It has been widely accepted that a stationary human body, such as a person when sitting or standing, acts as a single degree of freedom (SDOF) system in structural vibration. However, it is not clear what form the SDOF model should take and what are the appropriate parameters for the model. The significance of considering human body models in structural vibration comes from the fact that human involvement affects the dynamic behaviour of the structure when a crowd is present and that human body response is different from structural vibration. This forms the basis of this study.This thesis presents both experimental and theoretical studies to develop human body models. It examines the characteristics of two interaction human body models, determines the parameters of the two body models in structural vibration and explores their applications.A continuous model of a standing human body in vertical vibrations is first developed using an anthropomorphic model and two available natural frequencies obtained from shaking table tests. A standing human body is represented as a bar with seven mass segments using the anthropomorphic model and two stiffnesses of the model are identified using the two natural frequencies. The relationships between the continuous model and discrete body models are provided.The masses, damping ratios and stiffnesses of two interaction body models are identified by curve fitting of the measured apparent mass curves from shaking table tests in published biomechanics studies. In this identification process it was identified that one or two conditions have to be applied which can be derived from the outcome of the continuous body model.The characteristics of human-structure interaction models are investigated using both theoretical and experimental Fourier Response Functions. The comparative studies based on 10 tests help to show that the interaction body model is more appropriate than the conventional body model used in structural vibration, and identify the appropriate parameters for the interaction model. The theoretical study shows that the response of stationary people is always larger than structural vibration when human loads are applied, such as walking, jumping and bouncing. The conditions for observing two resonance frequencies are provided graphically for a human-structure system where the interaction body model is used.A method is proposed to identify the parameters of the interaction model through 45 free vibration tests of a standing person on a test rig. The identified values of the natural frequency and damping ratio of a standing body are not close to those from the biomechanics tests. Sensitivity studies show that the two parameters are sensitive to the input data, the damped natural frequency and damping ratio of the human-structure system, which are obtained from free vibration tests.As an extension of the application of FRF and the human-structure model, the optimum parameters of a tuned-mass-damper are obtained based on the concept of equivalent damping ratio of a SDOF structure system. The results are tabulated for practical use. An example of floor vibration induced by rhythmic crowd loads is provided to demonstrate the use of the optimum TMDs and shows the effect of vibration reduction.This thesis entitled “Models of a Standing Human Body in Structural Vibration” is submitted to the University of Manchester by Qingwen Zhang for the degree of Doctor of Philosophy in 2013.

Human-structure interaction is a relatively new topic that is not fully understood. There have been several human whole-body models from the research in body biomechanics and structural dynamics, which have been used in the study of human-structure interaction. It is not clear which body model is the most appropriate one. An interactive human body model was derived from a human-structure interaction model where a continuous standing human body was placed on a single degree-of-freedom (SDOF) structure. However, the dynamic parameters of the human body model cannot be determined accurately. In this thesis, a series of human-structure interaction experiments are conducted, which also leads to the identification of the dynamic parameters of the interactive body model and the assessment of the commonly used human body models. Two groups of 18 and 38 individual subjects participated in human-structure interaction experiment on a SDOF test rig with two different configurations. Two sweeping harmonic forces (6.6 and 13.2 N) were applied to the bare and occupied rigs. The repeatability of the tests was checked and confirmed. These experiments showed clearly two resonance frequencies of the human-structure system. It was also demonstrated that the dynamic parameters of the standing human body were independent of the test rig setup and of the subjects' gender. On the other hand, the vibration magnitude and the body masses significantly influenced the natural frequencies but not the damping ratios of the standing subjects. The fundamental natural frequency and damping ratio of the standing human body were about 6.6 Hz and 22% respectively. The identified dynamic parameters of the standing body can then be used to predict the responses of an occupied structure and the human body. Another group of 74 subjects were tested twice, with and without wearing shoes, which examined the effect of footwear on the dynamic parameters of the standing human body and on the dynamic response of the occupied rig. Only one sweeping harmonic force (13.2 N) was applied to the test rig. This study demonstrated that footwear significantly affected the dynamic parameters of the standing human body. The natural frequency and damping ratio of the standing body with bare feet are higher than those with footwear. When the two genders have the same body mass index (BMI), the maximum responses of the occupied rig are almost identical. When they have the same weight, the response of the rig occupied by the males was higher at the first resonance peak. The accelerations throughout the heights of two subjects were measured, which allowed a comparison between the predicted human whole-body acceleration and the measurements at different positions of the standing human bodies. The predicted frequency response functions (FRFs) had the same pattern as the measured ones and were larger than the measured responses at the head, neck and shoulders. The