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I have a 12 x 14 shed with 16 inch on center floor joists resting on sleepers on the two ends and in the center to support the down. However some of the 2x6 floor joists on the end are shy of being flush with the butt joint fronts (maybe 1/8 to 1/4 of inch due to end of one being skinnier) when resting on the sleepers. Can I shim under the floor joists to lift them up and if so what is the best method for this?

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With shed framing, 1/8" is rarely a concern. 1/4" is slightly more so, but still not much in this case. You could leave the joists resting down on the sleepers, install your floor sheathing, and build your walls with no ill effects. It's a very minor cosmetic issue if anything.

If you like, shim the rim up flush with the top of the joists. Just be sure that you aren't introducing humps in your floor, which would be a much more significant issue. Use a long level or other straightedge to check that out.

Correction: I see now that it's the rim that's low. Just float it. All the load of the walls and roof will be carried by the common joists. It's not a problem at all.

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  • Added a pic above. I ended up going with your first suggestion. I removed the screws and drilled in the toenail so everything is resting directly on the sleepers and not floating. There is a tiny lip at that corner joint (thinking of maybe just planing it down slightly but sounds like I don’t have too). Some other joists also didn’t seem flush and I am guessing it’s more imperfections so I bought these angle braces at Lowe’s which were thick enough to get the joists flush by slipping under them then screwing joist in as usual but wedding down metal plate. Does that seem sufficient? Nov 11, 2021 at 23:36
  • I'd say so, but I don't think there was a problem to begin with. :)
    – isherwood
    Nov 11, 2021 at 23:44

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