Suspension Footbridge Research Articles

Detecting bridge dynamics with GPS and triaxial accelerometers

GPS and triaxial accelerometers have been used in field tests to record the response of the Wilford Bridge, a suspension footbridge over the River Trent in Nottingham, to forced vibration excited by more than 30 people with a total weight of 2353 kg, as well as subsequent decayed free vibration and ambient vibration caused by casual pedestrian traffic and weak wind loading. A peak-picking approach based on the bandpass filtering technique and Fast Fourier Transform (FFT) is employed to extract dominant local vibration frequencies and relevant vibration amplitudes of the bridge. It is found that the maximum frequency discrepancies between ambient and forced vibrations and that for ambient excitation against decayed vibration are 2.5% and 3.0%, respectively. The maximum frequency difference between different excitation manners is less than 2%. This provides evidence that precise structural natural frequencies of the bridge can be estimated from either the responding measurements of decayed free vibration or ambient vibration. These estimated frequencies, using GPS and accelerometer measurements, match well with the predictions from a dedicated Finite Element (FE) model created for the bridge. This paper concludes that GPS is a viable tool for both structural deflection monitoring and natural frequency detection and the measurements from a triaxial accelerometer can be used to validate the estimated dynamics from the GPS measurements and improve the overall monitoring system performance.

Dynamic performance of slender suspension footbridges under eccentric walking dynamic loads

This paper treats the vibration of slender suspension footbridges caused by eccentrically distributed walking dynamic loads. A suspension footbridge model with reverse profiled cables in both the vertical and horizontal planes was used in this conceptual study, while SAP2000 package is adopted in the numerical analysis. The dynamic behaviour of slender footbridges under walking dynamic loads is simulated by resonant vibration caused by synchronous excitations. It is found that slender suspension footbridges with shallow cable profiles often have coupled vibration modes such as coupled lateral–torsional or coupled torsional–lateral modes. When these coupled vibration modes are excited by walking pedestrians, excessive lateral vibration can be induced. Results also show that the effects of the reverse profiled cables on the dynamic performance in different vibration modes are complex. Reverse profiled cables in the horizontal plane can significantly suppress the lateral vibration in coupled lateral–torsional modes, but slightly increase the lateral vibration in coupled torsional–lateral modes.

Ambient vibration testing and structural evaluation of an historic suspension footbridge

The paper summarises the ambient vibration-based assessment of an historic suspension footbridge, dating back to 1928. The footbridge is characterised by the timber floor system supported by two couples of cables, that were recently replaced. After the retrofit, the actual structural behaviour of the bridge were assessed by experimental and theoretical methods. The field tests included geometric survey of the deformed configuration due to dead loads, ambient vibration measurements and static load tests. The peak picking and the enhanced frequency domain decomposition techniques were used to extract the modal parameters from ambient vibration data and a very good correlation among the modal parameters identified from the two techniques has been found. Successively, the information obtained from the dynamic tests, combined with classic techniques of system identification, were used to adjust some parameters of a 3D finite element model of the footbridge. The results of the live load tests provided a further validation of the updated model that could be used as the baseline model for long term monitoring and to evaluate the overall safety of the investigated structure under the service loads.

Lateral vibration of footbridges by synchronous walking

On the T-bridge (a cable-stayed footbridge) the girder vibrated laterally with a frequency of 0.93 Hz, the natural frequency of the first lateral mode, when a large number of people crossed the bridge. Some pedestrians felt uncomfortable and unsafe. The girder was excited by the lateral dynamic force which was produced by the zigzag movement of pedestrians. Once the bridge started to vibrate, some of the pedestrians synchronized with the girder vibration, which further increased the girder response. The same vibration occurred on the London Millennium Bridge and the M-bridge (a suspension footbridge), where field measurements were conducted. A dynamic model was then proposed to evaluate the pedestrians’ synchronized dynamic forces. Overall behavior of the girder response calculated by this dynamic model agreed with the measured values on the bridges. It was found by parametric studies that smaller bridge damping and smaller bridge mass produced larger girder response. Higher pedestrian density also increased the girder response unless they were too crowded to walk normally.