effects of the mass ratio of a crowd to a SDOF structure and the natural frequency of the structure on the human-structure interaction were examined. It was demonstrated that, for a light crowd, such as seen on office floors, the occupied structure would respond less than the bare structure, where the human body acts like a tuned-mass-damper, while the body responses were higher than that of the bare structure. For a larger crowd, such as seen on grandstands, the responses of the occupied structure and the human body were both smaller than that of the bare structure although the body response was larger than that of the occupied structure. A comparison between the human-structure interaction model used in this study and three other models was conducted. The dynamic parameters of the models were identified from the above experiments, in which the natural frequencies of the body for the four models were similar. It showed that the predicted responses of the occupied structure were similar based on the four models. However, there were obvious differences in the predicted body responses. A detailed comparison between the proposed model, Griffin's models and the available measurements showed that the damping ratios used in Griffin's models were too high, which prevents the two resonance frequencies from being observed. In addition, the predicted human body response calculated by the proposed model is much higher than that from Griffin's models.

abstract: As more and more stadia structures nowadays are being built by making use of new high strength building materials which tend to be lighter than the "old" ones, composite systems and also the fact that engineers, contractors and clients want their structures as optimized as possible, in terms of minimal materials used, there is an inevitable side effect that comes with this. The result is that structures are more flexible, and thus they become susceptible to undergone vibration problems due to the action of dynamic loading. Pop/rock concerts, exhibitions, boxing matches, and so forth are staged to supplement the football/sport seasons. Consequently, stadia structures must resist not only static loading, but also dynamic loading, such as the human induced loads from various activities of the spectators which include, standing, jumping, stamping, clapping and dancing, particularly in response to touchdowns (in football matches) or musical beats (during concerts). Active and passive models of humans are studied to see how they influence the response in TCF Bank Stadium for different ranges in excitation frequencies, by performing dynamic analyses and comparing the results with the ones obtained from static analysis. Parameter estimation and system identification in mechanical sciences and structural engineering have become increasingly important areas of research in the last three decades. Many nondestructive testing methods are based on the concepts of system identification and parameter estimation. In this document, two parameter estimation algorithms are studied, namely the Equation Error Estimator and the Output Error Estimator, through the simulation of modal data obtained from a computer structural analysis program and comparisons of their results are presented so that future researchers are better informed about the two and therefore can decide which one would give the best results for their application. / Dissertation/Thesis / M.S. Civil and Environmental Engineering 2014

This study separately investigates how temperature as well as two real load-situations affects the modal damping ratio and natural frequencies of a 64.9m span steel arch footbridge. Measurements of acceleration have been completed which covers a temperature span of  to . The natural frequencies of the five investigated modes were observed to decrease 2-6% as the temperature increased. This effect was with the help of beam-theory and finite element modelling deduced to originate mostly from changes in Young’s modulus of the materials, but also geometrical changes in steel because of thermal expansion. Further investigation included a static mass in the form of packed snow that was estimated to weigh 14 tons. The natural frequencies were observed to remain unchanged while the modal damping ratios decreased. The second load-case was an uncontrolled mass-event where a large group of pedestrians travelled over the bridge as two cars stood stationary at the quarter-point of the span. A large increase (146%) of the damping ratio was observed while the natural frequency of the first mode decreased 4%. This change was suggested come from the human structure interaction (HSI) partially because the natural frequency of the human body is close to the first vertical frequency of the bridge thus making humans act like dampers on the bridge when close to resonance, and that the number of pedestrians contribute to the modal mass of the system, thus decreasing the natural frequency. / Denna studie undersöker separat hur temperaturen såväl som två verkliga belastningssituationer påverkar de modala dämpnings kvoterna och egenfrekvenserna hos en 64,9 meter lång stål-bågs gångbro. Mätningar av accelerationen i bron har genomförts som täcker en temperatur på -10°C till 10°C. De naturliga frekvenserna hos de fem undersökta moderna observerades minska 2–6% när temperaturen ökade. Denna minskning var med hjälp av balk-teori och finita element-modellering härled att troligen komma från förändringar i Youngs modul av materialen, men även geometriska förändringar i stålet på grund av termisk expansion. Vidare undersökning innefattade en statisk massa i form av packad snö som uppskattades att väga 14 ton. Egenfrekvenserna observerades förbli oförändrade medan de modala dämpnings kvoterna minskade. Det andra lastfallet var ett okontrollerat massevenemang där en stor grupp fotgängare gick över bron medan två bilar var stationära en fjärdedel in på brons längd. En stor ökning (146%) av dämpnings kvoten för den första vertikala moden observerades medan egenfrekvensen minskade 4%. Denna förändring föreslogs komma från interaktionen mellan människan och bron, delvis för att människokroppens egenfrekvens ligger nära brons första vertikala frekvens vilket gör att människan agerar som en dämpare när de är nära resonans med bron, och att antalet fotgängare bidrar till den modala massan av systemet vilket sänker frekvensen.

