Flying Buttresses • Openings and Spans • Bar Tracery and Linear Elements • Large Scale Construction and Transmission of Knowledge
HA2 Autumn 2005
Gothic Architecture: design and history
Outline
• Main design issues and innovations • Structural outline • Chronological development • Classical styles (France) • Outside the canon • Gothic in the UK • Case study: Burgos Cathedral
Gothic Architecture: design and history 2
Gothic Architecture: design and history Dimitris Theodossopoulos 1 HA2 Autumn 2005
Main design issues
• Definition – a sharp change from Romanesque? (St Denis 1130) • Major elements pre-existing (ribs and shafts, pointed arches, cross vaults) • Composition and scale • Light and height • Role of patrons (royal vs. secular foundations) and cathedral buildings • Strong technological input • European regional characteristics • Decline: decorative character and historical reasons
Gothic Architecture: design and history 3
Main design issues
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Gothic Architecture: design and history Dimitris Theodossopoulos 2 HA2 Autumn 2005
Technological innovations
• Dynamic composition • Dynamic equilibrium • Linearity – origin in Norman timber technology? • Role of the ribs (and shafts) • Spatial flexibility of cross vaults – use of pointed arch • Flying buttresses • Openings and spans • Bar tracery and linear elements • Large scale construction and transmission of knowledge
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The role of geometry
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Gothic Architecture: design and history Dimitris Theodossopoulos 3 HA2 Autumn 2005
Light
Contrast Durham Cathedral (1093-1133) and Sainte Chapelle in Paris (1240)
Gothic Architecture: design and history 7
Layout and behaviour
Nave (high) vaults: symmetrically supported by lateral walls and buttresses
Aisle (lateral) vaults: span between nave arcade and external wall
Ribs reinforce the intersection between the vaults (groins)
Gothic Architecture: design and history 8
Gothic Architecture: design and history Dimitris Theodossopoulos 4 HA2 Autumn 2005
Structural behaviour
Nave enclosed between the façade and the apse
Divided into regular bays, abutting each other longitudinally
Transverse thrusts counteracted by a system of flying buttresses
Rampant arches: lower tier (gravity), higher (wind)
Gothic Architecture: design and history 9
Failure pattern
Clerestory - natural light
Triforium and lateral wall passage
Cross-section fits haunches - not resting on vaults (porte-á-faux)
Nave’s weight carried with offset? Possible hinge
Balanced upper thrusts - weight carried vertically
Low stresses on base of piers
Gothic Architecture: design and history 10
Gothic Architecture: design and history Dimitris Theodossopoulos 5 HA2 Autumn 2005
Failure pattern
• Intrados: hinge line close to longitudinal vertex • Extrados: cracks parallel to edges
Serviceability limit: abutments’ displacement at 1/50 of transverse span
Failure observed at 1/20 of the span
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Development
• Vezelay • First experiments in 1130’s Domain Royal (France) St Denis, Paris (Abbot Suger) Sens (Arras, Noyon) • Durham (rib vaults) • Notre-Dame, Paris (in. 1163) • High Gothic Chartres (1194-1217) Bourges ( Reims Amiens (1220-28)
Gothic Architecture: design and history 12
Gothic Architecture: design and history Dimitris Theodossopoulos 6 HA2 Autumn 2005
Consolidation
• Rayonnant Gothic (1232-1270): Sainte-Chapelle, Beauvais • English Decorated (1250-1370): Lincoln, Exeter, Wells
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Consolidation
• German High Gothic Hallenkirche (Frauenkirche, Nuremberg) Cologne cathedral (in. 1248, fin. 19th c.)
