I realize you are also saying that it is common knowledge that loads such as the live loads of the falling floors of the towers were absolutely beyond any capacity of the lower floors ability to support them. Fine also-but you need to show some proof for that one.
Static load is a force, the force of gravity on structural materials.
Force = mass * acceleration.
Normally, in a tall building, a floor doesn't accelerate downward (that is, collapse) because the structure below it applies an upward force equal to the downward force of its weight. That's the static load.
But if a floor falls anyway, then in order to stop when it hits the next floor down, it has to accelerate. (The acceleration is upward, in order to decrease the downward velocity.) Suppose, for the sake of argument, that a single floor (let's say the top floor of a structure) free-falls to the floor below. When it hits the floor below, it has to decelerate in order to stop. At what rate must it decelerate? Let's say the floors are made of a thin uniform layer of reinforced concrete. Once the floor hits, it has to decelerate over a very short distance. Think about it: if a concrete floor hits another concrete floor below it, and then keeps moving another two inches past that point, it can only be because it's broken or collapsed the floor below it, in which case it will clearly not have stopped and will keep falling. But let's allow for a generous, unrealistically large amount of crumbliness in the falling floor, and say it has a whole inch of compression over which to decelerate.
Let's say the floors were 100 inches apart to begin with.
So the floor accelerates for a fall of 100 inches at g, the acceleration of gravity, from a standing start. And then it has 1 inch of deceleration, to return to a standing start. The floor's mass stays the same, but (it can be shown with a bit of simple but tedious algebra) that the acceleration of the "stop" must be 100 times g. So the dynamic force, m*a, needed to stop the falling floor is 100 times the static force needed to hold the floor in place normally.
Of course that's a much simpler model than the WTC (it better describes the phenomenon of "pancaking" which the experts agree did not happen in the tower collapses). But it shows how dynamic loads can easily be many times larger than static loads.
So that brings us back to the weight on the head analogy. My initial criticism of you analogy was that it would not leave the persons body in a 6 inch pile, not that your weight estimate was extreme (that was Bells problem. Also you said it was a quick analogy to check if I understood static load. Fine, that's fair, but then you make another reference to the analogy and now you want to drop the brick the distance of the floors in the trade center onto the persons head. Now you are getting plain just sloppy. Clearly to be an effective the objects need to be to scale. The person is considerably shorter than the bottom 93 floors of tower, so to drop it the distance of one of the floors is ridiculous. Here is a real attempt to develop a model or analogy of the event. 93 of the 110 floors are below, so that is 84 percent of the building that is below. If we use a 6 foot man as the representation of that lower part of the building then we need an object falling onto him that is 8 inches in height. We will give you the benefit of the doubt and will call 1 floor (the distance you choose of an initial drop) 1 percent of the structure. This would be a drop of about .84 of an inch (sorry I don't do metric this time of night). Anyway, a drop such as this certainly would not be noticed by most of the unusually thick craniums on this forum.. The likelihood of such a drop driving the persons body into a pile a couple of inches tall really starts to show the absurdity of your claim. Try to find me any example of of free standing material with these proportions, with this same percentage drop, that results in that material being squashed to something of one to two percent of its original height. Good Luck
The problem is, things don't scale that way. You're probably thinking that your body is about the same strength as a skyscraper -- perhaps signficantly stronger because it has so much less mass to support, or less because its main structural members are made of bone instead of steel, but somewhere in the same ballpark. But can that really be true? Imagine being paralyzed in a vertical position (to be more like a skyscraper, without the ability to use joints and muscles to absorb impact) and dropped one tenth of your height, perhaps about seven inches. Without being able to bend your knees, you'd get a bit of a jolt, but your bones would not break, and you would not be seriously injured, especially if you were constrained from toppling sideways after your feet hit the ground. Now imagine dropping a WTC tower from one tenth of its height, about 137 feet. Assume there's some sort of cable arrangement to prevent the tower from toppling sideways after its base hit the ground (as long as the cables don't arrest the fall itself). What do you think would happen?
It occurs to me that you might think the tower should, or would, survive this treatment intact. If so, it's because you have misleading intuitiion of how things behave when scaled up.
