• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

RFC: Bazant and Zhou Simple Analysis refuted

here is a constructive comment...

Send it to Bazant and Zhou, and ask them for critique, and a reply to your paper.

TAM:)
 
Fair enough, I will leave it to the Engineers here, and then look forward to reading the reply you get from B & Z when all is said in done...good luck.

TAM:)
 
Gregory:

I wonder if a mere chemist could pass comment?

On the other hand.......

Na,

let's leave it to the engineers!
 
O.K, I should note that GU's value for L is incorrect, as is his value of A. Hence his value for k is wrong.

You need to consider where the spring begins, and it is not at floor 103 when the spring was broken at floor 95...............
 
Last edited:
GregoryUrich said:
I have recalculated Bazant and Zhou's overload ratio with the result that progressive collapse is not predicted by the model. Please see the article:

http://www.cool-places.0catch.com/docs/Overload.pdf

Any constructive comments would be appreciated.
Click to expand...

Oh, well done. You have a building with a 46Hz longitudinal mode. Home nobody did any joggine in there...or fast walking.

and a static deflection of almost .2 inches at the floor 97/98 interface.
That translates (simplifying as you did) to nearly 20 inches at ground level.
You think so? That, me lad, is a very high strain that the foundation has to take up...

Calculating the stiffness by reducing to area of the verticals is ignoring all the work the designers went to in order to make the actual structure stiffer than its component parts.

ETA: And your assumption 4 is incorrect.
 
Last edited:
GregoryUrich said:
I have recalculated Bazant and Zhou's overload ratio with the result that progressive collapse is not predicted by the model. Please see the article:

http://www.cool-places.0catch.com/docs/Overload.pdf

Any constructive comments would be appreciated.
Click to expand...

Greg, what are you doing? Your paper was almost right before you changed it. You just added crap to give it a conclusion that you wanted.

The equation that you used is to determine the overload ratio of a mass impacting a spring. And then you go ahead and subtract out an event that happens after the peak impact load, why? The plastic energy E-plastic, dissipated by the columns happens AFTER the peak load is applied to them. You can't subtract the energy required to fail the columns before the mass even impacts the columns. This is the ******** that I'd expect Gordon Ross to perform, not you.

After your paper on mass and pe for the WTC I thought that you weren't a religious truther - dedicated to proving conclusion regardless of whether or not you have to fake the math to do it. Now I'm not so sure and it makes me sick. :(
 
Last edited:
Newtons Bit said:
Greg, what are you doing? Your paper was almost right before you changed it. You just added crap to give it a conclusion that you wanted.

The equation that you used is to determine the overload ratio of a mass impacting a spring. And then you go ahead and subtract out an event that happens after the peak impact load, why? The plastic energy E-plastic, dissipated by the columns happens AFTER the peak load is applied to them. You can't subtract the energy required to fail the columns before the mass even impacts the columns. This is the ******** that I'd expect Gordon Ross to perform, not you.

After your paper on mass and pe for the WTC I thought that you weren't a religious truther - dedicated to proving conclusion regardless of whether or not you have to fake the math to do it. Now I'm not so sure and it makes me sick. :(
Click to expand...

You got further into it than I did--I looked at the assumptions and croaked...
Failure occurs at YIELD. That's the start. Once it's bent, it is, to all intents and purposes, busted, broken, kaput.
 
GregoryUrich said:
I have recalculated Bazant and Zhou's overload ratio with the result that progressive collapse is not predicted by the model. Please see the article:

http://www.cool-places.0catch.com/docs/Overload.pdf

Any constructive comments would be appreciated.
Click to expand...

At no point did Bazant and Zhou claim that the overload ratio would predict collapse or arrest. It is merely a basic estimate of the overload ratio based on a spring with mass collision equation derived by the authors and also found in mechanics of solids texts.

I really cant think of any way to use this equation to predict collapse or arrest either, since in order to use it, the assumption of evenly distributed load has been made, and the safety factors for the perimeter and core columns were different if I recall correctly.

Equation 3 is what you want for their prediction on collapse/arrest.
 
GregoryUrich said:
I have recalculated Bazant and Zhou's overload ratio with the result that progressive collapse is not predicted by the model. Please see the article:

http://www.cool-places.0catch.com/docs/Overload.pdf

Any constructive comments would be appreciated.
Click to expand...

Eventually, all simple models will have to be compared to fully dynamic ones, which employ calculus throughout, to know where and by how much they are not accurate.

I'm going to be busy for the next 3 weeks studying for an exam. If I don't start a new job by then, I'll try and get into calculating something exact. One paper I'll check out I just ran into today:

Buckling of columns under variably distributed axial loads.
Vaziri, H H; Xie, J
Computers and Structures. Vol. 45, no. 3, pp. 505-509. 1992

A new numerical model for analyzing the buckling of columns with variably distributed axial loads is proposed in this paper. The presented method transforms the traditional eigenvalue problem into an initial boundary value problem which can be solved by numerical integrations. The buckling load is determined by a proposed two-step iterative procedure. Because of its concise and easy-to-implement form, the proposed method can be coded and used for analysis with a minimum requirement for the in-core memory storage of a computer. The proposed model is verified for a column with uniformly distributed axial loads, and the application of the method is demonstrated by analyzing columns with variably distributed axial loads and columns with varying cross-sections. Some interesting conclusions are made.

