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-Does inside refer to inside the dwelling or inside the chimney
-Step 1: Why a 2x4x13 sized support
Response to Comments
-Inside refers to the inside of the dwelling, I'll try to make that more clear.
-Step 1: A dimensioned 2 x 4 isn't really 2 inches by 4 inches, it is actually 1.5 inches by 3.5 inches. So for the middle support to fit in between the two studs as shown we need to take the 1.5 inch thickness of the stud off the support on either side, for a total of 3 inches. Since the top plate is 16 inches, we take 3 inches off that length and make the support 13 inches in length. This makes the wall square, taking into account the fact that the top and bottom plates sit on the studs, whereas the support sits in between.