Editing Dome (section)

== Excerpts ==
{{notelist
| refs =
{{efn|name=Downey definitions 1945
|{{harvnb|Downey|1946|pp=23, 25, 26}}: "Architectural historians who deal with the history of the dome have been baffled and sometimes led astray by the peculiar vague-ness of some of the literary passages which in some cases form the only evidence for the existence of certain domes or of certain types of domes. When the ancient authors mention a dome, they often call it a ''sphaira'' or a ''sphairion''. While inexact, in the geometrical sense, this is a perfectly comprehensible and justifiable method of describing an architectural element whose most prominent characteristic is its sphericity; and that the ancient writers were aware of the inexactitude, but also aware of the usefulness of the graphic image, is suggested by Procopius' reference to the main dome of the Church of the Apostles at Constantinople as ''τὸ σφαιροειδές'', which might be translated "the sphere-like structure."" [...] "Choricius, to the writer's present knowledge, is the only writer of this period who is careful enough to note that a dome or a semi-dome is a ''hollow'' spherical form." [...] "Naturally, if one wished to describe a dome vividly, the most arresting feature of its appearance was its sphericity, and everybody knew that if you called a dome a ''sphaira'', you called it this because it ''resembled'' a ''sphaira''; and it was understood that a dome was not a ''sphaira'' in the geometrical sense. This is of course what one would expect, and the phenomenon is by no means confined to post-classical Greek literature."
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{{efn|name=Smith definitions 1950a
|{{harvnb|Smith|1950|p=5}}: "To the naive eye of men uninterested in construction, the dome, it must be realized, was first of all a ''shape'' and then an ''idea''. As a shape (which antedated the beginnings of masonry construction), It was the memorable feature of an ancient, ancestral house. It is still a shape visualized and described by such terms as ''hemisphere, beehive, onion, melon, and bulbous''. In ancient times it was thought of as a ''tholos, pine cone, omphalos, helmet, tegurium, kubba, kalube, maphalia, vihdra, parasol, amalaka tree, cosmic egg, and heavenly bowl''. While the modern terms are purely descriptive, the ancient imagery both preserved some memory of the origin of the domical shape and conveyed something of the ancestral beliefs and supernatural meanings associated with its form."
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{{efn|name=Smith definitions 1950b
|{{harvnb|Smith|1950|p=6}}: "The domical shape must be distinguished from domical vaulting because the dome, both as idea and as method of roofing, originated in pliable materials upon a primitive shelter and was later preserved, venerated, and translated into more permanent materials, largely for symbolic and traditional reasons. 1. At the primitive level the most prevalent and usually the earliest type of constructed shelter, whether a tent, pit house, earth lodge, or thatched cabin, was more or less circular in plan and covered by necessity with a curved roof. Therefore, in many parts of the ancient world the domical shape became habitually associated in men's memories with a central type of structure which was venerated as a tribal and ancestral shelter, a cosmic symbol, a house of appearances and a ritualistic abode. 2. Hence many widely separate cultures, whose architecture evolved from primitive methods of construction, had some tradition of an ancient and revered shelter which was distinguished by a curved roof, usually more or less domical in appearance, but sometimes hoop-shaped or conical."
