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Footbridges are no longer mere conduits for pedestrians across channels of traffic or water. The modern footbridge is often a focal point in the urban landscapes with its design inspired by the culture and character of the location. The introduction of new, high-performance construction materials, combined with advances in engineering design have l...
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Citations
... Therefore, an accurate estimation of humaninduced vibrations is needed to avoid oversizing an FRP footbridge, which is directly related to the initial budget of a project. Since the first proposal from Archbold [25], several models [26,27] accounting for the dynamic parameters of the human body have been used to consider HSI on the dynamic response of footbridges. Under this approach, the mass, frequency, and damping ratio of the human body together with an external force are employed along with the properties of the structure, leading to a coupled human-structure vibrating system. ...
Due to the high strength-to-weight ratio of fibre reinforced polymers (FRPs), human-induced vibration problematic remains as a subject to be fully comprehended in order to extend the use of composites in Bridge Engineering. Thus, this paper studies an ultra-lightweight FRP footbridge, which presents excessive vertical vibrations when the fourth harmonic of a walking pedestrian is synchronised with the structure’s fundamental frequency. Focusing on the vertical bending mode, at 7.66 Hz, the bridge dynamic behaviour was assessed under the action of a single pedestrian crossing the facility at a step frequency of 1.9 Hz. As an over prediction of the footbridge response was computed using a moving force (MF) model available in a design guideline, a mass-spring-damper-actuator (MSDA) system was adopted to depict a walker. Hence, Human-Structure Interaction (HSI) phenomenon was considered. Employing the experimental results, parameters of the MSDA system were identified, leading to a HSI model that considers the first fourth harmonics of a walking human. Additionally, a parametric analysis was carried out, determining that the damping ratio of the human body and the load factor associated to the fourth harmonic are the most relevant parameters on the estimation of the response. The identified HSI model may be used as a first approximation to accurately predict the dynamic response of ultra-lightweight composite structures and should be extended to account for crowd-induced loads.
... Several studies have shown that pedestrians provide negligible additional damping to structures subjected to vertical vibration [14][15][16][17]. erefore, to depict the dynamic behaviour of the human body, some researchers have equated pedestrians to SMD system, which accounts for the effects of human mass, stiffness, and damping on the structure [18][19][20][21][22]. e moving SMD, introduced by Archbold [18], is applied into the HSI area and the SMD model has a better predictability in vibration response as compared to the MF model [20]. ...
... Several studies have shown that pedestrians provide negligible additional damping to structures subjected to vertical vibration [14][15][16][17]. erefore, to depict the dynamic behaviour of the human body, some researchers have equated pedestrians to SMD system, which accounts for the effects of human mass, stiffness, and damping on the structure [18][19][20][21][22]. e moving SMD, introduced by Archbold [18], is applied into the HSI area and the SMD model has a better predictability in vibration response as compared to the MF model [20]. Although the SMD model considers the dynamic properties of the human body and replaces GRF with a predefined mobility force with double-peak characteristics, it ignores the gait characteristics of the human body with switching legs in the walking process. ...
The excessive vertical vibration of structures induced by walking pedestrians has attracted considerable attention in the past decades. The bipedal walking models proposed previously, however, merely focus on the effects generated by legs and ignore the effects of the dynamics of body parts on pedestrian-structure interactions. The contribution of this paper is proposing a novel pedestrian-structure interaction system by introducing the concept of the continuum and a different variable stiffness strategy. The dynamic model of pedestrian-structure coupling system is established using the Lagrange method. The classical mode superposition method is utilized to calculate the response of the structure. The state-space method is employed to determine natural frequencies and damping ratio of the coupled system. Based on the proposed model, numerical simulations and parametric analysis are conducted. Numerical simulations have shown that the continuum enables the pedestrian-structure system to achieve the stable state more efficiently than the classic model does, which idealizes the body as a concentrated or lumped mass. The parametric study reveals that the presence of pedestrians is proved to significantly decrease the frequency of human-structure interaction system and improve its damping ratio. Moreover, the parameters of the bipedal model have a noticeable influence on the dynamic properties and response of the pedestrian-structure system. The bipedal walking model proposed in this paper depicts a pattern of pedestrian-structure interactions with different parameter settings and has a great potential for a wide range of practical applications.
... A collection of results from recent research has emphasized the role of pedestrians as dynamic systems that interact with the vibrating structure [17]. From a historical perspective, one of the first works that proposed the inclusion of pedestrians as dynamic systems was that of Archbold [18]. This was more of a procedure than an analytical formulation, in which the moving force was applied together with a single-degree-offreedom spring-mass-damper (SMD) model to consider the pedestrian action as a dynamic system. ...
