Fabulous Study for 911Truth: Moment Transfer by Gordon Ross
Today we consider Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC1, write by Gordon Ross, ME, June 2006 and pubblied on Journal of Fabulous study for 911 Truth.
Ross consider this:
-16 WTC's floors fall at 8.5 m/s, the weight and other parameters is take similar to Bazant's study.
-Bazant consider three phase of columns load into an elastoplastic model (not anelastic model!!!)
-Wave velocity in steel
Velocity = RADQ ( Bulk modulus / Density )
The propagation wave of the impact force would therefore travel a distance of 58.7 metres in a time of 0.013 second.
Then 58 floows have elastic deformation for every impact ....but he take only 16 floors (why?! becouse with 56 floor into a bad phisics demonstration he have the v = 0 and collapse stopped after 2-3 floor).
These storeys would thus suffe r an elastic deflection in response to, and proportional to, the failure load applied at the impacted floor. These deflections would themselves take time and allow the propagation wave to move further downwards again affecting more storeys.
With this he estimate 7 mm of elastics columns deformation for the 16 floors and for the Third Law of Newton (principle of action and reaction, F1 = -F2) and the moment transfer conservation (q1 = q2, m1*V1 = (m1+m2)*v2 + m3*alpha1*v2 + m4*alpha2*V2+...) he calcule a continue fall of mass that collapse, that was stopped after of joint the base of WTC.
Alpha-i was coefficients that consider a % of velocity based on a linear distribution of it with the floor (sixteenth floor / 16 floor, fifteenth / 16, ...first / 16).
With only 1 plans impact he calcule that: V2 = 16 * 8.5 / 28.5 = 4.8 metres per second.
Now the phisicals errors into this fabulous study for 911 truth is:
Consider an anelastic study with an elastoplastic model.
This is a really bad error!!!
An inelastic shock is based on an istant plastic deformation not elastoplastic, where the forces required to make the plastic deformation tending to zero.
With this assumption we can apply the third law of Newton and compare the force before the impact, due to te muvement, and the force after the impact, due to muvement.
dF/dt=0 and we take demonstrate the moment transfer conservation
F1=-F2 with F=ma
m*dv/dt=0 and d(mv)/dt=0 that dp=0 into 2 different time.
For this we take inelastic shock, in order to apply the third law of Newton !!!
With an pure elastoplastic model what we have?
We assume no linear buckling (that reduce the load that we can carge on a eulerian or not eulerian columns) and not any resistence reduction due to fast load charge or other similar resistence reduction due of unstatic load.
We consider a pure elastoplastic model, with a stress&strain behavior that have an linear behavior (and with the area an elastic forc in response) to the yield strength and an deformation with constant stress into plastic zone (deformation without force change to the break strain).
Into action and reaction, we have more columns that can oppose a force from zero to elastic force at yield strength.
This is a finite interval with an upper limit.
When if a suerior block of 16 WTC's floors fall into more columns we dont have a third law of Newton, becouse the columns can react only with upper limit of elastic forces.
First consideration is that the wave that diffuse into under floor (Ross consider 58 or 16 floor) was not controlled by the WTC's floor that fall (F = m*a = fall force), but is controlled by the elastic force reponse !!!
This was a really really really bad error of Gordon Ross.
Consider for example a pudding that have a really low yield stress limit.
If I put a finger into pudding i dont have any third newton's law and any reaction transferred by my finger to the pudding and dish plate.
Finger force goes to plastic and volumetric deformation.
We can take similar example with a jackhammer that shock a rock / concrete / wall.
With Ross unphsics model we have that we can apply moment transfert into partial wall area without any deformation consideration, as if there no need any deformation's law, also if into real wall shock with jackhammer we cant have a wall's muvement due to the hammer shock.
Unfortunately the scientific community consider that we can design/verify structural building with deformation law, and not with only balance of momentum transfer.. For this into university who study structural engineering or mechanical engineering make courses of building science or materials technology (but i suppose that people, like Ross, study...maybe I'm wrong in this supposition).
The third error of Ross is the assumption that velocity was distribute to the other floors in proportion with the floors and not with deformation law.
We can take for example the Terzaghi's effective stress law that schematizes the stress into terrain with a series of elastic spring, and see that we dont have a similar "floor distribution" that depends to the ground area that we take, but we have a stress law.
For this if we can take an really anelastic model (not elastoplastic) with balance of moment we dont consider a wave diffusion into WTC's columns to take more floor that reduce the velocity.
We need to consider an instantaneous break of floor shocked by the WTC's fall block (elastic forces and plastic force goes to zero) and an simply moment transfer balance (it is a really really really big simplification of an pancake collapse) that have with M1=M2=M3= ... M every other floor.
16*m1*v1 = (16*m1 + m2) * v2
or
v2 = v1 * (16/17) = 0.94 * v1
this really semplified model give only a 6% reduction of fall speed for every floor with not-linear progression.
