moving force model to be conservative as it does not consider interaction between the pedestrian and the moving bridge surface, while Clemente et al (2010) added that if the interaction between the pedestrian and the bridge is to be considered, the pedestrians should be modelled as ‘biological oscillators’. 1.2 Approach of this work In order to model the interaction between a pedestrian and the bridge surface, the authors have employed a moving spring mass damper (SMD) model to represent a single pedestrian (Caprani et al, 2011). This single degree of freedom SMD model captures changes in vertical forces applied to vibrating bridge surfaces. This SMD model is then moved across an idealized bridge at a velocity derived from a combination of pacing frequency and step length. The bridge used in the model is a simply-supported beam, chosen to be susceptible to excitation from typical pedestrian pacing rates. To model the footfall force, a time-varying harmonic force is applied to the pedestrian mass, as proposed by Fanning et al (2005). Input parameters for this model include pedestrian mass, step length, pacing frequency, pedestrian stiffness and damping properties associated with the pedestrian model. The aim of the work reported herein is to determine the sensitivity of the numerical models and estimated acceleration levels induced in the bridge to a range of input parameters related to the movement of the crossing pedestrians. The results from the SMD pedestrian model are thus compared to those estimated using the conventional moving force model. 2 USE OF SMD MODELS TO REPRESENT HUMAN LOADING 2.1 Human leg stiffness Rapoport et al (2003) stated that in repetitive physical activity, such as running, hopping and trotting, a subject bounces on the ground in a spring-like manner. Geyer et al (2006) state that walking is also a bouncing gait. This is due to knee, ankle and hip flexure throughout the gait cycle (Rapoport et al, 2003; Lebiedowska et al, 2009). Blum et al (2009) stated that leg stiffness is a key parameter of modelling legged locomotion. Lee and Farley (1998) and Geyer et al (2006) represented the human leg as a compliant spring-mass model while running and walking, respectively. Rapoport et al (2003) stated that constant mechanical stiffness may not be applicable to the human leg as joint stiffness is nonlinear in nature as damping may be present and as a result, a model which accounts for this damping may improve the model predictions Lee and Farley (1998) acknowledged that spring and damping elements have been incorporated into the legs of some models of walking in order to match ground reaction force (GRF) patterns observed in human walking. They report that the values used in these models are generally higher (kP =12-35.5 kN/m) than the leg stiffness values reported for normal walking (kP ≈11 kN/m). Geyer et al (2006) stated that these models are too complex to serve as conceptual models. The authors reference Dickinson et al (2000) and Srinivasan and Ruina (2005) as stating that, despite being inaccurate, the stiff-legged motion remains the mechanical concept for a walking gait. Geyer et al (2006) themselves state that not stiff but compliant legs are fundamental to the walking gait." @default.
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• W46785428 date "2011-01-01" @default.
• W46785428 modified "2023-09-23" @default.
• W46785428 title "A Parametric Study of Pedestrian Vertical Force Models for Dynamic Analysis of Footbridges" @default.
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• W46785428 doi "https://doi.org/10.21427/d79f8h" @default.
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