A very strained analogy. (Oops - that pun was unintended

)
The key error you are making I think is an order of magnitude issue. The jolt you look for is one where the total falling weight is significantly affected. The worst case jolt produced by "end on end axial contact" of the two parts of one column is too small to measure as that column instantly buckles under the overwhelming load. At least one and probably two decimal orders of magnitude less than the jolt you are looking for.
Yes I am aware of multiple columns. Multiple possibilities but they would be spread in time. (If you can visualise that reality given your apparent fixed view that the structure is of rigid geometry. It isn't)
I cannot think of a perfect analogy..
However. Think if a small paint brush. Cut all the bristles but one leaving the one protruding. Then drop the brush on that one bristle. Alternatively try to push something with that one bristle.