The NIST report, start to finish

Originally posted by exponent

Originally posted by psikeyhackr
My calculations indicate that a 45 inch sag should cause a 60 foot truss to tilt down 7 degrees at the ends.

That should pull the columns in less than 8 inches. Doesn't sound like a big deal to me.

Please show your working.

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.

60 feet * 99.2 = 59.52 feet So that is only 6 inches short of 60 feet. I said 8 inches because the sag should pull in a little more than perfectly straight bends but not all that much. So this making a big deal out of sagging looks like another Red Herring to me.

psik

Sorry, that was supposed to be 0.992

reply to post by exponent

Rather than try and convince you on my own, I'll just provide a third party source. here is an FEA analysis by an independent group from the UK.

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 tension 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? What was the vertical load the truss was supposed to be imposing on one support?

4.8kN/m2 x 9.15m = 43.9kN.

The model has failed to account for 26.5kN of load at each support AKA the majority of the vertical load.

reply to post by Azp420


I spotted an error in my post but am outside (apparently) of the four hour window to edit.

They are claiming the tensile forces in the bottom chord became too much for it when the top chord was also working in tension to help support the loading and the bottom chord yielded.

The bolded "tension" should actually read "compression." Sorry.

I also noticed that the maximum pull in action was achieved after less than 20 minutes. Unless I'm missing something, that interestingly leaves the columns in the configuration that caused their failure for around 40 minutes.

Good thread with nice structure. Flagged. (although I understand why its not popular )

reply to post by Azp420


I must say I don't understand how you got that 2nd value for vertical load (isn't that the load without any damage or heating?), but it seems to me that the 1st value can not be calculated like that because the trusses are not a prefect catenary. This is both because they are not likely to be uniformly heated and because even when heated (enough) the steel still has some of its strength left. Although I am not sure how much this will affect the calculation.

reply to post by psikeyhackr


In those tests the pull in is 0 inch, not 6 or 8 inch. The trusses simply became longer because of thermal expansion, giving them the ability to sag. In fact, when they are not yet hot enough, the expansion will put a push force on the columns, and the trusses are forced to sag. They only start to pull when they reach a temperature where the steel is hot enough to behave like a catenary. When the trusses cool down again they become shorter again and start pulling more.

reply to post by -PLB-

I must say I don't understand how you got that 2nd value for vertical load

This one?

4.8kN/m2 x 9.15m = 43.9kN

My apologies, I just noticed an error in my work. I am used to dealing with loads specified in per meter format in these situations rather than per square meter. My oversight caused me to neglect the 2m truss spacing in my calculation. It should look like this:

4.8kN/m2 x 2m x 9.15m = 87.8kN

4.8kN per meter squared is the UDL value used in the model. 2m is the width of floor each truss supports. 9.15m is the length of half the truss (each support carries half the load).

This new figure means the model failed to account for 70.4kN of load at each support, AKA the vast majority of the vertical load. This means the model claiming catenary action was responsible for large inwards forces on the columns is wildly inaccurate and should be treated with caution.

(isn't that the load without any damage or heating?)

I don't see how the damage or heating would change the load. In the model it has assumed to remain constant so I have done the same.

but it seems to me that the 1st value can not be calculated like that because the trusses are not a prefect catenary.

The claim is that the load carrying mechanism changes progressively to catenary action (after the bottom chord and several other members yield) in which the top chord takes most of the imposed load in tension (rather than in bending or in compression).

As you can see I have proven that this claim is rubbish. To achieve the pull in force claimed, the top chord would have to take the majority of the loading in bending, not tension. If the loading is enough to fail the bottom chord and several other truss members then it should be rather intuitive to most that there's no way the top chord would have the capacity withstand the combined bending and tensile forces.

Originally posted by Azp420
I don't see how the damage or heating would change the load. In the model it has assumed to remain constant so I have done the same.

I agree that the over all load doesn't change, but this is about the vertical load only right? Once there is a catenary action, the horizontal component of the load increases at the cost of the vertical component. So the over-all load in the model (using your data and assuming a perfect catenary) would be:

85/Cos(11.6) = 86.8kN

Which is awfully close to your estimate of 87.8kN. Though in reality there probably wont be a perfect catenary, so the vertical component would be larger, which can be explained by the office furniture.

The claim is that the load carrying mechanism changes progressively to catenary action (after the bottom chord and several other members yield) in which the top chord takes most of the imposed load in tension (rather than in bending or in compression).

As you can see I have proven that this claim is rubbish. To achieve the pull in force claimed, the top chord would have to take the majority of the loading in bending, not tension. If the loading is enough to fail the bottom chord and several other truss members then it should be rather intuitive to most that there's no way the top chord would have the capacity withstand the combined bending and tensile forces.

