9/11 Physics from Non-Experts

[Augustine]

5. In his derivation of Pdyn/Po, I think Bazant equates the design load capacity(mg) with his assumed mass of 58,000 tons (times g) for the upper part. I maintain there are two mgs one that should be used to establish the strain energy (mass1g) and one for design load capacity (mass2g). So the equation should really be:

Pdyn/Po = (1 + sqrt(1+2mass1gCh))/mass2g

6. Further, I believe 58,000 tons is overestimate for the mass of the upper part (mass1) by a factor of ~2.9 according to my work. His design load is also an underestimate of ultimare yield strength for the lower part. If I use my mass for the upper part and the 2.8 safety factor required by the code (refers to destructive testing of assemblies), I get Pdyn/Po of around 0.3 = no collapse. Don't forget, there is a sqrt on the upper part so it changes the ratio dramatically.

You need to go back and check your calculations, numbers, and formula. Keep in mind that all Pdyn/Po represents is the load magnification from impact. Altering the load above (i.e. lightening it) without modifying the stiffness (C) will actually result in greater load magnification (because you have a smaller object impacting a proportionally more rigid object). (Read Bazant's Addendum, he knows Po does not represent full load capacity.) Reducing the stiffness will result in less load magnification. However, there is a minimum stiffness required for the load above (which you can approximate as a lower bound). If you use dead load above only, select a reasonable ratio of dead load to live load, use the minimum stiffness of the floors immediately below only (i.e. assume that the entire tower structure from impact down to the ground is only as stiff as the columns at the impacted floor, a GROSSLY CONSERVATIVE assumption, because the tower is getting amazingly stiffer as you go down), you will still have an OVERLOAD, even with a FACTOR OF SAFETY.

 

[Furcifer]

oh, i will check back but when i indicated that wierzbicki had assumed a core plate thickness 67mm, you indicated your scaling produced a plate thickness of 71mm. I'm sure you can see how this plate thickness does not correspond to a mass of steel on the 96th floor of 285 short tons. You say the floor trusses alone weighed 143 tons (short?)This leaves 142 tons for structural steel in the core and exterior on this floor. The math doesn't work out.

 

[GregoryUrich]

Debris again

Does anyone know if WTC debris was removed to anywhere other than the Fresh Kills landfill?

I found a report by the operators of the landfill claiming the total debris handled to be 1,462,000 tons. The report states that 165,000 tons of steel were removed directly from the WTC site.

http://disaster.pandj.com/World%20Trade%20Center%20Forensic%20Recovery.pdf

I can't imagine there is a more reliable source.

This puts the total at 1,627,000 tons (1,480,000 metric tons) if no debris was handled elsewhere.

 

[Augustine]

1. Don't know.
2. No.
3. No.
4. Don't know.
5. Don't know.

A detailed calculation of the truss weight can be found here:
The article is anonymous but appears very detailed and carefully worked out.

Floor trusses and steel decking come to 14,300 tons. We would need to add floor framing for the mechanical floors which I suggest might be twice as heavy was probably less than 1200 tons. All together 15,500 tons or 15.5% of the total value I used. I have stated previously that I will take this into account.

Do you think it is reasonable to scale the rest linearly? A few pages ago, I did a quick calculation that showed my plate thicknesses would be slightly greater than the NIST values in the upper part of the building.

1. Think about it.
2. Try.
3. Think about it.
4. Do the math.
5. Think about it.

Appearing very detailed doesn't mean a thing. Ask any old-timer, and they will tell you that CAD drafting may make the drawings look great, but the downside is that sometimes the drawings look so nice and professional that you might overlook the fact that they have not been coordinated. I have seen very nice drawings myself that "appeared" very thorough that were not.
Truss calculations have errors. Look and you will find. Intermediate support angles are not exactly inconsequential, could add another 2500 to 3000 tons (swagging). Core beams need to be extracted. How accurate are numbers - contracts get revised, never seen a project go up without a mod. Miscellaneous steel is out there. Break out the spandrels.

Scaling linearly will introduce errors. How significant, I can only guess. If it were me, and this was something I felt was necessary, and I desired a +/- 3% degree of accuracy that you claimed before, I would simply pay the money, get the SAP file, and use the loads that have already been calculated by people working off the actual drawings. Or be comfortable with a larger degree of imprecision, say +/- 10-15% on dead load and +/- 10-20% on superimposed dead load and live load. The question is how accurate you really need to be (or feel you need to be).

 

[Furcifer]

(i.e. assume that the entire tower structure from impact down to the ground is only as stiff as the columns at the impacted floor, a GROSSLY CONSERVATIVE assumption, because the tower is getting amazingly stiffer as you go down),

This is a good point too Greg, ideally you will want to model this as a variable rate spring, to match your liner scaling. Like wise with the upper portion.

 

[Furcifer]

Scaling linearly will introduce errors. How significant, I can only guess. If it were me, and this was something I felt was necessary, and I desired a +/- 3% degree of accuracy that you claimed before, I would simply pay the money, get the SAP file, and use the loads that have already been calculated by people working off the actual drawings. Or be comfortable with a larger degree of imprecision, say +/- 10-15% on dead load and +/- 10-20% on superimposed dead load and live load. The question is how accurate you really need to be (or feel you need to be).

Yes exactly. The only other thing I can think of in addition to this is tracking down the invoicing for the steel. It is my understanding that most of the steel came from Japan. This may prove to be the easiest way. As it is a very simple method it may have already been tried, unsuccessfully.

 

[GregoryUrich]

oh, i will check back but when i indicated that wierzbicki had assumed a core plate thickness 67mm, you indicated your scaling produced a plate thickness of 71mm. I'm sure you can see how this plate thickness does not correspond to a mass of steel on the 96th floor of 285 short tons. You say the floor trusses alone weighed 143 tons (short?)This leaves 142 tons for structural steel in the core and exterior on this floor. The math doesn't work out.

