The pre-collapse inward bowing of WTC2

Another way to approach it is to take a simple example and analyse the vectors.

IF we have a rigid beam loaded with 2W at the centre there will be a downward force of W on each end support. And no pull in force.

Replace it with a rope. Still holding the same 2W load. Depending on the length of rope the support to weight - both sides will be a straight line (zero weight rope) and WHAT EVER the length of rope will determine the angle of each side. BUT the downwards force vector on each support will still be W

Now if the rope sags so that each end slopes downwards at 45 degrees:

1) The downwards force vector on each support will still be W;
2) The horizontal force vector will also be W - inwards; AND
3) The tension in the rope will be 1.414W

Pure geometry of the vectors. And at 45 degrees inwards pull = half the centrally applied download.

Now shorten the rope so that it slopes at 10 degrees below horizontal:
1) The downwards force vector on each support will still be W;
2) The horizontal force vector will now be 5.67 W - inwards; AND
3) The tension in the rope will be 5.76 W

Shorten again to 5 degrees slope:
1) The downwards force vector on each support will still be W;
2) The horizontal force vector will now be 11.43 W - inwards; AND
3) The tension in the rope will be 11.47W

At 2 degrees:
1) The downwards force vector on each support will still be W;
2) The horizontal force vector will now be 28.63W - inwards; AND
3) The tension in the rope will be 28.65W

At 1 degree - very close to horizontal:
1) The downwards force vector on each support will still be W;
2) The horizontal force vector will now be 57.29W - inwards; AND
3) The tension in the rope will be 57.29W

All that rope tension from a 2W load at the centre. ~30 times multiplier.

And a direct consequence of the vector geometry. Which shows why:
Oystein's hammocks needed a stronger rope; AND
Why JS Orling can see his anchor chain move the boat.

PLUS my exploitation of child labour worked - and my grandson could bend in that "perimeter column" by pushing the taut rope sideways.

AND why the natural - original - unaugmented weight of ONE WTC floor could exert a large inwards pull once the joists got hot enough to act like flexible ropes.
 
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...
AND why the natural - original - unaugmented weight of ONE WTC floor could exert a large inwards pull once the joists got hot enough to act like flexible ropes.
This would be limited by the strength of the seat welds.

I am trying to think how the inward pull of a partially rigid joist could be calculated. Think of a flexible panel of wood resting unrestrained on both ends on a seat. You step on it, the plank sags somewhat correspinding to your weight, the ends are correspondingly pulled in somewhat, but only until a new equilibrium is reached. Now nail the plank to the seats - you stepping on it will exert a lateral force on the nail, but I'd think it is not as large as the force with which a rope in the same shape as the plank would pull.
Back to nailed plank; you stand on it, it's in tension, but partly supported by its own vertikal strength. Now someone works on the underside of the plank with a planer, decreasing its thickness and thus diminishing its strength. That would increase the tension.
 
Not saying that heating of (mostly the inward side of) the perimeter columns was a major contributor, just that even 250C heating would contribute yet another slight allowance for bowing. Perhaps by linear expansion on the inward side more than by loss of strength.
If I were to guess what the greatest contribution was I would say load redistribution. Sagging trusses simply offered a mechansim by which bowing was preferentially inward over several floors where sagging trusses were.


tell me.....how does "sagging trusses", pull?
they don't.....they sag....there is NO 'extra' force being offered here....they will sag, IF, the fires present are HOT enough to do so

there is NO scientific validation WITHIN the NIST report that SAYS the trusses sagged and pulled from the fires present....the reason NONE of you can post any VALIDATION!

me thinks you have been looking at that lying RKOwens video of the CARTOON of the columns pulling in and then QUICKLY panning into a close-up of the collapse ALREADY in progress.....all to FRAUDULENTLY claim a bow occurring before collapse......that NO continuous video shows......


"sagging trusses are NOT a mechanism......but the FIRE is.

prove the FIRES PRESENT did what you claim occurred....

NO trusses within the core to act upon the core to DESTROY/push it to the ground.....steel touching steel from the hat truss to the bedrock....CONTINUOUS and uninterrupted...
elevators, stairways and landings all go in between these CONTINUOUS load bearing support columns......NO 'crush-down' mechanism......


“The core columns were designed to carry the building gravity loads and were loaded to approximately 50% of their capacity before the aircraft impact.... the exterior columns were loaded to only approximately 20% of their capacity before the aircraft impact” JOM, vol. 59, no. 11
Content from External Source

occurring 14.5% localized damage to each leaving 240 intact fireproofed load bearing vertical support on EACH towers impact floor which redistributed the load just as designed to do.


NIST: “Both WTC 1 and WTC 2 were stable after the aircraft impact, standing for 102 min and 56 min, respectively.
The global analyses with structural impact damage showed that both towers had considerable reserve capacity”
Content from External Source

you are welcome to post DIRECTLY from the 10,000+ page NIST report ANYTHING that supports the BULL you spew here......PICS are NOT a scientific findings, they can assist, but these pics are already labeled with this science.....

