Even I can see what's wrong here!!
Out of interest, has anyone come across a house collapse (or partial collapse) due to cutting out too much of joists?
I sometimes feel that although the rules are there for good reason, the tolerances are given to cover the rule makers in case of suing as opposed to how much strength a joist has when it's chopped about. I know this is illegal but I'd have thought that chopping 4"-6" width to a depth of under half out of a joist ain't going to pull the house down. (It's not something I would do either without consultation with a structural engineer - saying this to save on the flak!)
Perhaps I'm missing a point here?