2x4 or 2x6 for roof of run?

My coop is 12 x 20.... 2 x 6 longitudinal supports, supported about every 6-7 feet.... 12' 2 x 4's supported 6' in the center and 3' on the sides.... That cantilevers the load so there is load only on any 3' of the 2 x 4.... the 2 x 4's are laid flat.... 3' of snow load ain't much.... The entire run "floats" as does the coop.... sitting on treated lumber... the frost heave "should" move the entire structure as one piece... ( so it says in fine print )... side walls are ripped 2 x 6's.... Check out my "coop build" in my profile..... It hasn't seen chickens or a winter yet, soooooooooo I may be full of it on this coop and run design..... we'll see next year...... supposed to be an el-nino winter so we will get LOTS of snow this winter..... BTW.... I sloped the roof long dimension... 1/2" per foot....





 

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