Build Techniques

[lllazar]

I really wish i could do that, but with no mentor, and seeing as i practically have no partner, it is quite difficult to go "the whole nine yards". But, i do have a clear idea in my head from all that you guys have had to say.

1. There is a good correlation between stiffness and buckling strength.
2. There is a good correlation between density and tensile strength.
3. First test for the necessary density to hold the load (If your testing individual members, for the tower as a whole, would say, the vertical leg members each hold 1/4 of 15kg, or 3.75 kg?)

Also, can you explain how exactly you tested members for compression? And again, i can't thank you enough for this information, i learn something new every time i come to this thread and it's because of mentors/coaches like you!

[Balsa Man]

Illazar,
A big part of “science” (and engineering) is everyone involved learning and working from the collective “body of knowledge”, and adding the new things they find and learn to that body- this board is one little piece of that process. Its a fun process to be part of.

As to your list:

#1- comparing two pieces with the same cross-section and length, there is a very good correlation between stiffness and buckling strength; a defined mathematical relationship (in Euler’s Buckling Theorem- “E”, the Modulus of Elasticity). It’s the correlation between density and buckling strength that’s…..a bit loose- and challenging to get a working handle on. That’s because wood is grown, and not manufactured to tight specifications. Density is just the the most easily (non-destructively) measured property- a reasonable surrogate for stiffness, especially if you use/apply reasonable safety factors. As I noted before, our experience suggests that safety factors applied to…..strength (as in column failure) assumptions from density measurements for balsa need to be higher than those for bass. I’d add that the lower the density, the greater the appropriate safety factor

#2- yes, there is a very good correlation between density and tensile strength, but that has essentially nothing to do with behavior under compression/buckling

#3- a) yes, on a 4-leg tower, if your upper legs are vertical, leg load would be ¼ of total load. As the angle of the legs increases, that load increases.

Exactly how we do compression testing? I assume you mean with the test rig pictured in the gallery.
I'm almost sure I did an explanation last year- check archive for bridge. Briefly. Examine the two photos. The device has a bar. It has room to put…..something under the piece being tested. What you need to do is have the piece length + what ever is under it such that when you lower the bar into contact with the top, the bar is parallel. The test piece needs to be vertical. That’s what the two little triangles are for. The test piece is out on a little piece of plexi; the two triangles are pushed in so they provide a way of getting the test piece aligned vertical. Put a dot of CA on the bottom. Then pull the triangles back, out of the way of the bar, and you're ready to test.

On one end of the bar is the water container. The bar is balanced with a counterweight in the end away from the bucket, so that before you add weight (water) to the container, the load on the test piece is zero. The location along the bar (moving out from the pivot axis) of where it hits the test piece is the same as from the test piece to where the container is attached. That makes it a lever with a 2:1 ratio (each kilo of water that goes in puts 2kilos of force on the test piece). Add water (into funnel into container from measuring cup/graduated cylinder, whatever), keeping track of how much, till the test piece fails. The device has a “catch” for the bar, so it only falls about ¼ inch when the test piece fails. If you’ve been keeping track off liters/milliliters in, you know your weight; if you’re not sure, pour what’s in the container into measuring cup. The max length this device will take is about 10.5cm. Length isn’t that important, since from data at one test length, you can calculate strength at different lengths.

Suggestion if you don’t want or have time to build a rig to do this is to use the long piece and scale approach I described in last post. As I said there, done carefully, it is a heck of better than guessing– as in it will get you to a real - approximate, but real - value for what wood will carry the load you need, and what of the options you might be considering will do the job at the lowest weight. And that's the info you are looking for.
Cheers.

[SLM]

Here is my two cents on Strength vs stiffness ...

Stiffness can be viewed as a quantity that defines the relationship between force and displacement in a structural member. Using Jeff Anderson’s coil spring example above, let’s say we pull a spring with a force of 10 lbs causing it to elongate 5 inches (see image below), then the stiffness of the spring is 10 lb/ 5 in = 2 lb/in. Mathematically, this relationship can be written as: F = k d where F is axial force, d is axial displacement (caused by the force) and k is the stiffness coefficient for the spring.


