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.

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