Consider the following image (img_1)
I guess the whole thing is called a floor framing system and subfloor is a part of the system. So subfloor is a part of floor. is my understanding right?
Flooring – the difference between floor and subfloor? Is subfloor a part of floor
floorflooring
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You should be able to pull them up with a 12" long prybar and possibly a crowbar (3' to 4' long), if it is stubborn. Most that I have seen are put in with nails only. You may also need to have a circular saw handy in case some of the subfloor runs underneath a wall (in this case, you would want to make a clean cut of the subfloor piece, so you can remove the part that you need and leave the part under the wall intact).
As for reattaching the sheets, you should use 3" screws.
What you are calling a floor joist, appears to be much thicker than a 2x floor joist. Maybe like a 4x8 or something. So it's probably a "bearer" resting on the piers, which would explain why they are far apart. Typically you would then rest floor joists across those beams, (or use Simpson hangers if the floor needs to be nearly flush to the beams -- which is your situation).
This is typical ...
This is where you need to be with Simpson joist hangers:
Can you measure the thickness of the wood that you are calling a floor joist (which is really a bearer)? Also, that beam that is notched badly is not good (most likely). This would be the time to address that notch, which is fortunately very close to the wall. Can you measure the depth of the cut on that notch?
An easy way to do that would be to set a pier underneath the bearer so that no notched portion of the bearer is under stress.
Once you have addressed making sure that the bearer is properly supported, you can then hang joists between the two bearers you showed with joist hangers. Then you would put the subfloor and whatever choice of flooring you want on the joists.
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Best Answer
Subfloor is a part of the floor but has a different purpose. Without a solid sheet that spans the joints and the ends are supported, how can you install tile or wood flooring? In the oldest residential constructions I’ve seen, they used either two layers of thick wood planks (bottom acting as a subfloor) or boards run diagonally as the subfloor. Today, we almost exclusively see OSB, but the purpose is the same. It provides even support for the floor.