As so often in the past, SLM has provided us a beautifully detailed and presented analysis. As always, much appreciated.
Two intertwined things in the remainder of this post; a) continuing the fun, way down in the weeds, detailed, conceptual discussion with SLM, and b) some (personal) perspective on how advice on this board, and in coaching, fits into “the bigger picture.”
In any really complex problem – and we certainly have one here; in this case understanding; modeling, the forces in a wooden tower, taking into account both the dimensional and physical properties of all members, and a hanging, potentially moving load, any analysis is a) an approximation, and b) can encompass a single aspect (or member), a small of interacting aspects (or members), or the whole, dynamic structure. Approximations, by nature, make simplifying assumptions, either ignoring a factor or variable (because it’s very small compared to other variables), or assigning it what you know to be an approximate value that’s “close enough” to reality, so that you can do the analysis, and get the answer to the question you’re investigating to sufficient precision for your purposes. In reviewing what we’ve both had to say, there are differences in what we’re taking into account; what we’re assuming, and how we’re looking at the problem. I think I follow the analysis RJM has provided – I certainly don’t question (as in think there’s something wrong with) any aspect/result.
Diversion to point b): As I’ve said before, I am not a structural or any other kind of engineer; I have, over the years absorbed a fair amount of understanding of the engineering (from a number of engineers) around wooden structures – to a certain level, let me call it a practical level; understanding how key variables work, and how you can work with them – control them to “get to good results.” In coaching, an important aspect is…..how do I say this….balancing the level of intensity to time and interest realities. We see/deal with on this board (and within the teams we work with), a wide range of interest, commitment, intensity, and technical understanding. This goes from someone who has been building successfully for years and is really committed to finding that last few percent that will put them Nationals medaling range, to those that would be really happy to snag a Regional medal and are trying to figure out how to do that within the time they have around classes, orchestra, other clubs/activities, etc., and the rest of their lives, to folk that pop up on this board with questions like, “Gee, I got stuck with towers this year and don’t have a clue- where do I find instructions how to build one?” The level and nature of advice/guidance – what to focus on, what to ignore; how much time to invest in understanding, and various aspects of building (e.g., design, jig building building other construction tools, selecting wood, assembly, testing) – needs to be aligned with, most importantly, time available. My contributions to this particular discussion were from the time perspective; what’s a good – as in time-efficient - way for those in the “fairly serious to pretty darn serious” range to get a long way up the performance curve with a minimal time investment. How can you get pretty quickly to leg specs that are at least getting in the optimal range?
The technique/approach I’ve suggested:
-do a test build with legs of the same cross-section, spanning a range of density,
-test that build with a safety tower, so you can limit failure to a single break in a single member (leg),
-fix and reinforce the failed member, re-test, repeat as necessary till you get to a leg density that carries full load,
-and then build a tower using that leg density,
Is simply a way to get “pretty darn close”, pretty quickly, to a competitive tower (or bridge, or boomilever).
In this approach, and the analysis around it in my last post, the simplifications and assumptions include:
-That the inherent variability in wood means that any analysis – conceptual or testing – is only going to get you to/into a range. Inside that range, good wood selection skills will help narrow the “error bars”, but luck becomes a significant factor,
-That you’ve settled on the cross-section of the legs- the open question is what density,
-That density (at a given cross-section) is a sufficient indicator of the modulus of elacticity; that stiffness, within a reasonable range-10-ish percent, is a function of density,
-That you have enough experience/test data to have a cross-section, and a range of densities, and an exposed column length, that includes a leg that will carry full load,
-That the failure mode is limited to/driven by long-column buckling failure between bracing points (which implies the presumption that your column bracing scheme/approach is adequate to “pin” the bracing points along the long column (the leg), so that you functionally do have in the overall leg, a set of stacked, shorter columns, and that the transfer of axial leg forces to bracing system members that SLM lays out above is, for our purposes, negligible,
-Related to the assumption above is the assumption that the bracing system is…..adequately spec’d (i.e., over-engineered), such that column failure in a leg occurs before failure of a bracing member (if, in the testing approach outlined, the failure mode seen was to be bracing failure, the same fix/reinforce approach would be needed in that bracing component),
-That the leg density is sufficient to avoid compressive strength (a completely different parameter than column strength) issues/failure mode – that the wood is not so soft that the forces involved result in elastic shortening or crushing (inelastic compressive failure).
