This MSc thesis delves into the topic of human-induced vibrations in footbridges with the main focus on a case study concerning the Kolibki footbridge located in Gdynia, Poland. The bridge is an arch steel footbridge comprising four simply supported spans of which the longest (denoted P3) of 27,62 m is the main subject of the thesis. A series of experimental campaigns comprising both ambient and forced vibration tests using walking pedestrians were conducted on the bridge. Two types of normal modes of span P3 having either the arch or the deck in motion were identified, and the first vertical bending mode of the deck was found to have a natural frequency above 5 Hz falling outside the critical range defined by several guidelines. Despite the seemingly low susceptibility to human-induced vibrations, the forced tests demonstrated vertical accelerations exceeding the HiVoSS comfort levels when subject to a single walking pedestrian underlining the lively nature of the footbridge and the importance of higher-order harmonics of the load. In this context, the aim of the thesis is to numerically validate the dynamic behaviour of span P3 using the finite element (FE) method. Firstly, the thesis deals with the signal processing of the experimental data to identify the modes present in the dynamic response and to validate the modal damping ratios. Secondly, a series of FE-models of span P3 using Ansys APDL are developed. Specifically, a benchmark study addresses the effects of different modelling options and parameter variations of the structural components measured by averaged natural frequency errors and MAC-values. The main challenge was to simultaneously replicate the arch and deck modes with low frequency errors, high MAC-values, and a correct reproduction of the experimental order of modes. Two validated models were chosen: one minimising the averaged frequency error (6%) and one maximising the average MAC-value (0,97). Lastly, transient FE-simulations of some of the pedestrian tests covering both centred and eccentric trajectories are conducted. Two different load models are employed: (a) one in which the forces transmitted by the pedestrian are estimated from the accelerations of the pedestrian centre of mass, and (b) one from literature. Comparing with the experimental bridge signals, the thesis firstly concludes that having the simultaneous recordings of pedestrian and bridge accelerations is important to accurately estimate the pedestrian load and simulate the structural response. Secondly, good agreement with experimental data in frequency domain is found for all simulated tests. FFT peaks correspond to both the vertical/torsional modes of the deck and to multiples of the step frequency. In fact, up to the eighth harmonic of the pedestrian load is found to be significant in the response. However, uncertainties are associated to the role of the arch modes. Thirdly, the experimental and numerical signals are only partially correlated in time-domain, however, the RMS- and peak values are replicated well. The lack of correlation is partially attributed to inaccurate initial conditions and a high sensitivity to the chosen integration method and damping model. The liveliness of the footbridge is mostly due to a lack of dissipation mechanisms typical of all-welded steel bridges, and with uncertainties in the modal damping factors, specific attention was made for the damping modelling. Since more than two modes contribute to the response, accurate results with Rayleigh damping and the Newmark or HHT algorithms were difficult to obtain. Additionally, depending upon the damping model, some numerical signals were found to resemble the transient response of a stiff floor due to continuous heel impact as opposed to the build-up of resonance. However, in this thesis, the modal superposition method proved overall to be the most accurate in terms of RMS- and peak values, cross-correlations, and frequency content.
Questa tesi di laurea magistrale approfondisce il tema delle vibrazioni indotte dall'uomo nelle passerelle pedonali, con particolare attenzione a un caso studio, la passerella pedonale Kolibki (Gdynia, Polonia). La passerella pedonale ad arco in acciaio è composta da quattro campate semplicemente appoggiate, di cui la più lunga (indicata come P3) di 27,62 m è l'oggetto della tesi. Sulla passerella è stata condotta una serie di campagne sperimentali comprendenti test di vibrazione sia ambientale (AVTs) che forzata, con pedoni in movimento. I modi di vibrare identifica ti tramite gli AVTs, di due tipi, coinvolgono o solo l’arco o solo la soletta. Il primo modo di flessione verticale ha una frequenza naturale superiore a 5 Hz, al di fuori dell'intervallo critico definito da diverse linee guida. Nonostante l’apparentemente bassa suscettibilità alle vibrazioni indotte dall'uomo, le prove di vibrazione forzata hanno mostrato accelerazioni verticali superiori ai livelli di comfort HiVoSS anche per un singolo pedone in movimento, sottolineando la deformabilità della passerella e l'importanza delle armoniche di ordine superiore del carico. In questo contesto, l'obiettivo della tesi è di convalidare numericamente il comportamento dinamico della campata P3 utilizzando il metodo degli elementi finiti (FE). In primo luogo, la tesi si occupa dell'elaborazione del segnale dei dati sperimentali per identificare le modalità presenti nella risposta dinamica e convalidare i coefficienti di smorzamento modale. In secondo luogo, con un approccio di tipo ingegneristico, vengono sviluppati una serie di modelli FE della campata P3 utilizzando Ansys APDL. In particolare, uno studio di benchmark affronta gli effetti di diverse opzioni di modellazione e variazioni dei parametri dei componenti strutturali misurati da errori di frequenza naturale media e valori MAC. La sfida principale era replicare simultaneamente le modalità di arco e ponte con piccoli errori sulla frequenza, valori MAC elevati e una riproduzione corretta dell'ordine sperimentale dei modi di vibrare. Sono stati scelti due modelli: uno che minimizza l'errore sulla frequenza media (6%) e uno che massimizza il valore MAC medio (0,97). Infine, vengono condotte analisi transienti per alcuni test