Chris,
tfk said:
[intended statement] The fact that you do not understand something does not make it "double talk".
The fact that you don't understand something does make it "double talk".
Chris, I don't think that I've insulted you. If I have, I apologize. But i would appreciate if you show the same restraint.
As I mentioned, I AM a mechanical engineer with a 34 year, successful career doing it. I'll be happy to explain things to you as long as don't get snarky. I have truly had enough of that nonsense from twoofers.
tfk said:
I specifically did not get into "how to release" it.
Until you do you haven't shown that it is possible to use this stored energy to eject a beam laterally.
It was not my intention to show how it could be done. It was my intention to show that it is NOT, as CTers have claimed, IMPOSSIBLE.
tfk said:
This is the type of specious argument that you've been bringing up constantly. The SPECIFIC question that ole bill was jabbering about (it turns out incorrectly) was that there was "only enough energy storage capability in a steel box column, without kinking, to be thrown a couple dozen feet. But never 200, 400 or 500 feet."
I am not an engineer or mathematician but excuse me if I don't accept your analysis without some verifiable conformation.
I assume you meant "confirmation". The confirmation is trivial. You bend metal. Energy gets stored in the atomic distortion of the metal. When the external forces on the metal are released, the atomic structure returns to its undistorted, lowest energy configuration. This is the essence of the action of a spring. All of the above is incontestable. It is mechanics 101.
The only thing that you might question is "did I calculate the amount of deflection of the beam (while staying in the linear range) and the amount of energy stored correctly?"
The answer is "yep, I did". The calculations are trivial. After designing deflecting members for years (connectors, snap fits, etc.), I've got a good feel for what these numbers are. 5.3" of deflection for a 14" square box column that is 37 feet long is completely reasonable.
The next task, how much force is required, is also relatively simple. It's called the "Stoney equation" or "Storey equation" IIRC. It relates the relationship between force and deflection for a cantilever beam.
Normally, I'd have to calculate the stress & strain at every point in the beam. This would be a bit complex. Not really hard, but involved. However, there is a simplifying trick due to a guy named Castigliano.
Castigliano's Theorem is a mechanical version of "conservation of energy". This says that the internal energy stored inside an element is equal to the external energy applied to it. And this number is trivially easy to calculate. For ANY spring acting in the linear range, the internal potential energy (PE) is given by: PE = 0.5 * F * d. Where F = force (pounds) and d = deflection (inches) and the PE is then given in inch-pounds.
tfk said:
As I calculated, if one were to intentionally devise anchoring system that would allow you to pull back on the beam & arc it like a bow, and then cut the string, then it WOULD fly out at about 75 mph (remember that 54 mph was for a cantilever beam. You can get twice as much energy stored in a uniformly arced beam, for 41% more speed. Remember, energy goes as speed squared.
What kind of lateral force do you get when neither end is attached?
None, of course. But for EVERY single one of those beams, in the instant before it was unrestrained, it WAS restrained as a part of the towers. And in the descending debris, there were infinite combinations of forces to be applied to column assemblies that were churning around in the collapse.
tfk said:
As a direct result of this horizontal speed, if you fling this from an altitude of 1000', it'll travel about 800' horizontally.
Hold on there cowboy, before you discuss how far it will travel, establish the conditions that could bend a 3 beam section to maximum energy storage, rip it loose and still use that stored energy to propel it laterally. Seems to me you can't get all these conditions to occur.
As I said, my purpose was only to show that it was NOT IMPOSSIBLE for the columns to have been thrown using internally stored energy only, which I already knew, and to get an BOTE estimate of how far that might be. My job is done with that.
But, as you'll see in my preceding post, I've described a completely viable mechanism for throwing a beam assembly over 600'.
You're welcome.
tom