# Hang Christiaan Huygens! Here's a Better Suspension Bridge

Staff Writer

A bit of bridge-building wisdom that dates back to 17th century Dutch polymath Christiaan Huygens needs a rethink, reports a team of structural engineers. Following Huygens's lead, engineers have assumed that the best design for a suspension bridge relies on simple cables that hang between towers in an elegant curve. A more-complicated design uses less material and is therefore more efficient, according to the new work. But it's not likely to appear on roads, other experts point out.

In 1669, Huygens mused about hanging a cable between two supports to hold up a weight that was much heavier than the cable itself and was evenly distributed between the supports. That's essentially the arrangement in suspension bridges like the Golden Gate Bridge in San Francisco, California, in which a heavy roadway is suspended by thin hangers from two main cables stretching between two towers. Huygens deduced that the cable would take the shape of a parabola, a U-shaped curve. Since then, engineers have assumed that arrangement is the most efficient because it uses the least amount of material to support a given load, says Matthew Gilbert, a structural engineer at the University of Sheffield in the United Kingdom. In the 1980s, engineers proved the case--at least in the idealized situation in which the weight of the cables and hangers is insignificant compared with the roadway.

But that's not the whole story, say Gilbert and colleagues. The earlier calculation also assumes the cables can withstand tension but not compression. A simple parabola-shaped cable is not the best design in a more realistic situation that includes both forces, the researchers argue in this month's issue of Structural and Multidisciplinary Optimization. Using a numerical optimization program it developed, the team showed that in this case it's possible to reduce the amount of material required for a cable by replacing the ends with a complex network of small trusses called a Hencky net (see illustration). Just how much of the cable should be replaced depends on how much compression the material can take. If it can withstand as much compression as tension, then the more complicated geometry can reduce the amount of material needed for the bridge by 0.3%.

The researchers had expected a simple parabolic cable to be the optimal shape even if compression were allowed, and they were trying to reproduce that answer as a test of their software, Gilbert says. But the program kept spitting out the more complex structure. "We were trying to work out where we went wrong, and it ended up that the only option was that the current wisdom was wrong."

It's not surprising that the plain parabolic cable is not the best solution in a more realistic situation, says Tomasz Lewiński, a structural engineer at the Warsaw University of Technology. "If you change the problem, you get a different solution," he says. Lewiński says the new structure might not be that hard to make, as something like a Hencky net could be fashioned out of advanced composite materials.

But it wouldn't make much economic sense to build such a complicated bridge to save so little material, says George Rozvany, a structural engineer at the Budapest University of Technology and Economics. "There would be no savings at all because these complicated structures are extremely expensive to manufacture," he says. Still, he says, the new work is a good example of so-called structural topology optimization, which has already enabled engineers to reduce the weight of new airliners by up to 20%.

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