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I'm trying to determine the most structurally sound way to construct a support beam for a serious treehouse. There are four options I've mocked up below - the first two are individual knee brace variants (i.e. knee braces which are not connected to each other) and the second two are tri-beam / yoke / double-knee brace variants where the two knee braces share a connection point at the bottom. The center support bolt for the top beam and the bottom of the knee braces is something called a TAB (treehouse attachment bolt) or GL (Garnier limb). It is a 1-1/4 steel bolt with a 3 inch thick collar to provide more surface contact area with the tree (oak in this case). The fact that the tree is leaning is what causes there to not be an easy answer of what to do (i.e. option C but close to the tree).

What would be the best way to proceed? There will be thousands of pounds supported by this. The angle in A and B is approximately 12-15 degrees if that's helpful to know.

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On the basis of what I think your sketches show, option C or D is probably most favorable. Treehouse design will generally be controlled by gravity (weight). Depending upon the internal forces accumulated in the members, member size and possibly even species will be important. In general however, the connections will be most critical for long-term strength of the treehouse. Forces acting through members eccentric (offset) to the connections will present more difficult strength considerations.

Connection eccentricity presents problems with the timber members as well as the connectors. Tear-out, bearing and grain cracking are some of the member connection limit states to consider. Determination of the forces acting on eccentrically loaded connectors and the transfer of these forces from the members is more complex than for concentric connections. For eccentric connections several forces can act simultaneously including withdrawal (tension), bi-axial flexure and of course shear. Therefore, it is desirable to keep connections as concentric to the connected parts as possible.

The diagonal braces in options A and B appear to have the most eccentric connections. Options C and D are more concentric to the tree and the timber members. The TAB bolts however are eccentrically loaded and will be required to resist shear, bending and possibly withdrawal forces. Your intuition is correct in that keeping these TAB bolts as short as possible is desirable. However, TAB bolts are proprietary products. As such they have a specified strength. This strength can vary depending upon the species of the tree. They are specifically manufactured for the construction of treehouses with the apparent purpose of reducing or eliminating eccentricity by acting as an artificial limb wherever you need one.

So, if you are able to determine the forces acting on the TAB bolt, it can simply be compared to the manufacturer specified strength. Use of these products has an added advantage in that companies that manufacture them often provide technical support at no charge.

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