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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.