Thermal expansion of beam K3004, integrated instantaneous vs. mean coefficient of thermal exp

Mick West

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Staff member
Its nothing like that. But if you can't explain it thats OK.

It's more like a triangle vs. rectangle on top of a tall rectangle, but I thought that a bit hard to visualize. Look at what you did with the three stages.

As the formula used Delta T then it was clear to me that a step by step process could be used. I used the formula to check expansion from ambient to 300C ( 572F ) as follows :-

640.69 x 502 x 0.0000069968 = 2.25" ( new length 640.69" + 2.25" = 642.94" )

Then I applied the formula and coefficient for a further rise from 300C ( 572F ) to 500C ( 932F ) as follows :-

642.94 x 360 x 0.0000076808 = 1.78" ( new length 642.94" + 1.78" = 644.72" )

Again from 500C ( 932F ) to 600C ( 1112F ) as follows :-

644.72 x 180 x 0.0000080228 = 0.93" ( new length 644.72" + 0.93" = 645.65" )

Thus I had staged the event from ambient to 600C ( 1112F ) over three seperate calculations using Delta T logic and the new coefficient for each seperate event, and got final length 645.65" - an increase from 640.69" of 4.96".

As this was less than the 5.35" achieved by going in one stage from ambient directly to 600C in my initial simple calculation it indicated that using three stages had had a reducing effect. That led me to consider that if I had staged the calcs over 1042 stages representing each single degree F from ambient to 1112F then a further reduction would probably be seen.

Here's a rough visualization of what you did:


The area above the line represents the amount of expansion.
 
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Tony Szamboti

Active Member
Yeah, all debunked 9/11 Truth points immediately become moot points. :)
I acknowledged that you were right here and that I didn't realize they were giving averaged CTEs from room temperature to the temperatures in question in those non-constant steel CTE charts. One question I would have concerns what is done for steel out in the cold if those CTE are averaged from room temperature.

Finally though, it actually is a moot point, and you can't make much out of it in terms of helping the NIST report gain credibility, when the truth is the seat was 12" wide and their story has the problems of not being able to explain how they even get 6.25" of expansion, let alone the 8 or more inches needed when those omitted stiffeners get put back on the girder, and their alternative fails when the omitted beam stubs get put back on the G3005 beam.

Although the NIST WTC 7 report may get something right here and there, let's not forget that NIST has had to admit errors themselves and that the overall picture shows the report is non-explanatory based on the omissions, the failure to explain things like how one even gets 6.25" of expansion, and we shouldn't forget how the 8 story symmetric free fall was never explained. You need to start explaining these things if you actually believe the report is valid.

Additionally, before we go too far, I want to say there was always a problem with the 5.5" beam expansion distance to begin with, because the .580" thick web doesn't actually come off an 11" wide seat before the distance travelled is 5.79", so the 5.5" was not explanatory either. The 6.25" travel at least gets the web within 0.040" of being off the seat, but it is very unlikely that the beams would have been heated to the temperatures needed for that kind of expansion and even it is a moot point with the stiffeners on the girder.

It wasn't NIST's job to provide answers to moot points. Their job was to explain the collapse. They have not done that, as the omissions show they couldn't even get close without a little cheating, and I haven't seen you, or anyone else who still believes their hypothesis has merit, add anything that helps them in that endeavor.
 
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Tony Szamboti

Active Member
Two other problems for the NIST walk-off theory are

1. The girder locking up against the face of column 79 due to its own expansion, if it is at 500 degrees C that the NIST WTC 7 purports. The clearance between the tip of the girder and the web of column 44 is 0.916" and between the tip of the girder and the flange face of column 79 is 1.074". That is a total of 1.990" and at 500 degrees C (932 degrees F) Mick's chart shows the CTE is about 7.96 x 10e-6 in/in-deg F. So the expansion for a 45 foot long girder would be 3.7". This means each end of the girder would be compressed by about (3.7 -1.990)/2 = 0.855". If we consider the fact that the girder was beveled slightly at the ends and only half of the compression 0.855/2 = 0.4275" involved the full cross section of the girder the axial force would be

F = (0.4275 in. x cross sectional area x modulus of elasticity)/length
= (0.4275 in. x 38.3 sq. in x 29 x 10e6 lbs/sq. in)/540 in.
= 879,304 lbs.

That is a serious amount of force and if the coefficient of friction is just 0.2 the lateral frictional force the beams would be trying to overcome would be 0.2 x 879,304 lbs. = 175,861 lbs. at both ends of the girder. Only the close in K3004 beam would have any real force to apply to overcome the friction, as the others are far enough away that they would deflect the laterally weak girder first. K3004 would buckle at about 40,000 lbs, so there is no chance the friction could be overcome. This would also work both ways in the sense that the friction would prevent rock-off to the east also, as the column 79 end of the girder only handles about 65,000 lbs. of floor load and most of that would not be pulling laterally. I actually ran a finite element analysis of this and K3004 started to buckle. None of the other beams did, and the girder stayed on its seats.