Dynamic problems in footbridges, such as sensible vibrations caused by human induced loading, has on a number of occasions been observed. These vibrations are rarely an ultimate limit state problem, but can be perceived as unpleasant by the pedestrian. In design guidelines there are propositions for how to asses the dynamic problem. However, they only take the walking load into account. It has been shown that, in the case of a running load, accelerations that lie above the comfort zone can occur and that running loads are more severe than walking loads in some cases. It is possible that the running load case has to be considered in future guidelines, and finding a feasible design methodology demands a lot of work. In this thesis, a method aimed to be easily used by a designer is analyzed. The amplitude of acceleration received as a result from a dynamic analysis in a commercial FEM software, was reduced by reduction factors to generate accelerations closer to reality. This could be identified and verified against recommendations.

The study on Human Structure Interaction (HSI) effects represent a new research field in the design of pedestrian bridges. The presence of pedestrians on the structure affects the dynamic properties of the bridge, and these changes may be quantified in order to design pedestrian bridges in a more efficient way. The Dynamic Amplification Factor (DAF) curve shifts downward and towards the left when increasing number of pedestrians. The thesis, which is strictly connected to a journal paper to be submitted in 2021, includes a new formulation of the dynamic response through the DAF curves and an experimental campaign to verify the shift. A HSI model, based on Caprani continuous formulation, was created on MATLAB.To perform the experimental campaign, the Folke Bernadotte Bridge in Stockholm was chosen. The dynamic response due to a hammer test, was registered without pedestrians and with 35 pedestrians on the bridge. The dynamic properties of the bridge, such as natural frequencies, damping, mode-shapes, Frequency Response Function (FRF) are estimated in both cases. A Finite Element Model (FEM) is built on Abaqus, natural frequencies and mode-shapes are compared. Moreover, a running test is performed on the bridge and the single pedestrian loading is modelled as a moving harmonic. This test brings different values of stiffness and damping for the pedestrian to be compared to the values assumed in the HSI model for standing pedestrians.A quantification of the variation of the bridge properties due to Human structure interaction may lead to a new way to design pedestrian bridges considering pedestrians not only as loading sources of the structural system but also as dynamic vibration adsorbers (DVA).