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{{efn|name=Smith definitions 1950c
|{{harvnb|Smith|1950|pp=8–9}}: "The most primitive and natural shape, derived directly from a round hut made of pliable materials tied together at the top and covered with leaves, skins or thatch, was the pointed and slightly bulbous dome which is so common today among the backward tribes of Nubia and Africa (Fig. 93). This type of dome, resembling a truncated pine cone or beehive, is preserved in the tholos tombs of the Mediterranean (Fig. 63), the rock-cut tombs of Etruria and Sicily (Figs. 64, 65), in the Syrian qubab huts (Fig. 88), on the tomb of Bizzos (Fig. 61) and on many of the early Islamic mosques (Figs. 38-43). To distinguish this shape of dome from the geometric cone we will call it conoid, because of its recognized likeness to the actual pine cone. Other types of domical shapes, flatter and unpointed, were derived from the tent and preserved as tabernacles, ciboria and baldachins (Figs. 144-151). These tent forms, however, could be puffed-up and bulbous owing to the light framework of the roof, as is shown by the celestial baldachin above the great altar of Zeus at Pergamum (Fig. 106) and the Parthian dome among the reliefs of the arch of Septimius Severus at Rome (Fig. 228). There were also in Syria and other parts of the Roman Empire sacred rustic shelters whose ritualistic and domical coverings sometimes had an outward curving flange at the bottom of the dome as the thatch was bent out to form an overhang (Figs. 111-117). In other examples the curve of their light domical roof was broken by the horizontal bindings which held the thatch in place (Fig. 10). The hemispherical shape, which is today so commonly associated with the dome, undoubtedly acquired its geometric curve largely from the theoretical interests of the Greek mathematicians and the practical considerations of Roman mechanics. This Roman standardization of the domical shape, which made it easier to construct accurately in brick, stone and concrete, became the customary form of the antique domical vault."
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{{efn|name=Dodge definitions 1984a
|{{harvnb|Dodge|1984|pp=265–267}}: "Domes have been the subject of controversy for more than a century. The origins of dome construction and the ways in which it was applied have both been heatedly debated In the light of this, two questions arise. Have some scholars made too much of these matters, thereby creating unnecessary problems and a false controversy? And was there really any 'problem' as regards the dome and the square bay? The underlying issue, however, is that of terminology. Respected scholars have plunged into the debate, only to confuse the situation further by the omission of an adequate definition of terms. Where definitions are given, they are either inconsistent through the text, or do not correspond to those in general use. This leads to confusion, misunderstanding and 'problems with domes'. One thing that most scholars agree upon is that the dome is a kind of vault. R. J. Mainstone defines a dome as
:"A spanning space-enclosing structural element circular in plan and commonly hemispherical or nearly so in total form".
R. Krautheimer defines it as "a hemispherical vault" and the Penguin Dictionary of Architecture gives the following definition
:"A vault of even curvature erected on a circular base. The section can be segmental, semicircular, pointed or bulbous".
Thus it emerges that the term 'dome' is non-specific, a blanket-word to describe an hemispherical or similar spanning element. When such a vault is placed on a circular wall, as in the Pantheon in Rome, the 'Temple of Mercury' at Bala or the Tor de'Schiavi on the Via Praenestina, there is little disagreement or variation in the term applied to the roofing element; it is a dome. Problems start to occur in recent critical literature when such an element is placed over an octagonal, polygonal or square bay."
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{{efn|name=Dodge definitions 1984b
|{{harvnb|Dodge|1984|pp=268–270}}: "The Penguin Dictionary of Architecture gives the following definition of a 'domical vault':
:"A vault rising direct on a square or polygonal base, the curved surfaces separated by groins".
In American and some British publications this feature is called a 'cloister vault' and this has given rise to some of the terminological confusion. However, both Mainstone and Krautheimer, who both use the term 'cloister vault', do point out that it is also called a domical vault. Mainstone's definition is:
:"A vault approximating to the dome but polygonal rather than circular in plan";
and Krautheimer's definition is:
:"A vault composed of four, eight or twelve curved surfaces, as would result from the interpenetration of two, four or six barrel-vaults of equal height and diameter; also four-sided, eight-sided, etc, dome".
