Sagging wall needs to be lifted
I'm working on a house. I will be tearing out the bathroom and redoing it with a ceramic tile curbless shower.
The home is not built too well and the wall (non load bearing) with the door on it is run parallel to the floor joists. The wall does not sit on the floor joists and naturally has sagged. I want to slip one or two new joists under the wall to raise it back up to level again. Following are the specs
2 x 10 floor joists
12 ft span
I see two ways of doing this both which involve jacking up the wall near the center slowly to avoid cracking any drywall. The first option is to try and slip a new 2x10 joist under the wall. But how do I get the joist in there if the jack is holding up the wall? Do I put the jack to one edge of the wall (under the flooring obviously) and then slip the joist in beside it or would I be better to get 2 2x8's, nail them together, slip them into the cavity, jack them up under the wall and then block them at either end? Are there code issues? Code here actually says that the joists are oversized. They could have used 2x8's over the 12 ft span.
I like the latter approach because I may not get the wall completely back up so I can fudge the blocking at either end and I will be lifting on the whole length of the 2x8's rather a shorter timber if I use the first method.
Or am I completely off base and should use another method.
Thoughts would be appreciated.