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Originally posted by psikeyhackr
Simplification would mean the 60 foot truss was just bent down at the middle 45 inches with two straight 30 foot lengths. So the arcsin of 45/360 = 7.18 degrees The cosine of 7.18 deg is 99.2.
Originally posted by Azp420
This report proved nothing. I was forced to read the entire thing due to the poorly written abstract. It was basically six pages of them showing graphs and saying this is what our model produced, take our word that it is correct.
There are two very obvious problem with their model. They are claiming the tensile forces in the bottom chord became too much for it when the top chord was also working in compression to help support the loading and the bottom chord yielded. The top chord is then claimed to take over, somehow (no explanation given in the report) supporting the loading all on its own in an incredible catenary tensile manor that keeps angular deflection to only 11.6 degrees.
What is this massive tensile force keeping angular deflection to only 11.6 degrees? According to the graph from the report which you included in your post, a measly 85kN (rough eyeball from graph). So if 85kN is the horizontal component of this 11.6 degree catenary action, what is the value of the vertical component?
tan(11.6) x 85 = 17.4kN.
17.4kN? Isn't that a bit ridiculous?
Originally posted by -PLB-
the word "most" should be "part". Although the question is how much this is really an error. It doesn't state that this situation is actually reached, just that it progresses towards it (I think the truss will indeed fail before it reaches that situation).
Originally posted by bsbray11
Originally posted by ANOK
Originally posted by bsbray11
Is that for real? First time I've seen it.
They really think lightweight sagging trusses could rip the columns away like that?
That is not even the weak point of the system.
What's even worse is people actually believe that really happened.
Originally posted by ANOK
Is that for real? First time I've seen it.
They really think lightweight sagging trusses could rip the columns away like that?
That is not even the weak point of the system.
What's even worse is people actually believe that really happened.
the word "most" should be "part". Although the question is how much this is really an error.
It doesn't state that this situation is actually reached, just that it progresses towards it
So the compressive diagonals in the middle fail as last. As result there isn't a parabola, but more of a trapezium shape, which has a different (larger) angle than your 11.6 degrees.
Isn't that exactly the same as all simulation reports? What exactly do you expect them to do other than show you the input and output of their models?
I don't see how this is a problem with their model at all. Truss dynamics are pretty clear, once sufficient element breakages occur the upper chord will inevitably slip into tension.
Furthermore your quote of 11.6 degrees is given from your calculation of a figure I gave on a previous page, not this paper at all.
It would be if 11.6 was referred to in the paper.
There was a lot more discussion after this point, but nobody seems to have noticed that 11.6 degrees is based on your calculations of my example of deflection, not of any actual scenario.
Furthermore, if you were to look at your calculation you would realise that it predicts 0 vertical load with a flat truss.
Originally posted by esdad71
reply to post by ANOK
I haven't seen it but I am going to say it is wrong. Really? What is the matter with you. How about you go debunk it.
Originally posted by Azp420
the word "most" should be "part". Although the question is how much this is really an error.
I would be very surprised if this was not entirely intentional. If they did mean "part" that would mean the vast majority of load would be carried in bending by the top chord. I can provide calculations proving the top chord would no way near have the capacity to withstand the required combined bending and tension forces, but it should be intuitive to most that if the rest of the truss has already failed in the system bending, the top chord (which was designed to carry compressive forces) is not going to be the hero to step up and take the bending force on its own which buckled and yielded the rest of the truss.
I (and I think most people) would interpret their sentence to mean that situation was progressively reached. They stated "progressively" just so people knew it wasn't suddenly. It seems you are trying to fit your partial catenary view to their words.
By the time maximum deflection is reached (after only 20 minutes) it is back to a parabola. Also, while it is a trapezium, it is at deflections which are less than the maximum. So no, it probably never goes much above 11.6, and if it does, it is not in that configuration when it is causing the columns to fail.
The bolts would fail long, long, long before the column failed in double shear. If that's the kind of engineering used in the doco then the entire thing is no doubt full of bunk science.
Originally posted by -PLB-
Note that the claim is not that the pulling force made the columns snap but they buckled as result their loads. The pull force only put them a bit out of place, making the columns more susceptible to buckling.
NIST’s findings do not support the “pancake theory” of collapse, which is premised on a progressive failure of the floor systems in the WTC towers (the composite floor system—that connected the core columns and the perimeter columns—consisted of a grid of steel “trusses” integrated with a concrete slab; see diagram below). Instead, the NIST investigation showed conclusively that the failure of the inwardly bowed perimeter columns initiated collapse and that the occurrence of this inward bowing required the sagging floors to remain connected to the columns and pull the columns inwards. Thus, the floors did not fail progressively to cause a pancaking phenomenon.
