BananaPirate wrote:Balsa Man wrote:
I'm still having trouble understanding something about this bracing you're describing, even after I read the doc you put up on page 10 again. How do we know that the ladders will handle the compressive force and that the Xs will handle the tension forces? From the way they are positioned, I don't see much of a difference, other than that one is horizontal and one is diagonal. My interest in this topic has gone up a ton since the last invitational I went to, where a I saw quite a few teams successfully brace the legs with only 1/16*1/16 Xs and ignoring the thicker ladders.
So, how do we/you know they’ll handle the forces? A two part question; what are those forces?, and how do we pick/spec wood to carry the forces? The forces we’re interested in are those that will be there at max structure load (15kg)- the idea being to have just enough strength, or almost just enough strength to carry full load. If your tower blows up at 14,996, 97, 98gr, that’s good engineering.
It’s easy to understand/calculate/know the forces on the legs- with a precisely constructed, symmetrical tower (see discussion way back in this thread)- a quarter of the load put on the tower, multiplied by a factor to take into account the lean of the legs (1 over the cosine of the angle from vertical); for a 4-legged B-tower (meeting 29cm circle bonus), 3840gr, for C- tower 3810gr. With ‘push-down’ testing of sticks on a scale (discussed at length in this thread and the ‘Measuring/using buckling strength’ thread, we can know the buckling strength of an un-braced leg, and determine the ‘bracing interval’ that will give the leg (braced into a ‘stacked column’ of shorter segments) the buckling strength needed to carry full load.
What’s…..going on at the braced points, what the bracing is all about, is ‘locking the point’ where bracing is glued to the leg(s) in space; keeping it from moving when/if/as that point tries/wants to move. Looking at one braced point (call it B), on one leg; its midway between the braced points above (call that A) and below (call it C) it on the leg. As the load increases, the axial force on the leg increases. When that loads gets to the buckling strength of the segment A-C, what’s going on? That midpoint (were the bracing not there) would start to deflect, to bow, to buckle- toward one of the faces of the leg. That ‘side force’ is, when it just reaches the point of starting to buckle, is very small; as the load increases, the ‘side force’ increases- the leg is ‘trying harder’ to buckle. But as long as the point doesn’t move (is ‘effectively braced’), the force doesn’t get/can’t get very big. I can… envision a test apparatus with which you could do some reasonably accurate measurement, but it would be a bear to build.
Which way a braced point will want/try to deflect/buckle depends on …asymmetries- those little variations from perfect that are unavoidable- a little bit of bow in the stick, lass than perfect, straight line alignment, a little difference in buckling strength in one plane, vs the plane at 90 degees, grain imperfections. For a bracing system/configuration, you need to….cover/brace against both possibilities. If it tries to bow one way, tensile bracing (the Xs) sees the load, if it tries to bow at 90 degrees to that, compression bracing (the ladder) sees the load. They work independently, and come into play depending on which way the….asymmetries drive things. BTW, re: discussion of whether the crossing point of Xs should be glued, NOT in a ladders and X strips configuration; the strips need to be able to work independently. Where this comes in is ….as you get close to the limits (closing in on 15kg tower load)- the strips are very strong in axial tensile load- as long as they’re being pulled straight along their axis. They’re fairly brittle, and don’t tolerate bending/twisting when under tensile load very well; if the tower starts to twist/rack/lean a bit (which to some extent it may start to do near full load), if the strips are separate/not glued at crossing, that contact point between Xs can move a hair, and the strip being loaded by that …distortion stays straight, and holds on; if it’s glued at the crossing, that’ll put a bend in, and it may fail.
How we deal with that (and figure out strengths of bracing members needed to ‘hold the braced point in space’) is simply applying experience from past structures over the years- and that experience says that if the bracing pieces can handle around 1kg of force (axial compression force on the ladders, tensile force on the diagonals (X strips), things will hold. I recognize its entirely possible the…’critical force’ may be less, and also that if symmetrical alignment of ‘all the pieces’ isn’t pretty close to perfect, forcing onto the bracing may be more. But with good precise construction (that you can get to with a decent jig), 1kg is a…reasonable/useable/tested engineering number.
So, just like done with the legs, we can use 36” stick buckling strength measurement, and an inverse square table, we can figure out the buckling strength (and hence the density range we’ll find the needed buckling strength) for each of our ladder lengths. We do this with a 1kg ‘design load’ for the ladders. As discussed, we see, for 1/8” balsa, we’re down at the light end of the density range for sticks that will handle a 1kg design load. For ladder lengths up to around 15cm, 1/8 x 1/8 at about 0.8gr/36” stick will do the job/carry the load. That’s pretty darn light, unlikely to find sticks like that in the Hobby Lobby wood bins…. The lightest (36”) 1/8 stick I’ve ever gotten/found ( from Specialized Balsa) is 0.60gr ($10). Price is … up for 0.7-0.8gr sticks ($6-$8). For ladder lengths up to 18, 18.5cm, density range to get needed strength pushes up to 1.1, 1.15 gr/36” stick range. Just for reference, a 0.7gr 1/8 x 36” stick is at 4.74 pounds per cubic foot; a 1gr/36 at 6.77 #/cf.
