arches vaults - szt courses/6_special...statically determinate structure: 3-pin arch, if thickness...
TRANSCRIPT
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ARCHESVAULTS
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OVERVIEW
1st part
• Introduction masonry vaulted structures
• Design (arches and vaults)
ARCHES
• Structural analysis
• Geometry of arches – guiding factors
• Supporting conditions
2nd part
VAULTS
• Typology
• Structural analysis
• Geometry of vaults – guiding factors
• Supporting conditions
• Contemporary examples
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THE GOOD, THE BAD..FORM AND FORCES OF ARCHES
BOLTÍVEK 3
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MASONRY NO-TENSION MATERIALVAULTS MADE OF VOUSSOIRS
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LOADBEARING-CAPACITY OF ARCHESTHE THRUST LINE
THRUST LINEThe way compressive
forces follow to the
supports
LIMITED TENSILE CAPACITYNormal to
sections/mortar
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FUNICULAR STRUCTURES - BEST FORM
2D
3D
BENDING-
COMPRESSION TENSION
ARCH
SHELLS (VAULTS)
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Maritime Museum, Barcelona
LEGOING ARCHITECTURE REUSABLE ELEMENTS
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DESIGN - THEORY
BOLTÍVEK 9
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‚As hangs the flexible line, sobut inverted will stand therigid arch.’
Robert Hooke (1635-1703)
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Gateway arch, St. Louis –Eero Saarinen, 1947-1965
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St. Paul cathedral, London,
XVII. century.
Christopher Wren
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Taq Kasra, Ctesiphon (today Iraq) – 3-6.century AC
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Hanging model for the chapel of Colonia Güell, Barcelona
Antoni Gaudi, 1898
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John. A. Ochsendorf, MIT
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STRUCTURAL ANALYSIS- STABILITYANALYSIS OF MASONRY ARCHES
BOLTÍVEK 16
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• Geometry (eg. semi-circular)
• Loading
• (Material quailty)
• Support conditions
FACTORS INFLUENCING THE INTERNAL FORCE DISTRIBUTION OF ARCHESSEARCHING FOR THE THRUST LINE
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#SIDENOTE# SUPPORTING ARCHES
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(SEMI-CIRCULAR) ARCHSTRUCTURAL MODEL
Arch on fixed supports: indeterminate structure
Inifinetely many admissible thrust line
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(SEMI-CIRCULAR) ARCHSTRUCTURAL MODEL
Limit state analysis observes the structure on the verge of collapse.
The structure is then statically determinate due the formulation of plastic
hinges
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• Arches typically fail due to the loss of stability and not materialfailure!
• Assume masonry is ideal-plastic
=> Formulation of plastic hinges at the loaction of max. moments=> turns into a mechanism
• No tension
• Infinite compression
• No sliding
• MINIMUM THICKNESS ANALYSIS
CALCULATING THE THRUST LINELIMIT STATE ANALYSIS (J. HEYMAN)
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(SEMI-CIRCULAR) ARCHCALCULATING THE THRUST LINE/MINIMUM THCIKNESS
Statically determinate structure: 3-pin arch, if thickness is known, thrust line is
determined
If minimum thickness is searched for, it is derived based on the assumption of
the 5-hinge arrangement
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• Historical construction
• typically self-weight is dominant (significant thickness)
o Assymetric live/dead load
o MOVEMENT OF SUPPORTS!
• Insufficent thrusting
• Uneven settlement
• Earthquake
Conceptually the thrust line analysis is the same, as shown for thesimplest case of symmetric static load.
CAUSE OF DAMAGE/FAILURE
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ASSYMETRICAL LOADINGSTRUCTURAL MODEL
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GEOMETRY OF ARCHES
BOLTÍVEK 25
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LOADING-THRUST LINE-ARCH: FORM FINDING
• Parabola
• catenary
• semi-circle
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THRUST LINENECESSARY THICKNESS OF THE ARCH
• Straight arch • Semi-circular arch • Pointed arch
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• statics– it must be in equilibrium
• funcionality– eg. it must fit (height)
• Aesthetics/architectural considerations – it must look ‚nice’ (eg. semi-circular)
• technology– construction
WHAT INFLUENCES THE FINAL GEOMETRY OF AN ARCH?