I'm pretty sure it will work out if you use the correct dimensions for the core columns and take into account that the exterior columns had a plate thickness of 16mm. I may have blown the derivation for my famous summation but I checked it in excel so it should be correct.

 

[GregoryUrich]

Load magification is a new concept to me.

Altering the load above (i.e. lightening it) without modifying the stiffness (C) will actually result in greater load magnification (because you have a smaller object impacting a proportionally more rigid object).

When you say smaller do you mean less massive?

Does this mean that the lighter the impacting load causes more damage?

 

[Furcifer]

This works out to 191 Tons of the core columns on floor 96 alone.

(I used 67mm for this calculation, not your 71mm, as you can see this will only add more mass)

 

[GregoryUrich]

1. Think about it.
2. Try.
3. Think about it.
4. Do the math.
5. Think about it.

Appearing very detailed doesn't mean a thing. Ask any old-timer, and they will tell you that CAD drafting may make the drawings look great, but the downside is that sometimes the drawings look so nice and professional that you might overlook the fact that they have not been coordinated. I have seen very nice drawings myself that "appeared" very thorough that were not.
Truss calculations have errors. Look and you will find. Intermediate support angles are not exactly inconsequential, could add another 2500 to 3000 tons (swagging). Core beams need to be extracted. How accurate are numbers - contracts get revised, never seen a project go up without a mod. Miscellaneous steel is out there. Break out the spandrels.

Scaling linearly will introduce errors. How significant, I can only guess. If it were me, and this was something I felt was necessary, and I desired a +/- 3% degree of accuracy that you claimed before, I would simply pay the money, get the SAP file, and use the loads that have already been calculated by people working off the actual drawings. Or be comfortable with a larger degree of imprecision, say +/- 10-15% on dead load and +/- 10-20% on superimposed dead load and live load. The question is how accurate you really need to be (or feel you need to be).

This from the truss calc at www.takeourworldback.com:

The double trusses amount to 4790 * 12 * 10.38 = 596,642 ins^3.
The transverse trusses amount to 2012 * 12 * 5.19 = 125,307 ins^3.
The intermediate angles amount to 2896 * 12 * 3 = 104,256 ins^3.

This makes the total per floor volume of trusses 826,205 cubic inches or
13.54 cubic metres (which is nearly 1/1000th of the actual floor volume).
Assuming 7860 kg/m^3, the mass is 106,424 kg = 117.3 tons per floor.

 

[Augustine]

Load magification is a new concept to me.



When you say smaller do you mean less massive?

Does this mean that the lighter the impacting load causes more damage?

Load magnification. Imagine you are jumping off a 6' wall. You are landing on concrete, or you are landing in soft clay. One will hurt worse. It is the rigid surface, or the higher stiffness. The ratio of mg/C is lower for the concrete; consequently greater load magnification.
Smaller, less massive, yes. Smaller m.
More damage? Not necessarily. Just that, for a constant C, you will have proportionally greater magnification for a lighter mass.

 

[GregoryUrich]

This works out to 191 Tons of the core columns on floor 96 alone.

(I used 67mm for this calculation, not your 71mm, as you can see this will only add more mass)

I'll try to reproduce your number tomorrow. It's quite late over here and I need my beauty sleep...otherwise I get ugly.

 

[GregoryUrich]

Load magnification. Imagine you are jumping off a 6' wall. You are landing on concrete, or you are landing in soft clay. One will hurt worse. It is the rigid surface, or the higher stiffness. The ratio of mg/C is lower for the concrete; consequently greater load magnification.
Smaller, less massive, yes. Smaller m.
More damage? Not necessarily. Just that, for a constant C, you will have proportionally greater magnification for a lighter mass.

I don't see how I can adjust the stiffness. The stiffness is the stiffness based on the structure, so essentially more damage would be done to the upper part?

 

[beachnut]

I don't see how I can adjust the stiffness. The stiffness is the stiffness based on the structure, so essentially more damage would be done to the upper part?

Just what is your whole point? What are you trying to do? The WTC collapse without any explosives, so what is your point?

 

[Gravy]

When you can, Gregory. Thanks.

 

[Newtons Bit]

I don't see how I can adjust the stiffness. The stiffness is the stiffness based on the structure, so essentially more damage would be done to the upper part?

Of course you can. Since almost all floors are of equal height, the stiffness is just the averaged cross-sectional column area multiplied by the modulus of elasticity and then divided by then total height of the building.

 

[rwguinn]

Of course you can. Since almost all floors are of equal height, the stiffness is just the averaged cross-sectional column area multiplied by the modulus of elasticity and then divided by then total height of the building.

A*E/L is probably the best assumption there is. Generally, the windows and facade are cosmetic (parasitic mass) and won't contribute much, if anything, to axial stiffness-right?
Now, all you need are the cross-sectional areas of all the columns, all the way up, and use them as springs in series...
Watch your units...

 

[Newtons Bit]

Well, he supposedly already has the mass of them, it should be trivial to get a cross-sectional area.

 

[GregoryUrich]

When you can, Gregory. Thanks.

I'm searching for the paper. It was a whitepaper by some company somehow involved in insurance and/or the cleanup.

 

[GregoryUrich]

Of course you can. Since almost all floors are of equal height, the stiffness is just the averaged cross-sectional column area multiplied by the modulus of elasticity and then divided by then total height of the building.

Augustine is suggesting that I adjust the stiffness of the lower section based on less weight above. I can calculate the stiffness (which Bazant already did and I have not questioned), but should I manipulate it?