For the Xs, we’re looking for tensile strength- the ends are trying to pull apart. Same dynamics going on at the braced point, but in the opposite direction- braced point trying to move/deflect outward, away from the ladder end- the X strips are working as strings/cables, keeping the leg/braced point from pulling away/outward. Same level of forces to be managed/controlled. Just as buckling strength is a function of density, so is tensile strength. Its measured in force per unit area (e.g., pounds per square inch), and there’s data out there for balsa at various densities. From the table we’ve put together over the years, some numbers, developed from literature and our own testing (which is fairly easy to do- pull with hands for a rough feel/#, hang vertically, with a container you can add weight to on the lower end, add weight till it breaks).
While the ladder density range that ‘will work’ is near/at the lowest available, the workable density range for X-strips is… toward the high end of available range. It’s in Specialized Balsa’s ‘heavy’ to ‘extra heavy’ classifications ~15.5 to 21 pounds per cubic foot; 7gr to 9.5 gr/3 x 36 x 1/64th” sheets.
At the upper end of the range- 9.5gr 3x36 sheet; 1/16” wide strips will have a tensile strength about 3.25kg; at 3/32” width, about 5.1kg. At the lower end- 7.0gr sheet, 1/16” width, about 2.32kg, 3/32” width at about 3.48kg.
So, already being into another long post, on a quiet Sunday afternoon watching some football, let’s roll on and also talk about the issues around using (1/16”) sticks for diagonal bracing (vs really thin- 1/64” x 1/16 or 3/32nds) strips. Three aspects to consider:
1) the crossing of the sticks (in a ladders and Xs configuration)
2) the weight comparison (strips vs sticks, in a ladders and Xs configuration), and
3) bracing with just diagonals- 1/16 sticks, no ladders.
1) Crossing – with thin strips, both X strips are… very close to straight- at a 1/64th” thickness, they’re each bowed by ~1/128th”. With both put on ‘pre-tensioned’, the crossing….just helps a little bit to….tighten up that tensioning. If either one comes into tension load, that small deflection from ‘straight’ doesn’t materially reduce their tensile strength. With sticks, with both attached to outer faces of leg(s), they’re each bowed by ~1/32nd” (actually, unless you get into some tricky construction, one will be bowed just a bit, and the other by almost 1/16th”). If the one that’s bowed almost 1/16th” comes under tensile load, and is pulled…toward straightness, it will get longer, allowing braced point to move out. Not a lot, but it doesn’t take much for buckling to start. You can avoid by putting one on…in the plane of the legs (butt-jointed between the legs), or on the inside, instead of outside faces of the legs. Butt-joint will very likely not hold ~1kg tensile load (unless you add little gusset strips covering the joint; them + glue = more weight). Getting them on the back side/inside is….more difficult than putting them on the outside, but certainly can be done.
2) Weight comparison – so how, at the densities discussed for tensile strength for X strips, and densities needed in 1/16th sticks to carry design (~1kg) load, do the weights compare (for 1/16” wide strips from 9.5 gr sheet (heavy/conservative), and from 7gr sheet (light/pushing things)? Ran the numbers. I’m not going to take the space/time to lay it all out, but here’s how it comes out. At the conservative end, sticks at 0.25gr/36, strips at 0.19gr/36”, at the light end, sticks at 0.17gr/36”, strips at 0.14gr/36”. Strips are lighter either way you look at it. Not a lot, but with 175-225cm of X pieces, a few tenths of a gr in tower weight.
3) Just Xs, no ladders – Here’s where things get interesting, and….I don’t know. The following… gets kinda technical, and may get a bit hard to follow, but it’s interesting. It’s …cutting edge, in terms of any ….quantitative discussion, by anyone on this forum
1/16th” sticks at the low densities discussed in 2) have very low buckling strength (low density and low cross-section). Obviously, in an Xs only configuration, they have to handle/deal with both compression (buckling) loading and tensile loading. That says, I think, that while you get rid of the weight of ladders, you have to bump up density/weight of sticks. Don’t know how far. The other factor that comes into play is the “end conditions” of the column sections (the piece of leg(s) between braced points. Discussed this aspect of Euler buckling in the ‘Buckling strength-new info’ thread. With Ladders and Xs, those end points (braced points) are or approach “fixed/fixed”- the “effective length” is shorter, hence the buckling strength is greater. Discussed how you can take the buckling strength you measure doing a one finger pushdown on a scale (which is ‘pinned/pinned’ end conditions, and multiply it by 2.3, and take that value to calculate (using an inverse square table) the increased buckling strength you get by bracing at….whatever bracing intervals – to get your ‘stacked columns’ to a buckling strength at/above leg design load). With just Xs, the “end conditions” clearly are not “fixed/fixed.” I’m not sure what they are. But I do know (both from theory, that I’m trying to dig through math involved, and discussion of some tower testing with an S.O coaching friend) the bracing interval needs to be… significantly tighter than it does for ladders and Xs.
My current hypothesis is that instead of using a 2.3 effective length factor to apply to scale-measured pinned/pinned buckling strength to get fixed/fixed buckling strength, you need to use a 0.445 effective length factor, instead of a 2.3 factor. What that means in terms of bracing interval; an example (B-div tower). With leg sticks testing 16.5gr at 36”, with ladders and Xs, a 1/6th bracing interval will get you to a braced leg strength of 4968 gr (above 3840gr design strength; 1/5th bracing interval would get a braced leg strength of only 3450gr, not enough). With just Xs, it looks (with the 0.445 factor) like its going to take a 1/12th bracing interval to get to a braced leg strength of 3931gr. Think it would take 1/16th” sticks in the 0.4-0.45gr/36” range to work. Which approach is lighter (assuming the hypothetical 0.445 factor is correct)?? Time and testing will tell….
