Felling a Tree: the WTC

[spooked911]

An engineering professor* wrote to me:

"I recognized that the WTC design was probably inspired by the design of natural trees.

Most buildings are designed as a stack of diaphragms, supported only on the edges. The WTC "tube in tube" design was quite different.

Trees are a "tube in tube" design.

How do trees come down?

Last I checked, trees fall over, not straight down.

The possibility of having just one WTC collapse STRAIGHT down is about the same as the possibility of having a tree collapse STRAIGHT down. This is not impossible, theoretically, but it is impossible, realistically.

Now, consider there were TWO WTC towers that went STRAIGHT down, not just one.

Imagine seeing a tree collapse straight down, just turning into sawdust. Can you believe that after it was down, there wouldn't even be a pile of sawdust, but there would be an even coating of sawdust spread uniformly over the entire area?"

I think it is a pretty cool analogy.

*they wish to remain anonymous as they receive grant money from NIST and other government agencies, and do not want to jeopardize their career.

[pox americana]

1. Great analogy!

That's what first tipped me off: if the columns supporting the top chunks were weakened to the point where they started moving, why didn't the tops just tip or slide off?

[LARED]

2. Is that your statement

The possibility of having just one WTC collapse STRAIGHT down is about the same as the possibility of having a tree collapse STRAIGHT down. This is not impossible, theoretically, but it is impossible, realistically.

or the engineering professors?

BTW, the analogy is patently false. You are making a connection between inspiration and function where none exists.

[spooked911]

9. The statement was the professor's.

I certainly don't see how the analogy is "patently false".

And how do you know there is no connection between the inspiration and function?

[LARED]

14. Because

a tree's structure does not function like the WTC's structure. Do I really need to explain how they are vastly different? Hack has already done an excellent job of doing that.

The tube in tube like appearance of a tree's structure is just that; something that appears to be a tube in a tube but is not. The form of the tree truck may have inspired someone to create a tube in tube design of a steel structure, but after the inspirational moment the two entities function entirely differently.

[hack89]

3. So trees are 90 percent air? Interesting....n/t

[spooked911]

8. what does this have to do with the analogy?

the analogy is about structure, not about composition.

[hack89]

10. ???

The WTC was a structure of load bearing columns (think tree trunks) encompassing a bunch of empty space. A tree trunk is a homogeneous load bearing column (think steel beam) that could be combined with many other tree trunks to encompass a bunch of empty space. The proper analogy is to build a structure out of tree trunks and compare it with the WTC.

[spooked911]

11. Now you're a RedSox fan?

I thought you liked the Seahawks!

Anyway, I thought it was an interesting analogy. Obviously there are major differences between a tree and the WTC. But the point still remains that the core was crushed while the tower fell straight down. The tube within a tube design is not unlike a biological structure such as a tree.

[hack89]

17. Seattle fan by birth - Boston fan by marriage.

The Sox need all they can get right now, hence the switch.

[AZCat]

4. I don't think it is a particularly good analogy.

It seems your source hasn't thought this through. The primary difference I see between your example (a tree toppling) and the WTC collapse is that there is a significant difference in the relative strengths of the materials when compared to the forces involved. While the modulus of elasticity is not the only property that affects the behavior of a structure it is useful for comparison.

E of white oak = 8,600 MPa
E of 304 stainless steel = 193,000 MPa

Mass of white oak tree = 24m high with 3m Dia and a density of 0.725 kg/m^3 = 123 kg

Mass of WTC 1 = approx 500,000,000 kg

Ratio(tree) = 123/8600 = 0.014

Ratio(WTC) = 500000000/193000 = 2590 (about six orders of maginitude greater)

I'll let you draw your own conclusions.

[spooked911]

7. I don't see that your ratios mean anything except maybe that the WTC

should toppled over even more than a tree?

[AZCat]

12. Perhaps I should have been more clear.

The materials that make up the tree are stronger with respect to the forces involved in the tree falling than the materials that make up the WTC are with respect to the forces involved in the WTC falling.