"No conclusive evidence was found to indicate that pre-collapse fires were sever enough to have a significant effect on the microstructure that would have resulted in weakening of the steel structure." NIST NCSTAR 1-3C, p. 235

"no evidence the type of joining methods, materials, or welding procedures used was improper" NIST 1-3 p.99

"recovered bolts were stronger than typical". NIST 1-2 p.133

"no core column examined showed temp. above 250C" NIST 1-3 6.6.2

NCSTAR1-3 7.7.2 "because no steel was recovered from WTC7,it is not possable to make any statements about it's quality"
Content from External Source
prove the FIRES PRESENT allowed collapse to occur.....x3

be the FIRST!
 
This is the inward bowing thread.

a thread over something that DID NOT OCCUR!

tell me all about the 'EXTRA' force a 'sagging truss' possesses.....does heat ADD weight/force?

seems to me fire UNDER TRUSSES is NOT going to pull in a 32 foot perimeter columns tree inward that is NOT involved in fire....

and WHERE within the towers did this SUPPOSEDLY occur?
 
This would be limited by the strength of the seat welds.
The joist to column connection was the strength factor limiting the maximum pull-in force. From memory it was a couple of bolts which set the limit - not the welds. I rarely do the calculations - so many details focussed engineers competing on that low level stuff. So I almost always do the engineer manager's thing and look in overview to see if they have made macro level errors. Hence my interest in the "Challenge" from Enik to prove IB caused by joist pull-in using FEA. Newtons Bit took the challenge. Both of them active practitioners of FEA. One from the "truther" side. The other a relatively prominent forum debunker. And both lost the plot - united to attack me when I pointed out where they went astray. Same situation as the false assumptions T Sz made in Missing Jolt and Girder Walk-off. But - back to current focus - the details will be in the discussion on JREF/ISF.

My focus recently has deliberately been limited to explaining the principle of catenary sag force multiplication. I didn't want to confuse that discussion by reminding everyone that the joist<>column connection set the limit on IB force.

I am trying to think how the inward pull of a partially rigid joist could be calculated.
(Noises of rusty 73yo brain being engaged.)

(I thought I could explain it simply from basic principles.....but my first thoughts were wrong. I'll take a rain check and give it more thought. :oops: ) (Can explain qualitatively but cannot quantify it at this time.)
 
...all to FRAUDULENTLY claim a bow occurring before collapse......that NO continuous video shows......
Huh? Are you saying there was NO inward bow of perimeter columns observed before collapse?
Post #35 in this thread reproduces a photo from the final NIST report, showing the east face of the south tower almost a minute prior to collapse (release). I thinj it clearly shows inward bowing across almost the entire face. Do you agree, or disagree?

...steel touching steel from the hat truss to the bedrock....CONTINUOUS and uninterrupted...
Huh? Did you notice what the planes did?
And anyway, how does your claim invalidate the observation that columns bowed inwards on the floors most heavily affected by fires, where floors were actually seen to sag?
 
The joist to column connection was the strength factor limiting the maximum pull-in force. From memory it was a couple of bolts which set the limit - not the welds.
...
My focus recently has deliberately been limited to explaining the principle of catenary sag force multiplication. I didn't want to confuse that discussion by reminding everyone that the joist<>column connection set the limit on IB force.
It's something that JO occasionally points out - I think he thinks that the connectors are too weak to do anything significant to the spandreled perimeter columns.
Browsing NCSTAR1, I came across a couple of mentions that some percentage of the floor2perimeter connections had failed (I didn't bother to scan the context - observation from photos, or result of several partial FEAs they ran).

(Noises of rusty 73yo brain being engaged.)

(I thought I could explain it simply from basic principles.....but my first thoughts were wrong. I'll take a rain check and give it more thought. :oops: ) (Can explain qualitatively but cannot quantify it at this time.)
Qualitatively would be great. I don't require detailed formulas and actual numbers at this point - couldn't and would't check them anyway.
I am certain that such a discussion will introduce a few engineering terms to describe properties of steel elements that I am not familiar with (a matter of lacking both engineering training and foreign language vocabulary of the trade).
 
tell me.....how does "sagging trusses", pull?
they don't.....they sag....there is NO 'extra' force being offered here....they will sag,

Did you read the last dozen posts? Did you see the demonstration that econ posted? Do you have any understanding of force and physics at all?
 
tell me.....how does "sagging trusses", pull?
they don't.....they sag

In the same manner that a bowstring pulls the ends of the bow closer together when one draws back the arrow.

Every child understands that the fastest way between 2 points is a straight line. This is represented by the floor and the bowstring. And since neither the bowstring nor the floor can lengthen, when they are pulled away from being in a straight line, the 2 points that they connect to must become closer.
 
Being in the frozen north at the moment, I occurred to me that a visual demonstration might be done with a frozen rope.

A rope soaked in water could be frozen straight, so that it is a rigid rod. This can be rested on top of two supports - like two 2x4s. It can be nailed to the tops.

Then as the ice melts, the rope will sag, pulling in the supports, which will fall over.
 
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That is in direct conflict with the reports by Kevin Ryan who was privy to the results of actual trials in a furnace where he worked. He says that despite double the load and double the time being applied to the test that trusses actually sagged only 4". You will recall that he was concerned that NIST was using incorrect figures in their analysis and was disturbed that his protests via his own company were not being heeded. After going directly to NIST he was silenced by losing his job. We must accept that a 4" possible sag is insufficient to demonstrate the large inward bowing seen.
This is an earlier post in the thread, and I think it demonstrates a key misunderstanding - that the more sag there is the more pulling there is.

