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Check with local lumber yards to determine the snow-load and determine if the load capacity of the framing members are sufficient to carry the load. There are many questions to be answered, such as total span, are you using a beam to support the framing members, how much weight in pounds per square foot will the structure be supporting and what kind of wood is being used. Douglas fir for example is considerably stronger than hemlock fir, which is considerably stronger than "whitewood" which is just ordinary pine. Unfortunately my answer just results in more questions and doesn't really give you the information you need. In fact, I don't even know if a 2X6 framed roof would be strong enough especially if you live in an area that routinely gets a lot of snow. The simple answer is, I don't think a 2x4 framed roof will be strong enough.

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IRC shows for a 12' span with no snow load is 2x6 on 16" centers. UBC shows about the same. I'd go up one size if you have appreciable snow load. (ie 2x8) Also greater pitch will help with the snow load.

Answer: The two previous are well taken and true. I'm a 26 year frame carpenter. Never, but never use anything less than 2x6 members for framing roofs of any type. This would be the minimum requirement except when building dog houses.

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