Does the exclusion of stiffness from Nordenson's falling girder calculations demonstrate anything?

MikeC

Closed Account
In engineering terms it is considered a pin joint IIRC (it was 30 years ago!!) - it will transmit force along hte length of a beam connecting to it, bu no twisting or turning moment.
 

Jeffrey Orling

Senior Member
Tony...

I am not a physicist, nor a forensic engineer and I don't engineer the structure for the projects I do... My structure understanding ended in statics in college... and my knowledge is basic and intuitive... more than the average Joe but that's it.

Nordenson seems to be making a case that a single falling girder and attached whatever falling down one story would set of a progressive collapse one floor section after the next. I can't prove or disprove and comment on the math. My suggestion was take it up with him not with people on this or other forums. Let HIM defend his work.

My gut feeling... considering his stature and body of work and his reputation... is he probably knows what he is doing... More so than Professor Hulsey or Oystein, or Ozzie... or you and certainly more than Gage, or Cole, or Greg Roberts or Neils Harrit... all of whom speak like experts in structural engineering and most of the internet people on these forums.

I do know that there ARE progressive floor collapses... Ronan Point was one... Why not 7wtc? Nordenson goes on to detail how the frame failure progresses... gutting the interior and then leaving the perimeter moment frame unsupported and unbraced.

I don't know a single architect that does these sorts of calcs... Maybe you do... Ask Gage ;-)
 
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jaydeehess

Senior Member
After reading over this thread I realized I somehow replied to you instead of Jeffrey Orling, for whom I intended the comments saying he shouldn't make proclamations while also acknowledging that he didn't understand the math and found it confusing. They weren't for you.
I see. Complicating matters is that the "J" in jaydee is my first initial, for my first name, Jeffrey. I sometimes inexplicably read posts referring to Jeffrey, as directed at me. Quickly remembering that the poster did not know my name.
 

Tony Szamboti

Active Member
Tony...

I am not a physicist, nor a forensic engineer and I don't engineer the structure for the projects I do... My structure understand ended in statics in college... and my knowledge is basic and intuitive... more than the average Joe but that's it.

Nordenson seems to be making a case that a single falling girder and attached whatever falling down one story would set of a progressive collapse one floor section after the next. I can't prove or disprove and comment on the math. My suggestion was take it up with him not with people on this or other forums. Let HIM defend his work.

My gut feeling... considering his stature and body of work and his reputation... is he probably knows what he is doing... More so than Professor Hulsey or Oystein, or Ozzie... or you and certainly more than Gage, or Cole, or Greg Roberts or Neils Harrit... all of whom speak like experts in structural engineering and most of the internet people on these forums.

I do know that there ARE progressive floor collapses... Ronan Point was one... Why not 7wtc? Nordenson goes on to detail how the frame failure progresses... gutting the interior and then leaving the perimeter moment frame unsupported and unbraced.

I don't know a single architect that does these sorts of calcs... Maybe you do... Ask Gage ;-)
I do perform these types of calculations in my work and I am sure Dr. Nordenson is a fine structural engineer who is plenty capable. However, none of us are immune to occasional mistakes and it is clear that he made a mistake here by not considering the stiffness and deflection of the falling beam and girder assembly. There is a big difference in load applied to the impacted object and that experienced by the impacting object when the acceleration/deceleration takes place over a greater or lesser time frame.

The energy in a drop is the area under the acceleration/deceleration vs. time curve and it does not change for a given drop height of an item with a certain mass. It is the potential energy (mgh) turned into kinetic energy. While we can't change the energy involved, we can absorb it over more time, and the acceleration/deceleration peak, which is what affects the force involved, is lowered. Imagine a tall slender curve on an X-Y graph for something that is hard being dropped onto a hard surface and then imagine a lower but longer curve for the same item dropped from the same height onto a softer surface. The softer impact surface deflected and lowered the acceleration/deceleration peak even though the energy did not change. It is the same reason we put foam in packages. They allow for energy absorption over more time by deflecting. This lowers the deceleration of the item and thus the force it experiences due to its own mass times that deceleration.

Energy in a drop is absorbed as force x distance. For a given energy, if the distance it is absorbed over is small, because there is no deflection, then force will be high. The deflection can be in either the impacting object or the impacted object or both. It is the amount of deflection that ultimately determines what the forces involved are.

