Search Results (14)

Slender, lightweight and modern footbridges are particularly susceptible to vibrations induced by pedestrian activity. While extensive research has focused on vertical and lateral forces produced by walking, torsional moments generated by eccentrically walking pedestrians remain largely overlooked. Traditional assessments typically neglect these torsional effects, which can be critical when eccentric pedestrian loading excites torsional modes, especially in footbridges with asymmetric geometries. To address this, the paper considers the coupling between bending and torsional effects in both the pedestrian action and structure reaction, including pedestrian forces and moments, as well as bending-induced deflections and torsion-induced rotations of the cross-sections. A simplified method is also presented, allowing standard bending-only analyses to be easily adapted to include torsional effects using analytically derived correction factors. For validation, several experimental tests are conducted on an asymmetric curved footbridge located in Modena, Italy, characterised by coupled bending-torsional vertical modes and hosting different pedestrian densities, pacing frequencies, and crowd distributions (both uniform and eccentric). Experimental and numerical analyses demonstrate that neglecting torsional effects oversimplifies the assessment, highlighting the importance of accounting for bending-torsion coupling for the serviceability of asymmetric footbridges under eccentric near-resonance loading. Full article

Aging infrastructure is a growing concern worldwide, with many bridges exceeding 50 years of service, prompting questions about their structural integrity. Over the past decade, the deterioration of bridges has driven extensive research into Structural Health Monitoring (SHM), a tool for early detection of structural deterioration, with particular emphasis on remote-sensing technologies. This review combines a scientometric analysis and a state-of-the-art review to assess recent advancements in the field. From a dataset of 702 publications (2014–2024), 171 relevant papers were analyzed, covering key SHM aspects including sensing devices, data acquisition, processing, damage detection, and reporting. Results show a 433% increase in publications, with the United States leading in output (28.65%), and Glisic, B., with collaborators forming the largest research cluster (11.7%). Accelerometers are the most commonly used sensors (50.88%), and data processing dominates the research focus (50.29%). Key challenges identified include cost (noted in 17.5% of studies), data corruption, and WSN limitations, particularly energy supply. Trends show a notable growth in AI applications (400%), and increasing interest in low-cost, crowdsource-based SHM using smartphones, MEMS, and cameras. These findings highlight both progress and future opportunities in SHM of footbridges. Full article

Structures such as long-span footbridges, floors, and long cantilevers are vulnerable to vibration serviceability problems under crowd walking, which should be taken into consideration during the structural design, operation, and maintenance stages. Standards have been developed to enable designers to assess the vibration serviceability of structures using simplified load models that simulate crowd-induced loading. To facilitate engineers in quickly selecting appropriate standards for vibration serviceability design, ten current standards were collected which deal with the assessment of structural vibration serviceability under walking loads, including the French “Assessment of vibrational behavior of footbridges under pedestrian loading” (2006), the German “Design of footbridges guideline” (2007), the Chinese “Technical standard for human comfort of the floor vibration” (2019), etc. The ten standards were reviewed and evaluated from three aspects including the crowd loading model, structural response calculation method, and vibration serviceability evaluation standard in this paper. Through summary and comparison between standards, three directions for future improvement and perfection of the standards were proposed: the challenges of the improvement of the standards focus on the establishment of the refined stochastic load model, the analysis of the crowd–structure coupling system, and the modelling of multifactor coupling serviceability evaluation indexes. Full article

With the emergence of slimmer footbridges and the introduction of lighter materials, the challenge of vibrational comfort assessment becomes more and more relevant. Previous studies have shown that each pedestrian will act both as an inducer and a damper, referred to as human–structure interaction. However, this interaction is currently not implemented in design guidelines, which leads to a poor comfort estimation for small lightweight footbridges. Derived from smartphone-based vibration measurements, this paper provides an overview of the modal parameters at various pedestrian densities and a comfort assessment of a selection of simply supported GFRP and steel lightweight footbridges in Flanders. The results indicate that the initial structural damping ratios for GFRP bridges exceed the values set in design guidelines and that they increase with an increasing pedestrian density. Further, it is shown that the measured accelerations do not relate proportionally to the pedestrian density. From both results the relevance of human–structure interaction is confirmed. Finally, while the first natural frequency is analytically predicted accurately, the vertical accelerations are substantially overestimated. Here, a better estimation can be made based on the experimentally measured damping ratios. The results contribute to a better understanding of human–structure interaction and the vibration assessment of lightweight footbridges. Practical applications include optimizing footbridge design, focussing on better performance and improving safety and user experience. Full article