These two definitions exactly describe the Domus Augstana [''sic''] and Bostra examples. Rivoira'a [''sic''] definition of the Domus Aurea dome demonstrates how unnecessarily convoluted some terms get. He refers to it as a 'cloister vault dome'. He also calls the domical vault 'the ungroined cloister dome'. The term domical vault can be applied to such a vault on a square base, that is, made up of four panels, as Krautheimer points out. It is with this particular kind of domical vault that even more acute problems of definition have arisen in the past. Butler, in his description of the South Baths at Bostra, calls the octagonal dome, referred to above, an 'eight-sided dome'. The two square rooms of the complex (R and T on Butler's plan) were also vaulted. That over room R is still intact and Butler refers to it as a 'cloistered vault' or a 'square dome'. The first term, as already demonstrated, is the American term for the domical vault, but by its qualification as a square dome has caused some scholars to make some rather misguided statements. Ward-Perkins refers to the structure as a domical vault. Creswell refers to the 'square dome of the Praetorium at Musmiye (ancient Phaena), at the same time giving the French and German terms, voute en arc de cloître and klosterküppel. It is obvious from these that he means the domical or cloister vault. However, Swift calls this kind of vault "the so-called cloister dome on a square plan". By this definition it becomes obvious what kind of structure he is referring to, and he also gives Musmiye as an example."
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{{efn|name=Dodge definitions 1984c
|{{harvnb|Dodge|1984|p=277}}: "Dome A vault of usually even curvature erected on a circular base whose elements are set radially rather than corbelled. The profile can vary. The term can be applied in a general way to other domical forms (Such as the domical and sail vault)"
}}

{{efn|name=Trachtenberg definitions 1986
|{{harvnb|Trachtenberg|Hyman|1986|p=583}}: "Dome A curved vault that is erected on a circular base and that is semicircular, pointed, or bulbous in section. If raised over a square or polygonal base transitional squinches or pendentives must be inserted at the corners of the base to transform it into a near circle."
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{{efn|name=Fleming definitions 1991
|{{harvnb|Fleming|Honour|Pevsner|1991|pp=126–127}}: "Dome. Vault of even curvature on a circular base. The section can be segmental, semicircular, pointed, or bulbous. If a dome is to be erected on a square base, members must be interpolated at the corners to mediate between the square and the circle. They can be pendentives of squinches. A pendentive is a spherical triangle; its curvature is that of a dome whose diameter is the diagonal is the diagonal of the initial square. The triangle is carried to the height which allows the erection on its top horizontal of the dome proper. A squinch is either an arch or arches of increasing radius projecting one in front of the other, or horizontal arches projecting in the same manner. If squinches are placed in the corners of the square and enough arches are erected on them they will result in a suitable base-line for the dome. In all these cases the dome will have the diameter of the length of one side of the square. It can be placed direct on the circular base-line, when this is achieved, or a drum, usually with windows, can be interpolated. If the dome has no drum and is segmental, it is called a saucer dome. If it has no drum and is semicircular, it is called a calotte. Another method of developing a dome out of a square is to take the diagonal of the square as the diameter of the dome. In this case the dome starts as if by pendentives, but their curvature is then continued without any break. Such domes are called sail vaults, because they resemble a sail with the four corners fixed and the wind blowing into it. A domical vault is not a dome proper. If on a square base, four webs (cells) rise to a point separated by groins (see vault). The same can be done on a polygonal base. An umbrella, parachute, pumpkin or melon dome is a dome on a circular base, but also divided into individual webs, each of which, however, has a base-line curved segmentally in plan and curved in elevation."
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{{efn|name=Saylor definitions 1994
|{{harvnb|Saylor|1994|p=56}}: "dome, a hemispherical roof form."
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{{efn|name=Heyman definitions 1997
|{{harvnb|Heyman|1997|p=27}}: "A dome is a rounded vault forming a roof over a large interior space." [...] "The rounded vault of the dome can take many forms. Perhaps the simplest of these is a shell of revolution, in which every horizontal section is circular; an egg in an egg-cup is a shell of this kind."
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{{efn|name=Cowan definitions 1998
|{{harvnb|Cowan|Smith|1998|p=73}}: "A vault of double curvature, both curves being convex upwards. Most domes are portions of a sphere; however, it is possible to have a dome of non-spherical curvature on a circular plan, or to have a dome on a non-circular plan, such as an ellipse, an oval or a rectangle."
