Flooring – Sistering a joist – bathroom floor

There is a simple answer to this. Cut the angle matching the roof on the ceiling joist, slide it in on top of your wall and attach it to the side of the rafter. Then attach them together with small lags or carriage bolts. If you look at your picture the 8" joist will be in contact with the rafter well beyond your walls. The rafters will help carry the weight of the floor joists through the rafters down to the walls.

Don't worry about the rafters, you will be applying the weight soo close to the wall it will not put more stress on your rafters.

Construction adhesive would be a good idea too. Your Lag spacing may vary depending on the thickness of your rafter. Keep lags 2" from all edges and 3" from each other. Pre drill all the holes you don't want to risk splitting your rafter. Lags should be 3/8" or less. There is also of high strength screws/ lags that are smaller but just as strong as a standard lags that would work good.

You should shim under the loose joists with steel shims, not cement, because cement causes wood to deteriorate. Large galvanized washers and small steel plates can be used as shims. The framing block in between the joists are called bridging and in an old house I would space them about 4' on center. You can off set each row by 1 1/2" which will enable you to blind nail through the joists which minimizes toe nailing. Use 3/4 tongue. And groove ply glued and screwed to the joists and bridging. I would use pl400 for glue and 2" exterior screws spaced about 8" apart. If a second layer of ply is desired you should also glue and screw it the same as the first sheet. Try to hit the joists. Use a chalk line to mark the joists. If a solid wood finished floor is being installed 1 layer of 3/4 plywood is all you need.if a ceramic tile,stone or wood laminate floor is going in use 1/2 ac plywood over the sub-floor.