This 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 Sétra 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 ar...

SUMMARY: Finite element models for structures and vibrations often lead to second order dynamical systems with large sparse matrices. For large‐scale finite element models, the computation of the frequency response function and the structural response to dynamic loads may present a considerable computational cost. Padé via Krylov methods are widely used and are appreciated projection‐based model reduction techniques for linear dynamical systems with linear output. This paper extends the framework of the Krylov methods to systems with a quadratic output arising in linear quadratic optimal control or random vibration problems. Three different two‐sided model reduction approaches are formulated based on the Krylov methods. For all methods, the control (or right) Krylov space is the same. The difference between the approaches lies, thus, in the choice of the observation (or left) Krylov space. The algorithms and theory are developed for the particularly important case of structural damping. We also give numerical examples for large‐scale systems corresponding to the forced vibration of a simply supported plate and of an existing footbridge. In this case, a block form of the Padé via Krylov method is used. Copyright © 2012 John Wiley & Sons, Ltd.

Vibration serviceability under crowd-induced loading has become a key design criterion for footbridges. Although increased research efforts are put into the characterization of crowd-induced loading, including related interaction phenomena, and first-generation design guides are available, a major challenge lies in the further development and validation of prediction models for crowd-induced vibrations. Full-scale benchmark datasets that simultaneously register structural and crowd motion make an invaluable contribution to meeting this need by providing detailed information on representative operational loading and response data. Currently available datasets either (1) involve a (too) small number of pedestrians or (2) do not involve the simultaneous registration of pedestrian and bridge motion, or else they involve a footbridge (3) where only a single mode or a very limited number of modes are sensitive to walking excitation, (4) for which no suitable digital twin is available, or (5) that is not open access. This paper therefore presents a new and publicly available full-scale dataset collected specifically for the further development and validation of models for crowd-induced loading. The dataset is collected for a real footbridge, with a number of modes that are sensitive to pedestrian-induced vibrations, and with a digital twin available. The pedestrian and bridge motions are registered simultaneously using wireless triaxial accelerometers and video cameras. In addition to two data blocks involving purely ambient excitation, four data blocks are collected for two pedestrian densities, 0.25 and 0.50 persons/m², representing a total of more than 1 h of data for each pedestrian density. Analysis of the structural response shows that the different data blocks can be considered representative for the involved load case. The identified distribution of step frequencies in the crowd indicates a significant contribution of (near-)resonant loading for a number of modes of the footbridge. Furthermore, the dataset displays clear signs of human–structure interaction, suggesting a significant increase in effective modal damping ratios due to the presence of the crowd.

The vibration serviceability assessment of footbridges under pedestrian traffic requires a probabilistic approach considering the uncertainty in the dynamic behavior of the structure and the variability of multiple load parameters, such as the pedestrians’ arrival time and step frequency. In view of engineering applications, a major challenge lies in the development, verification, and validation of efficient prediction models. With this challenge in mind, this paper uses a spectral approach to predict the dynamic response induced by unrestricted pedestrian traffic. A spectral load model available in the literature is extended to account for multiple harmonics of the vertical walking load and for application to arbitrary mode shapes. Furthermore, a closed-form expression is proposed to estimate the variance of the multimode structural response taking into account both resonant and nonresonant contributions. The performance of the proposed approach is evaluated for a simply supported beam as well as a real footbridge where multiple modes considerably contribute to the overall structural response. The results show that the proposed approach allows a good and mildly conservative estimate of the structural response to be obtained.

This paper proposes a methodology to reconstruct the vertical GRFs from the registered body motion that is reasonably robust against measurement noise. The vertical GRFs are reconstructed from the experimentally identified time-variant pacing rate and a generalised single-step load model available in the literature. The proposed methodology only requires accurately capturing the body motion within the frequency range 1–10 Hz and does not rely on the exact magnitude of the registered signal. The methodology can therefore also be applied when low-cost sensors are used and to minimize the impact of soft-tissue artefacts. In addition, the proposed procedure can be applied regardless of the position of the sensor on the human body, as long as the recorded body motion allows for identifying the time of a nominally identical event in successive walking cycles. The methodology is illustrated by a numerical example and applied to an experimental dataset where the ground reaction forces and the body motion were registered simultaneously. The results show that the proposed methodology allows for arriving at a good estimate of the vertical ground reaction forces. When the impact of soft-tissue artefacts is low, a comparable estimate can be obtained using Newton’s second law of motion.

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.