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In this scenario, you would know something about arches, since complex masonry construction is what was, historically, superseded by concrete construction.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 load 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.