However the force from sagging is inversely proportional to the sag angle. It's at a max when the truss is not sagging, but is also inversely proportional to the stiffness.

Then you also have to account for the restraint force of the outer column, which would decrease as it bends, to a degree.

It gets complicated, but the point is that 4" sag in test conditions is not going to be proportional to the magnitude of inward bowing in the real world.
 
Being in the frozen north at the moment, I occurred to me that a visual demonstration might be done with a frozen rope.

A rope soaked in water could be frozen straight, so that it is a rigid rod. This can be rested on top of two supports - like two 2x4s. It can be nailed to the tops.

Then as the ice melts, the rope will sag, pulling in the supports, which will fall over.
In fact this is a factor to a point, with frozen lake ice. In early spring, Step onto an ice pan and see the edge get further from shore slightly.
 
This is an earlier post in the thread, and I think it demonstrates a key misunderstanding - that the more sag there is the more pulling there is.

However the force from sagging is inversely proportional to the sag angle. It's at a max when the truss is not sagging, but is also inversely proportional to the stiffness.

Then you also have to account for the restraint force of the outer column, which would decrease as it bends, to a degree.

It gets complicated, but the point is that 4" sag in test conditions is not going to be proportional to the magnitude of inward bowing in the real world.
Which does not preclude sagging trusses being the reason for preferential inward direction at bow initiation. Axial overload gave rise to bowing , truss sag made it inwards and once bowing inward began it cannot reverse direction and bow outwards. Absent removal of axial load, bowing will increase since bowing out of vertical reduces vertical load capacity.
 
a thread over something that DID NOT OCCUR!

tell me all about the 'EXTRA' force a 'sagging truss' possesses.....does heat ADD weight/force?

seems to me fire UNDER TRUSSES is NOT going to pull in a 32 foot perimeter columns tree inward that is NOT involved in fire....

and WHERE within the towers did this SUPPOSEDLY occur?
No, sag changes the direction of the weight vector. Did anyone ever say there was 'EXTRA' force other than you?

As far as sagging goes, what causes you to assume it did not occur? You do concede that perimeter column inward bowing occurred, right?
 
It gets complicated, but the point is that 4" sag in test conditions is not going to be proportional to the magnitude of inward bowing in the real world.

Complicated is certainly a good word to use. Various analagies have been put forward, such as ropes to replace trusses, then bow strings with a fixed length to pull outer fixed points inwards as a force is applied to the string, and then frozen ropes able to change from being a 'rod' into a hanging 'weight'. None address the real situation.

In reality the trusses are bolted at each end to columns. They are made composite with the concrete floors by shear studs. The coefficient of expansion of both steel and concrete are very similar, but differ widely over the rate of such expansion over time. To overcome this conflict the steel is fireproofed so that the concrete and steel expand together and retain the composite action to prevent breakup. All of the theorising in this thread starts with the assumption that a truss is an isolated element and can be examined alone.

NIST tried to make this possible by firing a shotgun at truss fireproofing to show that it all would be stripped away on impact by a plane and thus allow them to expose an unprotected truss in a simulated fire as it would be able to break free from the inconvenient composite floor structure. They then quite fraudulently claimed a 47" deflection after heating at double the temperature with double the load and for double the time. The actual deflection was 4.7" even after this unrealistic furnace exposure.

It isn't clear from the test whether the truss ends were fixed to stiff columns or just resting on supports. But what is well known is that steel expands with heat and will impart enormous axial forces which can easily shear the bolts at each end unless the truss buckles first. But what if the floor is still composite ? Buckling is then much less likely. Another complication right there. If the bolts break first then no inward bowing can happen as the truss is not connected to the outer columns.

If we assume that the concrete floor was destroyed by impact then some of this conflict is answered. But that still leaves a complication where a steel truss first of all expands axially well before it softens enough to begin to sag. Far from being a bow string with a pre-determined fixed length, it becomes a lengthening string of spaghetti with no strength to either push, or pull. The only force it can now impart is much more like Mick's defrosted wet rope except that in this case the wet rope is able to lengthen as the steel continues to expand as heat increases. Then we get back to the 4.7" sag in a simulated test and the geometry of what inward bowing would correspond to that central 'sag' distance.

One further thought. All of these various and variable scenarios have to occur identically with dozens of trusses at the same instant. You have to also assume that all the trusses that were on the opposite side to impact also lost their fireproofing and the floors were destroyed identically to the ones just discussed. All trusses achieved the same level of mechanical 'sag' and inward force at the same time despite wildly different fire exposures.

'Complicated' starts to look like an inadequate word.
 
All of these various and variable scenarios have to occur identically with dozens of trusses at the same instant. You have to also assume that all the trusses that were on the opposite side to impact also lost their fireproofing and the floors were destroyed identically to the ones just discussed. All trusses achieved the same level of mechanical 'sag' and inward force at the same time despite wildly different fire exposures.

'Complicated' starts to look like an inadequate word.
No, not all perimeter columns experienced inward bowing.
 
