A Question for Heiwa - WTC Safety Factors

[Architect]

Heiwa

You have claimed on the "gravity collapse" thread that:

Originally Posted by Heiwa

All steel structure is designed with FoS > 3.

Secondly, the towers have great redundancy. You can remove parts of perimeter walls, core structure and floors anywhere and nothing happens except local falures! Example - a plane slices a perimeter wall and damages core structure and floors.

Thirdly, if you read my articles carefully you find a fair amount of structural calculations to confirm above and the stability of the parts. Also is described the step by step method to do proper structural damage analysis, the latter which neither NIST nor Bazant & Co has done.

When challenged for a detailed analysis of this, you cross-referenced your own paper wherein it is noted:

Originally Posted by Heiwa

The above is a clear indication how the Towers were originally built by serious architects and engineers in the 1960's. Compressive static stresses in the primary structure columns were less than 1/3 of the yield stress of the steel before (obviously) ... and after serious damage (not so obvious but shown here)! The buckling stress of the column is virtually the same as the yield stress as the columns were arranged with spandrels. One reason why the static stresses were so low was that the designers had no access to computers to optimize (slender down) the construction. Manual calculations were done and to be on the safe side you added steel and built strong! And steel was quite cheap at that time. And US steel was good quality. The assumed yield stress 248 MPa was probably much higher in reality. NIST never checked the yield stress of the steel from the initiation zone in the rubble!

There was therefore plenty redundancy. A plane may crash into the bird cage and nothing happens. A big fire may break out and nothing happens. Why? Because the normal compressive stress in the supporting vertical structure is so low and if any column breaks or buckles, its load is transmitted to adjacent columns via the spandrels and the stress in adjacent columns increase a little. No global collapse is possible under any circumstances.

Evidently the columns got stronger (thicker plates, steel with higher yield stress) further down when the 'mass above' increases, but it is certain that the compressive stresses in the Towers never exceed 1/3 of the yield stress. Same applies for the buckling stresses.

I believe this analysis to be insufficiently detailed and, in particular, incorrect.

NIST tested the steel recovered from WTC (which in itself is of interest, as CTers usually claim it was all whisked away to China with unseemly haste). NIST NCS STAR 1-3D (http://www.fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf) confirms a range of actual values:

- Core webs ranged from as low as 31.1 to 41.9 ksi, ie. 86 to 116% of specificed strength.

- Core flanges ranged from 32.4 to a high 53.4 ksi, ie. 90 to 146% of specified strength.

Setting to one side the 31.1 and 32.4 ksi results, inasmuch as a small proportion of columns below failure point are unlikely to lead to any wider problem, let's take the lower maximum of 116% specified value.

Now, the NIST Demand to Capacity Ratios (DCR) are based upon specified strengths and NIST themselves note that there is effectively spare capacity up to actual (but varying) yield point/strength.

Core columns in WTC typically had a Demand to Capacity Ratio (DCR) of 0.83, ie a safety factor of 1/0.83=1.20. Now let's assume assume that the steel has an additional 16% beyond minimum yield value. This would reduce the DCR to 1.16/.83=1.4.

In other words we could increase the loads in these areas by up to 40% before yield point was reached and plastic (permanent) deformation begins. Of course this figure has lots of variables - most of the steel webs did not have such a high yield factor, some areas had DCRs well in excess of 0.83, and so on.

What we don't do is then add any significant additional allowance for tensile strength because (a) yield failure is already occuring and (b) gravity loads will be compressive, not tensile.

As I frequently mention elsewhere on the forums, one thing we also have to appreciate is that the structure of WTC is complex; in addition to dead and live loads, it will be dealing with (for example) transverse and shear loadings from the wind. There will be a degree of torsion due to differential loading. And so on. We would therefore have to look at the exact steelwork design in considerable detail before we could determine a safety factor for each. That's why engineers earn a lot of cash, and why complex modelling software was developed.

Nevertheless it is clear that the actual capacity of the core is not going to be anything like 300% or 3:1 before irreversible damage and failure begin to occur.

