Well, feel free to tell us what assumption you think went into it. I can list those those that are in the book.
Sure. The impacting mass was
rigid, and the other end was constrained by a
rigid surface.
In
Wave Motion in Elastic Solids by Karl F. Graff, p. 103, the ratio of initial impact force is given (eq. 2.4.25) for elastic-on-elastic vs. rigid-on-elastic collisions. The elastic body being impacted is a thin rod. This is:
1 / (1 + Z1/Z2).
Where Z1 is the impedance of the elastic impacting object, and Z2 is the impedance of the impacted elastic object.
Z is given by rho*A*c0, where
rho is density
A is area
c0 is the speed of sound
In the special case of the collision of rods of exactly the same dimensions and density, the impedances are equal, and thus the peak force will be 1/2 times that of the analogous rigid-on-elastic impact.
I look forward to your revelation on what assumption you believe is made. By the way, why did you not just type it in here instead of holding back like it is some great secret?
These qualitative impact of these "revelations" was made intuitively by me over 2 years ago. The above equations are from Chapter 2 of an 8 chapter book on elasticity theory. They are not "revelations", at all.
A more interesting question is, why did Dr. Bazant, who has co-authored numerous books (one of which I've glanced at, and seems to be well written) involving both elastic and plastic theory, cherry-pick his assumptions regarding
rigidity the way he did, so as to "derive" a fragility to the building that was greater than he suggested? Recall that in a subsequent paper (Bazant and Verdure), he made reference to his not-so-youthful indiscretion of a paper with Zhou. He had plenty of time to reflect on his paper with Zhou, and to publish a correction.
The Newton's Bit paper - even the new and improved one - also has un-explicated assumptions of rigidity, which invalidate his analysis. (I'll have more to say on those, later, but on his threads.) Actually, I think all of the analyses along the lines of Bazant-Zhou's original paper that ignore established theory are wrong - BZ, Ross, and Newton's Bit.
This is actually a much deeper problem than you might think. If you're curious what strain vs. time would look like in a real impact, see
http://metamars.i8.com/index.html
Notice that (apparently), the compressive stress wave is "one way". I.e., the reflected wave contributions are very small. (The data is represented two separate runs abreast, so don't misinterpret.) That tells me (I'm not 100% sure) that transmittance at the base is very high, so reflected compressive waves won't add to the net stress on the rod very much. Remember how these sorts of considerations were ignored by Manuel Garcia?
You might also ask yourself the question of why other JREF'ers, who have a technical background, did not bother to disabuse you of your mistaken notions of whether or not and how you mis-applied a mathematically correct solution to a physical problem.
Assuming the factor of safety is less than 2, then yes, I believe the collapse would occur. But keep in mind, collapse initiation is different than collapse continuation. The equation I am using relates to collapse continuation.
Well, you're wrong. My question to you regarding a drop of all of 1 mm should have been a clue that something was amiss in your reasoning. To amuse yourself, why don't you call the professors whose results you quoted, and ask them the 1 mm question?
You must have a very good electronic scale. We have specialized equipment where I work in order to capture data points quickly. Most home scales won't have the resolution that a professional scale has. This is regardless whether it is electric or not.
It's ok. I just checked, and it records about 15 pounds over my true weight when I first step on it. I don't really know the details of how it works, but I don't believe that constraints in "acquiring data points" have anything to do with not showing more than +15 pounds.
