Benchmark footbridge for vibration serviceability assessment under vertical component of pedestrian load

Vibration serviceability criteria are governing the design and determining the cost of modern, slender footbridges. Efficient and reliable evaluation of dynamic performance of these structures usually requires a detailed insight into the structural behaviour under human induced dynamic loading. Design procedures are becoming ever more sophisticated and versatile and for their successful use a thorough verification on a range of structures is required. The verification is currently hampered by a lack of experimental data that are presented in the form directly usable in the verification process

Quantification of dynamic excitation potential of pedestrian population crossing footbridges

Due to their slenderness, many modern footbridges may vibrate significantly under pedestrian traffic. Consequently, the vibration serviceability of these structures under human-induced dynamic loading is becoming their governing design criterion. Many current vibration serviceability design guidelines, concerned with prediction of the vibration in the vertical direction, estimate a single response level that corresponds to an "average" person crossing the bridge with the step frequency that matches a footbridge natural frequency. However, different pedestrians have different dynamic excitation potential, and therefore could generate significantly different vibration response of the bridge structure. This paper aims to quantify this potential by estimating the range of structural vibrations (in the vertical direction) that could be induced by different individuals and the probability of occurrence of any particular vibration level. This is done by introducing the inter- and intra-subject variability in the walking force modelling. The former term refers to inability of a pedestrian to induce an exactly the same force with each step while the latter refers to different forces (in terms of their magnitude, frequency and crossing speed) induced by different people. Both types of variability are modelled using the appropriate probability density functions. The probability distributions were then implemented into a framework procedure for vibration response prediction under a single person excitation. Instead of a single response value obtained using currently available design guidelines, this new framework yields a range of possible acceleration responses induced by different people and a distribution function for these responses. The acceleration ranges estimated are then compared with experimental data from two real-life footbridges. The substantial differences in the dynamic response induced by different people are obtained in both the numerical and the experimental results presented. These results therefore confirm huge variability in different people's dynamic potential to excite the structure. The proposed approach for quantifying this variability could be used as a sound basis for development of new probability-based vibration serviceability assessment procedures for pedestrian bridges

Modelling human actions on lightweight structures : experimental and numerical developments

This paper presents recent, numerical and experimental, developments in modelling dynamic loading generated by humans. As modern structures with exposure to human-induced loading, such as footbridges, building floors and grandstands, are becoming ever lighter and more slender, they are increasingly susceptible to vibration under human-induced dynamic excitation, such as walking, jumping, running and bobbing, and their vibration serviceability assessment is often a deciding factor in the design process. While simplified modelling of the human using a harmonic force was sufficient for assessment of vibration performance of more robust structures a few decades ago, the higher fidelity models are required in the contemporary design. These models are expected not only to describe both temporal and spectral features of the force signal more accurately, but also to capture the influence, psychological and physiological, of human-structure and human-human interaction mechanisms on the human kinematics, and consequently on the force generated and the resulting vibration response. Significant advances have been made in both the research studies and design guidance. This paper reports the key developments and identifies the scope for further research

Vibration serviceability of footbridges under human-induced excitation : a literature review

Increasing strength of new structural materials and longer spans of new footbridges, accompanied with aesthetic requirements for greater slenderness, are resulting in more lively footbridge structures. In the past few years this issue attracted great public attention. The excessive lateral sway motion caused by crowd walking across the infamous Millennium Bridge in London is the prime example of the vibration serviceability problem of footbridges. In principle, consideration of footbridge vibration serviceability requires a characterisation of the vibration source, path and receiver. This paper is the most comprehensive review published to date of about 200 references which deal with these three key issues. The literature survey identified humans as the most important source of vibration for footbridges. However, modelling of the crowd-induced dynamic force is not clearly defined yet, despite some serious attempts to tackle this issue in the last few years. The vibration path is the mass, damping and stiffness of the footbridge. Of these, damping is the most uncertain but extremely important parameter as the resonant behaviour tends to govern vibration serviceability of footbridges. A typical receiver of footbridge vibrations is a pedestrian who is quite often the source of vibrations as well. Many scales for rating the human perception of vibrations have been found in the published literature. However, few are applicable to footbridges because a receiver is not stationary but is actually moving across the vibrating structure. During footbridge vibration, especially under crowd load, it seems that some form of human–structure interaction occurs. The problem of influence of walking people on footbridge vibration properties, such as the natural frequency and damping is not well understood, let alone quantified. Finally, there is not a single national or international design guidance which covers all aspects of the problem comprehensively and some form of their combination with other published information is prudent when designing major footbridge structures. The overdue update of the current codes to reflect the recent research achievements is a great challenge for the next 5–10 years

