decagon roof support 9please help110

huangyhg

decagon roof support (please help!!)
the morning room is a decagon (10-sided) structure. each of the wall sections are 4'6-9/16" in length, 14'-0" across the flats, w/ a 9/12 roof slope, 40# snow load & 15# dead load. we want to frame the roof with 2x12's.
i am asking for is any input on the design and/or construction of a decagon structure without the use of ties (ie. ceiling joist collar ties) or a support post. the way i see it is that the top half of the rafters is the unsupported part of the roof system, as in using a load bearing ridge beam. so if that were the case, the only thrusting on the exterior walls would be the weight of the top half of the rafters. this area only equals 25% of the total roof load on a polygon roof system. the other 75% of the roof system would bear down on the exterior walls.
top half of rafter = 40 sq. ft.
live load = 40 psf
dead load = 15 psf
roof pitch = 9/12
dead load @ 9/12 pitch = 18.75 psf
live load = 40 psf
total roof load = 58.75 psf
40sq. ft. x 58.75 psf = 2,350#
2,350#/10 hip rafters = 235 per hip
each brace would have to resist 235# of roof weight.
is my thought process right? any input would be appreciated.
see link below.
for small gazebo's we have often used a galvanized steel band around the perimeter to resist the 'thrust' with stability against unbalanced loading provided by 'knee' braces at the columns.
you need to hire a structural engineer to design your roof.
uplift may be a concern as well.