Tim Wrote:
With no chance for evacuation, and with a one-fifth of a mile high building toppling sideways, fatalities might have reached 30,000 or more.
I'm not a structural engineer, but given that lateral structural strength
is likely only a fraction of vertical structural strength, it doesn't seem
to me that a tower like the WTC can do anything but collapse downwards.
One would think that when you began to tip it, it would fall apart long before you got the center of gravity where it didn't lie over the base.
Can a skyscraper really tip over intact, and flatten a distance on the ground equal to its height?
Perhaps John Young could leap in here with a professional opinion.
Like I said, I'm not a structural engineer, either. However, consider a stack of blocks (toy blocks) or cans.
(I just did the experiment with a stack of 8 soup cans...the stack tipped and the cans separated, of course, but the top can landed at about the height of the stack away from the base. So, even if the floors "fell apart," as you say, the can example suggests the toppling would still extend laterally for quite a ways. In fact, certain conservation laws make it hard for the toppling to be more tightly contained: the sections can't occupy the same space, and there are no forces pushing them in a direction orthogonal to the plane of toppling. In other words, not a lot of places for toppling sections to go except in the direction of the topple. Each section is not truly "separated," as when they fall straight down they get in the way of the section below them. Hence the toppling.)
If the tower begins to topple (e.g., if a major support is taken out, asymmetrically), the component of force along the building's axis should be _lessened_ (*) as the building tips. If the building was supported at 0 degrees of tilt, its normal position, then removing one side or one corner actually lessens the axial load.
(* roughly as the cosine of the angle from the normal, with the building axis force a maximum at 0 degrees and zero at 90 degrees, i.e., when the building is horizontal)
I think the nearly perfectly vertical collapse of the WTC towers was because of the pancaking of each floor into the floors below, as shown in the videos. Whether removal of one support triggers pancaking or toppling is more complicated than the blocks example, of course.
I freely admit that a more detailed calculation would be needed to determine what actually would happen. There are probably a bunch of calculations already on the Web. Seems like a nice homework problem for Structural Mechanics 1.
--Tim May
"As my father told me long ago, the objective is not to convince someone with your arguments but to provide the arguments with which he later convinces himself." -- David Friedman
