EIK - Session 2 Part 3
The Greek stone columns, they found they could go 18 diameters high before the column wanted to collapse one way or another that is the slenderness ratio the ratio of the diameter to length. And we have the steel columns that can get up, today, some of the very good steel, can get up to 36 to 1 before they now you see, when you load a column in compression, it wants to banana like that. It tends to go to arc of decreasing radius. Now 12 to 1, I made that bundle of 6" in diameter and 4' long, so eight to one is a very short column, it would be called, and it has really no tendency to banana at all. It's pretty much like just one stone section in a Greek column.
Now, I'm going to put this column under an hydraulic press. You know the hydraulic press, top member coming down, fantastic power being exerted here. And as the pressure comes down on each of the rods that are in there, you know they want to bend, but because they are in closest packing they can't bend towards each other. They can only bend away from one another that is the only possible freedom. So that is exactly what they start to do. And so, we keep loading it, and they want to go out like a cigar quite evenly. We have something called a neutral axis of a compression member. If you can load it very closely on the neutral axis then the load doesn't try to make it banana one way or another, the slenderness could make it go almost any direction just a little tiny force, it will go that way. Now, we find then, very evenly loaded in its center and being a short column, it tends to become like a cigar all the rods on the outside can bend away from one another, that's the only direction they can yield. Therefore as they do so, they were bound together, so it puts an enormous strain on the binding as they work against that binding, so while we are deliberately loading it in compression this way, the resultant goes into tension in a plane at 90 degrees. It's exactly opposite of what we did with the tension member going into compression. Here again, our friend precession.
In engineering that is called the Prosler effect. Often when somebody's name is being used, it obscures a function and it would be better to say precession than Prosler effect. Anyway, we have the generalized principle covering all of these. Now, having recognized these proclivities of compression members, I saw then a tension member, when I do tense it, tends then to go to an arc of greater radius; and here we have something quite different from the compression member trying to go to the arc of lesser radius. The tension member tries to straighten out, and tries then also to get all this effectiveness within the neutral axis. It tries to get in its own neutral axis to be, in a sense, most effective. Tension members really tend to gain strength as first used, and build up really quite a lot of strength.
Now, I found, that whereas there is a slenderness ratio in compression columns there was no limit length to cross section. There was no slenderness ratio in tension members. If you had a better alloy, they could be thinner and thinner. Yesterday I went into mass interattraction with you. The beautiful discovery of team play, really, of going from Kepler and Galileo to Newton, and we have then, there is a mass interattraction. And when we get to alloys of metal today, we know that the atoms are literally not touching one another they are simply in closer proximity, one to another.
I gave you the word "Synergy" yesterday and behaviors of whole systems as unpredicted by behavior of any of their parts considered separately. Chrome-nickel-steel is a very beautiful demonstration of Synergy in physics and chemistry. An alloy. We have a rule of thumb of man of yesterday, saying a chain is no stronger than it's weakest length, and that seemed to be very obvious. By the same way then, if I mixed together a number of different chemical elements, our candy making would suggest that when you can melt the sugar the whole thing comes apart. The nuts come apart. The nuts didn't fail, but the sugar comes apart whatever is the weakest element in that chain would be all you have to look at. The sugar in that peanut brittle, and so the sugar is the weak element, and the peanut brittle would be no stronger than the sugar.
Now, when we come to the metallic alloys, things do not happen in that particular kind of way. I'm going to take the chrome-nickel-steel, and we take in the testing materials for their strength. The tensile strength per cross section area, some kind of cross section area in America, the square inch. The tensile strength of a square inch of material, or psi., pounds per square inch, what is the cohesion of that material before it gets into two pieces? And, that is the most prominent of all the strength testings that are carried on to learn all about the structural strengths of materials.
So, when you are testing, there is a point where the material will yield, and that is considerable time before it fails, so the engineering usually then deals in that, you don't want to get to a yielding point, because then things are going to be in trouble. So, I'm going to take then the one is called ultimate and the other is yield. Stones, masonry for instance, have only about 50 pounds to the square inch tensile strength to the masonry itself. The stone is 50,000 pounds to the square inch compressional strength, so stone has had an enormous ability to carry loads, but no strength at all in cohering it comes apart.