A point load is infinitely stiff and has no deflection and thus will cause very high acceleration and deceleration of the impacted and impacting object. The only thing Dr. Nordenson's analysis has deflecting is the girder below and it is much stiffer at 10 to 12 inches from its seat than the long and flexible falling beam and girder assembly. What he has in his analysis is far from what would really happen here. The deflection of the impacting beam and girder assembly will make a big difference in the force experienced by the girder below and its seat and the analysis needs to be corrected to account for this.
 
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MikeC

Closed Account
So what is the PRACTICAL difference? It seems to me you don't know that either - and are assuming it is significant.
 

Jeffrey Orling

Senior Member
...

A point load is infinitely stiff and has no deflection and thus will cause very high acceleration and deceleration of the impacted and impacting object. The only thing Dr. Nordenson's analysis has deflecting is the girder below and it is much stiffer at 10 to 12 inches from its seat than the long and flexible falling beam and girder assembly. What he has in his analysis is far from what would really happen here. The deflection of the impacting beam and girder assembly will make a big difference in the force experienced by the girder below and its seat and the analysis needs to be corrected to account for this.
How then do you calculate the collapse of the floor sections of Ronan point? Why would they have more energy... enough to cause the cascading failure as one floor section drops on the the other? Presumably if the first one does it... it only gets "worse" and becomes unstoppable.

What's the difference between Ronan Point and 7 WTC?
 

Oystein

Senior Member
So what is the PRACTICAL difference? It seems to me you don't know that either - and are assuming it is significant.
Nordenson, who implicitly assumes an infinite stiffness for the falling girder (i.e. the falling girder absorbs no energy in the collision with the girder below other than the plastic deformation of the flange on the tip that is already accounted for), finds that the energy absorbed by the girder below (i.e. 100% of the net kinetic energy at the beginning of the impact) means a vertical force that is about an order of magnitude larger than the shear capacity of the affected connection. Therefore, he concludes, it wasn't possible for the connection to stay intact - the connection to c79 of the impacted girder would fail, that girder would fall on floor 11, fl11 would fail in the same way and fall on fl10 ... all the way to the ground.

Tony argues, and I agree, that Nordenso erred in not considering that the falling girder, too, would absorb some of the kinetic energy. How much? That depends on the stiffness of the falling girder relative to the stiffness of the girder below! Intuitively, Tony and I believe that the falling girder would be less stiff than the girder below, and that means, when you do the math, that the girder below would absorb less than 50% of the kinetic energy.
Tony has so far advanced two claims about how to calculate the stiffness of the falling girder, and the math results came out such that the girder below would not absorb not just less than 50% of the kinetic energy but less than 0.1%, with the remaining 99.9+% absorbed by the falling girder. This would be equivalent to a veritical force on the connection that is below its capacity by a factor or 3 to 5. This would mean that the connection would survive, and collapse would come to a halt.
I however disagree with Tony on his derivations of girder stiffness
. My hunch is that the falling girder would be somewhat stiffer than Tony's results, moving the equivalent vertical force closer to capacity and possibly into "we can't decide with much confidence whether or not connection would fail" territory, or maybe even "failure more likely than not" territory. If, say, the calculated force comes out at 50% of capacity (i.e., no failure, but somewhat close), then we'd have to remember that several of Nordenson's assumptions and values up to that point were on the conservative side - kinetic energy at the start may have been somewhat higher, capacity of the connection lower (there were fires on the 11th floor, too, that plausibly may have adversely affected the connection strength) Adjusting these conservative assumptions for more realistic ones, the result would tend to change toward "failure". On the other hand, I think there are some minor energy sinks that we haven't considered yet that would tend to move the result towards "survival".
(And of course my hunch about the best stiffness estimate could easily be mistaken either way - I haven't worked this out yet)

In short: The PRACTICAL difference is that the conclusion by Nordenson "floors collapse progressively all the way down and strip column 79 off of lateral support to the north, leading to column buckling, leading to total collapse" might have to be corrected to "floor 13 collapse is arrested by floor 12, no collapse progression started by this failure, we have to find some other initiating event".
 

