Mortise shear when in compression

I'm building a small treehouse (really, a tree platform) out of locust. Platform has eight beams, each extending 5 feet radially from tree. Each beam is supported by a strut; see attached figure: [img]http://pxrox.tumblr.com/[/img]

Beam & strut each fit into blocks that are lag-bolted to the tree. Beams have a dovetail mortise/tenon (no peg) to hold them into blocks, and will be tied together horizontally with screwed-in 2x6 flooring that goes all around the tree but extends only 4 feet out (last foot of beam will stick out, for "looks"). Design load (dead + live + snow) on each beam/strut is ~1,200 lbf.

Strut fits into the beam 3 feet out from tree. Angled at 45 degrees, the strut will exert ~1,000 lbf horizontally (outward) and ~1,000 lbf vertically (upward) on the beam (strut thus takes most of the weight load; resulting moments are neutralized by the blocks above & below the beam).

Strut has an oblique tenon (no peg; see figure, in red) to fit into the beam mortise. The mortise bearing shoulder is angled at 22.5 degrees, to take the toe of the oblique tenon. The mortise has ~1 x 5 inches of shear plane to resist the horizontal force. Locust has a max. shear strength parallel to the grain of ~2,500 psi, giving (in theory) the ability to resist ~12,500 lbf of shear. Seems like enough.

But, I am concerned about possible mortise shear-out, in part because a book on timber engineering (Construction en bois: Matériau, technologie et dimensionnement, by Julius Natterer, Jean Luc Sandoz, Martial Rey) suggested 30 (!) shear-resisting nails in the tie of an analogous rafter/tie design (admittedly with ~8x higher loads; see this link: Tenon Example ).

My (aesthetic) goal is minimal hardware...trying to do it the old-fashioned way! Should I be worried?

David

I would not be concerned with the joint where the brace meets the tie. More concern would be the beam to tree.

Glad to hear that one of two joints may be good! Would be interested in knowing more of your concerns on the dovetail. Here are some details:

The (irregular) beams are roughly triangular is cross-section, ~4 in. wide across the (slightly crowned) top and ~4 in. deep. The dovetail tenons have a nearly horizontal base that gently slopes upward (angle ~20 degr.) from bottom of beam (AT tree) toward the beam center (as you move away from the tree). Max. depth of cutout always less than one-fourth of beam depth; tenon length is fixed by the supporting block thickness---which holds the intricately shaped mortise---namely 2.5 in. The shear plane thus ends up being ~2.5 x 1.25 in., i.e. ~3 sq. in., giving ~7,000 lbf calc. max. shear load (which is 7x the max. anticipated load).

I plan to relieve the stress in the angular joint at the (non-tree, i.e. outward from tree) end of the tenon by cutting a gentle curve back down to the bottom of the beam. Probably ~3 in. long elliptical curve (not looking forward to this, as it will take a coping saw, and locust is really hard!).

(I had considered a dovetail with vertical sloping sides, but that would mean flipping the beams upside down, putting the broad face on the bottom. Not sure how this would affect beam bending, if at all, but it would give me no good surface on which to attach the decking.)

One other consideration makes me worry (much) less about the shear in the dovetail (which is, after all, going to be in tension to ~1000 lbf): The decking will form a screwed-into-all-beams continuous ring all around the tree. In other words, the deck itself will act to balance the tension loads on one side by the tension on the other, all the way around.

Thoughts?

David

Borhani, there is a great difference between the material strength values you might find on Woodweb or other sources and the approved design values for construction you will find in the National Design Specification {NDS}. For example, in table 4A, base design values for visually graded lumber, shear parallel to grain in red oak is 85 psi and white oak is 110 psi. No value stated for locust. On Woodweb red oak is 1780 psi and white oak is 2000 psi. My guess is that you should use a much lower design thresshold such as the value for white oak but be aware that most every wood species in the NDS is under 100 psi for shear parallel to grain.

