Overview of Ross's Momentum Paper

[Newtons Bit]

Appendix 1
Appendix 2

A Review of Energies And How They Are Dissipated of WTC 1 & 2.

The purpose of this article is to provide an easily accessible resource in which to debunk the claim that World Trace Center buildings 1 and 2 would resist the collapse once started.

As of Fall, 2007, only one papers exists that claims that the collapses would be arrested once started. That paper is Gordon Ross’ entitled, “Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC 1”. In this paper Ross identifies sources of energy that push the collapse and energy sources which resist the collapse. He finds that there is more energy to resist the collapse than energy that would progress it. His conclusion is wrong because he doesn’t understand some rather simple and basic concepts of physics and engineering.

The following is the summary of energy sources both pushing the collapse and resisting the collapse produced by Ross (SIC):

Energy Summary:
The energy balance can be summarised as

Energy available;
Kinetic energy 2105MJ
Potential energy Additional downward movement 95MJ
Compression of impacting section 32MJ
Compression of impacted section 24MJ
Total Energy available 2256MJ

Energy required;
Momentum losses 1389MJ
Plastic strain energy in lower impacted storey 244MJ
Plastic strain energy in upper impacted storey 215MJ
Elastic strain energy in lower storeys 64MJ
Elastic strain energy in upper storeys 126MJ
Pulverisation of concrete on impacting floor 304MJ
Pulverisation of concrete on impacted floor 304MJ

Total Energy required 2646MJ
Minimum Energy Deficit -390MJ

This summary can be easily explained. In the energy available section, Ross adds up the sources pushing the collapse. There is 2105MJ of potential energy available for the collapse. This is calculated as 16 stories of the WTC falling 3.7m (one full story). The other minor additions are potential energy gains as the building compresses.

Ross identifies the energy that resists the collapse as energy required. This can be divided into three sections: Momentum Losses, Column Strain Energy, and Concrete Strain Energy. Momentum Losses is a calculation of kinetic energy losses; Column Strain Energy is the energy required to rupture the columns such that they do not provide any more support; Concrete Strain Energy is the energy required to pulverize 20% of the concrete slab into 60 micrometer particles.

In the end, Ross is very wrong. A more accurate summary, proven later in this paper, is as follows:


Kinetic Energy available: 2105MJ

Kinetic Energy gains:
Potential Energy of the Upper Block + 64MJ
Potential Energy of the Lower Stories + 41MJ

Kinetic Energy Losses (including strain rates):
Loss of Kinetic Energy due to Inelastic Collision - 123MJ
Loss of Kinetic Energy due to Mass-With-Spring - 414MJ

Elastic Strain Energy of the Lower Stories - 213MJ
Inelastic Strain Energy of the Lower Story - 171MJ
Elastic Strain Energy of the Upper Block - 71MJ
Inelastic Strain Energy of the Upper Story - 171MJ

Pulverized Concrete - 0MJ

Total Energy Available + 2210 MJ
Total Kinetic Energy Losses - 1163 MJ
Total Energy Balance + 1047 MJ


The result as seen is a total kinetic energy gain after the first impact is 1047MJ. This means that the the collapse of the tower will not be slowed down or stopped and the collapse front will accelerate.

Momentum Losses:
To understand momentum and losses associated with it, a basic knowledge of collisions is required. There is always conservation of momentum in collisions. This can be stated by: Mass*Velocity before a collision is equal to the Mass*Velocity after the collision. This is commonly referred to as the Law of Conservation of Energy.

There are two general types of collisions: inelastic and elastic. This is best explained with the help of animations.


An elastic collision, animation created by Simon Steinmann.


An inelastic Collision, animation created by Simon Steinmann.

Objects involved in an elastic collision have the same amount of momentum before the collision afterwards. They also have the same amount of kinetic energy (1/2*Mass*Velocity) before and after the collision.

Inelastic collisions result in the two bodies becoming one and having one velocity. Because of conservation of momentum there is a loss of kinetic energy. This can be easily explained from the above animation.