Descriptors: Buckling; Mathematical models; Eigenvalues and eigenfunctions; Structural analysis; Boundary value problems; Integration; Computer applications
 
metamars said:
Eventually, all simple models will have to be compared to fully dynamic ones, which employ calculus throughout, to know where and by how much they are not accurate.
Click to expand...

Eventually, all fully dynamic models will have to be compared with experiments, to know where and by how much they are not accurate!
 
metamars said:
Eventually, all fully dynamic models will have to be compared with experiments, to know where and by how much they are not accurate!
Click to expand...

Some of that has been done already. The 1982 C.I.D., for example, was run partly to validate some of the FEA methods used in later software tools (and the NIST investigation, I think). You'd have to ask the structural guys here for building examples, but the NIST BFRL has been running (and funding grants for) experiments for some time now - it might not be a bad idea to check their site for articles.
 
For those of you beating up on Gregory, please be civil... I find problems with his paper too, but so what? It's properly posed, so we have to think about the replies, and we'll learn something. This alone sets it apart from the vast majority of Truther idiocy, about which one can only say, "huh??"

Anyway, as others have noted, the spring constant computed here is not supportable. I don't see any way for the whole 110 stories (or even the whole 90-odd stories of the "lower block") to participate elastically, let alone in compression.

So what is the correct value of the spring constant? I'd be tempted to hand-wave and say that we should only treat a column down to the next splice, i.e. three stories worth, but this is probably wrong too.

B&Z's estimate of C is also hand-wavey, of course. However, they choose what they call an optimistic value, i.e. all of the columns participate equally in opposing the collapse. I'm extremely reluctant to accept an order-of-magnitude adjustment to this value without more careful thought.

Also, regarding Ultimate Strength, what's computed in Gregory's writeup is the ultimate compressive strength, not the ultimate buckling strength, so it's overestimated. (Yes, B&Z's estimate is coarse and not quite correct either. Remember their paper came out in three days and with few actual WTC design details.)

Lastly, even if we accepted all of the calculations here, it should be noted that B&Z computed a generous estimate by discounting the effects of fracture, etc. So a result showing the "corrected" energy fraction was 0.81 instead of > 1 would also not guarantee collapse arrest, though it would prove the B&Z model was oversimplified, and a more thorough analysis required to answer the question once and for all.

Thoughts?
 
Gregory Urich:

And continuing the discussion of your calculation of k: You cannot expect to get a meaningful value of k by using "a single element with a combined cross sectional area of all the columns", and plugging the A value into k=AE/L. This ignores the role of the trusses, the visco-elastic dampers and the "tube within a tube" structure of the building...... That is why the formula for the free vibration of the tower:

Vibrational frequency (in rads/s) = Sqrt {k/M}

where M is the mass of the tower,

simply does not work for Bazant's, (or your), value of k.
 
I am not really sure what point 1 (Paragraph 4) regarding internal strain energy within the upper striuucture itself has to do with external effects.

As I said--I couldn't get past the assumptions. Assuming the entire height of the building for AE/L totally ignores all the work the designers did--and if we use that value, then the buckling calcs will likely show that the building collapses at 1 g, static. (I claim no buckling expertise, here)

Additionally, E is the slope of the stress-strain curve from 0 strain to yield--not to ultimate. That value is 29.9e6 lbf/in^2.
For steel, the stress-strain curve sharply drops at yield, and then is very nearly flat (orders of magnitude lower than 29.9e6) in comparison to the 0-yield value)
If you wish to average, be consistent. The E for steel will make rubber look stout at that slope.
It is always best to keep things linear. Once the material reaches yield, everything becomes non-linear--material, geometry--all of it. Load paths are also no longer valid--they have to be revised.

In short, using a linear value for ultimate leads you to false conclusions.
 
rwguinn comments:

Calculating the stiffness by reducing to area of the verticals is ignoring all the work the designers went to in order to make the actual structure stiffer than its component parts.
Click to expand...

Agreed. How did Bazant calculate the same quantity? The same way, no?



cmcaulif notes:

At no point did Bazant and Zhou claim that the overload ratio would predict collapse or arrest. It is merely a basic estimate of the overload ratio based on a spring with mass collision equation derived by the authors and also found in mechanics of solids texts.

I really cant think of any way to use this equation to predict collapse or arrest either, since in order to use it, the assumption of evenly distributed load has been made, and the safety factors for the perimeter and core columns were different if I recall correctly.
Click to expand...

Exactly. I'm surprised more people can't see that.

There are rather absurd assumptions which go into equating the gained kinetic energy of the upper "block" with the blow the lower columns receive, as if a 100% transmittance of energy isn't just a "cartoon".

Many assumtions IMPLICIT in the equations that can only exist in a place called "Theoryland".
 
Major_Tom said:
Exactly. I'm surprised more people can't see that.

There are rather absurd assumptions which go into equating the gained kinetic energy of the upper "block" with the blow the lower columns receive, as if a 100% transmittance of energy isn't just a "cartoon".

Many assumtions IMPLICIT in the equations that can only exist in a place called "Theoryland".
Click to expand...

I'm not sure what you mean by this MT. Bazant's equation is valid because it satisfies conservation of energy (kinetic energy of the mass turned completely into strain energy of the spring at the max deflection). It is however a massive simplification of a chaotic event.

I really don't think a whole lot can be gleaned from the equation in terms of predicting arrest though.
 
You must log in or register to reply here.

Back
Top Bottom