Peter Van den Broeck

Identification and Modelling of Vertical Human-Structure Interaction

Slender footbridges are often highly susceptible to human-induced vibrations, due to their low stiffness, damping and modal mass. Predicting the dynamic response of these civil engineering structures under crowd-induced loading has therefore become an important aspect of the structural design. The excitation of groups of pedestrians and crowds is generally modelled using moving loads but also the changes in dynamic characteristics due to human-structure interaction are found to significantly affect the footbridge response. The present contribution investigates the influence of the presence of the pedestrians onto the dynamic characteristics of the occupied structure by means of an extensive experimental study on a footbridge in laboratory conditions. The analysis shows that the natural frequencies slightly reduce due to the additional mass but more significant is the observed increase in structural damping. Similar observations are made on a in situ footbridge. This interaction is simulated using a coupled human-structure model in which the human occupants are represented by simple biomechanical models.

Numerical and experimental analysis of the vibration serviceability of the Bears' Cage footbridge

Abstract The Bears’ Cage footbridge is a slender steel structure with a single span. Its dynamic behaviour is predicted based on a refined finite-element (FE) model and the vibration serviceability is assessed according to the current codes of practice. The assessment indicates a high susceptibility to human-induced vibrations with disturbing vibration levels even for sparse pedestrian densities. To validate the predicted behaviour of the structure, an extensive experimental study is performed including static deflection and dynamic vibration tests. The analysis shows that statically, the longitudinal movement of the supports on one side of the span can be considered unconstrained, indicating a behaviour of the sliding pot bearings as designed. Due to the footbridge’s arch-like shape, the longitudinal stiffness of the supports highly influences the natural frequency of the fundamental bending mode. The analysis shows that the longitudinal stiffness of sliding pot bearings and the structural inherent damping ratio of the fundamental mode significantly reduces once an initial friction level in the sliding pot bearings is overcome as the result of a significant movement at the supports. The vibration serviceability is reassessed based on the calibrated FE model and shows that even for high pedestrian densities, maximum vibration comfort is ensured.

Numerical and Experimental Evaluation of the Dynamic Performance of a Footbridge with Tuned Mass Dampers

AbstractThis article presents an evaluation of the dynamic behavior of a slender steel footbridge before and after the installation of two tuned mass dampers (TMDs). The results of the experimental study show that the damping devices lead to an increase of the effective damping ratio of the critical mode. Additional tests involving the structural vibrations induced by a limited number of persons revealed that the TMD units are effective in reducing the structural response. However, the obtained reduction highly depends on the type of human excitation. To verify the response of the footbridge for large groups and crowds, a comprehensive numerical analysis is performed. The results are compared to the response predicted by the procedures of the Setra and HiVoSS design guides. For the bridge without TMD units, a significantly higher structural response is predicted by the design guides; the bridge has a short span and is lightly damped, so the steady-state resonant conditions assumed in the design guides are...

The impact of vertical human-structure interaction for footbridges

Abstract. To allow for a more accurate description of crowd-induced loading, the present study aims to provide the necessary insights into vertical human-structure interaction (HSI) phenomena, to date ignored in current load models. A parametric study is performed to investigate the effects of the mechanical interaction between pedestrians, represented by simple lumped parameter models, and the supporting footbridge. The most significant HSI-effect for the lowfrequency modes of a footbridge, is in the effective damping ratio of the coupled system which is much higher than the inherent structural damping. The effective damping ratio increases monotonically with the pedestrian density but is highly dependent on the natural frequency of the footbridge. In order to verify the findings, a comprehensive full-scale experimental study is performed on two footbridges. It is shown that the crowd-structure model is able to reproduce the experimentally identified dynamic characteristics of the coupled system.

Reduced-order models for vertical human-structure interaction

For slender and lightweight structures, the vibration serviceability under crowd- induced loading is often critical in design. Currently, designers rely on equivalent load models, upscaled from single-person force measurements. Furthermore, it is important to consider the mechanical interaction with the human body as this can significantly reduce the structural response. To account for these interaction effects, the contact force between the pedestrian and the structure can be modelled as the superposition of the force induced by the pedestrian on a rigid floor and the force resulting from the mechanical interaction between the structure and the human body. For the case of large crowds, however, this approach leads to models with a very high system order. In the present contribution, two equivalent reduced-order models are proposed to approximate the dynamic behaviour of the full-order coupled crowd-structure system. A numerical study is performed to evaluate the impact of the modelling assumptions on the structural response to pedestrian excitation. The results show that the full-order moving crowd model can be well approximated by a reduced-order model whereby the interaction with the pedestrians in the crowd is modelled using a single (equivalent) SDOF system.

