A while back I wrote about the odd 125th Street station on the 1 train. This is part of the original IRT subway, built around 1902 and opened in 1904. The line is in a tunnel to the south and to the north of that station, but grade drops sharply in a valley centered on 125th Street, so the train tracks come out of the ground, are on a high elevated structure at the station, and then go back underground. This is accomplished by having the train run more or less in a straight line as grade drops.
The picture above shows the station at the top, and the triple skew-arch bridge that carries it across 125th. That arch is, as far as I know, unique in the subway system. Other bridges are trestles – series of identical frames – or girders. In broad terms, there are three types of arches, at least as far as structural modeling goes. You can model an arch as continuous with its abutments (the end supports) and along its length. That’s a hingeless arch. You can model an arch with hinges at the abutments and at the center. That’s a three-hinge arch. Or you can model an arch with hinges at the abutments. That’s a two-hinge arch.
The three-hinge arch is statically determinate, which makes analysis easy, but it’s not a good model for a masonry arch, and most arches are masonry. The hingeless arch is the best fit for masonry. The two-hinge arch is conceptually sensible if you are building an iron or steel arch: the material changes from the abutments (masonry or concrete) to the metal of the arch, so having a moment break (a hinge) at that interface can be a reasonable model.
One of the nice thongs about structural design is that you can make reality fit your model. The meaning of a hinge in a model is that direct force and shear can be transmitted from one side to the other but bending moment can’t be. A little clever steel detailing, some castings, and the use of a large-diameter pin as a bearing element, and behind: a hinge.
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