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Mathematical model generates new bridge forms that really go the distance

Image credit: Helen Fairclough

A University of Sheffield study has identified new bridge forms using mathematical modelling, which could be used to build far longer bridges than are currently possible.

At present, the largest bridge span - measured as the distance of suspended roadway between towers - reaches just below 2km in the central portion of Japan’s Akashi Kaikyō Bridge. These long bridges are normally suspension bridges, which hang the deck using cables suspended vertically from the main cable, although cable-stayed bridges, which hang the deck using cables hung directly from towers, are becoming increasingly popular.

The longer the bridge, the greater the fraction of the structure is required to support the weight of the bridge itself. This can lead to a vicious cycle in which an increase in span requires more supporting steel, in turn increasing the weight of the bridge further and consequently limiting bridge span.

“The suspension bridge has been around for hundreds of years and while we’ve been able to build longer spans through incremental improvements, we’ve never stopped to look to see if it’s actually the best form to use,” said Professor Matthew Gilbert, the University of Sheffield civil engineer who led the research. “Our research has shown that more structurally efficient forms do exist, which might open the door to significantly longer bridge spans in the future.”

Gilbert and his colleagues incorporated mathematical theory developed in the 19th century – which can be used to find the best shape of a cable given the placement of heavy loads – into a modern optimisation model. This allowed them to identify entirely new bridge structures which would use the minimum amount of material possible for that length.

Elements of the designs were surreal, including a section of a bridge resembling a spoked wheel. In order to limit the suggested structures to those which were buildable, Gilbert and his colleagues replaced the many ‘spokes’ with smaller numbers of spokes contained within towers. These new forms keep load paths short and avoid sharp corners between tensile and compressive elements, allowing for forces from the heavy deck to be transmitted more efficiently throughout the bridge structure.

The new bridge forms could allow for a 5km bridge span – which would be necessary to cross the Strait of Gibraltar, for example – to be built with far less material than would be required using traditional bridge designs.

“This is an interesting development in the search for greater material efficiency in the design of super-long span bridges. There is much more work to do, notably in devising effective and economic construction methods, but maybe one day we will see these new forms taking shape across some wide estuary or sea crossing,” said Ian Firth, a director at COWI and co-author of the study.

However, the researchers cautioned that these new bridge structures could not be constructed until other forces were taken into account in their models, such as the forces of traffic and wind.

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