Could installing a furnace to the floor joists cause the floor to slope?
You got kind of a loaded question there. Depending on the dimentional size of the floor joist, the amount of given load, plus the distance between the floor joist all are factors in a sloping floor. Some others are probably going to be composite of the lumber and age of the lumber that was used. If you factor all this in, the additional weight of the furnace could cause some additional load on the floor joists. But for the most part, depending on the efficency of the furnace and the manufaturer of it, you are only talking about 100-300 pound including the evaporator weight. That should be well within the ability of even a pine 2"x6". This is a good sbject to ponder but I would look into what could be the major contributor to the excess load. I dont think you will find the furnace to be much of a problem. This is not my favorite way to do things, but if you don't have the room for a furnace, the only other alternative would be a combination unit. Hope some of this helps ease your mind, it now has mine racing.