As I pointed out earlier, the bending stress in the upper chord would be a lot less.
It doesn't seem intuitive to me that if a compressive diagonal fails, the upper chord also must fail. Seems to me only calculations or simulations can answer that.
Ok, but this is kind of speculative on your side
I agree that the paper isn't very clear, but the wording they used doesn't really influence the result of their work, that horizontal force is still there.
Again, not intuitive to me. Can you show the calculations? Note that the claim is not that the pulling force made the columns snap but they buckled as result their loads. The pull force only put them a bit out of place, making the columns more susceptible to buckling.
If it's not a pancake collapse, then what happens after the buckling hypothetically reaches some unspecified critical level?
Originally posted by Azp420
Your reasoning was full or errors and conclusion entirely incorrect.
Generally if a single element in a truss fails due to the truss being overloaded the entire truss will fail. If all the compressive diagonals have failed, as well as the bottom chord (leaving the tension diagonals with nothing to do), most people wouldn't give the top chord much hope to pick up that burden. I think the reason it is not intuitive to you is because the human brain is very good at filtering information and thought processes that contradict its beliefs.
If you would like to give accurate bending and tensile forces in the top chord which you think applied, and show how you got them, I will be able to give calculations describing if it has the capacity to withstand these.
The paper seems clear enough to me, I know exactly what they are saying. But you're right, the wording really doesn't make a difference. I've shown that whether or not catenary action took the majority of the load, the model is bunk.
What exactly was wrong?
I always try to go by evidence or proof rather than intuition. I could give it a go, but I am not a structural engineer, it would take me quite some time.
I can point out that bending stress would be less though.
Since the bending stress is linearly related to y, we know the bending stress is much lower in the lower part of upper chord.
But wouldn't it be quite a feat if you could prove NIST wrong and your intuition correct using your own model and calculations?
I have only seen you do calculation for a 100% catenary action. How is their model also bunk for partly catenary action?
Originally posted by Azp420
You cannot increase tensile forces in a member, increase bending forces in a member, and expect to have less internal stress in the member. It doesn't work like that. The added tensile forces are adding to the tensile stresses which are produced from the bending forces. This will cause the bottom of the member to tear open and fail.
May I ask what the evidence you are going by is in this case?
The neutral axis is where these compressive stresses meet tensile stresses and no stress exists. As you go lower in the upper chord the absolute value of y increases. The bottom of the upper chord is where you will find maximum stress.
It would be a feat, but I would liken it to someone making a climate change model which went against the UN status quo. Joe Public isn't knowledgeable enough to make an educated decision for himself so places his trust in the authority's model. NIST decided to keep their description limited to the highly technical collapse initiation. If they attempted to model the collapse itself every man and his dog would be pointing out the flaws in it.
I've described that in previous posts. It was proven bunk for any majority catenary action, and in the unlikely case of them completely misrepresenting their results, showed that it was highly unlikely the chord would not fail under the massive bending loads.
If I absolutely must provide numbers for proof though:
There would have been about a 322kNm moment (bending force) at the center of the chord. The chord was made up of two double angles 51 and 38mm deep. Double angles are used because it is a shape designed to resist axial loads. I'm not going to bother doing the calculations because I can tell you right now that a non-fire-damaged, 310UB46 (a 307mm deep beam with huge flanges at the top and bottom designed to take bending stresses) can only carry a 218kNm moment, and that's made from a higher grade of steel than was available when the towers were built!
I hope your intuition can see now that it will fail under a minority catenary action.
I was being a bit nit-picky, but my school really drilled into us how to write these things properly. I would have liked them to summarize the results in the abstract.
I also would have liked them to provide some calculations proving that the top chord has the capacity to withstand the claimed configuration and actions. I would have liked if the internal actions of the top chord were not kept hidden. A little bit of transparency, rather than just take our word for it.
My previous post(s) goes into the problem I have with this.
The example deflection you provided me with was exactly the same as the deflection claimed in the paper. 11.6 degrees still stands.
If you understand the calculation you will see this is working as intended. I am determining what the vertical component is of a load applied at a certain angle. If a truss is undergoing catenary action and it is perfectly flat, this means there is no vertical load.
Originally posted by NIcon
We even get to hear Shyam Sunder explain what we're looking at:
"What then happened after the inward bowing, there was a stage at which the critical amount of inward bowing took place and the columns snapped and essentially the columns, once they snapped, the inwardly bowed columns suddenly sprung back and out."