Cross Section vs Buckling Strength (?)

[kinghong1970]

So for the legs of a tower, the option are

1) 3/32 x 3/32 at 1gr/36"

vs

2) 1/8 x 1/8 at 1gr/36"

noticing that due to the increased "density" of the 3/32, the kids are having easier time in using jigs and making a tower.
when using a 1/8 at same mass/36" the density drops due to increased volume, and results in a softer wood... seeing some of the pieces deform and get compressed by even handling them and taping them.

so, question is, how does density play in buckling strength?
i've read in the past about tubes and why tubes are structurally stiffer than rods due to the increased surface area of both inside and outside of a tube.

does same apply in the above 2 examples where the increased surface area of the 1/8 will benefit in a tower?

Thanks in advance,

Al

[kinghong1970]

Ok, i think i just found the answer to my question...

Buckling Strength being related to the Area Moment of Inertia, I, the greater the area, higher buckling... sounds bout right in a overly simplified way?

[Random Human]

Ok, i think i just found the answer to my question...

Buckling Strength being related to the Area Moment of Inertia, I, the greater the area, higher buckling... sounds bout right in a overly simplified way?

Uhm no. Generally speaking, higher buckling is associated with greater volume, however density still matters.

[Unome]

Ok, i think i just found the answer to my question...

Buckling Strength being related to the Area Moment of Inertia, I, the greater the area, higher buckling... sounds bout right in a overly simplified way?

Uhm no. Generally speaking, higher buckling is associated with greater volume, however density still matters.

Greater cross-sectional area, but the same mass per unit length?

[kinghong1970]

Uhm no. Generally speaking, higher buckling is associated with greater volume, however density still matters.

ok so the buckling strength formula:


where

E = modulus of elasticity,
I = smallest area moment of inertia of the cross section of the column,
L = unsupported length of column,
K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.

so in the above formula, the Area Moment of Inertia is relevant to cross section of the wood.
but... E is now affected by density... hmmm...

so if the two cross section have the same density, then the E will be constant and only variable will be the I which is dependent on the area.
but now we're talking about 2 different densities here...

Greater cross-sectional area, but the same mass per unit length?

yes, good point.

so if the density is same for 3/32 vs 1/8 cross sections, then it's simple, but if we look at this

3/32 x 3/32 x 36"
volume 0.3164 cu in @ 1 gr
density = 3.16055 gr/cu in

1/8 x 1/8 x 36"
volume 0.5625 cu in @ 1 gr
density = 1.777 gr/cu in

its the higher density that makes it easy for the kids to handle...
just for fun, even looked at lighter balsa and bought a stick or two... they look like it will deform just by looking at it.

[Balsa Man]

Uhm no. Generally speaking, higher buckling is associated with greater volume, however density still matters.

ok so the buckling strength formula:


where

E = modulus of elasticity,
I = smallest area moment of inertia of the cross section of the column,
L = unsupported length of column,
K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.

so in the above formula, the Area Moment of Inertia is relevant to cross section of the wood.
but... E is now affected by density... hmmm...

so if the two cross section have the same density, then the E will be constant and only variable will be the I which is dependent on the area.
but now we're talking about 2 different densities here...

Greater cross-sectional area, but the same mass per unit length?

yes, good point.

so if the density is same for 3/32 vs 1/8 cross sections, then it's simple, but if we look at this

3/32 x 3/32 x 36"
volume 0.3164 cu in @ 1 gr
density = 3.16055 gr/cu in

1/8 x 1/8 x 36"
volume 0.5625 cu in @ 1 gr
density = 1.777 gr/cu in

its the higher density that makes it easy for the kids to handle...
just for fun, even looked at lighter balsa and bought a stick or two... they look like it will deform just by looking at it.

In the thread immediately below this one - "Wood" - I provided (back on Nov 21) a pretty detailed discussion of how and why cross section and density work together to drive buckling strength. You might want to review that. What it boils down to is bigger cross section at lower density is more weight efficient (i.e., higher scoring)- a properly designed and built tower w/ 1/8" legs will beat one using 3/32. That's.... just how it is

But, as you've discussed, there are building challenges using very low density wood; you have to be very careful handling it. Dings/dents during construction will significantly reduce strength vs what you'd have with un-damaged legs.

