dome

A dome () is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a matter of controversy and there are a wide variety of forms and specialized terms to describe them.

A dome can rest directly upon a rotunda wall, a drum, or a system of squinches or pendentives used to accommodate the transition in shape from a rectangular or square space to the round or polygonal base of the dome. The dome's apex may be closed or may be open in the form of an oculus, which may itself be covered with a roof lantern and cupola.

Domes have a long architectural lineage that extends back into prehistory. Domes were built in ancient Mesopotamia, and they have been found in Persian, Hellenistic, Roman, and Chinese architecture in the ancient world, as well as among a number of indigenous building traditions throughout the world. Dome structures were common in both Byzantine architecture and Sasanian architecture, which influenced that of the rest of Europe and Islam, respectively, in the Middle Ages. The domes of European Renaissance architecture spread from Italy in the early modern period, while domes were frequently employed in Ottoman architecture at the same time. Baroque and Neoclassical architecture took inspiration from Roman domes.

Advancements in mathematics, materials, and production techniques resulted in new dome types. Domes have been constructed over the centuries from mud, snow, stone, wood, brick, concrete, metal, glass, and plastic. The symbolism associated with domes includes mortuary, celestial, and governmental traditions that have likewise altered over time. The domes of the modern world can be found over religious buildings, legislative chambers, sports stadiums, and a variety of functional structures.

Etymology

The English word "dome" ultimately derives from the ancient Greek and Latin ''domus'' ("house"), which, up through the Renaissance, labeled a revered house, such as a ''Domus Dei'', or "House of God", regardless of the shape of its roof. This is reflected in the uses of the Italian word ''duomo'', the German/Icelandic/Danish word ''dom'' ("cathedral"), and the English word ''dome'' as late as 1656, when it meant a "Town-House, Guild-Hall, State-House, and Meeting-House in a city." The French word ''dosme'' came to acquire the meaning of a cupola vault, specifically, by 1660. This French definition gradually became the standard usage of the English ''dome'' in the eighteenth century as many of the most impressive Houses of God were built with monumental domes, and in response to the scientific need for more technical terms.

Definitions

Across the ancient world, curved-roof structures that would today be called domes had a number of different names reflecting a variety of shapes, traditions, and symbolic associations. The shapes were derived from traditions of pre-historic shelters made from various impermanent pliable materials and were only later reproduced as vaulting in more durable materials. The hemispherical shape often associated with domes today derives from Greek geometry and Roman standardization, but other shapes persisted, including a pointed and bulbous tradition inherited by some early Islamic mosques.

Modern academic study of the topic has been controversial and confused by inconsistent definitions, such as those for cloister vaults and domical vaults. Dictionary definitions of the term "dome" are often general and imprecise. Generally-speaking, it "is non-specific, a blanket-word to describe an hemispherical or similar spanning element." Published definitions include: hemispherical roofs alone; revolved arches; and vaults on a circular base alone, circular or polygonal base, circular, elliptical, or polygonal base, or an undefined area. Definitions specifying vertical sections include: semicircular, pointed, or bulbous; semicircular, segmental or pointed; semicircular, segmental, pointed, or bulbous; semicircular, segmental, elliptical, or bulbous; and high profile, hemispherical, or flattened.

Sometimes called "false" domes, corbel domes achieve their shape by extending each horizontal layer of stones inward slightly farther than the lower one until they meet at the top. A "false" dome may also refer to a wooden dome. The Italian use of the term ''finto'', meaning "false", can be traced back to the 17th century in the use of vaulting made of reed mats and gypsum mortar. "True" domes are said to be those whose structure is in a state of compression, with constituent elements of wedge-shaped voussoirs, the joints of which align with a central point. The validity of this is unclear, as domes built underground with corbelled stone layers are in compression from the surrounding earth.

The precise definition of "pendentive" has also been a source of academic contention, such as whether or not corbelling is permitted under the definition and whether or not the lower portions of a sail vault should be considered pendentives. Domes with pendentives can be divided into two kinds: ''simple'' and ''compound''. In the case of the ''simple dome'', the pendentives are part of the same sphere as the dome itself; however, such domes are rare. In the case of the more common ''compound dome'', the pendentives are part of the surface of a larger sphere below that of the dome itself and form a circular base for either the dome or a drum section.

The fields of engineering and architecture have lacked common language for domes, with engineering focused on structural behavior and architecture focused on form and symbolism. Additionally, new materials and structural systems in the 20th century have allowed for large dome-shaped structures that deviate from the traditional compressive structural behavior of masonry domes. Popular usage of the term has expanded to mean "almost any long-span roofing system".