I get your point, but to me its not that intuitive. It seem to me that the tension as result of bending in the lower chord would be equal to the compression force in the upper chord. Once the lower chord breaks these tension/compression forces are both in the upper chord. The lower part of the upper chord only needs to expand a very small amount in order to nullify it. It seems to me this can happen without failure.

reply to post by -PLB-

I agree that the over all load doesn't change, but this is about the vertical load only right? Once there is a catenary action, the horizontal component of the load increases at the cost of the vertical component.

If a 10kN vertical load is applied to a truss (including self-weight) then the sum of the reactions at the supports will have to be 10kN in the equal and opposite direction. The same is true for a piece of rope tied between two supports. Just because the rope will have larger horizontal components, doesn't mean it is exempt from this.

Draw a free body diagram if you need help visualizing it. F=ma, and because the entire system is static (no accelerations) the sum of forces in any direction on any element in the system must equal zero.

So the over-all load in the model (using your data and assuming a perfect catenary) would be:

85/Cos(11.6) = 86.8kN

Which is awfully close to your estimate of 87.8kN.

My figure of 87.8kN refers to the vertical reactional force in a support. Adding in the horizontal component will result in a much larger figure for the overall force at that support. I assure you it is only a coincidence that this is close to the number you have produced for the overall load in your top chord.

It seem to me that the tension as result of bending in the lower chord would be equal to the compression force in the upper chord.

So far so good (just want to add that before the concrete floor failed it shared the compression load with the top chord).

Once the lower chord breaks these tension/compression forces are both in the upper chord.

Yes, tension/compression stresses (in bottom/top half of member respectively) are in the upper chord, this is known as a bending force.

The lower part of the upper chord only needs to expand a very small amount in order to nullify it. It seems to me this can happen without failure.

If the lower part of the chord expands, all that does is increase the tensile stresses and also force the compression stresses to increase an equal amount.

Originally posted by Azp420

I agree that the over all load doesn't change, but this is about the vertical load only right? Once there is a catenary action, the horizontal component of the load increases at the cost of the vertical component.

If a 10kN vertical load is applied to a truss (including self-weight) then the sum of the reactions at the supports will have to be 10kN in the equal and opposite direction. The same is true for a piece of rope tied between two supports. Just because the rope will have larger horizontal components, doesn't mean it is exempt from this.

Draw a free body diagram if you need help visualizing it. F=ma, and because the entire system is static (no accelerations) the sum of forces in any direction on any element in the system must equal zero.

I agree, but I don't see how this is different from what I am saying though. Am I correct when I say that your 87.8kN figure is the same force as the 10kN figure in your example?

My figure of 87.8kN refers to the vertical reactional force in a support. Adding in the horizontal component will result in a much larger figure for the overall force at that support. I assure you it is only a coincidence that this is close to the number you have produced for the overall load in your top chord.

So basically, I don't really understand why there should be a 87.8 kN vertical force according to you. It seems to me your 87.8kN figure for the vertical force is only valid when the trusses are still intact, not when they are in catenary action. When the trusses are in catenary action, the force will be redistributed over a vertical and a horizontal component. The magnitude will remain the same (87.8 kN) just the direction changes.

Maybe I am just totally misunderstanding you. An image of what you mean would indeed help a lot.

If the lower part of the chord expands, all that does is increase the tensile stresses and also force the compression stresses to increase an equal amount.

It seems to me that when the truss plastically deforms there is no longer any stress as result of bending.

reply to post by -PLB-

Originally posted by -PLB-

Originally posted by Azp420
If a 10kN vertical load is applied to a truss (including self-weight) then the sum of the reactions at the supports will have to be 10kN in the equal and opposite direction.

I agree, but I don't see how this is different from what I am saying though. Am I correct when I say that your 87.8kN figure is the same force as the 10kN figure in your example?

What I meant to make clear, was that there must be reactions at the supports in an equal and opposite direction, which is the vertical direction, not the direction of the axis of the top chord.

The 87.8kN would be the same as 5kN in my example (load applied to one half, assuming equal distribution).

So basically, I don't really understand why there should be a 87.8 kN vertical force according to you.

If there is a downwards force applied then the sum of the support reactional forces must equal that downwards force in the upwards direction. This law does not break when the mechanism changes to catenary.

It seems to me your 87.8kN figure for the vertical force is only valid when the trusses are still intact, not when they are in catenary action.

See above, and in the picture I drew you.

When the trusses are in catenary action, the force will be redistributed over a vertical and a horizontal component. The magnitude will remain the same (87.8 kN) just the direction changes.

Maybe I am just totally misunderstanding you. An image of what you mean would indeed help a lot.

Here is an mspaint picture of a rope hung between two supports with a 10kN load applied in the middle. Just pretend the rope was correctly drawn as a triangle, I decided on that simple load after I'd already drawn it. Green are the reactional forces of a support. Self weight of rope is ignored.

