9/11 Physics from Non-Experts

[T.A.M.]

Google Scholar Search 1st hit...

Spatial and Temporal Variability of Live Loads

by Jong-Cherng Peir, Assoc. Member, ASCE, (Design Engr., Gibbs and Hill, Inc., New York, NY) and C. Allin Cornell, Assoc. Member, ASCE, (Assoc. Prof. of Civ. Engrg., MIT, Cambridge, MA)

Journal of the Structural Division, Vol. 99, No. 5, May 1973, pp. 903-922

TAM

Of course, the actual article itself, from 1973, would as Apollo20 has said, not likely be available on line...lol

Here is the abstract:

A probabilistic model of sustained live occupancy loads on buildings is presented, compared with data, and analyzed to produce equivalent uniformly distributed loads (EUDLs) for structural load effects corresponding to a specified probability of being exceeded. The model of load intensity is a linear form including building, floor, and local spatial variation. The latter term is assumed to have exponentially decaying spatial correlation. Temporal variation is assumed to occur at random times associated with changes of one or more independent occupants. Influence surfaces permit translation to structural load effects. The model is compared and fitted to data from the English Building Research Station office loads survey. Results for sustained and maximum lifetime sustained load effects are shown. Figures compare 99% EUDLs for column axial forces and beam moments versus model U. S. and Canadian building codes.

 

[Belz...]

However, in my line of work (NASA), we do perform weight calculations. Very, very, very sensitive ones. Millions of dollars are often spent to eliminate mere hundreds of grams!

Yah. Forget to bring in a few grams of moon dust and BAM! Off course.

 

[Augustine]

Augustine:

"Collapse was inevitable...."

Would that be with or without x-amount of steel at greater than 400 deg C?

And on the topic of live loads, three classic papers of relevance to the WTC live loads question would be:

Jong-Cherng Peir et al., "Spatial and Temporal Variability of Live Loads"

J. of the Structural Division... May 1973,

R. K. McGuire et al., "Live Load Effects in Office Buildings"

J. of the Structural Division... July 1974,

and,

B. Ellingwood, "Analysis of Live Loads in Office Buildings",

J. of the Structural Division... Aug 1977.

The numbers quoted in these papers are quite revealing...

What I am saying is: with the impact of the plane, and the fire temperature resulting from a certain amount of combustibles within the impacted floors, collapse was inevitable EVEN IF the floors above and below the impact zone were completely unoccupied. (Which, as you know from reading those papers, the floors were very likely far closer to the unoccupied load state than the fully loaded.)
Typical Live Load Statistics are also reproduced in Table C4-2 in ASCE 7 (Minimum Design Loads), and your references are in fact cited in the following excerpt:

It is well known that the floor loads measured in a live-load survey usually are well below present design values. However, buildings must be designed to resist the maximum loads they are likely to be subjected to during some reference period T, frequently taken as 50 years.

Interestingly enough, Ellingwood directed the development of the probability-based load criteria for limit states design that now appear in ASCE 7, AISC LRFD, ASCE Std 16 on LRFD for Engineered Wood Construction, ACI 318, and both national Model Building Codes. The live load reduction factors were in fact reworked while he was sitting on the ASCE 7 Committee, in 1982.

Also, as a point of interest, the live load for offices PER CODE is only required to be 50 psf (minimum). However, nearly every office building in metropolitan areas is designed for 100 psf. Simply put, you will not be able to lease out floor space to tenants without a 100 psf floor capacity. Law firms, financial firms, really ANY firm does not want to have to pay a consulting engineer to analyze or (God forbid) a contractor to retrofit a floor for a movable file system, or have an engineer revise their proposed layout for a library based on a 50 psf equivalent uniform load.

 

[Augustine]

Very interesting. Do you know where I can find them?

You can order reprints or electronic PDFs through ASCE. I would also encourage you to pick up ASCE 7. The more money going to ASCE, the more money they have to educate the public. The more educated the public is, the faster twoofer craziness (like CD) goes away. Win win all around!

 

[Augustine]

Nothing here about design, you are inferring that from the previous sentence. In my article I have compared my calculated mass to that reported in the several common sources as the actual weight. Are we in agreement that the actual weight was not 500,000 tons?

You can stop hassling me about being your idea of a twoofer. If I am, your berating me won't change anything. Since, I'm not it's just very annoying.

Fine. Go ask Robert Fowler what he meant. Perhaps you can argue with him too. (How long have I been asking you to actually talk to your sources?)
I do not see a single source of yours that uses the phrase "actual weight". Perhaps you are inferring they mean actual?
For the purpose of your calculations, I have no objections to you moving to the next step with your numbers as they are. That does not mean I think they are correct, or precise. It means that I think your errors are likely going to be insignificant in the final result. I would be very interested in your sensitivity analysis of the next step.

 

[Newtons Bit]

Augustine, you're a jerk. I'm going to spend this evening reading that paper now instead of doing something else. And it's all your fault!

Knowing where the loads in ASCE7/IBC came from is something worth doing. I just can't do it while severely inebriated.

 

[GregoryUrich]

Physics from Experts

Augustine wrote:

OKAY, now what EXACTLY is your criticism of Dr. Bazant's work?

I am here referring to:

"Why Did the World Trade Center Collapse?—Simple Analysis1
Zdeneˇk P. Bazˇant, F.ASCE,2 and Yong Zhou3
Abstract: This paper presents a simplified approximate analysis of the overall collapse of the towers ofWorld Trade Center in New York
on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load
carrying capacity, the whole tower was doomed.

