A Question for Heiwa - WTC Safety Factors

[metamars]

OK. There are your mistakes. (I assume you are using floor 97 with 33,000 tonnes total mass above as usual.)

In accord with the correct load distribution calculated by Urich [2007] (which concurs with S. W. Banovic, T. Foecke, W.E. Luecke, et al. “The role of metallurgy in the NIST investigation of the World Trade Center towers collapse”, JOM, vol. 59, no. 11, pp. 22-29, November 2007.)

the values you should be using are:

The mass acting on the core is closer to 19,500 tonnes.

The total core demand is 1,9081E+08 N.

Correct calculation of buckling stress here using the actual properties of the steel as opposed to your assumptions.

The load capacity of the core is 4,3603E+08 N.

Core DCR = 44% (FoS = 2.29) prior to aircraft impact damage.

Core DCR = 51% (FoS = 1.96) after aircraft impact damage.​

Greg, as you know, I have been working on a computer program to calculate stresses in a purely elastic, axial collision of a WTC top (floors 93 to 111) with the WTC base (floors 92 and down). In the process, I calculate a spring constant for each floor, using the mass of columns, only (no spandrels, e.g.). I also calculate the total mass for each floor, using the assumption that the mass remaining when you subtract the absolute total mass from the column masses, is to be evenly divided between 111 floors. (So, I ignore differences in spandrel weights, service floors, etc., and I completely ignore the basement floors).

Also, to repeat, I haven't carefully double checked everything, yet. Caveat emptor.

Even so, I read this thread and got curious as to how theoretical maximum load that is within the elastic limit compares to the static weight. I just added a few lines of code, and I am getting a ratio not of 3 or 5, but rather an overall ratio of about 60 (mks units):

Output:
Spring Constant at floor 92: 3965840390490.68
Total Mass floors 93 - 111: 43824141.6906478

Therefore, static load from WTC top is 429,476,588.568348
Force to get .002 compression at floor 92 is 30,695,604,622.3978

Do you have any comments on this wide discrepancy? Somehow, taking a normal eccentricity into account doesn't seem like it should make a column over 10X as weak, but then again, I'm not an engineer.


Whoa, after I posted the above, I noticed that my spring constant calcs were using total mass, instead of column mass. Here are the corrected figures:

Static load from WTC top is 429,476,588.568348
Force to get .002 compression at floor 92 is 1,971,244,221.96645

===================================

Spring constant calcs:

// compute spring constants; from F = (YA / L) * Delta_L = (YV / L^2) * Delta_L ,
// k = (Y(m/rho) / L^2 ) where Y is Young's modulus = 200 GPa

 

[Heiwa]

OK. There are your mistakes. (I assume you are using floor 97 with 33,000 tonnes total mass above as usual.)

In accord with the correct load distribution calculated by Urich [2007] (which concurs with S. W. Banovic, T. Foecke, W.E. Luecke, et al. “The role of metallurgy in the NIST investigation of the World Trade Center towers collapse”, JOM, vol. 59, no. 11, pp. 22-29, November 2007.)

the values you should be using are:

The mass acting on the core is closer to 19,500 tonnes.

The total core demand is 1,9081E+08 N.

Correct calculation of buckling stress here using the actual properties of the steel as opposed to your assumptions.

The load capacity of the core is 4,3603E+08 N.

Core DCR = 44% (FoS = 2.29) prior to aircraft impact damage.

Core DCR = 51% (FoS = 1.96) after aircraft impact damage.​

Well, I use mass 16 500 tons, total core cross area 2.1 m² and average yield stress 248 MPa (<critical buckling), so my (average) FoS is abt 3 of upper part C (and yours is 2.29).
The FoS of the core due to plane damages is of course of no importance.
A structure with FoS 3 or 2.29 cannot be rigid as suggested by NIST and Bazant & Co. You have to agree with that.

However, as I always say; the main observation/conclusion in my paper is that a small upper part C of a structure of many elements cannot crush the lower part A of the structure due to gravity alone and some local failures and nobody seems to be able to debunk that! FoS of local steel elements do not really matter.

You did not find anything wrong with that.

It seems plenty of people are trying to make models of various kind to prove the opposite, i.e. that upper part C of a structure can crush down lower part A of similar structure (a little stronger as it carried part C before) by dropping part C from a certain height and then allowing gravity alone to crush part A.

