ok more elaboration
the stresses are not constant if you take 10 as maximum 0 then - 10
there is probably only a few inches that are on 10+ or- 10 loads or indeed zero every where else the load is going up or down across the length breadth or width the calculations just decide where the load are best handled
as for removing too much timber no "big deal" [read on]
if you remove 70 percent of a structure [joist ] you remove probably 80 percent strength
the floor then deflects in that area until the adjoining joist take the the extra weight they in turn may deflect and transfer load to the next joist
the problem comes when the joist either side or the original joist can not give enough support and the deflection [sagging in the floor] goes so far as to bend the weakened joist so it breaks this can lead to further joist failure across the floor
another point worth mentioning the joist in any floor will in general be constant size throught the each floor this means that the joists are designed for the largest span on that floor [main bedroom for example]
in general bathrooms have quite small spans assuming there is a load bearing wall corrisponding beneath the bathroom walls this means you have joist that are probably bigger than nessisery
part of this will be offset by the bath full of water
but any extra goes towards a bigger safety margin