But in any event the above calculations all assume an intact core, and we know from the various NIST studies and eyewitness evidence that the cores suffered damage - around a third. This will obviously have reduced loadbearing capacity still further, and a simple pro-rata reduction of (say) 30% is likely to be wrong because the damage is concentrated in localised areas and hence these areas will be susceptible to accelerated failure under loads.

Now, Heiwa, can you produce similar calcs and figures to back up the "FoS>3" position you've adopted, or is it as substantial as your structural calculations?

[WildCat]

You're asking Heiwa for calcs? You are quite the optimist!

[Architect]

Specifically I'm asking for competent, detailed structural calculations. Not broad generalisations and irrelevent sweeping metaphors.

[Sunstealer]

Originally Posted by Architect

Specifically I'm asking for competent, detailed structural calculations. Not broad generalisations and irrelevent sweeping metaphors.

But that's all the entire truth movement have. I bet this thread is ignored or you'll get some dross posted.

[Architect]

Based on the current "fires" thread I'm going to go for "ignored". But that then allows me to cast it back at them later. And you never know, Heiwa might meander along.

[R.Mackey]

Just to be clear, you're asking for calculations from the guy who once said this:

Originally Posted by Heiwa

Weight (kg) or load (kg) = mass (kg). Yes, I am an engineer. What are you?

Ever get the feeling you're dealing with a guy who brought a teddy bear to a gunfight?

[GlennB]

And the guy who believes that Newton's horse can never move the stone, because action equals reaction?

[Architect]

Now now, lads. Let Heiwa stand, or more probably fail, on the basis of how he responds to this. If he does. But don't hold your breath for a cogent, reasoned response.

[BenBurch]

I'm still waiting for him to respond to the Crown Sheet thread...

[bill smith]

Originally Posted by Architect

Specifically I'm asking for competent, detailed structural calculations. Not broad generalisations and irrelevent sweeping metaphors.

Well if this is not the ultimate compliment I don't know what is. Heiwa's very own forum. I hope you have not bitten off more than you can chew Architect.

[Architect]

We'll see, Bill, we'll see. Now have you anything to bring to the table on this subject yourself?

[bill smith]

Originally Posted by Architect

We'll see, Bill, we'll see. Now have you anything to bring to the table on this subject yourself?

On this narrow a subject ? No, I don't think so. I will follow it with interest though. Well...perhaps an occasional comment.

[Architect]

Well Bill, that's more than Heiwa seems to be doing. Despite posting elsewhere on the site, he's carefully avoiding this thread. I'd be very interested to know why this might be.

[Heiwa]

Thanks for starting a thread with:

Heiwa

You have claimed on the "gravity collapse" thread that:


Originally Posted by Heiwa
All steel structure is designed with FoS > 3.

Secondly, the towers have great redundancy. You can remove parts of perimeter walls, core structure and floors anywhere and nothing happens except local falures! Example - a plane slices a perimeter wall and damages core structure and floors.

Thirdly, if you read my articles carefully you find a fair amount of structural calculations to confirm above and the stability of the parts. Also is described the step by step method to do proper structural damage analysis, the latter which neither NIST nor Bazant & Co has done.

Evidently I have never suggested that all steel structure is designed with FoS > 3. For certain items (subject to wear) you can use FoS = 6. For others you use FoS = 1.5.

Why do you start a new thread with a false quotation?

It is correct that WTC 1 structure had great redundancy. Remove 60% of all columns in a wall between 5 floors anywhere, bits of the floors inside these columns and some core columns and ... the tower still stands! Easy to prove.

It is also correct that NIST doesn't know how to do structural damage analysis. They can hardly do structural intact analysis!!

Example! When WTC 7 upper structure floors 16-47 free falls for 2.25 seconds and is only subject to small air resistance forces, NIST suggests that strong steel elements fail! It is not possible. Air resistance loads cannot break a steel element ... in free fall. Easy to prove!

What to do want to discuss? My articles on the Internet? Just copy/paste what you cannot understand and I will explain. In that way I will not get misquoted!