Frequency response function-based explicit framework for dynamic identification in human-structure systems

The aim of this paper is to propose a novel theoretical framework for dynamic identification in a structure occupied by a single human. The framework enables the prediction of the dynamics of the human-structure system from the known properties of the individual system components, the identification of human body dynamics from the known dynamics of the empty structure and the human-structure system and the identification of the properties of the structure from the known dynamics of the human and the human-structure system. The novelty of the proposed framework is the provision of closed-form solutions in terms of frequency response functions obtained by curve fitting measured data. The advantages of the framework over existing methods are that there is neither need for nonlinear optimisation nor need for spatial/modal models of the empty structure and the human-structure system. In addition, the second-order perturbation method is employed to quantify the effect of uncertainties in human body dynamics on the dynamic identification of the empty structure and the human-structure system. The explicit formulation makes the method computationally efficient and straightforward to use. A series of numerical examples and experiments are provided to illustrate the working of the method

Experimental characterisation of walking locomotion on rigid level surfaces using motion capture system

Low-frequency structures, such as footbridges and long-span floors, are often sensitive to variations in dynamic loading induced by pedestrians. As a result, the design of these structures using traditional deterministic approaches is being replaced by stochastic load models that can accommodate different styles of walking. To inform development and facilitate wider implementation of the new stochastic approaches, a database of experimental data characterising both inter- and intra-subject variability of gait parameters is required. This study aims to contribute to the development of such a database by providing a set of data for walking over rigid level surfaces. The motion capture system Vicon was used for simultaneous monitoring of the kinematic and kinetic gait parameters. Ten test subjects walking at 13 different speeds participated in the experimental programme. Novel experimental data on pacing rate, step length, step width, angular positions of the legs and the trunk, and the force amplitude were collected and statistically characterised. The acquired data are suitable for calibration of the bipedal pedestrian models intended for civil engineering applications

Measuring ground reaction force and quantifying variability in jumping and bobbing actions

This paper investigates variability in bobbing and jumping actions, including variations within a population of eight test subjects (intersubject variability) and variability on a cycle-by-cycle basis for each individual (intrasubject variability). A motion-capture system and a force plate were employed to characterize the peak ground reaction force, frequency of the activity, range of body movement, and dynamic loading factors for at least first three harmonics. In addition, contact ratios were also measured for jumping activity. It is confirmed that most parameters are frequency dependent and vary significantly between individuals. Moreover, the study provides a rare insight into intrasubject variations, revealing that it is more difficult to perform bobbing in a consistent way. The paper demonstrates that the vibration response of a structure is sensitive to cycle-by-cycle variations in the forcing parameters, with highest sensitivity to variations in the activity frequency. In addition, this paper investigates whether accurate monitoring of the ground reaction force is possible by recording the kinematics of a single point on the human body. It is concluded that monitoring the C7th vertebrae at the base of the neck is appropriate for recording frequency content of up to 4 Hz for bobbing and 5 Hz for jumping. The results from this study are expected to contribute to the development of stochastic models of human actions on assembly structures. The proposed simplified measurements of the forcing function have potential to be used for monitoring groups and crowds of people on structures that host sports and music events and characterizing human-structure and human-human interaction effects

