9/11 Physics from Non-Experts

rwguinn said:
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.
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That Bazant uses springs in his model is not the problem. The problem is that he doesn't model the upper part of the building as a spring.
 
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GregoryUrich said:
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.
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1. What you're thinking about is STRAIN energy, not displacement. There's a big difference. You also have to consider the unloading effects of the strain in the inelastic zone for the members below the critical floor.

2. The very first thing he does is look at the entire lower structure as a spring and determines what the force is by equating the strain energy to the potential energy. I suggest you read through that again.

3. Only a tiny fraction will go into the upper portion. Think about it long enough and you may figure out why. It has to do with #1.
 
Gravy said:
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?
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The correct answer is 4. You have to round up from 3.8 floors.
 
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Newtons Bit said:
1. What you're thinking about is STRAIN energy, not displacement. There's a big difference. You also have to consider the unloading effects of the strain in the inelastic zone for the members below the critical floor.

2. The very first thing he does is look at the entire lower structure as a spring and determines what the force is by equating the strain energy to the potential energy. I suggest you read through that again.

3. Only a tiny fraction will go into the upper portion. Think about it long enough and you may figure out why. It has to do with #1.
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Maybe you should read it again.

Bazant:

The downward displacement from the initial equilibrium position
to the point of maximum deflection of the lower part (considered
to behave elastically) is h + (P/C) where P = maximum
force applied by the upper part on the lower part and h = height of
critical floor columns (=height of the initial fall of the upper part 3.7m).
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Bazant's derivation of the equation for P is dependent on the displacement. The right side of the equations is mg[h + (P/C)] with P/C being the displacement.
 
GregoryUrich said:
Maybe you should read it again.

Bazant:



Bazant's derivation of the equation for P is dependent on the displacement. The right side of the equations is mg[h + (P/C)] with P/C being the displacement.
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Ah. I see P=f(P)
Makes a lot of sense to me. If I had no concept of math. And was a twoofer.
 
I have a problem with Bazant's paper. He models the whole steel structure as a spring, in actuality the exterior columns provided little to no support after the collapse began. I say we just use the core as the spring. Let's drop C to 61GN/m.
 
rwguinn said:
Ah. I see P=f(P)
Makes a lot of sense to me. If I had no concept of math. And was a twoofer.
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The equation for P is:

P = 1 + sqrt (1 + 2mghC)

which is the solution of the quadratic equation:

P^2 - 2P - 2mghC = 0

which is simply a restatement of:

mg[h + (P/C)] = P^2/2C

Why not drop the distracting blather and focus on the fact that Newton was wrong about the displacement.
 
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Newton wrote:

3. Only a tiny fraction will go into the upper portion. Think about it long enough and you may figure out why. It has to do with #1.
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Why not enlighten us on why the upper portion is magically impervious to the same forces effecting the lower portion?
 
GregoryUrich said:
Newton wrote:

Why not enlighten us on why the upper portion is magically impervious to the same forces effecting the lower portion?
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The impulse of restitution depends on the velocity of the object (assuming the colliding particles are the same material and same geometry) Since the velocity of the upper portion is much greater than the lower (8.5m/s>0m/s) the coefficient of restitution is higher for the upper mass. :)
 
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3bodyproblem said:
The impulse of restitution depends on the velocity of the object (assuming the colliding particles are the same material and same geometry) Since the velocity of the upper portion is much greater than the lower (8.5m/s>0m/s) the coefficient of restitution is higher for the upper mass. :)
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I don't like quoting Wikipedia but it's easier than formulating it myself.

Wikipedia:

The coefficient of restitution or COR of an object is a fractional value representing the ratio of velocities before and after an impact. An object with a COR of 1 collides elastically, while an object with a COR of 0 will collide inelastically, effectively "sticking" to the object it collides with, not bouncing at all.
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For two simliar objects colliding, the coefficient of restitution is the same and dependent on the relative velocity between the two objects. Or do objects magically get more impervious to force the faster they go relative to an arbitrary reference point?

Try the same problem in a boxcar moving at 10m/s. The first object rests on the floor with 0 velocity relative to the boxcar. The other object moves in the opposite direction of the boxcar at 5m/s. Is it the objects' velocity relative to a fixed point on earth, the objects' velocity relative to the boxcar, or the objects' velocity relative to each other that determines the COR.

Sorry dude, back to school for you.
 
kiss my posterior, google Newton's collision rule, maybe that will explain this to you better.
 
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3bodyproblem said:
kiss my posterior, google Newton's collision rule, maybe that will explain this to you better.
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Do I need to explain Newton's collision rule to you too? Or a better question, is there actually a rule called Newton's collision rule?
 
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Wiki is wrong Greg, you should never rely on Wiki. The coefficient of restitution is approximately the same, not the same. You need to realize Wiki is not a good source of information.
 
Pookster said:
Question for the board. Is this what's called "stundie" material?
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I may be well on my way to one if i don't find a text book here soon. :)

Does anyone remember deriving the impulse of deformation and impulse of restitution?

IS THERE A PARTICLE PHYSICIST IN THE HOUSE?
 
3bodyproblem said:
I may be well on my way to one if i don't find a text book here soon. :)

<snip>
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Well, I don't think it will match this one in quality.

Even the "edit" note seems to be stundie material, to me anyways:

Last edited by GregoryUrich : Today at 03:34 PM. Reason: Better question
 
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