Before the collision, the object on the left has:
KE = ½*m*v^2

After the collision, we know that the velocity is halved and the mass is doubled, thus:
KE = ½*(2m)*(1/2*v)^2
KE = ¼*m*v^2

Or a total loss of 50% of the total kinetic energy, this loss kinetic energy goes into the internal energy of the colliding objects. Specifically strain energy (the objects going squish and becoming one), heat energy and sound energy. This loss of kinetic energy is not a loss of total energy and it is a mistake that Ross makes that will be explored later.

Ross attempts to calculate the kinetic energy lost by the collision. He states,
A simple conservation of momentum calculation, ignoring these movements, would have, 16 falling storeys moving at 8.5 m/sec before impact, changing to 17 storeys moving at (8.5 * (16/17)) = 8 m/sec after impact. This does not reflect the fact that a minimum of 24 further storeys will be caused to move downwards at varying speeds.

To estimate and illustrate the further momentum changes we can assume that the storey which is 25 storeys from the impact remains static and the velocity of the 24 affected storeys will vary linearly from the velocity of the falling section to zero.

Momentum before impact = 16 storeys moving at 8.5 m/sec

Momentum after impact = 17 storeys moving at V2 m/sec + 1 storey moving at 23/24*V2 m/sec + 1 storey moving at 22/24*V2m/sec +……+ 1 storey moving at 2/24*V2 m/sec + 1 storey moving at 1/24*V2m/sec 16*8.5 = V2 (17 + 11.5)

V2 = 16 * 8.5 / 28.5 = 4.8 metres per second.

The first thing that Ross states is that there is an inelastic collision between the 16 upper stories and the story that they are impacting at the top of the upper block. 16 stories with a velocity of 8.5m/s will become 17 stories with a velocity of 8.0m/s. This is true. And results in a loss of 123MJ of kinetic energy.

Ross then states that 24 stories below this story will also deflect. This is also true. However, from the discussion above, we know that Ross makes a critical mistake: there is not an inelastic collision between the intact stories below the collapse front and the upper block. It is an elastic collision. We know this because there is no permanent deformation of the lower columns, they stay in the elastic stress-strain region, and that the masses did not impact and combine into one larger mass. An accurate way to address this problem is to assume these additional 24 stories are part of a spring with mass. For this analysis, see Appendix 1.

The results of the spring-with-mass analysis:
Loss of Kinetic Energy due to Inelastic Collision - 123MJ
Loss of Kinetic Energy due to Mass-With-Spring - 414MJ

In addition the additional energy gained due to potential energy is:
Potential Energy of the Upper Block + 64MJ
Potential Energy of the Lower Stories + 41MJ

It is important to note that the Loss of Kinetic Energy due to Mass-With-Spring is a gain in kinetic energy in the bottom portion of the structure. This energy is not immediately dissipated and it will accumulate on each successive impact of the upper block on the lower block. This energy manifests itself as vibrations in the lower structure, which will ultimately reduce the total strength of the lower columns. However this is outside the scope of this paper as it relates to the continuing progressive collapse and not just the first impact.


Column Strain Energy:
The strain energy in columns is rather simple to calculate, however Ross fails to understand the basic concept of inelastic buckling. A detailed analysis of the energy required to completely rupture the columns can be seen in Appendix 2.

Elastic Strain Energy of the Lower Stories - 213MJ
Inelastic Strain Energy of the Lower Story - 171MJ
Elastic Strain Energy of the Upper Block - 71MJ
Inelastic Strain Energy of the Upper Story - 171MJ

Concrete Strain Energy:
The “pulvierisation” of concrete is perhaps the biggest flaw in Ross’ paper. He lists a total of 608MJ lost from this event. In reality, the loss of kinetic energy due to pulverized concrete is ZERO MJ. Why is this? It’s already been accounted for. Recall that the loss of kinetic energy from an inelastic collision. This means that some of the kinetic energy is converted into heat, some into sound and the vast majority into strain energy. The strain energy category includes this pulverized concrete. In reality, core columns punching through the floor slabs, or concrete debris doing the same, would cause an additional amount of interal energy to be added into the concrete slabs. However the Ross model only allows the columns to land directly on top of each other, as this is most conservative to collapse prevention.