Human-Induced Vibrations of Footbridges: The Effect of Vertical Human-Structure Interaction

Slender and lightweight structures are often unduly responsive to human excitation. The concerns of vibration comfort and safety are strengthened by unexplored human-structure interaction (HSI) phenomena. The present contribution proposes a numerical model for pedestrian excitation including HSI. In addition to the well-known forces induced by a pedestrian on a rigid floor, the pedestrian is represented by a linear mechanical model to simulate the interaction with the supporting structure. Inspired by the body postures assumed during the walking cycle, the mechanical properties are chosen to represent the dynamic behaviour of the human body with one or two legs slightly bent. The effect of HSI on the structural response is evaluated for various footbridge parameters and pedestrian densities. It is shown that by taking into account HSI, the structural response is reduced. Furthermore, it is demonstrated that the unrealistic high acceleration levels as predicted by simplified force models are not reached as the result of HSI. It is concluded that the mechanical interaction with the crowd is relevant for the vertical low-frequency dynamic behaviour of footbridges.

Simulation of human-induced vibrations based on the characterized in-field pedestrian behavior

For slender and lightweight structures, vibration serviceability is a matter of growing concern, often constituting the critical design requirement. With designs governed by the dynamic performance under human-induced loads, a strong demand exists for the verification and refinement of currently available load models. The present contribution uses a 3D inertial motion tracking technique for the characterization of the in-field pedestrian behavior. The technique is first tested in laboratory experiments with simultaneous registration of the corresponding ground reaction forces. The experiments include walking persons as well as rhythmical human activities such as jumping and bobbing. It is shown that the registered motion allows for the identification of the time variant pacing rate of the activity. Together with the weight of the person and the application of generalized force models available in literature, the identified time-variant pacing rate allows to characterize the human-induced loads. In addition, time synchronization among the wireless motion trackers allows identifying the synchronization rate among the participants. Subsequently, the technique is used on a real footbridge where both the motion of the persons and the induced structural vibrations are registered. It is shown how the characterized in-field pedestrian behavior can be applied to simulate the induced structural response. It is demonstrated that the in situ identified pacing rate and synchronization rate constitute an essential input for the simulation and verification of the human-induced loads. The main potential applications of the proposed methodology are the estimation of human-structure interaction phenomena and the development of suitable models for the correlation among pedestrians in real traffic conditions.

Prediction of peak response values of structures with and without TMD subjected to random pedestrian flows

In civil engineering and architecture, the availability of high strength materials and advanced calculation techniques enables the construction of slender footbridges, generally highly sensitive to human-induced excitation. Due to the inherent random character of the human-induced walking load, variability on the pedestrian characteristics must be considered in the response simulation. To assess the vibration serviceability of the footbridge, the statistics of the stochastic dynamic response are evaluated by considering the instantaneous peak responses in a time range. Therefore, a large number of time windows are needed to calculate the mean value and standard deviation of the instantaneous peak values. An alternative method to evaluate the statistics is based on the standard deviation of the response and a characteristic frequency as proposed in wind engineering applications. In this paper, the accuracy of this method is evaluated for human-induced vibrations. The methods are first compared for a group of pedestrians crossing a lightly damped footbridge. Small differences of the instantaneous peak value were found by the method using second order statistics. Afterwards, a TMD tuned to reduce the peak acceleration to a comfort value, was added to the structure. The comparison between both methods in made and the accuracy is verified. It is found that the TMD parameters are tuned sufficiently and good agreements between the two methods are found for the estimation of the instantaneous peak response for a strongly damped structure.

Identification of Human-Induced Loading Using a Joint Input-State Estimation Algorithm

This paper uses a state-of-the-art joint input-state estimation algorithm to identify the modal load induced by a single pedestrian on a laboratory structure. The experimental setup involves a simply-supported concrete slab with a length of 7 m. A dynamic model of the lab structure is constructed from a finite element model that is calibrated using a set of experimentally identified modal characteristics. The estimated modal load as is compared with the numerically predicted modal load which uses the average single-step walking load as determined from direct force measurements, the location of the individual steps as identified from video processing and a numerical model of the structure. For the time interval where the pedestrian is crossing the slab, the estimated modal load is found to be in good agreement with the numerically predicted values. Following the last footstep of the pedestrian, the slab passes into a decaying free vibration whereby an exponentially decaying estimated input compensates for small errors in the modal properties.