Scientists harness computing power to design the perfect bridge


Scientists at the Technology University of Denmark have reinvented the design of suspension bridges. Their novel concept not only enables much longer bridge spans but also reduces the amount of building material — and with this the environmental impact of the construction.

Be it the Union Bridge, the oldest suspension bridge still in use, built on the border between England and Scotland in 1820; the iconic Golden Gate Bridge completed in 1937 in San Francisco; or the Great Belt Link that opened in 1997 in Denmark: many suspension bridges have become globally known landmarks and play a key role in connecting people and civil infrastructure. Now, ever longer bridges are being envisaged, for instance in Italy to connect the southern mainland region Calabria to Sicily, or in Norway to replace the ferries that are part of the north-south European route E39 — a project which involves some of the longest proposed bridge spans worldwide. However, the main spans of these planned bridges, meaning the length of the suspended roadway between the two lofty bridge pylons, are fast approaching the limit of what is possible to build using the conventional design of suspension bridges originating in the 1950s.

Above a main span of three kilometres, the bridge girder’s self-weight is quickly becoming the governing load, which means that the bridge cannot carry much else than its own weight. To build longer bridges, we have to rethink the design entirely.”

Mads Baandrup

Former PhD student at the Technology University of Denmark (DTU) now working for the engineering company COWI.

In addition, the construction of bridges and infrastructure consumes a lot of energy and produces considerable CO2 emissions. According to the 2019 Global Status Report of the UN Environment Programme, the construction industry is responsible for nearly 40 percent of total global CO2 emissions. A large portion of these emissions arises from the production and transport of building materials, primarily steel and concrete. Consequently, a way to reduce the environmental impact is to find methods to use less of those materials.

The Union Bridge opened in 1820 and is the oldest suspension bridge still in use today. It spans the river Tweed connecting England and Scotland.

Image credit: Wikimedia Commons, RHaworth

Supercomputing reveals possibilities for super-long bridges

These pressing problems are why Mads Baandrup and his co-workers in the group of professor Ole Sigmund and associate professor Niels Aage at DTU have downright reinvented the design of the bridge deck, the traffic-bearing element of suspension bridges. To ensure industrial applicability, the research was done in close collaboration with Technical Director Henrik Polk from COWI. The goal was to maximise the load carrying capacity of the bridge deck to enable a longer main span, while at the same time minimise material consumption. To achieve this, the scientists used topology optimisation, a computational method that has been used extensively in the car and aircraft industry, for instance to optimise combustion engines or wing shapes. “With the recently increased power of supercomputers we could adjust the method to apply it to large-scale structures”, says Baandrup. The results were recently published in Nature Communications.

Using the PRACE Joliot-Curie supercomputer at GENCI in France, Baandrup and his co-workers analysed a bridge element measuring 30 x 5 x 75 metres — a repetitive section that is representative for the whole bridge deck. This element was divided into 2 billion voxels, which are the 3D pendant of pixels, each no bigger than a few centimetres, and completely voided of its existing components to remove any trace of conventional design. The topology optimisation then determined whether each individual voxel should consist of air or steel. “In this way, the optimized structure is calculated from scratch, without any assumptions about what it should look like”, Baandrup explains.

The design of conventional bridge girders consists of straight steel plates placed orthogonally to stabilise the bridge deck. This concept is easy to build but does not provide the most efficient transfer of the loads on the bridge, namely from the bridge’s self-weight, the crossing traffic and the wind.

Image credit: Nature Communications ISSN 2041-1723 (online), Baandrup et al. (2020)

To make the calculation work, the scientists had to adjust their algorithm that was previously used to find the optimised shape of an aircraft wing (see paper, PRACE TopWing Success Story and Niels Aage’s PRACEdays16 presentation), to instead impose the symmetry inherent to all bridge decks. “In a process working towards optimisation in iterations that were parallelised on thousands of nodes, this was not trivial”, says Baandrup. The symmetry constraint provides the advantage of reducing computational time. To put it in perspective, the whole calculation would have taken 155 years on an ordinary computer, but it took only 85 hours using 16 000 nodes on Joliot-Currie.

The ideal girder design, determined after 400 iteration steps by topology optimisation (in grey), differs fundamentally from the conventional design and offers a more direct and therefore more efficient load transfer. From this ideal design, the scientists derived an interpreted layout made of curved steel diaphragms (the red panels).

Image credit: Nature Communications ISSN 2041-1723 (online), Baandrup et al. (2020)

Less material means more sustainable construction

The result of the topology optimisation has the look of an organically grown bridge. Instead of the traditional girder of straight steel diaphragms placed inside the bridge deck to reinforce and provide stability, the algorithm came up with a net of curved steel elements. “The software identifies the optimal structure but does not take into account if the structure is actually buildable”, Baandrup explains. Out of that ideal design, however, he and his colleagues extracted a concept which is constructible, and at a reasonable cost. This interpreted design consists of a girder made of bundles of curved steel plates that are thinner than the plates constituting the conventional design. This is viable and more efficient because the curved plates transfer the loads on the bridge deck a lot more directly into the hangers — meaning the vertical suspender cables that have to absorb the loads of a suspension bridge deck — than the traditional steel girders. Consequently, bridges designed in this way can be constructed to span a longer distance than conventional bridges with less material. In fact, the new design reduces steel consumption by 28 percent, resulting in a reduction of CO2 emissions in the same considerable magnitude.

In principle, a similar topology optimisation can be applied to other large building structures, such as high-rises or stadiums, in order to reduce the consumption of steel and concrete and thereby work towards a more sustainable construction. “Our results reveal a huge potential in rendering construction more ecological”, says Baandrup. “In the future, the construction industry should not only think about how to reduce cost but also how to reduce energy consumption and CO2 emissions. With our results, we believe we can initiate this discussion.”

Here, the design concept is applied to the 2682-metres-long Osman Gazi bridge near the city of Gebze in Turkey. From the organic-looking and highly complex optimisation result in the upper right, a simplified novel design was identified (shown as red panels). Compared to the conventional design (in blue), the curved, thin steel diaphragms lead to a 28 percent weight reduction for the bridge girder.

Image credit: Mads Baandrup, Niels Aage


  • Baandrup, M., Sigmund, O., Polk, H. and Aage, N.: Closing the gap towards super-long suspension bridges using computational morphogenesis. Nat. Commun. (2020). Link to paper.
  • Aage, N., Andreassen, E., Lazarov, B.S. and Sigmund, O.: Giga-voxel computational morphogenesis for structural design. Nature (2017) – Link to paper.
  • 2019 Global Status Report for Buildings and Construction. Link to report.

Project title: TopBridge – Topology optimization of bridge girders in cable supported bridges

Resources awarded

  • 17th call: 15 000 000 core hours on Joliot-Curie (SKL) hosted by GENCI at CEA, France
  • 10th call: 12 000 000 core hours on Curie hosted by GENCI at CEA, France

Research field: Mathematics and Computer Science

Read on: ScienceNode.

This article was first published on on 13 October 2008.

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