The dynamic behaviour of lightweight footbridges is often susceptible to HumanInduced Loads (HILs). Generally HILs are taken into account as moving harmonicfunctions in which the loading frequency represents the step frequency of the pedestrians.In this way, there may be resonance if the loading frequencies fall within therange of the natural frequencies of the bridge, potentially compromising the serviceabilitylimit state of the structure. Therefore, it is important to understand how toaddress and model HILs in the context of lightweight and slender structures. Furthermore,interesting effects can be considered in the field of footbridge dynamics,such as the Human Structure Interaction (HSI) effect. The HSI effect can be understoodwithin a framework in which pedestrians behave as Tuned Mass Dampers(TMDs), possibly modifying the dynamic behaviour of the footbridge. In addition,the evaluation of the dynamic response of a footbridge is usually made through atime consuming dynamic analysis using the Finite Element Method (FEM). Mostof the analysis of this type of slender structures rely on a prescribed stationary harmonicloading scenario, and this is usually done in the context of a walking crowdevent and not much attention is given to running load events.The aims of this research project are to study the influence of running and walkingloads on the dynamic response of footbridges as well as to investigate and developa closed-form method in order to simulate the dynamic behaviour of footbridgessubjected to HILs. This has been achieved by comparing different approachesin order to simulate running load events for a small number of pedestrians withrespect to experimental results (Paper I). In addition, the simply supported beamand the clamped-clamped beam (Paper II) are studied when subjected to a movingharmonic load in a closed-form framework. Then, a comparison between normalwalking and normal running conditions is made. Finally, a general closed-formsolution for the moving harmonic load problem (Paper III) is developed using the2D Bernoulli–Euler beam theory for a continuous beam system on elastic supports.The results from the study indicate that running is more critical than walking fora single pedestrian crossing, despite the fact that it is easier to achieve a steadystate condition in a normal walking event than in a normal running event. Finally,the general solution of the moving harmonic load problem is found and it can beused to solve any load spectra in the time domain, with its static component, for ageneral multi-span beam system. / Slanka och lätta gångbroar är ofta känsliga för dynamisk belastning från fotgängare.Dessa laster betraktas ofta som harmoniska funktioner där lastfrekvensenberor på stegfrekvensen. Resonans kan uppstå om stegfrekvensen sammanfallermed någon av brons egenfrekvenser vilket potentiellt kan överskrida föreskrivnavibrationsnivåer. Kännedom om dynamisk fotgängarlast är därför viktig, framföralltför dynamiskt känsliga konstruktioner. Samverkan mellan fotgängare ochbro kan också ge upphov till intressanta samband. Fotgängarna kan i detta sammanhangliknas med en massdämpare som kan ändra brons dynamiska egenskaper.Dynamiska analyser av gångbroar utförs ofta med FEM-analyser som kan varatidskrävande. Vanligen baseras analyserna på föreskrivna stationära harmoniskalaster, ofta baserat på gånglaster och sällan med beaktande av löparlaster.Syftet med denna uppsats är att undersöka inverkan av löpar- och gånglasters inverkanpå gångbroars dynamiska respons samt att utveckla en analytisk metod föratt simulera dessa laster och dess respons på broar. Detta har utförts genom attjämföra olika sätt att simulera löparlaster och jämföra broresponsen med experimentelldata (artikel 1). En analytisk lösning för rörliga harmoniska laster redovisasför fallet fritt upplagd och fast inspänd balk (artikel 2), med vilken inverkan av gångochlöparlaster jämförs. En mer generell analytisk lösning för rörliga harmoniskalaster (artikel 3) baseras på Bernoulli-Euler balkteori för kontinuerliga balkar påeftergivliga upplag.Resultaten från föreliggande arbete visar att för en enskild fotgängare är fallet medlöparlast mer kritiskt än gånglast, trots att det är lättare att uppnå ett fortvarighetstillståndför gånglaster jämfört med löparlaster. Den generella lösningen för rörligaharmoniska laster som redovisas kan användas för att lösa godtyckliga lastspektrai tidsdomän, inklusive dess statiska komponent, för generella balkar. / <p>QC 20210302</p>