As you can see, the magnitude does not remain the same. 10kN is applied, but the tensile force in the rope reaches 24.9kN. The magnitude of forces in the vertical direction however (as well as the horizontal), sum to zero.

It seems to me that when the truss plastically deforms there is no longer any stress as result of bending.

You are claiming 100% catenary action?

reply to post by Azp420


I see what you mean now. If both horizontal and vertical component are in the order of 80, the resulting force will be about 45 degrees instead of 11. That would indicate that there isn't a perfect catenary, so there must be tension from bending in the truss elements. Your argument is that this tension exceeds the maximal capacity, and you support that by the notion that lower chords failed. Your argument sounds reasonable, although I still think that the tension in the lower chord would be much higher than the tension in the lower part of the upper chord once the lower chord has failed. The further away from the neutral axis, the larger the tension, also see here. So I don't agree that when the lower chord fails the upper chord inevitably also fails.

To answer your last question, I don't think its a perfect catenary, but once the lower chord breaks, it starts behaving a lot more like a catenary, the tension from bending decreases and the pull force increases. Anyway, its good to see some reasonable arguments, even though I am not convinced (yet). Just on a side note, how do you explain the inward bowing as observed on photographic evidence?

I think everybody has made up their mind on it by now. I KNOW it was a controlled demolition. I KNOW the towers were brought down by explosives and others are in the same camp. What good does it do to debate people who treat the official conspiracy theory as a dogma and are imprevious to reason and logic? There is nothing to gain. In the end they do not care about the facts, they just want their version to "win" like a murdered in front of a jury wants his version of the truth to win, that he did not do it, when he did.

What is more important at this point is who did it and why and where to go from here.

Originally posted by Cassius666
I think everybody has made up their mind on it by now. I KNOW it was a controlled demolition. I KNOW the towers were brought down by explosives and others are in the same camp. What good does it do to debate people who treat the official conspiracy theory as a dogma and are imprevious to reason and logic? There is nothing to gain. In the end they do not care about the facts, they just want their version to "win" like a murdered in front of a jury wants his version of the truth to win, that he did not do it, when he did.

What is more important at this point is who did it and why and where to go from here.

edit on 26-4-2011 by Cassius666 because: (no reason given)

There are 15 year olds who for all of the time they can remember clearly have been told airliners destroyed the towers. They should be taking science courses that explain how REALITY WORKS.

Physics is not a matter of opinion where anyone can have whatever they want. But clowns in this country with degrees in physics have allowed 9/11 to become a RELIGION.

9/11 is the Piltdown Man incident of the 21st century.

psik

Originally posted by Cassius666
I think everybody has made up their mind on it by now. I KNOW it was a controlled demolition. I KNOW the towers were brought down by explosives and others are in the same camp. What good does it do to debate people who treat the official conspiracy theory as a dogma and are imprevious to reason and logic? There is nothing to gain. In the end they do not care about the facts, they just want their version to "win" like a murdered in front of a jury wants his version of the truth to win, that he did not do it, when he did.

What is more important at this point is who did it and why and where to go from here.

edit on 26-4-2011 by Cassius666 because: (no reason given)

So basically, you don't know how it happened or who did it but you kind of know who didn't do it and how it didn't happened. Where do you go from there? Well, this means all other humans are now suspects and everything BUT airplanes crashing into the buildings may be considered as a cause. Wow - good luck with that!

reply to post by Cassius666


I love it when you pop into threads to add nothing to the ongoing discussion, diverting people's attention and causing the thread to lose its topic. You are such a great poster. I think you are just fab.

reply to post by Varemia


I am just saying it how it is. Everything points to controlled demolition. There is absolutely nothing that points to the official conspiracy theory. At this point debating those who keep on championing the official tale are pretty much imprevious to facts. Its akin to telling a religious person that man sent people up in space and there was no god. If people elevate a certain believe to their personal dogma trying to convince them otherwise with reason and logic is a waste of everyones time. At some point you just have to accept that you will not change everyones opinion and cease your inquisition and spend your time and energy by cooperating with people who are more or less in the same boat as you.

reply to post by -PLB-

I see what you mean now. If both horizontal and vertical component are in the order of 80, the resulting force will be about 45 degrees instead of 11.

But under a catenary the resulting force must be at 11.6 degrees, therefore the model is rubbish. The claim is that catenary action takes most of the imposed load and any bending is minimal. Therefore anything close to 11.6 degrees is reasonable to take into account any minority bending forces.

Your argument is that this tension exceeds the maximal capacity, and you support that by the notion that lower chords failed.

I probably didn't make myself very clear, but you've mistaken my main argument for a passing comment I made about what seems intuitive. If I wanted to prove that I would have supplied mathematical proof.