Consider the following example: imagine a doll-house shaped like a two-story 2000 square foot (more or less typical U.S. suburban) house. Put a finger under one corner of the model, and lift up. What will happen? The doll house will tilt, of course, and remain completely intact.
You might think that this is due to the details of doll house construction. Most doll-house walls are thicker in scale than real walls, are solid wood or plastic rather than framework, have a flat rigid base that most houses don't have, and so forth. So instead, make the doll house a completely realistic model, using framework walls of exact scale studs, little tiny bricks, and so on. This won't be as strong as the conventional doll house, but it will be lighter, and I guarantee that you will still be able to lift one corner right off its foundations and tilt it with no damage.
Now try it with a real house. Dig a hole under one corner, and put a jack under it. (Pad the top of the jack with an appropriately scaled up giant rubber model of a fingertip, if you think it will help). Lift the corner with the jack. Will the house tilt? No, the corner will shear off upward while most of the rest of the house just sits there. (In fact, depending on how big a hole you dig to put the jack in, it might not even stay intact until you start lifting; it might start shearing downward under its own weight. Have you ever seen footage of what happens to a house when a sinkhole or flood erosion leaves one corner unsupported?)
Now try it with a 40-story building. Put your giant finger under a corner and start lifting. Will that whole corner shear upward like the corner of a house would? Probably not. Instead, your giant finger will break through the framework long before you can apply enough force to lift up the whole corner. It would be like trying to tilt a large wedding cake by lifting it from one edge of its bottom layer with a fork. The fork will just tear through the cake instead. Likewise, the giant finger would just pass through the framework of a large building until it did enough damage to cause a collapse of the sections above. (Substitute a powerful bomb for the giant finger, and you have a pretty good impression of what happened in the Oklahoma City bombing.)
And please consider, if you're thinking these analogies can't be valid because steel is a lot stronger than cake, you're missing the point about the importance of scale. I specified a large wedding cake because obviously you could easily tilt a cupcake with a fork with no deformation. But even a solid steel cupcake, if it were big enough, maybe somewhere around a half mile in diameter, would deform like jello rather than tilt if you tried to lift one side of its bottom edge.
So, you might think that a steel skyscraper should be able to survive a 100+ mph collision with the ground, or that damaged buildings should be able to topple sideways like cut-down trees, but they can't. That's the sort of false impression that might be gained from playing with much smaller scale models (perhaps made of K'Nex, Lego, Tinkertoys, or even building blocks) that are far more rigid relative to the scale. Any tall building, if pushed sideways by a sufficient force that's sufficiently well-distributed not to just tear through the framework, would fail near its base and begin collapsing vertically downward long before it tilted far enough to topple. Superman or the Hulk (or Mighty Mouse) might occasionally be depicted tilting a large building by lifting one corner and then putting it down again unharmed, but that couldn't really happen even if Superman really existed.
Speaking of toy models, the best toys that I'm aware of for getting an intuitive feel for the effect of scale on structural issues are the ones with rods that adhere magnetically to steel balls. (Unfortunately, they're expensive and you need a lot of them, at least several of the largest sets' worth, for this purpose.) The magnets are strong, so small structures feel very solid; you can toss them around, lift them by any one rod in the structure, and so forth (though any structure will usually break apart if dropped on the floor from a few feet). But since no individual connection can be stronger than allowed by the strength of the magnets (you get more strength if you arrange the polarities of the magnets carefully), and the rods and balls are rather heavy, larger structures run into interesting and realistic problems. For instance, you can build a tower only to a certain height, beyond which the bottom layer fails. Once a structure reaches a certain weight, it can only be lifted with great care, using both hands to distribute the force as much as possible. Larger still, and a model can't be lifted at all; if you try, your hands just crush the structure (if you lift from the bottom) or pull it apart (if you lift from the top).
Does this help explain why experienced structural engineers find it plausible that the wtc towers would continue to collapse (and implausible that the strength of the structures could arrest the collapse) once collapse began, under the conditions created by 9-11, without needing a detailed mathematical model of the exact process to convince them?
Respectfully,
Myriad