[alex04]

for convenience, this is the post in question

http://forums.randi.org/showpost.php?p=4481512&postcount=1851

Originally Posted by Heiwa

Thanks for starting a thread with:

Heiwa

You have claimed on the "gravity collapse" thread that:


Originally Posted by Heiwa
All steel structure is designed with FoS > 3.

Secondly, the towers have great redundancy. You can remove parts of perimeter walls, core structure and floors anywhere and nothing happens except local falures! Example - a plane slices a perimeter wall and damages core structure and floors.

Thirdly, if you read my articles carefully you find a fair amount of structural calculations to confirm above and the stability of the parts. Also is described the step by step method to do proper structural damage analysis, the latter which neither NIST nor Bazant & Co has done.

Evidently I have never suggested that all steel structure is designed with FoS > 3. For certain items (subject to wear) you can use FoS = 6. For others you use FoS = 1.5.

Why do you start a new thread with a false quotation?

It is correct that WTC 1 structure had great redundancy. Remove 60% of all columns in a wall between 5 floors anywhere, bits of the floors inside these columns and some core columns and ... the tower still stands! Easy to prove.

It is also correct that NIST doesn't know how to do structural damage analysis. They can hardly do structural intact analysis!!

Example! When WTC 7 upper structure floors 16-47 free falls for 2.25 seconds and is only subject to small air resistance forces, NIST suggests that strong steel elements fail! It is not possible. Air resistance loads cannot break a steel element ... in free fall. Easy to prove!

What to do want to discuss? My articles on the Internet? Just copy/paste what you cannot understand and I will explain. In that way I will not get misquoted!

Quote:

Evidently I have never suggested that all steel structure is designed with FoS > 3.

err that's exactly what you said in your post

Quote:

All steel structure is designed with FoS > 3.

It may not be exactly what you meant, but it would be helpful if you say exactly what you mean (be specific). I assume that you're saying that Architect is taking your quote slightly out of context?

Perhaps there is a slight language barrier? (i'm assuming that English is not your native language).

No disrespect is intended.

[Heiwa]

Originally Posted by alex04

for convenience, this is the post in question

http://forums.randi.org/showpost.php?p=4481512&postcount=1851








err that's exactly what you said in your post



It may not be exactly what you meant, but it would be helpful if you say exactly what you mean (be specific). I assume that you're saying that Architect is taking your quote slightly out of context?

Perhaps there is a slight language barrier? (i'm assuming that English is not your native language).

No disrespect is intended.

Yes, all steel structure elements (of WTC1 - generally the primary ones) that I have analysed in WTC 1 (listed in my article) have FoS>3, i.e. design stresses are very low. I assume reason for this is 1960's US building standards but I have not inquired further about that. Reason for FoS>3 is to provide redundancy, i.e. one or more elements may fail locally, while overall structure remains intact. One result of this is, e.g. that you can drop the upper structure part C on lower structure part A and only result is local failures of both parts in the contact interface and that part C remains on top of part A. Complete crush down of part A by part C is not possible and this I show in my articles.
If you read the complete articles you also find how the WTC structures were destroyed. Controlled demolition! I think I show that quite convincingly using my approach comparing with ship collisions. Others have done it better using other models and methods. Suggest you join AEtruth.org to ensure that a new, proper investigation is done.

[funk de fino]

Great, he shows up and then just lies about what he posted. What a waste of time.

[tsig]

Originally Posted by funk de fino

Great, he shows up and then just lies about what he posted. What a waste of time.

Seems to be a pattern. It's the same with his two mile claim. He first said it then denied he said it then tried to explain it only to say it again then deny it...


He sure is proud of his award though.

[Architect]

Originally Posted by Heiwa

Yes, all steel structure elements (of WTC1 - generally the primary ones) that I have analysed in WTC 1 (listed in my article) have FoS>3, i.e. design stresses are very low.

Please provide a source for this information, as I can determine no such detail in your paper (see quote above).

Quote:

I assume reason for this is 1960's US building standards but I have not inquired further about that.

You've not researched the matter?

Quote:

Reason for FoS>3 is to provide redundancy, i.e. one or more elements may fail locally, while overall structure remains intact.

