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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.
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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.
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Stonehenge, Salisbury Plain, England. Between 3000 BC
and 1500 BC. Purpose?
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Stonehenge:
Stone beams supported by stone columns
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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
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Ziggurat (temple) at Ur, 2125 BC
Mesopotamia
(Sumerians, 3500 to 1900 BC)
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Pyramids of Khafre &
Khufu at Giza, Egypt
(Old Kingdom: 2686-
2181 BC)
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Great Pyramid of Khufu, Giza, Egypt (Old Kingdom: 2686-2181BC). Angle 5152
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)
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Climbers on the Great Pyramid at Giza (note sizes of blocks)
Originally, smooth surface - faced with limestone - now
weathered away
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Bent Pyramid at Dahshur, Egypt, 2680-2565 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.
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Temple of Horus, Edfu, Egypt (3 stages between 237 BC and 57 BC)
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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
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Galileo'sDiscorsi, 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 columnas 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 turningmoment 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!
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Temple of Horus, Edfu, Egypt
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Temple of Horus, Edfu, Egypt
Hypostyle Hall
(hall of many columns)
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Parthenon, Athens, Greece, 447 BC. Deep stone beams, over closely-spaced columns
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The Parthenon stands atop the Acropolis, in Athens, Greece
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Parthenon
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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 Ioniccapital
Corinthiancapital
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Parthenon: Doric order; stone architrave, frieze and cornice
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Wooden beams
Wooden planks
Compacted clay Tiles
Roof structure of Greek Temple - very short spans
Stone columns
Stone architrave
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Arches:
Achieving large spans while
avoiding tension
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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 merelyresponded 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.
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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.
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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
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Packhorse Bridge, Scotland, 1717
Arch is inherently stable
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Arch is inherently stable
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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
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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.
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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 agradient of 0.4 per cent (0.4m per 100 m length).
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Possible falsework (or centering) scheme used for the Pont du Gard
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Pont du Gard: The three levels were built in dressed stone without mortar. The
projecting blocks supported the scaffolding during construction.
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Elements of a Roman Arch Bridge
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Aqueduct, Segovia, Spain. Built by Romans, 1st century AD.
39 m high
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Segovia, Spain
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Pons Fabricus (Ponte Fabrico), Rome, Tiber. Built in 62 B.C. by
L.Fabricius. Oldest surviving bridge in Rome. Still used by
pedestrians
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Pons Fabricius (Ponte Fabricio), Rome, Tiber. Built in 62 B.C. by
L.Fabricius. Oldest surviving bridge in Rome. Still used by
pedestrians
I i ti P F b i i
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Inscription on Pons Fabricius
The building inscription, found on four places, reads L(ucius)
FABRICIUS C(ai) F(ilius) CUR(ator) VIAR(um) FACIUNDUMCOERAVIT 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 floodof 23. Perhaps the small arch on top of the pier is meant.
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Pont St Martin, Aosta, Italy. 25
BC. Longest span Roman Arch
bridge (32 m).
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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.
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Colleseum, Rome,
70-80 AD, Emperor
Vespasian
187 m long, 155 m wide, 49 m high
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Arch of Titus, Rome, AD 81.
Triumphal Arch, celebrating victory in war
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Arc de Triomphe, Paris
Commissioned in 1806 by
Napoleon I, shortly after his
victory at Austerlitz, it
was not finished until 1836
L G d A h ( h G
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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
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Culverts and underpasses: soil provides support (pressure from all
sides - circular shape efficient).
R A h d G hi A h
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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
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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
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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)
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Romanesque: Church of Sainte-Foy, Conques, France, 1050-1120
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Cathedral of Notre Dame de Paris. 1150 -1220. Example of Gothic Architecture
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Notre Dame de Paris.
1150 -1220.
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Notre Dame de Paris
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Notre Dame de Paris:
North Rose Window.
Suspended in perfectequilibrium on a web of
stone, the immense north
rose window remains
intact after 700 years, itsintricately 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
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Notre Dame de Paris. Schematic sections showing the flying butresses
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Decorative features on tops of
columns (statues, pinnacles, as inNotre Dame, below) have
stabilising function
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Construction
of a Gothic
cathedral
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Bourges Cathedral,
France, 1214. Most
efficient flyingbuttress system ever
constructed.
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Sections through various French Gothic Cathedrals, showing progressive
development
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Amiens Cathedral,
France, 1220.
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Thrusts in flying buttresses
(left) and structure of a groin
vault (above)
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Dome: 3-dimensional equivalent of an arch.
Pantheon, Rome, 118-128 AD. Temple to all the gods
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Pantheon, Rome, 118-128 AD. Construction of the dome (concrete).
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Interior of dome of Pantheon is semi- circular (hemispherical)
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Outward thrust of the dome taken by 8 m thick composite heavy wall
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Pantheon: Interior.
Biggest clear span until 19th
century
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Pantheon: Interior.
Light provided by circular
hole (occulus) in the top
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Hagia Sophia, Istanbul, 537 AD. Largest church for 9 centuries.
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Hagia, Sophia, Istanbul,
537 AD. Interior,
showing support
system for central dome
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Hagia, Sophia, Istanbul, 537 AD. Schematic showing support
system for central dome
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Comparison of sizes of various domes
Underground water storage cistern, built by Justinian, Istanbul
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Underground water storage cistern, built by Justinian, Istanbul
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Santa Maria del Fiore,
Florence, Italy.
Begun in 1296.
Segmented domeadded by Brunelleschi
in 1436.
42 m span, 91 m high.
Built without
centering
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Santa Maria del Fiore,
Florence, Italy.
Begun in 1296. Dome
added by Brunelleschiin 1436.
42 m span, 91 m high.
Built withoutcentering
Shape is arch a quinto
acuto
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Dome of Santa Maria del Fiore, Florence, is not hemispherical,
but is made up of 8 segments.
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St Peters Basilica, Rome, Michaelangelo, 1546
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Dome of St Peters Basilica, Rome, Michaelangelo, 1546
Interior of St Peters
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Basilica, Rome, showing
dome resting on four arches
supported by four great
pillars
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Hanging chain analysis of Dome of St Peters, by Giovani Poleni, 1742
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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.
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Interior of Carmel
Mission. Built in 1793it 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 SantaLucia Mountains.
(Carmel, California)
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St Pauls Cathedral, London (1675-1708). Christopher Wren
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St Pauls Cathedral Dome
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St Pauls Cathedral Dome
(3 domes inside each other)
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Hookes hanging chain concept applied to the dome of
Christopher Wrens St Pauls Cathedral. The lantern on top of
the dome distorts the chain
Segrada Familia (Holy Family)Cathedral, Barcelona
hi GA
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Architect: ANTONI GAUDI
1852-1926
Started 1882still not finished
Many examples of Gaudi work
in Barcelona
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