The vibration serviceability of footbridges has evolved from the adoption of a single pedestrian crossing in the resonance condition to load cases in which several pedestrians cross the structure simultaneously. However, in spite of this improvement, pedestrians continue to be considered as applied loads in codes of practice. Recent research has pointed out that modeling pedestrians as dynamic systems is a step further in the search for a more realistic design approach. This is explored in this paper, focusing on the case of vertical vibration. A two-span cable-stayed test structure was selected, and accelerations were measured from single and group crossings, both at the
structure and at a pedestrian’s waist. Numerical simulations considering the pedestrians modeled as loads only and also as dynamic systems were implemented, and numerical and experimental time response vibration signatures were compared. Reductions of up to 25% and 20% in peak and RMS acceleration, respectively, were obtained when pedestrians were modeled as dynamic systems, in comparison with the less realistic model of pedestrians as loads only. Such reductions were shown to depend on the number of pedestrians involved in the group. The results, thus, highlight that pedestrian–structure interaction is an asset for the vibration serviceability design of footbridges.
... These parameters have been much-investigated in biomechanical engineering applications using measurements of rigid surface walking forces and accelerations of the human body centre of mass [25][26][27][28][29][30][31]. For structural vibration, Archbold [32], Caprani et al. [33], Archbold et al. [34], and Ahmadi et al. [13] adopted the MSMD model parameters from the biomechanics literature. Hashim et al. [35] determined dynamic properties of the standing (stationary) human body. ...
The interaction between structures and walking humans is an important factor in vibration serviceability assessment of slender, lightweight, and low-damping structures. When on bridges humans form a human-structure system and interact with the structural vibration. The conventional vertical moving force (MF) model neglects human-structure interaction (HSI) effects. In contrast, a moving spring-mass-damper (MSMD) model is shown to have the potential to incorporate HSI effects leading to more accurate vibration response prediction. The MSMD model parameters have been much studied in biomechanics. However, the literature lacks an experimental calibration of the MSMD model parameters on a vibrating surface for vibration serviceability design and assessment purposes. Consequently, an experimental-numerical methodology is developed to calibrate the MSMD model parameters in the worst-case (resonance) scenario by matching measured and simulated vibration responses. To facilitate simple implementation of HSI effects into engineering practice, results of simulation using a calibrated equivalent moving force (EMF) model are also shown. The walking force on rigid surfaces along with vibration responses of two lively full-scale laboratory footbridges are measured for 23 test subjects by performing a total of 295 trials on the two structures. A parametric study is first performed on the MSMD model using the experimental results. The experimental results of the Monash footbridge are then used as the training dataset to extract optimal MSMD model parameters. The results from the Warwick footbridge are used to validate the model. The validation tests results show a considerable improvement in the vibration response prediction using both models. It was found that when walking in resonance with the bridge, the walker can be modelled to have natural frequency equal to the resonant frequency of the bridge, and that the damping ratio is larger for heavier walkers.
... However, even among the SMD models, there are significant differences in the formulations, ranging from the absence of an analytical formulation [8][9][10], to the adoption of additional energy input that generates the pedestrian up and down movement by different means (e.g., actuators [11][12][13], heel movement [14], additional velocity term [15]), or else none of these additions [7,16,17]. ...
... The first model known to the authors that proposed the modelling of a moving pedestrian as a dynamic system when calculating footbridge vibrations was proposed in Archbold [8], see also Fanning et al. [9]. Being called later on in the literature as a Moving Oscillator, this model consists of applying a ground reaction force F(t) produced from walking on a rigid surface, simultaneously with a SMD model, the latter representing the dynamics of the pedestrian body. ...
... It should be noted that there is no specific analytic formulation presented in Archbold [8] and Fanning et al. [9] to represent the interaction between pedestrian and footbridge. This proposal is, thus, just a procedure to include the dynamics of pedestrian. ...
The last two decades saw an increase in the number of studies investigating the problem of excessive structural vibration due to pedestrian dynamic loads. Several models to represent the pedestrian action on the structure have been developed. The simplest model (used in most guidelines) consists of applying a moving force on the structure to predict its dynamic behaviour. However, it is now well known that this model cannot accurately estimate the dynamic response of the structure under human action. This is chiefly because the human body has its own dynamic properties, depending on the activity and posture, and the simplest model does not consider this when modelling a pedestrian. This way, single degree of freedom (SDOF) models considering stiffness, mass and damping of an individual have been initially presented. Such models have been compared with the simplest moving force model in terms of accuracy of the structural response. However, challenges remain in terms of dealing with its mathematical modelling, and validation with experimental measurements. In this context, this paper presents a discussion about the formulations of such SDOF models, in order to clarify conceptual and mathematical similarities and differences between such formulations. A basic formulation was identified to compare values that have been proposed for the body parameters, using as a reference experimental data obtained from tests carried out in resonance condition on a lively footbridge. The SDOF model and, generally, the values of body parameters proposed in the literature, performed well against experimental data. There was evidence that lower natural frequencies of the pedestrian body adopted in one of the formulations led to less accurate results, but further studies are needed to confirm this.
... As observed in the literature, it should be mentioned that the use of HSI models tends to slightly underestimate the actual structural response. 7,27,46,70,71 Errors about 10% and 40% in predicting the response of flexible footbridges submitted to walking loads are reported. 7,70,71 On the other hand, another study shows an overestimate response below 50%. ...
