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

Power Spectral-Density Model for Pedestrian Walking Load

This is the author accepted manuscript. The final version is available from American Society of Civil Engineers via the DOI in this recordIntensive vibrations may occur in slender structures like footbridges and long-span floors due to movement of pedestrians. Problems are usually treated in the time domain as Fourier series models of the forcing function, but most methods have disadvantages of neglecting the stochastic character of human walking, being computationally inefficient for random vibration analysis, and overestimating responses in the case of resonance. Meanwhile, frequency-domain models of other types of structural loading are efficient while being a more acceptable approach widely adopted for dealing with stochastic response problems. Hence, an experiment-based power spectral-density (PSD) model normalized to walking frequency and order of harmonic is proposed. To construct this model, 1,528 individual walking-load time histories were collected from an experiment on a rigid floor. These records were then linked to obtain a smaller number of longer samples for a good frequency resolution in spectral analysis. Using the linked samples and for a frequency normalized to mean walking frequency, PSD models in the range 1±0.05 for the harmonic and subharmonic are suggested as a Gaussian mixture with eight model parameters. Via the stationary and nonstationary stochastic vibration theory, the proposed model is used to predict the structural response in terms of root-mean square and peak of acceleration. The framework is finally tested via field measurements demonstrating applicability in practical design work.National Natural Science Foundation of ChinaState Key Laboratory for Disaster Reduction of Civil Engineerin

Dynamic loading factors of individual jogging forces

With increasingly popular marathon events in urban environments, such as in London and New York City, structural designers are faced with a great deal of uncertainty when assessing dynamic performance of bridges occupied and dynamically excited by people running. While the dynamic loads induced by people walking have been intensively studied since the infamous lateral sway of the London Millennium Bridge in 2000, reliable and practical descriptions of running excitation are still very rare and limited. This paper makes a step forward by bringing together a unique database of individual jogging force records and their simple mathematical model which can be used in everyday design practice. The forcing data has been collected in Vibration Engineering Section Laboratory in the University of Sheffield using a state-of-the-art instrumented treadmill, which is commonly used in clinical studies of human gait and sports biomechanics. The modelling strategy featuring Fourier harmonics of measured jogging force-time histories is adopted from a popular design guidelines for human walking excitation of structures. The results show a great scatter in the DLF data and no strong link with jogging footfall rate, which is the case with walking forces. This clearly suggests that traditional deterministic Fourier based approach is not the best modelling strategy for jogging loading. Uncertainty and inter-personal randomness of the force amplitudes indicate that stochastic - rather than deterministic models of jogging forces should provide more reliable predictions of the bridge dynamics. These forces could be modeled in a similar fashion as other key dynamic loading of structures characterized by great randomness and uncertainty, such as wind and earthquake

Review of Pedestrian Load Models for Vibration Serviceability Assessment of Floor Structures

This is the final version. Available on open access from MDPI via the DOI in this recordInnovative design and technological advancements in the construction industry have resulted in an increased use of large, slender and lightweight floors in contemporary office buildings. Compounded by an ever-increasing use of open-plan layouts with few internal partitions and thus lower damping, floor vibration is becoming a governing limit state in the modern structural design originating from dynamic footfall excitations. This could cause annoyance and discomfort to building occupants as well as knock-on management and financial consequences for facility owners. This article presents a comprehensive review pertinent to walking-induced dynamic loading of low-frequency floor structures. It is intended to introduce and explain key walking parameters in the field as well as summarise the development of previous walking models and methods for vibration serviceability assessment. Although a number of walking models and design procedures have been proposed, the literature survey highlights that further work is required in the following areas; (1) the development of a probabilistic multi-person loading model which accounts for inter- and intra-subject variabilities, (2) the identification of walking paths (routes accounting for the effect of occupancy patterns on office floors) coupled with spatial distribution of pedestrians and (3) the production of a statistical spatial response approach for vibration serviceability assessment. A stochastic approach, capable of taking into account uncertainties in loading model and vibration responses, appears to be a more reliable way forward compared to the deterministic approaches of the past and there is a clear need for further research in this areaEngineering and Physical Sciences Research Council (EPSRC)Qatar National Research Foundatio

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 assessment of office floors for realistic walking and floor layout scenarios: Literature review

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this recordOver the last two decades, office floors have been built progressively lightweight with increasing spans and slenderness. Therefore, vibration performance of office floors due to walking dynamic loads is becoming their governing design criterion, determining their size and shape, and therefore overall weight and embodied energy of the building. To date, floor design guidelines around the world recommend walking load scenarios in offices featuring some or all of the following standard characteristics: (a) walking loads are assumed to be periodic dynamic excitation represented by the Fourier series, including harmonics corresponding to up to the first four integer multiples of the pacing frequency of which at least one is exciting the floor at a resonant frequency and (b) single person walking. However, the literature surveyed provides evidence that such assessment methodology is potentially an over-simplification which as it does not reflect real walking load scenarios, since crucial features of the floor vibration source, path and receiver are missing. First, in terms of vibration source realistic scenarios need to feature: (a) moving rather than stationary walking forces; (b) stochastic nature of human gait; (c) simultaneous multiperson walking; and (d) human-structure interaction. Second, for the transmission path (i.e. office floor structure), two features are needed to consider: (a) realistic office floor layouts and (b) presence, or absence, of non-structural elements. Finally, for the vibration receivers (i.e. floor occupants): (a) vibrations calculated at floor locations occupied by users (instead of at the potential highest response location which may not be occupied); (b) actual period over which occupants feel vibration due to such excitation and (c) assessment of vibration levels based on their probability of occurrence. This paper therefore addresses these seldom considered but increasingly important features and discusses realistic approaches to floor design for vibration serviceability.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES

Parameter identification of pedestrian's spring-mass-damper model by ground reaction force records through a particle filter approach

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The spring-mass-damper (SMD) model with a pair of internal biomechanical forces is the simplest model for a walking pedestrian to represent his/her mechanical properties, and thus can be used in human-structure-interaction analysis in the vertical direction. However, the values of SMD stiffness and damping, though very important, are typically taken as those measured from stationary people due to lack of a parameter identification methods for a walking pedestrian. This study adopts a step-by-step system identification approach known as particle filter to simultaneously identify the stiffness, damping coefficient, and coefficients of the SMD model's biomechanical forces by ground reaction force (GRF) records. After a brief introduction of the SMD model, the proposed identification approach is explained in detail, with a focus on the theory of particle filter and its integration with the SMD model. A numerical example is first provided to verify the feasibility of the proposed approach which is then applied to several experimental GRF records. Identification results demonstrate that natural frequency and the damping ratio of a walking pedestrian are not constant but have a dependence of mean value and distribution on pacing frequency. The mean value first-order coefficient of the biomechanical force, which is expressed by the Fourier series function, also has a linear relationship with pacing frequency. Higher order coefficients do not show a clear relationship with pacing frequency but follow a logarithmic normal distribution.The authors would like to acknowledge the financial support provided by National Natural Science Foundation of China (51478346, 51778465) and State Key Laboratory for Disaster Reduction of Civil Engineering (SLDRCE14-B-16)

Stochastic Single Footfall Trace Model for Pedestrian Walking Load

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this record Developing a model for the dynamic force generated by a pedestrian's foot on a supporting structure (single footfall trace model) is crucial to advanced numerical analysis and vibration serviceability assessment of the structure. A reliable model needs to reflect the inter-subject and intra-subject randomness of human walking. This paper introduces a stochastic single footfall trace model in the form of a Fourier series in which body weight, walking frequency, and the first eight harmonics are treated as random variables. An experiment used 73 test subjects, walking at a range of pacing frequencies, to record force time histories and the corresponding gait parameters. Two variability descriptors were used to indicate inter-subject and intra-subject randomness. Further statistical analysis identified the relationships between key parameters as well as the probability distribution functions of random variables. In the final step, an application of the proposed single footfall trace model was developed and tested. The proposed model represented the experimental data well in both time and frequency domains.National Natural Science Foundation of ChinaState Key Laboratory for Disaster Reduction of Civil EngineeringEngineering and Physical Sciences Research Counci

Análisis por condición de servicio causado por vibración vertical inducida por peatones en estructuras

Civil engineering structures such as grandstands, slabs, footbridges and staircases have reported unacceptable vertical vibration when they are affected by human activities. Even when most of these structures are designed according to current guidelines and design codes, there are still misunderstandings in the human-structure interaction effects that, in some cases, may increase the vibration response compromising the structural serviceability performance. As a result, the serviceability load conditions due to pedestrian activities control, in most cases, the design for these structures. Therefore, a systematic overview regarding vertical pedestrian-structure interaction is carried out to demonstrate the need for a realistic analysis to properly incorporate these effects toward more rational structural designs. The discussion establishes a body of knowledge regarding pedestrian loads and structural responses, yielding the potential for more rational approaches to improving the analysis and design of pedestrian structures.Estructuras civiles tales como tribunas, losas, puentes peatonales y escaleras están presentando vibraciones verticales inaceptables cuando se ven afectadas por actividades humanas. Por lo tanto, todavía no se tiene claridad sobre los efectos producidos por la interacción entre el ser humano y la estructura que, en algunos casos, pueden llegar a aumentar la respuesta estructural comprometiendo el desempeño para condiciones de servicio. Un examen a las normas y códigos de diseño existentes, arroja una amplia gama de resultados, lo que demuestra que no son consistentes cuando las estructuras están expuestas a cargas inducidas por peatones. Este estudio tiene como objetivo identificar los mecanismos de vibración, los modelos matemáticos y los métodos para abordar la vibración vertical excesiva en las estructuras peatonales. Este análisis establece un conjunto de recomendaciones sobre las cargas que producen los peatones y las respuestas estructurales que pueden producir, lo que genera el potencial para futuros enfoques más racionales que mejoren el análisis y el diseño de estructuras peatonales

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