2. If it is at 500 degrees C the girder is well within the extended edges of the side plates of column 79 and they would only allow it to move 3.25" to the west. This would also work on both sides of the girder flange since there is a side plate on each side of column 79.
 
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Mick West

Administrator
Staff member
I try to focus here. Sort out one thing at a time. I try not to jump to conclusions.

The conclusion that the NIST report was fatally flawed is not a conclusion I'm at all ready to jump to. Not because I have any fondness for government, but because everything I've seen leads me to think the NIST investigation is a best effort attempt at discovering the truth by those involved. It's a massive report, from a massive, years long investigation. It's going to have some flaws. Large projects do. The Space Shuttle blew up twice because of human error, and they spent $196 billion on that. Humans make mistakes.

This though was not NIST's error. It was your error. You described it as "an extremely sophomoric thing", and yet NIST were actually entirely correct.

I'm a little slow, and I apologize for that. But experience has taught me, and this example illustrates, that arriving at conclusions swiftly is not always the best way or arriving at the right conclusions.

So I'm not going to leap to accepting your other problems. I would hope that you to might take at least a tiny little step back, and ask yourself if there is any way that NIST's broader hypothesis might possibly be correct.
 

Tony Szamboti

Active Member
Mick, it is obvious that you are not leaping to accepting the problems we have shown in the NIST WTC 7 report.

I am an engineer and well aware of the human ability to make mistakes. So I have indeed asked myself many times if the NIST report could possibly be right and unfortunately in the end, when considering all of the evidence, the answer has been an overwhelming no. The evidence against the NIST reports 's conclusions is too great for a minor math error, or misinterpretation of something that was already averaged for convenience, to salvage it. I made a minor error in the Missing Jolt paper at first and had to correct it, but it was far from something which changed the premise. In that case the correction strengthened it.

In this case it is like two cops clocking somebody at 150 mph on a 55 mph speed limit highway and in court it is determined that their radar guns were off by 10%. So the clocked car could have been doing 135 mph. It does not change the conclusion.

You need to ask yourself why those stiffeners and beam stubs were omitted. The answer when those questions are asked is usually fraud because the person involved could not get the answer they wanted while leaving in the items they omitted.
 
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Tony Szamboti

Active Member
Just thought I would post a recalculated spread sheet using the Mean CTE over the range from RT to the temperature in question with shortening included. See the attachment.

Using the Mean CTE at 600 degrees C one does get an expansion of 5.52" when sagging induced shortening is not included. However, at 600 degrees C the K3004 beam (a 644.75" long W24 x 55) deflects over 6 inches downward with an 87.5 psf floor load so shortening certainly comes into play and when it is included the net expansion is 5.36". To get the full 0.580" thick girder web off an 11" wide seat plate requires 5.79" of beam expansion. So 0.430" or 74% of the girder web thickness would have remained on the seat at 600 degrees C with an 11" wide seat plate.

What is also interesting is that the maximum possible expansion is 5.64" at 649 degrees C, as beyond that temperature shortening due to sagging increases more than expansion. So with the actual 12" wide seat plate, under the most favorable conditions for beam expansion, the 6.25" of travel that NIST now requires to move the girder web off the seat is completely impossible.

This is without even bringing up the omitted girder end flange to web stiffener issue, which would easily require more than 8.00" of beam expansion for the girder to fall off the seat. This issue is actually the coup de grace to the NIST girder walk-off theory and completely shuts the door on it. There is nothing to debate here.
 

Attachments

  • K3004 expansion using mean CTE from RT to temperature in question and shortening due to sagging.xlsx
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mynym

Banned
Banned
Yeah, all debunked 9/11 Truth points immediately become moot points. :)

They don't have a right to an overall "body of evidence" theory? That would be ironic. Because the unfalsifiable theories that you've built from a distorted body of evidence based on a denial of what it looked like to begin with and a simulation of an investigation later are still in the background no matter what is concluded here: "...multiple failures.... due to fire...."

