I am building a do-decagon ICF home.  12 sided.  4 : 12 pitch.  It is around 2600 square feet and has 12 - 5 1/2" x 18" glulam beams.  We are framing a 2" x 12" lattice roof structure on top of the beams. Beams will be exposed below.  The beams will be connected at the peak with a 6 foot engineered compression ring.   My question is how to insulate the roof?   After much research, I am thinking about using a closed cell spray insulation that will provide high insulation value and reduce any moisture problems.  Has anyone done anything like this?  Thoughts on practicality of this and effectiveness.  Cost is not a huge consideration although I do need it to be somewhat reasonable. My rough budget is around $1.00 per inch of foam per square foot.  I am also concerned about off gassing.  Thoughts?

Where are you? Insulation needs vary around the country, but 2" of anything doesn't work well in too many locations. Can you increase that depth?

So 2X12's in 12 sided rings across the top of the 18" gluelams?

If you dropped and framed in the ceiling a little lower than the bottom of the 2X12's to only leave say the bottom 1/2 or 2/3 of the beams exposed, that would leave you plenty of room to blow in loose fill(Leaving 1/2 the beam exposed would leave around 20" for an R70ish fill). I am thinking that is going to be way more cost effective than any foam you are going to be able to get in there, especially for 2600SF of roof area. It would also be pretty form fitting around the details of your 12 sided structure...

Even just filling the 2X12 cavities would get you around R40, not sure if that meets code where you are located(Oregon?), or would be appropriate for your specific altitude/climate...

Would loose fill have a moisture problem? I would think it would settle overtime and leave a non vented air gap at the top? I am in Oregon near Salem. Bob, the depth of the roof is 12 inches not 2. There is not an easy way to vent the roof. The rafters are perpendicular to the beams. We will be breaking ground soon. County just approved plans last week. Thanks for any input.

Dan, I'm not familiar how you "should" vent this type of roof. I certainly wouldn't put mush faith in the Plans Examiner who issued your building permit. I'd talk with a good architect who understands air flow and moisture issues.

That said, if you are thinking of hard foam, rather than blow in, etc try these folks:
www.universalconstructionfoam.com

You give them your drawing of the size, depth & length - they make it for you to fit. You don't have to cut, you just put the pre cut pieces into their places. They are jobbers and work with foam factories all over the country & can get the foam at a much better price than you could. They can also get the foam factories to cut to your spec, when the foam factories would not do it for you as a one off customer. I know they use to use a factory up by Tacoma for the Pacific NW, so freight isn't too bad, etc.

Hope this helps if you are thinking of a foam product - cut to fit.

Per the IRC, an unvented roof in climate zone 4C (that includes Salem OR) requires a minimum of R10 of the code-minimum R49 be air-impermeable (foam) applied directly to the underside of the roof deck, with the fiber insulation layer directly in contact with the air impermable foam See section R806.5:

http://codes.iccsafe.org/app/book/content/2015-I-Codes/2015%20IRC%20HTML/Chapter%208.html

Closed cell foam is one of the least "green" insulation materials there is, with a large amount of polymer per R, and usually blown with HFC245fa, a powerful greenhouse gas (1000x C02). Using any more than the minimum necessary for dew point control isn't down the world any favors.

Cutting rigid foam to fit on the interior is a risky proposition, even if you seal it in place with expanding foam. Any air leakage in any one of those cut'n'cobbled pieces can move significant amounts of moisture out to the roof deck. Ideally you would have the rigid insulation on the exterior side of the structural roof deck, which is far lower risk, provided you have met or exceeded the R10/R49 ratio of R-values.

Rigid foam comes in greener and less-green flavors too. XPS is blown with an HFC soup even more damaging than closed cell polyurethane, and as it escapes over a few decades it loses performance too. EPS has stable performance over decades and is blown with comparatively low impact pentane (7x CO2), as is polyisocyanurate.

A 2x12 cavity is 11.25" deep. If you filled it completely with damp sprayed (very low impact) cellulose it would give you about R42, so you would then need a minimum of R11 up top to meet IRC prescriptives for dew point control, and you'd have an R53 nominal center-cavity R value.

If you did it from the inside with 2"/R12 of closed cell foam on the underside of the roof deck you would have 9.25" for fiber insulation. With cellulose that would add R34, but you'd be just shy of the IRC's code min R49. If you filled it with damp-sprayed fiberglass (JM Spider) you would just make it on total R value, with a comfortable R-ratio relative to IRC prescriptives in section R806.5.

"Stabilized" damp sprayed cellulose as well as damp sprayed fiberglass do not have settling issue over time, due to the moisture activated adhesives used. But if you wanted certainty on that you could (for more money) "dense pack" it to prevent settling. For fiberglass you'd need a minimum of 1.8lbs per cubic foot density, for cellulose 3.2lbs .