9/11 Physics from Non-Experts

[R.Mackey]

Don't forget that the regular surveys were most likely focused on local overloading than global overloading, the latter of which has a statisical likelihood << 0.01 (the likelihood of local overloading).

From NIST NCSTAR1-2 pg 106:

Journal of Structural Division 1974, R. K. McGuire et al., "Live Load Effects in Office Buildings".

In the chapter, "Results of live load survey - Variance of sustained load", the mode is given as 0.45 kPa and 90% of the samples are less than 1.0 kPa. The average appears to be around 0.55 kPa = 11.5 psf. This would indicate that my use of 25 psf live load for the area outside of the core is more likely an overestimate than an underestimate.

Unless anyone can present more recent developments that would contradict this I think we should accept it?

Hello again GregoryUrich, thank you for supporting your live load estimates. I would still like to see some more recent references if possible, since the offices of 1974 are a little different than 2001 (in some ways heavier, e.g. denser staffing, but in other ways lighter -- who has oak furniture these days??), and it would also do to better understand how much of the WTC Towers daily usage fit this model, versus other uses like trading floors and shopping malls that would probably be heavier. However, until we find something more precise, I can accept your ballpark estimate for live load.

I still would like to revisit the superimposed dead load, however. There I'm sure you've underestimated. We won't find 250,000 tons of it, but it will put you more in line with the other calculations.

For example, here is the latest from Bazant et al.:

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/00%20WTC%20Collapse%20-%20What%20Did%20%26%20Did%20Not%20Cause%20It%20-%205-2007.pdf

Why not take a shot at dissecting the above article? A good place to start is:

1. Bazant uses a mass for the upper part that is at least 60% higher than the statistically predicted actual mass.

2. Bazant again neglects momentum transfer.

3. Bazant assumes that the upper part is totally immune to the forces affecting the lower part when in fact the upper part can not exert a force greater than the upper part itself is subjected to. Or rather, "crush up" begins at the first collision during collapse.

If I'm not mistaken, Bazant et. al. do not neglect momentum transfer. I haven't rederived the equations myself yet, but I believe the term F_m seen in their Equation 6 accounts for the momentum transfer. They are using a force-balance rather than an argument from conservation of momentum, required since this is a dissipative process, and therefore this expression is the correct form.

Dr. Greening is posting here, and I'm sure he could explain in more detail.

Furthermore, because of the term above, you will see that the mass effectively appears on both sides of the equations, and to first approximation can be divided out. I don't expect Bazant's et. al. prediction to vary significantly with changing mass estimates. They have the equations all set up, so this should be an easy thing to verify.

Regarding the third point, while it is true the upper block would suffer some damage through progressive impact, the relative mass of the upper block to the total descending mass rapidly diminishes as the collapse progresses. At no time is the force exerted greater than the upper mass experiences. Delaying "crush-up" until the end of the "crush-down" phase is a simplification, but not one that should have much effect on the final result.

 

[GregoryUrich]

...I still would like to revisit the superimposed dead load, however. There I'm sure you've underestimated. We won't find 250,000 tons of it, but it will put you more in line with the other calculations.

I am not satisfied with my superimposed dead load either. I haven't seen much in NIST regarding a unit SDL psf for the core. There is alot of stuff there: pipes, vents, cables, elevator stuff (pits, tracks, cables, counter weights, machine rooms), telephone closets, etc.

The SDLs for the mechanical floors is also difficult.

Outside the core NIST gives the design SDL as 8 psf, which I have used throughout.

I'll have to look at Bazant again regarding momentum.

 

[GregoryUrich]

If I'm not mistaken, Bazant et. al. do not neglect momentum transfer. I haven't rederived the equations myself yet, but I believe the term F_m seen in their Equation 6 accounts for the momentum transfer. They are using a force-balance rather than an argument from conservation of momentum, required since this is a dissipative process, and therefore this expression is the correct form.

Furthermore, because of the term above, you will see that the mass effectively appears on both sides of the equations, and to first approximation can be divided out. I don't expect Bazant's et. al. prediction to vary significantly with changing mass estimates. They have the equations all set up, so this should be an easy thing to verify.

Regarding the third point, while it is true the upper block would suffer some damage through progressive impact, the relative mass of the upper block to the total descending mass rapidly diminishes as the collapse progresses. At no time is the force exerted greater than the upper mass experiences. Delaying "crush-up" until the end of the "crush-down" phase is a simplification, but not one that should have much effect on the final result.