Jeffrey Orling

Senior Member
I am curious about the 3D geometry. Intuitively it seems that the collison would be not axially aligned and the failure could be related to the twisting of the lower assembly.

If the upper girder comes down it has sections of floor slab and the beams supporting it and framed into the 44-79 girder. Reducing this to 2D seems an over simplification.

Would the subsequent collapses below be identical to the first? What about the additional mass? Nordensen's cartoon diagram of the progression shows a sort of neat pile of slabs on grade.. or is this a pile of debris of 13 floors?
 

jaydeehess

Senior Member
I know its a highly specific thing but, does anyone know of any videos of a heavy girder rotating to impact in similar fashion as this set up? Industrial accidents for instance?
 

jaydeehess

Senior Member
I am curious about the 3D geometry. Intuitively it seems that the collison would be not axially aligned and the failure could be related to the twisting of the lower assembly.

If the upper girder comes down it has sections of floor slab and the beams supporting it and framed into the 44-79 girder.
Well it does and it doesn't. Recall that there were few studs installed and that they had broken. There is little to no composite action with the girder. Concrete floor mass would simply add to impact and dampen spring back.

Would the subsequent collapses below be identical to the first? What about the additional mass? Nordensen's cartoon diagram of the progression shows a sort of neat pile of slabs on grade.. or is this a pile of debris of 13 floors?
It would include falling mass of higher floors contributing to impact loading but in addition those lower floors would have some composite action from shear studs.(except possibly if the higher of the two floors experiencing fire was the initial failure. In that case one lower floor would have had less composite combination of floor and girder.
 

Jeffrey Orling

Senior Member
Well it does and it doesn't. Recall that there were few studs installed and that they had broken. There is little to no composite action with the girder. Concrete floor mass would simply add to impact and dampen spring back.
If the shear stud all broke... the concrete will still come down with the beams that supported them... and so will the superimposed dead loads. Why would the steel drop "ahead" of the concrete slab it supported broken shear studs notwithstanding. Seems like all the mass needs to be included... no?
 

jaydeehess

Senior Member
If the shear stud all broke... the concrete will still come down with the beams that supported them... and so will the superimposed dead loads. Why would the steel drop "ahead" of the concrete slab it supported broken shear studs notwithstanding. Seems like all the mass needs to be included... no?
the upper girder comes down it has sections of floor slab and the beams supporting it and framed into the 44-79 girder.
Your initial post appeared to still have girder attached to beams/floor.
Yes the girder, will come down ahead of floor. There will be cantilever resistance to the floor pan dropping, but with no composite connection to the girder means that the girder falls on its own. Floor mass impact will not be far behind the girder and IMHO would dampen spring back of the girder while adding to the forces on the lower floor.
TSz says that the initial impact of the girder will not fail the lower girder connection to col79. If true one notes that this is that particular impact, in isolation. Question is then, what happens next and what happens in addition.
 

Tony Szamboti

Active Member
If the shear stud all broke... the concrete will still come down with the beams that supported them... and so will the superimposed dead loads. Why would the steel drop "ahead" of the concrete slab it supported broken shear studs notwithstanding. Seems like all the mass needs to be included... no?
The reason the concrete in the northeast corner would not come down with the beams and girder if all of their shear studs were broken is the high strength welded wire grid in the slabs that would have been supported by the still stable beams to the west and the south.
 

Tony Szamboti

Active Member
Your initial post appeared to still have girder attached to beams/floor.
Yes the girder, will come down ahead of floor. There will be cantilever resistance to the floor pan dropping, but with no composite connection to the girder means that the girder falls on its own. Floor mass impact will not be far behind the girder and IMHO would dampen spring back of the girder while adding to the forces on the lower floor.
TSz says that the initial impact of the girder will not fail the lower girder connection to col79. If true one notes that this is that particular impact, in isolation. Question is then, what happens next and what happens in addition.
If the next floor down doesn't collapse then nothing happens.
 

Tony Szamboti

Active Member
I know its a highly specific thing but, does anyone know of any videos of a heavy girder rotating to impact in similar fashion as this set up? Industrial accidents for instance?
Yes, the Oakland highway overpass about ten years ago. I showed a slide of it on this thread. It did not collapse the lower deck.
 

Tony Szamboti

Active Member
YES!... but of course that is precisely what happened...not only did the girder and the floor around it collapse... but col 79 dropped as well.

