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Engineering Structures 101

Engineering Structures 101. Structural Engineering From the Beginning: Beams, Arches, Domes Professor Martin Fahey School of Civil & Resource Engineering, Room A1.08 (e-mail: fahey@civil.uwa.edu.au) www.civil.uwa.edu.au/for/students/undergraduate/online_teaching_resources/semester_two/610101.

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Engineering Structures 101

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  1. Engineering Structures 101 Structural Engineering From the Beginning: Beams, Arches, Domes Professor Martin FaheySchool of Civil & Resource Engineering, Room A1.08(e-mail: fahey@civil.uwa.edu.au) www.civil.uwa.edu.au/for/students/undergraduate/online_teaching_resources/semester_two/610101 (The pictures contained in this presentation were either downloaded from the Internet, or scanned in from books. The sources are too numerous to list).

  2. Newgrange, Ireland, 3200 BC80 m diameter burial mound, Boyne Valley (where I grew up!), 40 km from Dublin, built by pre-Celtic neolithic people (Tuatha de Dannan?). The lack of knowledge of the people who built makes it a very eerie place to visit.

  3. Newgrange, Ireland, 3200 BCExterior view of entrance, and interior of burial chamber. Note stone lintel.At sunrise on summer solstice (21 June) sun shines through window above entrance, down the long passage, and strikes an altar at the centre of the chamber.

  4. Stonehenge, Salisbury Plain, England. Between 3000 BC and 1500 BC. Purpose?

  5. Stonehenge: Stone beams supported by stone columns

  6. Mesopotamia:(“Land between two rivers” - the Euphrates and the Tigris)Start of “modern” civilisations?about 7000 BC.Ice age just finishing in Europe. Very fertile then - now desert (Iran/Iraq) Modern humans appeared about 160,000 years ago in Africa Did not flourish until extinction of the Neanderthals about 35,000 years ago

  7. Ziggurat (temple) at Ur, 2125 BCMesopotamia(Sumerians, 3500 to 1900 BC)

  8. Pyramids of Khafre & Khufu at Giza, Egypt(Old Kingdom: 2686-2181 BC)

  9. Great Pyramid of Khufu, Giza, Egypt (Old Kingdom: 2686-2181BC). Angle 51°52’146 m high, 2.3 million stone blocks, each 2.5 tonnes. Base is almost perfect square, 229 m sides. Aligned perfectly with cardinal points (N,S,E,W)

  10. Climbers on the Great Pyramid at Giza (note sizes of blocks) Originally, smooth surface - faced with limestone - now weathered away

  11. Bent Pyramid at Dahshur, Egypt, 2680-2565 B.CAngle changes from 54 to 43 degrees (attributed to foundation problems?). If it had been completed to original plan, it would have been the biggest pyramid in Egypt.

  12. Temple of Horus, Edfu, Egypt (3 stages between 237 BC and 57 BC)

  13. Beams: Tension and Compression Top half of beam in compression:Rock: strong in compression Bottom half of beam is in tension: Rock: weak in tension Maximum tensile stress mid-span Value varies in proportion to L2 Therefore, beams must be short if poor tensile strength Egyptian & Greek columns close together - column spacing < 2 x beam depth - very cluttered space

  14. « Galileo's Discorsi, his DialoguesConcerning Two New Sciences, were published in Leyden in 1638. The second new science is concerned with the mechanics of motion; the first gives the first mathematical account of a problem in structurai engineering. Galileo wishes to compute the breaking strength of a beam, knowing the strength of the material itself as measured in the tension test shown in the illustration. The drawing does not encourage belief that Galileo ever made such a test (although Galileo himself never saw the illustration - he was blind by the time the book was printed). The hook at B would have pulled out of the stone long before the column as a whole fractured. In the same way, it is thought that Galileo did not in fact drop balls of different weights from the Leaning Tower of Pisa. It is not known that Galileo ever designed crucial experiments of this sort, in order to prove or disprove a theory. What he did was to make crucial observations, from which ensued brilliant advances in every subject he touched ». Jacques Heyman « The Science of Structural Engineering » Imperial College Press This is the famous illustration for Galileo's basic problem - the breaking strength of a beam. Again, the drawing is not really representational, although there is a wealth of circumstantial detail. In this case the hook C may well have been able to carry the load, but the masonry at AB looks insufficient to resist the turning moment at the wall. It is interesting to note that Galileo actually got the statics completely wrong – he did not understand that the stresses on the cross section had to give zero net horizontal force. He thought that the stress distribution went from a maximum at the top, to zero at the bottom. He would have failed 1st year statics!