Gothic Architecture: design and history 14
Gothic Architecture: design and history Dimitris Theodossopoulos 7 HA2 Autumn 2005
Outside France
East Europe: Germanic influences, decorative potential of structural elements (St. Vitus, Prague)
Norway: “timber” Norman architecture (Nidaros Cathedral, Trondheim)
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Italy
Santa Croce, Florence (Arnolfo di Basilica di San Francesco, Assisi 13th c. Cambio, 1294 -1442 )
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Gothic Architecture: design and history Dimitris Theodossopoulos 8 HA2 Autumn 2005
Spain & Portugal
• Direct influences from (south) France in Castille • Earlier cistersian influences (romanesque appearance, ribbed vaults, chapels on transepts) • “Hallenkirche” type in Catalonia • Fusion with islamic tradition • Main cases: Toledo cathedral (in. 1224) Burgos 1221-1267 (major influence) Barcelona (in. 1298) • Manuelin style in Portugal (XV c.): ornamental richness with Flamboyant elements (Jeronimos, Lisbon)
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Spain & Portugal
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Gothic Architecture: design and history Dimitris Theodossopoulos 9 HA2 Autumn 2005
Decline and revival
• French Flamboyant (1350-1520) • English Perpendicular (1330-1540) • German Sondergotik
• Collapse of Beauvais 1284
• Vasari: term Gothic • Gothic Revival and national styles (Viollet-le-Duc, Pugin)
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High Gothic
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Gothic Architecture: design and history Dimitris Theodossopoulos 10 HA2 Autumn 2005
Durham and the ribs
• 1093-1133 • Earliest high-level ribbed vaults in Europe, 25m height • Ribs Smooth finish of groins Interpretation of Norman timber architecture Timber-frame vocabulary Together with shafts, convey unitary approach to construction design • Careful balance of massive construction with voids • Flying buttresses!
Gothic Architecture: design and history 21
St Denis (1140)
• Abbot Suger (1122-1151) • Major renovations at apse • First conscious composition of load-bearing elements into a new style • Ribbed cross vaults enabled geometry of ambulatory and plan flexibility • Stonework as light skeleton: large stained glazing, integrating role of light
Gothic Architecture: design and history 22
Gothic Architecture: design and history Dimitris Theodossopoulos 11 HA2 Autumn 2005
Notre Dame, Paris
• Started 1163 • Large scale applications: total height 32 m • Round piers balanced with emphasis on vertical elements • Major application of flying buttresses • Lack of confidence of masons – unsuccessful illumination
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Chartres and its School
• The first “classic” gothic church (1194-1217) • Engaged shaft piers • Classic gothic sculpture at portal • Quadripartite vaults (subs. sexpartite): uniform character • Balanced cross-section
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Gothic Architecture: design and history Dimitris Theodossopoulos 12 HA2 Autumn 2005
The School of Bourges
• Started 1195 • 5-naves: follows Paris model • Arcade occupies most elevation • Smaller clerestory - lighting • Less hierarchy between parts • Normal transfer of thrusts • Less popular than Chartres (Normandy) • Influenced Beauvais?
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Amiens
• 1220-1288 • Perception of space through movement: Horizontal, towards Altar Vertical, proportions of elevation • Uninterrupted vertical shafts • Height: 42.30 m ; span: 12.15 m • Triforium lets light in • Gradual dissolution of elevation – turning point
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Gothic Architecture: design and history Dimitris Theodossopoulos 13 HA2 Autumn 2005
Beauvais
• Collapse 1284 • Nave height 68m • Maximum expression of Gothic verticality and experimentation • Reconstruction halted after subsequent tower collapse
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Beauvais
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Gothic Architecture: design and history Dimitris Theodossopoulos 14 HA2 Autumn 2005
Gothic in Britain
• Length: delicate balance between verticality and horizontality • Moderate scale: measured excitement, less spatial explorations • Clear structural logic • Monastic foundations: transepts and choirs • Flat east end • Periods Norman (1066-1190) Early English (1175-1265) Decorated (1250-1370) Perpendicular (1330-1540) Reformation
Gothic Architecture: design and history 29
Canterbury