Or so it seems.
We are talking about whether girder A2001 falling off its seat at the 13th floor could have caused a propagation of the floors under it. I don't see how you can say that is what happened. There is also no evidence that column 79 buckled at or near the 13th floor.
 

jaydeehess

Senior Member
If the next floor down doesn't collapse then nothing happens.
"Next" as in directly following, wiithin milliseconds perhaps, of initial girder impact. The flooring and beams are detached from the girder but will be following the girder down. It represents more, albeit following in time, force. If initial girder contact damages the lower girder more damage may occur when the extra flooring and office contents mass also falls.
Your calcs, disputed by Ozeco, show less than required impact to fail the lower floor/girder.
Rather than conclude demolition, it would behoove you to investigate other plausible mechanisms that could contribute to collapse progression.
 

jaydeehess

Senior Member
We are talking about whether girder A2001 falling off its seat at the 13th floor could have caused a propagation of the floors under it. I don't see how you can say that is what happened. There is also no evidence that column 79 buckled at or near the 13th floor.
Yet that remains the only sequence for which there is ANY evidence. Outward visuals imply failure of col 79. They imply this failure occurred low down in the structure. They imply a horizontal progression of core failure
AND
the sole evidence of a driving mechanism for initial failure are the fires in the vicinity of col 79.
 

Tony Szamboti

Active Member
"Next" as in directly following, wiithin milliseconds perhaps, of initial girder impact. The flooring and beams are detached from the girder but will be following the girder down. It represents more, albeit following in time, force. If initial girder contact damages the lower girder more damage may occur when the extra flooring and office contents mass also falls.
Your calcs, disputed by Ozeco, show less than required impact to fail the lower floor/girder.
Rather than conclude demolition, it would behoove you to investigate other plausible mechanisms that could contribute to collapse progression.
I am saying the jury is still out as to whether a girder falling off its seat at column 79 at the 13th floor could have propagated a collapse. It does not look like it can develop enough force due to deflection cutting down the deceleration/acceleration and nobody has shown it could happen yet. Nordenson's analysis has been shown to be erroneous for not considering the beam and girder stiffness and deflection. My preliminary calculations show that when his analysis is corrected there is a good chance the math will show it won't.

The concrete won't follow the beams and girder because of the welded wire grid in the slab that is still supported adjacent to the northeast corner.

My main interest here is in explaining the collapse and I have not seen a plausible natural explanation thus far or been able to determine one myself.
 
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jaydeehess

Senior Member
I am saying the jury is still out as to whether a girder falling off its seat at column 79 at the 13th floor could have propagated a collapse. There is a good chance the math will show it won't. Nobody has shown it could happen yet, as Nordenson's analysis has been shown to be erroneous for not considering the beam and girder stiffness and deflection.
Yes Tony, we all know what you do and don't believe.
 

econ41

Senior Member
I do perform these types of calculations in my work and I am sure Dr. Nordenson is a fine structural engineer who is plenty capable. However, none of us are immune to occasional mistakesA and it is clear that he made a mistake here by not considering the stiffness and deflection of the falling beam and girder assembly.B
There is a big difference in load applied to the impacted object and that experienced by the impacting object when the acceleration/deceleration takes place over a greater or lesser time frameC..
Agreed to A, It is looking like you are right on B and C is the underlying issue of dampening of an impact load which has never been in doubt as a matter of principle ... the doubts have been about how it applies.

My commendation on this following concise explanation of the underlying principle of applied physics for Jeffrey (Sander) Orling
The energy in a drop is the area under the acceleration/deceleration vs. time curve and it does not change for a given drop height of an item with a certain mass. It is the potential energy (mgh) turned into kinetic energy. While we can't change the energy involved, we can absorb it over more time, and the acceleration/deceleration peak, which is what affects the force involved, is lowered. Imagine a tall slender curve on an X-Y graph for something that is hard being dropped onto a hard surface and then imagine a lower but longer curve for the same item dropped from the same height onto a softer surface. The softer impact surface deflected and lowered the acceleration/deceleration peak even though the energy did not change. It is the same reason we put foam in packages. They allow for energy absorption over more time by deflecting. This lowers the deceleration of the item and thus the force it experiences due to its own mass times that deceleration.