There are multiple factors involved. The two relevant ones for much of this discussion are:
1) The amount of remaining beam strength in whatever element we are considering - the extent to which it retains stiffness to span the gap; AND
2) The catenary tensions and pull in aspects resulting from the sagging.

Now the engineering physics principle that I started to explore for Oystein is that in any situation of multiple overlaid aspects you can analyse each aspect separately THEN add them up to get the overall conclusion.

So in the "partially flexible" situations the analysis is first how much beam stiffness is acting THEN overlay the extent of catenary action. Add the two - vector addition.

What isn't easy is identifying, separating and quantifying the two bits which is why I backed off in my response to Oystein.

However applying that to Mick's comments:

This is an earlier post in the thread, and I think it demonstrates a key misunderstanding - that the more sag there is the more pulling there is.
Correct. Being pedantic and avoiding the double negative risk. More sag does not mean more pull in. (Sideline - nor for a pure catenary does it mean more tension - transmission line wires can span longer with the same limit of maximum tension - provided the sag increases. It's in the geometry of a catenary.)
However the force from sagging is inversely proportional to the sag angle. It's at a max when the truss is not sagging, but is also inversely proportional to the stiffness.
The horizontal "pull-in" vector is actually inverse to the tangent of the sag angle. The tension in the catenary is inverse to sine of the sag angle. For a fully flexible rope that is the easiest part of the analysis. A flexible rope can only act in tension and the tension is precisely along the axis of the rope. That is the basis of the sequence of examples I calculated for post #161
Then you also have to account for the restraint force of the outer column, which would decrease as it bends, to a degree.
Yes - but that does not prevent analysis from the shape of the catenary. It is the "equal and opposite" reaction force. The catenary pull in aspect will still be determined by the geometry. (Provided it is a fully flexible "rope" OR a small cross section beam/joist - that is where the complications start to come in once the joist has significant depth.)
It gets complicated, but the point is that 4" sag in test conditions is not going to be proportional to the magnitude of inward bowing in the real world.
It is many times more complicated in the real world setting of WTC1-2 because all of the elements are interconnected in a range of 3D manners. The two biggies being that the Perimeter Columns were all very strongly interconnected by the spandrels and the floor joists were interconnected by the floor decking. That is why I have several times cautioned against assuming 2D simplified models e.g. in the context of the Usmani paper which Oystein referenced.

And - so far - we haven't considered the additional complications consequent of aircraft impact damage or fire effects.
 
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Further complicating matters wrt to sag, would be that the trusses were not evenly heated. The ends nearer the perimeter would likely have been cooler due to outside air mixing. In contrast, the middle and core end of the trusses could be a mix of cooler hotter for various trusses along the width of perimeter bowing.

Looking at a 2-d only gives a hint as to what a 3-d picture would look like as this apparently occurred not just across several trusses on one floor but over the height of a few floors as well.

However, while one may say that the inward pull of an individual truss would be nowhere near enough to cause a bow in of a perimeter column, we have this small force applied to many adjacent columns over three or so floors.

Now add in what in normal situation would be insignificant perimeter column heating.

Now add in what under normal circumstances would be additional axial loading that would easily be borne by the perimeter columns.

Complicated, anyone who says it isn't is not taking in account all factors. No ONE factor caused inward bowing.
 
No, sag changes the direction of the weight vector. Did anyone ever say there was 'EXTRA' force other than you?

As far as sagging goes, what causes you to assume it did not occur? You do concede that perimeter column inward bowing occurred, right?
No it didn't bow inward.. it buckled inward.
 
Hitstirrer hits several points I have mention in the past... the connection of these trusses was 2 - 3/4" bolts per truss (double trusses) would be 4 for the top flange. These bolts really only were meant to keep the trusses in place on the beam seats which were welded to the spandrels. All tension or compression would act as a shear force on these bolts. And I am quite certain that the bolts would shear before the 6 flanges of the 3 box columns would bend. And of course the truss material was only 1/4" thick I don't see that pulling in those flanges either.

The inward bowing was the facade columns buckling PERIOD from excessive axial loads... which were from redistributed loads via spandrels or from the hat truss PERIOD. The floor mass "guided" the buckling as the floors were likely collapsing inward when the perimeter columns they were attached to failed.

These cartoons depict what might have happened and why the facade bowed in. Sagging had little or nothing to do with the 55" deflection.

Note how few connections the trusses had to the panels... some had only 3 (mistake in first drawing.. fixed it) others had 6.
 

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No it didn't bow inward.. it buckled inward.
Better if you define what you mean by your use of those two terms JSO - because I cannot see the distinction you are trying to make.

AFAICS the fact that the perimeter "displaced inwards" is the significant fact. NOT what we call the mechanism which caused the inwards movement.
 
Further complicating matters wrt to sag, would be that the trusses were not evenly heated. The ends nearer the perimeter would likely have been cooler due to outside air mixing. In contrast, the middle and core end of the trusses could be a mix of cooler hotter for various trusses along the width of perimeter bowing.

Looking at a 2-d only gives a hint as to what a 3-d picture would look like as this apparently occurred not just across several trusses on one floor but over the height of a few floors as well.

