Advanced Fourier-based Model of Bouncing Loads

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record36th IMAC, A Conference and Exposition on Structural Dynamics 2018Contemporary design guideline pertinent to vibration serviceability of entertaining venues describes bouncing forces as a deterministic and periodic process presentable via Fourier series. However, fitting the Fourier harmonics to a comprehensive database of individual bouncing force records established in this study showed that such a simplification is far too radical, thus leading to a significant loss of information. Building on the conventional Fourier force model, this study makes the harmonics specific to each individual and takes into account imperfections in the bouncing process. The result is a numerical generator of stochastic bouncing force time histories which represent reliably the experimentally recorded bouncing force signals.The authors would like to acknowledge the financial support provided by PRIN 2015-2018 “Identification and monitoring of complex structural systems” and National Natural Science Foundation of China 347 (51478346) and State Key Laboratory for Disaster Reduction of Civil Engineering (SLDRCE14-B-16)

Number of successive cycles necessary to achieve stability of selected ground reaction force variables during continuous jumping

Because of inherent variability in all human cyclical movements, such as walking, running and jumping, data collected across a single cycle might be atypical and potentially unable to represent an individual's generalized performance. The study described here was designed to determine the number of successive cycles due to continuous, repetitive countermovement jumping which a test subject should perform in a single experimental session to achieve stability of the mean of the corresponding continuously measured ground reaction force (GRF) variables. Seven vertical GRF variables (period of jumping cycle, duration of contact phase, peak force amplitude and its timing, average rate of force development, average rate of force relaxation and impulse) were extracted on the cycle-by-cycle basis from vertical jumping force time histories generated by twelve participants who were jumping in response to regular electronic metronome beats in the range 2-2.8 Hz. Stability of the selected GRF variables across successive jumping cycles was examined for three jumping rates (2, 2.4 and 2.8 Hz) using two statistical methods: intra-class correlation (ICC) analysis and segmental averaging technique (SAT). Results of the ICC analysis indicated that an average of four successive cycles (mean 4.5 +/- 2.7 for 2 Hz; 3.9 +/- 2.6 for 2.4 Hz; 3.3 +/- 2.7 for 2.8 Hz) were necessary to achieve maximum ICC values. Except for jumping period, maximum ICC values took values from 0.592 to 0.991 and all were significantly ( p <= 0.05) different from zero. Results of the SAT revealed that an average of ten successive cycles ( mean 10.5 +/- 3.5 for 2 Hz; 9.2 +/- 3.8 for 2.4 Hz; 9.0 +/- 3.9 for 2.8 Hz) were necessary to achieve stability of the selected parameters using criteria previously reported in the literature. Using 10 reference trials, the SAT required standard deviation criterion values of 0.49, 0.41 and 0.55 for 2 Hz, 2.4 Hz and 2.8 Hz jumping rates, respectively, in order to approximate the ICC results. The results of the study suggest that the ICC might be a less conservative but more objective method to evaluate stability of the data. Based on these considerations, it can be recommended that a force time history due to continuous, repetitive countermovement jumping should include minimum of four (the average from the ICC analysis) and possibly as many as nine successive jumping cycles (the upper limit of the ICC analysis) to establish stable mean values of the selected GRF data. This information is important for both experimental measurements and analytical studies of GRF signals due to continuous, repetitive countermovement jumping

