Arch Structures
Gordon Batson
Clarkson University, Potsdam N.Y.
Of all structures built for various utilitarian purposes, a bridge and its structural components are the most visible. The load-carrying tasks of the principal structural components can be comprehended easily; the supporting cables of a suspension bridge are under tension induced by the weight and loads on the bridge.
The arch is another type of structure whose shape indicates that the loads are carried by compression. The arch can be visualized as an up-side-down suspension cable.
The stone arch is one of the oldest existing structures found in buildings, walls, and bridges. Other materials, such as timber, may have been used prior to stone, but nothing of these remains today most likely because of fires, warfare, and the decay processes of nature. Although stone arches were constructed prior to the Roman Empire, the Romans constructed some of the largest and most enduring stone arches.
Before the development of the arch, the principal method of spanning a space was the simple post-and-beam construction (Fig. 1a), in which a horizontal beam is supported by two columns. This type of construction was used to build the great Greek temples. The columns of these temples are closely spaced because of the limited length of available stones. Much larger spans can now be achieved using steel beams, but the spans are limited because the beams tend to sag under heavy loads.
The corbeled arch (or false arch) shown in Figure 1b is another primitive structure; it is only a slight improvement over post-and-beam construction. The stability of this false arch depends upon the horizonal projection of one stone over another and the downward weight of stones from above.
The semicircular arch (Fig. 2a) developed by the Romans was a great technological achievement in architectural design. The stability of this true (or voussoir) arch depends on the compression between its wedge-shaped stones. (That is, the stones are forced to squeeze against each other.) This results in horizontal outward forces at the springing of the arch (where it starts curving), which must be supported by the foundation (abutments) on the stone wall shown on the sides of the arch (Fig. 2a). It is common to use very heavy walls (buttresses) on either side of the arch to provide the horizontal stability. If the foundation of the arch should move, the compressive forces between the wedge-shaped stones may decrease to the extent that the arch collapses. The surfaces of the stones used in the semicircular arches constructed by the Romans were cut, or ``dressed,'' to make a very tight joint; it is interesting to note that mortar was usually not used in these joints. The resistance to slipping between stones was provided by the compression force and the friction between the stone faces.
Another important architectural innovation was the pointed Gothic arch shown in Figure 2b. This type of structure was first used in Europe beginning in the 12th century, followed by the construction of several magnificent Gothic cathedrals in France in the 13th century. One of the most striking features of these cathedrals is their extreme height. For example, the cathedral at Chartres rises to 118 ft and the one at Reims has a height of 137 ft. It is interesting to note that such magnificent Gothic structures evolved over a very short period of time, without the benefit of any mathematical theory of structures. However, Gothic arches required flying buttresses to prevent the spreading of the arch supported by the tall, narrow columns. The fact that they have been stable for more than 700 years attests to the technical skill of their builders and architects, which was probably acquired through experience and intuition.
Figure 3 shows how the horizontal force at the base of an arch varies with arch height for an arch hinged at the peak. For a given load P, the horizontal force at the base is doubled when the height is reduced by a factor of 2. This explains why the horizontal force required to support a high pointed arch is less than that required for a circular arch. For a given span L, the horizontal force at the base is proportional to the total load P and inversely proportional to the height h. Therefore, in order to minimize the horizontal force at the base, the arch must be made as light and high as possible.
With the advent of more advanced methods of structural analysis, it has become possible to determine the optimum shape of an arch under given load conditions.
One of the most impressive modern arches, the St. Louis Gateway Arch, designed by Eero Saarinen, has a span of 192 m and a height of 192 m (Fig. 4). The largest steel-truss arch bridge, the New River Gorge Bridge in Charleston, West Virginia, has s span of 520 m. Beautiful concrete arch bridges were designed and built in the 1920s and 1930s by Robert Maillart in Switzerland. The Sando Bridge in Sweden, a single arch of reinforced concrete, spans 264 m. Today, the arch is still the most common structure used to span large distances.
Figure Captions
Figure 1 Some methods of spanning space: (a) simple post-and-beam structure and (b) corbeled, or false, arch.
Figure 2 (a) The semicircular arch developed by the Romans. (b) Gothic arch with flying buttresses to provide lateral support. (Typical cross-section of a church or cathedral.) The buttresses transfer the spreading forces of the arch by vertical loads to the foundation of the structure.
Figure 3 When the height of an arch is reduced by a factor of 2, and the load force P remains the same, the horizontal force at the base is doubled.
Figure 4 The St. Louis Gateway Arch seen from the Mississippi River. This beautiful structure has the approximate shape of an inverted freely hanging cable.