With the deepest respect, we are quite aware of what safety factors are for. You have been challenged to provide evidence not that one was used during the design - that much is expected - but rather that it was greater than a factor of 3 especially inasmuch as the NIST test and modelling data seems to suggest something quite different.

Quote:

One result of this is, e.g. that you can drop the upper structure part C on lower structure part A and only result is local failures of both parts in the contact interface and that part C remains on top of part A. Complete crush down of part A by part C is not possible and this I show in my articles.

If you read the complete articles you also find how the WTC structures were destroyed. Controlled demolition! I think I show that quite convincingly using my approach comparing with ship collisions. Others have done it better using other models and methods. Suggest you join AEtruth.org to ensure that a new, proper investigation is done.

This is not a thread about your proposed collapse mechanism, rather it is purely concerned with the technical detail of your claim regarding safety factors. I would ask that you please avoid such un-necessary derails.

[tfk]

Architect,

Factors of safety are meaningful only for the intact buildings. They are calculated with the REQUIREMENT that the components be intact, that the loads be directed as designed.

Once the building has started to "disassemble", once unplanned loads are applied, then the factor of safety of the original structure is completely irrelevant. It doesn't matter if it is 2, 20 or 200.

"How much extra load carrying capacity does our intact, undamaged building have over its expected loads?" is a completely different question than "What is the likelihood of collapse if we smash some fraction of the building?"

Architect, you alluded to this at the end of your first post.

A second massive error that Heiwa makes in his statement that "a smaller portion of the building can never crush down a bigger section" is to assume - incorrectly - that you can average the stress & strain energy over the entire structure. Doing this ignores (& eliminates) stress & strain energy concentrations that are key to progressive collapse.

tom

[Architect]

I concur and, like yourself, make similar points in the "gravity" thread. What I'm trying to establish here is the basis for Heiwa's "FoS>3" claim and how he responds to the NIST data showing this to be incorrect.

[Architect]

Originally Posted by bill smith

Well if this is not the ultimate compliment I don't know what is. Heiwa's very own forum. I hope you have not bitten off more than you can chew Architect.

Originally Posted by http://www.topix.com/forum/topstories/TSBMT04T49GGG7HFO/p3722

bill smith wrote:
<quoted text>
I've ben following the arguments over there and nobody has debunked any statement that Heiwa has made. Otherwise they woud all be all over him like white on rice just as you see the jackals here jump on wounded prey. That hasn't happened over there. The best they have managed to do is the pizza boxes the sponge and the bed.
The Architect whiner should do what Heiwa told him to do and read the papers Heiwa has published with all relevent calculations already in and for which he has provided links..

Bill, You must be terribly disappointed with Heiwa's attempts on this thread thus far.

[Heiwa]

Originally Posted by tfk

A second massive error that Heiwa makes in his statement that "a smaller portion of the building can never crush down a bigger section" is to assume - incorrectly - that you can average the stress & strain energy over the entire structure. Doing this ignores (& eliminates) stress & strain energy concentrations that are key to progressive collapse.

tom

I would say that this is the error of NIST, Bazant, Seffen & Co. They apparently assume in their 1-D models some average stress/strain energy applied over 4000 m˛ WTC 1 cross area of structure shredding only the lower contact part of it, the damaged elements of which are then compressed into rubble, etc. Upper part C remains intact. Fantasy of course - and nothing to do with structural damage analysis. If you read my article you will find that only 0.05 kWh/ton rubble is apparently used to crush down WTC1 as per NIST & Co:s model. That is much too little. To shread, e.g. a car you need 36.7 kWh/ton or 734 times more energy.

You are 100% right that you have to study the 'stress/strain energy concentrations' and what they are up to, i.e. what happens where elements of upper part C contact lower part A and vice versa. The result is always only local failures and ... collapse/crush down/destruction arrest.

[KTB]

Hey heiwa, how about you just answer the question about "FoS>3"? You are getting tedious.

