Definitely check out your local lumber yard and see what they have in stock and what they can order. My local lumber yard had VASTLY better quality, selection, and prices than Home Depot. Home Depot does beat them on price (but not quality) for stuff that gets used a lot (2x4s and 14/2 wire), but I've found for larger lumber the lumber yard has better prices (and the electrical supply store beats them on large-gauge wire prices).
In So Cal, and I presume Nor Cal, the lumber is sold wet (this may be different in the southern US where the high humidity could take years for the lumber to dry outside). My best tip, and what I did, is buy 2X every piece of lumber you need. Store it flat on the floor in the garage, stacked up to keep weight on it, but with air spaces on the sides for a month, until the lumber dries out (you can also buy a moisture meter to check). Return the pieces that have warped and twisted and use the half that are still straight. You can also get a sense when you pick the lumber out - the stuff in the middle of the pile weighs far more than the pieces on the edges and will take longer to dry. If you are building a house, nailing everything together will tend to keep the lumber straight while it dries, but in a pergola there are probably not enough constraints to prevent warping and twisting while the lumber dries out.
I went with number 1 and above Douglas Fir. My lumber yard had a complete selection Redwood and Ceder in all the same sizes, but Cedar was 3X the price. After I built my pavilion, I wished I had used Cedar. The total lumber cost for my project in Doug Fir was $500, and I should have spent the $1500 for Cedar. (I think the Cedar may have been kiln dried as well - eliminating the need to pre-dry the lumber in the garage.)
Definitely use 6x6 for the posts, regardless of structural needs as it looks "right." Most of the time 4x4 is structurally adequate, but at 13' buckling is a concern and 4x4 might not be adequate, but 6x6 is plenty.
My project was a little different (not a carport), but the construction technique is the same.
In So Cal, and I presume Nor Cal, the lumber is sold wet (this may be different in the southern US where the high humidity could take years for the lumber to dry outside). My best tip, and what I did, is buy 2X every piece of lumber you need. Store it flat on the floor in the garage, stacked up to keep weight on it, but with air spaces on the sides for a month, until the lumber dries out (you can also buy a moisture meter to check). Return the pieces that have warped and twisted and use the half that are still straight. You can also get a sense when you pick the lumber out - the stuff in the middle of the pile weighs far more than the pieces on the edges and will take longer to dry. If you are building a house, nailing everything together will tend to keep the lumber straight while it dries, but in a pergola there are probably not enough constraints to prevent warping and twisting while the lumber dries out.
I went with number 1 and above Douglas Fir. My lumber yard had a complete selection Redwood and Ceder in all the same sizes, but Cedar was 3X the price. After I built my pavilion, I wished I had used Cedar. The total lumber cost for my project in Doug Fir was $500, and I should have spent the $1500 for Cedar. (I think the Cedar may have been kiln dried as well - eliminating the need to pre-dry the lumber in the garage.)
Definitely use 6x6 for the posts, regardless of structural needs as it looks "right." Most of the time 4x4 is structurally adequate, but at 13' buckling is a concern and 4x4 might not be adequate, but 6x6 is plenty.
My project was a little different (not a carport), but the construction technique is the same.
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