116. The Corbelled Arch
The arch brings in an inherently new principle of architecture. It is a device for carrying construction over an empty space without horizontal beams. But it may take two principal forms: the corbelled or “false” arch, and the “true” arch. Both are arches in form, but the blocks that form the curvature of one are not self-supporting; in the other they are.
The corbelled arch achieves its span through a successive projection of the stones or bricks that abut on each side of the open space. The stone at the end of the second course of masonry extends part of its length beyond the end stone of the first course. At the opposite side, the second course hangs similarly out above the first. In the third course, the end blocks again project beyond those of the second. The arrangement thus is that of two series of brackets, or two staircases turned upside down. The higher the masonry rises, the more do the clear space narrow and the two lines of hanging steps approach until they meet and the arch is complete. What keeps the projecting stones from toppling into the clear space? Nothing, obviously, but such weight as is put on their inner or embedded ends. Suppose a stone projects a third of its length beyond the one below, so that its center of gravity is still above the lower stone. It will then lie as placed. Suppose still another stone again projects a third of its length beyond the second. Its center of gravity now falling outside the lowest block, it will topple both itself and the second one. Only if other blocks are inserted behind will their counterweight hold up the projecting blocks. Obviously, there will be more such counterweights needed the higher the side of the arch rises. In general, the area of wall needed as counterweight is at least as great as the area of overhanging. If the arch is to clear ten feet horizontally—hanging over five feet from each side—there must be five feet or more of masonry built up on each side of the clear space. A corbelled arch forming a relatively small doorway in the face of a wall presents no difficulty, but a corbelled arch that stands free is impossible.
The same principle holds for the vault, which is a three-dimensional extension of the virtually two-dimensional arch. The hollow or half-barrel of the corbelled vault has to be flanked by a volume of building material exceeding its own content. This need eliminates corbelling as a possible method of rearing structures that rise free and with lightness. Hence the clumsy massiveness of, for instance, Maya architecture, which, so far as it employs the vault, often contains more building material than spanned space.
Another difficulty, beyond that of counterweighting, which besets the user of the corbelled arch, is that the projecting stones of each course are subjected to the same bending strain as a beam. The weight above strives to snap them in two.
The corbelled arch and vault have been independently devised and have also diffused. They were employed in gigantic Bronze age tombs at Mycenæ in Greece—the so-called treasure house of Atreus,—in Portugal, and in Ireland ([Fig. 41]). These developments seem historically connected. On the other hand the Mayas of Yucatan also built corbelled arches, which must constitute a separate invention. This parallel development differs from that of the true arch, which seems everywhere to be derived from a single original source.