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"Dead load" is the weight of the structure and permanent covering, if any. For a roof, that is the rafters, plywood, and shingles. "Live load" is the weight of people or objects assumed to be supported by the floor, floor/ceiling assembly, or roof. This includes a usual allotment of furniture, but one is expected to make adjustments for unusual situations (say for a room holding a piano collection). For residential occupancies, "dwelling" rooms are figured at 40 pounds per square foot. Some codes allow for "sleeping areas" to be figured at 30 pounds per square foot. "Attics" with storage are usually figured at 20 pounds per square foot live load. If your storage room is simply a partition wall, separating one part of a building from another, you should not need a thickened slab. If you (or someone down the road) plan to somehow support weight (beyond the weight of the wall itself) then you do. (This makes the wall a "bearing wall"). So floor joists spanning the room, or a ceiling atop it with at least 30 inches of clear space above, would justify additional support for the wall. (It is assumed that someone, someday, may store their rock collection on top of the ceiling, even if you don't plan to). The thickened slab you propose should meet most codes for up to a 40 PSF live load above the ceiling, assuming that you have reasonable soils below the slab.
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