[Architect]

Originally Posted by Heiwa

I would say that this is the error of NIST, Bazant, Seffen & Co. They apparently assume in their 1-D models some average stress/strain energy applied over 4000 m˛ WTC 1 cross area of structure shredding only the lower contact part of it, the damaged elements of which are then compressed into rubble, etc. Upper part C remains intact. Fantasy of course - and nothing to do with structural damage analysis. If you read my article you will find that only 0.05 kWh/ton rubble is apparently used to crush down WTC1 as per NIST & Co:s model. That is much too little. To shread, e.g. a car you need 36.7 kWh/ton or 734 times more energy.

<snip>

Heiwa

This is a thread specifically for your to support your claim that the factor of safety found at the towers was greater than 300% ("FoS>3"). A copy of your post, and my detailed response querying the veracity of your claim, form the OP. Should you wish to discuss gravity collapse models then you should go to that thread.

Now, are you able to defend your own proposition regarding safety factors with, for example, calculations or detailed references to codes? Or, to be quite frank, did you just make the figure up? And if it's the former, can you please explain to me, in detail, where my response to your claim is in error.

[Heiwa]

Originally Posted by KTB

Hey heiwa, how about you just answer the question about "FoS>3"? You are getting tedious.

Already answered several times above and in other threads. You missed THAT?

[Dave Rogers]

Originally Posted by Heiwa

Already answered several times above and in other threads. You missed THAT?

Heiwa has not, of course, done so. There is no post where he gives a source or calculations to justify his bare assertion that the WTC towers were built with a FoS greater than 3. This will be demonstrated by the fact that he will be unable, in reply to this post, to link to any such post, but will instead at most simply repeat his assertions.

Dave

[KTB]

Originally Posted by Heiwa

Already answered several times above and in other threads. You missed THAT?

The sad thing is that you actually believe this yourself. Well good luck with your calculations, you really rock.

[Heiwa]

Originally Posted by Dave Rogers

Heiwa has not, of course, done so. There is no post where he gives a source or calculations to justify his bare assertion that the WTC towers were built with a FoS greater than 3. This will be demonstrated by the fact that he will be unable, in reply to this post, to link to any such post, but will instead at most simply repeat his assertions.

Dave

Maybe you misunderstood my reply? Regardless, various FoS of the WTC structure components is of no importance as long as it is accepted that upper part C was built similar to lower part A, incl. FoS of elements.
The basic mistake of NIST and Bazant & Co when analyzing the destruction is that they treat the problem as a mechanical one of solids, where you can assume parts and elements to be rigid, i.e. they do no deform. In structural analysis evidently no part is rigid, as the whole purpose is to see how each non-rigid element deforms elastically and transmits the loads as forces and moments from one element to another. Structural damage analysis is the most advanced stage of structural analysis as then elements are deforming or have deformed plastically and/or failed and the whole layout of the structure under analysis change at every failure with associated modified load paths, etc.
It seems NIST and Bazant & Co have very limited experience of structural damage analysis or just simple structural analysis, as they introduce rigid elements and complete rigid parts in their models. As the rigid parts do not deform at all they evidently transmit forces without getting damaged. And then, e.g. FoS of elements inside this assumed rigid part bcomes of no interest to them.
Result? Horrendous conclusions that a small part of a structure (assumed rigid) can crush a bigger part of the same structure (assumed non-rigid) and similar; the small part (assumed rigid) accelerates through the big part, etc, etc. It is sad that NIST has adopted such stupid methods ... and the result is evident: to suit a misguided political agenda based on scientific nonsense.

It is quite funny to follow the supporters of this agenda here at JREF and their arguments. I have put most of the worst ones on ignore as they just repeat themselves and just study the more advanced ones. But it is the same nonsense, nevertheless.

[Dave Rogers]

Heiwa's responses to being caught in a lie:

(a) Claim he never said it.
(b) Admit he said it, but pretend it's true.
(c) Claim it doesn't matter.
(d) Accuse everyone else in the world of lying.

Basically, just like the small children he claims to be talking to.

Dave

[A W Smith]

Anders.

