Structural response and design criteria of footbridges with tuned mass dampers
Creators: name: Garcia Troncoso, Natividad Leonor
Publisher: name: Imperial College London
Year: 2020

description: Abstract During the last decades, the mitigation of the effects of human-induced vibrations has been one of the most critical aspects of footbridges construction. Unexpected vibrations of footbridges under pedestrian actions have shown the necessity of developing more realistic representations of loads transmitted by pedestrians, to obtain an accurate dynamic response. This representation should include all the energy introduced at each step and that their amplitude in the lateral direction is related to the dynamic response of the bridge. The London Millennium Bridge in the UK, the Passerelle Léopold-Sédar-Senghor in Paris, France and the Toda Park cable-stayed footbridge in Japan are some of the famous structures which have been experienced unexpected vibrations. These footbridges required the use of supplemental damping devices to control the human-induced vibrations after their construction. However, there are not guidelines or research work so far which account a realistic representation of pedestrian loads whilst considering these devices. Especially for the cases where the serviceability criteria cannot be fulfilled by using conventional approaches. Therefore, this research work includes a detailed literature review of studies concerning to footbridges typologies, pedestrian actions, serviceability criteria and supplemental damping devices. The main emphasis given here is to reduce human-induced vibrations in the vertical and lateral direction. As a result, on an exhaustive analysis of the literature review, girder and cablestayed footbridges using tuned mass dampers under a stochastic pedestrian load model are selected for further parametric studies. For this purpose, a set of footbridges are used to study the benefits of the tuned mass dampers under different pedestrian densities (0.2, 0.6 and 1.0 ped/m2) and two activities, leisure and commuting. This work has been carried out combining Abaqus, Matlab, Python and Fortran software packages. The main purposes of this study are to improve the understanding of the response of these bridges when TMDs are implemented and to provide design recommendations of optimal locations and properties of these devices. This is to mitigate the dynamic response in girder and cable-stayed footbridges under pedestrian actions. In this thesis, a methodology of implementation of TMDs and a detail design procedure are given as a guide to select tuned mass dampers when the maximum comfort is not achieved. The design procedure is complemented by the definition of a comprehensive set of design criteria on how to use supplemental damping devices at the design stage according to the comfort level, mean or maximum, to control the dynamic response in girder and cable-stayed footbridges under pedestrian actions. Based on the parametric studies in both typologies (girder and cable-stayed footbridges), it is shown that tuned mass dampers can be employed at the design stage with efficiencies up to 85% in the reduction of the dynamic response. This can only be achieved if the TMDs are correctly located. For this, it is required to represent and to check the structural accelerations according to the comfort limits. If these responses do not fulfil the serviceability criteria, it is necessary to identify the mode that has a larger contribution to that response. This mode can be identified by representing the response in the frequency domain. Afterwards, the TMD needs to be located at the maximum nodal coordinate where the modal shape dominates the response. In the case that the TMD location is not adequately selected, the TMD efficiency will be decreased, i.e. TMD efficiency ≤ 37%. In most of the cases, one tuned mass damper is enough to control humaninduced vibration. However, there are some cases where it can be required to consider more than one damper, e.g. for handling reasons due to one damper being bulky or due to the existence of other structural elements. For these cases, the tuned mass dampers employed at the same location have similar efficiency as when one TMD was employed. Besides, for girder footbridges, one vertical TMD can be split into more dampers as long as the location is the maximum nodal coordinates of those modal shapes dominating the response, having flexibility within the ±15% of the span length from that point (with variations of the efficiency around 1.0%). For cable-stayed footbridges with one and two towers, the location will be the maximum nodal coordinates, having a flexibility to shift them along the span, from that location, by ± 10%, and ±6%, with variations in the efficiency of around 9% and 2%, respectively. Likewise, for the lateral direction, the TMD can be split into more devices as long as the location corresponds to the maximum nodal coordinates of those modal shapes dominating the response, with a flexibility of locating the TMDs ±5% along the length from that location. In conclusion, several design recommendations including TMD mass ratio in accordance with the comfort level, span lengths, pylon shapes, pedestrian densities and activities are provided. Given that the characteristics of both typologies were obtained as representative of the built footbridges, this research work may facilitate the construction of similar footbridges structures whilst avoiding serviceability problems when a TMD is considered at the design stage.