ARCHESVAULTS
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
THE GOOD, THE BAD..FORM AND FORCES OF ARCHES
BOLTÍVEK 3
MASONRY NO-TENSION MATERIALVAULTS MADE OF VOUSSOIRS
LOADBEARING-CAPACITY OF ARCHESTHE THRUST LINE
THRUST LINEThe way compressive
forces follow to the
supports
LIMITED TENSILE CAPACITYNormal to
sections/mortar
FUNICULAR STRUCTURES - BEST FORM
2D
3D
BENDING-
COMPRESSION TENSION
ARCH
SHELLS (VAULTS)
Maritime Museum, Barcelona
LEGOING ARCHITECTURE REUSABLE ELEMENTS
DESIGN - THEORY
BOLTÍVEK 9
‚As hangs the flexible line, sobut inverted will stand therigid arch.’
Robert Hooke (1635-1703)
Gateway arch, St. Louis –Eero Saarinen, 1947-1965
St. Paul cathedral, London,
XVII. century.
Christopher Wren
Taq Kasra, Ctesiphon (today Iraq) – 3-6.century AC
Hanging model for the chapel of Colonia Güell, Barcelona
Antoni Gaudi, 1898
John. A. Ochsendorf, MIT
STRUCTURAL ANALYSIS- STABILITYANALYSIS OF MASONRY ARCHES
BOLTÍVEK 16
• Geometry (eg. semi-circular)
• Loading
• (Material quailty)
• Support conditions
FACTORS INFLUENCING THE INTERNAL FORCE DISTRIBUTION OF ARCHESSEARCHING FOR THE THRUST LINE
#SIDENOTE# SUPPORTING ARCHES
(SEMI-CIRCULAR) ARCHSTRUCTURAL MODEL
Arch on fixed supports: indeterminate structure
Inifinetely many admissible thrust line
(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
• 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)
(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
• 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
ASSYMETRICAL LOADINGSTRUCTURAL MODEL
GEOMETRY OF ARCHES
BOLTÍVEK 25
LOADING-THRUST LINE-ARCH: FORM FINDING
• Parabola
• catenary
• semi-circle
THRUST LINENECESSARY THICKNESS OF THE ARCH
• Straight arch • Semi-circular arch • Pointed arch
• 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?
Sardinia (fortess dated from the bronze age, Nuraghe „Su Nuraxi”, Barumini)
• 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
• Classical shapes still relevant for (almost) contemporary architecture
St. Josef church, Zabrze (PL)
Dominikus Böhm, 1931
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
Tama Art University Library , Tokyo (JP)
Toyo Ito & Ass.
SasakiStructuralCons., 2007
Classical shapes-
Unexpectedstructuralsolution
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
Tama Art University Library , Tokyo (JP) 2007
Classical shapes-
„Traditional” structural model, non-traditional constructiontechnique
ÖKK Centre, Landquart (CH)
Bearth&Deplazes
Fanzun AG, 2012
AESTHETICS +TECHNOLOGY= SEMI-CIRCULAR ARCH
ÖKK Centre, Landquart (CH) 2012
SEMI-CIRCULAR ARCHVAULTING TECHNIQUES, FORMWORK AND CENTERING
centering
With or without fomwork
NUBIAN VAULTINGNO FORMWORK
SEMI-CIRCULAR ARCHVAULTING TECHNIQUES, STEREOTOMY
Structural aspects were strongly
considered early on
(though first empirically)
FORM FOLLOWS FORCEEMPIRICAL
• Stereotomy of the
straight-arch
• Straight arch: height vs span
Rievaulx abbey, Yorkshire, XII. century. (GB)
Pointed arches (gothic)
empirical
FORM FOLLOWS FORCETHE HIGHER THE BETTER (MIGHTIER)
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
‚scientific’
• XX. century
Christkönig church, Bischofsheim (D), 1926
Dominikus Böhm
FORM FOLLOWS FORCETHE NOSTALGY OF THE TRUE FORM
FORM FOLLOWS FORCEOR ELSE
KunstmuseumRavensburg (D), 2013
Lederer-Ragnarsdóttir-Oei
Ingenieurbüro
Schneider & Partner
‚scientific’
• XXI. century
– non-structural form
FLYING BUTTRESSSUPPORTING STRUCTURES
BOLTÍVEK 44
STATICS OF ARCHES
ABUTMENTSTHRUSTING EACH OTHER
Pont du Gard (F)
Roman aqueduct,
I. sz.
Triumphal arch III. c AC.
Volubilis (MR)
ABUTMENTSLOTS OF ROOM LOTS OF STONE= BUTTRESS
#SIDENOTE2#CAN ADDITIONAL WEIGHT (E.G. INFILL, INCREASE OF THICKNESS) HELP A SLENDER ARCH IN DANGER?
YES NO
#SIDENOTE2#CAN ADDITIONAL WEIGHT (E.G. INFILL, INCREASE OF THICKNESS) HELP A SLENDER ARCH IN DANGER?