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{{efn|name=Mainstone definitions 2000a
|{{harvnb|Mainstone|2000|p=1}}: "Architecturally, the dome may be seen not only as a structure but also as shelter, spatial enclosure, silhouette, or symbolic form with divers connotations stemming from past uses. To review all these aspects of its history would be impossible in a brief survey."
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{{efn|name=Mainstone definitions 2000b
|{{harvnb|Mainstone|2000|p=1}}: "Structurally, I take the term dome to denote, as it normally does, a doubly curved form supported from below and acting primarily in arching compression as it spans the space it encloses."
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{{efn|name=Chilton definitions 2000a
|{{harvnb|Chilton|2000|p=131}}: "In the mind of an engineer a dome is structure with a very distinct behavior. It is a synclastically-curved, three dimensional surface, primarily stressed in compression under its own weight and applied loading, and made of a material resistant to such forces (usually masonry or some form of concrete). Circumferential tension forces that may occur at the base of a dome are usually resisted by a tension ring. However, a dictionary definition of the word dome may be less precise. For instance, in a typical concise dictionary a dome is defined as: -
:'dome, n., & v.t.l. Stately building, mansion, (poet.); rounded vault as roof, with circular, elliptical or polygonal base, large cupola; natural vault, canopy, (of sky, trees, etc.); rounded summit of hill etc.; hence domed, domic(al), dome-like, domy. 2. v.t. Cover with, shape as, dome. [F. f. It. duomo cathedral, dome, (& direct) f. L domus house]'
In the past the stately building often had a masonry dome whereas, due to the rapid expansion in structural systems that have become available in the 20th century, this is now less likely to be the case. This has led to many modern large-span structures being described as domes when their primary load-bearing system does not exactly accord with the engineering definition. Some actually work almost entirely in tension, although they still may be more or less dome-shaped (for example the Millennium Dome in Greenwich). This paper, therefore, addresses the conflict that now exists between the precise engineering and more general dictionary definitions of the term dome by reviewing the development of various types of lightweight and tensile domes during the 20th century."
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{{efn|name=Chilton definitions 2000b
|{{harvnb|Chilton|2000|p=143}}: "Although the name 'dome' was appropriately applied (in the strict engineering sense) to historical long-span structures of synclastic form, working in compression and using heavy materials with little tensile strength, this is not correct for many of the new lightweight structural systems. However, the name 'dome' in common usage has come to refer to almost any long-span roofing system. The answer, therefore, to the question posed in the title of this paper is "It depends!". A synclastic surface acting predominantly in compression is clearly a dome by name, by form and by engineering definition, whilst a structure acting mainly in tension (such as the Georgia Dome) is a dome in name alone. Between these extremes there are many shades of distinction."
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{{efn|name=McNeil definitions 2002
|{{harvnb|McNeil|2002|p=879}}: "A dome is a convex rounded roof covering the whole or a part of a building with a base on the horizontal plane which is circular, elliptical or polygonal. In vertical section the dome may be hemispherical, partly elliptical, saucer-shaped, or formed like a bulb (the so-called onion domes to be seen in eastern Europe)."
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{{efn|name=Parker definitions 2003
|{{harvnb|Parker|2003}}: "Definition dome [ARCHITECTURE] A hemispherical roof."
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{{efn|name=Curl definitions 2003
|{{harvnb|Curl|2003|p=220}}: "A domical vault is not a true dome. A dome is a vault with a segmental, semicircular, bulbous, or pointed section rising from a circular base."
