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RE: 9-11 Wackos

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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.




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