A question might still remain for some readers as to why so much of the concrete in the tower was turned into a fine particulate dust. The answer to that question lies not in the impact of one floor against another floor, but in the eventual impact of the entire structure into the ground. At that point, almost all of the available kinetic energy will be converted into internal energies. Again, some into heat, some into sound, but the vast majority into strain energy.

[Newtons Bit]

I know most people are going to think I'm insane or masochistic for doing this again. Maybe I'm both.

In any event, I still find that truthers cannot understand/accept that Ross is wrong so I'm trying to break down all the relevant parts of his paper and show how he goes wrong. This will probably be my last work on the subject.

[Gravy]

Originally Posted by Newtons Bit

I know most people are going to think I'm insane or masochistic for doing this again. Maybe I'm both.

I don't think so. This is the clearest explanation I've seen. Thanks!

[beachnut]

Originally Posted by Newtons Bit

I know most people are going to think I'm insane or masochistic for doing this again. Maybe I'm both.

In any event, I still find that truthers cannot understand/accept that Ross is wrong so I'm trying to break down all the relevant parts of his paper and show how he goes wrong. This will probably be my last work on the subject.

Ross's work is dead wrong.

[Brainster]

Terrific post.

[rwguinn]

Originally Posted by Newtons Bit

I know most people are going to think I'm insane or masochistic for doing this again. Maybe I'm both.

In any event, I still find that truthers cannot understand/accept that Ross is wrong so I'm trying to break down all the relevant parts of his paper and show how he goes wrong. This will probably be my last work on the subject.

Jebus H Christ on a pogo stick.
Look what you made me do (I had to... My brain Aches...)

[e^n]

A slight correction, you mention "concrete columns" in your second to last paragraph where I think you may mean 'core columns'? Otherwise looks excellent.

[Apollo20]

Newtons Bit:

1. Ross' main error (in my opinion) is that he mixes momentum and kinetic energy in his calculation and thereby "double-dips".

2. M1V1 = M2V2 is NOT the Law of Conservation of Energy. There are TWO conservation theorems in Newtonian mechanics, one for ENERGY and one for MOMENTUM, and these theorems are only valid for closed systems.

3. Are you seriously suggesting that NO concrete was pulverized BEFORE all of the Twin Towers "hit the ground"?

[Newtons Bit]

Originally Posted by Apollo20

3. Are you seriously suggesting that NO concrete was pulverized BEFORE all of the Twin Towers "hit the ground"?

I'm seriously suggesting you read the paragraphs. The ONLY energy that goes into straining the concrete is from the inelastic collision. This is 123MJ. That's it. Whatever is pulverized comes out of that energy. This is the only mechanic of the collapse that puts energy into the concrete.

It's not like some great entity from above sees the collapse and says, "hmm, there should be more pulverized concrete here, let's use some kinetic energy to do so!" and then tumbles the collapse some more to achieve this.

In reality, there is probably much more strain energy being put into the floor slabs. The reason for this is that the collapse does not happen as the Ross model suggests that it does. The columns did not fall exactly on top of one another. They penetrated through the floor slabs. The debris hit other debris, etc. But in this model, the only energy that can be used to strain the slabs is from the inelastic collision, and that's 123MJ (some of which goes into heat and some into sound).

Edit: in response for 2, that's a typo and will be fixed. I did alot of editing and used to have something about conservation of energy in there. Thanks.

[Apollo20]

Newtons Bit:

O.K. I see your point...

I guess the main thing is that anyway you cut it, Ross is wrong!

[Dave Rogers]

Originally Posted by Newtons Bit

I'm seriously suggesting you read the paragraphs. The ONLY energy that goes into straining the concrete is from the inelastic collision. This is 123MJ. That's it. Whatever is pulverized comes out of that energy. This is the only mechanic of the collapse that puts energy into the concrete.

It's not like some great entity from above sees the collapse and says, "hmm, there should be more pulverized concrete here, let's use some kinetic energy to do so!" and then tumbles the collapse some more to achieve this.

The same criticism is true, incidentally, of Kenneth Kuttler's letter to JON-ES, in which, in one section, he neglects the conservation of momentum and simply assumes that enough kinetic energy is subtracted from the system at each impact to pulverise all the concrete on a single floor to uniform 100µm particles. Clearly the peer reviewers at JON-ES don't understand the minor subtleties of Newtonian mechanics.

