WTC Collapse Simulation using Unity/Besiege

Mendel

Senior Member.
Building designs are unique and likely initial damage is unique.... Why would you expect "prediction" and how useful would it actually be?
I don't know why, I just know that he does:
Article:
Expectations: We expect, that we will be able to simulate failing building structures under hazardous impact to a degree that allows predictions, what building parts will resist the impact and where falling debris will accumulate. In a best case scenario the simulation will indicate where spatial pockets will be likely to be formed, that allow victims to survive.

How can you predict for a specific building if your calibration is post hoc?
Counter question: how can you use a software/method to answer engineering questions that has not been shown to correspond to the real world?

My main point is, the WTC simulation gets youtube views, but it doesn't make any engineer trust Bullet Constraints Builder.

Thomas B

Active Member
The toppling of the remaining columns likewise is "settled engineering" - Euler buckling.
Can someone provide the calculation for the Euler buckling of an isolated (fixed-free) core column of the Twin Towers?

Or just the numbers we'd need to plug into Omni's buckling calculator.

Thomas B

Active Member
Can someone provide the calculation for the Euler buckling of an isolated (fixed-free) core column of the Twin Towers?

Or just the numbers we'd need to plug into Omni's buckling calculator.
I've been playing around with this. (Here's my Omni calculation.) I've probably gotten something wrong, but it seems like a 1000-foot (fixed-free) box column with a 36" by 12" footprint and 2" walls would have a critical buckling load of about 5000 tons.

Since a real WTC column weighed less than 500 tons (100,000 tons / 240 columns = 416 tons) it's hard to see how it would buckle under its own weight.

I realize I'm assuming a uniform or "prismatic" (untapered) column and the actual WTC columns were tapered. But surely that would only make them even more stable?

What am I doing wrong?

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econ41

Senior Member
Counter question: how can you use a software/method to answer engineering questions that has not been shown to correspond to the real world?
You can't - your question isn't opposing my comment - you identify the same inappropriate method as I do from an alternate perspective. Our concerns are complementary.
My main point is, the WTC simulation gets youtube views, but it doesn't make any engineer trust Bullet Constraints Builder.
Which is also a complementary approach to my often explained distinction between two types of models or simulations. Viz the "look like" models for layperson purposes OR the professional versions. The "professional" ones are intended to demonstrate, often quantifiably, the applied physics for purposes of analysis. And those models may not "look like" the real event for reasons including "scaling".

econ41

Senior Member
What am I doing wrong?
You are analysing an abstract element that has some similarities to a WTC structural element. You seem to be assuming that your abstract model is part of WTC collapse when it is not. So what are you trying to prove? The calculations may, or may not be correct for your model. The model has no place in explaining WTC collapses.

If you are trying to assess a part of the actual WTC collapse mechanism you must start with a valid understanding of where your selected subsystem element fits in the real scenario of WTC collapse.

I am only aware of two situations where Euler buckling is a probable feature of the Twin Towers' collapse. The buckling of inwardly bowed perimeter columns which were the probable trigger of the initiation stage. And the ultimate collapse of the remnant "spires" >> the core columns that remained standing for some seconds after the ROOSD collapses. In both those cases, the observed failure did occur whether or not Euler was the explanation. And neither of them involved 1,000ft full-length columns, So, in both those situations, there is no "need" for Euler calcs other than for reasons of curiosity. And, for both those situations, Euler was not the sole factor. There were other factors in play. So beware any claims that attribute Euler Buckling as the cause.

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Thomas B

Active Member
there is no "need" for Euler calcs other than for reasons of curiosity.
That's a good enough reason for me. But I also think it strengthens the argument. If a truther did my calculation and said that the core columns were at least an order of magnitude too strong to experience slender-column buckling, I would want to show them how they're wrong.

The calculations may, or may not be correct
I think they have to be wrong if our account of the WTC collapses is correct. A single column in the simulation we're discussing, without any lateral support and with a height of the whole building, has to self-buckle, right?

And the ultimate collapse of the remnant "spires" >> the core columns that remained standing for some seconds after the ROOSD collapses.
Yes. This is the situation I have in mind.

