> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
> Behalf Of Gibson Jonathan
> Sent: Monday, July 03, 2006 12:07 PM
> To: Killer Bs Discussion
> Subject: Re: Physics Prof Finds Thermate in WTC Physical Samples
>
>
> How the debris we see falling {I would point out it's much more akin to
> exploding outward and then down} exterior to the building can match an
> interior descent flies in the face of logic. I simply cannot accept
> that the core structure, a thick _lattice_ of crossing steel, would
> offer the same resistance as the air outside slowing the debris.
That's not quite what happened. While conspiracy sites argue that the
building fell at the rate one would expect from free fall, other sites, and
my own analysis indicated that it took 2 seconds longer than what one would
expect from free fall.
As Charlie has pointed out, some debris did fall just a bit faster than the
building, which makes sense. Small debris, due to the square-cubed law, met
relatively high air resistance, which resulted in a lower terminal velocity,
so there is a point where the smaller loose debris did fall slower than the
lowest structure. To intuit this, think low long a dust cloud can remain in
the air, or think of why raindrops don't hurt when they fall on you.
> Recap, to believe this theory one has to accept that the interior steel
> structure has to completely and utterly fail up and down the entire
> length and I just don't see how a shock-wave from one collapsing floor
> can do this:
That's not really accurate. To believe this theory one needs to accept that
the physics of rigid objects can be counterintuitive at times. I'm not sure
why this would be hard to accept. I gave one model of this, which didn't
get much response, but I'll try another. I'm going to construct a toy model
(a very simplified steel girder building) and show how the physics works
with this building. The actual building is more complicated, of course, but
that's what the engineering & architecture finite element analysis programs
(I believe those are the kinda programs that are used) are for.
Anyways, my building is build of these items:
Rigid Steel Beams,
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Bolts
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Rigid steel floors
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The beams are bolted together at the corners, and the floors are put on top
of the horizontal beams. Only the bolts have any give to them, and that
give is rather small.
What keeps the building from collapsing? It's the bolts. Now, in reality,
there is more than 1 bolt per corner, and the corners are often welded
together. But, the basic physics of the question is not affected by the
difference.
The building is held up by the sheer strength of the bolt. Lets assume that
the building about the floor we are considering has a mass of 10,000 metric
tons. That means there is a force of about 2.5*10^7 Newtons on each of the
bolts (10,000 metric tons is 10^7 kg, acceleration due to gravity is 9.8
m/s^2, 4 bolts).
Let's have the bolts rated to 2.5*10^8 Newtons. That means that the
shearing force applied to the bolts needs to be 2.5*10^8 Newtons before the
bolts break.
So, let's have the floor immediately above the floor we are considering
collapse. Let's also assume that the distance between floors is 4 meters.
The top of the building, with a mass of 10,000 metric tons free falls those
4 meters.
It takes about 0.9 sec to free fall those 4 meters. The velocity after the
fall is about 9 m/sec. So, we have a rigid object falling at 9 m/sec
hitting another rigid object. The give, we are assuming, is in the bolts.
The critical question is "how far will the bolts bend before breaking?" The
reason for this is that, for the floor we are considering to hold the
falling mass, it must decelerate it to a stop before the mass falls enough
to bend the bolts beyond the breaking point.
Steel, as others observe, doesn't bend much over short intervals. Let's
assume a stress strain relationship for our toy model where 2.5*10^8 Newtons
of force strains the bolts 5 cm. Any greater force, even 1 more Newton,
breaks the bolts.
Given this, the falling floors are decelerated by the floor we are
considering until the deceleration of the mass is at 9 g's (we have to
consider the constant gravity force of 1 g). At this point, the bolts
break. Now, if we assume a linear stress-strain relationship (simplifies
the problem, but isn't essential), we can see the change in velocity of the
falling mass due to the resistance of the bolts.
Doing some handy-dandy math, with 1 msec steps, we find that the bolts shear
in less than 60 msec. During that time, the velocity of the falling mass
was reduced by about 0.25 m/sec from free fall.
By the time the mass falls another floor, it's speed increase, so it takes
less time to shear the bolts: about 40 msec....during which time the
velocity was reduced by another 0.17 m/sec from what free fall would be.
For each floor, the reduction in speed is less, as the bolts are broken in
less time.
I hope this was a straightforward explanation of the basic physics involved.
If anyone sees any problems with it, I'd be happy to review them. It is
true that I've simplified the problem, but going through the physics of the
simplification in my head, it doesn't change the nature of the problem.
Now, one may argue that this sort of analysis should be done without the
simplifying approximations of rigid beams and floors. It has been...that's
what the professional analysis is. I agree with them, which isn't
surprising....it just means that the first order approximations I made are
fairly reasonable.
So, I think we've gotten to the point where, in order to still say "I cannot
accept" the conventional explanation, then you will have to reject my basic
physics argument. I'd be very interested to see what flaws you might see in
this argument.
Dan M.
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