Circular roof woes

I used a circular metal center ring designed for yurts.

It has 8 spots to bolt in rafters (I am using 8' 2x4).

The span at the end is quite long - roughly 72" (6'). This is causing the plywood sheathing to dip in the middle as shown in the picture.

How much of an issue is this over time? I didn't want to use thicker plywood ($$$) or braces from the rafters but I am not sure how else to make this a bit more sound.

Thanks for any suggestions. Many learning opportunities here...

My first thought is to add more rafters or supports of some kind, but you are trying to avoid that. Do you live in an area that gets snow? If there is no snow load, and you cover the plywood well with some sort of water proof roofing... do you really need to worry about the sag at all?

Matthew, I would begin by adding eight "headers" between the rafters, such that they follow/support the joint in the OSB roof deck. From those headers, to the eaves, I would add two (maybe three) additional rafters.
If two more are added, you will have approximately a 2' span at the eaves; if three, it would become more like 18" span (the only issue being just how long that header piece ends up being, to allow for a spacing that looks even).

Another thing that would help is if the rafters were held back from the edge by either 3/4" or 1-1/2" to allow for a fascia board. The fascia would be nailed into the ends of all the rafters, and help to support the roof edge.

There's a reason that rafters are normally a maximum of 2 ft apart - often 18". Sag is it!
I was writing while Kenneth was posting and I agree with him completely!
As the roof is currently, it is under engineered. I was also going to suggest that the current 2x4's be upgraded to 2x6 at least. The people who built our barn overhang used 2x4's and the first winter after we bought the property, a heavier than average snowfall damaged one whole corner of the building.

OSB sags considerably more than plywood, and I agree that you need a lot more rafters. As noted, a ring header supporting the OSB joint will keep that from differential sag. At least two and better three rafters from that point to the eaves should stiffen the roof enough. A fascia or at least a 2x4 subfascia around the eaves will give straight edges, Without all of those things the roof will sag more.
I also note that the original rafters are supported on the midpoints of the ring of the frame, which is a poor structural design for all 2x4 construction. (I think the 2x4 rafters will be okay once more are added, as each rafter will be supporting a small slice of roof.) Adding more rafters (and causing the OSB to bulge up rather than sag at the middles as it is) will relieve the load on the frame headers.

Both an edit to my earlier post, and regarding Glenn's observations:

The current design, with rafters only at the ridges and also supported in the centers of the beams (rather than over the posts) is both:
A.) Not as strong as having the roof load directly bearing on the posts.
B.) complicating the addition of more rafters, since the plane of the roof and the top of the beam (beams, actually) are not equidistant, due to their 22.5* angle to the roof edge (in plan view).

If instead, you unfasten the roof, and rotate it such that the ridge rafters do bear directly over the posts, then the additional rafters would simply rest on the beams. It is possible that you could, or might need a small bird's-mouth cut in the rafters at the beams, but likely could get away with simply resting them, especially if you reuse those framing connectors.

Thank you everyone for your thoughtful suggestions. I'm going to try to wrap my brain around it all and get to action!

Matthew Burke wrote:Thank you everyone for your thoughtful suggestions. I'm going to try to wrap my brain around it all and get to action!

And please post pictures of the changes you make, so we can all learn from them!