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf

Issues:

1. Bazant models the plastic energy for compression of the lower part of the structure as a spring. The upper part should also be modeled the same way (i.e. two springs exerting pressure on each other). At maximum compression there is enormous force applied to the debris between the springs which likely accounts for the ejection of so much debris. This is also an energy sink.

2. Bazant doesn't take into account the momentum transfer due to the mass of the spring (the intact lower structure) being accellerated. This is a huge mass and requires alot of energy. I'm working out the numbers, but the displacement is dependent on a number of factors we should try to agree on. I will try to get to this shortly.

3. Bazant assumes that all energy will go into destroying the lower section of the tower when at least half of the energy will go toward destroying the upper section.

I have more but we can start with these.

 

[Furcifer]

1. Bazant models the plastic energy for compression of the lower part of the structure as a spring. The upper part should also be modeled the same way (i.e. two springs exerting pressure on each other). At maximum compression there is enormous force applied to the debris between the springs which likely accounts for the ejection of so much debris. This is also an energy sink.

Maybe Mackey remembers this better than I do, but kinetic energy of the upper mass is much greater than the "spring" can handle in a very small time period (delta t). It's kind of like a lead bullet striking a steel plate, the energy that goes into deforming the bullet is negligible and dropped from the equation.

 

[Gravy]

Gregory, the upper part isn't just (briefly) a spring, it's a falling spring. If you haven't already, you should probably read Bazant & Verdure's 2006 paper on the progressive collapse of tall buildings. Be sure to note that Bazant is assuming an even distribution of forces acting on all columns, which most definitely wasn't the case in reality. That's a huge assumption in favor of the building not collapsing.

 

[Furcifer]

3. Bazant assumes that all energy will go into destroying the lower section of the tower when at least half of the energy will go toward destroying the upper section.

I think this is wrong. Again i point to the lead bullet steel plate analogy. Most of the kinetic energy of the bullet is transferred to the steel and goes into penetrating the steel. Without getting out my texts and going over this I can't be certain, but this ratio is not 50/50. I'll check impulse and momentum energy transfer. Or someone around here will know for sure

 

[beachnut]

Augustine wrote:



I am here referring to:



http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf

Issues:

1. Bazant models the plastic energy for compression of the lower part of the structure as a spring. The upper part should also be modeled the same way (i.e. two springs exerting pressure on each other). At maximum compression there is enormous force applied to the debris between the springs which likely accounts for the ejection of so much debris. This is also an energy sink.

2. Bazant doesn't take into account the momentum transfer due to the mass of the spring (the intact lower structure) being accellerated. This is a huge mass and requires alot of energy. I'm working out the numbers, but the displacement is dependent on a number of factors we should try to agree on. I will try to get to this shortly.

3. Bazant assumes that all energy will go into destroying the lower section of the tower when at least half of the energy will go toward destroying the upper section.

I have more but we can start with these.

You have big problems with momentum. You are not going to do well in this class. Find a phone and call you mom, tell her there are serious doubts you will ever understand structural engineering or momentum transfer in a gravitational field.

 

[GregoryUrich]

Two completely different things

Maybe Mackey remembers this better than I do, but kinetic energy of the upper mass is much greater than the "spring" can handle in a very small time period (delta t). It's kind of like a lead bullet striking a steel plate, the energy that goes into deforming the bullet is negligible and dropped from the equation.

Physics fact book:

The 0.22 rimfire cartridge, which has a very small powder charge, sends its bullets on their way at between 370 m/s and 460 m/s.

Max velocity possible after 3,7m fall with no resistance. 8.6m/s.

Anyway, it is Bazant that proposes the spring mechanism. Either Bazant is wrong or Bazant is wrong.

 

[Furcifer]

Max velocity possible after 3,7m fall with no resistance. 8.6m/s.

mass of building >> mass of .22 rimfire

 

[rwguinn]

Physics fact book:


Max velocity possible after 3,7m fall with no resistance. 8.6m/s.

Anyway, it is Bazant that proposes the spring mechanism. Either Bazant is wrong or Bazant is wrong.

and the available energy at that time is 36.25 m^2/sec^2 times the falling mass.
your point is?

 

[GregoryUrich]

Gregory, the upper part isn't just (briefly) a spring, it's a falling spring. If you haven't already, you should probably read Bazant & Verdure's 2006 paper on the progressive collapse of tall buildings. Be sure to note that Bazant is assuming an even distribution of forces acting on all columns, which most definitely wasn't the case in reality. That's a huge assumption in favor of the building not collapsing.

The same argument applies to "crush upward".

 

[beachnut]

Physics fact book:


Max velocity possible after 3,7m fall with no resistance. 8.6m/s.

Anyway, it is Bazant that proposes the spring mechanism. Either Bazant is wrong or Bazant is wrong.

Or you do not understand physics, momentum or collision.

 

[Gravy]

The same argument applies to "crush upward".

Then here's a thought problem for you: assuming damage near the top of the building as on 9/11, what is the minimum number of WTC tower stories that would cause global collapse after falling one floor?

 

[rwguinn]

Or you do not understand physics, momentum or collision.

Or structural analysis.
Beams ARE springs! Hefty ones. Longitudinal stiffness is a function of A*e/L, shear stiffness a function of (L^3)/(Const*e*I)--where Const depends on end conditions.

 

[Furcifer]

Then here's a thought problem for you: assuming damage near the top of the building as on 9/11, what is the minimum number of WTC tower stories that would cause global collapse after falling one floor?

[hand raised, waving emphatically] I know I know!

 

[GregoryUrich]

and the available energy at that time is 36.25 m^2/sec^2 times the falling mass.
your point is?

Augustine asked me to explain the issues I have with Bazant's article.