Kupola

Za druga značenja, pogledajte stranicu Kupola (modul MSS).

Kupola Svete Sofije u Carigradu, iz 562. godine.

Kupola (od lat. cop(u)la preko ital. cupola — „svezak”) je poluloptasti izvod iznad prostorije, koja ima osnovu kružnice ili kvadrata. To je osnovni sferni luk koji je stvaran od dela kugle ili druge rotacione površine iznad kvadratnog ili mnogougaonog poligona kao osnove. Upotrebljavala se uglavnom u rimskoj arhitekturi, renesansi i baroku kao i vizantijskoj i islamskoj arhitekturi.

Terminologija

Poređenje generičkog „pravog“ svoda (levo) i korbalnog svoda (desno).

Kupola je zaobljeni svod napravljen od zakrivljenih segmenata ili ljuske revolucije, što znači da je luk rotiran oko svoje centralne vertikalne ose. Korištena terminologija je bila predmet kontroverze, sa nekonzistentnošću između naučnika i čak unutar pojedinačnih tekstova, ali se termin „kupola“ može smatrati „sveobuhvatnom rečju za opis hemisferičkog ili sličnog rasponskog elementa“.

Ponekad zvani „lažne“ kupole, korbel kupole ostvaruju njihov oblik produživanjem svakog horizontalnog sloja kamena malo dalje od donjeg dok se ne sastanu na vrhu. „Lažna“ kupola se takođe može odnositi na drvene kupole. „Istinskim“ kupolama se smatraju one čije strukture su u stanju kompresije, sa konstitutivnim elementima u obliku klinastog kamenja (voussoir), čiji sastavi su poravnati sa centralnom tačkom. Validnost toga je nejasna, pošto su kupole izgrađene ispod zemlje korbelnim kamenjem isto tako pod kompresijom od okružujućeg zemljišta.

Kao kod lukova, „osnova“ kupola je nivo od koga se kupola podiže. Vrh kupole je „kruna“. Unutrašnja strana kupole se naziva „intrados“ a spoljašnja strana se naziva „ekstrados“. „Lučni krak“ je deo luka koji leži oko polovine rastojanja između osnove i vrha.

Tamburi su cilindrični ili poligonalni zidovi sa prozorima koji podržavaju kupolu ili bez njih. Lanterna je ekvivalentna struktura preko okulusa kupole, koja podržava kupolu.

Karakteristike

Unutrašnje sile

Zidna kupola proizvodi potiske nadole i spolja. Oni se razmatraju u smislu dve vrste sila pod pravim uglovima jedne od druge. Meridionalne sile (poput meridijana, ili linije longitude na globusu) su samo kompresivne i povećavaju se prema bazama, dok su obručne sile (kao linije latituda na globusu) kompresivne samo na vrhu i napete u osnovi, pri čemu se tranzicija u hemisferičkoj kupoli pojavljuje pod uglom od 51,8 stepeni od vrha. Pritisci koji stvara kupola su direktno proporcionalni težini njegovih materijala. Utemeljene hemisferične kupole stvaraju znatne horizontalne potiske u njihovim lučnim kracima.

Za razliku od klinastih lukova, koji zahtevaju podršku za svaki element dok se završni kamen ne uspostavi, kupole su stabilne tokom konstrukcije, pošto je svaki nivo kompletan i samonosivi prsten. Gronja porcija zidane kupole je uvek pod kompresijom i lateralno je podržana, tako da ne kolapsira izuzev kao cela jedinica i niz odstupanja od ideala u ovoj površnoj gornjoj kapi su jednako stabilni. Pošto klinaste kupole imaju lateralnu podršku, one mogu da budu tanje od korespondirajućih lukova istog raspona. Na primer, hemisferična kupola može da bude 2,5 puta tanja od semikružnog luka, a kupola sa profilom ekvilateralnog luka može da bude još tanja. Optimalni oblik zidane kupole uniformne debljine je obrnuta katemptotna kriva, slična krivoj parabole. Ovaj oblik omogućava perfektnu kompresiju, bez naponskih ili savijajući sila da oslabljuju strukturu. Šiljati profili mnogih gotskih kupola se više približavaju ovom optimalnom obliku nego hemisfere, koje su bile preferentne u rimskoj i vizantijskoj arhitekturi pošto se kruz smatrao perfektnom formom. Dodavanje težine na vrh zašiljene kupole, kao što je teška kupola Firentinske katedrale, menja optimalni oblik da savršeno odgovara stvarnom zašiljenom obliku kupole.