con i pedoni in traiettoria sia centrata che eccentrica. A tal fine, si sono adottati due diversi modelli di carico: (a) uno in cui le forze trasmesse dal pedone sono stimate utilizzando i segnali di accelerazione del centro di massa del pedone e (b) uno con un modello di letteratura. Il confronto con i segnali sperimentali del ponte mostra l’importanza delle registrazioni simultanee delle accelerazioni del pedone e del ponte al fine di stimare accuratamente la forzante del pedone e simulare la risposta strutturale. In secondo luogo, si riscontra una buona coerenza con i dati sperimentali nel dominio della frequenza per tutti i test simulati. I picchi FFT corrispondono sia ai modi verticali/torsionali del ponte sia a multipli della frequenza del passo: anche l'ottava armonica del carico pedonale risulta significativa nella risposta. Le incertezze restano associate al ruolo dei modi dell'arco. In terzo luogo, i segnali sperimentali e numerici sono solo parzialmente correlati nel dominio del tempo, tuttavia, i valori RMS e di picco sono ben replicati. La mancanza di correlazione è parzialmente attribuita a condizioni iniziali imprecise e a un'elevata sensibilità al metodo di integrazione scelto e al valore dello smorzamento. Le eccessive vibrazioni della passerella sono dovute principalmente alla mancanza di meccanismi di dissipazione, tipici dei ponti in acciaio completamente saldati. Con le incertezze legate ai fattori di smorzamento modale, è stata posta particolare attenzione alla modellazione dello smorzamento. Poiché più di due modi contribuiscono alla risposta, è stato difficile ottenere risultati accurati con lo smorzamento alla Rayleigh. Inoltre, a seconda del modello di smorzamento adottato, si è trovato che alcuni segnali numerici erano più vicini alla risposta di un solaio rigido dovuta all'impatto continuo del tallone anziché a una risposta risonante. In questa tesi, il metodo di sovrapposizione modale si è dimostrato complessivamente il più accurato in termini di valori RMS e di picco, cross-correlation e contenuto in frequenza.
Experimentally based evaluation of the dynamic behaviour of a lively arch steel footbridge
Nariswari, Alexander
2024/2025
Abstract
This MSc thesis delves into the topic of human-induced vibrations in footbridges with the main focus on a case study concerning the Kolibki footbridge located in Gdynia, Poland. The bridge is an arch steel footbridge comprising four simply supported spans of which the longest (denoted P3) of 27,62 m is the main subject of the thesis. A series of experimental campaigns comprising both ambient and forced vibration tests using walking pedestrians were conducted on the bridge. Two types of normal modes of span P3 having either the arch or the deck in motion were identified, and the first vertical bending mode of the deck was found to have a natural frequency above 5 Hz falling outside the critical range defined by several guidelines. Despite the seemingly low susceptibility to human-induced vibrations, the forced tests demonstrated vertical accelerations exceeding the HiVoSS comfort levels when subject to a single walking pedestrian underlining the lively nature of the footbridge and the importance of higher-order harmonics of the load. In this context, the aim of the thesis is to numerically validate the dynamic behaviour of span P3 using the finite element (FE) method. Firstly, the thesis deals with the signal processing of the experimental data to identify the modes present in the dynamic response and to validate the modal damping ratios. Secondly, a series of FE-models of span P3 using Ansys APDL are developed. Specifically, a benchmark study addresses the effects of different modelling options and parameter variations of the structural components measured by averaged natural frequency errors and MAC-values. The main challenge was to simultaneously replicate the arch and deck modes with low frequency errors, high MAC-values, and a correct reproduction of the experimental order of modes. Two validated models were chosen: one minimising the averaged frequency error (6%) and one maximising the average MAC-value (0,97). Lastly, transient FE-simulations of some of the pedestrian tests covering both centred and eccentric trajectories are conducted. Two different load models are employed: (a) one in which the forces transmitted by the pedestrian are estimated from the accelerations of the pedestrian centre of mass, and (b) one from literature. Comparing with the experimental bridge signals, the thesis firstly concludes that having the simultaneous recordings of pedestrian and bridge accelerations is important to accurately estimate the pedestrian load and simulate the structural response. Secondly, good agreement with experimental data in frequency domain is found for all simulated tests. FFT peaks correspond to both the vertical/torsional modes of the deck and to multiples of the step frequency. In fact, up to the eighth harmonic of the pedestrian load is found to be significant in the response. However, uncertainties are associated to the role of the arch modes. Thirdly, the experimental and numerical signals are only partially correlated in time-domain, however, the RMS- and peak values are replicated well. The lack of correlation is partially attributed to inaccurate initial conditions and a high sensitivity to the chosen integration method and damping model. The liveliness of the footbridge is mostly due to a lack of dissipation mechanisms typical of all-welded steel bridges, and with uncertainties in the modal damping factors, specific attention was made for the damping modelling. Since more than two modes contribute to the response, accurate results with Rayleigh damping and the Newmark or HHT algorithms were difficult to obtain. Additionally, depending upon the damping model, some numerical signals were found to resemble the transient response of a stiff floor due to continuous heel impact as opposed to the build-up of resonance. However, in this thesis, the modal superposition method proved overall to be the most accurate in terms of RMS- and peak values, cross-correlations, and frequency content.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/235759