And neither of them involved 1,000ft full-length columns,
But shorter columns would only make them less susceptible to buckling. Halving the height quadruples the critical load. (The calculator confirms this nicely: 500 ft give 200K N, 250 ft gives 800K N.)

Euler was not the sole factor. There were other factors in play.
What was the other factor in the case of the spire?

econ41

Senior Member
That's a good enough reason for me. But I also think it strengthens the argument. If a truther did my calculation and said that the core columns were at least an order of magnitude too strong to experience slender-column buckling, I would want to show them how they're wrong.
But it is situation-specific. See next comment>

If you did meet a truther who is competent at the physics you would need an answer that is at least as correct as his and preferably better. I can not recall discussions with any typical truther who is that good. The four who were my respected opponent colleagues and who were good enough to keep me honest haven't been active for many years.
I think they have to be wrong if our account of the WTC collapses is correct. A single column in the simulation we're discussing, without any lateral support and with a height of the whole building, has to self-buckle, right?
Sure a single column that length would Euler buckle - I suspect even with your generous oversizing of the cross-section. BUT there was never a full-height free to buckle situation in the actual Twin Towers collapses. The two examples I gave are the only relevant ones I know of. And the "inwards bowing initiation trigger" was a case of buckling due to excessive length caused by the failure of bracing. Not Euler buckling under self-weight. Whilst Euler buckling was very likely part of the collapse of the "spires" there were probably other factors.
Yes. This is the situation I have in mind.
Yes, the spires.
But shorter columns would only make them less susceptible to buckling. Halving the height quadruples the critical load. (The calculator confirms this nicely: 500 ft give 200K N, 250 ft gives 800K N.)
I know - it's a square of the length situation.
What was the other factor in the case of the spire?
Vibration - probably resonant vibration - horizontal waving consequent on the massive effects of shearing off the floor joists and beams just a few seconds earlier. There may also have been some wind turbulence following the massive collapse around the "spires".

Thomas B

Active Member
even with your generous oversizing of the cross-section.
Did I oversize the cross-section? That might explain it. What's the correct figure?

Thomas B

Active Member
Did I oversize the cross-section? That might explain it. What's the correct figure?
Yes, the cross section was wrong. Here's the new calculation. It doesn't seem to make a difference to Euler buckling, since I got the area moment of inertia right. (If I did.)

It doesn't look like this column would buckle even with 5000 tons placed on top (1000 feet up). That's with no lateral support anywhere along its length. Even though its slenderness ratio is over 2100:1.

Obviously, it would have to balanced just-so. But still.

Like I say, I must be doing something wrong. In order to get the critical load around the weight of the column, I have to reduce its cross section by a factor of around 12. See this calculation.

And that, again, is for an untapered column.

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econ41

Senior Member
Like I say, I must be doing something wrong. In order to get the critical load around the weight of the column, I have to reduce its cross section by a factor of around 12. See this calculation.

And that, again, is for an untapered column.
Yes. Your main error is that you are pursuing a False Analogy. I've already identified why so the rest of the details are irrelevant.

As I expressed it on another forum many years ago: '"How many leaves on the seventh branch of the fourth tree?" is meaningless when you are in the wrong forest.'

Thomas B

Active Member
Your main error is that you are pursuing a False Analogy.
But I'm just trying to get the calculation right. You seem to be saying that it is. Are you saying that the core columns were individually self-supporting at their full height? And you're just assuring me that this is a completely unimportant fact? Or are you just explaining why you don't want to help me check my math?

"How many leaves on the seventh branch of the fourth tree?" is meaningless when you are in the wrong forest.
But "How tall can a tree grow?" is meaningful in any forest.

One interesting example for the use of the equation was suggested by Greenhill in his paper. He estimated the maximal height of a pine tree, and found it cannot grow over 300-ft tall. This length sets the maximum height for trees on earth if we assume the trees to be prismatic and the branches are neglected.
Content from External Source
https://en.wikipedia.org/wiki/Self-buckling

I don't know, but I imagine a steel box column can be designed to be taller than a tree.

