What size rafters are needed for a 13" span to support clay…

I’d like to point out that a Professional Engineer’s standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for planning purposes only (general sizing and budgeting) and is based on the information provided by you. All loading cases considered are for vertical loads only, no lateral analysis has been completed. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.

For your roof loading condition (13' clear span rafters), you could use:

Double 2"x6" members spaced at 12" o.c. (assuming Douglas Fir #2 grade)

This way you can keep your existing 2x6's and sister another 2x6 next to each of them. Then you would need to add an additional double 2x6 in between your existing 2x6's, so this will give you double 2x6 members spaced at 12" o.c.

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Starting from scratch, with 13' rafter spans, you could use 2"x10" Douglas Fir rafters (#2 grade) spaced at 16" o.c.

Or you could use 2"x8" Douglas Fir rafters (#2 grade) spaced at 12" o.c.

Good Luck with your project!

You are welcome