Collar ties necessary on gazebo?

A client has asked me to rebuild a gazebo. The original gazebo had some interesting load solutions, several were overloaded. Diameter is 19′, hexagonal shaped, roof pitch will be 3 or 4″ in 12. There will be light roof loading, resawn redwood 1x3s and 1x4s laid up horizontally (not a watertight roof). I will use either 4×4 or 4×6 posts with 4×6 beams on the perimeter connecting the posts, #1- 2×6 main rafters and 2×6 jack rafters to infill. I look at lots of gazebos, some have bottom chords/collar ties, some do not. What determines their use, or lack thereof? I understand the outward thrust issue. I built prefabbed yurts for a while; we drilled the outer ends of all the rafters and tightened a cable through them all to prevent outward motion. It seems so much cleaner to not busy up the inside with all the collar ties.
Replies
If you properly construct the outer band (eg, with a cable such as you describe, or at least heavily-connected joints) then you don't, in general, need collar ties (for a roughly circular gazebo). However, depending on the rest of the structure, you do need something to keep the outer band from deforming into an oval or what-have-you. Under ideal circumstances the rafters (if tightly tied in the center) will do this, but sometimes you may need a sort of horizontal knee brace, or some cross-ties.
Any time you have rafters you have outward thrust on the walls or beams that they're stting on. The amount of force you have depends on things like the pitch of the rafters and the loads you're dealing with.
No way can anyone even begin to answer your question without that information. And even if we do have that information, nothing that is said here will matter much. (Except for its educational value) You can't very well tell a building inspector that someone on the internet told you that you didn't need collar ties.
As has been stated/suggested, you can do it without collar ties/clg.jst. You can use a cable or steel band that you could conceal with a trim piece along with top/tie plates large enough to resist the lateral thrust between the corners. Or as I have done, you could use a restraining ring made from steel angles that has been designed to do both.
In any case, as has also been advised, get some one locally (ie an engineer type person) to do the calc's and design. It's not all that complicted, but you don't want the liability should it fail and injure someone. It could be a life altering event for everyone.
I am thinking that - like a Yurt - if you do the joinery on the surronding top plate beams or use a cable surrond, you do not need collar ties/raftrer ties
Thanks for the replies
Great to get replies. I have answered some posts, but never posted a question. I will present pitch (3 in 12 or 4 in 12) and load specifics to my engineer friend and see what his recommendation is. This is a light structure - no snow loads and not a weatherproof roof.
It is a low slope...
and 19' is big. Couple of principles involved in gazebos, and for the smaller units they don't really need bracing or collar ties because the triangular shape of the sheathed roof sections act as their own bracing. That said... 19' is a big span, and factoring in the low slope I would definitely want to sturdy things up. I'd try to pretty things up by making the rafters into curved bottom chord hammer trusses with a hole up to the cuppola...
As for leaving the roof partially open... I vote for permanence...
L