Vibrations are an issue of increasing importance in current footbridge design practice. More sophisticated footbridges with increasing spans and more effective construction materials result in lightweight structures and a high ratio of live load to dead load. As a result of this trend, many footbridges have become more susceptible to vibrations when subjected to dynamic loads. The most common dynamic loads on footbridges, other than wind loading, are pedestrian-induced footfall forces due to the movement of people. This paper concerns the experimental and numerical dynamic characterization of a newly built steel and wooden cable-stayed footbridge. The footbridge was dynamically tested in situ under ambient vibration, and the results allowed the real dynamic behavior of the footbridge to be captured. The dynamic response under pedestrian dynamic loads was also investigated and compared with the limitations provided by the main international codes and guidelines for footbridge serviceability assessment. A numerical model of the footbridge was also developed and updated based on the experimental outcomes. Then, the calibrated model was used to numerically assess the footbridge’s serviceability following the guideline prescriptions for pedestrian load simulation, and the design accuracy was also validated. This paper aims to increase the state-of-the-art knowledge about footbridge dynamic testing so as to support the design of new and futuristic structures as well as prove the effectiveness of using the requirements of codes and guidelines for footbridge serviceability assessment by adopting a calibrated numerical model. Full article

Developing new structural materials, such as composite materials, has provided many opportunities in bridge engineering. Among these materials, glass-fiber-reinforced polymers (GFRPs), in particular, have found applications in footbridges. However, some of the commonly recognized advantages of GFRPs, such as the high values of the strength/weight ratio, can also be considered disadvantageous for certain realizations, particularly when the composite material used in a footbridge is, for example, subjected to dynamic actions such as those that are induced by wind and walking and/or running users. The induced accelerations can reach high values in comparison to recommended thresholds. Further, the natural frequency decays during the service life, reducing the capacity of the frequencies to move toward the frequency content of the pedestrian step. In this framework, the presented research is devoted to the dynamic comfort assessment of a pioneering cable-stayed GFRP pedestrian bridge, Aberfeldy, which was assembled in 1992 in the eponymous small town, which is located in Scotland (UK). The assessment was numerically performed through a finite element (FE) model, which was tuned based on the literature data concerning geometry, structural details, and in situ-acquired frequencies. The analyses carried out in this study include the evaluation of the accelerations’ time histories, which were induced when simulating a set of pedestrian path scenarios, and the dynamic actions that occur during pedestrian traveling. Specifically, different values of velocity and step frequency were considered as well as the inclusion of walking and running movements. Then, based on the acceleration values, the assessments of comfort criteria for the current standards were elaborated while also recognizing that the peak accelerations—usually attained for short periods—cannot be the only parameters considered in evaluating the pedestrian bridge capacity. This investigation allowed a dynamic comfort rating to be established for the Aberfeldy footbridge. Full article

Current codes and guidelines for the dynamic design of footbridges often only specify the pedestrian-induced excitations. However, earthquakes may occur during the passing stage of pedestrians in earthquake-prone regions. In addition, modern footbridges tend to be slender and are sensitive to vertical ground motions. Therefore, we investigate the effects of vertical ground motion on pedestrian-induced vibrations of footbridges. A total of 138 footbridges with different materials, dimensions, and structural types are considered as the target structures. The classical social force model combined with the pedestrian-induced load is used to simulate crowd loads for the scenarios with six typical pedestrian densities. Furthermore, 59 vertical ground motions with four seismic intensities are taken as the seismic inputs. An amplification factor is introduced to quantify the amplification effects of vertical ground motion on human-induced vibrations of footbridges. Four machine learning (ML) algorithms are used to predict the amplification factor. The feature importance indicates that the scaled peak ground acceleration, the pedestrian density, and the bridge span are the three most important parameters influencing the amplification factor. Finally, the vibration serviceability of the footbridge subjected to both crowd load and vertical ground motion is assessed. Full article

Experimental and numerical studies for the structural and vibration serviceability assessment of a historic suspension footbridge adopting non-invasive surveys and low-cost equipment are presented. Field surveys have been carried out to determine geometric properties, ambient vibration tests have been performed to estimate the dynamic properties, and the dynamic response of the footbridge under the action of a single crossing pedestrian has been recorded. Based on field surveys, a 3D Finite Element model was built and was then calibrated against ambient vibration test results. The experimentally-measured maximum acceleration under the action of one crossing pedestrian is compared with the ones obtained numerically and analytically. Furthermore, vibration serviceability assessment under multi-pedestrian loading is carried out, adopting the simplified procedure recommended by a recent guideline. Results show that low-cost non-invasive dynamic testing is suitable to correctly identify the footbridge vertical natural frequencies and mode shapes, including higher-order ones, and to draw considerations about the state of degradation of the structure. Moreover, the level of vibration under the action of a single pedestrian can be estimated with sufficient accuracy using a simplified loading model, provided that the modal damping ratio is properly tuned. Full article