Improved model for human induced vibrations of high-frequency floors

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThe key UK design guidelines published by the Concrete Society and Concrete Centre for single human walking excitation of high-frequency floors were introduced more than 10 years ago. The corresponding walking force model is derived using a set of single footfalls recorded on a force plate and it features a deterministic approach which contradicts the stochastic nature of human-induced loading, including intra- and inter- subject variability. This paper presents an improved version of this force model for high-frequency floors with statistically defined parameters derived using a comprehensive database of walking force time histories, comprising multiple successive footfalls that are continuously measured on an instrumented treadmill. The improved model enables probability-based prediction of vibration levels for any probability of non-exceedance, while the existing model allows for vibration prediction related to 75% probability of non-exceedance for design purposes. Moreover, the improved model shifts the suggested cut-off frequency between low- and high-frequency floors from 10 Hz to 14 Hz. This is to account for higher force harmonics that can still induce the resonant vibration response and to avoid possible significant amplification of the vibration response due to the near-resonance effect. Minor effects of near-resonance are taken into account by a damping factor. The performance of the existing and the improved models is compared against numerical simulations carried out using a finite element model of a structure and the treadmill forces. The results show that while the existing model tends to overestimate or underestimate the vibration levels depending on the pacing rate, the new model provides statistically reliable estimations of the vibration responses. Hence, it can be adopted in a new generation of the design guidelines featuring a probabilistic approach to vibration serviceability assessment of high-frequency floors.The authors would like to acknowledge the College of Engineering, Mathematics and Physical Sciences in the University of Exeter for the financial support provided for the PhD programme of the first author. The authors would also like to acknowledge the UK Engineering and Physical Sciences Research (EPSRC) for the following research grants: Platform Grant EP/G061130/2 (Dynamic performance of large civil engineering structures: an integrated approach to management, design and assessment) and Standard Grant EP/I029567/1 (Synchronization in dynamic loading due to multiple pedestrians and occupants of vibration-sensitive structures)

Vibration performance of a lightweight FRP footbridge under human dynamic excitation

This is the author accepted manuscript. The final version is available from Springer via the DOI in this recordFibre-reinforced polymer (FRP) composites are increasingly used as main load bearing materials in design of pedestrian bridges. The FRP footbridges are typically characterised by high strength, and relatively low mass and stiffness. These properties could lead to excessive vibration response under human-induced dynamic loading. This paper studies dynamic performance of a 19.8 m long, simply supported, FRP footbridge exposed to walking and jogging. Moreover, the vibration response of this bridge is compared and critically evaluated against the response of an equivalent, in terms of natural frequency and span length, composite steel-concrete structure. The main factors that drive the vibration performance of the FRP structure are discussed and some recommendations for vibration serviceability checks are made.Engineering and Physical Sciences Research Council (EPSRC

Interaction between Walking Humans and Structures in Vertical Direction: A Literature Review

Realistic simulation of the dynamic effects of walking pedestrians on structures is still a considerable challenge. This is mainly due to the inter- and intrasubject variability of humans and their bodies and difficult-to-predict loading scenarios, including multipedestrian walking traffic and unknown human-structure interaction (HSI) mechanisms. Over the past three decades, several attempts have been made to simulate walking HSI in the lateral direction. However, research into the mechanisms of this interaction in the vertical direction, despite its higher likelihood and critical importance, is fragmented and incoherent. It is, therefore, difficult to apply and codify. This paper critically reviews the efforts to date to simulate walking HSI in the vertical direction and highlights the key areas that need further investigation

University Students Attitudes: Croatia Versus Turkey

We surveyed Croatian and Turkish business school students, from universities emphasizing globalization, to analyze whether consideration for travel to the USA is affected by attitude toward their own country and the USA The results from comparing and contrasting differences between these countries and differences between males and females in each country - and their counterparts in the other country - may also give an outlook to future business relationships between the USA and these countries. Based on a t-test, Croatian students ratings of the USA were significantly more positive, but there was no statistically significant difference in expectations to travel to the USA

Effect of group walking traffic on dynamic properties of pedestrian structures

The increasing number of reported vibration serviceability problems in newly built pedestrian structures, such as footbridges and floors, under walking load has attracted considerable attention in the civil engineering community over the past two decades. The key design challenges are: the inter- and intra-subject variability of walking people, the unknown mechanisms of their interaction with the vibrating walking surfaces and the synchronisation between individuals in a group. Ignoring all or some of these factors makes the current design methods an inconsistent approximation of reality. This often leads to considerable over- or under-estimation of the structural response, yielding an unreliable assessment of vibration performance. Changes to the dynamic properties of an empty structure due to the presence of stationary people have been studied extensively over the past two decades. The understanding of the similar effect of walking people on laterally swaying bridges has improved tremendously in the past decade, due to considerable research prompted by the Millennium Bridge problem. However, there is currently a gap in knowledge about how moving pedestrians affect the dynamic properties of vertically vibrating structures. The key reason for this gap is the scarcity of credible experimental data pertinent to moving pedestrians on vertically vibrating structures, especially for multi-pedestrian traffic. This paper addresses this problem by studying the dynamic properties of the combined human-structure system, i.e. occupied structure damping ratio, natural frequency and modal mass. This was achieved using a comprehensive set of frequency response function records, measured on a full-scale test structure, which was occupied by various numbers of moving pedestrians under different walking scenarios. Contrary to expectations, it was found that the natural frequency of the joint moving human-structure system was higher than that of the empty structure, while it was lower when the same people were standing still. The damping ratio of the joint human-structure system was considerably higher than that of the empty structure for both the walking and standing people – in agreement with previous reports for stationary people - and was more prominent for larger groups. Interestingly, it was found that the walking human-structure system has more damping compared with the equivalent standing human-structure system. The properties of a single degree of freedom mass-spring-damper system representing a moving crowd needed to replicate these observations have been identified

