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26th December 2007, 09:46 PM   #82
Newtons Bit
Penultimate Amazing

Join Date: Apr 2007
Posts: 10,016
Critical failure in understanding how structures work.

Zeuzzz has made a very critical error in his not quite so free-body diagram (there's actually more than just one, but I'll just touch on the important one).

The lower structure cannot impart a horizontal force of any magnitude into the upper block. The force he labels as Rf has two components, a vertical and a horizontal. I show the horizontal below. See the second figure below.

A normal undamaged structure can resist horizontal forces (typically referred to as a shear) such as wind and earthquake. In the case of wind forces, the wind pushes against the exterior frame work/columns, this force is delivered to the diaphragm (the flat plate you laymen call concrete floors) to the lateral elements that are parallel to that force. In our problem here, the diaphragm (floor plates) have been destroyed on the upper floors of the lower block. With an angle of 20 degrees and a tower width of 208ft we know that the height of the upper triangle is 71 ft. That's over 5 stories that have lost their diaphragm (no jokes please). The two column lines (that's half the tower, see the third figure below) that are normal to this force have no lateral capacity. The columns on the line that is parallel with the lateral force do have some lateral resistance, but not much without a diaphragm (this is due to stability, which is a textbook worth of information).

Ultimately, the only force the lower block applies on the upper block is a pure vertical force. But even then we need to step back and look at what is really happening. Zeuzzz makes the same error all the want to be scientist truthers make in assuming that the upper and lower block are homogeneous solid objects. They are not. They are an intricate lattice work of discrete steel members. These steel members are not falling on top of each other, they are eccentric and they are punching directly through the concrete without ever developing anything close to their full compressive capacity. It's not even the same order of magnitude.

If I were his professor, I'd give him an F. Not because of his lack of understanding of how buildings work, I'd never expect a physicist to have an understanding of that, but rather in the failure of being able to draw a simple moment diagram. Zeuzzz only shows the forces that INCREASE the rotation, he conveniently forgets a force that decreases the amount of rotation, which I've labeled as F4 in my first figure. F4 is larger than F1 (and not just because I made it a bigger font, ah hah!) because the force is based upon the size of the red triangle, or the weight above. For the enlightenment of the laypeople here, F1 would equal F4 when the angle of rotation is 45 degrees.

And for the record Zeuzzz, you didn't draw a MOMENTUM diagram, you drew a MOMENT diagram. Go take some basic courses.
Attached Images
 problem1.jpg (11.2 KB, 289 views) problem2.JPG (15.6 KB, 280 views) problem3.JPG (15.0 KB, 7 views)
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"Structural Engineering is the art of molding materials we do not wholly understand into shapes we cannot precisely analyze so as to understand forces we cannot really assess in such a way that the community at large has no reason to suspect the extent of our own ignorance." James E Amrhein