Timber Framers Guild Forums Tools Timber Engineering Low pitch rafter question

Hello, I own a small Timber framing company in Maine and I am currently cutting a frame which will be our new shop. The Shop is 40x80' and 16'posted. This project is a hybrid since it has conventional roof trusses 24" O.C.There is also an "ELL" that is to be 20'x20'. This small section is posted at 10' and I would like to use 6x6 hemlock rafters 10'on center(principal) and 3x6 purlins.I am planing on using a 3x6 half dovetail collar tie.

My question is will my rafters sag with such a low pitch 5/12? I am used to framing 10/12 and 12/12s usually and when I cut my first birds mouth yesterday it seeemed like there would be alot of down pressure. Any Suggestions would be greatly appreciated.

Keep in mind this is a response from a non-PE, mechanical engineer and timber frame amateur.

Making the following assumptions:
- rafters are only bearing on a plate and ridge beam (opposing rafters without a structrual ridge beam makes this condition worse)
- you have 40lb/ft^2 live load and 15lb/ft^2 dead load
- the hemlock is green when you raise it
- 5/12 pitch
- There is little joinery in the rafters (tusk tenon purlin joints are ok, but half lap or housed purlins and your collar tie would probably force the timber size to be increased)

You'd need 6x9 #1 hemlock rafters. The sag would be about 3/8".

If you stuck with a 6x6 #1 hemlock the sag would be 1-1/4" and the timber would fail or be permenantly deformed if/when a maximum load condition occurs.