A thorough and rigorous piece of work, NB, and thanks for posting. When I first realised that Ross had considered the KE lost through momentum transfer to be unavailable for pulverisation of concrete (I think you were the one who originally pointed it out), it was a jaw-dropping moment - I don't understand how anybody with the smattering of knowledge Ross clearly possesses (from the fact that he can articulate his arguments at all) can be so catastrophically wrong. Good work in setting it out in the clearest possible terms.

Dave

[CHF]

Did Ross' paper pass "peer-review" in the "journal of 911 stundies?"

[apathoid]

Great post, Newtons Bit. Usually most of the engineering technobabble here is over my head, so thanks for dumbing it down so that even us knuckle-draggers can understand it.

[ElMondoHummus]

NB: Thanks for this. Gordon Ross's thesis is one of the few I didn't have the knowledge to critique; this old Bachelor of Arts guy kept on the qualitative side of the sciences as much as he could (lemme tell ya, Physical Chemistry was pure hell for me; memorizing the Krebs cycle was so much easier to hack than P-Chem was).

[GregoryUrich]

It can clearly be seen in videos that the collapse begins between floors 97-98. Thus the PE should only be from 13 floors + roof and antenna.

A realistic mass of the upper part is 32,814 metric tonnes. This mass can only fall 2.794m before the trusses (29" depth) impact the floor below and momentum transfer/energy conversion begins.

Thus the available energy is around 900MJ which still gives us an energy deficit.

[R.Mackey]

You can't apply the lower mass only to the upper block. The energy losses are also lower using a lower mass-per-floor value. Also subtracting 29" of travel, assuming the lightweight lower chord structure of the floors will prevent further downward motion, is a gross oversimplification. The floors will collapse and the upper block will drop that additional 29".

Play fair, Gregory.

[Dave Rogers]

Originally Posted by GregoryUrich

It can clearly be seen in videos that the collapse begins between floors 97-98. Thus the PE should only be from 13 floors + roof and antenna.

A realistic mass of the upper part is 32,814 metric tonnes. This mass can only fall 2.794m before the trusses (29" depth) impact the floor below and momentum transfer/energy conversion begins.

Thus the available energy is around 900MJ which still gives us an energy deficit.

You're assuming that the trusses can transmit the forces to the columns without deformation, which doesn't sound like a reasonable assumption to me. Assuming collapse through the full height between floors gives available energy of 1036MJ, with a budget of 1063MJ to continue the collapse assuming that the columns of the lower section were undamaged and that all the columns strike end-on. Deformation of the floor trusses over the last 0.74m of that will require more energy - any idea how much? We know that a lot of perimeter columns were fractured, and modelling suggests that at least some core columns were fractured and/or damaged, so 1063MJ is an upper limit on the energy requirement since it assumes no damage. And, of course, the whole Bazant-Greening model that Ross uses has been deliberately biased against collapse by assuming column-on-column impact, which given the tilt of the upper section is geometrically impossible; column-on-floor impacts would require a much smaller energy for propagation in the early stages.

Dave

ETA: Curses, Mackey types faster.

[Dave Rogers]

Originally Posted by R.Mackey

You can't apply the lower mass only to the upper block. The energy losses are also lower using a lower mass-per-floor value.

I've asked Gregory twice whether he's re-calculated the strength of the structure to complement his re-calculation of the weight. The first time, he just said that the strength of the structure is the strength of the structure, or something similar, and the second time he didn't answer.

Gregory, have you re-calculated the strength of the structure based on the WTC blueprints?

Dave

[GregoryUrich]

Originally Posted by R.Mackey

You can't apply the lower mass only to the upper block. The energy losses are also lower using a lower mass-per-floor value. Also subtracting 29" of travel, assuming the lightweight lower chord structure of the floors will prevent further downward motion, is a gross oversimplification. The floors will collapse and the upper block will drop that additional 29".

Play fair, Gregory.

I have not said the chord structure will prevent further downward motion but rather that that is where the impact begins and energy starts to be dissipated. The collision is after a fall of 2,794m. If the chord structure does fail there will be elastic and inelastic strain energies associated with that also. I haven't read Newton's article yet so I don't know if that is somehow included in the inelastic collision energy loss.

