Eyebrow & Barrel Roof Dormer Structural Design

I received a set of plans to bid on for the roof framing only, that has 18 barrel roofs on the 7600 SQ FT house. The architect did a great job of designing the house, however the structural design for the barrel roofs with rolled eaves was missing details on how to support the rolled eaves.I think the main reason we don't see a lot of eyebrow dormers in California is due to the lack of structural engineering for eyebrow dormers. I'm hoping the following drawings will correct that problem. 

Typical structural design on the plans for the barrel roof with rolled eaves.

This is the shape of the barrel roof with rolled eaves.

This is the structural design I came up with to support the barrel vault roofs with rolled eaves. The internal ceiling will be a barrel vault with an elliptical valley and the exterior roof will be an eyebrow dormer with zero pitch.

For the bigger barrel roofs on this house this is the structural design I came up with to support the rolled eaves.

I've left some of the details out of these drawings for clarity. (Extra beams for the elliptical valley support) 

One of the things on this set of plans that really impressed me was the 135° eave angle with a 8:12 pitch on one side of the valley and an 10:12 pitch on the other side of the valley. If this was an 90° eave angle it wouldn't be a big deal. I can figure out  the plan angles for this 135° eave angle, but I'm wondering how the architect knew how to draw it out correctly? 

If you don't know the math for an eyebrow roof dormer, then contact Brent Green at DigCon and he'll make it for you.