I stand corrected. Bazant does take the momentum into account. Sorry, I was reading to fast.

I think it is important to note that if crush up begins early it consumes energy before the mass really gets moving which affects the fall time more significantly.

 

[beachnut]

Thanks for you candor. Honesty is a rare commodity.

And to be real honest, it does not matter how much you can prove the towers weighed, they were an impact, fire, gravity driven event as seen on 9/11. Explain why proof of being lighter makes a difference?

Just to be honest. No CD, no thermite, no beam weapon. Unless you have some proof of something, what is the big picture. I still have no idea what you think about the physics stuff, the tread topic.

 

[GregoryUrich]

And to be real honest, it does not matter how much you can prove the towers weighed, they were an impact, fire, gravity driven event as seen on 9/11. Explain why proof of being lighter makes a difference?

Just to be honest. No CD, no thermite, no beam weapon. Unless you have some proof of something, what is the big picture. I still have no idea what you think about the physics stuff, the tread topic.

WCT1 for example:

In Bazants first paper, he gave energy for plastic work a 12% of the PE (his PE) of the top part. Now he is taking into account the resistive energy for expelling air, comminution of concrete and momentum transfer. Comminution of concrete accounts for 10% of the total energy available. Momentum transfer accounts for more energy than the rest combined. Thus we are up in the neighborhood of 40-50% energy loss.

Consider a realistic in-service mass for the building which is a little more than half of Bazant's archaic 500,000 tons and also a PE less than half of the PE Bazant uses. Essentially most of the energy is used up and little is left to accellerate the mass. The conclusion is a very long fall time or even an incomplete collapse.

 

[rwguinn]

WCT1 for example:

In Bazants first paper, he gave energy for plastic work a 12% of the PE (his PE) of the top part. Now he is taking into account the resistive energy for expelling air, comminution of concrete and momentum transfer. Comminution of concrete accounts for 10% of the total energy available. Momentum transfer accounts for more energy than the rest combined. Thus we are up in the neighborhood of 40-50% energy loss.

Consider a realistic in-service mass for the building which is a little more than half of Bazant's archaic 500,000 tons and also a PE less than half of the PE Bazant uses. Essentially most of the energy is used up and little is left to accellerate the mass. The conclusion is a very long fall time or even an incomplete collapse.

So, we're down to 4 choices:
1. Every Engineer, scientist, society, and associuation which has investigated the collapse and come to the NIST conclusion is wrong; or
2. The buildings are stiil there, everyone is too blind to see them; or
3. You might be mistaken; or
4. there is another mechanism out there everybody with any expertise and experience in the field of structural engineering and analysis has missed

Which one you betting on?

 

[GregoryUrich]

So, we're down to 4 choices:
1. Every Engineer, scientist, society, and associuation which has investigated the collapse and come to the NIST conclusion is wrong; or
2. The buildings are stiil there, everyone is too blind to see them; or
3. You might be mistaken; or
4. there is another mechanism out there everybody with any expertise and experience in the field of structural engineering and analysis has missed

Which one you betting on?

4.

Do you still think the building weighed 500,000 tons?

I just calculated the collapse time for crush down only (96 floors) with Bazants energy for plastic work and momentum transfer only (no other losses) and got > 14 seconds.

 

[beachnut]

4.

Do you still think the building weighed 500,000 tons?

I just calculated the collapse time for crush down only (96 floors) with Bazants energy for plastic work and momentum transfer only (no other losses) and got > 14 seconds.

That is a little longer than what I got with a simple model. Yet the WTC had parts still falling at 30 seconds. Models.

I only had 10 or 20 percent longer than free fall for the energy to destroy the entire tower floor by floor. In reality parts of the WTC stood for more than 20 seconds, and the entire WTC did not fall. So? Still no CD, no thermite, and no inside job. What is next?

 

[GregoryUrich]

More nonsense from Bazant and Co.

Bazant's latest paper insists that 80% of the total mass hit the bedrock traveling at approximately 47m/s. That is > 4x10^11 Joules of energy, or 25,000 times the energy for a 2.1 Richter scale quake as measured at the LDEO.

 

[Newtons Bit]

Greg: Is that as an impulse or spread out over time? The richter scale measures the PEAK energy, not the sum.

 

[rwguinn]

Greg: Is that as an impulse or spread out over time? The richter scale measures the PEAK energy, not the sum.