You are correct though, some of the energy losses will be reduced, however not the strain energies which will be higher because the failure will take longer.

[R.Mackey]

Originally Posted by Dave Rogers

I've asked Gregory twice whether he's re-calculated the strength of the structure to complement his re-calculation of the weight. The first time, he just said that the strength of the structure is the strength of the structure, or something similar, and the second time he didn't answer.

Gregory, have you re-calculated the strength of the structure based on the WTC blueprints?

Dave

Me too. I've pointed out over and over and over again that the collapse and its timing is largely dependent on momentum transfer from one block to another -- compared to these energy sinks, the actual strength is fairly small in the dynamic situation, which is why Ross uses such absurdly unrealistic momentum transfer arguments to hand-wave his result.

Momentum transfer is invariant with the mass of the Tower, since both upper and lower blocks are likely to have been overestimated by the same factor. Therefore, no change.

[R.Mackey]

Originally Posted by GregoryUrich

I have not said the chord structure will prevent further downward motion but rather that that is where the impact begins and energy starts to be dissipated. The collision is after a fall of 2,794m. If the chord structure does fail there will be elastic and inelastic strain energies associated with that also. I haven't read Newton's article yet so I don't know if that is somehow included in the inelastic collision energy loss.

The net result will be to move some energy from the "pre-impact" energy budget to the "during impact" energy budget, but the total will be unchanged. You simply took it out completely. Dirty pool, old man.

[GregoryUrich]

Originally Posted by Dave Rogers

I've asked Gregory twice whether he's re-calculated the strength of the structure to complement his re-calculation of the weight. The first time, he just said that the strength of the structure is the strength of the structure, or something similar, and the second time he didn't answer.

Gregory, have you re-calculated the strength of the structure based on the WTC blueprints?

Dave

The strength of the structure is still the strength of the structure. It doesn't change with mass...only reserve strength does. I've been very busy at work so I haven't really done anything in this regard for the last month. I would base the strength of the structure on the SAP2000 data rather than the blueprints. If I get some time to look at this I'll post it.

[Dave Rogers]

Originally Posted by R.Mackey

Me too. I've pointed out over and over and over again that the collapse and its timing is largely dependent on momentum transfer from one block to another -- compared to these energy sinks, the actual strength is fairly small in the dynamic situation, which is why Ross uses such absurdly unrealistic momentum transfer arguments to hand-wave his result.

The collapse timing, yes. But there is a valid question as to whether there was enough energy in the first collision to propagate the collapse at all, which is why this aspect is still worth discussing. Once the first impact is over and the building's still falling, then it's end of storey.

Dave

[e^n]

Originally Posted by Dave Rogers

then it's end of storey.

Dave

Ba-dum-tisk!

As usual the lack of any serious criticism is telling.

[Dave Rogers]

Originally Posted by GregoryUrich

The strength of the structure is still the strength of the structure. It doesn't change with mass...only reserve strength does. I've been very busy at work so I haven't really done anything in this regard for the last month. I would base the strength of the structure on the SAP2000 data rather than the blueprints. If I get some time to look at this I'll post it.

The strength of the structure is linearly proportional to the cross-sectional area of the support columns, and the mass of the steel in the structure is also linearly proportional to the cross-sectional area of the support columns. Therefore the strength and the mass are both dependent on the same parameter, albeit in different ways. I think you need to re-calculate the strength of the structure before you can draw any conclusions from the recalculated mass.

Dave

[GregoryUrich]

Originally Posted by R.Mackey

The net result will be to move some energy from the "pre-impact" energy budget to the "during impact" energy budget, but the total will be unchanged. You simply took it out completely. Dirty pool, old man.

I think this two phase collision is a bit more complicated than you are making it. Can we have a discussion without insinuations that I'm trying to trick anyone?

I have to go for now but I'll probably be on later.

[GregoryUrich]

Originally Posted by Dave Rogers

The strength of the structure is linearly proportional to the cross-sectional area of the support columns, and the mass of the steel in the structure is also linearly proportional to the cross-sectional area of the support columns. Therefore the strength and the mass are both dependent on the same parameter, albeit in different ways. I think you need to re-calculate the strength of the structure before you can draw any conclusions from the recalculated mass.

