Kathryn Cramer

An animation of how the I-35 Bridge could have collpased with the failure of only 3 pieces

Yifan Hu at Wolfram Research has come up with a computer model of the I-35 bridge that shows how the bridge could have collapsed with the failure of only 3 pieces. He explains:

The picture below shows the computed stresses in a simple 2D model of the I-35W bridge, with red meaning more stress. (I got the geometry from news pictures.) There are definitely aspects of the model that are not realistic. For example, the weight of the trusses themselves isn't included. And, of course, it's in 2D.

So what happens if one of the trusses weakens?

It's easy to include this in the computation by adding an upper bound on the stress in that truss. That just adds another inequality--which FindMinimum has no problem with.

One can actually compute all this in real time inside Manipulate. Here's an animation of the result:

One sees that when the truss with maximal stress weakens (shown in yellow), the stress spreads out to other parts of the bridge. If one weakens the next truss, then the stress propagates further. And when one weakens yet another truss, then the constraints can't be satisfied at all any more--so there is no static equilibrium for the bridge, and the bridge cannot stay standing.

See it HERE.

A New Kind of Bridgebuilding: Stephen Wolfram on How We Might Design Better Bridges in the Future

In a short essay "The Space of All Possible Bridge Shapes," composed in response to the Minneapolis bridge collapse, Stephen Wolfram suggests design principles that could lead to stronger bridges:

. . . it's been known for a while that the best networks don't have that kind of simple structure. In fact, they almost seem in some ways quite random.

Well, what about bridges? I strongly suspect that there are much better truss structures for bridges than the classic ones from the 1800s--but they won't look so simple.

I suspect one can do quite well by using simple rules to generate the structure. But as we know from NKS, just because the rules to generate something are simple, it doesn't mean the thing itself will look simple at all.

Two students at our NKS Summer School (Rafal Kicinger and Tom Speller) have investigated creating practical truss structures this way--and the results seem very promising.

So what should the bridges of the future look like? Probably a lot less regular than today. Because I suspect the most robust structures will end up being ones with quite a lot of apparent randomness.