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{{efn|name=Kurtz definitions 2004
|{{harvnb|Kurtz|2004|p=378}}: "Dome" [...] "1. A construction in the form of a spherical cap realized on a circular or polygonal plan. 2. The internal surface of a dome. Syn. with CUPOLA. 3. A surface of revolution generated by any meridian curve turning around a vertical axis. Horizontal sections are circular rings and the dome picks up on its bearings by a circular belt. 4. Syn, with CAVITY; OPEN; POT-HOLE"
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{{efn|name=Osborne definitions 2004
|{{harvnb|Osborne|2004|p=11}}: "While dome has become the most used English geometric and architectural term for "a large hemispherical, approximately hemispherical or spheroidal vault" (Delbridge, 1981), cupola is the older term."
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{{efn|name=Harris definitions 2005
|{{harvnb|Harris|2005|p=319}}: "Dome 1. A curved roof structure spanning an area; often hemispherical in shape. 2. A square prefabricated pan form; used in two-way joist (waffle) concrete floor construction. 3. A vault substantially hemispherical in shape, but sometimes slightly pointed or bulbous; a ceiling of similar form. Also see geodesic dome and saucer dome."
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{{efn|name=Ching definitions 2007
|{{harvnb|Ching|Jarzombek|Prakash|2007|p=761}}: "A vaulted structure having a circular or polygonal plan and usually the form of a portion of a sphere, so constructed so as to exert an equal thrust in all directions."
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{{efn|name=Davies definitions 2008
|{{harvnb|Davies|Jokiniemi|2008|p=118}}: "Dome 1 a hollow, flattened or raised hemispherical roof structure, often of masonry, which rests on a circular, square, or polygonal base. See below. See types of dome illustration. See classical temple illustration. bulbous dome, see onion dome. drum dome. glass dome. half dome. melon dome, see umbrella dome. onion dome. parachute dome, see umbrella dome. pendentive dome. pumpkin dome, see umbrella dome. sail dome, sail vault. saucer dome. semi dome, see half dome. umbrella dome. 2 see domelight."
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{{efn|name=Ambrose definitions 2008
|{{harvnb|Ambrose|Harris|Stone|2008|p=41}}: "A concave structural element, erected on a circular base, and usually the shape of a semi-sphere. A dome has a curved surface and functions much like an arch, but provides support in all directions. Larger domes often have two or even three layers: the top and bottom are decorative, while the centre layer is structural and supports the other two. Domes can be segmental, semicircular, pointed or bulbous."
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{{efn|name=Coates definitions 2009
|{{harvnb|Coates|Brooker|Stone|2009|p=76}}: "A dome is a structural element conventionally used to cover large spaces. It is defined as an arch that has been rotated around its vertical axis."
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{{efn|name=Palmisano definitions 2010
|{{harvnb|Palmisano|Totaro|2010|p=519}}: "The absence of a common language is one of the reasons why nowadays there is a very big gap between the Architect and the Engineer. The introduction of new materials and techniques during the Industrial Revolution and the born of the first polytechnics in the 18th century, led to a different cultural approach to the design causing the born of different languages between Architects and Engineers. Nowadays, with the widespread of very complicated works of the architecture there is a huge need to bridge the gap between Architects and Engineers. In this context, focusing the attention on masonry domes, this paper aims at highlighting that Load Path Method seems to open new prospects in the search for a common language between engineers and architects to give voice, in harmony and in a single design, to formal, aesthetical, functional and structural aspects. According to LPM, a dome can be seen as a system of meridian arches joined by the parallel circles. The arches draw the paths of the vertical loads while the parallel circles draw the paths of the unbalanced thrusts. In fact, differently from the arches, in dome the equilibrium of the thrusts in every node is always possible because of the presence of the parallels."
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{{efn|name=Clarke definitions 2010
|{{harvnb|Clarke|2010|p=79}}: "dome A vault of even curvature over a circular base; the section can be segmental, semicircular, pointed, or bulbous. If a vault is erected over a square base, squinches or pendentives must be inserted at the corners to connect the dome to the base."
