Boomilever B/C

[jma]

We tested our 2nd boomilever today. The compression members started to bend @ 6.1 kg so we stopped loading. Is the reason the ladder was forming a wave shape because of weak compression members? Or is there any other reason?
We used:
Ladder compression members 1/4 x 3/16 cut from balsa sheet, X bracing every 4 cm with 1/8 square balsa.
2 pairs vertical connected tention & compression members with 1/32 square.

[iwonder]

That's pretty neat I wouldn't stop just because it's bending, by the way... The really lightweight booms will probably end up with some bends in them. Though it is unlikely it would hold all 15kg if it was bending at 6kg. I doubt the 1/32 square is doing much for you... but personally I'd up the density of your compression members and make the compression-tension members bigger/closer together.

[Balsa Man]

A quick terminology, and physics check. So we can be talking about the same thing...

Member(s) angling/coming down from bolt(s) - are "tension members"- with a load out on the distal end, they are in pure tension loading. The arms/members coming out, horizontally from the wall, that the tension members connect to at the distal end- where the load block goes, are "compression members"- under load, they see pure compression loading. Bracing pieces, put perpendicullary between compression members like the rungs of a ladder are ladders, or ladder bracing. Bracing between two compression members in the form of Xs are X-braces.

Was the "wave shape" in the compression members in the Y- plane- vertical, up and down, or in the X-plane, horizontal, side to side?

I think I understand you have 2 (each side) 1/32nd sq pieces running between tension members and compression members. They will do nothing to prevent upward movement (buckling initiation) in the compression members.

I suspect the buckling (wave shape) is in the Y-plane- vertical- the bracing (because it's 1/32nd, and only 2) is not preventing buckling . You can increase buckling strength in the Y-plane by increasing the vertical cross section dimension in the compression member(s), or increasing the density, or both

[UQOnyx]

I finished my second boomilever. I used bass for my compression cords and I got awesome results, and the total was still lower than 20g. What would be a good efficiency score for a boomilever?

[Balsa Man]

I finished my second boomilever. I used bass for my compression cords and I got awesome results, and the total was still lower than 20g. What would be a good efficiency score for a boomilever?

See the discussion under Ongoing Contest (Scores).....

[iwonder]

Thinking about the forces inside the base here...

Wouldn't the shear forces in the base as a whole be coplaner to the testing wall because the face farthest from the wall is under compression and the face closest to the wall be in tension, thus there's a shearing force in between the two? Is this why the end grain is more efficient?

[Balsa Man]

Thinking about the forces inside the base here...

Wouldn't the shear forces in the base as a whole be coplaner to the testing wall because the face farthest from the wall is under compression and the face closest to the wall be in tension, thus there's a shearing force in between the two? Is this why the end grain is more efficient?

Close.
Let's take the case of a "base" carrying 2 tension members, on either side of the bolt. Same thing, but 1-sided, if only 1 tension member. The tension- the pull on the T-members is trying to bend the base. The bolt/washer holds the middle in-place, the end(s) are pulled/bent away from the wall. This is the same sort of loading you see/get in a beam, when you put a point load on in the middle- it tends to bend.

You are absolutely correct that on the wall side, this bending puts the "wall skin" in tension, and the "away from the wall" skin in compression. Just like with a point-loaded I-beam- the upper flange in compression, the lower in tension (Google/wiwipedia up beams, for more info. As you move down through the web of the beam, compression in the upper portion, decreasing as you get to center- nothing at the center, tension increasing as you go toward the bottom flange.

It is the separation of the two skins that gives you bending resistance - cross-section; that and the tensile and compressive strength of the hi density skins. What the end grain is all about, is it's strength holding the skins in place. Many kilos of pull. If you put the 1/2 balsa w/ grain parallel to the wall (side-grain)- using really light balsa, the bolt head/washer will crush into it, , break the skin, and the base piece will bend and break. The end grain is MUCH stronger against crushing. The skins stay in-place, it doesn't crush, and it doesn't bend

[jma]

. but personally I'd up the density of your compression members and make the compression-tension members bigger/closer together.

Thanks

[jma]

Was the "wave shape" in the compression members in the Y- plane- vertical, up and down, or in the X-plane, horizontal, side to side?

It was in the Y-plane-vertical.

I think I understand you have 2 (each side) 1/32nd sq pieces running between tension members and compression members. They will do nothing to prevent upward movement (buckling initiation) in the compression members.

We added these tension-compression connectors to keep the compression ladder from being flimsy so we thought 1/32 would be ok.