In context, it's all a moot point. Even if the beam expanded or didn't expand but the floors did and then didn't or the shear studs might have been there in a simulation of an investigations but then were not in another simulation of the vivid imaginations of NIST, etc. It's all ultimately a moot point until people state their over all theories in a series of verifiable/falsifiable ways. Interesting hobby in the meantime, though.
 

gerrycan

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Banned
Err, no. The topic of the thread is not going to change later. In this case it's agreed that NIST were correct, on this one small point. There's nothing to see about later.
There seems to be a bit of a debate re your assumption, however, as has already been said, the real issue is how far the girder can be pushed, and there are variables elsewhere that you have not yet taken into account. As with buildings, claims and criticisms can have an inbuilt factor of redundancy, and the one made in the videos certainly does, regardless of your claims on this thread, which I am not quite ready to accept yet.
 

gerrycan

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Mick, I have been fairly busy, but I am looking into it. Just saying that I am not willing to accept it without thoroughly checking it first. Something in there doesn't quite look right maths wise.
 

gerrycan

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Banned
Sure, I think you are wrong. I think you are taking a maximum value possible that in no way relates to what would happen in the real world or would be replicated in a realistic FEA. But like I said, for the purposes of this debate I am happy enough to concede that point and allow you to deal with it in the thread that you started specifically for it, so we can get to the issue in question here. So, rather than maximum expansion, what do you think the maximum distance that the beam can push the girder would be?
 

Mick West

Administrator
Staff member
Sure, I think you are wrong. I think you are taking a maximum value possible that in no way relates to what would happen in the real world or would be replicated in a realistic FEA. But like I said, for the purposes of this debate I am happy enough to concede that point and allow you to deal with it in the thread that you started specifically for it, so we can get to the issue in question here. So, rather than maximum expansion, what do you think the maximum distance that the beam can push the girder would be?

So, just to be clear, you agree that when YOU calculated the maximum expansion at 4.67", you were wrong? In this:
upload_2013-10-31_14-49-51.png
 

gerrycan

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Banned
So, just to be clear, you agree that when YOU calculated the maximum expansion at 4.67", you were wrong? In this:
Nope. As far as real world calculations go, i think we overestimated it as we did with every other variable that could be in favour of NISTs story. However, you have a thread elsewhere for this very topic. We can talk about it there sometime. So where you getting the extra 1.75" from? And that figure presumes you are correct with 5.5" and accounts for no stiffener plates.
 

Tony Szamboti

Active Member
So you don't agree you used the wrong coefficient there? Tony has already agreed it was wrong.

Yes, I did at first, but after looking at the information available I am no longer sure that the Worcester Polytechnic Institute graph for the CTE at various temperature for ASTM A572 was an average from room temperature for each temperature in question. It was not labeled as such. I think we need to verify that the 8.2 x 10e6 in/in-deg.F CTE that NIST would have used to get 5.5" of expansion for the 53'-8 11/16" long beams at 1,112 degrees F (600 degrees C) was in fact an average from room temperature to 1,112 degrees F.

Otherwise the charts are useless except for something starting at room temperature. I don't know that you have proven that that CTE is an average.
 

Mick West

Administrator
Staff member
Yes, I did at first, but after looking at the information available I am no longer sure that the Worcester Polytechnic Institute graph for the CTE at various temperature for ASTM A572 was an average from room temperature for each temperature in question. It was not labeled as such. I think we need to verify that the 8.2 x 10e6 in/in-deg.F CTE that NIST would have used to get 5.5" of expansion for the 53'-8 11/16" long beams at 1,112 degrees F (600 degrees C) was in fact an average from room temperature to 1,112 degrees F.

Otherwise the charts are useless except for something starting at room temperature. I don't know that you have proven that that CTE is an average.

Tony that graph is utterly meaningless. It's not a reference. It's just something she GENERATED from the generic SPFE/AISC formula α = (6.1+ 0.0019T) ×10^−6. It's not even specific to ASTM A572 steel. The other sources in the thread confirm that it's a mean value.
 

Tony Szamboti

Active Member
Tony that graph is utterly meaningless. It's not a reference. It's just something she GENERATED from the generic SPFE/AISC formula α = (6.1+ 0.0019T) ×10^−6. It's not even specific to ASTM A572 steel. The other sources in the thread confirm that it's a mean value.
We talked more about it on the Skype call and Hit Stirrer did find a chart which gave instantaneous and mean CTEs for several steel alloys. It validated what you were saying and everyone now agrees that you were right that the CTE NIST used was a mean from room temperature to 600 degrees. So we will correct that area of the argument.

However, as you seem to also agree it doesn't change the overall argument that with the omitted structural features included the NIST claim that the girder would be pushed or rocked off its seat is impossible.

It is also interesting that the debate here caused us to consider the expansion possibilities at the east side exterior. I hadn't seen the K3004 beam connection at column 38 before and the previous assumption was that it was fully rigid. My calculations show the shear stud restraint would certainly cause the two 7/8" diameter ASTM A325 erection bolts to break there before all 28 shear studs would fail on the beam. There is about 3/4" clearance between the end of the beam and the web of the column and the sharp corner of the beam would compress at least 1/4" when forced against the web, so the beam would expand at least an inch to the east. This leaves a net westward expansion of 4.5 inches, which couldn't cause a girder fall off an 11 inch seat, let alone a 12 inch wide one, and certainly not with stiffeners on the girder.
 
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