Dave

I agree this needs to be looked at. Nonetheless the cross-sectional area of the columns is not a variable. It is a known constant (for any paticular member). That's what I mean by "the structure is still the structure".

[beachnut]

Originally Posted by GregoryUrich

It can clearly be seen in videos that the collapse begins between floors 97-98. Thus the PE should only be from 13 floors + roof and antenna.

A realistic mass of the upper part is 32,814 metric tonnes. This mass can only fall 2.794m before the trusses (29" depth) impact the floor below and momentum transfer/energy conversion begins.

Thus the available energy is around 900MJ which still gives us an energy deficit.

Sad, you are still trying to back in explosives or thermite. Bang, bang, is missing, and you mean 3.7 m (or more depending on the floors below due to the fire and impact parts of the building are already gone), or are you making up stuff like Jones and your gang of truth who make up lies about 9/11? You have to do better, because the floors below your cherry picked floors are not even all there. OOps, but you also are missing some mass in your building model.

[Newtons Bit]

Originally Posted by GregoryUrich

It can clearly be seen in videos that the collapse begins between floors 97-98. Thus the PE should only be from 13 floors + roof and antenna.

A realistic mass of the upper part is 32,814 metric tonnes. This mass can only fall 2.794m before the trusses (29" depth) impact the floor below and momentum transfer/energy conversion begins.

Thus the available energy is around 900MJ which still gives us an energy deficit.

I'm basing all of my calculations off of Ross's assumption for the mass of the buildings and cross-sectional area of steel. I can lower the mass to what you have shown, but I'd also lower the cross-sectional area of steel. This means that the stiffness of the lower structure is reduced, the elastic strain energy is reduced and the plastic buckling energy is reduced. It'd have the same net effect one way or another. Even without considering lowering the stiffness of the steel, there would not be an energy deficit. The elastic spring underneath the inelastic collision cannot take away more energy than is available.

I just did a quick check with my spreadsheet of there being an available 900MJ of kinetic energy (and the steel cross-sections still remaining) and the collapse progresses. It's SLOWER (at about 2.5m/s), but it still progresses. The reason for this is that the elastic-spring-with-mass below the top story of the lower block is now moving slower as well, and thus absorbing less kinetic energy.

Even if there was only 1MJ of free energy after the inelastic collision, strain energy of the columns and additional potential energy gains, the collapse would still continue.

If you want, I can send over the spreadsheet to you and you can see how it works. It might make more sense to you if you see how the calculations are iterative.

And please don't try and say that the floor trusses are going to absorb more than 1.0MJ. Okay, maybe 2.0MJ. It's ridiculous to assume that they would not just fold at the connection between the deck and top chord.

[Newtons Bit]

A quick sanity check, you show in your mass/pe paper (which I reference alot btw) that there is a total of 165,000kg of steel on the floor 16 stories below the roof. This corrosponds to:

363,000lb of steel or a total of 740cu.ft of steel. Dividing by the height of the building we get a cross-section of 60.9sf. or a total of 8780in^2. I'm using 10,400in^2. This makes a big deal, as the strain energy goes down as well as the structure deflects more which means that the strain rate and DIF is lower.

[Quad4_72]

Bookmarked. There is a lot of mathy stuff going on in here so I think it is best that I go. But great post!

[rwguinn]

Originally Posted by GregoryUrich

The strength of the structure is still the strength of the structure. It doesn't change with mass...only reserve strength does. I've been very busy at work so I haven't really done anything in this regard for the last month. I would base the strength of the structure on the SAP2000 data rather than the blueprints. If I get some time to look at this I'll post it.

[GregoryUrich]

Originally Posted by beachnut

Sad, you are still trying to back in explosives or thermite. Bang, bang, is missing, and you mean 3.7 m (or more depending on the floors below due to the fire and impact parts of the building are already gone), or are you making up stuff like Jones and your gang of truth who make up lies about 9/11? You have to do better, because the floors below your cherry picked floors are not even all there. OOps, but you also are missing some mass in your building model.