I see nowhere your worksheets or calculations proving a safety factor of 300% ("FoS>3").. You keep saying you have answered this but it is perfectly clear to all you have not. You have been caught in a lie. Your work is nothing more than false assertions and errors of omission.

Answer the op or concede.

[Architect]

Originally Posted by Heiwa

Maybe you misunderstood my reply? Regardless, various FoS of the WTC structure components is of no importance as long as it is accepted that upper part C was built similar to lower part A, incl. FoS of elements.

Anders

You were the one who raised the issue of Factor of Safety as supporting evidence that the lower structure had sufficient integrity to restrain the overall collapse.

Having been asked to justify this statement, inasmuch as calculations of actual demand to capacity ratios are significantly less, you have claimed that the Factor fo Safety is "of no importance".

I assume that you realise how this appears. Either:

(a) The FoS is not relevant and you introduced spurious material in support of your argument, or

(b) You have been unable to support your claim.

Whichever it is, it doesn't look very good, does it? And if it's (a), then I think you have to retract the post you originally made on the subject.

So, which is it?

[Gravy]

Originally Posted by Heiwa

The basic mistake of NIST and Bazant & Co when analyzing the destruction is that they treat the problem as a mechanical one of solids, where you can assume parts and elements to be rigid, i.e. they do no deform.

Guess what? Claiming something doesn't make it true.

Quote:

It seems NIST and Bazant & Co have very limited experience of structural damage analysis or just simple structural analysis...

Says the guy who thinks the Twin Towers were analogous to pizza boxes and towers of lemons.

Why did you lie about the factor of safety?

[Heiwa]

Originally Posted by A W Smith

Anders.

I see nowhere your worksheets or calculations proving a safety factor of 300% ("FoS>3").. You keep saying you have answered this but it is perfectly clear to all you have not. You have been caught in a lie. Your work is nothing more than false assertions and errors of omission.

Answer the op or concede.

I have answered that one several times, which is perfectly clear to me. See http://heiwaco.tripod.com/nist0.htm#3 . Just click and look. Scroll down to 5.3.

Any problem? It deals with the primary structure - the columns. Pretty strong - to say the least.

Redundancy is then provided by the spandrels. Remove 70% of the wall columns in the north wall, i.w.o. floors 93-98 and nothing really happens.

Reason? These columns were low stressed in the first place, FoS>5 w.r.t. static loads, and the load was just transmitted via the spandrels to the adjacent intact structure, incl. all the other walls.

Why are you so concerned about F.o.S.? You do not like my conclusion that upper part C can never crush lower part A? Or all observations that upper part C is destroyed by controlled demolition before part A suffers the same fate? Let's discuss those instead. They are more interesting.

Why does NIST invent a stupid theory that little part C can destroy big part A because PE>SE without any calculations of PE or SE? Why do Bazant & Co have to assume that part C is rigid while part A below is not in a 1-D model where a rigid line C compresses a non-rigid line A? These people seem to lack imagination. Can't they come up with cleverer propaganda?

It was not necessary. Any US person with relevant qualifications that queried the NIST/Bazant nonsense was quickly fired from his job! So the rest shuts up. No solidarity there. Lack of moral fibre throughout.

Except my hero Richard Gage and his team at http://AE911truth.org. Join them.

[A W Smith]

Originally Posted by Heiwa

I have answered that one several times, which is perfectly clear to me. See http://heiwaco.tripod.com/nist0.htm#3 . Just click and look. Scroll down to 5.3.

Any problem? It deals with the primary structure - the columns. Pretty strong - to say the least.

Redundancy is then provided by the spandrels. Remove 70% of the wall columns in the north wall, i.w.o. floors 93-98 and nothing really happens.

Reason? These columns were low stressed in the first place, FoS>5 w.r.t. static loads, and the load was just transmitted via the spandrels to the adjacent intact structure, incl. all the other walls.

Why are you so concerned about F.o.S.? You do not like my conclusion that upper part C can never crush lower part A? Or all observations that upper part C is destroyed by controlled demolition before part A suffers the same fate? Let's discuss those instead. They are more interesting.

