Today I re-stumbled on a Calvin and Hobbes comic that I first saw in my high school physics class:

Bridge Testing

The question was: how do you test bridges in real life to make sure they’re safe? I actually totally forgot and decided to think about how I might do it from first principles.

Prelude: How do you test fishing line strength?

I’m an angler, so I first thought about fishing line. Assuming your line is created uniformly, you can test line emitted from a process by simply adding tension until it breaks. Then you can be reasonably sure that the line is that strong all the way through. You don’t know for sure (you’re assuming something about the uniformity of your production process) but if you do enough tests and use some other metrics for line uniformity, you can be pretty sure.

Since 8lbs test (line that is rated for 8lbs of weight) is minimum 8lbs, anglers often say that the static load is a little higher, since fishing line manufacturers can’t go making false promises. If I were a fishing line manufacturer, I’d then find a process that generates something like 12-16lbs strength by break test, and then even go ahead and test it for 8lbs (it shouldn’t break – then you could in theory test the whole length of line and be certain that 8lbs would be fine).

Does line testing weaken the underlying thing? I’m assuming under certain parameters the answer is no. But I don’t know what those parameters are. And obviously under certain parameters you might expect the material to indeed weaken.

Unfortunately it’s not so easy with bridges, as you can’t keep building new bridges. Or can you?!

Bridges: Naive Approach

Continuing my thought experiment. I’m assuming for smaller bridges if I were going about it with my current knowledge (very little knowledge about material science or civil engineering) I’d rapidly prototype using some basic materials – not a full bridge but perhaps just the structure. Maybe with wood. I could hang weights along the structure and see if it was a sturdy enough concept.

I could test its maximum load empirically, then as I replace the pieces (say, wood with metal or concrete), I could potentially take some more measurements about the relative load-bearing strengths of these materials and then extrapolate.

If I cared, I could write a software simulation that factored in the physics and material qualities. Then, knowing nothing about civil engineering, I could write an optimization program / genetic algo to evolve a bridge design. I could even factor in the materials costs and optimize for strength / cost.

Bridges: Real Life

Luckily in real life civil engineering, material science, and basic physics give us a good framework for simulating bridge behavior. And bridge simulation software does exist already, so no need for me to go do those things myself.

But say 10 years pass and you want to know how strong the bridge is now. After all, the materials weaken and the assumptions made at construction time may be inaccurate.

I googled and found this Michigan Department of Transportation report which was really helpful for understanding how it was done in 1996. While it’s possible things have changed since then (~20 years) it made a lot of sense.

First, they made some theoretical projections as to what the reaction of the bridge would be if load was applied, under various conditions.

Then they literally drove tanks onto the bridge. Tanks were the heaviest thing they could use, it seems. They mentioned being worried about stress of higher-than-average-weight michigan trucks, so they were going for max load testing.

After tanks got on the bridge, they looked for various signs of stress. I imagine there are ways to see how taut a line is, or how flexed/unflexed some rebar-inforced concrete is.

Then, given that the very heavy tanks didn’t break the bridge, they took their observations home to help make future projections. Anything lighter than the tanks driving across the bridge could be reasonably sure they were safe, at least for a while.