Energy in a drop is absorbed as force x distance. For a given energy, if the distance it is absorbed over is small, because there is no deflection, then force will be high. The deflection can be in either the impacting object or the impacted object or both. It is the amount of deflection that ultimately determines what the forces involved are.

A point load is infinitely stiff and has no deflection and thus will cause very high acceleration and deceleration of the impacted and impacting object...
All that basic physics agreed. A good summary

The only thing Dr. Nordenson's analysis has deflecting is the girder below and it is much stiffer at 10 to 12 inches from its seat than the long and flexible falling beam and girder assembly. What he has in his analysis is far from what would really happen here. The deflection of the impacting beam and girder assembly will make a big difference in the force experienced by the girder below and its seat
The two flexibilities are in parallel - not series. Excuse the "lay persons language" of the next bits of explanation.

Nordenson has accounted for the energy that is dissipated - used up - lost - consumed in the earlier failures and the deformation of the flange at the point of impact. BUT the NET energy remaining at the time we are considering - the start of "dampening" as the impact occurs - is still "live" - still available hence the "NET". It is becoming temporarily stored in bending strain energy - in two beams - until EITHER the connection fails or it doesn't fail and some complicated oscillation starts.

Let's take the next step down the path. Because the two beams are in parallel as far as energy flow goes (physically in series BUT that is not how the energy "sees" it.) the net energy will flow two ways. And it will split those two ways in inverse proportion to the stiffnesses of the two beams. So - if the falling beam is (say) 1/9th the stiffness of the lower beam the energy will flow 90% to the falling beam and 10% to the lower impacted beam.

So Nordenson only has 10% of the NET energy he thought he had.

And I picked the 10% - 90% split for simplicity of explanation - in the Nordenson figures is is about 7 or 8:1 so Nordenson saw about 6-7-8 times oversupply of energy. (The exact number doesn't matter - yet - till we get the principle on the table.)

The actual outcome depends on the actual stiffness in play for that falling beam. If is even less stiff than my guess then your intuition is correct - there will not be sufficient energy flowing to the lower beam and via it to fail the girder<>column connection.

If the falling beam is stiffer than my guess then there will be enough energy flowing to the impacted beam to fail the connector.

And in that second scenario of "failure" Nordenson's outcome conclusion would be correct BUT he would be in the position of being "right for the wrong reasons".

And the odds are your way Tony that the beam is much less stiff (???) I don't accept your "hundreds" but even 10 times makes your claim on that aspect of the Nordenson paper valid.

However:
and the analysis needs to be corrected to account for this.
Why? For who? It was a paper prepared for legal purposes for a past and concluded action. Why would his clients need corrections at this late stage? Who else has standing to ask for corrections?
 

econ41

Senior Member
So what is the PRACTICAL difference? It seems to me you don't know that either - and are assuming it is significant.
IMNSHO - no difference whatsoever.
1) The IMPLIED goal here is "Prove CD";
2) The path to that - acknowledged by Tony at post #5 - is "Denigrate and discredit NIST";
3) ...
N) Tony's specific single issue focussed goal here is prove Nordenson was wrong -- on one point.

I think I summarised the overall "logic" at my Post #6.

... How does an error in Nordenson's report have the slightest effect on the status of the NIST report?

Interesting logic - I'll leave it for someone to identify the Formal Fallacy. Bill said "A". Fred said "B". Fred is wrong THEREFORE Bill is wrong? :(
We are seeing progress on understanding the single issue in focus. The overall status is IMO unchanged - and it makes no "PRACTICAL difference" :rolleyes:
 

Tony Szamboti

Active Member
IMNSHO - no difference whatsoever.
1) The IMPLIED goal here is "Prove CD";
2) The path to that - acknowledged by Tony at post #5 - is "Denigrate and discredit NIST";
3) ...
N) Tony's specific single issue focussed goal here is prove Nordenson was wrong -- on one point.

I think I summarised the overall "logic" at my Post #6.


We are seeing progress on understanding the single issue in focus. The overall status is IMO unchanged - and it makes no "PRACTICAL difference" :rolleyes:
The "NIST" report on WTC 7 might as well be called the "missed" report because it does not hold up to scrutiny and seems to be an attempt to promote an impossible explanation for what appears to be political reasons. Things like the omission of the girder stiffeners, ignoring the lateral trapping of the girder by the column 79 side plates, and falsely claiming there were no shear studs on the girder all show the report is bogus.