Thanks, important info. I got my values from Mechanical Properties of Wood (Ch. 4) by David W. Green, Jerrold E. Winandy, and David E. Kretschmann. Why the difference from NDS?

I should add that I referenced the 1991 edition of NDS.

I cannot strictly account for difference between the material lab tests to failure and approved design values but consider this: the lab test evaluates what the sample can withstand right now under a set of specific conditions and design values give authoritative assurance on performance without degrade over decades under much wider conditions. In a way the tests tell us that wood is strong and design values tell us that time is the leveler.

After much reading, I have to admit I still don't understand the discrepancy. Perhaps we're referring to different shear values, or applying them to different (and perhaps inappropriate) situations?

From what I can tell, "Fv" = the NDS "Design Value for Shear Parallel to Grain"; Fv seems to be used to determine whether the "actual" (parallel, horizontal) shear stress within a horizontal beam is allowable, or not. You would think that Fv should equal the "Shear Parallel to Grain", yet Fv is about 10- or 20-fold lower, on the order of 100 psi.

By contrast, the tabulated values for "Shear Parallel to Grain", for Black Locust, are 1,760 psi [green] and 2,480 psi [12% moisture content]. These values do not vary more than about 2- or 3-fold, with locust being one of the highest, and some cedars & firs being the lowest, ~600 psi.

The *actual* beam shear stress, "fv", is calculated according to a standard formula. In a rectangular beam, for instance, fv is based on the (vertical) shear force P (e.g., half the load if the beam is supported only at the ends) and the beam breadth & height, b & h: fv = 3P/2bh. fv less than Fv is OK; fv greater than > Fv is bad, signalling possible failure.

I have not been able to find exactly how the low NDS Design Fv values are determined or estimated. One document suggested that Fv = 40 + 266*G, where G is the wood specific gravity. Another, from the USDA Forest Service, says:
(My locust has essentially no checking; it's solid like a rock.)

Does anyone know how the Design Fv is really determined, or why it is so much lower than the measured (literally, by shearing wood blocks) Shear Parallel to Grain value?

Or are Roger and I just mixing apples & oranges, and the shear I originally was worried about (e.g., a mortise giving way) is not the same shear as what the NDS is talking about (because it's assuming worst-case-scenario beams)?

Thanks,
David

Yes, we might be mixing apples and oranges, how about a bunch of bananas? The first banana is I referred to the 1991 NDS values, unfortunately values for shear parallel to grain have been doubled since 1991. Link to 2005 NDS Supplement

http://www.awc.org/pdf/2005-NDS-Supplement.pdf

Sorry about that. Still leaves an order of magnatude of difference between values established in the lab and the approved design values.

For clarity, my first post related to the shear plane calc in your second post. It is established practice to use NDS Fv value times shear plane area to evaluate joint strength for dovetails.

Awesome, thanks Roger. Locust seems much like Oak or Maple in many respects, so an Fv value of ~200 psi seems reasonable to use.

The joint I described in my second post is indeed much like a dovetail. Based on the above Fv value, I do need the restraining effect of the decking---the dovetail itself could only hold ~600 lbf (about half of what is needed).

The mortise in my first post has a shear area of ~5 sq. in. if I include only the *bottom* plane of the mortise in the area calculation. Including the sides as well gets me up to ~12 sq. in., for ~2400 lbf, about twice what I need. Is it OK to include bottom & sides of a mortise in the shear area calculation?

Thanks again for your valuable input!
David

David, I honestly am confused by your first and last post. When framers speak of shear planes, we are concerned with the supporting grain beyond the joint, aka relish. When joints apply force close to and towards the beams end and when tenons are expected to be in tension, then end distance and relish become a matter of concern. So with a strut close to the end, we take tenon depth times end distance times NDS Fv value times 2 equals the force the joint can safely resolve. We multiply by 2 because there will be two shear planes of equal area. For pegs we take center line of peg to end distance times tenon thickness times Fv times number of pegs times 2 [two shear planes per peg} equals force limit. In the case of your strut to beam joint, you have ample end distance.

