tjhubo
I do not understand your idea well. Are you consdering to check the effect of basement slab load on the soil bearing capacity for your strip footings?
If the basement slab are not separated from the building structure (frame, tie-girder…) of course we have to count the basement slab load transferred to strip footings via grounding tie-girders. In this case we have load pressure under footing bottom, just check the soil bearing capacity to verify the whether it is satisfied or not.
If the basement slab are separated from the building structure, so the basement loads are not transferred directly to the strip footings. But we still have to consider this load as a surcharge. The actuall soil bearing capacity must be decreased by this load value. And then just check the strip footing with decreased value of soil bearing capacity.
Hope to help you.