My argument is this:

The model failed to account for 70.4kN of load at each support, AKA the vast majority of the vertical load. This means the model claiming catenary action was responsible for large inwards forces on the columns is wildly inaccurate and should be treated with caution.

If the models describing catenary action are rubbish then I do not believe catenary action to be responsible for the columns pull in.

To answer your last question, I don't think its a perfect catenary, but once the lower chord breaks, it starts behaving a lot more like a catenary, the tension from bending decreases and the pull force increases.

That is the claim, but I'm yet to see anything proving this is what occurred.

Just on a side note, how do you explain the inward bowing as observed on photographic evidence?

As I'm still very new at looking at the initiation of the collapse (the gold is in the collapse itself), I will refrain from speculating about this until I know more about it. I've also never never seen those photos of the inward bowing. Do you or anyone have them handy?

Originally posted by Azp420

But under a catenary the resulting force must be at 11.6 degrees, therefore the model is rubbish. The claim is that catenary action takes most of the imposed load and any bending is minimal. Therefore anything close to 11.6 degrees is reasonable to take into account any minority bending forces.

I probably didn't make myself very clear, but you've mistaken my main argument for a passing comment I made about what seems intuitive. If I wanted to prove that I would have supplied mathematical proof.

My argument is this:

The model failed to account for 70.4kN of load at each support, AKA the vast majority of the vertical load. This means the model claiming catenary action was responsible for large inwards forces on the columns is wildly inaccurate and should be treated with caution.

If the models describing catenary action are rubbish then I do not believe catenary action to be responsible for the columns pull in.

I don't find this much of an issue as this can easily be explained by the fact that it is not a perfect catenary. So you would expect the horizontal force to be smaller than it would in a perfect catenary. You could also do your calculation the other way around, and start of with a vertical force of 87.8 and calculate the corresponding horizontal force. I get 427kN, which is about 5 times larger than the force in the model in that paper. It just shows that it wasn't a perfect catenary, I don't see why the model is rubbish altogether.

As I'm still very new at looking at the initiation of the collapse (the gold is in the collapse itself), I will refrain from speculating about this until I know more about it. I've also never never seen those photos of the inward bowing. Do you or anyone have them handy?

From the NIST report:

reply to post by -PLB-

I don't find this much of an issue as this can easily be explained by the fact that it is not a perfect catenary.

The numbers don't lie. There are huge discrepancies in the numbers, far too great to be explained away with "not a perfect catenary." The claim was that catenary action took the majority of the load. The numbers show is cannot be the case, so its not only a case of imperfect catenary action, its a case of any catenary action must have been a vast minority in comparison with the bending action.

You could also do your calculation the other way around, and start of with a vertical force of 87.8 and calculate the corresponding horizontal force. I get 427kN, which is about 5 times larger than the force in the model in that paper.

So clearly the model in that paper is rubbish. You cannot then assume that catenary action is responsible. Look at how many other trusses have undergone the phenomenon then tell me why we should just assume it to be the case. By the way, the tensile load on that 427kN force is starting to get to the point where it would fail the bolted connection and probably the top chord. Especially if it was as heated as much as is claimed.

From the NIST report:

Thanks.

Originally posted by Azp420
The numbers don't lie. There are huge discrepancies in the numbers, far too great to be explained away with "not a perfect catenary." The claim was that catenary action took the majority of the load. The numbers show is cannot be the case, so its not only a case of imperfect catenary action, its a case of any catenary action must have been a vast minority in comparison with the bending action.

So clearly the model in that paper is rubbish. You cannot then assume that catenary action is responsible. Look at how many other trusses have undergone the phenomenon then tell me why we should just assume it to be the case. By the way, the tensile load on that 427kN force is starting to get to the point where it would fail the bolted connection and probably the top chord. Especially if it was as heated as much as is claimed.

I see your point. In the sentence:

The load-carrying mechanism changes progressively to catenary action, shown in Fig. 8(c), in which both the slab and top chord carry most of the imposed load in tension rather than in balanced compression and tension with the bottom chord"

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). Also, the text before that says:

The second compressive diagonal, which was seen to have the highest compressive load-ratio in the simply supported condition, is the first to buckle. Through a progressive load redistribution process, illustrated in Fig. 8(b), the compressive diagonals then successively buckle at the same temperature.

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.

Anyway, I am not sure if the whole model can be called rubbish because of that one sentence. Maybe it is a mistake/bad wording from the writers that need rectification. Or maybe the effect I describe above accounts for it. A reaction from the writers would help. I must say I am not really qualified to do such in depth reviews of these kind of papers, but it seems you indeed spotted a possible error. Still, the concept of sagging trusses as a whole as explanation for the inward bowing is still plausible my opinion.