Elements

The word " cupola" is another word for "dome", and is usually used for a small dome upon a roof or turret. "Cupola" has also been used to describe the inner side of a dome. The top of a dome is the "crown". The inner side of a dome is called the "intrados" and the outer side is called the "extrados". As with arches, the "springing" of a dome is the base level from which the dome rises and the "haunch" is the part that lies roughly halfway between the base and the top. Domes can be supported by an elliptical or circular wall called a "drum". If this structure extends to ground level, the round building may be called a " rotunda". Drums are also called " tholobates" and may or may not contain windows. A " tambour" or "lantern" is the equivalent structure over a dome's oculus, supporting a cupola.

When the base of the dome does not match the plan of the supporting walls beneath it (for example, a dome's circular base over a square bay), techniques are employed to bridge the two. One technique is to use corbelling, progressively projecting horizontal layers from the top of the supporting wall to the base of the dome, such as the corbelled triangles often used in Seljuk and Ottoman architecture. The simplest technique is to use diagonal lintels across the corners of the walls to create an octagonal base. Another is to use arches to span the corners, which can support more weight. A variety of these techniques use what are called "squinches". A squinch can be a single arch or a set of multiple projecting nested arches placed diagonally over an internal corner. Squinches can take a variety of other forms, as well, including trumpet arches and niche heads, or half-domes. The invention of pendentives superseded the squinch technique. Pendentives are triangular sections of a sphere, like concave spandrels between arches, and transition from the corners of a square bay to the circular base of a dome. The curvature of the pendentives is that of a sphere with a diameter equal to the diagonal of the square bay.

Materials

The earliest domes in the Middle East were built with mud-brick and, eventually, with baked brick and stone. Domes of wood allowed for wide spans due to the relatively light and flexible nature of the material and were the normal method for domed churches by the 7th century, although most domes were built with the other less flexible materials. Wooden domes were protected from the weather by roofing, such as copper or lead sheeting. Domes of cut stone were more expensive and never as large, and timber was used for large spans where brick was unavailable.

Roman concrete used an aggregate of stone with a powerful mortar. The aggregate transitioned over the centuries to pieces of fired clay, then to Roman bricks. By the sixth century, bricks with large amounts of mortar were the principle vaulting materials. Pozzolana appears to have only been used in central Italy. Brick domes were the favored choice for large-space monumental coverings until the Industrial Age, due to their convenience and dependability. Ties and chains of iron or wood could be used to resist stresses.

The new building materials of the 19th century and a better understanding of the forces within structures from the 20th century opened up new possibilities. Iron and steel beams, steel cables, and pre-stressed concrete eliminated the need for external buttressing and enabled much thinner domes. Whereas earlier masonry domes may have had a radius to thickness ratio of 50, the ratio for modern domes can be in excess of 800. The lighter weight of these domes not only permitted far greater spans, but also allowed for the creation of large movable domes over modern sports stadiums.

Experimental rammed earth domes were made as part of work on sustainable architecture at the University of Kassel in 1983.

Shapes and internal forces

A masonry dome produces thrusts downward and outward. They are thought of in terms of two kinds of forces at right angles from one another: meridional forces (like the meridians, or lines of longitude, on a globe) are compressive only, and increase towards the base, while hoop forces (like the lines of latitude on a globe) are in compression at the top and tension at the base, with the transition in a hemispherical dome occurring at an angle of 51.8 degrees from the top. The thrusts generated by a dome are directly proportional to the weight of its materials. Grounded hemispherical domes generate significant horizontal thrusts at their haunches.

The outward thrusts in the lower portion of a hemispherical masonry dome can be counteracted with the use of chains incorporated around the circumference or with external buttressing, although cracking along the meridians is natural. For small or tall domes with less horizontal thrust, the thickness of the supporting arches or walls can be enough to resist deformation, which is why drums tend to be much thicker than the domes they support.

Unlike voussoir arches, which require support for each element until the keystone is in place, domes are stable during construction as each level is made a complete and self-supporting ring. The upper portion of a masonry dome is always in compression and is supported laterally, so it does not collapse except as a whole unit and a range of deviations from the ideal in this shallow upper cap are equally stable. Because voussoir domes have lateral support, they can be made much thinner than corresponding arches of the same span. For example, a hemispherical dome can be 2.5 times thinner than a semicircular arch, and a dome with the profile of an equilateral arch can be thinner still.

