MS11.7 - Footbridge Vibrations

The increasing slenderness and lightness of modern footbridges make the vibration serviceability assessment a key aspect for their design and maintenance. Vibration assessment of footbridges relies on an in-depth knowledge of the footbridge dynamic behavior as well as on reliable models of human-induced loads. A promising approach to the characterization of footbridge dynamic behavior is represented by computer vision-based techniques. Over the past few years, computer vision-based monitoring has acquired increasing importance thanks to the availability of high resolution and frame rate consumer-grade cameras. In contrast to traditional monitoring systems relied on dense sensor networks, computer vision-based monitoring requires the installation of one or more cameras from different measuring points together with, if necessary, some targets on the monitored structure. The high performance of consumer-grade cameras and the contactless and non-destructive nature of the computer vision approach can make this technology particularly suited to the dynamic monitoring of footbridges. Nevertheless, the accuracy that can be reached in terms of displacement measurements and identified modal properties needs to be investigated. In this context, the paper presents the short-term dynamic monitoring of a steel footbridge based on computer vision techniques. An action camera was adopted to acquire videos with 4k resolution and 60 fps (frame per second). The structural deflection caused by both a jumping pedestrian and the wind were recorded from different measurement positions. The post-processing of the video frames (image processing, noise filtering, …) is presented and discussed in the paper. Special attention is paid to the use of circular targets placed on the footbridge, which allowed for the identification of vertical deflections smaller than one pixel. A traditional accelerometer-based monitoring system is also installed on the footbridge for validation purposes. Displacements evaluated through a double integration of the measured accelerations are compared to those obtained from the image processing. Results demonstrate the high potential of computer vision-based systems for the monitoring of structures and infrastructures.

Vibration serviceability (VS) under human-induced loading has become a key design criterion for footbridges, in particular involving crowded conditions. Decisive parameters in the VS assessment are the probability distribution function (PDF) of the step frequencies in the crowd and human-structure interaction (HSI). In the literature, the PDF of the step frequencies is described by a Gaussian distribution. It is generally assumed that for increasing pedestrian densities, the mean step frequency decreases and the standard deviation increases. HSI on the other hand, describes the mechanical interaction between the human body and the supporting structure. In the vertical direction, this phenomenon has shown to have a significant impact on the dynamic behavior of the coupled crowd-structure system. The most significant HSI effect is the effective modal damping ratios of the coupled crowd-structure system that are much higher than the inherent modal damping ratios of the empty footbridge. Despite the extensive research in the last two decades, there is still a lack of experimental research for the validation of models for crowd-induced loading. The aim of this contribution is to verify experimentally the reliability of an equivalent spectral model (ESM) for crowd-induced loading [1,2] in the vibration serviceability assessment of footbridges. To this end, the Eeklo Footbridge benchmark dataset is used [3], involving four data blocks for two pedestrian densities (0.25 pedestrians/m² and 0.50 pedestrians/m²). In this dataset, the footbridge and pedestrian motion are registered simultaneously and the trajectory and time-variant pacing rate of every pedestrian in the crowd has been identified. Analysis shows that the PDF of the step frequencies in the crowd can be well represented by a Gaussian distribution. The ESM, function of the PDF of step frequencies and the average weight of the pedestrians, is then used to predict the structural response. HSI is in turn accounted for by means of an equivalent 2DOF-system representing respectively a structural mode and the crowd [4,5]. The reliability of the ESM is assessed comparing the power spectral density function of the recorded structural response and the one obtained theoretically from the equivalent crowd-structure 2DOF system and modelling the loading through ESM. [1] G. Piccardo and F. Tubino, “Equivalent spectral model and maximum dynamic response for the serviceability analysis of footbridges”, Engineering Structures, 40, pp. 445-456 (2012). [2] A. Ferrarotti and F. Tubino, “Generalized Equivalent Spectral Model for serviceability analysis of footbridges”, Journal of Bridge Engineering ASCE, 21(12): 04016091 (2016). [3] K. Van Nimmen, J. Hauwermeiren and P. Van den Broeck, “Eeklo Footbridge: benchmark dataset on pedestrian-induced vibrations”, Journal of Bridge Engineering ASCE: 05021007 (2021). [4] K. Van Nimmen, P. Van den Broeck. Forthcoming. “Using full-scale observations on footbridges to estimate the parameters governing human-structure interaction” Bridge Engineering. [5] F. Tubino, G. Piccardo, “Tuned Mass Damper optimization for the mitigation of human-induced vibrations of pedestrian bridges”, Meccanica 50, pp. 809-824 (2015).

The hangers are the important element on suspension bridges that transfer the forces from the deck to the main cable. To verify their capacity and identify possible risks, the forces transferred by the hangers and the corresponding tension must be determined. However, this is often done using standard equations for determining cable forces. Due to the different lengths of the hangers and the way in which their tensioning is achieved, the effects of boundary conditions occur that need to be taken into account and that require an update of the finite element model at the local level (when the whole bridge structure is observed). This paper presents a method for determining the cable tension of hangers that combines the experimentally determined dynamic properties (natural frequencies and mode shapes) and the numerical model updating. In addition to the usual approach based on the determination of the natural frequency of hangers, this paper presents an approach based on the mode shapes of the hangers. Special attention is paid to the boundary conditions coefficient. The method is applied in suspension bridge case study.