YES NO
L'église Saint-Pierre,
Chartres (F) XI-XIV.sz.
ABUTMENTSNO ROOM LOTS OF STONE= FLYING BUTTRESS
FLYING BUTTRESSSTATICS
Dome, Florence (I)
XIII-XV.c.
ABUTMENTSNO STONE, NO ROOM = IRON TIE-RODS
COLUMNBUTTRESSING, CAPITAL, BRICKLAYING
COLUMNCAPITAL, BRICKLAYING
Why is bricklayingimportant?
• Effect of shear
• Brick – non-isotropic material!
Orientation =>compressivestrenght of brick
Only 10-20% percent on theside!
COLUMNBUTTRESSING
Sagrada Familia, Barcelona (E), 1882-, Antoni Gaudi
WALLBUTTRESSING, BRICKLAYING
#SIDENOTE3#HOW STRONG IS MASONRY?
#SIDENOTE3#HOW STRONG IS MASONRY?
masonry steel [N/mm2]
#SIDENOTE3#HOW STRONG IS MASONRY?
1-10 : 200masonry steel [N/mm2]
LEMONSQUEEZERFORM AND FORCES OF VAULTS
BOLTÍVEK 60
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
GEOMETRIC CLASSIFICATIONSIMPLE VAULTS
(Elliptical)hemispherical
dome
sail vault(pendentives)
Barrel vault
SIMPLE
St. Peter cathedral, Rome (I), XVI-XVII. c
SIMPLE
Grand Central Oyster Bar, NY (USA), 1913, Rafael Guastavino (contractor)
SIMPLE
St. Engelbert church, Köln (D), 1932, Dominikus Böhm
COMPLEX
Groin/Rib/Cross vault
Pavilion vaultDome on
pendentives
COMPLEX
St. Engelbert church, Köln (D), 1932, Dominikus Böhm
COMPLEX
St. Johan Baptist church, Neu-Ulm (D), 1926, Dominikus Böhm
FREE-FORM VAULT
Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
STABILITYSTRUCTURAL ANALYSIS OF VAULTS
BOLTÍVEK 70
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
VAULTS AS SERIES OF ARCHES - CRACKSWHY SHOULD WE LET THE PANTHEON CRACK?
ARCHES VS VAULTSSTRUCTURAL MODEL
Pantheon, Rome (I), II.c AC.
SIMPLE VAULTSSTRUCTURAL ANALYSIS ORANGE SLICE VS SHELL MODEL
[szeletelés az összetett formáknál]
COMPLEX VAULTSSTRUCTURAL ANALYSIS
COMPLEX VAULTSSUITABLE STRUCTURAL MODEL (BUILDING)
Santa Maria del Mar, Barcelona XIV. c.
GEOMETRY OF VAULTS
BOLTÍVEK 77
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)
• Low height
• Flat vault-[El Escorial, XVI. c]
• Resulting thrusting forces (horizontal) are large!
FUNCTIONAL REQUIREMENTS+CONSTRUCTION TECHNOLOGY=FLAT VAULTS
ECONOMICAL SOLUTION OF GOOD QUAILTY QUICKLYCATALAN VAULTING /TIMBREL VAULTING
• Flat and thin
• fireproof
• Complex geometry
• No formwork
• Optional reinforcement with steel
CONSTRUCTION TECHNIQUECATALAN VAULTING
Chapel, Colonia Güell, Barcelona (E), 1898 Antoni Gaudi
Caputto Fruit Plant (UR), 1972, Eladio Dieste
Earth Pavilion, London (GB), 2010, Michael Ramage, Peter Rich, Tim Hall
Droneport,
15. ArchitecturalBiennale, Venice (I), 2016
Foster & Partners
ODB
HORIZONTAL THRUSTBUTTRESSING VAULTS
BOLTÍVEK 86
HORIZONTAL THRUST
Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
STEREOTOMYRIBS/EDGES
Age-old problem – role of the rib: ornamental orstructural/constructional
RIB VAULT OR SHELL
VAULTSOF TODAY
BOLZOZATOK 90
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
Mapungubwe National Park Interpretation Centre (ZA), 2009
Michael Ramage, John Ochsendorf, Peter Rich, James K. Bellamy, Philippe Block
Earth Pavilion, London (GB), 2010, Michael Ramage, Peter Rich, Tim Hall
Mock-up/test vault, ETH Zürich (CH), 2012, BRG
15. Architectural Biennale, Venice (I), 2016, solano benítez
Droneport, 15. Architectural Biennale, Venice (I), 2016, Foster & Partners, ODB
Armadillo Vault, 15. Architectural Biennale, Venice (I), 2016, BRG
BIENNALEDESIGNING AND CONSTRUCTING VAULTS
BOLTÍVEK 98
Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures
https://vimeo.com/60064510
THANK YOU FOR YOUR ATTENTION!