Hi all,

I'm laying out tenons on floor joists (drop-in's where the 8x8 sill is fully supported and tusk tenon's where not supported) and have a question about calculating sheer stress at the joint.

The joists are 4 x 9's and I'm considering 4"x4" tenons for the drop-in's and 4x2" tenons below a 2" upper shoulder for the tusk version (with the underside tapered on all).

Looking at Ed Levin's calculations on page 72 of the TFG Timber Framing Fundamentals book, it appears that a simple 4 x 4 joist would have less shear stress on it (at the joint) than a 4 x 9 joist reduced to 4 x 4 at the tenon.

My question is this: Where is that additional force coming from when the ratio of joist depth to tenon depth increases?

Thanks in advance!

(For those of you who also frequent the Forestry Forum, you'll note that I've asked the same question there. Just trying to reach all with the question.)

Hi Kevin,
What formula are you using, exactly? For a sharp notch (instead of a gradual reduction) for a 4x9 down to a 4x4 you pay a "penalty" by increasing the shear stress by a factor of d'/d bacause it's concentrated in one spot.
I suggest reconsidering your joist sizing though, and make them wider. Having joists that are deeper than the carrying sill is odd.

Will,

I haven't sorted out how to express a formula in a simple HTML format, so here's an attempt at it all on a single line:

Force = (3 times the load)divided by (2 x (tenon width x tenon depth)), then multiplied by ((joist depth/tenon depth)squared)

If you have a copy of the TFG book, it's on page 72, midway down the right column.

The reason for joists that are deeper than the carrying sill is because they extend over a 14' span in the forebay. (The sill is supported by the foundation at one end, and is atop posts at the outer end of the forebay.) I'd submit a drawing, but the darned electrons are all frozen up here tonight and my internet connection is about as slow-flowing as the beet juice in my tractor tires (okay, maybe it's me that moving slow . . . )

Kevin,
You can eliminate the "...then multiplied by ((joist depth/tenon depth)squared)..." factor if it's a gradual reduction, which would be the same if it was a straight 4x4 all the way. Shouldn't be "squared", tho. That may be a misprint; I'll check the book next time I'm at the Heartwood library.
Again, that factor is a penalty for having a square notch at the reduction.

Will,

Thanks for offering to take a look and clarify.

Essentially the entire page in the article is devoted to demonstrating the change in sheer forces on a tenon as a result of the reduction. (At the end of the section, Ed writes of the drop-in tenon, "this joint is not acceptable.") According to Ed's calculations, the sheer value ranges from 35 psi for a soffit tenon (entire 6" depth of joist housed in sill) to 182 psi for a drop-in dovetail (4" deep tenon after a 2" reduction at the joint - experiencing a six-fold increase in sheer forces as a result of dovetail and the 2" reduction). In the middle of the range is the tusk tenon (my preferred joint) with a 1.5" reduction coming in at 83 psi (still nearly 3 times the force calculated for the soffit tenon).

I've been aware of the need for tapering the reduction, but this is the first source that I've seen claiming an exponential rise in force at the reduction. Any help at understanding the mathematical basis for the calculations will be greatly appreciated!

Kevin,
Note that the drop-in dovetail is also narrower at the throat where it enters the beam. The fact that the shear (not sheer) force rises exponentially as the timber section decreases is just the nature of the beast; I can't explain the derivation of the formula but trust it is so.
EXCEPT that d/dn squared factor is a misprint, I believe. I will consult the editor. This chapter in the book is a reprint from Timber Framing #38, and this section is different than the calculations in the original. The NDS formula calculates the allowable shear rather than the actual shear (like the article)and uses a squared factor. That may be where the confusion (by the author/editor) arises. I'll report back.
Please call me if you have more questions on your original issue.

Also note that the NDS specifies that beam notches should not exceed 1/4 the depth, and I would never go past 1/2 the depth in practice, so notching a 9" joist down to 4" is excessive, IMO, even though the formula might work. Call it intuition, but also the nature of wood,

Will,

Thanks!

I suppose that, in addition to the tenon, I could fit them into a 4x6x1 housing. Hopefully that will reduce the shear forces.

I'd sized the 4x9 joists to give me an l/d deflection of 1/523 (well within the 1/360 threshold). I guess I'd assumed that by limiting the deflection, I'd also be reducing the horizontal shear as well. Still trying to wrap my head around it. Thanks again for all your feedback.

The NDS changed the allowable shear formula in 1991 to square the factor mantioned above.

Oops: NDS edit was in 2001, not 1991.

Will,

Thanks again for helping me find out what happened with the formula.

Here's a brief explanation that I came across:

Review of ASTM procedures used to establish allowable shear stresses revealed that shear values were being reduced by two separate factors for effects of splits, checks and/or shakes. One of these adjustments was made to the base value, the other was an adjustment to design values for grade effects. In 2000, ASTM standard D245 was revised to remove one of these adjustments, which resulted in an increase of nearly two for allowable shear design values; however, grade effect adjustments were eliminated.

In the 2001 NDS Supplement, shear design values for sawn lumber are generally 1.95 times higher than values printed in the 1997 edition in response to the change in ASTM D245. With this change, shear-related provisions in the NDS were reevaluated and modified where necessary to provide appropriate designs.

As I interpret it, allowable values were changed due to the elimination of some adjustments, then the formula for calculating the stress was adjusted to bring it in line with that change to allowable. Is that the general gist of it?