Modern footbridges are often lively structures, characterized by natural frequencies that fall in the range of pedestrian activities, such as walking, running, and jumping. Therefore, serviceability assessment under human-induced excitation is crucial both at the design stage and during the footbridge lifetime. This paper presents and validates two different FE models of an existing footbridge with very complex geometry: the Streicker Footbridge at the Princeton University Campus. It represents a benchmark in the field as a testbed for vibration serviceability assessments under pedestrian excitation. The real structure is equipped with strain and temperature sensors that are currently used to collect measurements in both static and dynamic modes for research and educational purposes in Structural Health Monitoring (SHM). Based on detailed drawings of the Streicker Footbridge, a three-dimensional beam-based model was developed to represent the complex behavior of the full-scale benchmark bridge. Subsequently, a more refined discretization of the bridge deck adopting shell elements was inserted. The bridge Finite Element models were validated against available SHM data concerning static and dynamic tests. The relevant ANSYS APDL script files along with an example of pedestrian jumping application are available upon request for further research developments on the relationship between pedestrians and the benchmark footbridge. Full article

The use of glass fibre reinforced polymer (GFRP) composites in civil engineering structures has seen considerable growth in recent years due to their high strength, low self-weight, and corrosion resistance, namely when compared to traditional materials, such as steel and reinforced concrete. To enable the structural use of GFRP composite materials in civil engineering applications, especially in footbridges, it is necessary to gather knowledge on their structural behaviour, particularly under dynamic loads, and to evaluate the ability of current design tools to predict their response. In fact, excessive vibration has a major influence on the in-service performance (comfort) of slender structures as well on their service life. The use of composite materials that combine high damping capacity with relatively high stiffness and low mass can provide functional and economic benefits, especially for footbridges. This paper aims to investigate the dynamic behaviour of GFRP free-supported beams to evaluate their modal characteristics (frequency, damping, and modal shape). To assess the benefits of using a structure made of pultruded GFRP rather than a conventional material—steel, a comparative analysis between the dynamic characteristics of GFRP and steel beams is performed. To specifically address material damping and to minimize the interference of the boundary conditions, the beams are tested in a free condition, resting on a low-density foam base. The results show that the damping capacity of GFRP is much higher than that of steel, as the measured damping factor of GFRP is five times higher than that of steel for the same boundary conditions and similar geometry. Furthermore, the fact that the frequencies of the tested specimens resemble for the two different materials highlights the perceived damping qualities of the polymer-based composite material. Finally, an energy method for evaluating the influence of the scale factor on material damping is applied, which made it possible to infer that the damping varies as a function of frequency but is not explicitly affected by the length of the specimens. Full article

In this study, the human-induced dynamic performance of modern footbridges equipped with either classical reinforced concrete (RC) or innovative glass fiber-reinforced polymer (GFRP) composite deck slabs were investigated and compared. The numerical studies were carried out for two bridges: a three-span cable-stayed footbridge and a three-span continuous beam structure. Two variants of both bridges were taken into consideration: the footbridges equipped with traditional RC slabs and the structures benefitted with GFRP slabs. The risk of resonance as well as the vibration serviceability and the comfort criteria assessment of the footbridges with different slab materials were assessed. The investigation revealed that the footbridges, both cable-stayed and beam, benefitted with the GFRP slabs had higher fundamental frequency than those with the traditional RC slabs. The footbridges with the GFRP slabs were less exposed to the resonance risk, having fundamental frequencies above the limit of the high risk of resonance. The effect of shifting up the natural frequencies by introducing GFRP slabs was more remarkable for the lightweight beam structure than for the cable-stayed footbridge and resulted in a more significant reduction of the resonance risk. The calculated maximum human-induced accelerations of the footbridges benefitted with the GFRP slabs were meaningfully higher than those obtained for the footbridges with the RC slabs. The study proved that, with the same GFRP slab, meeting vibration serviceability and comfort criteria limits in the case of very lightweight beam structures may be more problematic than for cable-stayed footbridges with more massive structural systems. In the research, particular attention was paid to examining the impact of higher harmonics of the moving pedestrian force on the structures benefitted with the GFRP composite slabs. It occurred that in the case of footbridges, both cable-stayed and beam, equipped with the RC slabs higher harmonics of human force did not play any role in the dynamic performance of structures. However, in the case of the footbridges benefitted with the GFRP slabs, the impact of higher harmonics of the pedestrian force on the dynamic behavior of structures was clearly visible. Higher harmonics excited accelerations comparable to those executed by the first harmonic component. This conclusion is of great importance for footbridges equipped with GFRP slabs. The fundamental frequency may place a footbridge in the low or even negligible risk resonance range and the higher frequencies corresponding to vertical modes may be located above the limit of 5 Hz that ensures avoiding resonance. Nevertheless, the fact that fundamental modes are so responsive to higher harmonics significantly increases the risk of resonance. The amplification of the dynamic response may occur due to frequencies related to second or third harmonics (i.e., being half or a third of the natural frequencies). In such cases, full dynamic analysis of a footbridge at the design stage seems to be of crucial importance. Full article