Correct me if I'm wrong, but doesn't the seismometer measure acceleration? Conversion to Richter would include variables shuch as location, activation area, depth, and other things.
AFAIK, nobody has actually put the collapses int an earthquake comparison, at least not seriously...

 

[Newtons Bit]

I thought it was a log function of energy (at the peak in the wave). To get acceleration, you need to start messing with some other stuff. I use the crap in IBC all the time, but even that is empirical.

Wikipedia to the rescue! http://en.wikipedia.org/wiki/Richter_scale

 

[Furcifer]

Greg: Is that as an impulse or spread out over time? The richter scale measures the PEAK energy, not the sum.

You should be able to take the area under the curve and arrive at a fair estimate of the energy dissipated, then equate it to a mass.

 

[rwguinn]

I thought it was a log function of energy (at the peak in the wave). To get acceleration, you need to start messing with some other stuff. I use the crap in IBC all the time, but even that is empirical.

Wikipedia to the rescue! http://en.wikipedia.org/wiki/Richter_scale

As I thought, from the references- Seismometers measure force, and derive deflection from it--in general. An accelerometer can measure acceleration, but to measure actual deflection, you need a reference point. Seismometers use the F=KX principle, with a fixed mass on a spring. The earth moves, the internal mass doesn't, the spring stretches, and you measure strain. That is an accelerometer. It all depends on how you use it. The fact that they huge huge (relatively) masses and wimpy springs, whilest a PCB 305 is a lot smaller doesn't me they don't work the same (OK, I dated myself--anybody stiull use 305's). It is a matter of what you are measuring.
From the USGS page and wikipedia. They are force gages, or accelerometers.
Actual earthquake magnitude is derived based on other factors, and is merely a relative indicator of energy. It is not actual energy--it is peak, as you said. Total energy would involve the area under the whole curve.

ETA-I see 3 body beat me to the integration bit

 

[Apollo20]

A few comments on seismic signals and the WTC collapse:

A seismic event may be considered to involve the creation of simple harmonic earth waves of amplitude x and period T. The trace amplitude, A, on a standard torsion “Wood-Anderson” seismograph is about 3000x cm and it may be shown that if the seismographic measurement is made at a distance d kilometers from the center of a shock of duration t seconds, the total seismic energy, E, is given approximately by:

E = 18600 d^2 t (A/T)^2 joules

Richter was the first researcher to compute the magnitude and energy of an earthquake from Wood-Anderson records – see for example his paper in Bull. Seism. Soc. Am. 32, 163 (1942). Unfortunately, however, the Wood-Anderson seismograph is not commonly used today, having been largely superseded by instruments with inductive pick-ups that show linear response to ground velocity rather than displacement. Nevertheless, modern instruments can generate an “equivalent” W-A seismogram and hence report a local or Richter magnitude and seismic energy.

According to researchers at the LDEO Observatory in Palisades New York, the energy propagated as seismic waves from the collapse of each WTC tower was about 10^7 joules or less than 0.1 % of the gravitational potential energy stored in these buildings. Interestingly, it has been estimated that for the famous Port Chicago explosion on July 17, 1944, produced by the accidental detonation of 1,800 tons of TNT equivalent, about 0.1 % of the energy of the blast went into seismic waves.

 

[Furcifer]

I wonder what mass they assumed in this calculation at LDEO?

 

[GregoryUrich]

A few comments on seismic signals and the WTC collapse:

A seismic event may be considered to involve the creation of simple harmonic earth waves of amplitude x and period T. The trace amplitude, A, on a standard torsion “Wood-Anderson” seismograph is about 3000x cm and it may be shown that if the seismographic measurement is made at a distance d kilometers from the center of a shock of duration t seconds, the total seismic energy, E, is given approximately by:

E = 18600 d^2 t (A/T)^2 joules

Richter was the first researcher to compute the magnitude and energy of an earthquake from Wood-Anderson records – see for example his paper in Bull. Seism. Soc. Am. 32, 163 (1942). Unfortunately, however, the Wood-Anderson seismograph is not commonly used today, having been largely superseded by instruments with inductive pick-ups that show linear response to ground velocity rather than displacement. Nevertheless, modern instruments can generate an “equivalent” W-A seismogram and hence report a local or Richter magnitude and seismic energy.

