CommunityJoist Support Dilemma

Joist Support Dilemma

I have a 1960s cape cod.  My first floor bathroom had popcorn ceilings, so I tore down the ceiling and noticed that the space above was open to the rafters and roof. So Ileft it open since a high ceiling improves the size of the bath.  Problem is the second floor bedroom extends over into the bathroom space about 4 ft but not quite the center of the open ceiling space. And the wall of it goes up to the apex of the roof. Im fine with having the upper wall there – I'm thinking of hanging a huge picture on it, but the joists that held the ceiling up are in the way, across the whole bath. Id like to get rid of them so its open, but i cant simply cut them because they support the second story floor. I would cut them to where the upper bedroom wall starts but again; they stick out from the bathroom wall frame 4 ft. and not sure if thats enough to cantilever enough support to hold the partial floor of the second story without additional support from a cross beam. What's the best to support this with –  a beam on the room's adjacent wall frames, or anchor it to inside of the the roof? preferably without puting a support pole in the middle of my bathroom.

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