I suspect the buckling (wave shape) is in the Y-plane- vertical- the bracing (because it's 1/32nd, and only 2) is not preventing buckling . You can increase buckling strength in the Y-plane by increasing the vertical cross section dimension in the compression member(s), or increasing the density, or both

Thanks

[Balsa Man]

Glad to be able to be of some help.

OK, let's take things to the next level.

Review discussions on how buckling works- and how bracing to reduce "effective length" increases buckling strength. That's what your x-braces between compression members are doing, in the X-plane. The effective length with 10, 4cm bracing intervals is 4cm; 1/10th the total length. The buckling strength of each of those 4cm sections is 100 (10 squared) times the buckling strength of the (un-braced) full 40cm member. With the bracing, you've created a "stacked column" with the buckling strength of each of the braced sections. That's in the X-plane.

So, looking at the X-plane buckling strength:
Depending on the density of the wood you're using, you may be... over-bracing. You can check that with the "scale test" I've described before. Take a 40cm piece- put it vertically on a scale; push down, note the weight at which buckling starts. Using the inverse square relationship in Euler's buckling equation, figure out bracing interval needed. With 2 compression members, each needs to carry about 20kg. Let's say the 40cm piece buckles (in the X-direction - the short (3/16ths) cross-section) at 1kg. That means if braced at the mid-point-half way; L/2, buckling strength goes to 4 (2 squared); braced at 1/3 intervals (13.33cm), buckling strength goes to 9kg (3 squared). Braced at 1/4 intervals (10cm), buckling strength goes to 16kg; at 1/5th intervals (8cm) goes to 25kg. Also, depending on the separation between compression members, and the density of your 1/8th x-bracing pieces, you may be suing too much wood. You could try, instead of single 1/8th (between, or on top of, or on the bottom), pairs of 1/16th braces. At the same density, 1/2 the weight; at say 50% higher density, 75% of the weight.

As I've said before, Y-plane bracing is more problematic. Running braces between the tension members and the compression members is neither very effective, nor (weight) efficient. Experience suggests the best way to increase Y-plane stiffness - buckling strength is to increase the Y-plane stiffness-the Y-plane buckling strength of the compression member itself. From Euler's equation, that stiffness (buckling strength) is a function of E x I. I is the cross-sectional moment- for simplicity, the cross-sectional dimension. E (the modulus of elasticity) is the ...inherent stiffness. It is a function of density; (roughly), double the density, you double E.

Increasing the Y-dimension at the same density increases mass. Increasing density increases mass. Increase both density and cross section, mass increase is multiplicative. Say you double the Y dimension (x2)- mass doubles. Double the density (x2), mass doubles. Double both the Y-dimension and the density, and the mass quadruples (x4), Same relationships apply to E x I - the buckling strength coming from cross section and density; double cross section dimension, double I; double density, double E; double both, and E x I quadruples.

Experience suggests that for 1/4 inch cross-section, to get a buckling strength on the order of 20kg, you'd have to go to very high density- as in HEAVY. If you were to go that way, note that X-plane stiffness/buckling strength would go up, too, increasing the bracing interval (effective length) needed-reducing the amount of X-plane bracing. So, is there a more weight-efficient way to get to the stiffness needed, than using a heavier, solid member? Turns out, there is.

First, a couple of things to study/play with, and understand:
http://www.explorelifeonearth.org/curso ... 0Euler.pdf
http://paws.wcu.edu/radams/intro_to_beam_theory.pdf

The take-away from this information is this. The wood near the (long) axis is contributing little to the (buckling) strength/stiffness; that strength is mostly coming from the wood out at the edges.. By going to a hollow - box-beam - construction, you can get greater buckling strength, at less weight, than a solid member. It is, I would argue, a better- a more weight-efficient way than trying to get more Y-plane stiffness with external (T-member to C-member) bracing.

For instance- looking at your current 3/16 x 1/4. Looking at the cross section area, you have12- 1/16th " squares. If you were to try a box- with top and bottom strips 1/8th wide x 1/16th thick, and side strips/plates 1/32nd" thick x 3/8ths wide, with the side plates glued to the edges of the top & and bottom strips, you end up with a box 3/16th" wide, by 3/8th" tall (same X-dimension, 33% longer Y-dimension. The cross section area of the wood is down to 10 1/16th squares- assuming the same density wood, add in glue weight- about the same weight as the solid , with more than 1/3 greater stiffness in the Y-plane (the glue planes, with E >> that of the wood, add to the stiffness). Say double the density of the 1/32nd plates - increases weight (160%), but Y-plane E (hence E x I -stiffness) doubles.....

A place & some concepts to start from, and play with.....