  15. Temple of Horus, Edfu, Egypt

  16. Temple of Horus, Edfu, EgyptHypostyle Hall (hall of many columns)

  17. Parthenon, Athens, Greece, 447 BC. Deep stone beams, over closely-spaced columns

  18. The Parthenon stands atop the Acropolis, in Athens, Greece

  19. Parthenon

  20. Doric capital Ionic capital Corinthian capital Three types of columns (three “orders”) used in Greek buildings: Doric, Ionic and Corinthian The top (“capital”) of each column type is different- in fact, whole style & proportions of each are different

  21. Parthenon: Doric order; stone architrave, frieze and cornice

  22. Compacted clay Tiles Wooden beams Wooden planks Stone architrave Stone columns Roof structure of Greek Temple - very short spans

  23. Arches: Achieving large spans while avoiding tension

  24. A simple masonry arch is made from identical wedge-shaped voussoirs - it is built on falsework, since it cannot stand until the last stone, the keystone, is in place. Once complete, the falsework (the ‘centering’) may be removed, and the arch at once starts to thrust at the river banks. Inevitably the abutments will give way slightly, and the arch will spread. Figure (b), greatly exaggerated, shows how the arch accommodates itself to the increased span. The arch has cracked between voussoirs - there is no strength in these joints, and three hinges have formed. There is no suggestion that the arch is on the point of collapse - the three-hinge arch is a well-known and perfectly stable structure. On the contrary, the arch has merely responded in a sensible way to an attack from a hostile environment (gravity). In practice, the hinges may betray themselves by cracking of the mortar between the voussoirs, but larger open cracks may often be seen.

  25. An arch supports vertical forces by generating compression between the “voissoirs” of the arch. The arch abutment must be capable of supporting the resulting horizontal thrust.

  26. An arch with three hinges can be stable - in fact many arches are built this way deliberately Four hinges are required in an arch for collapse. Picture shows “snap-through” failure

  27. Packhorse Bridge, Scotland, 1717Arch is inherently stable

  28. Arch is inherently stable

  29. A stone beam with small span-to-depth ratio (such as those in the Parthenon) may act as a three-pin arch if it cracks at the centre, and may not necessarily collapse

  30. Pont du Gard, Nimes, southern France. Aqueduct. Built by Romans, -15 BC to 14 AD. The Romans perfected the use of the arch, and used it widely.

  31. This aqueduct, over the river Gard, is 275 metres long and 49 m high. Part of an aqueduct nearly 50 km long that supplied Nimes with water. On its first level it carries a road and at the top of the third level, a water conduit, which is 1.8 m high and 1.2 m wide and has a gradient of 0.4 per cent (0.4m per 100 m length).

  32. Possible falsework (or “centering”) scheme used for the Pont du Gard

  33. Pont du Gard: The three levels were built in dressed stone without mortar. The projecting blocks supported the scaffolding during construction.

  34. Elements of a Roman Arch Bridge

  35. Aqueduct, Segovia, Spain. Built by Romans, 1st century AD. 39 m high

  36. Segovia, Spain

  37. Pons Fabricus (Ponte Fabrico), Rome, Tiber. Built in 62 B.C. by L.Fabricius. Oldest surviving bridge in Rome. Still used by pedestrians

  38. Pons Fabricius (Ponte Fabricio), Rome, Tiber. Built in 62 B.C. by L.Fabricius. Oldest surviving bridge in Rome. Still used by pedestrians

  39. Inscription on Pons Fabricius The building inscription, found on four places, reads “L(ucius) FABRICIUS C(ai) F(ilius) CUR(ator) VIAR(um) FACIUNDUM COERAVIT EIDEMQUE PROBAVEIT”, meaning that Lucius Fabricius as curator of the roads ordered the construction of the bridge. In smaller letters is added that Marcus Lollius and Quintus Aemilius Lepidus, the consuls of 21 BCE, improved the bridge. This may refer to adjustment made necessary after the great flood of 23. Perhaps the small arch on top of the pier is meant.

  40. Pont St Martin, Aosta, Italy. 25 BC. Longest span Roman Arch bridge (32 m).

  41. Anji, (or Great Stone) Bridge, Jiao River, China, 610 AD, Li Chun. Still in use. Described by Ming Dynasty poet as “new moon rising above the clouds, a long rainbow drinking from a mountain stream”.

  42. Colleseum, Rome, 70-80 AD, Emperor Vespasian 187 m long, 155 m wide, 49 m high

  43. Arch of Titus, Rome, AD 81. Triumphal Arch, celebrating victory in war

  44. Arc de Triomphe, Paris Commissioned in 1806 by Napoleon I, shortly after his victory at Austerlitz, it was not finished until 1836

  45. La Grande Arche (the Great Arch), La Defense, Paris, is not actually an arch. One of the great projects initiated by Francois Mitterand, President of France, in the 1980s

  46. Culverts and underpasses: soil provides support (pressure from all sides - circular shape efficient).

  47. 4/5B B B Roman Arch compared to Gothic Arch Gothic Arch: Pointed. Example shown is “a quinto acuto” - two circular segments with radius = 4/5 of the base Roman Arch: semi-circular (“Romanesque” architecture)

  48. Gothic “a quinto acuto” arch Inverted “hanging chain” shape (pure compression - no bending). Arch in this shape would have no bending in any part. “Hanging chain” (catenary) shape (Pure tension - no bending) An “inverted catenary (chain) is the ideal shape for an arch. Gothic arch “a quinto acuto” is very close to ideal shape - therefore can be very thin and still be stable

  49. For stability, a circular Roman arch supporting only its own weight must be thick enough to contain an equivalent “inverted catenary” arch Therefore, Romanesque architecture typically very massive (“heavy”)

  50. Romanesque: Church of Sainte-Foy, Conques, France, 1050-1120

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