bill,
For the rest of you, my name is Tom. As bill well knows.
Being capriciously annoying and insulting is one of his few talents.
-so you wan to come out of the closet ? I still uggest that you are talking about the properties of steel as opposed to cardboard while I was talking about the structure of the box column.
I know precisely what you were talking about, bill. You're playing in my sandbox.
Almost 30 years ago, I generated the fundamental equations by which my company at the time (an electronic connector manufacturer, a division of Teledyne) designed every one of it electronic connectors for several years. Until the era of PC FEA programs arrived.
This exercise is precisely an exercise in analyzing force, deflection, and energy storage in cantilever beams.
If you bend a box column of whatever stiff aterial it will kink very early in the bending. Less bend....less stored potential energy...no spring out 200 feet....uniformly throughout the building.
And your analysis here is uninformed and, by the worst insult possible in the engineering world, simply wrong.
You are confusing the amount of deflection for the amount of stored energy. These are two independent quantities.
If you were sufficiently astute & had paid attention when you read my last post, to which you are now responding, you would have noted that I pointed this out explicitly there. I gave you two examples of deflected beams. One of them had an enormous amount of deflection (the play-doh one) and the second had virtually none (the glass one), and yet both had exactly the same amount of stored energy - approximately zero.
This example shows that the two quantities (deflection and stored elastic energy) are independent of each other.
So your statement that "less bend ... less stored potential energy", just ain't necessarily so. And in the case of the 32' long box columns of the WTC tower beams, it just ain't true at all.
For your edification, there is a theorem - Castigliano's Theorem - that equates the external work done to any structure to the stored energy in that structure (or component). It will tell you that if F = the force applied to a beam and d = the deflection of that beam, then the potental energy stored in the beam (PE) is equal to PE = 0.5 * F * d. (As long as you stay below the elastic limit).
It is NOT the force that determines the stored energy. It is NOT the deflection. It is the product of the two numbers.
And here you can see that LARGE amounts of potential energy can be stored in very stiff beams by having the force (F) be a high number.
tk