My local store has a limited selection and for framing an exterior wall my choices are using 1-1/4" x 6" and somehow double them or 2-1/4" x 10" and cut each of them at the 6" width. Using 1 x 6 would be much easier so my question is if it's possible and what would be the best way to do that. Just double them at 16", maybe fasten together? I would prefer not to build 2 x 10 exterior walls to save some space inside the house. These would be exterior load bearing walls, 8' high. Thanks.
Buy the 10" boards and rip them in half for two 5" studs for the least amount of waste, or to 3-1/2" if you want readily available windows and doors to fit in your openings which is going to be your next problem. Since the wood is spruce, follow IRC building codes for 2x4 SPF load bearing/exterior walls. At 8' tall and 16" on center spacing you can support most roofs, but don't support both a floor and a roof on it without asking us or reading up on it first. Use closed cell sill sealer to separate the bottom plate from direct contact with concrete/masonry, or just find pressure treated lumber for the bottom plate instead.
The Code allows for “Alternative materials, design and methods of construction.” (See ICC 104.11.) However, the Building Official “May require supporting data when necessary to assist in the approval.”
I wouldn’t be concerned about using 1 1/4” x 5” studs. You’ll need to be careful about your nailing patterns as @JimStewart mentioned.
I can tell you that residential construction is grossly over-designed. That is to say, most materials do not reach their “working stress” limits. Using studs that are slightly less thick (and slightly less wide) than a standard stud, is of little concern for strength and stability.
If you’re not using the Building Department for inspections, then you’ll need to be vigilant in adequate and proper framing practices, (i.e.: lapping double top plate, nailing of sheathing, etc.)
Thickness of the stud is not as critical as the width. (Until a few years ago, we used 2x4 at 24” oc construction. Yes, some of the really old construction used 2”x4” studs, but the sheathing was lap boards.)
Some other issues you maybe consider: 1) standard batt insulation is designed for 5 1/2” deep x 16” oc (or 24” oc) stud space. Compressing it in a 5” space will reduce its thermal resistance AND the studs will be 1/4” further apart, so the insulation will not completely fill the width of the stud space allowing a thermal “gap”, 2) you may want to use a double trimmer for bearing at headers, and 3) you may need two trimmers for stiffness to secure door jambs in lieu of single trimmer.
Generally, framing is not one of the big costs of construction. The savings may not out weigh the hassle. ..but it all adds up.