Journal of Bridge Engineering

Modern footbridges are often characterized by architectural demands for light, slender, and long structures that may lead to excessive vibration problems. In past decades, occurrences of pedestrian-induced vibration on footbridges have been reported, notably at the Toda Bridge in Japan, the Millennium Bridge in London, and the Solferino in Paris. In 1989, we observed a peculiar type of lateral vibration at the Toda Bridge during the passing of congested crowds. Hundreds of pedestrians walked in a synchronized manner among themselves, which created remarkable lateral vibration in the structure. Approximately 10 years later, public attention on pedestrian-induced lateral vibration increased significantly when the Solferino Bridge in Paris and the Millennium Bridge in London showed a similar phenomenon during the passing of congested crowds. These three most well-known cases have triggered extensive study, and pedestrian-induced vibration has emerged as an important topic in vibration study. A considerable amount of research, experiments, published reports, and design guidelines on this topic has been produced over the last two decades. The intriguing questions regarding the phenomenon are, how do we formulate lateral pedestrian force, and how do we conceptualize excitation and synchronization mechanisms? To find the answers, many models have been proposed and validated numerically or experimentally. This paper is aimed at providing a critical conceptual review on the development of studies on pedestrian-induced lateral vibration of footbridges. Focus is placed on the development of pedestrian load modeling, the conceptualization of excitation and synchronization mechanisms, design guidelines, and vibration countermeasures.

This article describes the results of extensive full-scale experiments carried out on two lively footbridges recently built in Milan, Italy. The objective of the study was to assess the dynamic characteristics of the bridges and the expected vibration level induced by pedestrians. A preliminary vibration analysis of the bridges revealed their potential sensitivity to human-induced vibrations in the vertical direction. Two sets of experiments were carried out, one before and one after the installation of tuned mass dampers. Furthermore, bridge vibrations during a marathon event were recorded and analyzed. Experimental and analytical results were compared for several loading scenarios.

In 1999 and 2000, the two vibration incidents at the Paris Passerelle Solferino Bridge and the London Millennium Bridge triggered a major revision of existing knowledge concerning footbridge response to pedestrian-induced actions. In the last 15 years, an incredibly large amount of research has emerged on the topic. Although researchers have provided many valuable scientific contributions regarding the understanding and modeling of pedestrian-induced vibrations of footbridges, there is still a need to determine what real improvements have been achieved in design procedures. This article provides a critical overview of the methodologies proposed over the last four decades, as well as their code implementations, and summarizes the actual advances available that consultants can use to their advantage in bridge design.

In this paper, a biomechanical crowd–structure interaction model is proposed and further implemented to adequately estimate the energy exchange between pedestrians and a footbridge. The proposed model focuses on the vibrations in the vertical direction, and it allows for taking into account the change of the modal properties of the structure due to the presence of the pedestrians, thus improving the numerical estimation of the response of the structure under pedestrian flows. The model involves two submodels, namely (1) a pedestrian–structure interaction submodel and (2) a crowd submodel. The first submodel follows from a modal projection of a system with two degrees of freedom, which simulates the behavior of each pedestrian, on the vibration modes of the structure. The parameters of this model have been estimated from the accelerations recorded on a real footbridge. For the second submodel, the crowd behavior is simulated via a multiagent method. The performance of the resulting overall model is assessed by correlating the experimental and numerical dynamic of a real footbridge under a group of pedestrians at different controlled step frequencies. In particular, the change in the first natural frequency induced by the pedestrian–footbridge interaction is discussed in detail. The proposed model leads to numerical results that exhibit good agreement with the recorded experimental values. Therefore, it becomes a valuable tool for estimating the change on the modal properties of a footbridge induced by the crowd–structure interaction phenomenon.

Aluminum structures provide a high strength-to-weight ratio, are corrosion resistant, and are esthetically pleasing. Hence, their use in bridge construction has recently begun to increase, especially for pedestrian bridges. Because of their relative light weight as compared with other structures, they often exhibit fundamental vertical frequencies outside the range of normal pedestrian walking frequencies. Despite this, they tend to be lively structures, easily excited by pedestrians, resulting in large-amplitude accelerations. An experimental program was undertaken by the authors to study the vibration characteristics and performance of three full-scale aluminum pedestrian bridges, two in the laboratory and one in the field. Although the lowest fundamental frequencies for all three bridges fall outside the normal range of pedestrian walking frequencies, there is the possibility of higher harmonics of walking loads near resonance or in resonance with the fundamental vertical mode. The aluminum bridges studied were instrumented and subjected to a range of pedestrian-load tests to understand the performance of existing periodic models in predicting the dynamic response. The performance of these models (assuming pedestrian forces to be a summation of harmonics) has thus far only been assessed for cases in which the fundamental frequency is resonant with the first harmonic of walking, often considered the most severe case for design. This is the first time, to the knowledge of the authors, that these models have been studied for the case of bridges that are nonresonant with the fundamental mode. This article notes important observations regarding the performance of these models in predicting the serviceability of bridges made out of lightweight materials, such as aluminum, for cases in which the higher harmonics of pedestrian walking are either nonresonant or near resonance with the fundamental vertical flexure mode.