• Reconstruction after fire 5/9/1174 till 1184 • Pioneering construction following Durham • Master-mason: William of Sens • Shrine of St. Thomas a Becket (+1170) • Choir: abrupt junction of piers to upper structure • Sexpartite vaults • Linearity emphasised by leaner ribs and Purbeck shafts
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Gothic Architecture: design and history Dimitris Theodossopoulos 15 HA2 Autumn 2005
Wells
• Construction 1186-1215 • The first English Gothic church • Modest scale (height 20.5 m) • Design based on pointed arches • Elegant use of shafts in piers (stone colour, proportions, light) • Stiff-leaf capitals • Horizontal emphasis – weak vertical articulation • Unique 3D treatment of screen-type façade
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Lincoln Cathedral
• Reconstruction (1192-1280) by St. Hugh after earthquake 15/4/1185 • Uniformly carried out scheme • Transepts and projections: effect of diffusion and lack of concentrated spatial effects • Linear pattern Carved and linear elaboration (Purbeck shafts) Improved verticality Extensive tierceron ribs, unified by ridge-rib
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Gothic Architecture: design and history Dimitris Theodossopoulos 16 HA2 Autumn 2005
Lincoln
Gothic Architecture: design and history 33
Lincoln
• English vocabulary • Inspirations from Canterbury • Height 25 m., tot. span 24 m • Proportions: vault too low, piers are slender and sparse • Unsatisfactory façade • Later innovations in vaulting and scale improvements at Angels Choir Clerestory and triforium Sharp intonations “Crazy” vaults
Gothic Architecture: design and history 34
Gothic Architecture: design and history Dimitris Theodossopoulos 17 HA2 Autumn 2005
Westminster abbey
• Norman church restructured 1245-69 by Henry III • Return to French influences (chevet, scale and proportions, triforium) and vaults (Lincoln more popular) • Bar window-tracery – skeleton becomes an infill • Transition to (Geometrical) Decorated • Ridge ribs • Segmental window as equilateral triangles
Gothic Architecture: design and history 35
Salisbury
• Construction 1220-1284 (spire 1380) • Great length (144 m), 6 times the width (24 m) • Projections and double transepts • Improved proportions enable lightness and elegance • Nave: horizontal lines too sharp • Mouldings highlight depth of elevation • Interior too perfect? • Linear emphasis on façade • Spire and external layout
Gothic Architecture: design and history 36
Gothic Architecture: design and history Dimitris Theodossopoulos 18 HA2 Autumn 2005
Perpendicular (1330-1540)
• Reaction to contemporary Flamboyant (1350-1520) • Classical precision in craftmanship • Preference for Hall Church layout and single volumes • Perpendicular mullions used to support glazing of free openings – required more horizontal transoms • Deeper springing of vaults and gradual integration of triforium to clerestory • Fan vaults: combination of (Anglo- Norman) corbelling and tierceron ribs
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Perpendicular - King’s College
• Tudor foundation 1446-1515 (John Wastell) • Fan vaults • Heavy transverse arch separating bays • Twelve rectangular bays (plan: 7.37 by 12.6 m) • Fan vaults Pendentive function of cone and stone laying Stiff spandrels and low bending stresses
Gothic Architecture: design and history 38
Gothic Architecture: design and history Dimitris Theodossopoulos 19 HA2 Autumn 2005
The Cathedral of Burgos
• Supported on slope of citadel hill and underground chapels • Latin cross in plan: Longitudinally enclosed and fixed by a façade incorporates deep buttresses and spires East end: ambulatory and chapel of the Constables of Castile is added ring of radial chapels at apse Two-level cloister braces SE quarter Similarly stiffened facades at transepts
Gothic Architecture: design and history 39
Plan
Gothic Architecture: design and history 40
Gothic Architecture: design and history Dimitris Theodossopoulos 20 HA2 Autumn 2005
Load-bearing elements
• Crossing tower: focal point of scheme supported on heavy pilasters (reconstruction after collapse in 1539) • Nave elevation: typical division • Nave arcade: pointed arch; tas-de-charge has a large offset • Top windows occupy most of clerestory but do not compromise the lateral stability of wall • Double tier of flying buttresses • Stone units: accurately dressed limestone (caliza de Hontoria) • Load-bearing capacity of the stone masonry in good condition
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External views
Gothic Architecture: design and history 42
Gothic Architecture: design and history Dimitris Theodossopoulos 21 HA2 Autumn 2005
Ambulatory
