Presentation on theme: "Engineering Structures 101 Structural Engineering From the Beginning: Beams, Arches, Domes Professor Martin Fahey School of Civil & Resource Engineering,"— Presentation transcript:
Engineering Structures 101 Structural Engineering From the Beginning: Beams, Arches, Domes Professor Martin Fahey School of Civil & Resource Engineering, Room A1.08 ( (The pictures contained in this presentation were either downloaded from the Internet, or scanned in from books. The sources are too numerous to list).
Newgrange, Ireland, 3200 BC 80 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.
Newgrange, Ireland, 3200 BC Exterior 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.
Stonehenge, Salisbury Plain, England. Between 3000 BC and 1500 BC. Purpose?
Stonehenge: Stone beams supported by stone columns
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
Ziggurat (temple) at Ur, 2125 BC Mesopotamia (Sumerians, 3500 to 1900 BC)
Pyramids of Khafre & Khufu at Giza, Egypt (Old Kingdom: BC)
Great Pyramid of Khufu, Giza, Egypt (Old Kingdom: BC). 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)
Climbers on the Great Pyramid at Giza (note sizes of blocks) Originally, smooth surface - faced with limestone - now weathered away
Bent Pyramid at Dahshur, Egypt, B.C Angle 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.
Temple of Horus, Edfu, Egypt (3 stages between 237 BC and 57 BC)
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 L 2 Therefore, beams must be short if poor tensile strength Egyptian & Greek columns close together - column spacing < 2 x beam depth - very cluttered space
« Galileo's Discorsi, his Dialogues Concerning Two New Sciences, were published in Leyden in 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!
Temple of Horus, Edfu, Egypt
Temple of Horus, Edfu, Egypt Hypostyle Hall (hall of many columns)
Parthenon, Athens, Greece, 447 BC. Deep stone beams, over closely-spaced columns
The Parthenon stands atop the Acropolis, in Athens, Greece
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 Doric capital Ionic capital Corinthian capital
Parthenon: Doric order; stone architrave, frieze and cornice
Wooden beams Wooden planks Compacted clayTiles Roof structure of Greek Temple - very short spans Stone columns Stone architrave
Arches: Achieving large spans while avoiding tension
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.
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.
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
Packhorse Bridge, Scotland, 1717 Arch is inherently stable
Arch is inherently stable
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
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.
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).
Possible falsework (or “centering”) scheme used for the Pont du Gard
Pont du Gard: The three levels were built in dressed stone without mortar. The projecting blocks supported the scaffolding during construction.
Elements of a Roman Arch Bridge
Aqueduct, Segovia, Spain. Built by Romans, 1st century AD. 39 m high
Pons Fabricus (Ponte Fabrico), Rome, Tiber. Built in 62 B.C. by L.Fabricius. Oldest surviving bridge in Rome. Still used by pedestrians
Pons Fabricius (Ponte Fabricio), Rome, Tiber. Built in 62 B.C. by L.Fabricius. Oldest surviving bridge in Rome. Still used by pedestrians
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.
Pont St Martin, Aosta, Italy. 25 BC. Longest span Roman Arch bridge (32 m).
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”.
Colleseum, Rome, AD, Emperor Vespasian 187 m long, 155 m wide, 49 m high
Arch of Titus, Rome, AD 81. Triumphal Arch, celebrating victory in war
Arc de Triomphe, Paris Commissioned in 1806 by Napoleon I, shortly after his victory at Austerlitz, it was not finished until 1836
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
Culverts and underpasses: soil provides support (pressure from all sides - circular shape efficient).
Roman Arch: semi-circular (“Romanesque” architecture) B 4/5B B Gothic Arch: Pointed. Example shown is “a quinto acuto” - two circular segments with radius = 4/5 of the base Roman Arch compared to Gothic Arch
“Hanging chain” (catenary) shape (Pure tension - no bending) Inverted “hanging chain” shape (pure compression - no bending). Arch in this shape would have no bending in any part. Gothic “a quinto acuto” arch 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
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”)
Romanesque: Church of Sainte-Foy, Conques, France,
La Madeleine, Vezelay, France: interior, nave, Typical Romanesque church
Cathedral of Notre Dame de Paris Example of Gothic Architecture
Notre Dame de Paris
Notre Dame de Paris
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 13 m 17 m
Notre Dame de Paris. Schematic sections showing the “flying butresses”
Decorative features on tops of columns (statues, pinnacles, as in Notre Dame, below) have stabilising function
Construction of a Gothic cathedral
Bourges Cathedral, France, Most efficient flying buttress system ever constructed.
Sections through various French Gothic Cathedrals, showing progressive development
Amiens Cathedral, France, 1220.
Thrusts in flying buttresses (left) and structure of a groin vault (above)
Dome: 3-dimensional equivalent of an arch. Pantheon, Rome, AD. Temple to “all the gods”
Pantheon, Rome, AD. Construction of the dome (concrete).
Interior of dome of Pantheon is semi- circular (hemispherical)
Outward thrust of the dome taken by 8 m thick composite heavy wall
Pantheon: Interior. Biggest clear span until 19th century
Pantheon: Interior. Light provided by circular hole (“occulus”) in the top
Hagia Sophia, Istanbul, 537 AD. Largest church for 9 centuries.
Hagia, Sophia, Istanbul, 537 AD. Interior, showing support system for central dome
Hagia, Sophia, Istanbul, 537 AD. Schematic showing support system for central dome
Hagia, Sophia, Istanbul, 537 AD.
Comparison of sizes of various domes
Underground water storage “cistern”, built by Justinian, Istanbul
Santa Maria del Fiore, Florence, Italy. Begun in “Segmented dome” added by Brunelleschi in m span, 91 m high. Built without “centering”
Santa Maria del Fiore, Florence, Italy. Begun in Dome added by Brunelleschi in m span, 91 m high. Built without “centering” Shape is arch “a quinto acuto”
Dome of Santa Maria del Fiore, Florence, is not hemispherical, but is made up of 8 segments.
St Peter’s Basilica, Rome, Michaelangelo, 1546
Dome of St Peter’s Basilica, Rome, Michaelangelo, 1546
Interior of St Peter’s Basilica, Rome, showing dome resting on four arches supported by four great pillars
“Hanging chain” analysis of Dome of St Peter’s, by Giovani Poleni, 1742
Gateway Arch, St Louis, USA. This free-standing arch is 630 ft. high and the world's tallest. Built of triangular section of double-walled stainless steel, the space between the skins being filled with concrete after each section was placed. Looks like perfect “inverted catenary” shape.
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, California)
St Paul’s Cathedral, London ( ). Christopher Wren
St Paul’s Cathedral Dome
(3 domes inside each other)
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”
Segrada Familia (Holy Family) Cathedral, Barcelona Architect: ANTONI GAUDI Started 1882 – still not finished Many examples of Gaudi work in Barcelona