I have demolished the bathroom shown in the picture (below) and am ready to remodel it. Before I can do that though, I have to figure out what to do about this joist which has been severed by the stack pipe.
Obviously I'm going to leave the stack pipe where it is and work around it. I know you're supposed to sister damaged joists with more wood of the same size or possibly steel. A curved piece of steel which could attach the severed joist to the remnant sticking out of the wall would be perfect but I don't know where to get a piece of steel like that.
For description purposes let's say the top of the photo is North and the left side of the photo is West. The toilet drain is going to be removed and replaced with a new drain running South of the stack pipe instead of East as it is now. It will pop up out of the underfloor just out of picture range off the SouthWest edge. The shower drain will remain close to where it is now; I haven't decided exactly where it will go, but it isn't going to move very far. I will also run it North or NorthWest into the stack instead of East then North then West like it is now. The shower faucets can be moved slightly. The HVAC vent can be moved/removed to accommodate the shower drain.
So there will be room to run a short 2x8 perpendicular to the severed joist and the one just South of it. But that's the only part I know. The NorthWest corner of whatever floor I put in there is still going to be weak. You should have seen how easy it was to break through when I demolished it. It was a cheap waterlogged drywall frame, not even cementboard, and no real floor - just more drywall.
I can sort of figure out these other problems like moving the plumbing, but I think I need advice on the severed joist because the new floor needs to be supported properly. I want to make a floor running right up to a frame which I will build around the stack. The floor should obviously be level with the rest of the floor. But there isn't much there to support a floor in the NorthWest corner. There's not much there to support the frame either, but that's just for looks - nobody's going to be standing on the frame. And there's not going to be any water or flooring putting weight on this vertical frame.
Also important, I'm going to have to support the stack on something while I'm cutting it and replacing sections of it. So it would be nice to have joists I can trust to clamp it to.
So I'm looking for someone who knows more about this than me (which is probably most people) to suggest how to sister that partial joist to make the floor strong enough.
This might not be very important but the severed joist is not as level as the other joists are. It's not a big difference though.
One more question. The vent pipe for the shower drain is vertical for about 1' before it joins the stack. I want to regain as much floor space as possible and not have to build more framing than necessary. So how high above the shower drain does this vertical vent pipe have to be? I'd like to run it under the floor instead of up. There's lots of room for this plumbing under not just this floor but also underneath the joists, still hidden above the ceiling below it.
You need more advice than we can give you in this forum. What does the building department say about securing that joist and your cutting through the next one for the toilet drain, if you do not run it below the ceiling? At the very least you have to anchor that joist to the adjacent brick wall.