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RE: 9-11 Wackos
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- Subject: RE: 9-11 Wackos
- From: Joel gordon <joelgordon(--nospam--at)gmail.com>
- Date: Fri, 25 May 2007 15:31:51 -0400
Once the first floor(s)
collapsed they entered freefall. These floors then collided with the floor
below. The colums then would resist the falling mass. The amount of
resistance they can offer depends on the ratio of design stress to buckling
stress and the maximum buckling length. If the column cannot do enough
work on the falling mass it will fail and another floor will be added to the
mass. Now this mass will be in free fall until it collides with the next
floor. This will be repeated until either the columns can slow down the
mass and stop the collapse or until all floors are collapsed.
So basically a number of
floors fail and the mass falls at free fall until it hits the floor below;
then the columns resist until failure over some buckling length (they can
only buckle so far until either the column fails or the beam to column
connections fail). The mass then is in free fall for the remainder of the
floor to floor height.
It is easy to setup a
spreadsheet to model this behaivor. Assumptions need to be made about how
many floors initially failed, the column saftey factor, maximum buckling
length of the column, and the floor to floor height. Then calculate the
velocity and time at the initial impact assuming initial velocity of zero and
freefall for the full floor to floor height. Calculate the work done by
the columns on the mass(Saftey factor X buckling length X mass X gravity) if
this is greater than the kinetic energy of the mass before impact no failure
occurs. Otherwise, subtract the column resistance from the kinetic energy
before the impact and calculate a new velocity based on the new mass. Use
the average of new velocity and impact velocity and the buckling length to
average the impact time. Now calculate the impact velocity at the next
floor and time to reach the floor based on the free fall distance of the floor
to floor height minus the buckling length of the previously failed columns and
the velocity after the last impact. Just repeat this for all
floors.
If you assume faluire
took place on the 94 floor, all floors above initially failed, floor to floor
height of 12'-3", a column safety factor of 2, and a maximum buckling length of
1 foot, I calculate that the total time of collapse is approximately 12
seconds.
buckling length 2 feet -
13.4s
3 feet - 17.5s
4 feet - 41 s
5 feet - collapse stops at 92 floor
From: ECVAl3(--nospam--at)aol.com [mailto:ECVAl3(--nospam--at)aol.com] Sent: Friday, May 25, 2007 1:52 PM To: seaint(--nospam--at)seaint.org Subject: Re: 9-11 Wackos In a message dated 5/25/2007 10:33:37 A.M. Pacific Daylight Time,
gmse4603(--nospam--at)gmail.com writes:
Freefall: mass and acceleration....an ever increasing mass (each floor falling on another) and acceleration (those things were too heavy to reach terminal speed from wind resistance) ...makes perfect sense to me. Maybe I just don't get it but, in my mind, when an object in motion meets a
stationary object, there is a lose of momentum thereby slowing down the
acceleration process. Is this wrong? I'm still puzzled as to how the WTC towers
collapsed at nearly the same time as an object in freefall would take to fall
the same distance.
S.Macie, P.E. See what's free at AOL.com. |
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