However, while one may say that the inward pull of an individual truss would be nowhere near enough to cause a bow in of a perimeter column, we have this small force applied to many adjacent columns over three or so floors.

Now add in what in normal situation would be insignificant perimeter column heating.

Now add in what under normal circumstances would be additional axial loading that would easily be borne by the perimeter columns.

Complicated, anyone who says it isn't is not taking in account all factors. No ONE factor caused inward bowing.
All true BUT I'm currently trying to help us get the two main foundation bits of physics correct. THEN we can add the other complications in once the foundation understanding is near enough correct.

If we try to address the full complicated scenario in one broadside we will remain lost.
 
All true BUT I'm currently trying to help us get the two main foundation bits of physics correct. THEN we can add the other complications in once the foundation understanding is near enough correct.

If we try to address the full complicated scenario in one broadside we will remain lost.
My frustration occurs as people seem to get focused on specifics, whether a 1d or 2d vision of the trusses , or the idea that pull in must be viewed as THE cause of inward deformation of the columns.

By all means tackle one item at a time as long as it is kept in the back of the mind of all readers that no one aspect was completely responsible for this aspect of the pre-collapse period, or indeed for collapse itself.
Its my history with trotters that causes my caveat, however at times I note debunkers losing sight of the overview.

We are in a nice forest, the trees and wild flowers are nice individually, but its still a forest.
 
Hitstirrer hits several points I have mention in the past...
...hit the points maybe -- but misses the many answers already posted. Some of them multiple times.
the connection of these trusses was 2 - 3/4" bolts per truss (double trusses) would be 4 for the top flange. These bolts really only were meant to keep the trusses in place on the beam seats which were welded to the spandrels. All tension or compression would act as a shear force on these bolts.
That has already been identified and at least partially dealt with by me and others. Bolt shear set the limit on the maximum pull-in force. So you are preaching to the choir on that aspect.
And I am quite certain that the bolts would shear before the 6 flanges of the 3 box columns would bend. And of course the truss material was only 1/4" thick I don't see that pulling in those flanges either.
Your position has been made clear many times. I understand it. You are not correct. You are asserting that pull in would not cause ANY inward bending. That is wrong. It would not cause MUCH pull-in but that means SOME. The true situation is that it would not cause MUCH. Not ZERO. Certainly not 55" but that is a given in the current discussion scenario. But SOME - the discussion then leads to HOW MUCH - and it was almost certainly enough to cause the perimeter movement to go inwards rather than outwards.
The inward bowing was the façade columns buckling PERIOD from excessive axial loads... which were from redistributed loads via spandrels or from the hat truss PERIOD.
I disagree with both those assertions as I have both stated and explained many times. No point repeating yet again.
The floor mass "guided" the buckling as the floors were likely collapsing inward when the perimeter columns they were attached to failed.
That statement confuses me. It looks like you are having a bet both ways - saying what me and others are saying but coming at it from a different slant. Contradicting what you posted in the previous sentences.
 
This sounds like we are splitting hairs here. When I column buckles from compression it bows... it can also fail by completely crushing. We didn't see that. We saw the loads creep up (we didn't actually see that) but when they exceeded capacity the columns buckled in classic manner by BOWING. We saw several columns... in it act like a membrane and stresses could move laterally because of the very deep spandrels. When you apply a point load to the edge of a vertical sheet of plywood, for example... the entire bottom edge bearing on the ground will see that point load. The facade was like a sheet of vertical plywood and the hat truss applied local point loads to... and that's the best explanation of where the excessive axial load came from.
 
Ozzie... when something bows it need not be buckling (my definition)... it sags like a string or a cloth... it's a curved shape. When something buckles from axial compression the shape it takes is a bow... or if it were curved to begin with it would bend more.

I don't dispute the catenary principle... but the movement looks like buckling to me... something like what was depicted in the cartoons... perhaps not precisely... but similar.

This is really a matter of the scale of forces here... when we see a 55" deflection... the asymmetric loading of the facade by the columns DID contribute to the bowing. But it doesn't account for it which is what I thought NIST claimed.

No one seems to want to address how the facade BUCKLED... where did the extra load stress come from and how did it get there?
 
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My frustration occurs as people seem to get focused on specifics, whether a 1d or 2d vision of the trusses , or the idea that pull in must be viewed as THE cause of inward deformation of the columns.

By all means tackle one item at a time as long as it is kept in the back of the mind of all readers that no one aspect was completely responsible for this aspect of the pre-collapse period, or indeed for collapse itself.
Its my history with trotters that causes my caveat, however at times I note debunkers losing sight of the overview.

We are in a nice forest, the trees and wild flowers are nice individually, but its still a forest.
What grade of apology do you need? Will "grovelling" suffice. :oops:

Seriously it is a rare occasion when you or I need to remind the other of the full context. I am always aware of it and sorry if it looked as if I had lost the plot.

Not so.

My wife has been assembling a 1000 piece jigsaw on a table next to mine - her usual office temporarily re-allocated to grandson accomodation. (Including the one who did the definitive experiment on "catenary sag" reported preciously.) She has been frustrated by one corner of the puzzle. But neither she nor I lost sight of the full picture. At any stage including when there was one heap of 1000 bits....I wont take the analogy further. :rolleyes:
 
Ozzie... when something bows it need not be buckling (my definition)... it sags like a string or a cloth... it's a curved shape. When something buckles from axial compression the shape it takes is a bow... or if it were curved to begin with it would bend more.