Influence of low-frequency vertical vibration on walking locomotion

Walking locomotion has been a subject of studies in diverse research fields, such as computer, medical, and sport sciences, biomechanics, and robotics, resulting in improved understanding of underlying body motion and gait efficiency and pathology (when present). Only recently, a detailed understanding of kinematics and kinetics of the walking locomotion has become an important requirement in structural engineering applications due to an increasing sensitivity of modern, lightweight, low-frequency, and lightly damped footbridges to pedestrian-induced dynamic excitation. To facilitate development, calibration and verification of pedestrian models requires experimental characterization of walking gait parameters and understanding whether and how these parameters are influenced by the structural vibration. This study investigates whether low-frequency vibrations in the vertical direction affect seven walking locomotion parameters: pacing frequency, step length, step width, angle of attack, end-of-step angle, trunk angle, and amplitude of the first forcing harmonic. Three participants took part in a testing program consisting of walking on a treadmill placed on both stationary and vibrating supporting surfaces. The collected data suggest that an increasing level of vibration results in an increase in step-by-step variability for the majority of parameters. Furthermore, the existence of the self-excited force, previously observed only in numerical simulations of walking on pre-excited bridge decks, was confirmed. In addition, the deck vibration tended to have a beneficial effect of reducing the net force induced into the structure when walking at a pacing rate close to the vibration frequency. Finally, it was found that the vibration level perceptible by a pedestrian is one to two orders of magnitude larger than that typical of a standing person, and that the sensitivity to vibration decreases as the speed of walking increases

A spectral pedestrian-based approach for modal identification

The dynamic behaviour of footbridges is characterised by modal properties such as natural frequencies, mode shapes, damping ratios and modal masses. Their estimation via modal tests often requires expensive or difficult-to-operate equipment (e.g. shaker and instrumented impact hammer) or, sometimes unavailable high signal-to-noise ratios in tests relying on natural (e.g. wind, airborne noise and ground-borne vibration) excitation. In addition, the modal properties determined in modal tests do not necessarily apply to the structure under pedestrian traffic in case of amplitude-dependent frequencies and damping ratios. The current work proposes a novel approach that stands in contrast to the widely used tests, based on modal identification using an excitation induced by a single pedestrian. In order to account for estimation and observation uncertainties, the relationship between the power spectrum of the response and its modal properties is described with a likelihood function. It is shown that it is possible to reliably estimate modal properties using pedestrian walk forces measured in the laboratory, and dynamic responses measured when the same pedestrian is crossing a footbridge at timed pacing rates. The approach is validated using numerical and field data for a 16.9 m long fibre reinforced polymer footbridge. This work paves a new way for simple and low cost modal testing in structural dynamics

Quantification of Dynamic Excitation Potential of Pedestrian Population Crossing Footbridges

Due to their slenderness, many modern footbridges may vibrate significantly under pedestrian traffic. Consequently, the vibration serviceability of these structures under human-induced dynamic loading is becoming their governing design criterion. Many current vibration serviceability design guidelines, concerned with prediction of the vibration in the vertical direction, estimate a single response level that corresponds to an "average" person crossing the bridge with the step frequency that matches a footbridge natural frequency. However, different pedestrians have different dynamic excitation potential, and therefore could generate significantly different vibration response of the bridge structure. This paper aims to quantify this potential by estimating the range of structural vibrations (in the vertical direction) that could be induced by different individuals and the probability of occurrence of any particular vibration level. This is done by introducing the inter- and intra-subject variability in the walking force modelling. The former term refers to inability of a pedestrian to induce an exactly the same force with each step while the latter refers to different forces (in terms of their magnitude, frequency and crossing speed) induced by different people. Both types of variability are modelled using the appropriate probability density functions. The probability distributions were then implemented into a framework procedure for vibration response prediction under a single person excitation. Instead of a single response value obtained using currently available design guidelines, this new framework yields a range of possible acceleration responses induced by different people and a distribution function for these responses. The acceleration ranges estimated are then compared with experimental data from two real-life footbridges. The substantial differences in the dynamic response induced by different people are obtained in both the numerical and the experimental results presented. These results therefore confirm huge variability in different people's dynamic potential to excite the structure. The proposed approach for quantifying this variability could be used as a sound basis for development of new probability-based vibration serviceability assessment procedures for pedestrian bridges