Theory Imposed on Reality

by Don Friedman on December 15, 2017

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.

“The Bridge”

December 5, 2017

Some great construction photographs of the Verrazano Narrows Bridge: here. I’ve worked on a few pedestrian bridges in the last thirty years and one dam, but that’s it: otherwise my projects have all been buildings. But bridges occupy a chunk of my brain and always will because of their nature as expressed engineering. There are a […]

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Everything In A City Is Manmade – Even The Water

November 30, 2017

Continuing with yesterday’s theme… New York is located on two medium-sized islands (Manhattan and Staten Island), a portion of a large island (Brooklyn and Queens are the west end of Long Island), a piece of mainland (the Bronx) and a whole bunch of small islands in the surrounding waterways. Those waterways include small streams (e.g., […]

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Everything In A City Is Manmade

November 29, 2017

Another great article from Karrie Jacobs, this one on Prospect Park: here. I’m not even going to attempt to summarize it. You should read it because it’s a fascinating look at how parks in New York have developed over the last 150 years. Jacobs’s painstaking descriptions of the work that went into the creation of […]

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Expounding on a Neat Trick

October 30, 2017

I talked a bit about this type of detail recently but I was surprised to learn that I hadn’t posted these pictures. This is a middle-third of the 1800s tenement in Hell’s Kitchen that was built with retail space on the first floor. The wood joists of the floors and roof span left to right, […]

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Different Types of Efficiency

October 19, 2017

I seem to keep coming back to train station roofs as I write. That’s happening partly because I travel by train a good amount so I’m looking at those roofs, and partly because they tend to have exposed structure designed by engineers with little or no separate architectural design, which may not make them beautiful […]

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Detailing For The Forces

October 17, 2017

A big part of structural design is “detailing,” which is drawing the way various pieces of a building  are connected. The bridge above (click to enlarge all of the photos) is in Wrocław and has a shorter span than the average American suspension bridge of any era. I walked over it a number of times […]

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Road Trip: An Orphaned Wall

October 16, 2017

Seen on the street in Ottawa… I’ve mentioned orphans walls once before. They are what’s left when old walls are incorporated into new buildings in a manner that makes it difficult or impossible to demolish the wall when the original building is demolished. In this case, the light-red wall with white trim obviously belonged to […]

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Not Quite What They Meant

October 1, 2017

An idyllic small-city residential street: But let’s look close up at that sign: A sign to warn drivers that children are playing (and might, for example, chase a loose ball into the street) is a good thing. This sign, though, is a bit confusing. If the children are playing on a seesaw then they’re not […]

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Planning For Future Floods

September 30, 2017

The South Ferry subway station after Hurricane Sandy, courtesy of the MTA: Here’s a good article on infrastructure improvement, specifically on repairs to mitigate future disasters: 6 rules for rebuilding infrastructure in an era of ‘unprecedented’ weather events. The third rule, “Design for climate change” jumped out at me as it’s something we see every time we […]

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