The I-35W bridge was two arch-cantilever trusses, with smaller trusses parallel to the river supporting the roadway. Each of the main trusses rested on two concrete columns, one on each side of the river. The design highlights a characteristic design tradeoff: a truss like this is statically determinate, which means that the all the forces in every element can be calculated exactly. [Actually the connections among the truss elements appear to be capable of transmitting some bending, so it’s not a completely pure determinate design.]. It also means that the whole truss depends on the integrity of every piece: cut one element in a truss and the whole thing folds up. A statically indeterminate structure is one in which the forces in one or another part depend on the stiffness of other parts and the connections among them; the calculation is complicated and the forces one comes up with are not so certainly what the parts actually bear, but a statically indeterminate structure can survive the failure of one or another part. A simple example is a beam across, say, four supports. If it is cut or broken in the middle span, it could still stay up as a pair of cantilevers.
(I’m astonished that I could not learn the foregoing, meaning simply a picture of the bridge as built, from any media source including television and newspapers, except this little graphic in the NYT and eventually a much more complete little flash player box, also in this morning’s NYT, that I can’t figure out how to link to. There’s one remarkable video on CNN, from a security camera, showing the actual collapse in progress, with the center span failing at the supports and falling more or less intact, after which the cantilevers at the end fell outward. Having seen this video, I will make the conjecture that the bridge deck was calculated as a composite top chord of the trusses and failed in tension over the supports. If this is true, the deck repair may well have been a contributing cause of the failure. Watch this space; if I’m right, I will feel like a tree full of owls and you will definitely hear about it.)
It does not follow that indeterminate structures are better or stronger; structural design is a matter of making things as strong as they need to be, with allowances for uncertainties like the load they will have to carry, the actual strength of their component materials when new and after they’ve been in the weather for a while, and the like. Because the actual forces in their parts are less certainly known, indeterminate structures have to be somewhat overdesigned compared to determinate ones: the difference is in what the material is comfortable with (on the whole, concrete “likes” being poured into large integrated indeterminate structures, while steel is especially suited to trusses made of small parts in determinate networks. Anything can be made as strong as desired at a price; for example they could have filled in the river with dirt around a couple of big pipes, at the price of river navigation; the issue here is choosing the right kind of risk/cost combination.
The contrast between these kinds of design has irresistible analogies to human systems. Management can be made discrete and determinate, with very specific tasks assigned to individuals and units, or it can be more fluid and overlapping; the latter form tends to be more adaptable to crisis or surprise, but less accountable and efficient in normal operation as it’s not always possible to know just what anyone is doing at the moment. Would you rather know exactly whose fault everything is, or trade some accountability and precise knowledge for redundancy?
One of the systems important in bridge survival is inspection and maintenance. Steel is mostly iron, and iron really wants to become iron oxide, which it does if it’s wet and does really fast if it’s wet with salt water from the sea or snow removal. Hence, at the least, endless painting. It also changes its crystalline structure when it’s flexed again and again (this kind of fatigue is not the same as breaking a paperclip by bending it a few times beyond its elastic limit), becoming brittle and liable to cracks that can hide under the paint. The steel that reinforces concrete bridge decks is at risk of corrosion when the concrete develops little cracks and salt water leaks in. This is a big deal because it’s invisible, hence all the deck replacements with green (epoxy-coated) reinforcing steel you often drive by. Generally, structures outdoors, and many indoors, should be thought of as a combination of a large initial investment and an infinite stream of maintenance, inspection, and repair.
Unfortunately the nature of infrastructure is a challenge to politics. Spending money to maintain a bridge means taxes with nothing to show the voters (except traffic obstruction); no-one ever named a paint job or a repair after a local hero, but buying a big new piece of something is another matter. A wise society would constitutionally require that every capital investment require an untouchable endowment for eternal maintenance, to be cashed in only if the original structure is demolished. But such an endowment could double the initial cost of the bridge or building, and that’s a downer for a pol in a close race. It’s sort of like having a glorious war for a couple of months and then flubbing the occupation that follows, to choose an example completely at random, or not bothering to keep up levees so they will actually prevent a flood, to choose another. Anyway, posterity never done nuthin’ for us, right? Maintenance, even more than new construction, also confronts public administrators and elected officials with a truly poignant and often paralyzing moral choice between hiring the incompetent generous campaign donor and hiring the capable low bidder with a good record who has done nothing to advance the public interest (as defined, of course, by your reelection prospects or just your personal net worth if you’re an appointed official). The choice between having a bridge maybe fall to pieces after your term in office, and having your career hit an electoral bump (certainly, right now) is surely such a hard call that we shouldn’t begrudge our leaders the big bucks we don’t pay them (until their lobbying and sitting-on-boards career phase).
Aggravating this irresponsibility is something I can only describe as a loss of pride in our common works. The idea that something as wonderful as a collective provision of public transit should be trashed by selling advertisements all over the sides of the buses, or that parks and schools and subway stations and streets shouldn’t be beautiful and kept that way by gardening and sweeping and painting, is simply beyond my understanding. How anyone can know that the National Parks are falling to pieces before our eyes and not be enraged at something so coarse and stingy being done in our name simply escapes me. The little signs along the highways saying that if this or that local business hadn’t picked up the litter it would be lying there still are an abomination.
Get ready for a long period – I figure this will not bore governors’ staffs, Fox and CNN for weeks to come…OK, days – of soul-searching and resolving and pointing with alarm about infrastructure maintenance. Then we can go back to practicing underwater vehicle escape (key concept: don’t try to open the door until the car is nearly full of water).