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Sardinia (fortess dated from the bronze age, Nuraghe „Su Nuraxi”, Barumini)
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• Roman Empire
• Sacred character+circle is easy to inscribe (eg. compass)
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
Pont du Gard (F)
Roman aqueduct(watercourse),
I. c. AC
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• Classical shapes still relevant for (almost) contemporary architecture
St. Josef church, Zabrze (PL)
Dominikus Böhm, 1931
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
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Tama Art University Library , Tokyo (JP)
Toyo Ito & Ass.
SasakiStructuralCons., 2007
Classical shapes-
Unexpectedstructuralsolution
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
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Tama Art University Library , Tokyo (JP) 2007
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Classical shapes-
„Traditional” structural model, non-traditional constructiontechnique
ÖKK Centre, Landquart (CH)
Bearth&Deplazes
Fanzun AG, 2012
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
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ÖKK Centre, Landquart (CH) 2012
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SEMI-CIRCULAR ARCHVAULTING TECHNIQUES, FORMWORK AND CENTERING
centering
With or without fomwork
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NUBIAN VAULTINGNO FORMWORK
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SEMI-CIRCULAR ARCHVAULTING TECHNIQUES, STEREOTOMY
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Structural aspects were strongly
considered early on
(though first empirically)
FORM FOLLOWS FORCEEMPIRICAL
• Stereotomy of the
straight-arch
• Straight arch: height vs span
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Rievaulx abbey, Yorkshire, XII. century. (GB)
Pointed arches (gothic)
empirical
FORM FOLLOWS FORCETHE HIGHER THE BETTER (MIGHTIER)
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Hanging model, chapel for the Colonia Güell,
Barceolna, 1898
Antoni Gaudi
Structural engineering (scientific approach)
• XVII. century Robert Hooke - concept
• XVIII. century Strength of materials,
structural analysis in the modern
engineering sense
• XIX. c. rediscovery of gothic +graphic static
FORM FOLLOWS FORCEEXPERIMENTS
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‚scientific’
• XX. century
Christkönig church, Bischofsheim (D), 1926
Dominikus Böhm
FORM FOLLOWS FORCETHE NOSTALGY OF THE TRUE FORM
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FORM FOLLOWS FORCEOR ELSE
KunstmuseumRavensburg (D), 2013
Lederer-Ragnarsdóttir-Oei
Ingenieurbüro
Schneider & Partner
‚scientific’
• XXI. century
– non-structural form
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FLYING BUTTRESSSUPPORTING STRUCTURES
BOLTÍVEK 44
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STATICS OF ARCHES
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ABUTMENTSTHRUSTING EACH OTHER
Pont du Gard (F)
Roman aqueduct,
I. sz.
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Triumphal arch III. c AC.
Volubilis (MR)
ABUTMENTSLOTS OF ROOM LOTS OF STONE= BUTTRESS
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#SIDENOTE2#CAN ADDITIONAL WEIGHT (E.G. INFILL, INCREASE OF THICKNESS) HELP A SLENDER ARCH IN DANGER?
YES NO
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#SIDENOTE2#CAN ADDITIONAL WEIGHT (E.G. INFILL, INCREASE OF THICKNESS) HELP A SLENDER ARCH IN DANGER?
YES NO
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L'église Saint-Pierre,
Chartres (F) XI-XIV.sz.
ABUTMENTSNO ROOM LOTS OF STONE= FLYING BUTTRESS
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FLYING BUTTRESSSTATICS
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Dome, Florence (I)
XIII-XV.c.
ABUTMENTSNO STONE, NO ROOM = IRON TIE-RODS
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COLUMNBUTTRESSING, CAPITAL, BRICKLAYING
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COLUMNCAPITAL, BRICKLAYING
Why is bricklayingimportant?
• Effect of shear
• Brick – non-isotropic material!
Orientation =>compressivestrenght of brick
Only 10-20% percent on theside!
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COLUMNBUTTRESSING
Sagrada Familia, Barcelona (E), 1882-, Antoni Gaudi
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WALLBUTTRESSING, BRICKLAYING
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#SIDENOTE3#HOW STRONG IS MASONRY?
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#SIDENOTE3#HOW STRONG IS MASONRY?
masonry steel [N/mm2]
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#SIDENOTE3#HOW STRONG IS MASONRY?
1-10 : 200masonry steel [N/mm2]
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LEMONSQUEEZERFORM AND FORCES OF VAULTS
BOLTÍVEK 60
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Does it work as
a shell or
series of arches?
