Ryan, in case you haven't seen it, take a look at post #1510 in the "Why a one-way crush down is not possible" thread. I've done some maths to put behind the rather obvious point that a jolt wouldn't be seen if the upper block is tilted. Tony's replied to it once, but now I think he's carefully pretending it doesn't exist. Let me know if you want a copy of the spreadsheet that I calculated it from (although it's one of mine so it may not be entirely clear, or even intelligible!)
Dave
Hey Dave,
I'd like to see your numbers.
I scanned thru your post #1510. One thing that I don't get regarding your stress-strain model for A36. Perhaps I'm not reading it right.
You say
Dave Rogers said:
Next, I consider the case where an upper block of mass M of this structure falls on a lower block. I'm assuming that the angle of tilt is small enough that each column of the upper block impacts on the corresponding column of the lower block. For the behaviour on impact, I'm taking a greatly simplified model of column failure, in which the resistive force increases linearly up to the ultimate strength at 0.2% compression, then decreases linearly to zero at a further 3% compression. This has the useful property that the energy absorbed by the column is approximately correct, therefore the impulse applied to the upper block is reasonable."
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It seems to me that this will give you only about 50% of the energy absorption capability of the steel.
Usually the 0.2% stain level is the yield strength, instead of the ultimate strength, of course.
NIST gives a good models for stress strain in NCSTAR 1-3D, Appendix D - for both room & elevated temperatures. Plus they give models for high strain rate properties in Appendix E.
Those ought to do you. But if you need something simpler...
A quick & dirty, but still accurate (in terms of energy absorption), would be a linear stress-strain up to the average stress between the yield & ultimate strengths ((sy + su)/2), and a constant stress from there up to failure strain levels.
I've taken the column length as 4m, representing the height of a single floor. I'm also assuming that the moment of inertia of the upper block is very large, and that its rotational velocity is zero throughout the collision; in other words, the tilt angle is taken to be invariant."
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The use of 1 story columns will, I believe, result in significant errors. I believe that an unavoidable aspect of the 3 story, staggered columns produced an unexpected weakness to progressive collapse, and an effect that will have a significant impact on the specific effect that you are trying to model: the jolts.
The reason for this is, of course, the fact that, by the time the upper block has reached any particular floor, 2/3rds of the supports have already been destroyed prior to the impact, taking with them far more than 2/3rds of the stuctural integrity of that floor.
I don't have a bunch of time right now, but I'll offer comments once I see your spreadsheet.
BTW, I applaud this effort of yours.
Tom