Potisci ka spoljašnjosti u donjem delu hemisferične zidane kupole mogu se neutralisati korišćenjem lanaca ugrađenih oko obima ili sa spoljnim podupiračem, iako je pojava pukotina duž meridijana prirodna. Za male i visoke kupole sa malim horizontalnim potiskom, debljina podržavajućih lukova ili zidova može da bude dovoljna da spreče deformacije, iz kog razloga su tamburi obično znatno deblji neko kupole koje nose.

Tipologija

Skice prelaza iz kvadratne osnove na kružnu ua konstrukciju kupola na pandantifima (levo) i na trompama (desno)

Izlazna tačka forme kupole je polovina površine kugle kao geometrijskog elementa. Ako je kupola viša možemo je smatrati za eliptičku - produženu, a ako je niska za pritisnutu. U svom gornjem delu može biti zatvorena ili otvorena i imati okulus na koji se često nadovezuje lanterna koja služi za osvetljavanje kupole, a mogu se pojaviti i ovalni ili kružni otvori na njoj za osvetljenje. Kupola može biti ojačana rebrima koja mogu biti sa unutrašnje strane i sa lica. Ako je konstruisana nad kvadratnom osnovom, prelaz od kvadrata ka kružnim oblicima može biti sa pandantifima ili pomoću trompi. Između pandantifa i kupole može se nalaziti tambur koji po pravilu ima otvore.

• 
  Kupola na pandantifima
• 
  Kupola na pandantifima sa tamburom

Istorija

Kupola katedrale u Firenci

Najjednostavniji oblici kupole sreću se kod Eskima u igluima, dok je najstarija kamena kupola poznata iz praistorijskog naselja na Kipru iz 6000. godine p. n. e. Kupolu je upotrebljavala rimska antika na Panteonu u Rimu koja je bila do izgradnje kupole na Santa Mariji del Fiore u Firenci najveća kupola uopšte.

Izrazito se kupola upotrebljavala u vizantijskoj arhitekturi i islamskoj arhitekturi gde je rešeno podizanje kupole iznad kvadratnih osnova. Dalje su se kupole jako upotrebljavali u renesansnoj i baroknoj arhitekturi ali se javljaju i u daljim arhitektonskim stilovima sve do današnjih dana.

Primeri

Panteon

Najpoznatiji primjeri kupola u svjetskoj arhitekturi su rimski Panteon, Aja Sofija u Istanbulu te Bazilika Svetog Petra u Rimu.

• 125. p. n. e.: Panteon, Rim, Italija - Ø 43,3 m
• 547: Bazilika San Vitale, Ravena, Italija- Ø 16 m
• 563: Aja Sofija, Istanbul, Turska - Ø 31 m
• 1434: Santa Marija del Fjore, Firenca, Italija- Ø 45 m
• 1593: Bazilika Svetog Petra, Rim, Italija — Ø 42.34 m
• 1708: Katedrala Svetog Pavla, London, Engleska — Ø 34 m
• 1737: Karlskirhe, Beč - Ø 25 m
• 1743: Frauenkirhe, Drezden, Nemačka — Ø 26,15 m
• 1929: Grosmarkthale, Lajpcig, Nemačka — Ø 66 m
• 2000: Eden prodžekt, Kornvol, Engleska — Ø 125 m

Vidi još

• Kube
• Luk (oblik)
• Svod

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