MS11.5- Footbridge Vibrations

Vibration serviceability under human-induced loading has become a key design criterion when determining the structural shape and dimension of footbridges. Over the last two decades, the vibration serviceability of footbridges under walking excitation has been widely investigated. However, little to no attention has been paid to running actions as a design load. The concerns about the impact of dynamic running actions (single person or in group) have grown significantly as (1) the involved load amplitudes are significantly higher than for walking, (2) the dominant frequency spectrum is different from walking and (3) footbridges are progressively more exposed to running due to the increased focus on a healthy lifestyle. So far, however, no expertise is available on running excitation as a load scenario for civil engineering structures. The state of the art involving dynamic running actions is limited to single-person load models valid for running on a rigid laboratory floor. The load model presented by currently available standards and design guidelines represents a single or a small group of runners as perfectly periodic and perfectly synchronized individuals. The structural response is then calculated assuming resonant conditions with each of the relevant structural modes. These unwarranted assumptions risk to lead to unrealistically high predicted vibration levels that compromise any slender structural design or require the installation of expensive vibration mitigation devices. The development of realistic load scenarios for running excitation requires input on (1) intra-person variabilities, (2) inter-person variabilities and (3) human-structure interaction phenomena specifically for the running actions, and their impact on the resulting structural response. In this contribution, it is first shown how vibration measurements on the lower back of a running person can be used to reconstruct the vertical dynamic running load. Second, this technique is used to collect information on the in-field running behavior of individuals and groups. This data is then used to identify and characterize intra- and inter-person variabilities of the dynamic running load. Based on these results, the impact of these variabilities on the resulting structural response is investigated numerically. Finally, recommendations are formulated for further research and development of procedures for the vibration serviceability assessment of footbridges under dynamic running actions.

Slender footbridges are predominantly sensitive to human-induced vibrations. While in the past two decades the main focus was on pedestrian-induced vibrations, topical research questions investigate the dynamic impact of running actions. In comparison to the walking load, these running actions involve higher load amplitudes, a different dominant frequency content and discontinuous contact between the feet and the footbridge. The load model that is currently applied for running actions in the Vibration Serviceability Assessment (VSA) of footbridges is only applicable for a single runner and does not account for Human-Structure Interaction (HSI) phenomena. These phenomena involve (1) active HSI where the body locomotion is influenced by the motion of the supporting structure and (2) passive HSI where the human body acts as a mechanical system resulting in a coupled human-structure system with modified modal parameters. For walking, HSI has a normative impact on the resulting structural response and therefore on the VSA of footbridges. The question now is whether HSI also occurs for running actions and if this is relevant to be accounted for in the VSA of footbridges. To facilitate the identification, characterization and eventually the development of load models including HSI for running, experimental data is required. The present work presents the results of an extensive measurement campaign that has been performed involving 8 participants to investigate active HSI for running actions. A treadmill is placed on a vibrating footbridge that is excited by a shaker at a desired frequency and structural acceleration level. For reference purposes, the measurements are repeated on a rigid laboratory surface. The applied measurement setup is suitable for both indoor and infield measurements and allows the simultaneous registration of the contact forces, the body motion and the structural response. The participants are equipped with in-shoe pressure sensors and an accelerometer fixed to the lower back. In addition, a treadmill is instrumented with an optical movement analysis system to capture multiple relevant running motion metrics, such as the flight and contact time, on a step-by-step basis. Analysis of the running metrics indicates the existence of active HSI and the vital role it may play in the VSA of footbridges. Depending on the amplitude of the footbridge vibrations and ratio between the pacing rate and the frequency of the footbridge vibrations, the normal running locomotion of the participants is modified. The modification in running motion furthermore has a clear impact on the resulting structural response.