Effect of sensory stimuli on dynamic loading induced by people bouncing

Prediction of dynamic loads induced by groups and crowds of people bouncing is a hot topic among designers of grandstands and floors in entertaining venues. Using motion capture technology transferred and adapted from biomedical research, this study aims to investigate effect of visual, auditory and tactile cues on the ability of people to coordinate or synchronise their bouncing movements in groups of two. The numerical results showed a great significance of such stimuli on people's mutual interaction during bouncing, signifying that their effect should be considered in developing much-needed models of crowd dynamic loading of structures due to coordinated rhythmic activities. © The Society for Experimental Mechanics, Inc. 2013

Concurrent repeatability and reproducibility analyses of four marker placement protocols for the foot-ankle complex

Multi-segment models of the foot have been proposed in the past years to overcome limitations imposed by oversimplified traditional approaches used to describe foot kinematics, but they have been only partially validated and never compared. This paper presents a unique comparative assessment of the four most widely adopted foot kinematic models and aims to provide a guidance for the clinical interpretation of their results. Sensitivity of the models to differences between treadmill and overground walking was tested in nine young healthy adults using a 1D paired t-test. Repeatability was assessed by investigating the joint kinematics obtained when the same operator placed the markers on thirteen young healthy adults in two occasions. Reproducibility was then assessed using data from three randomly selected participants, asking three operators to repeat the marker placement three times. The analyses were performed on sagittal kinematics using curve similarity and correlation indices (Linear Fit Method) and absolute differences between selected points. Differences between treadmill and overground gait were highlighted by all the investigated models. The two most repeatable and reproducible investigated models had average correlations higher than 0.70, with the lowest values (0.56) obtained for the midfoot. Averaged correlations were always higher than 0.74 for the former and 0.70 for the latter, with the lowest obtained for the midfoot (0.64 and 0.51). For all investigated models, foot kinematics generally showed low repeatability: normative bands must be adopted with caution when used for comparison with patient data

A framework for experimental determination of localised vertical pedestrian forces on full-scale structures using wireless attitude and heading reference systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A major weakness among loading models for pedestrians walking on flexible structures proposed in recent years is the various uncorroborated assumptions made in their development. This applies to spatio- temporal characteristics of pedestrian loading and the nature of multi-object interactions. To alleviate this problem, a framework for the determination of localised pedestrian forces on full-scale structures is presented using a wireless attitude and heading reference systems (AHRS). An AHRS comprises a triad of tri-axial accelerometers, gyroscopes and magnetometers managed by a dedicated data processing unit, allowing motion in three-dimensional space to be reconstructed. A pedestrian loading model based on a single point inertial measurement from an AHRS is derived and shown to perform well against benchmark data collected on an instrumented treadmill. Unlike other models, the current model does not take any predefined form nor does it require any extrapolations as to the timing and amplitude of pedestrian loading. In order to assess correctly the influence of the moving pedestrian on behaviour of a structure, an algorithm for tracking the point of application of pedestrian force is developed based on data from a single AHRS attached to a foot. A set of controlled walking tests with a single pedestrian is conducted on a real footbridge for validation purposes. A remarkably good match between the measured and simulated bridge response is found, indeed confirming applicability of the proposed framework.The research presented here was funded by EPSRC (grant EP/I029567/2). Authors thank Devon County Council for permitting the experimental campaign to be conducted on Baker Bridge in Exeter, UK, and Dr Erfan Shahabpour (supported by EPSRC grant EP/K03877X/1) for providing access to and assisting with measurements on the ADAL-3D treadmill at the University of Sheffield (funded by EPSRC grant EP/E018734/1)