Interestingly, the tallest tree in the world the world, Hyperion, happens to be 380 feet, or about 35 stories. The WTC "spires" were about 40 and 60 stories each. It seems that, after the progressive collapse, what was left of the cores was less stable than a redwood tree in a forest.

Of course, a redwood tree standing right next to a collapsing Twin Tower might not do so well. I wonder how Hyperion would deal with

Vibration - probably resonant vibration - horizontal waving consequent on the massive effects of shearing off the floor joists and beams just a few seconds earlier. There may also have been some wind turbulence following the massive collapse around the "spires".

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econ41

Senior Member
But I'm just trying to get the calculation right
In the context of WTC Twin Towers collapses as per several previous posts.
But I also think it strengthens the argument. If a truther did my calculation and said that the core columns were at least an order of magnitude too strong to experience slender-column buckling, I would want to show them how they're wrong.

I think they have to be wrong if our account of the WTC collapses is correct.
You are (were before you changed topics) discussing WTC collapses and how to prove a truther wrong about WTC collapses. Which is exactly the question I responded to.

. You seem to be saying that it is. Are you saying that the core columns were individually self-supporting at their full height? And you're just assuring me that this is a completely unimportant fact? Or are you just explaining why you don't want to help me check my math?
Read my post #167

And your derail into this pretending to misunderstand the metaphoric aphorism is inappropriate:
But "How tall can a tree grow?" is meaningful in any forest.

One interesting example for the use of the equation was suggested by Greenhill in his paper. He estimated the maximal height of a pine tree, and found it cannot grow over 300-ft tall. This length sets the maximum height for trees on earth if we assume the trees to be prismatic and the branches are neglected.
Content from External Source
https://en.wikipedia.org/wiki/Self-buckling

I don't know, but I imagine a steel box column can be designed to be taller than a tree.

Interestingly, the tallest tree in the world the world, Hyperion, happens to be 380 feet, or about 35 stories. The WTC "spires" were about 40 and 60 stories each. It seems that, after the progressive collapse, what was left of the cores was less stable than a redwood tree in a forest.

Of course, a redwood tree standing right next to a collapsing Twin Tower might not do so well. I wonder how Hyperion would deal with
.. and, once again, you ignore my answer to a question that you asked.

Thomas B

Active Member
And your derail into this pretending to misunderstand the metaphoric aphorism is inappropriate:
.. and, once again, you ignore my answer to a question that you asked.
I asked a math question and you answered with a metaphor. I'll ask again directly:

Is my calculation of the critical load of a prismatic 1000-foot (fixed-free) box column with a 36" by 12" footprint and 2" walls correct? Or is it way off? (My calculation puts it at about 5000 tons.)

Am I right to assume that if this column weighs under 300 tons (a cubic foot of steel weighs less than 500 pounds and the column I've desribed would contain about 1200 cubic feet of steel) it would not self-buckle under no additional load, even without any lateral support along its length?

Am I right to assume that, being tapered, not prismatic, a real WTC core column would be less likely to self-buckle when its lateral support is removed?

You don't have to answer these questions. But please don't claim to have answered a question you have merely dismissed.

econ41

Senior Member
I asked a math question and you answered with a metaphor. I'll ask again directly:
False. You asked a question about the collapse of the WTC Twin Towers and included a math question for an example that was not legitimate for Twin Towers. I provided a correct response for the Twin Towers scenario and explained why your example did not belong in that scenario.
Is my calculation of the critical load of a prismatic 1000-foot (fixed-free) box column with a 36" by 12" footprint and 2" walls correct? Or is it way off? (My calculation puts it at about 5000 tons.)
Where does a 1000-foot long column fit in the Twin Towers collapse scenario? So that Euler buckling is a legitimate part of your stated goal to explain the collapse to a truther? Which columns have a 36" by 12" "footprint"? AND a 2" wall thickness? AND which could undergo Euler buckling in the Twin Towers collapses?
Am I right to assume that if this column weighs under 300 tons (a cubic foot of steel weighs less than 500 pounds and the column I've desribed would contain about 1200 cubic feet of steel) it would not self-buckle under no additional load, even without any lateral support along its length?
I don't know and I am not providing a calculating service for off-topic speculations.
Am I right to assume that, being tapered, not prismatic, a real WTC core column would be less likely to self-buckle when its lateral support is removed?

