Ridge beam scarf joint

[davyoungnz]

Hi,

I'd like to know if there's a feasible way to go about scarfing a ridge beam with a pentagonal cross-section. Is the method illustrated in the attached drawings acceptable? This scarf joint only occupies the rectangular portion of the total cross-section.  

Cheers,
David

[Jim_Rogers]

Without knowing the full roof system design, it's hard to say. But normally, I believe, that ridge beams don't have a lot of tension in the gable-to-gable direction. The scarf you have drawn is for a tension joint. A simple scarf may work.
Such as this:


 

Good luck with your project.

Jim Rogers

[davyoungnz]

Hi Jim,

Thanks for your reply - your contributions are invaluable and you have a diagram handy for every construction scenario!

I have a few follow-up questions, if you don't mind...

I've attached a drawing of the intended roof system - I believe it's called a principal rafter, common purlin roof. I imagine this roof system subjects the purlins/ridge beam to less tension than the principal purlin, common rafter system due to the extra weight of the rafters on the purlins/ridge beam in the latter system (given the same roof sheathing). Is this the case?

Could the wall plates be scarfed the way you illustrated as well or are they generally subject to greater tension than the ridge beam and therefore require a scarf joint designed to work under tension? 

If a beam of pentagonal cross-section were to be scarfed the way I illustrated, should the scarf joint be longer than four times its depth due to the extra (un-scarfed) height of the beam?   

Thanks again,
David
     

[Jim_Rogers]

It's hard to reply with any certain accurate answers. One factor would be snow loads (if any) and wind loads on the gable ends of the building.
There are lots of things to consider.
Normally, I don't consider plates or ridges of having much end-to-end tension, unless there is a big wind load. And that the frame is intended to be constructed in a "high wind" area along a coast.
If the frame is sheltered by trees and or other natural wind obstructions is another thing to consider. For example, if a frame is sitting on top of the hill with no trees around it; vs in a grove of trees in a valley.
Maybe someone else can offer some other advice.

Jim Rogers

[beenthere]

If in doubt about tension, can always lay in a routed-in and hidden cable to hold the joints in beams together in tension. 

[Don P]

I'm usually just trying to get the job done under the requirements. The building code says supported beam ends only. Beyond that it requires an engineer. I've not seen engineering for scarfs so the joints go over supports.

If you go here;
Design Standards | Pacific Lumber Inspection Bureau (plib.org)

Download the first publication, Typical Details. Scroll down to page 7 fig(s) 3.
The title is the way they are considering the design of that connection. They consider the stiffer beam, in this case the side of the joint closest to a support, to be the supporting member the one furthest from a support to be the supported member. I'm not saying that saddle is the only way simply that is the way I see that suspended set of beams working short of using an actual full length continuous beam, and they do grow trees that long, it might be worth it.

[davyoungnz]

Jim, thanks for the pointers - I'll certainly take that into consideration.

Thanks for the suggestion, beenthere. I assume the cable would span the joint and be bolted into the beam either side of the joint - is this the case?

Thanks, Don - I can't argue with the practicality of that solution; however, I'm trying to limit my use metal fasteners for no other reason than the alluring charm of an all-wood solution. For the wall-plate, a full length continuous beam may well be the go, as you've mentioned...

My main concern with scarf joints in loaded beams is their resistance to vertical bending; there seem to be a number of scarf joints, notably the wedged, stop-splayed, undersquinted and tabled scarf joint, that perform well under tension and in vertical shear, but not so well in vertically applied bending, the resistance to which is critical in load-supporting members like wall-plates.

I came across a study titled Testing Scarf Joints in Bending (here's the link: https://ftet.com/sites/default/files/2018-07/TF98JointTesting.pdf). In it, the authors test a number of scarfed beams in vertical bending to destruction. They concluded that, on average, under vertical bending scarfed beams have the capacity to support somewhere in the vicinity of 30% of the load of an equivalent size solid beam (given the same species of wood, of course).

I chanced upon a scarf joint that's very similar to the wedged, stop-splayed, undersquinted and tabled scarf joint, but I suspect has significantly more resistance to vertical bending. I've attached a diagram of the scarf joint below (here's a link to the original source: https://www.medieval-carpentry.org.uk/S_to_Z.html). Has anyone used this joint? It would be interesting to see it tested to destruction as above, but at the same time a shame to see the invested craftsmanship destroyed!

On related but separate note, I've been contemplating the optimal position for a scarf joint in a loaded beam. Given that the supporting posts are knee-braced, moment/shear analysis suggests that the least bending and shear stress is directly above a post between two knee braces. I've attached a diagram in which I exaggerated the beam deflection to illustrate this. I believe that the optimal location for a scarf joint is between the two points of inflection (within the span indicated in red in the diagram). Does anyone agree with this, or have I gone gravely wrong somewhere...?

Edit:

I went gravely wrong above...