As I've said repeatedly, I am not trying to back any position. I am trying to understand something that doesn't yet make sense to me. This should be clear by my revising the building mass upward after discussion here and more in depth analysis.

The floors at which collapse started are backed by EVIDENCE. Do you have evidence to the contrary? If you can't provide such, it will be obvious to everyone that your claim is spurious.

I've asked you repeatedly to reveal what mass is missing in my building model. You have not responded so it is obvious your claim is bunk.

Vaild point about some of the floor being missing though. Nonetheless, according to NIST it is a rather small portion.

Engage the arguments and drop the ad-hominim attacks or you are back on ignore.

[GregoryUrich]

Originally Posted by Newtons Bit

I'm basing all of my calculations off of Ross's assumption for the mass of the buildings and cross-sectional area of steel. I can lower the mass to what you have shown, but I'd also lower the cross-sectional area of steel. This means that the stiffness of the lower structure is reduced, the elastic strain energy is reduced and the plastic buckling energy is reduced. It'd have the same net effect one way or another. Even without considering lowering the stiffness of the steel, there would not be an energy deficit. The elastic spring underneath the inelastic collision cannot take away more energy than is available.

I just did a quick check with my spreadsheet of there being an available 900MJ of kinetic energy (and the steel cross-sections still remaining) and the collapse progresses. It's SLOWER (at about 2.5m/s), but it still progresses. The reason for this is that the elastic-spring-with-mass below the top story of the lower block is now moving slower as well, and thus absorbing less kinetic energy.

Even if there was only 1MJ of free energy after the inelastic collision, strain energy of the columns and additional potential energy gains, the collapse would still continue.

If you want, I can send over the spreadsheet to you and you can see how it works. It might make more sense to you if you see how the calculations are iterative.

And please don't try and say that the floor trusses are going to absorb more than 1.0MJ. Okay, maybe 2.0MJ. It's ridiculous to assume that they would not just fold at the connection between the deck and top chord.

I think you are vastly underestimating the truss matrix. It is the equivalent of approx 5000 sq in of steel.

Now that I think about it, the connections at the core and outer wall would probably go first. For the upper floor, bolt strength would be inconsequential so all that is left is the gusset plate on the outside, so I guess you are right.

The only thing is, once the floor is dissociated from the structure only the vertical components are left to transfer momentum/energy. This may mean that the lower floor would remain intact as the connections are built to support weight and therefore much stronger. That is, until the next floor above starts the second impact.

[GregoryUrich]

Originally Posted by Newtons Bit

A quick sanity check, you show in your mass/pe paper (which I reference alot btw) that there is a total of 165,000kg of steel on the floor 16 stories below the roof. This corrosponds to:

363,000lb of steel or a total of 740cu.ft of steel. Dividing by the height of the building we get a cross-section of 60.9sf. or a total of 8780in^2. I'm using 10,400in^2. This makes a big deal, as the strain energy goes down as well as the structure deflects more which means that the strain rate and DIF is lower.

This is an answer to Dave's question above. I think your value is probably correct for the cross section. I think you meant: divided by the height of one floor (12ft). Since the collapse was probably 3 floors above it would be slightly less.

[beachnut]

Originally Posted by GregoryUrich

As I've said repeatedly, I am not trying to back any position. I am trying to understand something that doesn't yet make sense to me. This should be clear by my revising the building mass upward after discussion here and more in depth analysis.

The floors at which collapse started are backed by EVIDENCE. Do you have evidence to the contrary? If you can't provide such, it will be obvious to everyone that your claim is spurious.

I've asked you repeatedly to reveal what mass is missing in my building model. You have not responded so it is obvious your claim is bunk.

Vaild point about some of the floor being missing though. Nonetheless, according to NIST it is a rather small portion.

Engage the arguments and drop the ad-hominim attacks or you are back on ignore.

You signed the petition; and you are a 9/11 truther. That makes all your work biased junk until checked. You are off on your mass; find it yourself, you left out some stuff; you are the one seeking truth by way of the liars in 9/11 truth. You are the one who did you work, you are the one who needs to find the error. Maybe I missed something, I wonder if you missed the 50 tons I have, and the… (find your errors yourself) I think someone who tries to act all cool and like you are still looking already signed the Petition of BS. Do you need me to post the petition again that you signed to remind you of your bias on this topic as you try to be cool about your bias.

