Suspension bridge design may not be the best

January 15, 2010 by Lin Edwards report
Forms found to be more optimal than a parabola to carry a uniform load between pinned supports (compressive elements shown in blue). Image credit: Matthew Gilbert

( -- A team of structural engineers from the University of Sheffield in the UK say the assumptions originating with 17th century Dutch engineer Christiaan Huygens may need to be re-examined. Huygens assumed the best design for a suspension bridge was based on towers and simple cables hanging between them to support the weight, but the Sheffield group say a more complex design using less material would be more efficient.

The Huygens idea is behind well-known suspension bridges such as the Golden Gate bridge in San Fancisco and the Akashi-Kaikyō Bridge in Japan, which is around 700 meters longer. Basically, the road or railway is suspended from thin hangers dropping from two cables that stretch between the two towers. The cables automatically form a U-shaped curve, or parabola, and this arrangement has been assumed to be the most efficient.

Matthew Gilbert and his colleagues from the Department of Civil and Structural Engineering noted that the calculations assumed the cables could withstand tension but not compression, but in reality both forces are in play. They developed a numerical layout optimization program to check the optimal design and were surprised to find Huygens' parabolic arch rib or cable was not optimal, and the amount of material needed for the cabling could be reduced if the ends were replaced with a network of truss bars known as the "Hencky net". Gilbert said they expected the parabolic design to be confirmed and they tried to work out what was wrong when their software continually nominated the more complex design. "It ended up that the only option was that the current wisdom was wrong," Gilbert said.

The amount of cable that can be replaced depends on the level of compression the material can withstand. If it can take tension and compression to an equal degree, using a net can reduce the amount of material needed to build the bridge by 0.3%. Other structural engineers have pointed out that this small reduction in material may not provide an economic justification for making a more complicated , since they would undoubtedly be more expensive to manufacture.

The work is published in the January edition of the Structural and Multidisciplinary Optimization journal.

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More information: Optimum structure to carry a uniform load between pinned supports, Structural and Multidisciplinary Optimization,

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4.5 / 5 (6) Jan 15, 2010
A truss structure could add unwanted windage, provide unwanted nooks and crannies for salt corrosion and bird droppings, require multiple connections that may corrode unpredictably...

Occam's Razor time, mayhaps ??
1 / 5 (1) Jan 15, 2010
hope Occam doesn't shave of the truss while in suspension...
4.7 / 5 (3) Jan 15, 2010
For a gain of only 0.3% it would undoubtedly cost more due to the complexity.
Huygens 17th Century invention standing up to modern CAD and modelling is impressive.
4 / 5 (8) Jan 15, 2010
A free hanging cable does not form a parabola, but a catenary.
4.3 / 5 (3) Jan 15, 2010
A free hanging cable does not form a parabola, but a catenary.

My first thought, as well. However, these aren't exactly free-hanging cables: there's a roadway suspended underneath, and it's constrained to be [mostly] straight. So that's a different weight load per length of cable for the various sections of the curve, which I can only assume pulls down the sides of the hyperbola, and turns it into a parabola...
4 / 5 (1) Jan 16, 2010
"If it can take tension and compression to an equal degree, using a net can reduce the amount of material needed to build the bridge by 0.3%"

Name for me a cable that can withstand compression and tension to an equal degree, and I will name for you a column.

As an engineer, this article is so far from making sense that I have to hope that the author butchered the original meaning.
4.8 / 5 (4) Jan 16, 2010
As an engineer, this article is so far from making sense that I have to hope that the author butchered the original meaning.

I'm an engineer too and have just read the actual paper referred to: http://www.spring...4721655/

Basically the paper isn't about suspension bridges (I don't think these are mentioned once...). What it says is that the least weight (i.e. mathematically most optimal) structure to carry a uniformly distributed load between pinned supports is not a single parabolic element -if the material can withstand both tension and compression. Instead a truss is more optimal. This overturns established wisdom and is an interesting finding. I guess the author of this news article was trying to bring the work to life by referring to suspension bridges (whose cables are approximately parabolic because the approx. uniform deck weight is high in comparison to the weight of the cables). But the new form clearly doesn't look very practical to build
3 / 5 (1) Jan 16, 2010
Thanks for clarification, Fred2002 !

I suppose an approximation would be to replace part of the 'not quite catenary' with a 'tension tube', either simply-cylindrical or triangular truss...

Snag then is connecting the flexible 'catenary' cable to the rigid portions. IIRC, one advantage of cable staying is that you can 'dissect' a very big cable into a multiple-point anchorage, safely dispersing the load...

Back to Occan's Razor again ??
1 / 5 (1) Jan 18, 2010
BTW The concept "uniform load" does not apply to railway bridges, since a train may be heavy enough to deform the span of a traditional suspension bridge. Therefore, such bridge designs are not used for train or train+road bridges.
not rated yet Jan 20, 2010
Even if the idea isn't relevant to a suspension bridge cable, it might be relevant to the inverse, an arch bridge. However, as already noted the extra cost of fabrication of the Hencky net exceeds the material benefit.

Also, the analysis assumes no buckling, which is untrue for a real structure and would again mean the Hencky net is not optimum.

Does the research overturn established wisdom? Not really. The press seem to be assuming that there's a belief that the optimum form of structure to carry a uniform load is parabolic. But actually, all that Huygens and others proved was that a member with no bending stiffness subject to a uniform load would naturally take up a parabolic profile, which is not the same thing at all. That particular misconception seems to come from the paper's abstract itself.

Birger - there are railway suspension bridges, one of the largest being the Tsing Ma Bridge in Hong Kong, which carries both road and rail without any problem.

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