I once gave a presentation called “Why hasn’t that fallen down yet?” It was about some of the differences between how structure used to be designed and the way it’s designed now, and how some things that look bad in old buildings are actually okay.
This isn’t one of those. Behold, a butchered slab on the Upper West Side:

That’s a cinder-concrete draped-mesh slab, with a concrete encased spandrel beam on the left. The hole for the drain was chopped through the slab, cutting a number of wires in the mesh in the process, and the hole was filled some plywood scraps supported by the mesh and a piece of black iron. Presumably some kind of pourable patch was placed over the top to make it look okay from there; possibly a tile floor was laid over the patch.
Why hasn’t this fallen down?
There are some basics that apply to pretty much any structure. For example, the design live load is far higher than the likely live load in an apartment bathroom, and non-structural elements (e.g., large stone tiles) may help bridge over this area. But the specifics are more interesting. Draped mesh floors rely solely on the spanning wires (in this case, the ones running left-right) for their strength. The loss of concrete doesn’t weaken the slab. Cutting wires obvious does weaken the slab, but the cross-wires (and to a lesser degree, the slab itself) can spread the load sideways to the next intact wire at each edge of the hole. That increases the load on those wires, probably beyond their original design capacity. But the maximum allowable stress used in the design of the wires is lower than we’d use today, and there’s no reason not to use the modern value, which gets us back to a workable design. The plywood is strong enough to span a foot or so, and there we are: all elements of the floor in this area accounted for.
That’s not to say this is okay. If I saw a plumber chopping structure I’d yell at them to stop; in cases like this I recommend repairing the wire to restore the original load path. What happens if the next apartment renovation in the future cuts the wires next to this area? What if someone installs a claw-foot bathtub that puts a large concentrated load right here?

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