You try to prove the WTC could not collapse; your mass paper is your attempt to show not enough mass to start the fall, but you failed to make your point. You believe in silent explosives or thermite, your signing the petition seals the deal. Talk is all you can do, you have no evidence to support 9/11 truth; be happy you are in a group, when seen by other engineers, of nuts. When I share your work and 9/11 experts work with other engineers they just say you guys are "nuts". Not the kind you eat.

[Newtons Bit]

Originally Posted by GregoryUrich

I think you are vastly underestimating the truss matrix. It is the equivalent of approx 5000 sq in of steel.

Now that I think about it, the connections at the core and outer wall would probably go first. For the upper floor, bolt strength would be inconsequential so all that is left is the gusset plate on the outside, so I guess you are right.

The only thing is, once the floor is dissociated from the structure only the vertical components are left to transfer momentum/energy. This may mean that the lower floor would remain intact as the connections are built to support weight and therefore much stronger. That is, until the next floor above starts the second impact.

Trusses aren't going to be able to carry much of any compressive force. The web members at the ends and their connections are likely fairly stout, as there is a great amount of shear there. However towards the middle, the shear is approximately zero. I doubt the webs were designed for more than a thousand pounds in the middle of the truss. These areas will just crumple. It's an afterthought.

You've also assumed that the floor slab above is going to fall EXACTLY straight down so that the truss is taking a pure vertical force In reality, it's going to be slightly skewed (if not seriously skewed), and this skew is going to introduce a lateral force into these trusses. The metal deck which supports the slab is connected to the trusses. And if they're anything like how they're built today, there's a 5/8" diameter puddle weld burnt through the metal deck to the truss. These are typically spaced fairly far apart in composite floor decks (@12"o.c. or 18" o.c. or so). These puddle welds have almost zero capacity to resist lateral forces. They could probably be bent off by hand. The trusses are going to fold inwards and lay flat against the deck. That's going to add maybe 2" to the total slab height.

But as far as using the right weights and the right cross-section of steel and the correct location of the collapse, it's not my fight. I'm using Ross's assumptions. I've laid out the calculations fairly well, you should be able to follow them and come up with your own energy budget. I've already taken a quick look at it and it doesn't make a big difference one way or another.

[LashL]

Originally Posted by Newtons Bit

I know most people are going to think I'm insane or masochistic for doing this again. Maybe I'm both.

Not at all. Fantastic work, and very helpful to the non-engineers among us. Thanks!

[GregoryUrich]

Originally Posted by beachnut

You signed the petition; and you are a 9/11 truther. That makes all your work biased junk until checked. You are off on your mass; find it yourself, you left out some stuff; you are the one seeking truth by way of the liars in 9/11 truth. You are the one who did you work, you are the one who needs to find the error. Maybe I missed something, I wonder if you missed the 50 tons I have, and the… (find your errors yourself) I think someone who tries to act all cool and like you are still looking already signed the Petition of BS. Do you need me to post the petition again that you signed to remind you of your bias on this topic as you try to be cool about your bias.

You try to prove the WTC could not collapse; your mass paper is your attempt to show not enough mass to start the fall, but you failed to make your point. You believe in silent explosives or thermite, your signing the petition seals the deal. Talk is all you can do, you have no evidence to support 9/11 truth; be happy you are in a group, when seen by other engineers, of nuts. When I share your work and 9/11 experts work with other engineers they just say you guys are "nuts". Not the kind you eat.

So you say I have missed 50 tons. What percentage of the total weight is that? Not really significant, but I'll be glad to include it if you point it out. One more chance to engage the argument.

[Apollo20]

Gregory:

Accorging to MIT "the design load for one floor (of the WTC) is usually taken to be 460 kg/m^2". This is presumably the live load. I would add that the combustible load is a certain percentage of this, and 25 % or more would appear to be reasonable....

However,

NIST use a combustible load of only 20 kg/m^2.

I don't know why.......

What do you think about these numbers?