Originally posted by bsbray11
Is there any way you can summarize your calculations for those of us without the program?
I suggest to download the programm and try to read the code.
Matlab is a simple to understand program language, with exception of the ':' char
All you need to know is that expression like this:
for t = 1:100,
is a loop where t is counts from 1 to 100 in step of 1. The rest should be readable.
or v(3:5) means element 3 and 4 and 5 of the variable v.
means all element of v.
A summary of the core:
As explained it is based on momentum conservation
First of all you need to see that I splitted the tower in a 3 body/mass system:
1) The MoveingBlock-Mass, thats total mass (includes everything) of the tower above the plane impact, and this gets reducted 1 floor for each step
2) The CollapseZone-Mass, initial Mass of 1 floor, but collects the mass of +1 floor form the MoveingBlock Mass (as long as there the moveing mass
has floor lefts) + 1 floor from the 'fix standing' Mass for each step of of collapse.
3) The Fix-Standing-Mass wheras in each step of the of collapse only 1 Floor Mass is included in the crash calculation.
The core/heart is a loop over the count of Floor's from the plane impact zone 'down' to ground. Each Floor is one step of the collision.
In the loop I calculate 3 thing.
The Time it takes for the Moveing-Mass to fall down 2! Floors and it's endspeed.
The Time it takes for the CollapseZone-Mass to fall down 1 Floor and it's endspeed
Formula: %s=a*t*t/2 + v0*t
%t = -v0/a +/- sqrt(((vo/a)*(v0/a)+(2*s/a));
The Momentum before the Crash with the One Fix Floor. (= mass * endvelocity of MoveingBlock and mass * endvelocity of the CollapseZoneMass)
The speed after of the MoveingBlockMass + CollapseMass + 1 Floor
after the collision (velocityAfter = Momentum / (TotalMassOfAllBodysInTheCollision))
Note: it's a tripple nonelastic collision we calculate. It doesnt play a role which of the 2 bodies hit first and which as last..this is the end
condituin after all 3 hit each other.
Now that we have the spee dbefore the collision and after we can calculate what energy of the collision became free.
EkineticBefore = (m1*v1^2) / 2 + (m2*v^2) /2
EkineticAfter = mTotalAfter * vAfter^2 / 2
EnergyLose = EkinBefore - EkinAfter;
This energy is the energy that usually becomes convertet into heat energy or into (steel) bending or into pwdering concrete.
In my model I used 100% of this energy to convert concrete into powder.
(there is a factor in the program you can set CollisionEnergyUsedForPowderingFactor = 1; %1= 100% of the free energy will be...)
The powder Mass I then subtract of the concrete part of the CollapseZone-Mass.
since the most part will be blown outside of the building. (there is also a factor)
And this is the end of that loop and all said becomes repeated for every floor left till down to the ground.
One speciall thing is that I only know two mass typestill now: steel and concrete. And everything is eighter the one or the other. Only concrete will
be crushed, steel not.
An expansion I did to see in my second post (the dashed lines) is to take into account the steel structure of the tower.
In every step of the collaps I do not add the full steel of one floor anymore but a well calculated Factor of it that takes into account that the core
steel as well as the perimeter wall steels of the Fix-Standing-Mass do not add to the collapse. (the perimeter walls got blown outside and the big
core steel does not cut and add steel floor by floor. So only the trusses really contribute. Howver I dashed that line because of course someone
might see this different,The Factor is a parameter you can set.