Is a roundwood reciprocal roof structure strong enough for a living roof?

My plan is to build several smaller more or less circular buildings. I would use poles to erect the main structure:
-posts that are in the ground
-a ring beam on top of these posts
-rafters (supported by the ring beam) that make a reciprocal roof
Most buildings would be 6m diameter (6 posts; 28 square meters), and 1 building would be 12m diameter (12 posts; 113 square meters).
I would like to have a living roof with wildflowers to create a bee-friendly habitat. This could weigh up to 250 kg/m2.

1: Is this possible for these diameters, or should I keep my roofs as light weight as possible?
2: How do I calculate the diameters of the different posts, ring beam poles, rafters?
I believe it's better/easier to have many smaller rafters than few bigger ones, but I'm not sure how many I should use of which diameter?

If you have experience with (round)wood building, or have an engineering background, could you share your thoughts please?
Thanks for the help!

Hi Philippe, welcome to permies!

I am not the engineer you're looking for(or any kind of engineer, for that matter)...

But, if he happens along, he'll definitely need to know about snow load, if that's a thing where you are?


I would expect to use more than 6 poles for a 6M diameter building; that's nearly 19M circumference, so your poles would be quite widely spaced, meaning your ring beams would need to be quite large... (Of course the distance isn't just the circumference divided up, but it gives a rough idea.)

What species of wood are available to you?

What equipment is available to you?

Dillon Nichols wrote:Hi Philippe, welcome to permies!

I am not the engineer you're looking for(or any kind of engineer, for that matter)...

But, if he happens along, he'll definitely need to know about snow load, if that's a thing where you are?


I would expect to use more than 6 poles for a 6M diameter building; that's nearly 19M circumference, so your poles would be quite widely spaced, meaning your ring beams would need to be quite large... (Of course the distance isn't just the circumference divided up, but it gives a rough idea.)

What species of wood are available to you?

What equipment is available to you?

Hi Dillon, thanks for your reply!
As for now, I am doing as much preparatory work as possible, but I still have to buy my piece of land and all of the necessary equipment. So I do not know for sure which types of wood will be available to me.
I will live in Portugal, so snow load is not really relevant.

That is big. You probably could make it strong enough, but it would not be the best use of resources.

R Scott wrote:That is big. You probably could make it strong enough, but it would not be the best use of resources.

How do you mean, best use of resources? Could you recommend an alternative?

Getting that big with that large of a span between posts probably means very large roundwood. So large it starts having problems of supporting its own weight. It takes way more total lumber to support those large spans. And a crane to erect them.

More perimeter posts and rafters to distribute the load, using lightweight potting soil mix to reduce the load, moving the posts in and cantilever the outer portion of the roof.

There are lots of ideas to think about. But until you get the land and know the resources available, impossible to give a right answer.

R Scott wrote:Getting that big with that large of a span between posts probably means very large roundwood. So large it starts having problems of supporting its own weight. It takes way more total lumber to support those large spans. And a crane to erect them.

More perimeter posts and rafters to distribute the load, using lightweight potting soil mix to reduce the load, moving the posts in and cantilever the outer portion of the roof.

There are lots of ideas to think about. But until you get the land and know the resources available, impossible to give a right answer.

Thanks Scott!

Could you explain the 'cantilever' principle? Does this mean that I use the weight on the peripheral portion of the rafters to counterbalance the weight on the inside portion? I've been thinking about that, and I'm not sure if that helps... The 'inside' weight will still be the same, and the problem is inherently that the rafters themselves can't handle that... Or am I seeing this wrong?

A few thoughts:

I think the 6m diameter is doable with some engineering calculations. The 12m sounds very large though. I can't imagine each rafter spanning 6m (about 20') with that kind of load on it. One thing that can help both structures, especially the large one, is if you can build a second ring inside the building to support the rafters mid-span. I don't know if that could work based on the interior spaces you have planned.