The correction of the Nordenson analysis will add another nail in the coffin of that ignominious tome and fraud known as the NIST WTC 7 report as it never even bothered to show the falling girder would cause a collapse propagation of the floors below. It just assumed and pronounced it.

My personality doesn't lend itself to playing along with a fraud. There needs to be a new investigation so nobody has to.
 
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Tony Szamboti

Active Member
Agreed to A, It is looking like you are right on B and C is the underlying issue of dampening of an impact load which has never been in doubt as a matter of principle ... the doubts have been about how it applies.

My commendation on this following concise explanation of the underlying principle of applied physics for Jeffrey (Sander) Orling

All that basic physics agreed. A good summary


The two flexibilities are in parallel - not series. Excuse the "lay persons language" of the next bits of explanation.

Nordenson has accounted for the energy that is dissipated - used up - lost - consumed in the earlier failures and the deformation of the flange at the point of impact. BUT the NET energy remaining at the time we are considering - the start of "dampening" as the impact occurs - is still "live" - still available hence the "NET". It is becoming temporarily stored in bending strain energy - in two beams - until EITHER the connection fails or it doesn't fail and some complicated oscillation starts.

Let's take the next step down the path. Because the two beams are in parallel as far as energy flow goes (physically in series BUT that is not how the energy "sees" it.) the net energy will flow two ways. And it will split those two ways in inverse proportion to the stiffnesses of the two beams. So - if the falling beam is (say) 1/9th the stiffness of the lower beam the energy will flow 90% to the falling beam and 10% to the lower impacted beam.

So Nordenson only has 10% of the NET energy he thought he had.

And I picked the 10% - 90% split for simplicity of explanation - in the Nordenson figures is is about 7 or 8:1 so Nordenson saw about 6-7-8 times oversupply of energy. (The exact number doesn't matter - yet - till we get the principle on the table.)

The actual outcome depends on the actual stiffness in play for that falling beam. If is even less stiff than my guess then your intuition is correct - there will not be sufficient energy flowing to the lower beam and via it to fail the girder<>column connection.

If the falling beam is stiffer than my guess then there will be enough energy flowing to the impacted beam to fail the connector.

And in that second scenario of "failure" Nordenson's outcome conclusion would be correct BUT he would be in the position of being "right for the wrong reasons".

And the odds are your way Tony that the beam is much less stiff (???) I don't accept your "hundreds" but even 10 times makes your claim on that aspect of the Nordenson paper valid.

However:

Why? For who? It was a paper prepared for legal purposes for a past and concluded action. Why would his clients need corrections at this late stage? Who else has standing to ask for corrections?
The lateral spring rates (lateral stiffness) of the two girders are in series, not parallel, as they act in the same line of action. You could say their axial spring rates are in parallel but that isn't involved here.

The force applied to the girder below in the Nordenson analysis is probably about 20 times too high and the actual force is not enough to shear the seat of the girder below and cause collapse propagation.
 
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MikeC

Closed Account
The "NIST" report on WTC 7 might as well be called the "missed" report because it does not hold up to scrutiny and seems to be an attempt to promote an impossible explanation for what appears to be political reasons. Things like the omission of the girder stiffeners, ignoring the lateral trapping of the girder by the column 79 side plates, and falsely claiming there were no shear studs on the girder all show the report is bogus.

The correction of the Nordenson analysis will add another nail in the coffin of that ignominious tome and fraud known as the NIST WTC 7 report as it never even bothered to show the falling girder would cause a collapse propagation of the floors below. It just assumed and pronounced it.

My personality doesn't lend itself to playing along with a fraud. There needs to be a new investigation so nobody has to.
It stands up to lots of scrutiny - just not yours. And yours is of the variety that suggests errors but does not actually show that they exist.

"The correction of the Nordenson analysis" may or may not show something relevant - but your assumption it will be SO IMPORTANT as to negate the NIST findings is not actually based on anything other than your wishful thinking as far as I can tell. As is your assertion of fraud, and that there is a need for a new investigation - it seems entirely in your own mind.