Authors: Laura Purpura, Hüseyin Güner, Sébastien Hoffait & Vincent Denoël. Nowadays, improvements in design and manufacturing methods and a more efficient use of structural materials make it possible to design slender and lighter structures such as footbridges. However, these lightweight structures are prone to higher levels of vibrations due to ambient forces such as wind or pedestrians. It is not unusual that footbridges are used for marathons where a large group of people would load the footbridge to higher levels causing possible structural disorders. The comfort of pedestrians must also be guaranteed under more usual loading. Therefore, it is just as important to study the behavior of the structure before its construction as to make verifications after construction. Indeed, reality is often different from simulations, and this can be revealed by dynamic testing experiments on the structure after it has been built. There exist several approaches to modal identification. In this work the vibration testing and modal analysis of a footbridge using the Operational Modal Analysis with eXogenous (OMAX) forces method will be performed. The OMAX method takes into account both the unmeasured ambient forces and measured artificial forces. In our case, an artificial force is imposed using an in-house designed shaker. In this method, the ambient forces are considered as a real part of the excitation and not as noise, as it would be in any other experimental modal analysis. In other words, it is a combined operational-experimental method used to identify the modal characteristics of the footbridges. The advantages of this method are (i) that smaller shakers can be used, which is more convenient and less costly, due to the high amplitude of the artificial forces; (ii) moreover, since the modes are excited by the artificial forces it is possible to obtain the modal masses and thus mass-normalized mode shapes, which is not possible with a classic method relying only ambient excitation; (iii) furthermore, ambient forces are usually confined to a narrow frequency band, so that only a small number of modes can be identified. A larger frequency range can be covered using a shaker, (iv) finally, it is known to give higher accuracy in the results compared to other identification methods, (v) last but not least, from a practical point of view, using OMAX for the identification of the modal properties of a footbridge does not require to close the footbridge to the pedestrian traffic, which is a significant advantage for the experimental testing of existing in-use footbridges. The method has been used and verified on a measurement campaign on the Tilff cable-stayed footbridge, and by basing the identification procedure on shaker forces created with a shaker developed at the University of Liège. Application of the OMAX method allowed to improve the quality of the identification up to a certain traffic level. To assess the accuracy of the method, the results of the method applied to ambient vibrations where respectively 1, 5, 8 and 10 persons are crossing the footbridge are analyzed.

Tibetan footbridges are very slender, light and flexible structures, and are used in mountainous terrains, often to overcome deep valleys. Consequently, these structures are very sensitive to the dynamic wind action, not only in terms of stability and ultimate resistance but also serviceability limit states. A Tibetan bridge with a span of about 215 m has been designed in the North of Italy. The deck is suspended by four main cables running at a height of more than 110 m from the bottom of a V-shaped valley. The structure is stiffened by two stabilizing cables, running below the bridge and outside the planes of the main cables, and connected to the deck through a system of hangers. The deck consists of a system of steel profiles and bracings, supporting an about 1 m-wide porous steel grid working as walkway. For the ultimate limit states, the possibility that the grid is iced or covered by snow has also to be considered. The lateral protective nets are very porous, supported by a system of horizontal elements and vertical struts. The resulting structure is very light and presents many low-frequency modes. Moreover, several modes exhibit very similar shapes and close vibration frequencies. The bridge has recently been tested in the CRIACIV Wind Tunnel Laboratory in Prato, Italy. A sectional model of the deck and suspension cables was reproduced at the scale 1 : 7.5. A set of static tests allowed measuring through a pair of high-frequency force balances the aerostatic coefficients of the deck. Noteworthy is the significant value of the drag coefficient. Afterwards, the model of the bridge was elastically suspended in the wind tunnel by means of eight coil springs, using also several cables to restrain the unwanted degrees of freedom. Transversal and rotational (torsional) vibrations were allowed, and the aerodynamic derivatives were measured through a free-vibration procedure (Bartoli et al., 2009). The aerodynamic damping for the oscillations in the mean wind direction was estimated based on the classical quasi-steady theory. Mean wind angles of attack of ±5 deg were considered in addition to the baseline null incidence. Afterwards, the results of modal analysis and wind tunnel tests were employed to perform frequency-domain calculations of the bridge dynamic response under stationary turbulent wind. The effect of considering a simplified aerodynamic admittance function was also investigated. The structure exhibited a significant susceptibility to the wind excitation, including some concerns about flutter stability. Under moderate mean wind velocities, non-negligible lateral and torsional oscillations are expected, requiring the setting of a limit wind speed for the closure of the bridge. Finally, the considered Tibetan bridge resulted to be a very interesting case study to address the problem of wind-induced vibrations from both ultimate and serviceability points of view. References: Bartoli, G., Contri, S., Mannini, C., Righi, M. (2009): Toward an improvement in the identification of bridge deck flutter derivatives. Journal of Engineering Mechanics 135 (8), 771-785