I don't dispute the catenary principle... but the movement looks like buckling to me... something like what was depicted in the cartoons... perhaps not precisely... but similar.

This is really a matter of the scale of forces here... when we see a 55" deflection... the asymmetric loading of the facade by the columns DID contribute to the bowing. But it doesn't account for it which is what I thought NIST claimed.

No one seems to want to address how the facade BUCKLED... where did the extra load stress come from and how did it get there?
Agree, but was it then simple coincidence that it buckled inwards or was there some mechanism by which inwards would become preferential? I believe its very plausible that a small inward force from the sagging floors across a lond span of the perimeter and on more than one vertically adjacent floors made sure the bow of buckling deformation occurred inwards.
 
What grade of apology do you need? Will "grovelling" suffice. :oops:

Seriously it is a rare occasion when you or I need to remind the other of the full context. I am always aware of it and sorry if it looked as if I had lost the plot.

Not so.

My wife has been assembling a 1000 piece jigsaw on a table next to mine - her usual office temporarily re-allocated to grandson accomodation. (Including the one who did the definitive experiment on "catenary sag" reported preciously.) She has been frustrated by one corner of the puzzle. But neither she nor I lost sight of the full picture. At any stage including when there was one heap of 1000 bits....I wont take the analogy further. :rolleyes:

Grovelling sufficient to completely unnecessary. puzzle analogy understood. As an aside: My three year old grandson has taken to liking jigsaw puzzles though on a much smaller scale than 1000 pieces.
 
Agree, but was it then simple coincidence that it buckled inwards or was there some mechanism by which inwards would become preferential? I believe its very plausible that a small inward force from the sagging floors across a lond span of the perimeter and on more than one vertically adjacent floors made sure the bow of buckling deformation occurred inwards.

The floors didn't have to sag to provide the asymmetrical load guiding the buckling.... the were cantilevered in a sense and there was a moment.
 
The confusion lies in sorting out several synchronous physical actions*. I'm not sure of this myself, but here goes...

It's a structural coupling problem. A virtual pivot may form at some point within a structure where local forces are adjusting to meet progressive coupled buckling movements.

It's a catenary problem as mentioned above.

But initially it's a stability problem. Buckling's alternative solution both produces and requires a side force in order to allow a downward movement.

These can couple to augment the second force but more importantly join to produce a structural torque as well. This manner of exchanging potential energy for rotational energy would doom previously unthreatened structure. The building structure would "squirm".

It all ends badly.

* With three co-operating effects working from different points in their design, it isn't surprising to me that the two tower structures found quite different ways of collapsing.
 
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The confusion lies in sorting out several synchronous physical actions*.
Absolutely. And those "several" interact in space and time. And the "space" aspect - I'll avoid the "jargon big words" - involves parts of the Tower(s) from single components >> local sub assemblies >> larger groupings >> ?? >> ??? >> Whole of tower.
I'm not sure of this myself, but here goes...

It's a structural coupling problem. A virtual pivot may form at some point within a structure where local forces are adjusting to meet progressive coupled buckling movements.

It's a catenary problem as mentioned above.

But initially it's a stability problem. Buckling's alternative solution both produces and requires a side force in order to allow a downward movement.

These can couple to augment the second force but more importantly join to produce a structural torque as well. This manner of exchanging potential energy for rotational energy would doom previously unthreatened structure. The building structure would "squirm".

It all ends badly.
Agreed - and there's more of the same.

* With three co-operating effects working from different points in their design, it isn't surprising to me that they found quite different ways of collapsing.
Do you mean the three towers? If so two were similar in overall mechanism but different in details.
 
Time I responded to this challenge/request from Oystein.
...Qualitatively would be great. I don't require detailed formulas and actual numbers at this point - couldn't and would't check them anyway.
The challenge was to explain then calculate the proportions of loads arising from a semi flexible beam which results in forces attributable to BOTH (a) pure beam action AND (b) so called "catenary sag".

Here is the first stage explanation in "qualify" mode - not "quantify" mode. Yet. Using Oystein's "flexible panel of wood" as the model - we can translate to other situations later if necessary and possible.

Situation 1 - panel resting on supports, no nails, load applied. The panel bends under the centrally applied single point load. At gross macro level there are three forces - all vertical. One of "W" downwards in the centre and two of 0.5W upwards - one at each support.
Note carefully:
A) No matter what happens inside that macro system those three forces will not change. Through all the following inside the system modifications they remain the same. Put your bank account on it.
B) The curve of bending is a form of parabola resulting from the linear change of bending moment from ZERO at the support to a maximum of 0 .25WL at the centre. (0.5W the force at the end, acting over a moment arm of 0.5L - where L is length of beam or rather the horizontal distance between supports to be pedantic.) :

Situation 2 - as above but nails inserted. The sag is not as much at the centre. And the shape of the sag is different. Less maximum sag because there is some catenary action superimposed. AND if the nails don't move the whole game gets several orders more complicated BECAUSE the catenary action depends on sag occurring. And it is the sag due to catenary NOT the sag of the curved shape due to bending moment.