Your whole argument is based around assumptions - that there are political reasons in the first place for example.

Why should anyone take you seriously?
 

MikeC

Closed Account
The lateral spring rates (lateral stiffness) of the two girders are in series, not parallel, as they act in the same line of action. You could say their axial spring rates are in parallel but that isn't involved here.

The force applied to the girder below in the Nordenson analysis is probably about 20 times too high and the actual force is not enough to shear the seat of the girder below and cause collapse propagation.
Figures?? Calculations to support this?? You know - actual evidence?
 

Mick West

Administrator
Staff member
Please try to stick to the actual science here, and leave out speculations about motives and biases.
 

Oystein

Senior Member
Figures?? Calculations to support this?? You know - actual evidence?
I developed the math in the PDF I uploaded earlier:
https://www.metabunk.org/attachments/nordenson_b5_calculations-pdf.17106/
There's a table with results for 5 values of falling girder stiffness.

econ is correct that energy absorption by the two beams is inversely proportional to their stiffnesses.
The Force we are looking for scales with the square root of the energy absorbed by the girder below.
Tony is correct that the jury is still out on where the result lands, as we haven't agreed on how to determine the stiffness of the falling girder. We agree that, intuitively, it is much less stiff than the girder below.
The table in my PDF shows that, when the falling girder's stiffness is 0.78% the stiffness of the girder below (59.2 kip/in versus 7627 kip/in), the girder below absorbs 0.77% of the kinetic energy, and the resulting force is 8.8% (square root of 0.77%) of Nordenson's result, i.e. 639 kips. That is nearly the shear capacity of the connection (632 kips).

So here's where the jury is out on:
  • If the stiffness of the falling girder is significantly larger than 60 kip/in, then the resulting force is larger than capacity and the connection will fail
  • If the stiffness is significantly smaller than 60 kip/in, then the connection will survive.
  • If the stiffness is in the general ballpark around 60 kip/in, then all the imprecisions in all the numbers we have, and all the little effects that so far have been ignored, make it impossible to decide either way.
econ, by the way, is mistaken to say that the springs are in parallel - conceptually, they are in series. My math shows that that's "how the energy sees it" - coming from the angle of solving the energy balance, I proved that the effective stiffness is that of springs in series. But that mis-speak didn't invalidate anything in the rest of his posts earlier today / yesterday (depending on time zone).

The earlier discussion of if and how the mass of the concrete slab, steel girder and beams would have to be considered missed the plot: The starting net kinetic energy for the girder-girder impact scenario under scrutiny here has been fixed by Nordenson; he derived it from his SAP2000 model of the floor assembly, and it includes the girder and a portion of the slab area in the north-east corner.
The beams framing into the girder are of course loading the girder, and the concrete cannot seriously be considered to be far behind the steel elements
 

econ41

Senior Member
The lateral spring rates (lateral stiffness) of the two girders are in series, not parallel, as they act in the same line of action. You could say their axial spring rates are in parallel but that isn't involved here.
I could say that Tony but I wont.

I just did you a big favour in Post #146 and spoon fed you the explanation as to how your claim could be correct. I only explained the "parallel energy flow" case because that is what your claim requires.

Here's why:

Some energy is caught up as bending strain energy causing the loss of energy you are claiming Tony. That energy is still in the "falling" beam - it is the strain energy associated with the bending of that beam and labelled as "A".

The same deflection you are asserting Tony and I am agreeing that it is there. Fact is however there is energy in that deflected beam THEREFORE it has not passed though at "B" to the beam below.

However some energy passes to the lower beam at "B". AFAICS no one is denying there are those two lots of energy. They are the Nordenson NET energy divided into two components.

Energy - anything going two separate ways is parallel by my use of language. And by my language "serial" means one after the other.

(And for any members coming new to the topic who have not been mentally working through the issues remember that the time frame we are discussing is the brief interval from drop>>impact>>into the first stage ONLY of a potential rebounding and oscillatory cycle.)

...The force applied to the girder below in the Nordenson analysis is probably about 20 times too high and the actual force is not enough to shear the seat of the girder below and cause collapse propagation.
Could well be true as I explained in broad concept in Post #146. It depends very much on the actual flexibility/stiffness of the dropping beam which forms a parallel path for the diversion of the still live - not "dissipated" energy. Try tracking energy flow.