The optimal shape for a masonry dome of equal thickness provides for perfect compression, with none of the tension or bending forces against which masonry is weak. For a particular material, the optimal dome geometry is called the funicular surface, the comparable shape in three dimensions to a catenary curve for a two-dimensional arch. Adding a weight to the top of a pointed dome, such as the heavy cupola at the top of Florence Cathedral, changes the optimal shape to more closely match the actual pointed shape of the dome. The pointed profiles of many Gothic domes more closely approximate the optimal dome shape than do hemispheres, which were favored by Roman and Byzantine architects due to the circle being considered the most perfect of forms.

Symbolism

According to E. Baldwin Smith, from the late Stone Age the dome-shaped tomb was used as a reproduction of the ancestral, god-given shelter made permanent as a venerated home of the dead. The instinctive desire to do this resulted in widespread domical mortuary traditions across the ancient world, from the stupas of India to the tholos tombs of Iberia. By Hellenistic and Roman times, the domical tholos had become the customary cemetery symbol.

Domes and tent-canopies were also associated with the heavens in Ancient Persia and the Hellenistic-Roman world. A dome over a square base reflected the geometric symbolism of those shapes. The circle represented perfection, eternity, and the heavens. The square represented the earth. An octagon was intermediate between the two. The distinct symbolism of the heavenly or cosmic tent stemming from the royal audience tents of Achaemenid and Indian rulers was adopted by Roman rulers in imitation of Alexander the Great, becoming the imperial baldachin. This probably began with Nero, whose " Golden House" also made the dome a feature of palace architecture.

The dual sepulchral and heavenly symbolism was adopted by early Christians in both the use of domes in architecture and in the ciborium, a domical canopy like the baldachin used as a ritual covering for relics or the church altar. The celestial symbolism of the dome, however, was the preeminent one by the Christian era. In the early centuries of Islam, domes were closely associated with royalty. A dome built in front of the mihrab of a mosque, for example, was at least initially meant to emphasize the place of a prince during royal ceremonies. Over time such domes became primarily focal points for decoration or the direction of prayer. The use of domes in mausoleums can likewise reflect royal patronage or be seen as representing the honor and prestige that domes symbolized, rather than having any specific funerary meaning. The wide variety of dome forms in medieval Islam reflected dynastic, religious, and social differences as much as practical building considerations.

Acoustics

Because domes are concave from below, they can reflect sound and create echoes. A dome may have a " whispering gallery" at its base that at certain places transmits distinct sound to other distant places in the gallery. The half-domes over the apses of Byzantine churches helped to project the chants of the clergy. Although this can complement music, it may make speech less intelligible, leading Francesco Giorgi in 1535 to recommend vaulted ceilings for the choir areas of a church, but a flat ceiling filled with as many coffers as possible for where preaching would occur.

Cavities in the form of jars built into the inner surface of a dome may serve to compensate for this interference by diffusing sound in all directions, eliminating echoes while creating a "divine effect in the atmosphere of worship." This technique was written about by Vitruvius in his ''Ten Books on Architecture'', which describes bronze and earthenware resonators. The material, shape, contents, and placement of these cavity resonators determine the effect they have: reinforcing certain frequencies or absorbing them.

Types

Beehive dome

Also called a ''corbelled dome'', or ''false dome'', these are different from a 'true dome' in that they consist of purely horizontal layers. As the layers get higher, each is slightly cantilevered, or corbeled, toward the center until meeting at the top. A monumental example is the Mycenaean Treasury of Atreus from the late Bronze Age.

Braced dome

A single or double layer space frame in the form of a dome, a ''braced dome'' is a generic term that includes ''ribbed'', '' Schwedler'', ''three-way grid'', ''lamella'' or ''Kiewitt'', ''lattice'', and ''geodesic domes''. The different terms reflect different arrangements in the surface members. Braced domes often have a very low weight and are usually used to cover spans of up to 150 meters. Often prefabricated, their component members can either lie on the dome's surface of revolution, or be straight lengths with the connecting points or nodes lying upon the surface of revolution. Single-layer structures are called ''frame'' or ''skeleton'' types and double-layer structures are ''truss'' types, which are used for large spans. When the covering also forms part of the structural system, it is called a ''stressed skin'' type. The ''formed surface'' type consists of sheets joined together at bent edges to form the structure.

