I am going to attempt to paint a picture first, if this does not work then I will upload a picture. The picture I am painting is what I am guessing happened. We have an older home...1950's. From what we can tell, there were a few mods done to the house over time. A normal kitchen...about 12 x14, with steps leading down to the basement. Well...now picture that when the basement access was cut out in the floor, that left several floor joist shorter than they were when they extended to the block wall on the other side of basement. My question is, it seems no matter how you try to take this load to the load bearing block wall in basement....you would have to have support here ( where the floor joist are cut)? I do not see how framing techniques could compensate for this. Anyhow, where I have "no support here", there is a wall directly over this and thus this floor runs down hill to this area. The "no support here" includes the entire line. It is not a main load bearing wall but I would like to lift this back up(its over basement)and add some support to keep it from sagging again. Any suggestions would be appreciated.