It is a futile exercise as part C will be damaged by part A and then be stopped. Quite easy to show with, e.g. full scale simulations of any structures.

 

[Architect]

Heiwa

Simply stating that "I use mass of..." is not appropriate; this thread has been started specifically for you to support your assertion that FoS>3 - something which you have wholly failed to do, and something which several posters here have shown to be wrong. I'm afraid that I must press you to clarify your position, and your calculations, on this issue.

Moreover you try to claim once again that FoS is not relevant to the collapse mechanism, albeit that this is now caveated in respect of core damage. Yet you quite specifically and clearly used FoS in support of your arguments regarding gravity-driven collapse. Now you can't have it both ways - either it is important, in which case you need to clarify your figures properly, or it isn't and you deliberately introduced spurious material. Which is it?

 

[Heiwa]

Heiwa

Simply stating that "I use mass of..." is not appropriate; this thread has been started specifically for you to support your assertion that FoS>3 - something which you have wholly failed to do, and something which several posters here have shown to be wrong. I'm afraid that I must press you to clarify your position, and your calculations, on this issue.

Moreover you try to claim once again that FoS is not relevant to the collapse mechanism, albeit that this is now caveated in respect of core damage. Yet you quite specifically and clearly used FoS in support of your arguments regarding gravity-driven collapse. Now you can't have it both ways - either it is important, in which case you need to clarify your figures properly, or it isn't and you deliberately introduced spurious material. Which is it?

FoS is just a description of the capacity over demand of an element in an intact structure and gives you a feeling of the redundancy of the structure.

Re 'gravity-driven collapses' you should by now know my position, i.e. a small upper part C of a structure of many elements cannot crush the lower part A of the structure due to gravity alone and some local failures.

Try to debunk that! KISS.

 

[Furcifer]

FoS is just a description of the capacity over demand of an element in an intact structure and gives you a feeling of the redundancy of the structure.

And FoS>3 is a lie to exaggerate that "feeling".

Architect nailed it, spurious -3 a: of falsified or erroneously attributed origin : forged b: of a deceitful nature or quality

ps- It takes about 30 seconds to show that most building code is going to have FoS around 2 for any element. Greg's calculation reflects this, and if memory serves NIST places it around 1.5.

 

[Heiwa]

And FoS>3 is a lie to exaggerate that "feeling".

Architect nailed it, spurious -3 a: of falsified or erroneously attributed origin : forged b: of a deceitful nature or quality

ps- It takes about 30 seconds to show that most building code is going to have FoS around 2 for any element. Greg's calculation reflects this, and if memory serves NIST places it around 1.5.

NIST confirmed WTC 1 was not built according to code?

However, as I always say; the main observation/conclusion in my paper is that a small upper part C of a structure of many elements cannot crush the lower part A of the structure due to gravity alone and some local failures and nobody seems to be able to debunk that! FoS of local steel elements do not really matter.

Try to debunk that! Try to build a model with two parts C and A of similar structure that collapses when C drops on A!

 

[Heiwa]

Based on mass 16500 tons, cross area 2.1 m² and yield stress 248 MPa FoS is abt. 3. Where is the lie?

 

[metamars]

Based on mass 16500 tons, cross area 2.1 m² and yield stress 248 MPa FoS is abt. 3. Where is the lie?

The M-FOS at floor 92 is:

1,971,244,221.96645 N / 429,476,588.568348 N = 4.59

For the uninitiated, M-FOS is "metamars factor of safety".

 

[Furcifer]

NIST confirmed WTC 1 was not built according to code?

Yes they did! After the impacts and subsequent fires...

 

[moorea34]

My calculations are at ...

Somewhere else in my paper I show that the critical buckling stress of a core column exceeds yield, assumed properties of the steel, &c.

.