For catenary sag to happen without the nails moving the beam must get longer - beam elasticity in tension occurs due to the catenary tension the catenary sag is causing. Yes it is a self balancing "circularity" of causes <> effects.

So the catenary sag effects set a balance point where the lengthening of the beam gives sufficient catenary sag to cause the lengthening (Play the 'Earwiggo Song')

THEN those catenary effects aspects come into balance with the beam and bending moment aspects.

The catenary action has brought some horizontal forces into the picture...

BUT the overall macro picture of vertical forces is still W and 2 x 0.5W

So that the TOTAL of the vertical force vectors remains W counteracted by 2 x 0.5W

So how do we quantify how much is to due beam and how much due catenary sag?

The obvious first order guess is to measure the DIFFERENCE of maximum central deflection "D" without then with nails.
Dnonails - Dwithnails = Difference due to catenary

Calculate how much catenary sag would be needed to cause that much extra deflection and that is the amount taken off the bending moment beam action deflection. Therefore it is the amount that must be in catenary sag.

And the big elephant in the room?

The shape of the virtual catenary is linear sided triangle where as the beam bending is parabolic. AND the angle of the beam is not the angle for the axis of the virtual catenary.... BUT given that the deflections are small the differences may not matter....much. (It is similar to sine ~= tangent for small angles - see my previous post 161.)

But I doubt that many would be following even this far. :eek:


It is the sort of thing that most engineers in practice would look up in Table xciiv on page 241 of the Manual. And they never go back to basics once they leave college.

Leave it to silly 73yo nuts in 9/11 internet discussions to reveal their limits when working from basics. :oops:

So there you are Oystein - warts and all. Zero guarantee. No money back warranty.

I am certain that such a discussion will introduce a few engineering terms to describe properties of steel elements that I am not familiar with (a matter of lacking both engineering training and foreign language vocabulary of the trade).
..at least I avoided those. ;)
 
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@Hitstirrer
Just a couple of explanations of your key points.
Complicated is certainly a good word to use. Various analagies have been put forward, such as ropes to replace trusses, then bow strings with a fixed length to pull outer fixed points inwards as a force is applied to the string, and then frozen ropes able to change from being a 'rod' into a hanging 'weight'. None address the real situation.
Most members' and all of my posts are addressing valid component parts of the relevant physics.
In reality the trusses are bolted at each end to columns. They are made composite with the concrete floors by shear studs. The coefficient of expansion of both steel and concrete are very similar, but differ widely over the rate of such expansion over time. To overcome this conflict the steel is fireproofed so that the concrete and steel expand together and retain the composite action to prevent breakup. All of the theorising in this thread starts with the assumption that a truss is an isolated element and can be examined alone.
...and put into the full context. So stop the innuendo that there is something wrong with examining parts of the whole and their assembly into the whole.
NIST tried to make this possible by firing a shotgun at truss fireproofing to show that it all would be stripped away on impact by a plane and thus allow them to expose an unprotected truss in a simulated fire as it would be able to break free from the inconvenient composite floor structure. They then quite fraudulently claimed a 47" deflection after heating at double the temperature with double the load and for double the time. The actual deflection was 4.7" even after this unrealistic furnace exposure.
We are not discussing NIST. So your points are moot whether or not they are true.
It isn't clear from the test whether the truss ends were fixed to stiff columns or just resting on supports. But what is well known is that steel expands with heat and will impart enormous axial forces which can easily shear the bolts at each end unless the truss buckles first. But what if the floor is still composite ? Buckling is then much less likely. Another complication right there. If the bolts break first then no inward bowing can happen as the truss is not connected to the outer columns.
You are repeating known aspects of the facts. If you disagree with them say so and drop the inference that there is something wrong.
If we assume that the concrete floor was destroyed by impact then some of this conflict is answered. But that still leaves a complication where a steel truss first of all expands axially well before it softens enough to begin to sag. Far from being a bow string with a pre-determined fixed length, it becomes a lengthening string of spaghetti with no strength to either push, or pull. The only force it can now impart is much more like Mick's defrosted wet rope except that in this case the wet rope is able to lengthen as the steel continues to expand as heat increases. Then we get back to the 4.7" sag in a simulated test and the geometry of what inward bowing would correspond to that central 'sag' distance.
Multiple "missing the point" assertions which have already been addressed in recent discussion. Plus a couple of implied falsehoods.
One further thought. All of these various and variable scenarios have to occur identically with dozens of trusses at the same instant. You have to also assume that all the trusses that were on the opposite side to impact also lost their fireproofing and the floors were destroyed identically to the ones just discussed. All trusses achieved the same level of mechanical 'sag' and inward force at the same time despite wildly different fire exposures.
All three assertions are false. The stage of collapse being discussed was a cascade failure which initiated global collapse. The cascade failure involved several different types of mechanism. And multiple instances in a sequential "cascade". There is no requirement for those mechanisms to be identical replicates of a single mechanism which is the false premise in all three of your assertions. AND it is a strawman (times three) because no one posting in this discussion has postulated that requirement for identical replications of a single model.
'Complicated' starts to look like an inadequate word.
Even that bit is wrong. It is an inadequate word. Has been for a long time. So "starts" is falsified. "We" have known it for a long time.
 