• Only takes
compression
• Made of
blocks
• Thickness
FORCES
St. Johan Baptist chruch, Neu-Ulm (D), 1926, Dominikus Böhm
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GEOMETRIC CLASSIFICATIONSIMPLE VAULTS
(Elliptical)hemispherical
dome
sail vault(pendentives)
Barrel vault
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SIMPLE
St. Peter cathedral, Rome (I), XVI-XVII. c
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SIMPLE
Grand Central Oyster Bar, NY (USA), 1913, Rafael Guastavino (contractor)
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SIMPLE
St. Engelbert church, Köln (D), 1932, Dominikus Böhm
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COMPLEX
Groin/Rib/Cross vault
Pavilion vaultDome on
pendentives
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COMPLEX
St. Engelbert church, Köln (D), 1932, Dominikus Böhm
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COMPLEX
St. Johan Baptist church, Neu-Ulm (D), 1926, Dominikus Böhm
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FREE-FORM VAULT
Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
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STABILITYSTRUCTURAL ANALYSIS OF VAULTS
BOLTÍVEK 70
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VAULTS AS SHELLSFUNICULARS
Masonry is no-tension
material!
Shells are not neccessarily
compression only
structures
Mapungubwe National Park Interpretation Centre (ZA), 2009
Michael Ramage, John Ochsendorf, Peter Rich, James K. Bellamy, Philippe Block
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VAULTS AS SERIES OF ARCHES - CRACKSWHY SHOULD WE LET THE PANTHEON CRACK?
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ARCHES VS VAULTSSTRUCTURAL MODEL
Pantheon, Rome (I), II.c AC.
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SIMPLE VAULTSSTRUCTURAL ANALYSIS ORANGE SLICE VS SHELL MODEL
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[szeletelés az összetett formáknál]
COMPLEX VAULTSSTRUCTURAL ANALYSIS
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COMPLEX VAULTSSUITABLE STRUCTURAL MODEL (BUILDING)
Santa Maria del Mar, Barcelona XIV. c.
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GEOMETRY OF VAULTS
BOLTÍVEK 77
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WHAT INFLUENCES THE SHAPE OF A VAULT
• Statics, equilibrium- supports
• Functional requirements– maximal height+fireproof barrier eg. (slab)
• Aesthetics, architectural intention
• Contstruction technology – (centering, formwork)
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• Low height
• Flat vault-[El Escorial, XVI. c]
• Resulting thrusting forces (horizontal) are large!
FUNCTIONAL REQUIREMENTS+CONSTRUCTION TECHNOLOGY=FLAT VAULTS
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ECONOMICAL SOLUTION OF GOOD QUAILTY QUICKLYCATALAN VAULTING /TIMBREL VAULTING
• Flat and thin
• fireproof
• Complex geometry
• No formwork
• Optional reinforcement with steel
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CONSTRUCTION TECHNIQUECATALAN VAULTING
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Chapel, Colonia Güell, Barcelona (E), 1898 Antoni Gaudi
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Caputto Fruit Plant (UR), 1972, Eladio Dieste
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Earth Pavilion, London (GB), 2010, Michael Ramage, Peter Rich, Tim Hall
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Droneport,
15. ArchitecturalBiennale, Venice (I), 2016
Foster & Partners
ODB
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HORIZONTAL THRUSTBUTTRESSING VAULTS
BOLTÍVEK 86
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HORIZONTAL THRUST
Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
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STEREOTOMYRIBS/EDGES
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Age-old problem – role of the rib: ornamental orstructural/constructional
RIB VAULT OR SHELL
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VAULTSOF TODAY
BOLZOZATOK 90
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REDISCOVERY OF CATALAN-TILE VAULTING
• Due to the (3) oriented layers actsas a surfacestructure!
• Applicable tofreeform vaults,
• Current trends: digital formfindingand optimization
• Developingcountries: potentialcheap/plenty labor, scarce material
• Research, biennale
CONTEMPORARYVAULTING TECHNIQUES
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Mapungubwe National Park Interpretation Centre (ZA), 2009
Michael Ramage, John Ochsendorf, Peter Rich, James K. Bellamy, Philippe Block
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Earth Pavilion, London (GB), 2010, Michael Ramage, Peter Rich, Tim Hall
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Mock-up/test vault, ETH Zürich (CH), 2012, BRG
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15. Architectural Biennale, Venice (I), 2016, solano benítez
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Droneport, 15. Architectural Biennale, Venice (I), 2016, Foster & Partners, ODB
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Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
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BIENNALEDESIGNING AND CONSTRUCTING VAULTS
BOLTÍVEK 98
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Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
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Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
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Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
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THANK YOU FOR YOUR ATTENTION!