Analysis

Inverted Arch Foundations Are Upside-Down Fun

by Don Friedman on October 5, 2017


Every once in a while during design, I remind myself of what various types of structural member do, as a way of thinking about what I need done. For example, the simplest definition of a “beam” that I can come up with is “a linear structure that carries load at right angles to its long axis.” Since most loads on beams are gravity load and therefore vertical, most beams span horizontally. Similarly, a “column” is a linear structure that carries load primarily parallel to its long axis.

The word “linear” in the beam definition doesn’t just mean that beams have cross-sections that are relatively small compared to their length. It means that beams have to work in bending because there isn’t room inside them for the curved load path of an arch. That may sound like nonsense, but bear with me for a minute. Beam action, AKA bending, depends on having a material capable of resisting both tension and compression. Arch action only requires compression. But beams can be quite slender, while aches have to have geometry that works for the given load. The choice between them, from a structural designer’s point of view, is a trade-off of material requirements versus geometric requirements. If you have a “good” material, you can use a beam; if you have a lot of space you can use an arch.

To the topic at hand…if you imagine yourself in the days before reinforced concrete, how would you build a foundation for a series of heavily-loaded piers? You could build stepped footings, cantilevering masonry out a little at a time, but they take up a lot of room. In this scenario, you would know something about arches, since complex masonry construction is what was, historically, superseded by concrete construction. An arch, going back to my definitions, is a curved line of compression that carries load in the plane of the curve and perpendicular to the line. Or, from another perspective, an arch is a way to turn a loadĀ distributed along a line into concentrated loads at the line’s ends using only compression.

If you’re sufficiently familiar with arches and masonry, and faced with the problem of building a foundation for a series of piers, and are clever, you might say to yourself: why not flip an arch upside down and use it to turn concentrated loads at its ends into a load distributed along the line? If that inverted arch is resting on soil, this is one way to spread the pier loads so that they don’t exceed the soil’s bearing capacity.

The picture above is the first time I’ve seen an inverted-arch foundation in rubble, but they’re not that hard to find in brick. The most visible example in New York these days is the Corbin Building. Thanks to the incorporation of this building into the Fulton Center, you can take an escalator up through the foundation level of Corbin, and look at the inverted arch foundations on one side and fake inverted arches on the other.

Here’s a photo of the southwest corner of the building’s foundations before the renovation:


The pier in the center is the corner of the building above; the space beyond the inverted arches ahead and to the left is vault space below the sidewalks. Note the terra-cotta tile-arch floors on steel beams for the cellar floor above.

The problem with inverted arches is related to the problems with regular arches; they are not good at handling asymmetric loads and differential movement. For example, in the Corbin picture we see three piers that have three different loads. But the inverted arches have no way to distribute the loads exempt evenly. In this case it was not a problem because the building sits on good soil, but a similar foundation on soft soil would crack and deform. One of the important steps in te development of modern structure was the change to isolated footings that could be sized specifically for the individual load in each pier or column.

Putting engineering aside, I love the way inverted arches make pictures look like they’re upside down.

Blatant and Odd Fakery

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The entrance to a garage in a late-1980s, maybe early 1990s apartment house is dead center in that photo. I can’t stop staring at the “flat arch” above the opening. Someone went to a lot of trouble to make the stone veneer (which is most likely in front of concrete block back-up) look like this […]

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Jack Arches Are Arching Action

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That’s my artistic photo of two windows in an 1880s building in upstate New York with jack-arch heads. The term “jack arch” is variously defined but usually means a flat or low-curvature segmental arch. There’s a fanciful story that the name comes from the resemblance of the arch to the hats that the jacks in […]

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Not Amenable To Easy Analysis

September 27, 2017

Not our project: While discussing a project recently with our client, it became clear that part of our work was going to require arch analysis of a masonry lintel. (The project is a bit sensitive, so I’m going to be vague about the specifics of the location and owner, which fortunately does not require being […]

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Arching Action Visible

September 25, 2017

I’ve talked before about the phenomenon called “arching action” but you’ll never see a better demonstration than this. Ignore the wood “studs” in that picture, they’re just supports for the now-removed plaster and lath. The real story here is a brick wall, two wythes/8 inches thick, with no lintel at the door. The thin wood […]

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Failure In An Expected Pattern

September 20, 2017

The animated picture above is from The General, a 1926 Buster Keaton movie. (Click on the picture to enlarge it.) In the era before computer graphics, and when the use of scale models for special effects led to disappointing results, Keaton got a realistic train crash in the obvious manner: he crashed a train and […]

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The Turning Point In Frame Technology

July 5, 2017

Ben Evans has a very nice piece on the evolution of technology here: Not Even Wrong. It’s not a completely new idea, but he states it well: there is evolution of a given technology within a type, and there’s development of new types that require new ways of design and analysis. These two kinds of […]

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Jurassic Silliness

May 20, 2017

I’m not sure Jurassic World needed structural analysis, but it’s got it now.

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Honest Critique

February 11, 2017

Not a McMansion: Architects are first exposed to critique in school, where students discuss the various failings of each other’s work. I witnessed this as an outsider and was astonished at the extent of criticism. Nothing prepared me for McMansion Hell, Kate Wagner‘s website that eviscerates overlarge suburban houses on a weekly basis.

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Arching Action, Too

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One of the odd administrative aspects of running a blog is that I get statistics on how people arrive here. A blog post from last spring, “What Is Arching Action?” is now our third-most popular post, with a few people arriving here almost every day after searching for those words. (As of today, that blog […]

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