For aesthetic reasons and due to an increased demand for cost-effective and environmentally friendly civil engineering structures, there is a trend in designing light and slender structures. Consequently, many modern footbridges are susceptible to excessive vibrations caused by human-induced loads. To counteract this, today's design guidelines for footbridges generally require verification of the comfort criteria for footbridges with natural frequencies in the range of pedestrian step frequencies. To ensure that a certain acceleration limit is not exceeded, the guidelines provide simplified methodologies for vibration serviceability assessment. However, shortcomings of these methodologies have been identified. First, for certain footbridges, human-structure interaction (HSI) effects might have a significant impact on the dynamic response. One such effect is that the modal properties of the bridge change in the presence of a crowd; most importantly, the damping of the bridge is increased. If this effect is neglected, predicted acceleration levels might be overestimated. Second, as a running person induces a force of greater amplitude than a walking person, a single runner might cause a footbridge to vibrate excessively. Hence, the running load case is highly relevant. These two aspects have in common that they are disregarded in existing design guidelines. For the stated reasons, the demand for improvements of the guidelines is currently high and, prospectively, it might be necessary to require the consideration of both the HSI effect and running loads. Therefore, this licentiate thesis aims at deepening the understanding of these subjects, with the main focus being placed on the HSI effect and, more precisely, on how it can be accounted for in an efficient way. A numerical investigation of the HSI effect and its impact on the vertical acceleration response of a footbridge was performed. The results show that the HSI effect reduces the peak acceleration and that the greatest reduction is obtained for a crowd to bridge frequency ratio close to unity and a high crowd to bridge mass ratio. Furthermore, the performance of two simplified modelling approaches for consideration of the HSI effect was evaluated. Both simplified models can be easily implemented and proved the ability to predict the change in modal properties as well as the structural response of the bridge. Besides that, the computational cost was reduced, compared to more advanced models. Moreover, a case study comprising field tests and simulations was performed to investigate the effect of runners on footbridges. The acceleration limit given in the design guideline was exceeded for one single person running across the bridge while a group of seven people walking across the bridge did not cause exceedance of the limit. Hence, it was concluded that running loads require consideration in the design of a footbridge. / På grund av estetiska skäl och en ökad efterfrågan på kostnadseffektiva och miljövänliga konstruktioner är merparten av de gångbroar som konstrueras idag förhållandevis lätta och slanka. Med anledning av detta ökar risken för att stora svängningar uppstår på grund av dynamisk belastning från människor på bron. För att motverka att detta inträffar kräver dagens normer att komforten verifieras för gångbroar med egenfrekvenser inom området för människans stegfrekvens. Komforten verifieras genom att säkerställa att ett visst accelerationskriterium inte överskrids. För detta ändamål finns handböcker som tillhandahåller förenklade beräkningsmetoder för uppskattning av accelerationsnivåer. Brister i dessa beräkningsmetoder har emellertid identifierats. För det första kan olika typer av människa-bro-interaktion (HSI) ha en betydande inverkan på responsen hos vissa broar. Exempel på en HSI-effekt är att brons modala egenskaper förändras när människor befinner sig på bron; i huvudsak sker en ökning av brons dämpning. Om denna effekt inte tas i beaktande föreligger stor risk att överskatta förväntade accelerationsnivåer. För det andra är kraften från en löpare större än kraften från en gående person vilket gör att en ensam löpare på en gångbro kan ge upphov till accelerationsnivåer som överskrider gränsvärdena för komfort. Löpande personer är därför ett mycket relevant lastfall. Befintliga normer uttrycker inte explicit att någon av dessa aspekter bör tas i beaktande. Behovet av förbättrade riktlinjer för hur normerna bör tillämpas är därför mycket stort och i framtiden kan det bli nödvändigt att kräva att både HSI-effekter och löparlaster tas i beaktande. Därför syftar denna licentiatavhandling till att bidra till en fördjupad förståelse inom dessa två ämnen, med huvudfokus på ovan nämnda HSI-effekt i allmänhet och hur den kan beaktas på ett enkelt, noggrant och tidseffektivt sätt i synnerhet. En numerisk undersökning av HSI-effekten och dess inverkan på den vertikala responsen hos en gångbro genomfördes. Resultaten visar att HSI-effekten reducerar den maximala accelerationen och att störst reduktion erhålls då folksamlingen och bron har ungefär samma egenfrekvens och då folksamlingens massa är stor i förhållande till brons massa. Vidare utvärderades två förenklade metoder för beaktande av HSI-effekten vilka kan implementeras av konstruktörer med grundläggande kunskaper inom strukturdynamik. Det konstaterades att båda metoderna uppskattar HSI-effekten såväl som brons respons förhållandevis väl samtidigt som de reducerar beräkningstiden något jämfört med mer avancerade metoder. Effekten av löpare på gångbroar studerades genom en fallstudie med fältmätningar. Utifrån resultaten från dessa fältmätningar kunde det konstateras att accelerationsgränsen som anges i normerna överskreds när en ensam löpare sprang över bron men inte när en grupp på sju personer gick i takt över samma bro. Därför drogs slutsatsen att löparlaster bör tas i beaktande vid dimensionering av en gångbro. / <p>QC 20180320</p>