I know some of the math involved in sizing beams. The formulas apply to sawn lumber, and while I don't know how they translate to roundwood, the general principles probably hold true. One is that the strength of a rafter is proportional to the width, but proportional to the square of the depth. That is why rafters and joists are placed on edge. So when rafters get bigger (well, specifically deeper), they get exponentially stronger. I think your idea of many smaller rafters being better than fewer larger ones is not true in this case. One big rafter might be twice as strong as two small ones. Again, not sure how this relates with round wood. With boards, you can add a lot of depth to the rafter while adding hardly anything to the dead load of the roof. If you want to double the diameter of a round rafter, the weight of it is quadrupled.

I think roundwood can be a great use of smaller diameter and lower quality trees. But in some cases, I think you may get more "bang for your buck" with sawn lumber, and I don't just mean in the financial sense. (Now that I think of it, someone should invent a way of growing trees with wide, flat trunks instead of round. Why not? They can grow square watermelons!)

Also, the deflection of a beam is proportional to the cube of the span. This is why longer spans get increasingly difficult to support very quickly. All things equal, a 6m rafter will sag 8 times more than a 3m rafter. Here is where the mid-span support will pay dividends for you.

One thing to keep in mind for a reciprocal frame, or any round building with "radial" rafters, is that 3/4 of the weight is on the outer half of the rafters. It is not a uniform load. That might affect the size of rafters and the placement of mid-span support.

Ben de Leiris wrote:A few thoughts:

I think the 6m diameter is doable with some engineering calculations. The 12m sounds very large though. I can't imagine each rafter spanning 6m (about 20') with that kind of load on it. One thing that can help both structures, especially the large one, is if you can build a second ring inside the building to support the rafters mid-span. I don't know if that could work based on the interior spaces you have planned.

I know some of the math involved in sizing beams. The formulas apply to sawn lumber, and while I don't know how they translate to roundwood, the general principles probably hold true. One is that the strength of a rafter is proportional to the width, but proportional to the square of the depth. That is why rafters and joists are placed on edge. So when rafters get bigger (well, specifically deeper), they get exponentially stronger. I think your idea of many smaller rafters being better than fewer larger ones is not true in this case. One big rafter might be twice as strong as two small ones. Again, not sure how this relates with round wood. With boards, you can add a lot of depth to the rafter while adding hardly anything to the dead load of the roof. If you want to double the diameter of a round rafter, the weight of it is quadrupled.

I think roundwood can be a great use of smaller diameter and lower quality trees. But in some cases, I think you may get more "bang for your buck" with sawn lumber, and I don't just mean in the financial sense. (Now that I think of it, someone should invent a way of growing trees with wide, flat trunks instead of round. Why not? They can grow square watermelons!)

Also, the deflection of a beam is proportional to the cube of the span. This is why longer spans get increasingly difficult to support very quickly. All things equal, a 6m rafter will sag 8 times more than a 3m rafter. Here is where the mid-span support will pay dividends for you.

One thing to keep in mind for a reciprocal frame, or any round building with "radial" rafters, is that 3/4 of the weight is on the outer half of the rafters. It is not a uniform load. That might affect the size of rafters and the placement of mid-span support.

Very interesting stuff! Thanks Ben!
Yesterday, I've been doing some research on types of forces and how to calculate them. Definitely very useful to understand these things!
Things that I'm considering right now are:
-downscaling
-using sawn lumber instead of roundwood
-having extra supports somewhere under the rafters. I've heard of this idea before (by Tony Wrench), but I had the impression that he suggested to not necessarily put one under each rafter. Not sure how useful that would be... Also not sure how we would incorporate these from a practical viewpoint. Normally, you construct all the rafters on top of a Charlie stick. When you remove this one, everything 'falls into place'. How to correctly measure and put the extra post on the right place, so that it supports but not bulges

Maybe just assemble everything as usual. Then, after removing the Charlie stick, put your secondary posts in. It would probably be a certain amount of trial and error, but I'm thinking to make it easier, you could intentionally make them slightly loose. Like 1/8", or a couple mm, just enough to keep you from having to do any real precise joinery. Then when the roof is loaded down the rafters would bend and settle onto the posts. You'd just have to make sure the secondary posts were well seated before hand so they don't settle themselves. Or you could just lean the post in or out slightly until it contacts the rafter solidly, as long as you don't mind it a couple degrees out of plumb.

