Chapter 15 Probabilistic Analysis of Human-Structure Interaction in the Vertical Direction for Pedestrian Bridges Federica Tubino Abstract This paper deals with the quantification of the effects of human-structure interaction in the vertical direction for footbridges. Analyses are based on the study of a coupled system of the footbridge, modeled as a continuous dynamic system, and pedestrians, schematized as moving single-degree-of-freedom systems, characterized by random dynamic properties. The equivalent dynamic properties of the coupled system are estimated based on a state-space approach. Results of Monte Carlo simulations show that pedestrians can strongly modify the dynamic properties of the footbridge, especially regarding the damping ratio. A numerical application to some literature examples shows that the model is able to reproduce experimental findings on real footbridges. Keywords Footbridges • Human-structure interaction • Monte Carlo simulations • Probabilistic analysis • Serviceability 15.1 Introduction Modern footbridges are very slender structures with low damping characteristics, and they are often characterized by natural frequencies falling within the range of typical human step frequencies. Thus, the can be very sensitive to humaninduced vibrations and their serviceability assessment is becoming a central step in their design. Recent guidelines [1–5] and research papers (e.g. [6]) provide simplified procedures to deal with their serviceability analyses. The author of the paper has introduced an equivalent spectral model for human-induced forces on footbridges in unrestricted pedestrian traffic [7], which has been validated both experimentally [8] and numerically [9]. Then, the model has been generalized in order to taken into account pedestrian interaction in crowded conditions [10]. All these procedures are based on simplified expressions of pedestrian-induced forces, which neglect human-structure interaction. Recent literature has recognized that human-structure interaction could have a determinant role in the assessment of human-induced vibrations of footbridges. Concerning vibrations in the lateral direction, it is widely recognized that synchronization between pedestrians and footbridge motion may lead to instability problems (e.g. the London Millennium Bridge). Many models have been introduced in the literature in order to model lateral synchronization. Dealing with vibrations in the vertical direction, experimental measurements on real structures seem to demonstrate that human-structure interaction is beneficial, providing an equivalent additional damping to the footbridge [11–13]. Thus, experimental tests in laboratory conditions have been carried out on scaled footbridges, confirming the results on real structures [14]. Analogous findings have been reported for staircases [15, 16]. Different models have been proposed in the literature to deal with human-structure interaction in the vertical direction, mainly representing pedestrians as equivalent single-degree-of-freedom or multi-degree-of-freedom systems [17–19], as an inverted pendulum [20], or as a bipedal walking model with damped compliant legs [21, 22]. In the analysis of grandstands and stadia occupied by humans, some researchers have been modeling sitting or standing humans as single- or multi- degree-of-freedom systems and analyzed the properties of the coupled system from a deterministic [23] or probabilistic [24] point of view. The main issue in the analysis of human-structure interaction in footbridges is the representation of pedestrian motion both in terms of the dynamic characterization of moving pedestrians (experimental measurements available in the literature mainly deal with sitting or standing humans) and in the analysis of the dynamic properties of the coupled dynamic system composed by the footbridge and the moving pedestrians. Within this framework, two papers have been recently published where pedestrians have been modelled as moving SDOF systems with random dynamic properties [25, 26]. In [25], the interaction among pedestrians is neglected, and an application to a specific footbridge with fixed dynamic characteristics is shown. In [26], a modelling framework based on a microscopic model of F. Tubino ( ) Department of Civil, Chemical and Environmental Engineering, University of Genova, Via Montallegro 1, 16145, Genova, Italy e-mail: federica.tubino@unige.it © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_15 117
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