Will the beams run the long way or the short way on this 18 x 22/24 cabin? In any case, the outer beams will be better protected from weather, and make for stiffer floor joists, if they are set in a foot or so from the rim joist. I would also set the pillars in a foot or so from the ends of the beams for the same stiffening benefit.
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The amount a piece of wood will shrink lengthwise, called longitudinal shrinkage, is so small—typically about 0.1% to 0.2%—that it is usually inconsequential to the volumetric shrinkage." So you can expect less than 1/2" of total longitudinal shrinkage in your beams, pretty much negligible.
You will of
course want to use the straightest logs you can find with no twist to the grain, to minimize movement after placement. Aside from peeling, and flattening the whole top and the bottom at pillar locations, will you be doing more surfacing? Depending on the species, there may be significant checking (long cracks).
Ash and maple which split easily for
firewood are especially susceptible to this, and if the grain twists it may cause significant distortion of the bearing surface. Nailing at least a couple of places where each joist sits on the beam may help restrain movement, and if the floor framing and subfloor is finished before checking starts, the whole floor will resist distortion.