MS11.1 - Footbridge Vibrations

The Author considers the dynamic analysis of the pedestrian crowd on the bridge. The key assumptions in this project are random values of the walking velocities, no interaction between pedestrians, and no traffic effects. The recurrent neural networks superimpose the weighted responses generated by N pedestrians walking individually across the bridge at different points in time. The approach of the algorithm is to evaluate each pedestrian, and their GRF and simulate the response of the structure. After all, responses have been calculated, the recurrent neural networks superimpose the responses to determine the overall structural response during the simulation window. The hypothesis is that N pedestrians cross the bridge in a 30-minute window. The arrival times (onto the bridge) are distributed according to Poisson distribution. The pedestrian movements or the distribution can be validated by GPS traces This is something you can look into if developing a more rigorous simulation. The modal force and response for each pedestrian result shifted along the time axis to match their random start time. and the Poisson distribution of the arrival time. In the successive step, the algorithm can calculate the combined crowd-induced loading and response simply by superimposing the data for each pedestrian individually according to the weighted sum method. Finally, the algorithm can plot the crowd loading and total modal response. This is the modal response so it corresponds to the response at the mid-span location of the beam. The response at any other point along the beam can be obtained using the mode shape. Obtained the crowd--induced dynamic displacement, the algorithm can numerically differentiate this vector of numbers twice to obtain the vertical acceleration of the bridge/beam. This result represents a good step as vibration serviceability limits are usually reported in terms of acceleration. The advantages of Recurrent Neural Networks are mainly three. The first is that they can process inputs of any length. Therefore the number of people can be an independent variable. This is in contrast to other networks that can only process fixed-length inputs. As a result, we can use RNN with both short and very long sequences without changing the architecture of our network. The second advantage is that the hidden state acts as some kind of memory. As the network processes the elements of a sequence one by one, the hidden state stores and combines information about the entire sequence. The algorithm can consider the mass effect of Pedestrians. The mass effect can be an innovative aspect of the relationship between modal frequency and pacing frequency. Finally, the third advantage of Recurrent Neural Networks is that weights can be variable through time phases. This allows the network to maintain the same size (with the same number of parameters) for variable-length sequences.

Human-induced loads may produce resonance when the forcing frequency coincides with the natural frequency of the system. In this work, the dynamic measurements performed on a pedestrian cable-stayed bridge in Uppsala, Sweden are presented. The dynamic properties of the system have been identified and different loading scenarios are evaluated. A comparison between the theoretical and measured acceleration of the bridge is made using a detailed finite element model. Different modelling aspects are considered and evaluated by studying their influence on the natural frequencies of the system such as the cable system, railings, deck, and boundary conditions. Moreover, a parametric analysis of the boundary conditions of the system is presented and the calibration of the model is performed with reference to the identified frequencies. Special focus is given to the resonant response of the cable system potentially compromising the serviceability limit state of the structure. Furthermore, a simulation of a crowd event is presented, and the human-structure interaction effect is taken into account over the studied bridge. A considerable reduction of the dynamic response of the system is found, highlighting the importance of this phenomenon and its need to be considered in the current design guidelines.

The progressive incursion of increasingly resistant and lightweight materials in the construction industry added to the hypothesis of a global regeneration of urban structures based on new architectural and engineering requirements of greater technical and aesthetic demands, has generated that civil structures such as bleachers, stairs, slabs, and especially pedestrian bridges present a high susceptibility to excessive vibrations due to the action of dynamic loads, where the most frequent source of excitation is the one induced by human activity, especially human walking. These anthropic loads present adaptive phenomena, due to structural vibrations, generated by the coupling effects of the existing Human-Structure Interaction (HSI). In general, two main aspects are considered in the effects of HSI in this type of civil structures. The first one estimates change in the dynamic properties, due to the additional presence of a non-stationary mass on it. The second aspect refers to the degree of coupling between the people in transit, as well as between them and the structure. Although research on the effects of IHE has increased considerably in recent years, these aspects have not yet been fully detailed and addressed. Therefore, this research focused, firstly, on developing a Multiaxial Dynamic Platform called the Human-Structure Interaction Multiaxial Test Framework (HSI-MTF), with the objective of acquiring three-dimensional loads induced by human gait under the effects of lateral harmonic motions. Secondly, an experimental campaign was conducted with seven test subjects (TS) without motor impairment conditions, mass ranges of 64.0→80.0 kg and heights between 1.66→1.79 m; to whom, gait loads were acquired and evaluated under lateral sinusoidal movements, with displacements between 5.0→50 mm and a frequency content of 0.7→1.3 Hz. The lateral loads induced by human gait during the HSI-MTF flexible surface displacement protocols determined that for displacements less than 20.0 mm the gait frequency content remains predominant in combination with that induced by the HSI-MTF. However, for larger displacements the predominant frequencies in the loads are those induced by the HSI-MTF; furthermore, for load amplification factors values of up to 35.0% of the SP weight were reached for displacements on flexible surfaces, compared to an average of 5.0% for rigid surfaces. For vertical loads, of which there was no record in the literature under this condition, amplifications of up to 30.0% and relevant changes in their frequency content were calculated, in comparison with the walking loads on rigid surfaces.

Among the load scenarios considered for the serviceability assessment of human-induced footbridge vibrations, is that of the transient action of a single pedestrian or a small group of pedestrians. Although such action is stochastic due to the variability of gait parameters, Standards and Guidelines assume it is deterministic, and equal to that coming from the “worst pedestrian ever” for the given footbridge. Such approach is sound from an Engineering point of view, but does not allow control of the probability of failure. It also has the advantage that it can be applied to footbridges with any structural system. In this paper, firstly the analysis of peak accelerations is developed according to prEN1991-2:2018 (Eurocode 1 - Actions of structures, Part 2: Traffic loads on bridges) for a number of simple supported footbridges, for which a closed-form acceleration response is available, both in vertical and lateral directions. Then, a probabilistic procedure by the authors is used to evaluate the probability of exceedance of the calculated acceleration. The procedure uses empirical cumulative density functions of the peak acceleration obtained through Monte Carlo simulations. To this aim, a European Standard Population of walkers is defined based on literature data, to account for the variability of pedestrian and gait characteristics. It is found that the probability of exceedance of the acceleration calculated according to prEN1991-2:2018 is not uniform among the footbridges considered. A comparison between the peak acceleration evaluated in accordance with prEN1991-2:2018 and the characteristic values obtained by the probabilistic procedure is also performed. Finally, a probability-based model is proposed for the evaluation of the characteristic value of the footbridge peak acceleration due to single pedestrians or groups of pedestrians. The latter is easily codifiable, and has the advantage of allowing control of the probability of failure; on the other hand, it has the drawback of being limited to footbridge with sinusoidal mode shapes.