You don't have to answer these questions.
As you know I will usually answer any relevant questions that are on topic. .
But please don't claim to have answered a question you have merely dismissed.
Mendacious innuendo.

Jeffrey Orling

Senior Member
The columns were tapered as they progressed upwards. That's your first error. It's settled engineering that the working load of a column is reduced when it does not have lateral support. Twin tower columns were a stack of 3 story height lengths with no lateral bracing at the end connections, but bracing at floor levels. 7WTC had 2 story length columns.
Note that guy wires are used to support tall antennas because they cannot self support and resist wind loads. Lateral steel braced the core columns and much of it was destroyed by the collapsing floors which also induced vibrations and instability.

Thomas B

Active Member
The columns were tapered as they progressed upwards. That's your first error.
Did you miss this?
Am I right to assume that, being tapered, not prismatic, a real WTC core column would be less likely to self-buckle when its lateral support is removed?
I'm wondering if there is anything wrong with my math as far as you can tell. Or with the idea that, under no load (after ROOSD) the core columns would be more stable than if they had not been tapered?

Twin tower columns were a stack of 3 story height lengths with no lateral bracing at the end connections,
Not stacked like blocks, though, right? I'm pretty sure they were spliced together with bolted connections. Cf.
Column splices in multi-storey construction are required to provide strength and continuity of stiffness about both axes of the columns. Typical bolted column splices used for rolled I section and hollow section members are shown in the figure on the right.
Content from External Source
https://www.steelconstruction.info/Simple_connections#Column_splices

There's a difference between imagining that the spires collapsed because of slender-column issues and imagining they were a stack of 30 or 40 blocks held together only by gravity and friction. This, of course, points to a problem with the simulation as described in the OP.
There are no connections between blocks, meaning the structure is held up only by gravity so has no strength other than the weight of blocks and friction.
I'm pretty sure we need to imagine (model, simulate) the columns as spliced for what Wikipedia calls "continuity of stiffness".

From a debunking point of view, the OP simulation provides an unfortunate model because it basically describes a building that has been demolished (each column has been cut every three stories). So by looking somewhat like the collapse of the Twin Towers it does more to confirm the truther's theory than to debunk it.

Thomas B

Active Member
Where does a 1000-foot long column fit in the Twin Towers collapse scenario? So that Euler buckling is a legitimate part of your stated goal to explain the collapse to a truther? Which columns have a 36" by 12" "footprint"? AND a 2" wall thickness? AND which could undergo Euler buckling in the Twin Towers collapses?
Are these dimensions way off? What dimensions would you use?

If the real dimensions would suggest a column that was much more vulnerable to buckling with its lateral support removed (as in the post-ROOSD situation of the core), then we're well on our way to identifying my error.

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Thomas B

Active Member
It's settled engineering that the working load of a column is reduced when it does not have lateral support.
Yes, but the actual load of the spire had been reduced to virtually zero (leaving only the load-bearing structure). So the question is whether the removal of lateral support puts the column in a self-buckling situation (there's no other load on the spire than the weight of the spire itself). I've tried to approximate this by comparing the critical load of a column to its actual weight. And it seems like there's an order of magnitude difference.

Thomas B

Active Member
Euler calculations are for self buckling.. no additional load required.
I know the theory. I'm looking for help applying it in practice. You're under no obligation to help, of course.

Jeffrey Orling

Senior Member
I know the theory. I'm looking for help applying it in practice. You're under no obligation to help, of course.
I am not an engineer nor mathematician.... I understand the theory of columns which are too slender (defined by Euler) will self buckle.

Thomas B

Active Member
I understand the theory of columns which are too slender (defined by Euler) will self buckle.
Those are useful illustrations. Thanks. (I think they're based on the corner core columns, which were the biggest.)

