In last week’s stream (Trunk Bending Pt. 1), @ryan mentioned “beefing up” the anchoring lag bolt to hold the rebar down since it started to shift/tear.
In ice climbing, we place screws into the ice as protection to catch falls, similar to this lag bolt in soft wood. Maximizing the shear strength of a screw in soft or brittle ice where your life depends on it is obviously important.
Perhaps unintuitive, but the optimal angle for an ice screw placement is with the head of the screw 10-15 degrees towards the force pulling against it (under perpendicular) instead of directly perpendicular or away. This spreads the force more evenly across the screw and the threads as well as through the medium you’re screwing into. Instead of placing the screw straight into the ice perpendicular the expected force a fall (downward), we’re taught to screw slightly upward into the ice with the head of the screw 10-15 degrees under perpendicular.
You can actually see this as the lag bolt begins to tear in Trunk Bending Pt 1. The outer edge of the wood above the bolt has a huge compressive load on it. Eventually the soft wood compresses/tears right above the lag bolt and the bolt head shifts up but continues to hold as the force redistributes further along the screw and the threads (and some tension removed from the system due to the shift). By placing the lag bolt head closer to 15 degrees above horizontal (under perpendicular to the force), we may have avoided this tearing.
I did a quick analysis of the bending stresses on the trunk and the rebar and came to the conclusion that the rebar should be 40% of the diameter of the trunk based upon the modulus I could find for pine. The 3/4" (#6) rebar was obviously too small based upon this, but I doubt that 1.6" rebar is necessary (I guessed the trunk as 4" diameter at the cut). Therefore, the modulus of the live trunk must be less than the published values for pine. It will be interesting to see what size rebar works - my guess is that 1" (#8) may work and that 1.25" (#10) will work.
Placing the screw towards the force pulling it is so counter intuitive at first sight.
I don’t know if wood behaves differently than ice, but if the science takes into consideration a soft medium with different crushing points, it would stand to reason that a tree trunk should be no different.
Amazing article!
@Jason how long have you been ice climbing? Any memorable moments/achievements?
Fascinating stuff @Jason!
Do you ever use a dead man anchor? Iv placed a few in Scotland, and always found it interesting how at 50 degrees the blade will try to bury itself into snow under load.
When testing anchors in concrete, they tend to pull out a cone of the substrate, with the length of the anchor equal to the raidious of the face circle. From what I can see from your article, there is a lot more leaverage going on than just the shear load. The real question is how to minimise damage to the wood fibers?
I never took a fall on an ice screw, but I remember placing them in groups when it got scary to share the load on the ice. Maybe a group of small bolts angled a bit more in line of the load?
What do you guys think about the angle of the jack? In my opinion I feel like moving its location down the rebar, creating a perpendicular angle to the trunk would be more effective. It seems that the force would be better applied if it was coming from somewhere closer to 90 deg. instead of the obtuse angle that was attempted. Not to mention this would shift the leverage point closer to the wood block and reduce the amount of deflection that we were seeing at the top of the rebar. Also additional room to crank the jack…
Interesting question about the angle of the jack. The analysis becomes more complex when the two beams (trunk and rebar) are not parallel. Off the top of my head the force on the jack should be minimized if the angles between the jack and both the rebar and the trunk are the same. Since the trunk already bends towards the rebar in this case that would mean placing the rack lower on the rebar. However, will also increase the force pulling the rebar up out of the soil.
Someday I will solve this statics problem in detail along with the strength of materials (mechanics of materials) problem I commented upon earlier.
I really look forward to the seeing Ryan’s experience/experimental solution to the problem since that is apt to define some of the input values to the theoretical solution. Theory is only a guide - I want to see results.
It seems that the crux of the bend is in the lower anchor.
I think that if you move the jack down, you will lose the mechanical advantage of the long lever arm?
For a completely different approach, perhaps you could chose to fix a lower anchor at the time of repotting. If this was inserted vertically from below into the center of the trunk you would get maximum strength with minimal damage, although you would have to be careful where the wire comes past the nebary. You would have to wait until the tree had re-established, but you would then have to option of replacing the wood block with a turn buckle, tying the wire off on the top point, and opening the turn buckle to make the bend, like drawing a bow. It would take longer, but would be more elegant. (Wire rope grips would be needed to keep the turn buckle in place on the wire.)
Looking at the problems from last week: re-bar bending, re-bar creeping upwards and taking the block below the cut upwards with it. Possible remedies. Heavier re-bar, placing block a little lower to allow for some upward creep, holding the re-bar down by using a pipe wrench on the re-bar near the block. This would necessitate a second person (Troy) to hold the pipe wrench while Ryan concentrates on tightening the clamp. After the wedge mouth closes, could the pipe wrench be removed as the maximum necessary force to close the cut would be over? If not, could the hole at the end of the pipe wrench be wired to the base of the re-bar and held in place.
Another consideration is cutting a little more at point where the two wedge planes meet in order to reduce the amount of force needed to close the gap.
Thinking out loud. An interesting engineering challenge.
