Can my run support a roof?

Something you may want to consider is replace one side with the larger timbers & then fasten timbers on the top of the other side to make a sloped roof. For most roofing you want at least a 4/12 pitch. Meaning for every 12 inches of span you want the roof rise to be 4 inches. Depending on your post height you may be able to cut one side down to make it sloped. Maybe even put gutters on and do rain collection waterer for a future improvement.

For some examples say for a flat roof look under an uncovered wood deck to see what will hold your snow load and build like that.
 
Looking at your picture, some of your joist will land over the 4x4 post. Its the ones in between the post that i would be concerned with, there would be two joist between each post, on 2 foot centers. If you could strengthen the top by putting a 2x10 around the perimeter, fastened to the post and your 2x4s to strengthen in between the post i think that part would be good. Now, the other concern would be the 12 foot span. Too much for 2x6s at 2 foot oc, especially being flat with a snow load. I would increase those to 2x8s, 2x10s if you get deep snow, its heavy.

Would it work to attach the 2x10s to the sides of the 4x4 posts (so they'd form a rectangle around the top of the inner perimeter) rather than have them sit on top or replace the 2x4s between posts? Is that what you mean? Would doing it that way be significantly less strong than sitting them atop the 4x4s?
 
Something you may want to consider is replace one side with the larger timbers & then fasten timbers on the top of the other side to make a sloped roof. For most roofing you want at least a 4/12 pitch. Meaning for every 12 inches of span you want the roof rise to be 4 inches. Depending on your post height you may be able to cut one side down to make it sloped. Maybe even put gutters on and do rain collection waterer for a future improvement.

For some examples say for a flat roof look under an uncovered wood deck to see what will hold your snow load and build like that.
I considered doing a pitched roof but it feels too complicated. Maybe it's not. I don't know anything about building. I'm trying to learn.

Thanks!
 
Would it work to attach the 2x10s to the sides of the 4x4 posts (so they'd form a rectangle around the top of the inner perimeter) rather than have them sit on top or replace the 2x4s between posts? Is that what you mean? Would doing it that way be significantly less strong than sitting them atop the 4x4s?
Absolutly, the strength is in the width of the board. Inside is fine, vertical. Make sure to make a good connection to the 2x4s between the post as well as the post itself.
 
If you aren't comfortable with framing (though a single pitched roof is pretty easy, and as @aart says, there are plenty of "how to" on shed building that will show everything you need to know, there is another option if you have the budget for it. Look into Pole Barns. Because what you have is the basics of a pole barn. 4x4s (or 6x6s) set into the earth at regular spacing. You should be able to easily find preformed trusses for the 12' spans.

One truss would be placed at every pair of 4x4s in the short direction. Purlins would be attached to connect them (basically, slats of wood running parallel to the long walls, nailed or screwed to the trusses). The roofing would then be connected to that. Around here (using 6x6s and metal trusses) 10' spans are not uncommon. You should be able to easily do the same with pre-engineered wooden trusses, likely at a cost of about $100 each or thereabouts. Then you don't need to know much of anything about the framing. Your purlins will likely add similar cost, would prices being what they currently are, then its your roofing materials themselves.
 
Would it work to attach the 2x10s to the sides of the 4x4 posts (so they'd form a rectangle around the top of the inner perimeter) rather than have them sit on top or replace the 2x4s between posts? Is that what you mean? Would doing it that way be significantly less strong than sitting them atop the 4x4s?
Fastening to the side puts all the load on the fasteners. Either a notched post or fastening the 2x lumber on top of the post gives the most strength.
 
If you aren't comfortable with framing (though a single pitched roof is pretty easy, and as @aart says, there are plenty of "how to" on shed building that will show everything you need to know, there is another option if you have the budget for it. Look into Pole Barns. Because what you have is the basics of a pole barn. 4x4s (or 6x6s) set into the earth at regular spacing. You should be able to easily find preformed trusses for the 12' spans.

One truss would be placed at every pair of 4x4s in the short direction. Purlins would be attached to connect them (basically, slats of wood running parallel to the long walls, nailed or screwed to the trusses). The roofing would then be connected to that. Around here (using 6x6s and metal trusses) 10' spans are not uncommon. You should be able to easily do the same with pre-engineered wooden trusses, likely at a cost of about $100 each or thereabouts. Then you don't need to know much of anything about the framing. Your purlins will likely add similar cost, would prices being what they currently are, then its your roofing materials themselves.
I'll look into that, thanks!
 

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