That mess is the edge of a stoop. It’s shored, so obviously it’s got problems, but ignoring that issue for a second, the first question we should be asking is “How did this thing ever stand up?” It’s brownstone, which is to say weak stone with a tendency to come apart from weathering. Each step is an individual block of stone, with a shape that’s close to a triangular prism, except for the inch or so overlap where the blocks touch. The far side of each block (from where I was standing) is resting on a brick cheek wall under the stoop, but the near ends of the blocks are basically floating. There’s no cheek wall on this side to allow for access to a basement door directly below the main door at the top of the stoop.
The individual blocks of stone aren’t cantilevered from the far cheek wall because they don’t have any kind of connection there that could resist the cantilever moment. They’re not arching from top to bottom because there’s no load path that would work. There is one other detail, barely visible above:
There’s a wrought-iron strap running along the underside of the stair, a few inches in from the free edge of the stones. This picture also shows a pretty severe spall of the underside of the platform/top step.
That strap, roughly 1/4 inch by an inch, is far too weak and flexible to carry the free edge of the steps by acting as a beam. That’s plenty of cross-section for a catenary, except it’s not taut and not fastened at the ends in a manner that could resist tension. The strap has to be the answer to how this has functioned because it’s the only thing there, but how? I should also point out that it doesn’t really matter except for the sake of curiosity, because the entire stoop was rebuilt.
It seems to me that the combination of stones and strap are acting similarly to a tension-rod girder (or, for that matter, a reinforced-concrete beam), with a continuous line of compression through the stone balanced by tension in the strap. Under those conditions, the strap doesn’t need to be anchored anywhere for full tension, just at each stone for a small portion of the tension. This would work and, more importantly, it’s a solution that masons could have come upon without having to do any numerical analysis. In more geometrically-forgiving stoops, there’s a masonry arch below the free side of the steps to create.a cheek wall with a door opening in it. At this building there simply wasn’t room. It’s not difficult to imagine masons, faced with this kind of problem again and again, trying different solutions and finding that adding a metal strap fastened to each step worked.
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