jaydeehess
Penultimate Amazing
This is an easy problem to solve!
We have 80 glass elements of certain mass, m, spaced 500 mm apart. How the spacing is arranged must be clarified; some sort of supports I assume, the bottom one, carrying 80 m, stronger than the top one, carrying nothing but expecting to be impacted by a bowling ball.
Inertia is the name for the tendency of an object in motion to remain in motion, or an object at rest to remain at rest, unless acted upon by a force.
Thus, the tower of 80 glass elements/supports is at rest and the bowling ball comes dropping down in motion.
What happens at impact? Well, it depends on the strength of the top glass element and the bowling ball - the two elements in contact only! If the top element at rest is reinforced, armored glass and doesn't break, it will transmit forces on the supports below and on the bowling ball. The bowling ball may actually break or bounce or one or more supports below.
As we say: You have to start at the top to get things changed in a structure (or organisation).
In the example above, the 79 glass elements below the top one have not got a clue what the top glass element and bowling ball are up to, when they meet.
If this situation is supposed to be analogous to the WTC towers at all then it has to be the glass itself that supports the legs laterally. That is to say that the glass is connected directly to the legs which in turn keeps the legs vertical which in turn allows the structure to remain upright.
Let's assume that the legs are each a continuous column with welded on glass floor seats and bolts or rivets holding the glass to the seats.
The mass hitting the next glass 'floor' is increased by the mass of broken glass from the floors above it.
Will the floors eventually arrest the fall?
Not if the falling mass exceeds the load capacity of the glass and in the case of the towers the mass that was hitting the floors far exceeded even the static load that an individual floor was designed to hold. So in our analogy one would have a bowling ball of sufficient mass that even if it were simply and carefully placed on the glass 'floor' that 'floor' would crack and fail. Note that this is not to say that the legs would not be able to support such a mass. In fact the whole purpose of the legs is to take the mass loading of the entire structure above any height whereas the floors need only support the mass expected on any individual floorspace
Add in any dynamic loading at all, much less any additional mass loading of falling glass, and the collapse through the glass floors will acellerate, not decellerate.
As the floors break away in this analogy the legs will be increasingly long unbraced columns. They will bend due to their inherent instability and may actually buckle before the last 'floor' fails. At any rate they will fall over when the last 'floor' fails.
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