I think the mid-span support is fairly easy to approximate. Build the system on the charlie stick and let it settle to its equilibrium position before any other load is put on it, then set the mid-span posts to fit. When the roof sheathing goes on, the additional dead load will cause the mid-span posts to start to take this load, and soil or live loads will progressively equalize the load distribution (assuming there is a small amount of flexibility in the rafters). Wood does creep somewhat over the long term, so loads will tend to equalize assuming the distribution is calculated to be theoretically uniform.

Cantilevering the roof edges for large overhangs will definitely reduce the bending moment near the center of the structure, at the cost of considerably increasing the moment at the outer posts. Since roundwood is not uniform diameter, the larger ends will be significantly stronger in bending and shear. You will have to decide based on load calculations whether the butts of the rafters should be in or out. I presume there is standard practice for this.

Having mid-span supports would make me a lot more comfortable with a reciprocal roof for the long term, as my understanding is that all the rafters depend on each other. This means that if any one of them breaks, the entire roof will collapse. Catastrophic failure mode is not something I like to contemplate; I would prefer a system that can localize a failure and give time for repair.

Ben de Leiris wrote:I can't imagine each rafter spanning 6m (about 20') with that kind of load on it. One thing that can help both structures, especially the large one, is if you can build a second ring inside the building to support the rafters mid-span. I don't know if that could work based on the interior spaces you have planned.

Also, the deflection of a beam is proportional to the cube of the span. This is why longer spans get increasingly difficult to support very quickly. All things equal, a 6m rafter will sag 8 times more than a 3m rafter. Here is where the mid-span support will pay dividends for you.

One thing to keep in mind for a reciprocal frame, or any round building with "radial" rafters, is that 3/4 of the weight is on the outer half of the rafters. It is not a uniform load. That might affect the size of rafters and the placement of mid-span support.

i like that idea, of the inner ring and the outer ring to support the rafters.
one idea is, especially since you say you want to build multiple "pods" - build different segments around a central, partially roofed but somewhat open courtyard area. or perhaps a greenhouse/atrium like space in the center, with the different one or two room structures surrounding it.

One thing about roundwood strength calculations: as it has all its fibers continuous, it will be stronger than a sawn timber of precisely the same shape. I expect there are figures somewhere for this, but if you figure from standard sawn lumber calculations, you will at least have a safety factor automatically inserted.

Glenn Herbert wrote:One thing about roundwood strength calculations: as it has all its fibers continuous, it will be stronger than a sawn timber of precisely the same shape. I expect there are figures somewhere for this, but if you figure from standard sawn lumber calculations, you will at least have a safety factor automatically inserted.

Ok. Thanks Glenn!
I also found this forum on LinkedIn (architecture for humanity), where they apparently regularly discuss reciprocal structure questions:
https://www.linkedin.com/groups/142881/profile

Hey there, would be curious to hear how this turned out?   I have a oval green house structure I need a roof for that has a diameter of about 30x25ft, and thought a reciprocal roof would be a great/natural choice!  I just failed to realize the span required and that 16ft length poles wouldnt do it.  Then I have to consider snow load etc.  So instead of winding it I have to get back to basics an ensure my ducks are in order.  Would be great to hear more about this project.  Regards

Some people guess and it works,
some people guess and it does not work!
I am a Civil Engineer and this sort of stuff should be straight forward to me, but its not.
Experience counts a lot.

Try and find somebody who has done something similar to your plan.
Otherwise use post and beam construction which is simple and failsafe.

That’s great advice and I totally agree.  Just a matter of finding someone who specializes. I already have the poles and the fairly large span is what complicates things. Not locked into the reciprocal roof.  Just need something safe, looks good and reasonable cost.  

For a greenhouse, I can't imagine that a totally clear span is critical. Adding one post in the center would make the structure very simple.