I purchased some land a few years back, which had a very small cabin built in the middle of the woods on the back corner of the property. When I began, I had absolutely NO construction or carpentry experience at all, so please keep that in mind and be gentle! Believe me, had I known how messed up this arraignment was, I would have tore it down and began anew; alas, that time has passed, and now I am trying to go back and right some of the mistakes in my endeavor to increase the strength and longevity of this place.
Let me try to explain what I'm working with here and perhaps that will help to clarify.
The cabin started [by the previous owner] as 6, 6x6 treated posts, sunk into the ground, on 8' centers. 6x6x16 beams laid across the posts and 7'-4" treated 2x6 joists were spanned at 16" o/c between the 6x6x16 beams and hung with joist hangers. The outer spans between the beam ends were spanned with a 2x12 [running parallel with the 2x6 joists, I guess you could call them header boards?] The rest is pretty standard, 2x4 walls, etc. The original footprint was 16x8.
Eventually, two more identical spans were added by me, when I decided to enlarge the cabin with the 6x6 posts [I sunk them to 48", the depth that the previous owner stated he had sunk the original six posts] and beams with the 2x6 joists running in between, again the 2x6 floor joists are 7'4" between the 6x6x16 cross beams, hung with joist hangers. Total size is now 24'x16'. Basically, I copied the engineering [if you want to call it that] of the previous owner and tripled the cabin's size, if that makes any sense? Subfloor consists of two sheets of 3/4" plywood.
The cabin is built on a slight slope, downhill at an angle from one corner to the opposite corner. The low corner has the bottom of the joists approximately 16-18" off the ground, the high corner is about 36". Everything under the subfloor is treated and the posts are soaked each spring with a petroleum/tar solution, to inhibit termites and carpenter ants from coming up through the treated posts. The joists, beams, posts, and ground beneath are bone dry, no water runs underneath, even during a downpour. I can get under the cabin to work, but it's tight; digging under the cabin is impossible.
Last year, I finished the inside of the cabin and installed an elevated 3x5 hearth, covered in 2" flagstone with a 300lb woodstove. This spring, I was doing some checking on the subfloor, as I was preparing to cover it with Ditra or Hardi for my ceramic tile. I noticed some slight bowing in the floor towards the 4 joists that the hearth/stove was resting on. The rest of the cabin floor is dead level, doesn't give, doesn't squeak. The floor resting on these joists I mentioned, when using a level, dip down to a low point about 3/16". I am going to presume that the stove/hearth is ALOT of weight on those 2x6 floor joists despite the short span.
From what I have read, especially in older homes, undersize floor joists are common, and no one notices until they place a large load upon the joists or are looking to install tile, as in my situation. I have been checking this site, as well as others, for solutions. The problem is, no two members of any forum can agree on ANY solution.
Basically, I have seen quite a few recurring opinions, and the ensuing argument both for and against each. Making it worse are always 'engineers' who argue and throw out calculations, both for and against, and no one ever seems to come up with a solid answer. In my case, I have seen many recommend cutting the span in half with a perpendicular beam on foundation piers. It is totally impractical, if not impossible in my case due to the nature of the crawlspace.
I have narrowed my options down to a few that I am aware of...
Sistering with 2x6s.
Sistering with joists larger than 2x6s [but then I run into what to do with the extra depth unsupported at each end where it would connect with the 6x6x16 crossbeams.
Sandwiching the joists with Plywood/OSB.
Some have suggested making an upside down 'T' using 2x4s or 2x6s laid parallel to the existing joists, glued and screwed.
Can anyone give me some direction here?