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Even with a slab on grade, you need footings at the perimeter to below the frostline (which I don't know the depth of in Ohio, but I'd guess it's in the neighborhood of 2 1/2 to 3'). There are what's called "Frost-proof Shallow Foundations", which rely on layers of insulation to isolate the building from frost heave, but they haven't caught on much yet. That may be what you saw when you said there were slabs with no footings.
Not to be harsh, but I'd seriously think hard before diving in to "building some duplexes" if you're having to ask basic questions like this, though. On top of all the other complexities of homebuilding, attached housing adds a host of fire-rating issues to the construction process.
Bob
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