Editing Arch (section)

== Basic concepts ==
=== Terminology ===
{{Redirect|False arch|an arch-like construction that uses offsetting of the stones or bricks, "corbelling", to close the span|Corbel arch}}
A '''true arch''' is a load-bearing arch with elements held together by compression.{{sfn | Woodman | Bloom | 2003 | loc=}} In much of the world introduction of the true arch was a result of European influence.{{sfn | Woodman | Bloom | 2003 | loc=History }} The term '''false arch''' has few meanings. It is usually used to designate an arch that has no structural purpose, like a [[proscenium arch]] in theaters used to frame the performance for the spectators, but is also applied to [[Corbel arch|corbelled]] and [[Triangular arch|triangular]] arches that are not based on compression.{{sfn | Woodman | Bloom | 2003 | loc=False}}{{sfn | Woodman | Bloom | 2003 | loc=Triangular}}

[[File:Arch illustration.svg|thumb|upright=1|Masonry arch elements]]
A typical true [[masonry]] arch consists of the following elements:{{sfn|Boyd|1978|p=90}}{{sfn | Wilkins | 1879 | pp=291-293}}{{sfn | Woodman | Bloom | 2003 | loc=Structure}}
# [[Keystone (architecture)|Keystone]], the top block in an arch. Portion of the arch around the keystone (including the keystone itself), with no precisely defined boundary, is called a '''crown'''  
# [[Voussoir]] (a wedge-like construction block). A [[compound arch]] is formed by multiple concentric layers of voussoirs. The '''rowlock arch''' is a particular case of the compound arch,<ref>{{M-W|rowlock arch}}</ref> where the voussoir faces are formed by the [[brick header]]s.{{sfn|American Technical Society|1908|p=111}} 
# '''Extrados''' (an external surface of the arch) 
# [[Impost (architecture)|Impost]] is block at the base of the arch (the voussoir immediately above the impost is a [[springer (architecture)|springer]]). The tops of imposts define the '''springing level'''. A portion of the arch between the springing level and the crown (centered around the 45° angle{{sfn | Woodman | Bloom | 2003 | loc=Haunch}}) is called a '''haunch'''. If the arch resides on top of a [[column]], the impost is formed by an [[Abacus (architecture)|abacus]] or its thicker version, [[dosseret]].{{sfn | Woodman | Bloom | 2003 | loc=Dosseret}}
# '''Intrados''' (an underside of the arch, also known as a ''[[soffit]]''{{sfn | Woodman | Bloom | 2003 | p=}}) 
# '''Rise''' (height of the arc, distance from the springing level to the crown)
# [[Clear span]]
# [[Abutment]]{{sfn | Beall | 1987 | p=301}} The roughly triangular-shaped portion of the wall between the extrados and the [[Division (architecture)|horizontal division]] above is called ''[[spandrel]]''.{{sfn | Woodman | Bloom | 2003 | loc=Intrados}}

A (left or right) half-segment of an arch is called an ''arc'', the overall line of an arch is ''arcature''{{sfn | Woodman | Bloom | 2003 | loc=Arc}} (this term is also used for an [[Arcade (architecture)|arcade]]).<ref>{{M-W|arcature}}</ref> [[Archivolt]] is the exposed (front-facing) part of the arch, sometimes decorated (occasionally also used to designate the intrados).{{sfn | Woodman | Bloom | 2003 | loc=Archivolt}} If the sides of voussoir blocks are not straight, but include angles and curves for interlocking, the arch is called "[[Joggle (architecture)|joggled]]".{{sfn | Woodman | Bloom | 2003 | loc=Joggled}}

=== Arch action ===
[[File:Arch action English.png|thumb|Arch (A) action diagram in comparison with a beam (B)]]
A true arch, due to its rise, resolves the vertical loads into horizontal and vertical reactions at the ends, a so called '''arch action'''. The vertical load produces a positive [[bending moment]] in the arch, while the inward-directed horizontal reaction from the spandrel/abutment provides a counterbalancing negative moment. As a result, the bending moment in any segment of the arch is much smaller than in a beam with the equivalent load and span.{{sfn | Au | 1960 | p=169}} The diagram on the right shows the difference between a loaded arch and a beam. Elements of the arch are mostly subject to compression (A), while in the beam a bending moment is present, with compression at the top and tension at the bottom (B).

In the past, when arches were made of masonry pieces, the horizontal forces at the ends of an arch (so called '''thrust'''{{sfn|Calvo-López|2020|p=8}}) caused the need for heavy abutments (cf. [[Roman triumphal arch]]). The other way to counteract the forces, and thus allow thinner supports, was to use the [[counter-arch]]es, as in an [[Arcade (architecture)|arcade]] arrangement, where the horizontal thrust of each arch is counterbalanced by its neighbors, and only the end arches need to [[buttressed]]. With new construction materials (steel, concrete, [[engineered wood]]), not only the arches themselves got lighter, but the horizontal thrust can be further relieved by a [[Tie (engineering)|tie]] connecting the ends of an arch ([[bowstring arch]]).<ref name=britannica>{{Britannica|32510}}</ref>

=== Funicular shapes ===
{{main|Funicular curve}}
When evaluated from the perspective of an amount of material required to support a given load, the best solid structures are compression-only; with the flexible materials, the same is true for tension-only designs. There is a fundamental symmetry in nature between solid compression-only and flexible tension-only arrangements, noticed by [[Robert Hooke]] in 1676: "As hangs the flexible line, so but inverted will stand the rigid arch", thus the study (and terminology) of arch shapes is inextricably linked to the study of hanging chains, the corresponding curves or polygons are called ''funicular''. Just like the shape of a hanging chain will vary depending on the weights attached to it, the shape of an ideal (compression-only) arch will depend on the distribution of the load.{{sfn|Allen|Ochsendorf|West|2016|p=40}}
<gallery>
File:Analogy between an arch and a hanging chain and comparison to the dome of St Peter's Cathedral in Rome.png|Analogy between an arch and a hanging chain and comparison to the dome of [[Saint Peter's Basilica]] in Rome ([[Giovanni Poleni]], 1748)
File:Maqueta funicular.jpg|A complex funicular model ([[Church of Colònia Güell]] by [[Gaudi]], 19th century)
</gallery>

[[File:Pressure polygon.png|thumb|Arch diagram with pressure polygons drawn. A defect at the R-S portion of the intrados makes the arch susceptible to extra force along the line M-N, where the polygon curve can be pushed out of the envelope of the arch causing a collapse]]
While building masonry arches in the not very tall buildings of the past, a practical assumption was that the stones can withstand virtually unlimited amount of pressure (up to 100 [[Newton (unit)|N]] per mm<sup>2</sup>), while the tensile strength was very low, even with the mortar added between the stones, and can be effectively assumed to be zero. Under these assumptions the calculations for the arch design are greatly simplified: either a reduced-scale model can be built and tested, or a funicular curve ([[pressure polygon]]) can be calculated or modeled, and as long as this curve stays within the confines of the voussoirs, the construction will be stable{{sfn|Calvo-López|2020|pp=8-9}} (a so called "[[safe theorem]]").