How to raise a wooden floor above a basement (old porch floor) 8 - 10" to the same height as the adjoining room
What you’re talking about in this case is technically a ledger attached to the studs. I presume you’re going to need to pass an inspection, and in any case you want the floor to do its job, which means there are calculations to be done to determine how much load each stud ends up holding. Not all screws are appropriate for a job like this. The article I reference just below talks about Simpson Strong-Drive SDWS timber screws, and provides some computations as well. The screws have to have high sheer strength so they won’t break off, and you don’t want them to rust out and fail in the future. Here is an interesting page on the subject:
https://www.jlconline.com/how-to/framing/attaching-a-ledger-to-studs_o
Classic time-tested construction is post and beam. The posts are set on a foundation, and the beams sit on top of the posts (or a rim joist and the ends of the floor joists sit on top of a foundation). Basically, everything is stacked so that load is transferred straight down in a vertical column to the foundation. Gravity does all of the work. Fasteners like nails and screws (or holes and dowels) keep things aligned vertically so that nothing slips sideways and gravity keeps the structure up instead of pulling it down.
But in this case, you would obviously have to either build a parallel foundation to support the floor (a hard expensive job) or hang the floor off of existing structure. There is a good chance that attaching a ledger with the right fasteners and using joist hangers is legal where you live. It can definitely be strong enough if done correctly.
Remove the sheetrock high enough to attach the ledger in direct contact with the studs. You can leave the sheetrock in place higher on the wall.
Make sure you measure twice before attaching the ledger so that your subfloor and flooring don’t end up 1/2” higher or lower than your kitchen floor.
Run your joists across the shorter distance. This does at least two things. First, you can use narrower joists because each one carries a smaller load over a shorter span. Second, each of the studs that the ledger is attached to will carry a smaller load, because the load will be distributed across more studs down the longer wall(s).
Use metal joist hangers attached to the ledger with appropriate (high sheer strength) nails or screws (typically nails).
If you’re using dimensional lumber for your joists they might differ very slightly in width from one to the next. This can make your floor uneven. In that case use hangers with a flat face that do not hook over the top of the ledger. That way you can adjust the hangers individually so that the tops of the joists are exactly even with the top of the ledger.
If a joist has any bow to it, set it so that it arches up instead of dipping down. But get them as straight as possible. Lumber can twist and warp if it’s cut from relatively young, green trees and cut into boards before the wood has dried sufficiently.
Better yet, buy engineered joists. They’ll be identical in width and won’t have any bow to them.