In the case of the French manual, the drawing seems to me to be of a major rafter landing with a scant tenon with a nailed cleat supporting the load, not applicable to your case.

Describing a joint with word is at times tricky to put out and receive. How about drawings? Hard to misinterpret a simple sketch. The first picture was perfect.

A picture IS worth a thousand words! [img]http://pxrox.tumblr.com/[/img]

From top to bottom, pics of the strut mortise, the "dovetail" tenon and its mortised support block (assembled & disassembled), and my home "test" of shear Fv (described in the pics). I get an "Fv at failure" of ~500 psi, and my test specimen held at an experimental Fv of 200 psi, so 200 psi (tested rather amateurishly on the actual wood!) seems safe.

Roger, we're on the same page RE: relish. In the picture of the dovetail, the shear plane I'm referring to is horizontal, from the base of the triangular face (away from the camera; this is where the stress-relieving curved cut needs to go) back to the end of the beam (outlined in red) --- about 1.25 inches across the breadth of the beam by 2.5 inches along its length (the block is 2.5" thick). ~3.125 sq. in * 200 psi = ~600 lbf. Not quite what I need (~1200 lbf), but as I mentioned before, the decking should take quite a bit of the tension load (please let me know if you think not!).

For the dovetail, I can't multiply by 2, as you said, due to the unusual geometry.

For the strut mortise/tenon, I can multiply by 2. But, why are there considered to be only two shear planes in a mortise? I can see why a peg has two, but doesn't a mortise have *three* defining shear planes---both sides and the bottom?

David

I take it you will not be using any fastener at the dove tail located at the tree trunk? Question would that hold with out the decking, No. So you will be relying on the decking. I am trying to picture that.

I wasn't planning on fasteners between beam and tree...just the dovetail, the mortised block below, and the block above (to counteract the moment). New sketch, showing a top view, to illustrate how I think the deck will serve to counterbalance the outward tensions in the beams, and hold things together. [img]http://pxrox.tumblr.com/[/img]

I could add a vertical peg or a lag bolt linking the beam to the support block. Limited opportunities for placement: center of hole would be about 1" from end of beam. Calculation with a 1/4" lag bolt gives what seems like an absurdly small load capacity:
AWC Connection Calculator
ASD lateral loading, lag screw, single shear; mixed oak of 2.5" thickness for both members; main loaded at 90, side at 0 degrees to grain; 1/4 x 4" lag bolt gives 140 lbs. Value doesn't change when both angles are 90 degrees, which seems very wrong...

Thoughts? (Wrong use of the calculator?)

Calculation based on shear out of a bolt gives about: 2 (shear planes) x 1" (from end) x 2.5" (deep) x 200 psi (Fv) = 1,000 lbs. That would get me where I need to be.

How would a peg do? I haven't paid much attention to how big a peg should be, but 3/4 seems like a minimum size, and there seems (intuitively) not enough relish---in the 2.5" total width I have to work with---to take a peg.

I would be tempted to drill a hole through the beams, 10-12 inches from the tree, thread a cable and pull it taunt via some manner. Perhaps even better would be far out at the ends or in a notch at the end of the beam. A tension band?

That would be pretty straightforward, and it certainly wouldn't hurt, but I wonder if its overkill.

The deck will be Doug Fir 2x10's. Screwing a 2x10 to beams with three #10 screws at each end (>1.5" of relish) gives ~500 lbs of lateral (tension) load. There will be five rows of 2x10's, laid side by side, going out from tree...giving something like a 2,500 tension load.

Do you think that such a properly-screwed-on decking will itself serve as the tension band?

Nothing wrong with a little over kill.

Right you are!

I recommend overkill. Something American architects and engineers today don't value as highly as they should.

Overkill in my opinion is the difference between a house that will stand for 100 years and one that can stand for 500 years.
We can engineer it to the requirements of the materials and conditions as they exist now, but conditions change, materials degrade.