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{{efn|name=Ching definitions 2011
|{{harvnb|Ching|2011|p=62}}: "A vaulted structure having a circular plan and usually the form of a portion of a sphere, so constructed as to exert an equal thrust in all directions."
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{{efn|name=Parker definitions 2012a
|{{harvnb|Parker|2012|p=97}}: "Dome, a cupola; the term is derived from the Italian duomo, a cathedral, the custom of erecting cupolas on those buildings having been so prevalent that the name dome has, in the French and English languages, been transferred from the church to this kind of roof [See Cupola.]"
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{{efn|name=Parker definitions 2012b
|{{harvnb|Parker|2012|p=90}}: "Cupola (Ital.), a concave ceiling, either hemispherical or of any other curve, covering a circular or polygonal area; also a roof, the exterior of which is either one of these forms, usually called a dome, and in Latin tholus."
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{{efn|name=Burden definitions 2012
|{{harvnb|Burden|2012|p=155}}: "Dome: a curved roof structure that spans an area on a circular base, producing an equal thrust in all directions. A cross section of the dome can be semicircular, pointed, or segmented."
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{{efn|name=Gorse definitions 2012
|{{harvnb|Gorse|Johnston|Pritchard|2012|p=115}}: "dome 1. A structure that has a hemispherical roof. 2. A curved layer of rock strata, formed by an upward fold."
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{{efn|name=Brett definitions 2012
|{{harvnb|Brett|2012|p=20}}: "Dome a vaulted roof; normally circular or polygonal in plan and semicircular, segmental or pointed in section. See also Cupola and Squinch."
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{{efn|name=Davies definitions 2012
|{{harvnb|Davies|Jokiniemi|2012|p=143}}: "Dome 1 a hollow, flattened or raised hemispherical roof structure, often of masonry, which rests on a circular, square, or polygonal base. See Types included as separate entries are listed below: bulbous dome, see onion dome; drum dome; half dome; melon dome, see umbrella dome; onion dome; parachute dome, see umbrella dome; pendentive dome; pumpkin dome, see umbrella dome; sail dome, sail vault; saucer dome; semi dome, see half dome; umbrella dome. 2 see domelight."
}}

{{efn|name=Hourihane definitions 2012
|{{harvnb|Hourihane|2012|p=301}}: "Rounded vault covering an interior space. A very small dome roof, for example a lantern mounted on the eye of a dome proper (e.g. St Paul's Cathedral, London), is known as a cupola. In Italian cupola is used for a monumental dome." [...] "A dome can either be composed of curved segments or be a shell of revolution. The dome at Florence Cathedral by Filippo Brunelleschi (1377-1446) is segmental, octangular at every section. A shell of revolution is generated by rotating an arch about a vertical central axis. To produce a hemispherical surface the arch will be semicircular, but and shape of arch, similarly rotated, will give rise to a shell of revolution; and every horizontal cross-section is still circular. The simplest form of dome is that of such a shell of revolution: for example, the inner masonry dome of St Paul's Cathedral is roughly hemispherical, and has an open eye, while the main dome is conical; but both are shells of revolution, as is the surface of the timber outer dome. A dome can have either a single or a double shell."
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{{efn|name=Harris definitions 2013
|{{harvnb|Harris|2013}}: "Dome 1. A curved roof structure spanning an area; often hemispherical in shape. 2. A vault substantially hemispherical in shape, but sometimes slightly pointed or bulbous; a ceiling of similar form."
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{{efn|name=Murray definitions 2013
|{{harvnb|Murray|Murray|Jones|2013|p=151}}: "dome A structure that can be either circular in plan, or oval, hexagonal, octagonal, or a combination of these forms. It may have a high profile, or hemispherical, or flattened."