Dear Heiwa,

Why have you changed this text TODAY in your site

Remember that the outer core columns are extremely solid, e.g. no. 501. It is an H-beam with two flanges 17x3.5 inch connected by a 2.2x12.6 inch web. In metric terms the flanges are 430x90 mm and the web is 56x320 mm. Such thick plates, 56 and 90 mm cannot buckle under any circumstance when the compressive stress is only 30% of yield stress, even if the temperature is 500°C. The (smallest) moment of inertia I of this section is about 120 000 cm4 and its radius of gyration r is thus of the order 35 cms. With a free length l of 350 cms the slenderness ratio (l/r) is 10! Removing three floors as support and the free length is 1 400 cms and the slenderness ratio is still only 40! Such a column will not buckle!

by this one

§7.2 of page ...nist1.htm

Remember that the outer core columns are extremely solid, e.g. no. 501. It is an H-beam with two flanges 17x3.5 inch connected by a 2.2x12.6 inch web. In metric terms the flanges are 430x90 mm and the web is 56x320 mm. Such thick plates, 56 and 90 mm cannot buckle under any circumstance when the compressive stress is only 30% of yield stress, even if the temperature is 500°C. The (smallest) moment of inertia I of this section is about 120 000 cm4 and its radius of gyration r is thus of the order 11 cms. With a free length l of 350 cms the slenderness ratio (l/r) is 32! Such a column will not buckle! Same for the wall columns that have a radius of gyration r of abt 15 cms and a slenderness ratio of 24, when supported by spandrels and floors. We know how the core columns were joined and that it seems most failed at their weld planes, with little to no buckling involved.



???

Because I have written TODAY in my site that you don't know how is calculated the radius of gyration ??

 

[Heiwa]

Dear Heiwa,

Why have you changed this text TODAY in your site

Remember that the outer core columns are extremely solid, e.g. no. 501. It is an H-beam with two flanges 17x3.5 inch connected by a 2.2x12.6 inch web. In metric terms the flanges are 430x90 mm and the web is 56x320 mm. Such thick plates, 56 and 90 mm cannot buckle under any circumstance when the compressive stress is only 30% of yield stress, even if the temperature is 500°C. The (smallest) moment of inertia I of this section is about 120 000 cm4 and its radius of gyration r is thus of the order 35 cms. With a free length l of 350 cms the slenderness ratio (l/r) is 10! Removing three floors as support and the free length is 1 400 cms and the slenderness ratio is still only 40! Such a column will not buckle!

by this one

§7.2 of page ...nist1.htm

Remember that the outer core columns are extremely solid, e.g. no. 501. It is an H-beam with two flanges 17x3.5 inch connected by a 2.2x12.6 inch web. In metric terms the flanges are 430x90 mm and the web is 56x320 mm. Such thick plates, 56 and 90 mm cannot buckle under any circumstance when the compressive stress is only 30% of yield stress, even if the temperature is 500°C. The (smallest) moment of inertia I of this section is about 120 000 cm4 and its radius of gyration r is thus of the order 11 cms. With a free length l of 350 cms the slenderness ratio (l/r) is 32! Such a column will not buckle! Same for the wall columns that have a radius of gyration r of abt 15 cms and a slenderness ratio of 24, when supported by spandrels and floors. We know how the core columns were joined and that it seems most failed at their weld planes, with little to no buckling involved.



???

Because I have written TODAY in my site that you don't know how is calculated the radius of gyration ??

What site do you have? I have never visited it and I haven't got a clue who you are! But you are right - I corrected a typo in my article today. Doesn't change the conclusions, though: the main observation/conclusion in my paper is that a small upper part C of a structure of many elements cannot crush the lower part A of the structure due to gravity alone and some local failures and nobody seems to be able to debunk that! FoS of local steel elements do not really matter.

Try to debunk that! Try to build a structure with two parts C and A of similar structure that collapses when C drops on A!

 

[GlennB]

...
I corrected a typo in my article today....

Typo ?

 

[Architect]

I think that Heiwa's tactic is for us to identify the many shortcomings in his paper, he'll fix 'em to the point where we can't respond, and then he'll flog it around the doors as the paper that beat the debunkers.

 

[Architect]

FoS is just a description of the capacity over demand of an element in an intact structure and gives you a feeling of the redundancy of the structure.

Designed safety factors give you a "feeling" for the redundancy of the structure which, in turn, presumably means that one analysing the structure doesn't have to produce meaningful - or indeed accurate - structural calculations? Is that your position?

However, back to reality.

Simply stating that "I use mass of..." is not appropriate; this thread has been started specifically for you to support your assertion that FoS>3 - something which you have wholly failed to do, and something which several posters here have shown to be wrong. I'm afraid that I must press you to clarify your position, and your calculations, on this issue.