... 7,27,46,70,71 Errors about 10% and 40% in predicting the response of flexible footbridges submitted to walking loads are reported. 7,70,71 On the other hand, another study shows an overestimate response below 50%. 61 Besides, walking load tests on staircases revealed an underestimation up to 18.8%. ...
The study of the human‐structure interaction (HSI) using biodynamics models has gained attention lately. Several studies have demonstrated that the passive (standing still) and active (bobbing/bouncing or walking) persons can act for the benefit of the structural system by considering their body dynamic properties. Nevertheless, little concern has been addressed regarding the HSI during jumping loads on floors. This kind of human load is often considered as a “force‐only” model by design guides, and the body dynamics is disregarded. Therefore, aiming at filling this gap, this work investigates experimental and numerically an individual jumping on a vibrating (flexible) floor mounted in the laboratory. The active HSI was evaluated considering both single and two degree of freedom models in time and frequency domains. Besides, the assessment of the human body dynamic parameters (spring, mass and damper) was carried out based on optimisation techniques. The results show the potential benefit of taking into account the active HSI in near‐resonant cases to the detriment of a force‐only model.
... This model was given a stiffness which is similar to reported leg stiffness values and the mass of the pedestrian was applied and subjected to a dynamic force component as above. This model provided extremely accurate predictions of mid-span accelerations in the case of a footbridge which was subjected to 100 individual pedestrian crossings [14]. ...
Pedestrian loading on flexible structures such as footbridges, grandstands and lightweight floors is an area, which is receiving significant attention from the research community of late. One of the key parameters in determining the structural response is the frequency of the bridge. The authors are currently researching pedestrian-induced loading on flexible structures and also the use of FRP materials in construction. This paper describes the amalgamation of these two discrete research interests by detailing the material testing, design and construction of a laboratory-scale FRP composite footbridge. The bridge was constructed from glass fibre reinforced polymer (GFRP) composite beams, with GFRP lateral bracing. This structure supports a timber deck. The bridge is lightweight and the span can be altered from 6.5m to 8.0m clear span to adjust the structural response, by altering the natural frequency and magnitudes of displacements. The bridge can also be fixed in position through the use of removable intermediate supports. The bridge also has a force plate mounted at mid-span, facilitating direct measurement of the reaction force between the pedestrian and the structure. This paper presents the results of preliminary walking trials on this bridge in both the fixed and free suspension states, and across a range of spans, allowing analysis of the interaction between pedestrian loading and the structural response of flexible structures.
... Therefore, the second modelling approach describes a human body as a mechanical system, often composed of masses connected with springs and dampers. The simplest one is a linear oscillator having a single mass, spring and damping accompanied by a vertical GRF [22], followed by models of multiple lumped masses connected with linear springs and dampers [23][24][25][26][27]. More complex are biomechanically inspired inverted pendulum models [11,[28][29][30][31][32] and multibody link segment models of the whole human body [33]. ...
This paper proposes a model of a self-sustained oscillator which can generate reliably the vertical contact force between the feet of a healthy pedestrian and the supporting flat rigid surface. The model is motivated by the self-sustained nature of the walking process, i.e. a pedestrian generates the required inner energy to sustain its repetitive body motion. The derived model is a fusion of the well-known Rayleigh, Van der Pol and Duffing oscillators. Some additional nonlinear terms are added to produce both the odd and even harmonics observed in the experimentally measured force data. The model parameters were derived from force records due to twelve pedestrians walking on an instrumented treadmill at ten speeds using a linear least square technique. The stability analysis was performed using the energy balance method and perturbation method. The results obtained from the model show a good agreement with the experimental results.
... (1) SDOF Models. Archbold [60] used a finite element model to simulate the vertical effects of an SDOF MSD model of a single pedestrian walking across a footbridge structure and compared its results with a force-only model. The parameters of the SDOF walking human model were adopted from biomechanics literature for standing and running people. ...
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.
... Indeed, this concept has been well developed in the VBI area (Filho [41], Olsson [42], Lin and Trethewey [43], Kwon et al. [44], Majumder and Manohar [45]). According to our literature survey (Table 1), the moving SMD was introduced by Archbold [46] into the HSI area. He used an SMD model in a commercial FE program with crowd synchronization and found that the predicted vibration response is not linearly proportional to the level of crowd synchronization; no analytical formulation was presented for the model [47]. ...
In this paper, human–structure interaction system models for vibration in the vertical direction are considered. This work assembles various moving load models from the literature and proposes extension of the single pedestrian to a crowd of pedestrians for the FE formulation for crowd–structure interaction systems. The walking pedestrian vertical force is represented as a general time-dependent force, and the pedestrian is in turn modelled as moving force, moving mass, and moving spring–mass–damper. The arbitrary beam structure is modelled using either a formulation in modal coordinates or finite elements. In each case, the human–structure interaction (HSI) system is first formulated for a single walking pedestrian and then extended to consider a crowd of pedestrians. Finally, example applications for single pedestrian and crowd loading scenarios are examined. It is shown how the models can be used to quantify the interaction between the crowd and bridge structure. This work should find use for the evaluation of existing and new footbridges.