Why does NIST invent a stupid theory that little part C can destroy big part A because PE>SE without any calculations of PE or SE? Why do Bazant & Co have to assume that part C is rigid while part A below is not in a 1-D model where a rigid line C compresses a non-rigid line A? These people seem to lack imagination. Can't they come up with cleverer propaganda?

It was not necessary. Any US person with relevant qualifications that queried the NIST/Bazant nonsense was quickly fired from his job! So the rest shuts up. No solidarity there. Lack of moral fibre throughout.

Except my hero Richard Gage and his team at http://AE911truth.org. Join them.

Quote:

5.3 Compressive Stresses in the primary Structure Columns - less than 1/3 of the Yield Stress
The mass above the walls at floors 94-98 is thus about 16 500 tons supported by 236 wall columns (total cross area 3.54 m˛). Therefore each wall column on average supports 70 tons.
The compressive stress in the wall column at floors 94-98 with cross area 150 cm˛ is thus abt 467 kgs/cm˛ or 46 MPa or 18.8% of the yield stress (abt 248 MPa) of the steel.
NIST suggests that the static loads will be increased 35% in the East wall and 30% in the West wall (all 100% intact) due to load transfers just prior collapse, i.e. the compressive stresses in columns there becomes 62.1 and 59.8 MPa, which is still only 25% and 24% if the yield stress. Actually these are the increased stresses you would expect due to wind under hurricane conditions.
The mass above the core is also 16 500 tons supported by the 47 core columns with total area 2.1 m˛. On average each core column carries abt 351 tons so the average compression is 786 kgs/cm˛ or 78 MPa or 31.7% of yield. The outer core columns carry more mass and the outer corner core columns the most load, e.g. no. 501 with cross area 950 cm˛. It may carry as much as 750 tons.
The compressive stress in the no. 501 core column at floors 94-98 is thus abt 789 kgs/cm˛ or 78 MPa or 31.7% of the yield stress of the steel. It is assumed that the compressive stress in the other core columns is abt the same or less.
NIST suggests that the load in the core is reduced 20% just prior collapse, i.e. the stresses are reduced. However, some core columns may have been damaged in the initiation zone so in all probability the stresses in the remaining columns may have remained at 30% yield stress.
The reason why original the static stresses are higher in the core than in the perimeter walls is that the wall columns are also designed to absorb dynamic wind loads

and here in all its glory is your error of omission

http://en.wikipedia.org/wiki/Buckling

Quote:

In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment, which does not form part of the primary forces to which the member is subjected.

[Architect]

Let's play a game called "compare and contrast". First, Heiwa:

Originally Posted by Heiwa

5.3 Compressive Stresses in the primary Structure Columns - less than 1/3 of the Yield Stress
The mass above the walls at floors 94-98 is thus about 16 500 tons supported by 236 wall columns (total cross area 3.54 m˛). Therefore each wall column on average supports 70 tons.
The compressive stress in the wall column at floors 94-98 with cross area 150 cm˛ is thus abt 467 kgs/cm˛ or 46 MPa or 18.8% of the yield stress (abt 248 MPa) of the steel.
NIST suggests that the static loads will be increased 35% in the East wall and 30% in the West wall (all 100% intact) due to load transfers just prior collapse, i.e. the compressive stresses in columns there becomes 62.1 and 59.8 MPa, which is still only 25% and 24% if the yield stress. Actually these are the increased stresses you would expect due to wind under hurricane conditions.
The mass above the core is also 16 500 tons supported by the 47 core columns with total area 2.1 m˛. On average each core column carries abt 351 tons so the average compression is 786 kgs/cm˛ or 78 MPa or 31.7% of yield. The outer core columns carry more mass and the outer corner core columns the most load, e.g. no. 501 with cross area 950 cm˛. It may carry as much as 750 tons.
The compressive stress in the no. 501 core column at floors 94-98 is thus abt 789 kgs/cm˛ or 78 MPa or 31.7% of the yield stress of the steel. It is assumed that the compressive stress in the other core columns is abt the same or less.
NIST suggests that the load in the core is reduced 20% just prior collapse, i.e. the stresses are reduced. However, some core columns may have been damaged in the initiation zone so in all probability the stresses in the remaining columns may have remained at 30% yield stress.
The reason why original the static stresses are higher in the core than in the perimeter walls is that the wall columns are also designed to absorb dynamic wind loads