Moreover you try to claim once again that FoS is not relevant to the collapse mechanism, albeit that this is now caveated in respect of core damage. Yet you quite specifically and clearly used FoS in support of your arguments regarding gravity-driven collapse. Now you can't have it both ways - either it is important, in which case you need to clarify your figures properly, or it isn't and you deliberately introduced spurious material. Which is it?

Answer the points put to you.

 

[Heiwa]

Dear Heiwa,

Why have you changed this text TODAY in your site

Dear Bastion.

Well, it was not due to you!

Salutations distingués

Heiwa

 

[Architect]

Enough of your hissy fit. This thread is for you to support your claim that FoS>3. That you have made a significant change to your website following criticism here is noted, even if you didn't have the balls to flag it up yourself. Now, answer the technical issues put to you.

 

[Heiwa]

will

Enough of your hissy fit. This thread is for you to support your claim that FoS>3. That you have made a significant change to your website following criticism here is noted, even if you didn't have the balls to flag it up yourself. Now, answer the technical issues put to you.

Yes, this thread is A question to Heiwa &c and you have got the answer. And there is no significant change to my web site.
Of course I spent some space in my article to debunk the suggestion that upper part C would perfectly impact lower part A column/column to produce crush down, but that is a non-starter for obvious reasons. No broken column can ever impact itself after failure.

So I changed the assumption! I disconnected part C, lifted it with a crane and dropped it so column/column impact takes place. Result? Well lower part A compresses like a spring (assuming the elements do not fail) and that's it. Same thing with upper part C + that it bounces. No crush down! Details are given in the article. Happens every time similar, flexible structures collide as assumed. Compare pizza boxes, sponges, lemons.

But it could never take place at WTC 1! Part C is suggested to drop and then it must contact part A columns/floor and part A will also contact part C columns/floor, local failures will be produced in both parts ... and arrest will soon follow.

You see the contact is not between similar structures! A column hitting a thin floor is not a lemon hitting a lemon. It is a knife hitting a lemon.

But it doesn't happen either! A column hitting a floor!

So what happens? If you read my article carefully, you will see that part C is destroyed prior to even touching part A!! Why is that?

Well, it is not due to FoS 3 or 2.29 of the columns. So I will not spend more time on FoS.

Unless you can debunk; the main observation/conclusion in my paper is that a small upper part C of a structure of many elements cannot crush the lower part A of the same structure due to gravity alone and some local failures to start it! FoS of local steel elements do not really matter.

Try to debunk that! Propose a structure with two parts C and A of similar structure (C has previously been carried by A) that is crushed down, when C drops on A! To me it is a paranormal event but maybe you can explain?

Then we can discuss! In a friendly and lively way!

 

[Architect]

Heiwa

Let's be quite clear. On the gravity collapse thread you posted a claim in support of your argument. This stated, unequivocally, that the safety factor at the towers was greater than 300%. Your actual quote is "FoS>3".

You have been challenged to prove this figure. And you have not. In fact, as we scan through the pages, we find that all you've done is produce a half-baked discussion on yield in individual elements. There is no substantive back-up.

Posters have pointed to significant errors in your calculations. Gregory has shown you how one might actually progress an argument. And another poster caught you changing your own website on the sly to reflect the criticisms put to you here.

Whenever you're pressed, you return to gravity collapse. These derails have been singularly unsuccessful. Every single time, you are brought back to the issue of how you calculated factor of safety and how you address the demand to capacity information.

Now, after 3 pages, the best you can muster is:

Well, it is not due to FoS 3 or 2.29 of the columns. So I will not spend more time on FoS.

I think we can only draw the conclusion that you can't, in fact, substantiate your claims about safety factors. You pulled the figure out of the air. Whether because you just don't understand building structures and genuinely think you're right, or whether you're just unwilling to accept the truth, I don't know. And frankly I don't care.

You see, Heiwa, what's clear from this thread is that your approach - your paper - is founded on sand. You just don't get structures, or buildings, or the WTC. You're not a player, and you never will be. And I'm going to remind you of this every time I see a new, incorrect claim. You gave it your best shot, and were found wanting.

 

[DGM]

Try to debunk that!

So to just be clear you want us to debunk, "because I said so"?

Did I get that right?

 

[Architect]

DGM et al; I suggest we set this thread to one side for now and leave it as it is, a perfect example of Heiwa's inability to support information which he presented in support of his own argument. A perfect metephor for the Truth Movement as a whole.