The lateral vibration serviceability of slender footbridges has been the subject of many studies over the last few decades. However, in spite of the large amount of research, a common criterion has not been set yet. Although the human–structure interaction phenomenon is widely accepted as the main cause of the sudden onset of high amplitudes of vibration, the current design recommendations do not include an expression for the auto-induced component of the pedestrian action and, as a consequence, it is not possible to evaluate the footbridge comfort once the lock-in effect has developed. Hence, the purpose of this paper is to propose a general formulation, which allows the analysis of the different load scenarios that the footbridge will experience during its overall life cycle. An important advantage over most current design guidelines is that the procedure permits the evaluation of the comfort level of the footbridge, even with crowd densities above the “critical number”, and thus takes informed decisions about the possible use of external devices to control the vibration response, depending on the probability of occurrence of the problem. The performance of the proposed method is successfully evaluated through numerical response simulations of two real footbridges, showing a good agreement with the experimental data. Full article

In this work, an examination on the modal properties of a single-span steel-frame footbridge is presented. The footbridge is situated in Jawornik (Lesser Poland). The footbridge is symmetrical since its main structure consists of two steel frames of the same shape. The boundary conditions for both frames are the same as well. The study was completed on the basis of numerical as well as experimental investigations. For finite element (FE) analysis, a 3-D model of the single-span steel-frame footbridge was created. For the experimental study, a research scheme for in situ tests was developed. Three kinds of excitation techniques were used during the in situ tests: shock excitation, operational vibration, and slow sine sweep testing. Different functions that estimate natural frequencies, i.e., the power spectral density function (PSD) and the frequency response function (FRF), were applied. The modal assurance criterion (MAC) was used as a mathematical tool for the verification of the mode shapes of natural vibrations obtained in experimental and numerical ways. Good compatibility was recognized between the results obtained for experimental and numerical procedures in terms of both the natural frequency and the mode of vibration. The identified and verified values of the five consecutive natural frequencies of the footbridge were smaller than 5 Hz, but they were recognized as being located outside the frequency range defined as having “maximum risk of resonance”. The numerical and experimental modal analysis revealed that all modes corresponding to the natural frequencies from the 0–5 Hz range have both a symmetrical and an anti-symmetrical nature. In particular, the first vertical mode, which can play a central role from the serviceability of the footbridge point of view has a symmetrical shape. The results of the research might be applicable to the dynamic study of the structure type considered in the analysis, i.e., for the dynamic assessment of a single-span steel-frame footbridge with a relatively large mass as well as stiffness. The investigation proved that ambient vibration modal experiments are enough for the experimental investigation of the modal properties of the structure. Full article

Contemporary design codes and guides for vibration serviceability assessment include some simplifications in load modelling. The same statistical distribution of the inter-pedestrian variability of the step interval (frequency) is proposed for all applications. Moreover, walking loads are considered to be periodic. The intra-pedestrian variability of the step interval is neglected. A more realistic load modelling trying to overcome the limitations of the codes is intended in this paper. Instead of a single mean value of the inter-pedestrian distribution of walking speed, a range of possible variation, which account for the real variations that occur in practice depending on the footbridge location and usage, is considered. An enhanced model is proposed in this paper to reproduce statistically both the intra- and inter-pedestrian variability of the step interval as a function of the walking speed distribution. This innovative model is then applied to study the sensitivity of the vertical response of footbridges to the variability of the step interval and to evaluate the influence of the aforementioned simplifications on the predicted characteristic responses. For this purpose, low-frequency footbridges excited by single-pedestrian crossings are chosen. The response is statistically characterized through Monte Carlo numerical simulations including 720 different configurations and 10,000 load cases in each configuration. Results of the study provide an overview of the influence of the footbridge and load parameters on the responses, which can be useful in practical applications where human–structure interactions are negligible. As for the simplifications of the codes, it is found that either using a single distribution to model the inter-pedestrian variability of the spatiotemporal parameters or neglecting the intra-pedestrian variability can lead to a significant underestimation of the characteristic response of footbridges. Full article