Now, the challenge put to Heiwa:

Originally Posted by Architect

NIST tested the steel recovered from WTC (which in itself is of interest, as CTers usually claim it was all whisked away to China with unseemly haste). NIST NCS STAR 1-3D (http://www.fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf) confirms a range of actual values:

- Core webs ranged from as low as 31.1 to 41.9 ksi, ie. 86 to 116% of specificed strength.

- Core flanges ranged from 32.4 to a high 53.4 ksi, ie. 90 to 146% of specified strength.

Setting to one side the 31.1 and 32.4 ksi results, inasmuch as a small proportion of columns below failure point are unlikely to lead to any wider problem, let's take the lower maximum of 116% specified value.

Now, the NIST Demand to Capacity Ratios (DCR) are based upon specified strengths and NIST themselves note that there is effectively spare capacity up to actual (but varying) yield point/strength.

Core columns in WTC typically had a Demand to Capacity Ratio (DCR) of 0.83, ie a safety factor of 1/0.83=1.20. Now let's assume assume that the steel has an additional 16% beyond minimum yield value. This would reduce the DCR to 1.16/.83=1.4.

In other words we could increase the loads in these areas by up to 40% before yield point was reached and plastic (permanent) deformation begins. Of course this figure has lots of variables - most of the steel webs did not have such a high yield factor, some areas had DCRs well in excess of 0.83, and so on.

What we don't do is then add any significant additional allowance for tensile strength because (a) yield failure is already occuring and (b) gravity loads will be compressive, not tensile.

As I frequently mention elsewhere on the forums, one thing we also have to appreciate is that the structure of WTC is complex; in addition to dead and live loads, it will be dealing with (for example) transverse and shear loadings from the wind. There will be a degree of torsion due to differential loading. And so on. We would therefore have to look at the exact steelwork design in considerable detail before we could determine a safety factor for each. That's why engineers earn a lot of cash, and why complex modelling software was developed.

Nevertheless it is clear that the actual capacity of the core is not going to be anything like 300% or 3:1 before irreversible damage and failure begin to occur.

But in any event the above calculations all assume an intact core, and we know from the various NIST studies and eyewitness evidence that the cores suffered damage - around a third. This will obviously have reduced loadbearing capacity still further, and a simple pro-rata reduction of (say) 30% is likely to be wrong because the damage is concentrated in localised areas and hence these areas will be susceptible to accelerated failure under loads.

Essentially, Heiwa's figures bear little resemblance to reality. Why might this be?

[Heiwa]

Originally Posted by A W Smith

and here in all its glory is your error of omission

http://en.wikipedia.org/wiki/Buckling

Yes, but in the case of WTC columns the buckling stress exceeds the yield stress so the yield stress is the critical stress. Explained elsewhere is my paper. Pretty strong columns, to say the least.

Thanks for visiting my web site. There is plenty to learn there.

[Gravy]

Originally Posted by Heiwa

Yes, but in the case of WTC columns the buckling stress exceeds the yield stress so the yield stress is the critical stress. Explained elsewhere is my paper. Pretty strong columns, to say the least.

In what engineering arena is "I made everything up" an acceptable response to thoughtful criticism?

[R.Mackey]

Imagineering.

[beachnut]

Originally Posted by Heiwa

Yes, but in the case of WTC columns the buckling stress exceeds the yield stress so the yield stress is the critical stress. Explained elsewhere is my paper. Pretty strong columns, to say the least.

Thanks for visiting my web site. There is plenty to learn there.

... one can learn you base your conclusions on delusions not science.

An Aluminum aircraft cut the outer shell like butter, and cut core columns. There goes your super strength of steel beat by Aluminum. No wonder the planes I fly were strong, they can cut steel.

Your web page is joke to engineers.