[kinghong1970]

Len,

thank you very much for all your input, not only on this thread but on this event in general.
sometimes it's a bit overwhelming but definitely good stuff.

i'll take some time to read over the "wood" thread again.

as for the question on hand, i figured that the lighter but bigger cross section at the cost of some density is the better route... but wow.. these balsa woods are no joke.

i consider myself to be quite ocd and with some decent set of woodworking skills have helped me... at cost of my sight being more nearsighted now... (hahaha)
but i too find myself deforming the wood at ridiculously light density when i'm trying out some ideas and doing some mock builds.

now put middle school kids on these... at cost of $6.95/36" this can be quite a challenge indeed!

the tower woes...

thanks again!

Al

*edit/ facepalm over mixing metric and imperial units on the density calculations... /sigh

[Balsa Man]

Len,

thank you very much for all your input, not only on this thread but on this event in general.
sometimes it's a bit overwhelming but definitely good stuff.

i'll take some time to read over the "wood" thread again.

as for the question on hand, i figured that the lighter but bigger cross section at the cost of some density is the better route... but wow.. these balsa woods are no joke.

i consider myself to be quite ocd and with some decent set of woodworking skills have helped me... at cost of my sight being more nearsighted now... (hahaha)
but i too find myself deforming the wood at ridiculously light density when i'm trying out some ideas and doing some mock builds.

now put middle school kids on these... at cost of $6.95/36" this can be quite a challenge indeed!

the tower woes...

thanks again!

Al

*edit/ facepalm over mixing metric and imperial units on the density calculations... /sigh

Al, its good to hear my input's being helpful. Wish there were a way to make it easy to .... chase down a given topic/issue, but the nature of the forum- responding to topics as they pop up... is what it is.

I've got one builder with the B team I'm working with who has been able to... reasonably master the level of care it takes to work with 1/8" in the 0.7gr/36 range. I think what really helped him was 2 things. One, I did a build early in the season last year to try to show him what a really careful build looked like. Explained about thinking of the wood as "moulded marshmallow, and how two, We ....played with a couple of 0.7 sticks - cut to 15cm pieces, BS tested, got some pairs with pretty well matched BSs, Took 1 (with no dents/damage), pushed down on scale to buckling failure, the took the next, did various 'damage'- a little dent, squeezing enough to smoosh in a little (like 1/32" or so), and tested it to failure. The damaged always tested weaker.

[kinghong1970]

Len,

I've worked with couple of kids on some build events... and i've also given them pieces of 0.7g/36" 1/8" balsa to play with and get them familiarized with it but wow, talk about finding that diamond in the rough thing... most kids these days don't have any experience in model building... i remember i had air conditioning ducts packed with model planes, ships and tanks that i had to "hide" from parents... lol

i've also spent some time building a "test" tower and see what the limitations and expectations are for such a task... i have to say that it is challenging for sure.

jig helps... last year, made a straight legged jig out of 1/2" MDF and realized the sheer weight of MDF was enough to deform the 1/8" balsa... hahaha

[Balsa Man]

Len,

I've worked with couple of kids on some build events... and i've also given them pieces of 0.7g/36" 1/8" balsa to play with and get them familiarized with it but wow, talk about finding that diamond in the rough thing... most kids these days don't have any experience in model building... i remember i had air conditioning ducts packed with model planes, ships and tanks that i had to "hide" from parents... lol

i've also spent some time building a "test" tower and see what the limitations and expectations are for such a task... i have to say that it is challenging for sure.

jig helps... last year, made a straight legged jig out of 1/2" MDF and realized the sheer weight of MDF was enough to deform the 1/8" balsa... hahaha

Your comments on model building....took me back to my young days. One of the greatest things I got from my dad was the teaching of the process of turning a concept/desire into physical reality; you want to make something that does something; how do you figure it all out, and with resources-tools, materials, and skills you have access to, make it come together. It was a big surprise to me when after like 8 years coaching my two sons, I took on coaching a team, and found how rare that kind of learning was.