Effects of structural nonlinearity and along-span wind coherence on suspension bridge aerodynamics: Some numerical simulation results

The response of suspension bridges to wind excitation is studied by means of numerical simulations with a specifically developed finite element program implementing full structural nonlinearities. A pure time-domain load model, linearized around the average configuration, is considered. The self-excited effects are included through the indicial function formulation, whereas the buffeting is considered according to the quasi-steady model. The response under turbulent wind, both fully and partially correlated, is evaluated through a Monte Carlo approach. A simplified structural model is considered, where only two cross-sections are modeled. This allows a high reduction of the number of degrees of freedom (DoFs) but maintains many characteristics of the true bridge, precluded to the classical 2-DoF sectional-model (e.g. considering more than two modes, including structural nonlinearities, introducing along-span wind coherence). The case studies of a long-span suspension bridge and a light suspension footbridge are analyzed. It is observed that structural nonlinearities deemphasize the presence of a critical flutter wind velocity, as they limit the oscillation amplitudes. On the other hand, fully correlated flow may produce an important underestimation of the structural response.

Resonant vibration of shallow suspension footbridges

A cable-supported footbridge model with pre-tensioned cables in vertical and horizontal planes is proposed to investigate the vibration characteristics of shallow suspension footbridges under walking dynamic loads in this conceptual study. In this bridge model, the tension forces in the supporting cables can be adjusted by introducing pre-tensions to the reverse-profiled cables, and therefore the natural frequencies can be altered to cover the frequency range of dynamic forces induced by pedestrians. In the numerical analysis, SAP2000 is adopted to study the vibration properties and dynamic response under walking loads. The synchronous response of the bridge structure is stimulated by resonant vibration. The crowd walking loads are modelled as uniform loads acting on the whole bridge deck and they consist of three parts: vertical dynamic force, lateral dynamic force and vertical static force. Numerical results show that for a shallow suspension footbridge the lowest frequencies correspond to lateral and torsional vibration modes which are always combined together and become two types of coupled modes: coupled lateral–torsional modes, as well as coupled torsional–lateral modes. As an example, a bridge model with fundamental frequency of 0·75 Hz in the lateral direction has been studied. It is found that the vibration in the lateral direction is quite different from that in the vertical direction and that damping has significant effect on the vertical vibration but small effect on the lateral one. Moreover, vertical static load has significant effect on the lateral vibration when the bridge structure vibrated in coupled modes.

Load deformation characteristics of shallow suspension footbridge with reverse profiled pre-tensioned cables

Cable supported structures offer an elegant and economical solution for bridging over long spans with resultant low material content and ease of construction. In this paper, a model of shallow cable supported footbridge with reverse profiled pre-tensioned cables is treated and its load deformation characteristics under different quasi-static loads are investigated. Effects of important parameters such as cable sag and pre-tension are also studied. Numerical results performed on a 3D model show that structural stiffness of this bridge (model) depends not only on the cable sag and cross sectional areas of the cables, but also on the pre-tension in the reverse profiled cables. The tension in the top supporting cables can be adjusted to a high level by the pre-tension in the reverse profiled bottom cables, with the total horizontal force in the bridge structure remaining reasonably constant. It is also evident that pre-tensioned horizontally profiled cables can greatly increase the lateral horizontal stiffness and suppress the lateral horizontal deflection induced by eccentric vertical loads.

Integrating a Global Positioning System and Accelerometers to Monitor the Deflection of Bridges

During the design phase of a bridge, certain characteristics are assumed, such as traffic and wind loading. In reality, however, these characteristics can vary, therefore it is very important that the health of such a structure is monitored to evaluate whether it is holding up to the true loading. Due to the ever-increasing size and cost of these structures, it is vital that any anomalies from the expected deflections are detected as soon as possible, allowing remedial action to be taken, and hence trying to prevent disastrous consequences. The use of a kinematic global positioning system (GPS) now allows subcentimeter accuracy to be achieved at a rate of up to 20 Hz, and at maximum distances from the reference GPS receivers to the bridge receivers of up to 20 km. This makes such a system capable of detecting the deflections of long bridges. In addition, accelerometers have been proven useful for such monitoring, allowing precise readings at rates of up to 1,000 Hz. However, both systems have their limitations. A GPS is limited partly by multipath and cycle slips, relatively low frequency of data, as well as the need to have good satellite coverage, while accelerometers are limited due to the fact that the derivations (velocities, displacements) from the original uncompensated acceleration readings will drift over time. The integration of the two systems, however, results in a hybrid arrangement that helps to eliminate the disadvantages of the two separate units. This paper presents an integrated monitoring system, consisting of Leica CRS1000 series and SR530 dual frequency code/carrier phase GPS receivers and a Kistler triaxial accelerometer. One of the SR530 GPS receivers and the accelerometer are physically integrated, and their data are synchronized. Using spectrum analysis, main natural frequencies of a monitored suspension footbridge are identified from the hybrid system. A simple data processing algorithm is presented, as well as the results from field trials to show the potential applications of such a system.