The attached beam deflection pattern (a big sag before the first knee brace and after the second knee brace; crowning above the knee braces and a slight dip above the post) only applies to a specific case, in which the posts are spaced four metres apart and the tops of the knee braces are one metre from the top of their corresponding post (horizontal centre-to-centre distance).  

I have convinced myself that there's no "one size fits all" when determining the optimal position for a scarf joint in a loaded beam. It's a case-by-case basis problem that depends on two things:

• post spacing
• knee brace spacing

Or to put it succinctly, the optimal position for a scarf joint in a loaded beam is a function of the spacing between the supports.

Here's a link to a free beam calculator that allows you to calculate the shear/moment/deflection in a beam and thereby determine the optimal position for a scarf joint - https://clearcalcs.com/freetools/beam-analysis/au

This is my thinking...until someone convinces me otherwise...

Cheers,
David

[davyoungnz]

I realise I've taken this thread off-topic, but just thought I'd share my closing thoughts on beam analysis - I don't think it's as useful as I first thought... 

I imagine knee braces have some 'give' in them (some more so than others depending on design) and therefore cannot be approximated by a pinned support like a post can. Modelling knee braces as pinned supports assumes one could replace them with posts without significantly changing the deflection/moment/shear of the beam in question - this seems intuitively wrong. 

I defer to those with practical experience on this matter (e.g., the posters that contributed earlier). Sorry for the ramble...

On another note, does anyone have any thoughts on the tenoned scarf joint I referenced in my last post? I understand it'd take more time to craft than a typical scarf joint, but in an application where resistance to tension, torsion and, most critically, vertical bending are important, might its benefit not outweigh this (given one has the skill/time/inclination to craft it)?   

Cheers,
David 

[GRadice]

You might want to invest in a copy of Chris Hall's monograph on Japanese splice joints:

https://thecarpentryway.blog/2011/06/tajcd-volume-iii-now-complete/

He doesn't go much into the engineering aspects of them but he does describe why you might want to choose one over another.

[Brad_bb]

I'm less experienced than Jim or Don, but I have a few questions/thoughts.



 

You're calling your roof system a principle rafter system, but my understanding is that in a principle rafter system, you'd have big principle rafters in your bents similar to the size of your posts or a bit bigger?  In the sketch you show little bitty rafters(B).  Additionally, it looks like you have separate pieces of your post below and above the tie beam.  I would want that to be one single stick for simplicity and strength.  Additionally you have and angle cut on top of that post(B) for the rafter as well as on the ridge beam(C).  If you do common rafters, you can eliminate those cuts and leave them square. You can notch/birdsmouth the rafters.
Lastly, we don't see another side or 3d view of the roof.  With large principle rafters you have smaller girts joining the principle rafters.   I'm assuming you're design is like that?  I'm thinking about whether it would be simpler doing common rafters and notching them versus the joinery of the principle system here?  You'd need top plates for common rafters to sit on.  I'm assuming you are just at the sketching out phase so maybe some things to think about.

Is this a house or an outbuilding?  If a house, common rafters may make it easier to install a skylight if you want to.  It also lends itself to horizontal roof decking(T&G). 

[GRadice]

Here is a version of the Japanese kanawa tsugi that might work. This doesn't show the vertical wedge that locks it together in the center. From Chris Hall's monograph.

 There are plenty of youtube videos that show how to make it.

[davyoungnz]

Gary, thanks for directing me to that resource - wow, 200+ pages dedicated to the splice/scarf joint!

I didn't know about the kanawa tsugi joint. I see it has been designed to resist tension, shear, torsion and vertical bending like the one I referenced above, but with the (potential) advantage of being easier to construct - very interesting.

Hi Brad_bb, thanks a lot for taking the time to comment on my sketch. I didn't provide enough detail - sorry! I've attached another sketch that'll clarify things, hopefully. I've drawn inspiration from this plan - https://timberframehq.com/24x36-king-post-truss-outbuilding/.

The aim is twofold - to construct a small, single room, livable cabin and to exercise my (limited) skills in joinery. I'm located in the North of New Zealand and have a block of land populated by numerous totara trees - it's this species I intend to use for the construction of the cabin. Here's some information on totara - https://www.heartlandtimbers.nz/totara-specifications-and-finishes/.

Cheers,
David

[Brad_bb]

Hi Brad_bb, thanks a lot for taking the time to comment on my sketch. I didn't provide enough detail - sorry! I've attached another sketch that'll clarify things, hopefully. I've drawn inspiration from this plan - https://timberframehq.com/24x36-king-post-truss-outbuilding/.

That plan is as I described.  There's no angle cut on the top plates or the ridge beam.  Not sure why you're trying to cut the angles on those.  Just seems to unnecessarily complicate.  You just notch your rafters to sit on the top plate and the ridge beam.

[davyoungnz]

Hi Brad,

The part you labelled as 'B' in my drawing is intended to represent vertical roof sheathing nailed/screwed into the wall-plate/purlins/ridge beam, not a rafter. I realise now I shouldn't have included it in the drawing as it doesn't constitute a part of the framing.

Cheers,
David