Slender structures such as footbridges may be sensitive to vibrations. But by means of smart calculations and experiments, researchers ensure that pedestrians and joggers don’t have to tremble in fear when approaching a bridge.
A placard on Albert Bridge in London reads: ‘All troops must break step when marching over this bridge’. It's there to prevent the bridge from vibrating with the cadence of soldiers marching in perfect synchrony.
For small-span bridges, a small group of pedestrians or joggers can be enough to make the bridge vibrate, especially if the structure in question is quite slender. That’s what the Structural Mechanics Research Group on the Technology Campuses in Ghent and Aalst is trying to prevent.
The researchers study the vibrations induced by people when they walk, jog or jump on footbridges, floors, stairs or stands in stadiums. “It’s not so much about the strength of the structures: they’re more than sturdy enough to support crowds,” says Professor Peter Van den Broeck. “What we're interested in is the comfort of the user: do you feel safe when crossing a footbridge?”
For the London Millennium Bridge the answer was ‘No, sir’. Two days after its opening in June 2000, the bridge had to be closed because it was wobbling too much. The modification works took two years.
What we're interested in is the comfort of the user: do you feel safe when crossing a footbridge?
The example illustrates that prevention is the best – or less complex and costly – cure. Prevention in this case means predicting the vibration levels of a footbridge in the design phase. “If you know to expect high levels of vibration in advance, you can decide to make the structure heavier, for example. But the bridge will lose some of its elegance,” says Professor Van den Broeck.
Another solution is to include a TMD (Tuned Mass Damper) in the design: a vibration-damping device that is incorporated into the bridge. “It consists of blocks connected to the bridge deck by springs and dampers that transfer the vibration when you walk or run across the bridge. They're usually well hidden, but designers sometimes deliberately leave them visible. That’s the case for the Parkbos bridge over the E40 in Ghent, for instance. If you run across it, you can see the dampers vibrate slightly.”
But how do you determine whether this type of adjustment is necessary when designing a bridge? Among other things, you have to determine the sensitive frequencies of the structure: if the rhythm of the pedestrians matches those frequencies, the bridge will vibrate. Researchers are still refining the mathematical models that exist to predict the vibration levels. And for that they need to experiment in the field – or rather: on the bridge.
This explains why, a few years ago, 150 students wearing brightly coloured caps were seen walking across a footbridge in Eeklo. “When so many people are walking or jogging across a bridge at the same time – which we had the students do – you would expect high vibration levels,” says postdoctoral researcher Katrien Van Nimmen. “But the human body itself has a certain mass and stiffness, and also absorbs vibration energy. So we actually function a bit as a damper ourselves when we walk across a bridge. You want to be able to take this effect into account in the design phase, to avoid including a vibration damper unnecessarily, for instance. That's why we had our students on the bridge for this experiment.”
The researchers equipped the bridge with so-called acceleration sensors, which are also used to record earthquakes. The students wore smaller sensors and brightly coloured caps so that the researchers could map the timing of their footsteps and their individual walking routes. It was the first time that an experiment on this scale simultaneously recorded the walking behaviour of pedestrians and the vibration levels of a footbridge.
From Albert to Albi
The experiment provided data that also helps other research groups to develop realistic and reliable prediction models. The expertise of Professor Van den Broeck and his colleagues is highly regarded in the academic world, but also in engineering offices in Belgium and abroad. The researchers are regularly asked to carry out vibration analyses in the design phase of bridges for pedestrians or cyclists, but also to make measurements afterwards and check whether a structure behaves the way it was designed to. “On average, we analyse three to four bridges a year as commissioned by the industry. These case studies are often also the subject of our students’ master's theses.”
“For example, we’ve now been asked to carry out an analysis of the vibration levels for a new bridge for cyclists and pedestrians over the Albert Canal in Antwerp. And abroad, we’ve already done work for the French city of Albi, which is on the Unesco World Heritage list. They are building a magnificent footbridge along a historic viaduct. The design is by the Belgian engineering firm Ney + Partners.”
Professor Van den Broeck's research group is not the only one at KU Leuven to study vibrations. “Within our Department of Civil Engineering, for example, there are colleagues specialised in vibrations caused by traffic,” says Professor Van den Broeck. “And there’s also a lot of expertise on the measurement techniques themselves: the algorithms and software we use were developed by colleagues in the department.”
This engineering knowledge can also build bridges to other disciplines. “For a doctoral research project that specifically studies the effect of people running, we’re currently collaborating with colleagues from the Faculty of Movement and Rehabilitation Sciences. They are interested in the forces at play in the human body, while we look at the forces that travel from the body to a structure. It's a good common ground for collaboration.”
Finally, Professor Van den Broeck points out that this type of research is becoming even more important now that we are fighting climate change. “Mining and processing materials consumes a lot of energy, so we will have to use them more sparingly. In other words: we will have to build lighter structures. This also means that the vibration sensitivity of structures becomes an important aspect.” It's a clear message to future students: build (sustainable) bridges.