10/11/2005

Bridges, by James Sogi

Mechanical Engineers have numerous formulas to determine the forces that act on the structure of a bridge and can use their calculations to predict the points at which the greatest stresses concentrate. The formula help compute the vectors and the angles of the forces. The formula could use radial measure rather than the sines and cosines for measures of direction. There are four forces: tension, compression, dynamic and shear. Computing the forces identifies the amount of and point of possible structural failure to prevent collapse. The main relevant measurements are the stresses on each cable and on the abutment at the end of the structure where the greatest forces act.

On a suspension bridge, "The lines of force are spread sideways and vertically, as if they repel each other. Why do the lines of force not simply run straight along under the bridge? The energy density at a place is proportional to the square of the stress, for elastic material. Therefore the minimum energy state is found when the stress field is diffuse. Halving the stress at a place divides the energy density by four. The distribution of stress and strain is the one that minimizes the total energy. Spreading it or shrinking it would increase the strain energy. The stresses near the anchorages are more complicated, because the cables induce tensions, which are present along with the compressions already described."

In the Markets we see bridge like structures such as the one that appeared at 9/29- 10/4. Unlike a bridge we know the market structure will collapse, the question is where and when. As we saw, the stress was greatest out at the end of the abutment of the right side of the bridge and focused down on a narrow point at 2:15 on fed day causing enough stress to cause failure there. A simple computation on the number of bars gives information on the amount of stress and load as does the width of the range as the area under abutment to spread the strain. Put this image next to a 1/2 hour chart of SP 9/28- 8/6.

Discussing this theory at our Spec Dinner the most foremost and well known technical analyst suggested that this is nothing more than a double top. True indeed, but I suggest that this is another way of looking at the same phenomenon with the added advantage of having a ready made mathematical framework built in to give precision and predictive power above the technical visual indicators for those more inclined and might more closely identify the particular bar where structural failure is likely to occur. The amount of the force also might give information as to length of the subsequent drop upon structural collapse.