Theory Imposed on Reality

That’s a fine, very-short-span bridge in the Ramble in Central Park. Honestly, it feel ridiculous to call it a bridge when the space below it resembles, more than anything else, a door, but what else could it be? One pedestrian path crosses over another, and a wall of large ashlar blocks has a hole in it. The Ramble is my least favorite feature in the park – its complex and picturesque tangle of paths, ravines, and miniature streams feels forced and cutesy to me – but I love the way the masonry of the wall is simply laid up next to and on top of the boulder on the left.

How does the heavy masonry span across the opening? Any way it wants.* There’s a true arch of carefully-shaped voussoirs defining the opening. There’s plenty of masonry wall above the opening and to either side, which means we could define arching action at many different locations and it would work. and the span is so short that the stones will work in bending. For example, the horizontal band of large stones right above the arch keystone could consist of corbels holding up the center stone, with that stone working in bending.

Here’s the trick to reading a structure like this: it doesn’t matter which of those analytic mechanisms is correct because they all work. They may very well all be true simultaneously. If we could examine the state of stress in each stone and each joint, from a distance, in 3D,** we’d probably find that it doesn’t exactly match the model for any of the mechanisms I mentioned above because all are working together. The various mechanisms are the physical inverses of boundary conditions in calculation: they show what is possible. For example, if there wasn’t enough masonry to the side of the opening for gravity to counteract the arch thrust, the masonry arch and arching action mechanisms would fail in theory and the masonry would have to be working in bending. If the stones were smaller, the bending mechanism wouldn’t work. If the voussoir stones were shaped the wrong way, the formal arch mechanism wouldn’t work but arching action would.

My point, other than thinking too much about a very small bridge, is that all analysis is modeling and all models are imperfect descriptions of reality. If we analyze the masonry arch as an arch and it works, we can say with confidence that we know the arch is capable of carrying the load. We can’t say we know the actual state of stress, because all the parts of reality that our model ignores, including specifically the presence of other possible load paths, may change the stresses.

* Yes, it is an old joke. It’s been carefully maintained and preserved.

** But that state of perfect knowledge does not exist.