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{{efn|name=Curl definitions 2015
|{{harvnb|Curl|Wilson|2015|pp=236–237}}: "Cupola, essentially a species of vault, constructed on a circular, elliptical, or polygonal plan, bulbous, segmental, semicircular, or pointed in vertical section. It can be built on top of a structure the plan of which is identical to that of the dome: if that structure's wall is circular or elliptical it is a drum (often pierced with windows) as in a rotunda. However, domes usually provide cover for a square- or rectangular-planned building or compartment, so adjustments are made to facilitate the transition from the square to the circular, elliptical, or polygonal base of the cupola or dome. This is achieved by means of pendentives (fragments of a sail-vault, resembling a species of concave, distorted, almost triangular spandrels, rising up from the corner at the top of the right-angled compartment to the circular or elliptical base of the drum or cupola) or squinches (small arch or series of parallel arches of increasing radius spanning the angle of the square compartment). Both the drum and cupola will have a diameter the same dimension as the side of the square on which the whole structure stands. Types of dome include: calotte: low cupola or saucer dome of segmental vertical section, like a skull-cap; cloister-vault: as domical vault; domical vault: cloister-vault, not a true dome, but formed of four or more (depending on the shape of the base) cells or webs forming groins where they touch vertically and rising to a point; melon: as parachute; Pantheon: low dome on the exterior, often stepped, resembling that of the Pantheon in Rome, and coffered on the interior, widely copied by Neo-Classical architects; parachute: melon, pumpkin, or umbrella dome standing on a scalloped circular base and formed of individual webs, segmental on plan, joined on groins or ribs. Each web has a concave interior and convex exterior so it resembles a parachute, rather than an umbrella; pumpkin: as parachute; sail dome: dome resembling a billowing sail over a square compartment with its diameter the same dimension as the diagonal instead of the side of the square below, enabling the structure to rise as though on pendentives but continuing without interruption. Pendentives are really part of a sail-dome and themselves are a species of sail-vault; umbrella: as parachute."
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{{efn|name=Palmer definitions 2016
|{{harvnb|Palmer|2016|p=123}}: "The dome, which is created from an arch turned on its axis 360 degrees, is traditionally considered one of the most important Ancient Roman architectural inventions."
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{{efn|name=Guedes definitions 2016
|{{harvnb|Guedes|2016|p=174}}: "The dome may be regarded as the three-dimensional counterpart of the arch. In its true circular form, a vertical arch is rotated around a vertical axis and sweeps out, at every level, a continuous circular horizontal ring. Loads can be transmitted both along the meridian lines of the vertical arches and around the horizontal rings."
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{{efn|name=Jannasch definitions 2016
|{{harvnb|Jannasch|2016|pp=745–746}}: "A funicular masonry dome experiences no hoop stresses, whether tensile or compressive, so it is always on the verge of bursting. Shallow spheric domes maintain compressive stresses in each course and are therefore more stable than the "ideal" funicular form. Viable non-funicular domes also include Herrero's flat vault at the Escorial, and Mackenzie's 1840 concept of an inverted fan vault." [...] "Masonry domes are often explained as free-standing arches rotated around a central axis, or as half-arches swept between a tension ring at the base and an ocular compression ring at the top. Such concepts aren't entirely inaccurate, but they are far from complete. They undervalue or ignore the circumferential compression in each course upon which the rising dome depends and which remains active in many completed structures. They also tend to ignore the vertical shear resistance that prevents inner and upper portions of the dome from crashing vertically down through outer and lower portions, and the horizontal shear resistance that allows lower parts of the dome to contain the thrust of upper parts. Visualizing the dome as a rotated arch implies that the bedding faces between subsequent courses of masonry need to be more or less normal to the section, which is the case in an arch, but not the case in a dome. Lastly, free-standing arches must be thick enough to contain their funicular. This is not true of domes. That the arch and funicular don't really explain of the structural behavior of domes should be clear from real world examples. The conical domes at Pisa and elsewhere, for example, the shallow domes of Byzantium, and the circular vaults at the Escorial are far from funicular. None of them would succeed if "un-rotated" into arches."
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