Vibration control study of a suspension footbridge using hybrid slotted bolted connection elements

A hybrid finite element of a slotted bolted connection element (SBCE) is developed which constitutes a frictional damper and two truss elements. The damping mechanism of the damper is based on the micro-slip elements in the contact surface, and the damping properties can be designed for any specific requirements by adjusting several design parameters which in turn, depends on the physical parameters of the joint. Simulation studies are reported on the vibration mitigation of a suspension footbridge due to pedestrian loading with twenty-eight SBCEs. The dynamic load model reported in the London Millennium Footbridge [Struct. Eng. 79 (2001) 17] is adopted. Recommendations on the design of parameters of the dampers are given. The damping by energy dissipation in the structure is discussed with reference to the time response history of the structure and the hysteretic loops of the dampers.

Hungerford Bridge millennium project—London

The £50 million Hungerford Bridge millennium project in London provides two stunning new cable-stayed footbridges across the Thames, one on each side of Charing Cross railway bridge. Effectively it recreates Brunel's 1846 suspension footbridge to Hungerford market, the piers of which remain in the railway bridge structure. Heightened fears over unexploded bombs in the river bed led to a major redesign just after work started but a switch to the NEC contract helped ensure a smooth completion.

VIBRATION CHARACTERISTICS OF A SUSPENSION FOOTBRIDGE

A suspension footbridge located in a tourist attraction in Singapore has a suspended span of 35 m and was designed for static pedestrian and wind loads. In common with other bridges of this type, it is a light, efficient structure and has a lively dynamic performance.Distributed parameter and finite element models were used to understand the vertical plane behaviour of the bridge and a prototype dynamic test using impact excitation was conducted to check the models and investigate the dynamic response.The first two vertical vibration modes were found to occur at the same frequency, 2 Hz, as the average pedestrian footfall. Response to pedestrians was simulated using linear and non-linear models of a moving excitation source.

Dynamic investigation of a suspension footbridge

This paper describes the analytical and experimental investigation of a 50 m span pedestrian suspension footbridge in Central Wales, UK. In the analytical study modelling of the three-dimensional structure determined vibration modes involving deck, towers and cables. The prototype testing employed hammer (impact) testing and excitation by pedestrians to determine the corresponding measured modes. The testing showed that adequate descriptions of the vibration characteristic of flexible structures can be obtained without artificial forcing but that appropriate instrumentation should be used. The validated analysis showed that the concrete panelling in the bridge and other structural details have a significant effect on stiffness and the testing demonstrated the susceptibility of this lightly damped structure to pedestrian-induced vibration.

Stochastic response of suspension bridges to earthquake forces

AbstractThe purpose of the paper is to study the applicability of stochastic methods for determining the response in the vertical plane of long‐span bridges to earthquakes. The bridges are of the modern type, with flexible towers, box‐decks and inclined hangers, Humber and Bosporus being used as the main examples, although some useful information is obtained by studying a small suspension footbridge. The input ground acceleration is that of the Pacoima Dam record of the 1971 San Fernando event, but use is also made of filtered white noise.Because the stochastic approach is essentially an attempt to abstract usable information which could otherwise be obtained from a lengthy time‐history approach, the procedure adopted here is to compare the same parameters obtained in these two ways, as far as possible. In particular, the maximum values of displacements and bending moments are considered.The essential question to be answered is whether the short length of earthquake records, coupled with the large natural periods of vibration of long‐span bridges, allows sufficient response information to be generated to make statistical parameters meaningful. The short‐span (50 m) footbridge gives no cause for concern here, but the detailed comparison with time‐history solutions shows that the stochastic approach for both Bosporus and Humber has to be cautiously assessed, particularly if some trailing zeros are not added to the earthquake record. However, general conclusions are not made, because only one earthquake record has been used.