Structural response and design criteria of footbridges with tuned mass dampers
File(s)
Author(s)
Garcia Troncoso, Natividad Leonor
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2020-01
Date Awarded
2020-07
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Ruiz-Teran, Ana Maria
Stafford, Peter
Sponsor
Secretaria Nacional de Educación Superior, Ciencia, Tecnología e Innovación del Ecuador (SENESCYT)
Escuela Superior Politécnica del Litoral (ESPOL)
Publisher Department
Civil and Environmental Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)