The earliest known form of roofing for spaces within stone structures is that of corbelling. These date on the Greek Islands to around 4500 BC. Some of the tombs have imitations of corbelling carved in rock, but show that the principle was known and imitated. The picture to the left is an entrance to a tomb at Tholos of Clytemnestra, whose vaults are as tall as the diameter of their chambers. The lintel blocks alone are worthy of the name Cyclopean. The builders were obviously concerned about heavy weight resting directly on the massive lintel. They used the corbel to remove the direct over bearing.
Below is corbelling illustrated by Dieter Arnold in his Building In Egypt, Oxford University Press, 1991. This is within the 4th Dynasty of the Old Kingdom, circa 2600 BC.
The photograph on the left is another shot showing corbelling in the Meidum pyramid.
But another technique was used to prevent the heavy over load from bearing on a cavity within the massive stone structures. Mammoth blocks were placed on a slope, butted against one another, just as in a modern sloping roof, to deflect the load as side thrust and back to the stone mass. This may seen in many examples from the Old Kingdom.
The entrance door to the Khufu pyramid is typical. The drawing to the left shows the extreme concern expressed by the designer. First he placed horizontal lintels over the door. Then he placed sloping thrust blocks over those. And all of that for an entrance that did not measure more than a meter in width. The picture on the right obscures the true structure.
The great concern felt by the builders is also seen in the King's chamber. Petrie, in his Pyramids and Temples of Gizeh remarked about the huge granite beams laid across the width of the chamber, Section 53, page 81:
The roof of the chamber is formed of nine granite beams, of the following breadths, (53-inches mean) the two side beams partly resting on the ends of the chamber . . .
These roofing–beams are not of "polished granite", as they have been described; on the contrary, they have rough–dressed surfaces, very fair and true so far as they go, but without any pretence to polish. Round the S.E. corner, for about five feet on each side, the joint is all daubed up with cement laid on by fingers. The crack across the Eastern roof–beam has been also daubed with cement, looking, therefore, as if it had cracked before the chamber was finished.
This cracking must have been of great concern to the builders. As Petrie notes, it must have happened while the chamber was still under construction. As stated by Dieter Arnold in Building in Egypt:
After these rather modest beginnings (in the Step Pyramid of Zoser) flat granite ceiling beams 2 meters thick cover the crypt of Cheops, which is 5.2 meters wide. But its builders - perhaps irritated by cracks that opened during the construction - distrusted its stability and added a fantastic system of five relieving chambers on top. The four lower ones were roofed with horizontal granite beams; the uppermost one, with a pointed saddle roof of limestone.
The following illustration is from Arnold.
One may deduce that the builders were uncertain of themselves. Had they been able to compute the weight, and the thrust from various directions, they may not have created such a bizarre relief system. Or it may be that the horizontal movements they encountered from an earthquake created sufficient alarm that they went to such extraordinary lengths to prevent further alteration to the chamber dimensions. We know from the measurements of Piazza Smyth, Petrie, and others that the chamber uniquely displays mathematical properties.
This method of relieving load on a cavity within the massive stone structures continued for the next thousand years. Then other designs began to develop. The following illustrations are from the temple of Hatshepsut, circa 1450 BC. Here a corbelling of the stones is carved into a circular arch. In the first example the saddle roof is still employed.
The gradual evolution toward a true arch is seen in illustrations from Amenirdis, Shepenwepet I, and Nitocris, circa 750 BC. Here keystones come into play to provide stability to the arches. The dimensions (shown in meters) are clearly smaller than the Great Pyramid King's chamber, for example. The values in Royal Cubits of 20.62 inches are 2.08, 2.25, and 1.87. Flinders Petrie would have expressed them as cubits of 21.46, 23.22, and 19.29 inches respectively.
The illustrations above and to the left show how the arch was being used in the New Kingdom and the Ramessid period, circa 1500 to 1100 BC. The dimensions are in cubits.
The larger picture below is of a scene near the Zoser Complex, but not within it.
In both pictures the arches are composed of mud bricks. We can see how well they stood the test of time, since they have been preserved in the dry desert air for 3500 years.
The Romans then borrowed these designs for the Coliseum and Aquaducts with which we are so familiar.
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