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ARCH Structures including SAP2000, Wolfgang Schueller

Refer to:<br>(1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016, published originally by Prentice Hall, 1996, (2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller, 2015. <br>

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ARCH Structures including SAP2000, Wolfgang Schueller

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  1. ARCH Structures including sap2000 Prof. Wolfgang Schueller

  2. For SAP2000 problem solutions refer to “Wolfgang Schueller: Building Support Structures – examples model files”: https://wiki.csiamerica.com/display/sap2000/Wolfgang+Schueller%3A+Building+S upport+Structures+- If you do not have the SAP2000 program get it from CSI. Students should request technical support from their professors, who can contact CSI if necessary, to obtain the latest limited capacity (100 nodes) student version demo for SAP2000; CSI does not provide technical support directly to students. The reader may also be interested in the Eval uation version of SAP2000; there is no capacity limitation, but one cannot print or export/import from it and it cannot be read in the commercial version. (http://www.csiamerica.com/support/downloads) See also, (1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016, published originally by Prentice Hall, 1996, (2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller, 2015. The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller

  3. THE USE OF ARCHES •Memorial arch • Arch bridge • Roof support structures • Arched roof structures including domes • Arched cables • Wall penetration • Arched buildings • etc.

  4. Arch geometries

  5. The arch is part of the frame family, but distinguishes itself by providing a continuous one-member enclosure without having any abrupt kink points along the geometry. The internal forces flow smoothly along the arch and are not concentrated at points of sudden change of form, assuming that the external loads are distributed evenly; concentrated loads ideally should be located at kink points. The use of arches in architecture has a long history. In Europe, the semicircular arches of the Romans were adopted again as an essential part of architecture during the Romanesque period. Transformation from the round arch to the slender pointed arch happened in the Gothic period about nine hundred years ago. In contrast to high-pointed arches are the flat, segmental arches used for bridges during the Renaissance period in Italy. Today, arches have an important place in architecture in defining building spaces and as bridges in public spaces. The infinite possible applications of the arch principle can only be suggested by

  6. Arches as enclosures

  7. Arches

  8. Examples of arch structres

  9. HISTORICAL DEVELOPMENT In the past, the arch together with the barrel arch and the arch-like vault were among the few structural systems that made it possible to span larger distances by using masonry with its low tensile capacity. Probably the first arches built were based on the corbelling principle, where horizontal masonry courses projected slightly beyond the previous course. These corbeled arches are false arches that do not develop lateral thrust, which is the basic characteristic of true arches.

  10. Treasury of Atreus, c. 1325 BC, Mycenae

  11. Ishtar Gate (reconstructed), Babylon, c. 575 BC

  12. Palace of Ctesiphon, now Taq-i-Kisra, near Bagdad, Iraq, c. 400 AD

  13. The Roman Aqueduct, Segovia, Spain, ±50 AD

  14. Coliseum, Rom, Italy, 80 AD

  15. Interior, Coliseum, Rom, Italy, 80 AD

  16. Arch of Constantine, Forum, Rome, AD315

  17. Constantine Basilica, Trier, Germany, 310 AD

  18. Palatine Chapel, Aachen Cathedral, Aachen, Germany, c.800 AD, Odo of Metz Arch

  19. Basilica of the Holy Apostles, Cologne, Germany, 11th– 13th century

  20. Cathedral of Notre Dame de Paris, 1150 - 1220

  21. Notre Dame de Paris, 1150 -1220

  22. Notre Dame de Paris. Schematic sections showing the “flying buttresses”

  23. Notre Dame de Paris: North Rose Window. Suspended in perfect equilibrium on a web of stone, the immense north rose window remains intact after 700 years, its intricately interlocking blocks so exact they ring when struck. Though individual blocks may be removed for repairs without collapsing the whole, only minor buckling has occurred 17 m 13 m

  24. Thrusts in flying buttresses (left) and structure of a groin vault (above)

  25. Construction of a Gothic cathedral

  26. Amiens Cathedral, Amiens, France, 1269

  27. Amiens Cathedral, France, 1269

  28. Amiens Cathedral, Amiens, France, 1269

  29. St. Pierrre, Beauvais, 1247

  30. Bourges Cathedral, France, 1214. Most efficient flying buttress system ever constructed.

  31. Sections through various French Gothic Cathedrals, showing progressive development

  32. Cathedral of Palma, Majorca - photoelastic Study by Robert Mark

  33. St. Lorenz, Nuremberg, ±1500

  34. St. Mary, Pirna, Germany, beginning 16th cent.

  35. Ponte Vecchio Bridge, Florence, 1367

  36. Ponte Santas Trinita, Florence, 1569

  37. Rialto Bridge, Venice, 1591

  38. Anji Bridge located in Zhaoxian County of Hebei Province was built in the Sui Dynasty (581-618). Anji Bridge is a single span stone arch bridge in China, and it is also the oldest extant bridge of China. It is also known as the Zhaozhou Bridge with a history of about 1,400 years, it is reputed as The First Bridge Under Sky.

  39. Arched Bridge, the Summer Palace in Beijing, China, 1750

  40. Charles Bridge, Prague, Czech Republic, c. 1400

  41. It may have been Robert Hook (1670), who was the first to relize from a scientific point of view that the catenary is the funicular response of the arch weight. Christopher Wren introduced the concept of the catenary dome shape with the conical brick dome supporting the cupola of St. Paul’s Cathedral, London (1970). But Giovanni Poleni was the first to actually use a model of string and lead weights to obtain the thrust line of St. Peter in Rome (1743) and thus was able to make his recommendations for the number of tension rings required to prevcent bfurther cracking of the cupola.

  42. Dome of Santa Maria del Fiore, Florence, , Italy, 1436, Filippo Brunelleschi Arch

  43. Santa Maria del Fiore, Florence, Italy. Begun in 1296. Dome added by Brunelleschi in 1436. 42 m span, 91 m high. Built without “centering” Shape is arch “a quinto acuto”

  44. Dome of St Peter’s Basilica, Rome, Michaelangelo, 1546

  45. “Hanging chain” analysis of Dome of St Peter’s, by Giovani Poleni, 1742

  46. St Paul’s Cathedral, London, 1710, Christopher Wren Arch

  47. Hooke’s “hanging chain” concept applied to the dome of Christopher Wren’s St Paul’s Cathedral. The “lantern” on top of the dome distorts the “chain”

  48. St Paul’s Cathedral Dome (3 domes inside each other)

  49. Interior of Carmel Mission. Built in 1793 it is an interesting design in that the walls curve inward towards the top, and the roof consists of a series of inverted catenary arches built of native sandstone quarried from the nearby Santa Lucia Mountains. (Carmel, CA) Mission San Carlos Borromeo, Carmel, CA, 1793, Manuel Estevan Ruiz Arch

  50. Centenary Hall, Breslau, Ger. (now Wroclaw, Pol.), Max Berg, 1913, Dyckerhoff & Widmann

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