Hopefully, someone can help calculate the height at which these columns would be too slender.

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econ41

Senior Member
Euler calculations are for self buckling.. no additional load required.
Correct. And a point I've made in previous posts. @Thomas B is persisting with a situation that did not arise in the actual Twin Towers collapses. And two more points which @Thomas B is not taking into account. The "inwards bowing" that appears to have triggered the "initiation" cascading failure was not Euler - but the related issue of excessive unbraced length AKA "exceeding the critical length". And the "spires" scenario almost certaily incorporated a mix of factors as per my previous response to a question.. "Euler buckling" >> Yes. "Oscillatory vibration" post ROOSD >> Yes. And wind gusting turbulence > probably.

The big issue is that we will never be able to know the balance of those factors. And, even if "Euler" was sufficient in its own right, it is not guaranteed to cause immediate collapse so vibration or wind could still be the trigger.

And that is IMNSHO as much as we can say about the spires example. Which is a legitimate issue which did occur in the real collapse.

Speculation about a non existent 1000 foot example - with or without an imposed load added to Euler "self weight" has no relevance to the actual collapses.
Those are useful illustrations. Thanks. (I think they're based on the corner core columns, which were the biggest.)
@Jeffrey Orling is probably the best qualified to help you whilst ever you need to pursue this abstracted situation using real structural data in an hypothetical situation which did not arise in the real event.
Hopefully, someone can help calculate the height at which these columns would be too slender.
Which again raises the same issue. "Too slender?" for what? What scenario are you envisaging? Because, as it stands, it has no relevance to the actual twin Towers collapses.

The splices I believe were mostly welded for the box sections. The box sections transitioned to rolled H sections at some point.... you can look that up the link is not handy.
Yes.

Jeffrey Orling

Senior Member
Econ41 makes the very germane point that there were external forces in play which led to the collapse of the spire aside from strength reduction from the slenderness ratio (Euler).

Thomas B

Active Member
"Too slender?" for what? What scenario are you envisaging?
columns which are too slender (defined by Euler) will self buckle.
the "spires" scenario almost certaily incorporated a mix of factors as per my previous response to a question.. "Euler buckling" >> Yes. "Oscillatory vibration" post ROOSD >> Yes. And wind gusting turbulence > probably.
Euler buckling happens under conditions that can be specified mathematically. Since you think that Euler buckling was indeed a "factor" in the collapse of the spire, I'm just asking you to express this view in terms of the mathematical properties of the columns.

Speculation about a non existent 1000 foot example - with or without an imposed load added to Euler "self weight" has no relevance to the actual collapses.
OK. Specify the lengths and loads that lead you to saying that "Euler buckling" was, "yes", a "factor".

Like I say, I can't get the math to work out. As you point out, even at "non-existent" lengths and loads the core columns don't seem to get anywhere near a "critical" situation for Euler buckling.

Even if the spire had consisted of only a single unsupported core column running the whole length of the tower (which would certainly have been more vulnerable to collapse than the structure we in fact observed collapse), it would not have collapsed on its own.

If there's something wrong with my math, I'd like to know. If there isn't, I'd like to know that too. The idea that the math just doesn't matter isn't satisfying to me. But I understand that it's good enough for you.

econ41

Senior Member
Euler buckling happens under conditions that can be specified mathematically. Since you think that Euler buckling was indeed a "factor" in the collapse of the spire, I'm just asking you to express this view in terms of the mathematical properties of the columns.
I already have to the extent that it is possible to do so. And despite your persisting in ignoring my answers to questions.

Which part of this explanation do you not understand
And the "spires" scenario almost certainly incorporated a mix of factors as per my previous response to a question.. "Euler buckling" >> Yes. "Oscillatory vibration" post ROOSD >> Yes. And wind gusting turbulence > probably.

The big issue is that we will never be able to know the balance of those factors. And, even if "Euler" was sufficient in its own right, it is not guaranteed to cause immediate collapse so vibration or wind could still be the trigger.