The materials that were used in the WTC are more likely to bend (either elastic or plastic bending) during a collapse than the materials that make up a tree. That is why the tree maintains structural integrity throughout the collapse and the WTC towers didn't.

[pox americana]

15. The conclusion I draw is that there aren't many oak trees in AZ.

123 kg = 271 pounds, pretty light for a 79' oak tree.

[AZCat]

16. Whoops - you're right

That's what happens when I try to convert from IP to metric. The error is in my value for density - it should be 725 kg/m^3, not 0.725 kg/m^3 (a significant error). My apologies - I have updated the results below:

Ratio(tree) = 123000/8600 = 14

Ratio(WTC) = 500000000/193000 = 2590 (about two orders of maginitude greater)

[AZCat]

20. Aargh! Let's try this again...

Suddenly I seem unable to do simple math problems...

The tree should be 1 meter in diameter, not 3!

Again...

Mass of tree = 13,670 kg

Ratio(tree) = 13670/8600 = 1.6

Ratio(WTC) = 500000000/193000 = 2590 (about three orders of maginitude greater)


Mea culpa.

[pox americana]

23. It'll be our little secret.

:)

p.s. get a new slide rule!

[Make7]

5. Now where have I heard the tree-inspired-design idea before?

Let me see....oh, yeah...

A tree is not a homogeneous material!

She claims to be an engineering professor too. Interesting...

-Make7

[spooked911]

6. Engineering professors must think alike then!

:)

[LARED]

13. Nice find.

No wonder the good "professor" is anonymous.

[spooked911]

18. To clarify: why the WTC1 and 2 were like trees

The twin towers were tall thin structures that supported a lot of weight but were not completely rigid and in fact swayed in the wind. Trees are also tall thin structures that support a lot of weight but are not completely rigid and sway in the wind.

Both have a tubular design-- the WTC has the inner core ring and the outer shell ring. Trees grow as rings around rings.

This is merely an analogy of course, it can only go so far.

But it is worth thinking about how a tree would fall and how a tube-within-a-tube-structured tower would fall when damaged.

[LARED]

19. Here's what you fail to understand

Trees do not grow as rings around rings. They are not a tube in tube; they only look that way. The rings are simply different looking cells that grow in the fall every year and happen to be a different color. It's all wood. No air, no inner or outer discrete structures. It's a homogeneous structure.

Nothing at all like the WTC.

http://www.newton.dep.anl.gov/natbltn/500-599/nb516.htm

[spooked911]

21. I'm laughing because surely this is the

stupidest response I've seen from you yet.

Wood is a "homogenous structure"

:rofl: :rofl: :rofl:

[LARED]

22. Wow, if that's the stupidest response yet

I must be doing okeedokee

Enjoy your laugh, but I have to admit I fail to see the humor or why it's stupid. Is it stupider than comparing a tree to the WTC?

[pox americana]

24. Saying "it's all wood" is like saying "it's all structure"

which isn't so far from the truth.

[hack89]

25. If a building equals a tree

what does a steel column in that building equal?

[pox americana]

26. Nobody said "equals," but probably a heartwood cell.

"Heartwood - The central, woody core of a tree consisting of inactive tissue that has support as its only function."

http://micro.magnet.fsu.edu/trees/glossary.html

[AZCat]

27. Perhaps more important than homogeneity...

Steel is isotropic, while wood is anisotropic. We can argue about an engineering definition of homogeneity (difficult because the properties of wood can vary widely even within the same species) but the anisotropy of wood is what forces baseball players to take care when stepping up to the plate. If the ball is hit on the wrong side of the bat, the chances of a broken bat are greater because wood is weaker in one direction than another. The bat must be swung so that the ball makes contact with the bat along the grain, not against the grain.

Fascinating stuff...

link for the geeks:
The effect of wood grain on vibrational modes of a wood bat

[petgoat]

28. " wood is anisotropic" but the fact that the rings are concentric means

that the real load on a tree little resembles the load on a bat oriented
the wrong way--because the splitting-the-grain-line load, while it may
be imposed on a piece of lumber is not going to be imposed upon a tree.

[AZCat]

29. Sure it is...

It is imposed axially.