According to researchers at the LDEO Observatory in Palisades New York, the energy propagated as seismic waves from the collapse of each WTC tower was about 10^7 joules or less than 0.1 % of the gravitational potential energy stored in these buildings. Interestingly, it has been estimated that for the famous Port Chicago explosion on July 17, 1944, produced by the accidental detonation of 1,800 tons of TNT equivalent, about 0.1 % of the energy of the blast went into seismic waves.

So lets look at the accidental detonation.

This is a surface detonation where less than half of the destructive force has even a vector component perpendicular to the surface. Wikipedia states that there were two explosions the larger being a ship that was being loaded (the ship located as ships often are, in the water). It is hard to know what the circumstances were regarding distance to bedrock but the above factors make clear that this is an entirely different situation from a huge compacted mass colliding directly with the bedrock.

Comparison of seismic energy:

Bazant total PE = approx 8.5x10^11
LDEO seismic energy = 1.0x10^7

SE/PE = 0.0000117 = 0.001%

Can an explosion over water be 100 times as effective at transferring energy as a compacted mass traveling at 47m/s hitting bedrock? The answer is clearly no. The conclusion must be that either the accumulated mass or the velocity (or both) as provided by Bazant et al. are in error.

I calculated the mass of one tower based on the specific mass numbers provided by Bazant et al. in the latest paper and got 566,000 short tons. Do you believe this is a realistic mass?

 

[rwguinn]

So lets look at the accidental detonation.

This is a surface detonation where less than half of the destructive force has even a vector component perpendicular to the surface. Wikipedia states that there were two explosions the larger being a ship that was being loaded (the ship located as ships often are, in the water). It is hard to know what the circumstances were regarding distance to bedrock but the above factors make clear that this is an entirely different situation from a huge compacted mass colliding directly with the bedrock.

Comparison of seismic energy:

Bazant total PE = approx 8.5x10^11
LDEO seismic energy = 1.0x10^7

SE/PE = 0.0000117 = 0.001%

Can an explosion over water be 100 times as effective at transferring energy as a compacted mass traveling at 47m/s hitting bedrock? The answer is clearly no. The conclusion must be that either the accumulated mass or the velocity (or both) as provided by Bazant et al. are in error.

I calculated the mass of one tower based on the specific mass numbers provided by Bazant et al. in the latest paper and got 566,000 short tons. Do you believe this is a realistic mass?

Ever do any research? Even waves pounding a beach generate seismic waves.
There are many types of waves generated by an event--see wikipedia , as well as others. An explosion on the ground (or in water) will generate lateral waves as well as vertical (compressive) waves, covering a full hemisphere, unless the charge is shaped, or well above ground level. Since I know little about seismology, I'll leave it there.
But do not pretend expertise in an area you do not know--you're then showing just how little credibility any other statements you make have.
http://en.wikipedia.org/wiki/Seismic_wave

 

[GregoryUrich]

Ever do any research? Even waves pounding a beach generate seismic waves.
There are many types of waves generated by an event--see wikipedia , as well as others. An explosion on the ground (or in water) will generate lateral waves as well as vertical (compressive) waves, covering a full hemisphere, unless the charge is shaped, or well above ground level. Since I know little about seismology, I'll leave it there.
But do not pretend expertise in an area you do not know--you're then showing just how little credibility any other statements you make have.
http://en.wikipedia.org/wiki/Seismic_wave

I suggest you take out a patent on a water tipped pnuematic hammer. It will be a fantastic success. First flood the quarry with a layer of water then hammer away at the water surface. Since this is 100 times more effective at transferring energy than hammering on the actual bedrock, it should be a fast and inexpensive way to mine!

If anyone else assumes I am pretending to be knowledgable in the area of seismology or explosives, please let me put your fears to rest. I know very little about seismology and explosives. On the other hand, I do have a fairly good grip on basic physics.

 

[beachnut]

I suggest you take out a patent on a water tipped pnuematic hammer. It will be a fantastic success. First flood the quarry with a layer of water then hammer away at the water surface. Since this is 100 times more effective at transferring energy than hammering on the actual bedrock, it should be a fast and inexpensive way to mine!

If anyone else assumes I am pretending to be knowledgable in the area of seismology or explosives, please let me put your fears to rest. I know very little about seismology and explosives. On the other hand, I do have a fairly good grip on basic physics.

No CD. When you finally get all the numbers right you will have the WTC falling from impact and fire. Hurry, you are looking truthy.