Cloister vault

Also called ''domical vaults'' (a term sometimes also applied to sail vaults), ''polygonal domes'', ''coved domes'', ''gored domes'', ''segmental domes'' (a term sometimes also used for saucer domes), ''paneled vaults'', or ''pavilion vaults'', these are domes that maintain a polygonal shape in their horizontal cross section. The earliest known examples date to the first century BC, such as the Tabularium of Rome from 78 BC. Others include the Baths of Antoninus in Carthage (145–160) and the Palatine Chapel at Aachen (13th – 14th century). The most famous example is the Renaissance octagonal dome of Filippo Brunelleschi over the Florence Cathedral. Thomas Jefferson, the third president of the United States, installed an octagonal dome above the West front of his plantation house, Monticello.

Compound dome

Also called ''domes on pendentives'' or ''pendentive domes'' (a term also applied to sail vaults), compound domes have pendentives that support a smaller diameter dome immediately above them, as in the Hagia Sophia, or a drum and dome, as in many Renaissance and post-Renaissance domes, with both forms resulting in greater height.

Crossed-arch dome

One of the earliest types of ribbed vault, the first known examples are found in the Great Mosque of Córdoba in the 10th century. Rather than meeting in the center of the dome, the ribs characteristically intersect one another off-center, forming an empty polygonal space in the center. Geometry is a key element of the designs, with the octagon being perhaps the most popular shape used. Whether the arches are structural or purely decorative remains a matter of debate. The type may have an eastern origin, although the issue is also unsettled. Examples are found in Spain, North Africa, Armenia, Iran, France, and Italy.

Ellipsoidal dome

The ellipsoidal dome is a surface formed by the rotation around a vertical axis of a semi-ellipse. Like other "rotational domes" formed by the rotation of a curve around a vertical axis, ellipsoidal domes have circular bases and horizontal sections and are a type of "circular dome" for that reason.

Geodesic dome

''Geodesic domes'' are the upper portion of geodesic spheres. They are composed of a framework of triangles in a polyhedron pattern. The structures are named for geodesics and are based upon geometric shapes such as icosahedrons, octahedrons or tetrahedrons. Such domes can be created using a limited number of simple elements and joints and efficiently resolve a dome's internal forces. Their efficiency is said to increase with size. Although not first invented by Buckminster Fuller, they are associated with him because he designed many geodesic domes and patented them in the United States.

Hemispherical dome

The ''hemispherical dome'' is a surface formed by the rotation around a vertical axis of a semicircle. Like other "rotational domes" formed by the rotation of a curve around a vertical axis, hemispherical domes have circular bases and horizontal sections and are a type of "circular dome" for that reason. They experience vertical compression along their meridians, but horizontally experience compression only in the portion above 51.8 degrees from the top. Below this point, hemispherical domes experience tension horizontally, and usually require buttressing to counteract it. According to E. Baldwin Smith, it was a shape likely known to the Assyrians, defined by Greek theoretical mathematicians, and standardized by Roman builders.

Onion dome

''Bulbous domes'' bulge out beyond their base diameters, offering a profile greater than a hemisphere. An ''onion dome'' is a greater than hemispherical dome with a pointed top in an ogee profile. They are found in the Near East, Middle East, Persia, and India and may not have had a single point of origin. Their appearance in northern Russian architecture predates the Tatar occupation of Russia and so is not easily explained as the result of that influence. They became popular in the second half of the 15th century in the Low Countries of Northern Europe, possibly inspired by the finials of minarets in Egypt and Syria, and developed in the 16th and 17th centuries in the Netherlands before spreading to Germany, becoming a popular element of the baroque architecture of Central Europe. German bulbous domes were also influenced by Russian and Eastern European domes. The examples found in various European architectural styles are typically wooden. Examples include Kazan Church in Kolomenskoye and the Brighton Pavilion by John Nash. In Islamic architecture, they are typically made of masonry, rather than timber, with the thick and heavy bulging portion serving to buttress against the tendency of masonry domes to spread at their bases. The Taj Mahal is a famous example.

Oval dome

An ''oval dome'' is a dome of oval shape in plan, profile, or both. The term comes from the Latin ''ovum'', meaning "egg". The earliest oval domes were used by convenience in corbelled stone huts as rounded but geometrically undefined coverings, and the first examples in Asia Minor date to around 4000 B.C. The geometry was eventually defined using combinations of circular arcs, transitioning at points of tangency. If the Romans created oval domes, it was only in exceptional circumstances. The Roman foundations of the oval plan Church of St. Gereon in Cologne point to a possible example. Domes in the Middle Ages also tended to be circular, though the church of Santo Tomás de las Ollas in Spain has an oval dome over its oval plan. Other examples of medieval oval domes can be found covering rectangular bays in churches. Oval plan churches became a type in the Renaissance and popular in the Baroque style. The dome built for the basilica of Vicoforte by Francesco Gallo was one of the largest