Analysis

When Is An Arch Not An Arch?

by Don Friedman on November 15, 2017


That’s the F/G subway, paralleling 9th Street in Brooklyn, where the tracks cross over Fourth Avenue. The train is elevated here because it crosses over the Gowanus Canal a little to the west at the Smith/9th Street station. As the tracks head east, to the left, they stay at roughly the same elevation as the ground rises (the slope of Park Slope) and so head back underground.

There’s some fine art-decoish brickwork at the station, but what grabs my attention is the structure that carried the load of the trains across the 100-foot width of Fourth Avenue. That big green arch is steel, one of I believe four parallel arches at this spot, and serves as a bridge. There’s another, older subway line under Fourth Avenue (the R/N/D), so a vertical section through this spot is quite complicated.

The thing is, that’s not really an arch. It’s an “arch.” An arch carries vertical load through compression, and has both vertical (gravity) and horizontal (thrust) reactions at its base. This is a structural element that used to be called a “one-bay bent”: two columns that are moment-connected to the beam that connects them. The tip-off is the corner, visible (where the arch bends down on the right into the brick of the station entrance) as a widening of the arched member. That widened corner is the moment connection.

Here’s where classification starts to break down. The arch foundations are buried in the ground, so in theory they could be designed for the horizontal thrust. The thrust would be pushing away from the old buried train tunnel, so it wouldn’t harm it. So if we allow for thrust, the arch could be working as an arch. In other words, once we allow for thrust, arching action exists. The proper shape for a uniformly-loaded arch to remain solely in compression is an inverted catenary curve, but the loading here isn’t uniform. A train can be in the station and uniformly loading the arch, it can be approaching from the Manhattan end of the line and loading the west half of the arch, or it can be approaching from the Brooklyn end of the line and loading the east half of the arch. Arches that have to carry radically different loading cases either have to be very thick to allow for the different compression paths through their material or they have to be able to carry local bending. Similarly, if an arch has a less-than-ideal curve to it, it either needs to be thick or it needs to carry local bending.

What would an arch that can carry local bending look like? It would be a material that can take tension as well as compression like, say, steel. And in areas of sharp curvature it would be wider because of the concentration of bending caused by the geometry. In other words, it would look a lot like the arch above.

The division between arches and one-bay bents is based (1) whether the material is capable of carrying bending as well as compression and (2) on how we choose to analyze them. In this case, given the heavy loads from the trains, it makes more sense to look at this as a bent, but that’s really a matter of taste.

Arching Action Index

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I’ve been caught up in writing about arching action recently, and I thought it might make sense to collect all of the posts on this topic in one place. So: What Is Arching Action? Arching Action, Too Not Amenable To Easy Analysis Arching Action Visible Jack Arches Are Arching Action If I post again on […]

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Physically Impossible

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Inverted Arch Foundations Are Upside-Down Fun

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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 […]

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Blatant and Odd Fakery

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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

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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

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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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