We have, then, metals taken out of the stone that brought then tensile strengths from the 50 pounds per square inch of masonry up to something like mild steel primarily the iron with some carbon, this has a tensile strength in the commercially available materials relative purity, where we get an ultimate in the mild steel of about 60,000 pounds to the square inch as ultimate, and yielding at about maybe around 50,000. We have the carbon, manganese and so forth in there in chrome, nickel, steel, the three prominent constituents are the iron and the chromium and the nickel. The chromium has a tensile strength of about 70,000 psi; the nickel about 80,000 psi; so the weakest is the iron at about 50-60,000 psi. And you say, then, we'll put these things together and the weakest adulterates the whole, like the sugar, and you never can have any more strength than the weakest component. That has been the everyday thinking, and for this reason alloys have really surprised man tremendously, because as I said society does not think synergetically. It assumes that all you have to know is about the parts and they add up. Now, chrome-nickel-steel I find that it does not come apart tensily in the tensile testing at the weakest, or where the iron would yield. We find then let's try the chromium side well it doesn't come apart; try the nickel 80,000 we're going to say a chain is now as strong as it's strongest link; and we find that at 80,000 it doesn't yield at all. In fact, we don't get it to yield until we get to 350,000 psi! Supposing I say, I want to try to understand this extraordinary phenomena by saying, I'm going to say, "a chain is as strong as the addition of the strengths of all of its links." Which everybody would say is absurd, so I'm going to take 60,000 + 70,000 and that gives me 130,000 + 80,000 gives me 210,000, but it doesn't yield till 350,000. Now, how did that happen? Well, this is the way that it occurs:
I want you to think then about the geometries I gave you yesterday of structural systems, like the tetrahedron. I can take two tetrahedra of four stars each and I can interrelate them symmetrically so that they are now eight stars in critical proximity and they take the position of the eight corners of the cube, with a cube having two tetrahedra in it, because each square face had two diagonals and you could take the cube and add the red set of diagonals, and you'll find that those are the six edges of the red tetrahedron; and you add the other diagonal of each race, the blue set, and that's the blue tetrahedron. You'll find the two come together with the eight points.
Now, remember our mass attraction. These atoms now there were only four, and their distance apart was the edge of the tetrahedron, which is on the cube, is the diagonal of the face of the cube. Now, each of these eight stars, the nearest one is a leg, or the edge of the cube away, not the diagonal away; therefore, the critical proximity has been very greatly increased; so each atom now has three other atoms much closer to them than the original three. They have four cases of each having three, and remember that the interattraction increases to the second power of the relative proximity. So the coherence has gone up enormously. Then we find that we have that cube now with the eight corners, we find that there are six faces, so I can take an octahedron which has six vertexes and they will exactly match the mid-faces of the cube, so each one of these elements coming in are just one of the such beautiful symmetry symmetrical structural systems of the atoms. So I then finally have all the interpositioning of them, all in the same distance from the same common center; and we find the mass interattractiveness has just gone up exponentially. That's how we get the 350,000 psi. In other words, here we have an alloy that's like the milky way. I take two stars in the milky way and I have another star included half way between the two, and the interattraction is going to be four-folded, because they don't touch each other.
Now, I want you to understand, then, how then alloying is highly synergetic and really appreciate that word. So I find then, here is chrome-nickel-steel with its very high synergetic effectiveness of tensile strength, and these things really began to fascinate me very much. So I saw that tension members were not limited by cross-section relation to length, if I could get a better material, I could make them longer and longer and thinner and thinner. That's exactly what went on in the history of suspension bridges. The first suspension bridges were actually made with great iron lengths very great cross section and very short span. You come to the Brooklyn bridge is the first one where we were using cable, and they used piano steel wire, which was one of those alloys. At a time when the mild steel was only about 50,000 and he got 70,000 with his piano steel wire; so he had relatively delicate cables carrying all of that extraordinary traffic with its enormous span.
Then we came to George Washington Bridge, and we had gotten very much finer, because the alloys had so improved. And each one of these bridges were getting up the Golden Gate and then finally Verrazzano we're down to very, very good cables, where you not only have greater loads and greater lengths, but actually less sections of materials per given load. I saw then that we were approaching, because there is no limit ratio of length to cross section in tension, that we were approaching infinite length and no cross section at all! And I said, "is that talking nonsense?" So I said, well, because tension goes then tends to occur in arcs of very large radius, therefore I'd better think about some very big systems. So, let's think Celestial here. Let's think for instance about the earth and the moon. And I see we can fly a little airplane right through the line between the center of gravity of the moon, and the center of gravity of the earth, and nothing happens. You don't sever anything. The fact that this then turned out to be the scheme of the Universe, where nature was using discontinuous compression and only continuous tension which was invisible to you and I because of this extraordinary mass interattraction which is invisible which made it so perplexing what those planets were doing, to those early observers. Apparently, then, the great structural scheme of Universe I found these enormous masses interattracting one another the earth and the moon with these enormous distances in between them.