This house has 2 5/8" x 8" (true dimensions) floor joists on 16" centers spanning roughly 23' on the first floor. The house is 2 stories with a 50 PSF load. There is a wall in the middle of the joists that runs perpendicular about 10'. The wall is running from the exterior wall to the interior of the house.
When I took down the drywall I noticed the joists aren't sitting with full contact on the wall, there's about a 1/2 in gap between the top plate of the wall and the floor joist.
I was wondering if this wall was a load-bearing wall even if the floor joists were not fully in contact with the wall?
The house was built in the 1920s, the framing is rough cut lumber, I'm not exactly sure what species of wood it is (my guess is long-leaf pine). But all the framing is much thicker than standard framing lumber. Wall studs are also 2" x 4" true.
I also noticed that the doorways were framed without jack studs supporting the header, and the header is a 2" x 4" nailed into the studs. Is that something to address as well?
Edit: I added a rough sketch of the floor plan to the house. Also, if I were to add a support beam in place of the wall. What would be a sufficient sized beam?