We can view a truss member as a spring and write F = k d. For regular trusses, k= EA/L where E is modulus of elasticity of the material, A is cross-sectional area of the member and L is member length.

What is the relevance of the stiffness to tower design? If you want to control joint displacements in a tower, then you need to pay attention to the stiffness of the members and the structure. In general, the higher the stiffness, the less the tower is going to displace when subjected to applied loads. However, if you are only concerned with the strength of the tower, not its displacement, then you don’t need to worry too much about stiffness.

As was mentioned by Mr. Anderson, in engineering, STIFFNESS and STRENGTH do not mean the same thing. The strength of a member (or a structure) is not directly related to its stiffness. If you have two structures (X and Y), and X has a higher stiffness than Y, then it does not always follow that X is stronger than Y.

Proof by Example: Two members in a truss structure (labeled X and Y) are in tension. They both have the same cross-sectional area and are made of the same elastic material, but Y is twice as long as X. Since here member stiffness equals to EA/L, then member X has a higher stiffness than member Y (X is stiffer than Y). However, since tensile strength does not depend on length (it depends on the material and section properties), then X and Y have the same strength.

[jander14indoor]

Couple of comments back to SLM.

Stiffness has additional important effects in these building events and should not be looked on as less important than strength.
It is in fact more important in preventing buckling then in preventing joint displacement as most of the weight supporting members of a tower (unlike the bridges) are under compression not tension. Increasing the buckling resistance of an unsupported member, WITH NO WEIGHT GAIN, allows longer unsupported lengths, less bracing, lower OVERALL weight.
For balsa, it is a non-destructive indicator of strength. Note, here I'm talking about material stiffness of the wood which does NOT change with geometry, not the stiffness of a beam of wood.

Note, there's a third convenient characteristic of balsa in the non-linear relation of strength and stiffness to density. If buckling is a critical failure mode (and it certainly is in compression) you can actually end up with a better beam by going to a lower density piece and increasing the cross section so the overall mass is the same as a denser piece. The material itself will be higher in specific stiffness (stiffness per unit mass) AND the larger cross section is geometrically stiffer by the 4th power of the cross section in the direction of bending. 1.4 (linear dimension to double size for example) to the 4th power is 3.8 times stiffer geometrically!! Again, allowing longer unsupported spans, less bracing, less weight.

And as a counter to the example about stiffness not being strength in the SYSTEM sense. Put those two pieces under compression. If long and thing enough (and many pieces in SO structures are) that buckling is the failure mode instead of breaking, the shorter one will carry a FAR higher load before buckling than the longer one.

Jeff Anderson
Livonia, MI

[lllazar]

Good to know jander, i think i may just reconsider making the base legs 3/16....

[SLM]

Couple of comments back to SLM.

Very informative discussion. Since this is more related to design than construction technique, I am going to post some additional comments on this topic on Design thread.

[S4BB]

We just finished putting our tower jig together and posted an image up in the gallery section. Designed it in CAD and used a laser cutter to cut the parts from acrylic, took about 10 minutes of cutting. We are hoping it will help with alignment when we put the tower together.

[lllazar]

Wow, well ours is almost done but yours look so much more intricate...I used cardstock and balsa However, it still gets the job done quite well, the only difference is that our chimney section jig is seperate form the base jig - it just made things a lot easier and we had to sacrifice very little so all in all it turned out quite well. I think the use of accurate jigs in towers is going to really help with the structural stability, with such a tall structure, you really need to make sure nothing is off center and imbalanced...nice job though, autocad and laser cutting would be awesome but sadly our school only has a mediocre woodshop at that

[iYOA]

We are having an extremely tough time trying to connect the top and base so that the tower is straight. Does anyone have suggestions for this?

[hpfananu]

We're also having that same problem...