And that is IMNSHO as much as we can say about the spires example. Which is a legitimate issue which did occur in the real collapse.
And, if my hint about the dynamic reality of an "Euler and other factors" collapse is unclear - just ask tho I can not see how the status can be made more clear. An "Euler Buckling" collapse takes place in a time frame.. It is not an instantaneous process and in the WTC spires situation, it is not possible to say how much "cause" of the collapse was Euler and how much was other factors. For the simple reason that we cannot quantify the "other factors".

Now you persist in asking me to check your maths even tho' I've explained several times why it is irrelevant.
Like I say, I can't get the math to work out. As you point out, even at "non-existent" lengths and loads the core columns don't seem to get anywhere near a "critical" situation for Euler buckling.

Even if the spire had consisted of only a single unsupported core column running the whole length of the tower (which would certainly have been more vulnerable to collapse than the structure we in fact observed collapse), it would not have collapsed on its own.

If there's something wrong with my math, I'd like to know. If there isn't, I'd like to know that too.
OK - if it will help. Post the values you assume and the Euler Calculation method you are using and I will check the "sums" of your maths.

The idea that the math just doesn't matter isn't satisfying to me. But I understand that it's good enough for you.
Remember you are the one who has moved the goalposts. Please stop misrepresenting me. I have clearly explained why the maths is irrelevant to the original question. I also understand that you want to pursue your curiosity down a rabbit burrow issue. Give me the necessary data AND sufficient of your calls and I'll do a check.

Thomas B

Active Member
OK - if it will help. Post the values you assume and the Euler Calculation method you are using and I will check the "sums" of your maths.
What information do you need that is not provided in my posts #163 (note the link to the Omni calculator)?
I've been playing around with this. (Here's my Omni calculation.) I've probably gotten something wrong, but it seems like a 1000-foot (fixed-free) box column with a 36" by 12" footprint and 2" walls would have a critical buckling load of about 5000 tons.

Since a real WTC column weighed less than 500 tons (100,000 tons / 240 columns = 416 tons) it's hard to see how it would buckle under its own weight.
which updated in my post 169, because you pointed out that my cross section was "generous". I had not substracted the hollow interior of the column, but this turned not to matter because the critical load depends on the second moment of inertia, not the cross sectional area, it seems.

So...
Like I say, I must be doing something wrong. In order to get the critical load around the weight of the column, I have to reduce its cross section by a factor of around 12. See this calculation.

My most recent calculation was done using values I provided in post #173:
Is my calculation of the critical load of a prismatic 1000-foot (fixed-free) box column with a 36" by 12" footprint and 2" walls correct? Or is it way off? (My calculation puts it at about 5000 tons.)

Am I right to assume that if this column weighs under 300 tons (a cubic foot of steel weighs less than 500 pounds and the column I've desribed would contain about 1200 cubic feet of steel) it would not self-buckle under no additional load, even without any lateral support along its length?

I'm using Euler's critical load formula as an approximation of Greenhill's "self-buckling" formula. All of this is at the very edge of my (very rusty) scientific and mathematical abilities, so I'm looking for help from people who can just plug in the numbers and work out the answer.

If you think a different formula and different values are more appropriate, then by all means use them.

But, surely, the general idea that these are knowable properties of columns (and structures made of them) is correct.

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Thomas B

Active Member
PS (@econ41 )

The easiest way to put this is probably:

Assuming the dimensions given in @Jeffrey Orling's post #181 what is the critical height of a (fixed-free) column that has the properties of each section, using Greenhill's formula for self-buckling as given in Wikipedia?

That is, instead of having a tapered column that follows the plan Jeffrey provides. Just imagine a series of prismatic columns with the cross sections he provides standing side by side. I'm assuming the thicker ones will have a higher lmax.

And if my original calculations are correct, I'm expecting all them to be well over 1000 feet.

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econ41

Senior Member
PS (@econ41 )

The easiest way to put this is probably:

Assuming the dimensions given in @Jeffrey Orling's post #181 what is the critical height of a (fixed-free) column that has the properties of each section, using Greenhill's formula for self-buckling as given in Wikipedia?

