I'm attempting to size beams for a loft in a cabin that's being built and I want to make sure my calculations and assumptions are correct. I'm an engineer (geotechnical) with little structural experience. I blew the dust off a few books and did a little research. Here's what I've come up with.

The loft will be ~12 feet deep by 22 feet wide. I'm trying to size beams to span the 22' width with no support. I assumed 4 beams spaced 3.5 ft c/c using eastern white pine. I analyzed the beams for a live load deflection (30 psf live load and 1/360th of length for an allowable deflection), combined load deflection (LL of 30 psf and dead load of 10 psf and an allowable deflection of 1/240th of length), and performed a bending evaluation.

For eastern white pine, I assumed E=900,000 psi, a density of 30 psf, an an extreme fiber stress of 575 psi. I'm not sure how wood is graded, so I think I'm conservative with these values. Our sawyer indicated that there's virtually no knots in the wood. I ended up calculating that and 8 x 12 will be acceptable.

I want to be certain that the beams are sized appropriately before they're cut. I think my calculations are correct, but the bending evaluation has me worried a bit. I'm also concerned about the working stress analysis; should a factor of safety be incorporated into the design? Any help or suggestions would be apprectiated.
Mike