Especially in a situation like I see here, tying into a live tree and such, conditions will change significantly over time.

Will this have a roof?

No roof planned, just deck & railing. Snow loads calculated based on a worst case (flat, exposed roof) scenario. A sloped roof would perhaps double dead load (to 20 lb/sq. ft), but it might significantly lower the snow load, for no net change (but would need to check, if it ever comes to that). By the way, the snow load is almost half of my total calculated load.

Decking + tension cable sounds like a good plan (even though the wood won't last 500 years!). I don't want this to fall down.

Gave some thought today on how to assemble this thing...a bit tricky. I think two temporary guy ropes/wires from ~3 feet out on each beam back to the tree, ~3' above the planned attachment point and off to either side, will let the beam dangle in place, allowing "easy" adjustment of horizontal (level) and lateral (perpendicular to tree) positioning. I can then mark, drill, and bolt in the beam support block, fit the strut, mark/drill/bolt it's block, etc. Also plan to tack on a temporary 2x4 between the beams to give lateral stability, prior to proper decking installation.

Fun project, but it is taking some serious time & work! Thanks for all the great ideas and suggestions.

I was thinking of a different direction for the frame system.
One that wraps around the tree and gives some space for the tree to grow in diameter.

Just a thought.

Rooster

http://s453.photobucket.com/albums/qq254/crwtimberframe/?action=view&current=Treehousedeck02.jpg

http://s453.photobucket.com/albums/qq254/crwtimberframe/?action=view&current=Treehousedeck.jpg

Hi Rooster, I considered that but I couldn't think of how to do it.

The tree is pretty large already (weeping willow, ~3' diameter, topped off by a storm at ~25' and now putting on a new "head of hair"), so I'm hoping my radial beam arrangement will work for a decade or two. As the tree grows I think I may need to trim the innermost decking, so that it doesn't strangle the tree. I plan on leaving a ~3" gap between the deck and the tree to delay this eventuality.

At some point, I might need to loosen the lag bolts a bit, to relieve compression on the support blocks as the cambium grows outward. I might even need to replace all the decking/rails eventually, lest they get slowly driven into higher and higher tension.

On the other hand, I have read on several tree house sites that trees often grow around support structures, especially if they don't make a band around the tree [which is considered bad form], just slowing enveloping the supports in cambium/bark. That's why I went with radial support beams (even though they're really a pain to attach to the tree!)

I'm too far into at this point to do a major redesign, but I would be interested to learn how what you suggest might be accomplished!

David

photobucket not working nicely for me, but I managed to grab one of your images, the one with the iris-like, pseudo-tangential supports. Picture re-posted here in case others are having trouble accessing it also: Rooster's Design

Don't you think this design would strangle the tree as it grew? The timbers can't open like an iris unless there were no decking, though I suppose you could have floating deck plates that could move past one another...

Well, for starters, it isn't timber-framed. The joists are 3x8 and timber-screwed together...creating an inner circumference that is larger than the widest part of the tree trunk. The joists could be pre-assembled flat on the ground in 4 seperate sections... with a 2x4 temperarily securing the tops of the joists, in each section, in the precise orientation. Each section could be lifted into position, secured to the trunk with timber-screws and using a spacer block, and supported by using a couple of 2x4 as legs under the ends of the joists. Each section can be secured to each adjacent section around the trunk. Truts can then be installed to transfer the load...and the "legs" can be removed....or something like that. haha

Good luck,
Rooster

The inner diameter is set large enough to allow the tree to grow during the lifetime of the deck...25 years? Removeable blocks can be changed out as the tree grows.

Interesting idea. Strut support blocks would be removable/replacable? Also, would the structs act not only to support the load but also to prevent any sway (as the round "hole" in the middle would not actually touch the tree)? Seems really tricky...

P.S. - your pictures I couldn't see: IE vs. Firefox; the TFG forum seems to play a bit better w/ IE.