arches vaults - szt courses/6_special...statically determinate structure: 3-pin arch, if thickness...

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


Tama Art University Library , Tokyo (JP)

Toyo Ito & Ass.

SasakiStructuralCons., 2007

Classical shapes-

Unexpectedstructuralsolution


Tama Art University Library , Tokyo (JP) 2007

Classical shapes-

„Traditional” structural model, non-traditional constructiontechnique

ÖKK Centre, Landquart (CH)

Bearth&Deplazes

Fanzun AG, 2012


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

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?


masonry steel [N/mm2]


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


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

BIENNALEDESIGNING AND CONSTRUCTING VAULTS

BOLTÍVEK 98

Catenary Studies, Design week 2016, BME Department of Mechanics, Materials and Structures

https://vimeo.com/60064510

https://vimeo.com/60064510

THANK YOU FOR YOUR ATTENTION!

arches vaults - szt courses/6_special...statically determinate structure: 3-pin arch, if thickness...

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