Saturday, July 24, 2010

Incredible Insight, felt in your bones

The master masons of antiquity are often described as having an intuitive sense of stresses, load bearing and stress analysis. It is sometimes said that they “felt it in their bones,” and were able to translate this intuitive sense into an articulated design for masonry.

The thigh bone figures prominently in this schema. The ancient symbol of freemasonry uses skull and crossbones: the crossbones include the femur, or thighbone. This symbol is also known by the Greek letters Chi and Rho, which are taken to represent Christ. This is all fundamental, significant and important symbolism. The Chi may be taken as the thighbones, and the Rho may be taken as the skull.

In a masonry barrel vault (or semi-circular) arch, the most critical section is known as the “haunch.” A haunch is defined as the upper thigh in humans. This corresponds to the femur.  Here is a wonderful discussion of haunches from 1838.

In a semicircular arch –whether a cylindrical arch or a dome- there are compressive forces due to gravity, pointing down; and there are thrusting forces, pointing out. As we come down from the top or crest of the arch, the compressive forces (meridional forces) change to tension forces (hoop forces) at a specific location in the arch, known as the haunch. This haunch occurs at 51degrees 51’ in the arch.

This location in the arch (look at this link) is where the catenary thrust lines come closest to the inside surface of the arch (known as the intrados). It is the location where exterior loading is most necessary to strengthen the arch. This is done by moving the thrust force lines closer to the center of the wall, as discussed earlier.

If we look at the design I use to join arches at right angles to each other, which I discussed earlier in this blog, these arches abut each other at the precise location of the haunch. That is, arches serve to reinforce and support one another by meeting precisely at 51degrees 51’, at the haunch. It seems there is something fundamental occurring here.  I came across this independently, this is a drawing from one of my patents.

It further seems that this critical angle of the haunch within an arch has been known since very early in masonry. The specific angle of the haunch –as occurring at 51degrees51’- appears to have been known by the ancient masons of Egypt. The great pyramids were developed over time and across generations. They perhaps reached their highest state in the pyramids of Giza.

The slope, or angle of the ancient pyramids at Giza is specifically 51degrees51’. I find this amazing.

How much did the masons of antiquity know? How did they arrive at their knowledge? Was it all gained empirically, or theoretically, or some combination of the two? Did they feel it in their bones?

We have already seen how these ancient masons developed simple geometric rules which refuted theories proposed and propounded by Galileo. We will continue to look at some of the knowledge developed by early masons in the context of current knowledge and engineering analysis. This is a fascinating subject which merits further investigation.

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