Do you mean the three towers?
We both must have stared at what I wrote simultaneously. :)

WTC7 had fewer options to develop rotational energy, but the internal line of columns could possibly have taken one.

Up close to chaos, all approaches to analysis are moot and speculative, unfortunately. (Legging it here…)
 
@econ41 You said " Just a couple of explanations of your key points."

You explained nothing. Lets look again at your 'explanations'.

#1 First you said - " Most members' and all of my posts are addressing valid component parts of the relevant physics."

#2 Then - "...and put into the full context. So stop the innuendo that there is something wrong with examining parts of the whole and their assembly into the whole."

#3 And - "We are not discussing NIST. So your points are moot whether or not they are true."

#4 Followed by - "You are repeating known aspects of the facts. If you disagree with them say so and drop the inference that there is something wrong."

#5 And - " Multiple "missing the point" assertions which have already been addressed in recent discussion. Plus a couple of implied falsehoods."

#6 Then - " All three assertions are false. The stage of collapse being discussed was a cascade failure which initiated global collapse. The cascade failure involved several different types of mechanism. And multiple instances in a sequential "cascade". There is no requirement for those mechanisms to be identical replicates of a single mechanism which is the false premise in all three of your assertions. AND it is a strawman (times three) because no one posting in this discussion has postulated that requirement for identical replications of a single model."

#7 Lastly - "Even that bit is wrong. It is an inadequate word. Has been for a long time. So "starts" is falsified. "We" have known it for a long time."

Now I have carefully considered your 'explanations' a few times and find that they explain nothing. #1 is your opinion only. #2 just restates your refusal to consider the interaction of all elements at play and seek to just focus on one tiny detail at a time. #3 The NIST input is not relevent ? #4 Is this meant to be an 'explanation' too ? #5 a bare assertion #6 the nearest that you got to an 'explanation' - but on close examination once again fails. #7 Point scoring only.

If you would like to try again to 'explain' feel free. But seriously, this thread is becoming like a bunch of ancient theologians debating how many angels can dance on the head of a pin. My original post was intended to start a real debate that considered the interaction of every part of the building and not just focus on each tiny part in isolation.

But you decided to attack this approach whilst claiming that you would 'explain' it to me. You even found it necessary to take issue when I expanded on how inadequate the word 'complicated' was - which incidentally did tend to give away your intentions in your post.

My own thoughts on the demise of the twin towers and WTC7 have been covered in other threads but of course can't be discussed here without contravening the rules on off topic discussions. At risk of censure I will just say that 'core drop' would cause all attached trusses and girders to pull the outer walls inwards as observed. And as the first observable movement at collapse of WTC1 was the antenna - sat on top of the core - then until that possibility is examined as part of the later inward bowing sightings, then I see no merit in endless debates going in circles whilst ignoring the possibility of core drop as a cause of bowing.
 
Hitstirrer et al may recall that I have tried to move the discussion of the demise of the twin towers to the initiation of the collapse which I believe would be core driven. Back a few years ago this concept seemed to have some support but the mechanism... the transition from static to dynamic were not taken up. This thread is titled ... the pre collapse IB of WTC. I believe both towers show IB and it was not actually pre collapse but it was in the TRANSITION from static to dynamic.... at least what can be seen from the outside. I suspect that there were things "moving" during the initiation or pre collapse phase and most are not visible.

In 7wtc we see the EPH, WPH and some swaying before "collapse" or "release". In 1 WTC we see the antenna tilt and descend. And there may also be various jets of gas/flames, smoke seen in 1 or 2. There were fires burning and fires destroy things... it distorts materials as well.

Since the buildings collapse there was something going inside which destroyed capacity... where and how and the mechanisms are hardly discussed. The ROOSD process does a great job once things got going. 7WTC drops much like a CD.. with the structure at the bottom somewhere sufficiently weakened and so it can't support what above. (DUH).

For the twin we know the components that are inside... how they are connected (more or less) and what they are doing structurally... Obviously the integrity of the structure was undermined by fire/heat plus the mechanical damage from the planes. So heat appears to drive the loss of integrity... the destruction of capacity.

No.... the steel did not lose capacity by melting... It did not get that hot. Heat had to do something else to the frame to destroy capacity. Heat weakens steel and concrete and it also causes it to expand... and can facilitate it being shaped as it acts in a *plastic" manner... probably at higher temps.

My sense is that the main operator driving integrity loss was expansion of steel and likely the beams connecting the columns one to another. Expansion can lead to bolts shearing, column end mis alignment and loss of capacity. A cold column which is not aligned properly to the one below has inadequate bearing and the loads it carries must be redistributed or picked up by other columns. The loads do not disappear!

Heat must be whittling away at capacity by some how forcing misalignment of columns... perhaps coupled with some capacity loss from heating. None of this is observed because it took place in the core!

The IB was not pre collapse but was the transition from static to dynamic and was evidence that the facade where the bowed in facade was saw loads exceeding capacity... the top was already moving down!

This discussion has gone on and about pull in by trusses. That is not what increased capacity at those pulled in columns and a few mm of pull in would not have turned those columns to non performing.
 
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