Here - a free "hint" - if you put the springs in series the more flexibility - less stiffness - the upper one has the MORE energy passes through to the lower beam "spring". Exactly the reverse of what your claim needs.
 

Oystein

Senior Member
...
Energy - anything going two separate ways is parallel by my use of language. And by my language "serial" means one after the other.
...
Could well be true as I explained in broad concept in Post #146. It depends very much on the actual flexibility/stiffness of the dropping beam which forms a parallel path for the diversion of the still live - not "dissipated" energy. Try tracking energy flow.

Here - a free "hint" - if you put the springs in series the more flexibility - less stiffness - the upper one has the MORE energy passes through to the lower beam "spring". Exactly the reverse of what your claim needs.
Perhaps you could, in layman's language, say that strain energy build-up is "parallel", but when talking about springs, which the beams are, the technically and physically correct language demands that we talk of "springs in series" as opposed to "in parallel":
https://en.wikipedia.org/wiki/Series_and_parallel_springs
Again, check the math in my PDF, it shows that the effective stiffness is that of springs in series.

I am confident that Tony won't take your final "hint", for it is wrong, and the exact opposite is true. You already put it the right way in post #146:
"if the falling beam is (say) 1/9th the stiffness of the lower beam the energy will flow 90% to the falling beam and 10% to the lower impacted beam"​
I.o.w. "if you put the springs in series the more flexibility - less stiffness - the upper one has the LESS energy passes through to the lower beam spring" and the MORE to the falling beam.
 

Polly Math

Member
Perhaps you could, in layman's language, say that strain energy build-up is "parallel", but when talking about springs, which the beams are, the technically and physically correct language demands that we talk of "springs in series" as opposed to "in parallel":
https://en.wikipedia.org/wiki/Series_and_parallel_springs
Again, check the math in my PDF, it shows that the effective stiffness is that of springs in series.
When you came up with your 16X figure in your pdf table, was that really just coincidence that you applied a simply supported beam stiffness, or did you choose that figure because of Nordenson's value?
Wouldn't the girder in essence be levering the 44 end upward on a given fulcrum, whos position on the girder will be proportionally further south with the amount of remaining support from the NE beams. Defining this point is required to ascertain the final K value. For the record, I agree with Tony on the stiffness, and believe that Nordenson will tell you the same. He has worked backwards instead of defining the state of the girder.
Also see page 13 re springs in series. Don't take this as critisism please. I am enjoying watching this discussion. Thank you.
http://arxiv.org/pdf/0911.2029.pdf I agree that the series/parallel differentiation is important.
 

Jeffrey Orling

Senior Member
Are these values for the lower 12th floor assembly assuming a stone cold... pristine strength condition? If so I find that preposterous. The fires that were impacting the 13th floor surely including fires below on the 12th floor. If so wouldn't that change the outcome of a "collision" of the 13th floor falling on the 12th?
 

Polly Math

Member
Are these values for the lower 12th floor assembly assuming a stone cold... pristine strength condition? If so I find that preposterous. The fires that were impacting the 13th floor surely including fires below on the 12th floor. If so wouldn't that change the outcome of a "collision" of the 13th floor falling on the 12th?
You might be surprised at how low the temp would be on the top of the concrete slab. The WWM is still below 300C in the ARUP analysis.

Quick addition - I should also have mentioned that the welded mesh will be crucial, and should be accounted for in the calculation.
 

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jaydeehess

Senior Member
You might be surprised at how low the temp would be on the top of the concrete slab. The WWM is still below 300C in the ARUP analysis.

Quick addition - I should also have mentioned that the welded mesh will be crucial, and should be accounted for in the calculation.
I believe that JO was referring to the temp of the lower girder and associated seat on col 79.

If TSZ is correct then this consideration DOES very much become relevant.

As would, imh non-engineer opinion, the contribution of following falling floor and office contents mass.
 
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jaydeehess

Senior Member
Re:series/parallel
A series arrangement of springs would see greater compression of the weaker spring but that energy is then still available in oscillations. With the stronger spring oscillating at a different freq there would be possibility of all the energy concentrated at the connection of both springs.

In parallel, the weaker spring compresses and oscillations take place in isolation from the stronger one.
 
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