This article presents an evaluation of the dynamic behavior of a slender steel footbridge before and after the installation of two tuned mass dampers (TMDs). The results of the experimental study show that the damping devices lead to an increase of the effective damping ratio of the critical mode. Additional tests involving the structural vibrations induced by a limited number of persons revealed that the TMD units are effective in reducing the structural response. However, the obtained reduction highly depends on the type of human excitation. To verify the response of the footbridge for large groups and crowds, a comprehensive numerical analysis is performed. The results are compared to the response predicted by the procedures of the Sétra and HiVoSS design guides. For the bridge without TMD units, a significantly higher structural response is predicted by the design guides; the bridge has a short span and is lightly damped, so the steady-state resonant conditions assumed in the design guides are not reached for pedestrians who cross the bridge at a normal walking speed. For the bridge with TMD units, the design guides predict a significantly lower structural response than do the more detailed numerical simulations because the critical mode is highly damped and no longer dominates the structural response. In addition, the effectiveness of the damping devices is considerably less than that expected on the basis of the corresponding increase in effective damping ratio because crowd-induced loading is near-harmonic and transient, not harmonic.

Many spectacular pedestrian bridges were designed and constructed recently. Owing to their special shapes, it is expected that various types and a wide range of vibration frequency components will be induced by pedestrians. To avoid accidents and reduce risk, the vibration characteristics of pedestrian bridges during their service life must be carefully assessed. The most direct and reliable way to study the vibration characteristics of a structural system is through field vibration tests. In this paper, a series of full-scale field vibration tests (including ambient, forced, and free vibration tests) were carried out on a pedestrian bridge at City University of Hong Kong (CityU). The difficulties encountered in the field tests are reported. The recently developed Bayesian methods were utilized to determine the modal parameters of the bridge based on measurements from all three kinds of tests. In addition to the most probable values (MPVs) of modal parameters, the associated posterior uncertainties were also analytically calculated. Four modes were identified, including three vertical bending modes and one torsional mode. The accuracy of the identified modal parameters was assessed through the posterior uncertainty. Because the amplitudes of the vibration in the three kinds of tests were different, the modal parameters determined from these kinds of tests were compared and discussed. Suggestions related to the proper use and potential vibration problems during the lifecycle of pedestrian bridges were provided based on the analysis results.

Through their biomechanical properties, pedestrians interact with the structures they occupy. Although this interaction has been recognized by researchers, pedestrians’ biomechanical properties have not been fully addressed. In this paper, a spring-mass-damper (SMD) system, with a pair of biomechanical forces, was used to model a pedestrian for application in vertical human–structure interaction (HSI). Tests were undertaken in a gait laboratory, where a three-dimensional motion-capture system was used to record a pedestrian’s walking motions at various frequencies. The motion-capture system produced the pedestrian’s center of mass (COM) trajectories from the captured motion markers. The vertical COM trajectory was approximated to be the pedestrian SMD dynamic responses under the excitation of biomechanical forces. SMD model parameters of a pedestrian for a specific walking frequency were estimated from a known walking frequency and the pedestrian’s weight, assuming that pedestrians always walk in displacement resonance and retain a constant damping ratio of 0.3. Thus, biomechanical forces were extracted using the measured SMD dynamic responses and the estimated SMD parameters. Extracted biomechanical forces from all test trials were expressed with third-order Fourier series. It was found that the amplitude of the first-order biomechanical forces changed with the pacing frequency and that it fit a linear model. Amplitudes of the second- and third-order biomechanical forces were found to be scattered and not closely related to walking frequency. A generalized extreme value distribution was fit to each of the amplitudes. Phases in the model for biomechanical forces were not related to pacing frequency, and a mean value of the phases is proposed.

A 142-m, three-span continuous footbridge over the Esino River (Italy) is considered as a case study to illustrate a number of challenging aspects in its static and dynamic design. The adoption of an optimized steel deck with a variable cross section together with the use of external prestressing tendons in the central span allows a substantial reduction of structural weights. The resulting footbridge requires a proper model for the assessment of its behavior up to the ultimate limit state as well as attention to vibration control under pedestrian loading at the service limit state. The former issue is addressed through the use of a specifically developed material and geometric nonlinear finite-element formulation. Regarding vibration control, an original combination of two different systems is used, i.e., high damping rubber (HDR) stripes and tuned mass dampers (TMDs). The HDR stripes, applied between the steel deck and the concrete floor, increase the overall damping of the footbridge, whereas the TMDs significantly reduce the accelerations at the most critical frequencies. The design of this nonconventional solution for vibration control is discussed, and the results of experimental tests in the early stage of the footbridge construction are illustrated. The experimental results allow the validation of the structural model used in the design as well as the evaluation of the influence of the HDR stripes and of the nonstructural components on the modal properties of the completed footbridge, permitting fine-tuning of the TMDs before they are installed.

A low-cost vibration-monitoring system was developed and installed on an urban steel-plated stress-ribbon footbridge. The system continuously measures the acceleration [using 18 triaxial microelectromechanical system (MEMS) accelerometers distributed along the structure), the ambient temperature, and the wind velocity and direction. Automated output-only modal parameter estimation based on the stochastic subspace identification (SSI) was carried out to extract the modal parameters (i.e., the natural frequencies, damping ratios, and modal shapes). Thus, this study analyzed the time evolution of the modal parameters over data monitoring for 1 year. First, for similar environmental/operational factors, the uncertainties associated with the SSI-based techniques used and to the acceleration records used were studied and quantified. Second, a methodology for tracking the vibration modes was established, because several of them with closely spaced natural frequencies were identified. Third, the modal parameters were correlated against external factors. It has been shown that this stress-ribbon structure is highly sensitive to temperature variations (frequency changes of more than 20%) with strongly seasonal and daily trends. Fairly simple dynamic multiple regression models for the lowest persistent vibration modes were derived, and excellent correlations for some of them were obtained. These correlations enable the influence of these uncertainties on modal estimates to be removed, thus facilitating their use as damage-sensitive features.