The NIST report completely fails to deal with the important dynamic aspects of the tipping of WTC 1 & 2 since the Final Report only deals with tipping as a problem of STATICS. NIST's "global collapse ensued" mantra is a total cop-out, whereby the problem of the collapse is abandoned before it has begun!
To make matters worse, NIST give TWO descriptions of the pre-collapse events: one where the upper section tilts BEFORE collapse, and the other where the upper section TILTS AND FALLS at the same time. I guess NIST had too many authors.
Even Bazant and Zhou (B&Z) do a better job than NIST on this problem since they at least consider the ANGULAR VELOCITY, d(theta)/dt, of the upper section of the South Tower. Their formula shows that, for a given angle of tilt the angular velocity depends on SQRT {3g/h)} where h is the height of the upper section. Hence the rate of tipping is fixed by the dimensions of the upper section. B& Z's formula is ok but it uses an approximation for the moment of inertia, I, of the upper block that ignores the WIDTH of the Tower. Fortunately, it is a simple matter to correct this using I = 1/3 M{h^2 + 1/4w^2} where w is the width of the Tower. If this improved formula is used, reliable values of d(theta)/dt may be calculated for any tilt angle. Integration of the equations also allows the time to reach a particular tilt angle to be derived.
TROUBLE IS, THESE THEORETICAL TIMES ARE MUCH LONGER THAN THE OBSERVED TIMES (which may be measured quite accurately from any of a number of available videos)
So, the bottom line is this:
The top section of WTC 2 tipped at a FASTER angular velocity than is physically possible for a body freely rotating about a pivot at its base!
Now add in some resistance to the tipping from column loading and the problem only gets worse!
I would therefore ask all of you sheeple story fans out there to put away those finite element calculations for a while and check this out..... then please explain how the top of WTC 2 tipped so fast.
PE = m x g x h
Consider the mass of just the top floor of the building.
PE= m *9.8*413= 4073m
Mass is, by definition, simply a measurement of how much force a given amount of material will exert AT REST on an object that is resisting gravity.
SOOOO
The top floor would hit the ground with the same force as a 4073 story building, if that fall was unimpeded.
Now let's consider the fall of the top 30 stories.
They fell through the 3-5 floors of damaged sections and impacted the building below with some amount of force.
Let's call the distance accelerated as 3 floors and be generous. This is 11 meters.
Acceration of an object for 11 meters at 70% of gravity(dan's figure), would yeild an ending velocity of:
v^2= 2ad=2*9.8*.7*11=150=v^2, find the square root of 150, and bada bing, you get 12 meters per second
Subs ute this into the kinetic energy equation:
ke= 150*.5*m=ke=75m
This means the 30 foot section impacts the undamaged portion with the kinetic energy of SEVENTY FIVE TIMES ITS MASS.
Think about this for a moment.
The lower section of the building is designed to hold that 30 stories stationary plus a safety margin of 10 or 20%. So the maximum force that the underlying structure could apply to that falling section is 1.2 times its mass.
Further:
That falling section having as much kinetic energy as 75 times its mass means that it is effectively applying the same amount of force at the impact point that a 2270 story building would. if you held it stationary. (simple math: 30*75)
For the statement "the building would not have collapsed without explosives" implies that the building could have been TWENTY TWO TIMES TALLER THAN IT ACTUALLY WAS without collapsing.
STILL FURTHER
Your calculations seem to imply that the building structure below could absorb 30% of the falling energy.
IN JUST THE FIRST 11 METERS OF A 400 METER COLLAPSE THERE IS 62 TIMES THE AMOUNT OF FORCE REQUIRED TO COLLAPSE THE BUILDING.
Your assumption of about 1/3 the energy used to collapse the building is about 20 times what is reasonable. (1/62*20= 1/3) (more actually, if you consider the further distance and mass)
What happens, then when MORE mass is added AND accelerated?
Even if half the mass falls away or off to the side, there is still FAR more force and energy than would be needed to collapse the building WITHOUT ANY EXPLOSIVES.
----------------------------------------------------------------
YOU'RE the one reading these bull websites without doing any critical thinking, and *I* am "sheeple"?
I really don't have the time to look into those calculations, but I will guess that they go something like this:
The real pivot point is not really on the side they suppose.
xxxxxxxxxxxxxxxx
X ................. Z
X ..................Z
Remove Z and where is your pivot point? X
All those happy fun calculations probably assume that when you remove Z the pivot point is at Z.
Go back and look at the assumptions used in that website dan, and tell me I am wrong.