OK,, finally, back to point a)- SLMs and my analysis (and a fun discussion that I’m enjoying learning from):
My 5th assumption- around the bracing system – is an aspect where we are looking at the problem differently – focusing on different aspects, making different assumptions. The whole topic of what’s going on in bracing, what works how, and “best” is a separate, major consideration that’s been discussed, analyzed, and debated over a lot over the years. I recognize my perspective is….simplified, doesn’t account for/take into consideration all the static and dynamic forces involved in a loaded structure. SLM’s analysis (as I understand it so far) gets to the point/conclusion of over-engineering (i.e., ending up with excess weight due to leg stiffening) through consideration of the distribution of compressive force through both legs and diagonal bracing members. My analysis is simplified (correctly or not), a) by ignoring the weight of bracing, b) by focusing to/assuming the operative failure mode to be buckling column failure between bracing intervals, and c) by my….operative, experiential (and only somewhat theoretical) understanding of how and why the “compression ladders and tension Xs” bracing system we use “works.”
My operative understanding goes like this;
We’re talking about square cross-section compression members (legs). They are aligned such that their flat sides face each other. In a 4-legged tower, that means they are oriented such that their edge corners “point” to the middle of the tower- if you sliced across and looked down vertically, you would see four diamonds, out at some distance around the center, with one point of the diamond point toward the center, and the sides of two adjacent diamonds parallel to each other. The load on the tower results in axial compressive force on the legs- essentially equally distributed.
Looking at any individual leg, first without bracing in place, and then with it in place. The axial force at some level is going to induce buckling- at or near the center of the exposed length, it will start to bow. In a square cross-section, the direction of that buckling will be in one of four directions - toward one of the flat sides; the area moment of inertia (“I” in Euler’s Buckling equation) is less in those directions – those two planes - than it is in the planes across the diagonal of the cross-section.
If you put (ladder) bracing in at the midpoint – square cross-section pieces butted up against and joining the flat leg sides, they will resist the buckling of the legs toward each other. Up to some load, they will prevent buckling in that direction. The axial compressive force on each ladder, as long as the column/leg doesn’t actually move in deflection is very low, compared to the axial force along the leg (i.e., the ladders can be of a lot lower density wood than the legs, and “work.” If the bracing interval is “correct” (close enough for the stiffness of the leg so that the exposed column length will carry the design load), you’ve turned the longer leg section into two “stacked columns” sufficiently strong to carry the design load, relative to buckling failure of the legs toward each other- the inner sides of the “diamonds” are braced – they are not going to move, to fail moving toward each other.
Now, the other two buckling failure directions/planes are toward the outer flat faces of the legs/diamonds- the legs moving apart from each other. If you run thin strip Xs (as I’ve said before, we use 1/64th x ~1/16th fairly high density balsa for these) between the ladders (as shown in SLMs figures, above), those strips see tensile axial load when the legs try to buckle away from each other (and also if the whole structure starts to twist or rack). Just as the ladders prevent buckling of the legs toward each other, the Xs prevent buckling away from each other. With all 4 potential buckling failure directions constrained, the braced point doesn’t move.
As I’ve mentioned before, these X strips need to be put on taught, so, just as the legs can’t start to flex/deform in toward the ladders, they can’t because of the X-strips straightening out/stretching, start to flex/deform away. They work purely in tension (up to the point of overall significant structural deformation, which almost instantly leads to failure) - they, in conjunction with the ladders could be threads – like cable stays are used in “real” structures.
Yes, this is simplified. The much more complex matter of overall structural dynamics, stiffness, etc matters. But in the force ranges, and size of structures we’ve been dealing with, its worked to produce….competitive structural efficiencies. Chimney legs 55cm long will be pushing the experience envelope to a new level, though, for sure
See anything I’m materially missing or mis-understanding here?
Fort Collins, CO