Spandrel (structural engineering) → Rib

choi

(1) "[T]he chapel takes its name from Pope Sixtus IV, who had it built between 1473 and 1481."  en.wikipedia.org for "Sistine Chapel." Sistine Chapel is basically a "barrel vault." Id (meaning from the same, preceding source). The same Wiki page also says of the ceiling that prior to MichelangeloL "The barrel vault was originally painted brilliant-blue and dotted with gold stars."
(2) Last night I could not fathom the purpose of spandrels in Sistine Chapel, in terms of structural engineering, architecture, or mechanics -- especially why each of them is bound on both sides like a equilateral triangle. Today I finds nothing in the Web. However, I did find something -- in general.

(3)
(a) vault
https://en.wikipedia.org/wiki/Vault
(may refer to "vault (architecture), an arched form above an enclosed space")
(b) vault (architecture)
https://en.wikipedia.org/wiki/Vault_(architecture)
(section 1 Vault Types, section 1.3 Barrel vault: "A barrel vault is the simplest form of a vault and resembles a barrel or tunnel cut lengthwise in half")
(c) barrel vault
https://en.wikipedia.org/wiki/Barrel_vault

Please read introduction and section 2 Engineering issues, as well as a photo whose caption reads, "Nave of Lisbon Cathedral with a barrel vaulted soffit. Note the absence of clerestory windows, all of the light being provided by the Rose window at one end of the vault."
(d) The first sentence of paragraph (2) says a spandrel in Sistine Chapel "is bound on both sides like a equilateral triangle." The boundaries are "ribs."
(i) rib vault
https://en.wikipedia.org/wiki/Rib_vault
(A) Quote:

introduction: "Thin stone panels fill the space between the ribs. This greatly reduced the weight and thus the outward thrust of the vault [as see in section 2 Engineering issues of the Wiki page for 'barrel vault']. The ribs transmit the load downward and outward to specific points, usually rows of columns or piers [and wall in between windows, in the example of Sistine Chapel]. This feature allowed architects of Gothic cathedrals to make higher and thinner walls and much larger windows. * * * The earliest surviving example in Islamic architecture is at the Mosque–Cathedral of Córdoba in al-Andalus, which predates the earliest Romanesque examples by a century.

section 2 Cross vaults, section 2.1 Islamic architecture: "n the Moorish architecture of Spain, Islamic architects used these ribbed vaults more visibly." + section 2.2 Romanesque architecture

Refrain from reading these two sub-sections until you view groin vault
https://en.wikipedia.org/wiki/Groin_vault
("(also sometimes known as a double barrel vault or cross vault) is produced by the intersection at right angles of two barrel vaults, The word 'groin' refers to the edge [represented by a rib] between the intersecting vaults_

Conceptually, "intersection at right angles of two barrel vaults" can be understood if one views the illustration in this Wiki page, whose caption reads, "A groin vault (with pointed Gothic profile) viewed from the underside, showing the arris or 'groin.' " Here in this illustration, you see two barrel vaults intersect at right angle. And the illustration is exactly the same as the first photo of this page.
(B) Please read
section 3 Function, particularly the diagram whose caption reads, "The dynamics of a rib vault, with outward and downward pressure from ribs balanced by columns and buttresses. The pieces in the model can stand by themselves, without cement. (National Museum of French Monuments, Paris)."
(C) Click "Mosque–Cathedral of Córdoba" (which was originally built as a mosque but after Spaniards expelled Moors, the mosque was repurposed as a cathedral.

Mosque–Cathedral of Córdoba
https://en.wikipedia.org/wiki/Mosque–Cathedral_of_Córdoba
(section 1 History, section 1.4 Expansions of the mosque [under Moors]: "At the beginning of al-Hakam's extension, the central 'nave' [quotation marks are used because nave is a term for a structure inside a (Christian) church] of the mosque was highlighted with an elaborate ribbed dome (now part of the Capilla da Villaviciosa). More famously, a rectangular maqsura area around the mosque's new mihrab was distinguished by a set of unique interlacing multifoil arches. The rectangular area within this, in front of the mihrab, was covered by three more decorative ribbed domes [photo to the right on text; specifically at the top of the photo]")
(ii) In the preceding quotation, "Capilla da Villaviciosa" does not lead to a link, but Wiki does have a page for it. See
Capilla de Villaviciosa (Mezquita-catedral de Córdoba)
https://es.wikipedia.org/wiki/Capilla_de_Villaviciosa_(Mezquita-catedral_de_Córdoba)
(photo)

maqsurah
https://en.wikipedia.org/wiki/Maqsurah


(4) Rib Vault (architecture), Encyclopaedia Britannica, undated.
https://www.britannica.com/technology/rib-vault

-----------------------https://www.britannica.com/technology/rib-vault
rib vault, also called ribbed vault, in building construction, a skeleton of arches or ribs on which masonry can be laid to form a ceiling or roof. Rib vaults were frequently used in medieval buildings, most famously in Gothic cathedrals. Similarly to groin vaults, rib vaults are constructed from two, sometimes three, intersecting vaults, which can be of different widths but must be of the same height. The medieval mason used pointed arches—probably adopted from Islamic architecture in Spain. Unlike the round arches used in Romanesque cathedrals, pointed arches could be raised as high over a short span as over a long one. The arches are located at the joints of the vaults and carry the weight of the ceiling.

The rib vault arose out of medieval masons’ efforts to solve the challenges associated with supporting heavy masonry ceiling vaults over wide spans. The problem was that the heavy stonework of the traditional arched barrel vault and the groin vault exerted a tremendous downward and outward pressure that tended to push the walls upon which the vault rested outward, thus collapsing them. A building’s vertical supporting walls thus had to be made extremely thick and heavy in order to contain the barrel vault’s outward thrust. Consequently, windows were few and small in Romanesque churches, and interiors were dark and heavy. Medieval masons solved the problem about 1120 with a number of brilliant innovations—first and foremost, the rib vault. The arching and intersecting stone ribs support a vaulted ceiling surface that is composed of mere thin stone panels. This greatly reduced the weight (and thus the outward thrust) of the ceiling vault, and, since the vault’s weight was now carried at discrete points (the ribs) rather than along a continuous wall edge, separate widely spaced vertical piers to support the ribs could replace the continuous thick walls. The round arches of the barrel vault were replaced by pointed (Gothic) arches, which distributed thrust in more directions downward from the topmost point of the arch.

Decades of experimentation produced vaulting that was light, strong, open, versatile, and applicable everywhere. Combined with such other innovations as flying buttresses, rib vaults allowed Gothic buildings to become, in succession, broader and taller. How their visual appearance changed is easy to see if one compares, for instance, the tall and airy 13th-century Reims Cathedral in France with the stout 11th-century Durham Cathedral in England.