That is, instead of having a tapered column that follows the plan Jeffrey provides. Just imagine a series of prismatic columns with the cross sections he provides standing side by side. I'm assuming the thicker ones will have a higher lmax.

And if my original calculations are correct, I'm expecting all them to be well over 1000 feet.
What value did you use for Moment of Inertia ("I")? How did you derive it? << That is the first thing I would check.

THEN - have you ensured dimensional consistency? What units are you using Imperial? If so which version? OR Metric? I"ll assume SI.

Jeffrey has cross-sectional dimensions in inches but your length is in feet. Where do you convert?

Thomas B

Active Member
THEN - have you ensured dimensional consistency? What units are you using Imperial? If so which version? OR Metric? I"ll assume SI.

Jeffrey has cross-sectional dimensions in inches but your length is in feet. Where do you convert?
I'll double check this but I think the Omni calculator did the conversions for me.

Thomas B

Active Member
have you ensured dimensional consistency? What units are you using Imperial? If so which version? OR Metric? I"ll assume SI.
I think this is the key. I have no idea how to make the units consistent.

Let's say we want lmax to be in meters.

Rounding things a little...

density (ρ) is 8000 kg/m^3
Young's modulus (E) is 200 GPa
the cross-sectional area (A) of my smaller columns was .11 m^2

the acceleration due to gravity (g) is about 10 m/s^2
second moment of area (I) was .01 m^4

I'm assuming it's Young's modulus and the density that need to be converted.

otherwise we get

EI = 200(.11) = 22
pgA = 8000(10)(.01) = 8000

EDIT:

EI = 200(.01) = 2
pgA = 8000(10)(.11) = 8800

The cube root of 22/8000 2/8800 meters is not much of a max length for a steel box column!

So, as you can see, I'm out of my depth. But if we convert these numbers to consistent units we should get something more realistic.

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econ41

Senior Member
So, as you can see, I'm out of my depth. But if we convert these numbers to consistent units we should get something more realistic.
So am I. I'm 81 yo - trained and did my engineering practice in imperial units in the slide rule era finishing just as calculators were coming into vogue. Long before PCs and FEA.

I'm suspecting that we have some missing (or surplus) decimal places in the application of the metric units. Have you done the calls in Imperial? I cannot identify where the problem may lie without going back to the textbooks to check every one of the Metric units >>> especially for "missing" or "additional" zeros. I suspected that the problem could be with the Moment of Inertia. But that seems to be OK.

Thomas B

Active Member
especially for "missing" or "additional" zeros.
If I convert gigapascals to pascals in E the answer seems to come out to 115 meters. That's for my original, smaller columns, so it may be in the ballpark. Consider: they are 12 inches on the shorter side, along which we measure the second moment of inertia (I). Greenhill (1881, p. 73) found that a pine tree with a 20" diameter could be 300 feet. (Also, if you look at his examples in that paper it does seem like we need more zeros in E.)

Jeffrey Orling

Senior Member
Note that there was bracing that remained between columns that survived at the lower levels and.... the calculation should be done to using the minor axis.

psikeyhackr

Member
I hadn't thought of this before.View attachment 51649
The Eiffel Tower is 10,000 tons of wrought iron and hardly supports anything besides it's own weight. Merely 16 of the standard floor slabs in the North Tower would weigh as much as the Eiffel Tower. Multiple sources describe the ET as exponential. If the tower could be divided up into 82 12 foot slices what would be the weight of iron in each slice?

The Twin Towers had the same problem with the lower portion having to support more weight but even more of a problem with wind since they did not get thinner toward the top.

So how can any accurate physical model be made without steel distribution data?

Mendel

Senior Member.
The Twin Towers had the same problem with the lower portion having to support more weight but even more of a problem with wind since they did not get thinner toward the top.
Yes. That's why the facade of the Twin Towers was designed as a box column, with the floors providing bracing. It's very different from the Eiffel tower.
So how can any accurate physical model be made without steel distribution data?
Thankfully, the construction drawings provide that data to those who need it.

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