Gothic Architecture: design and history 43
Roof
Gothic Architecture: design and history 44
Gothic Architecture: design and history Dimitris Theodossopoulos 22 HA2 Autumn 2005
Nave
Gothic Architecture: design and history 45
Vaults
• Quadripartite ribbed cross vaults • Nave vaults span 5.3 x 10.4 m Longitudinal vertex emphasised by rib Vaults next to transept and façade have complex net of tierceron ribs Transverse vault is stilted - thrusts are applied with offset from springing • Aisle vaults: Span 6.3 x 5.3 m Transverse vertices are longer - a smooth curve was applied to reduce deflections • Transverse thrusts: contained by double flying buttresses capped by pinnacles
Gothic Architecture: design and history 46
Gothic Architecture: design and history Dimitris Theodossopoulos 23 HA2 Autumn 2005
Buttresses
Gothic Architecture: design and history 47
Construction history
Gothic Architecture: design and history 48
Gothic Architecture: design and history Dimitris Theodossopoulos 24 HA2 Autumn 2005
Upper structure
• Simulation as parabolic barrel vault running along axis of nave, stiffened by transverse vaults • Hoop stresses S22 are low • High thrusts are balanced by the flying buttresses • Central portion spreads outwards • The stiffer transverse web transmits horizontal deformation onto the wall - tension develops between vault and clerestory crown • Compression along straight vertex of transverse vault
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Upper structure
• Compression increasing at haunches indicate part of weight of vault is supported by ribs and springings • Thrust twists longitudinal web • Rib is crucial: guarantees good execution and continuity between webs • Sharp change in curvature stiffens adjoining webs and stops spread of high stresses between webs • The symmetrically supported nave cross vault functions as an assembly of four barrel vaults that form a common boundary along the groins • If ribs are weak, each web behaves as a cantilever - deflections increase towards keystone
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Gothic Architecture: design and history Dimitris Theodossopoulos 25 HA2 Autumn 2005
Flying buttresses
• High hoop compressive stresses at top edge and tension at bottom edge (abutment): indicators of good performance • Spandrel fill: provides a wider area for the application of the thrust • Counteraction exceeds thrust of vaults (upper tier) • Role of upper tier: contain thrusts developing due to wind
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Lateral wall
• Forces from upper structures are transmitted on triforium area mainly vertically • Low compressive forces at pier extension - maximum 1 N/mm2 • Sharp increase in compression at tas- de-charge transition- but maximum is 2.4 N/mm2
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Gothic Architecture: design and history Dimitris Theodossopoulos 26 HA2 Autumn 2005
Possible failure pattern
If wall not properly braced transversely during construction, nave’s weight is carried with offset
Area will rotate and function as a hinge: lateral wall bursts outwards at top and inwards above capital
If thrusts carefully balanced, weight of upper structure is carried to the ground
Normal stresses on piers are below crushing strength of masonry: stresses at base = 1 N/mm2
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Lower structure
• Vault contained between arcade and pier buttresses • Lateral thrusts are asymmetrically contained • Domical pattern: probably chosen intuitively to reduce bending • Nave arch fully stabilised by upper weight - mainly compression in hoop direction (max. 0.39 N/mm2) • Load twists the vault from adjacent vault - transverse rib stiffener is crucial • In-plane, shear deformation similar to nave
Gothic Architecture: design and history 54
Gothic Architecture: design and history Dimitris Theodossopoulos 27 HA2 Autumn 2005
Lower structure
• Domical layout: reduces deformations and enhances two-way behaviour • Diagonal ribs organically bonded into the webs, acting as stiffeners • High tensile forces: cracks anticipated on apex of the edge on the wall and at front haunches • Cracks along longitudinal vertex should not develop • Inspections show there have been repairs at the haunches - the wind has activated the flying buttresses and consequently reduced torsion of the bay
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Conclusions
• Successful original design: stresses overall below strengths; deflections low and no signs of instability • Continuity of the fabric is a fundamental assumption: update of support conditions of the main load-bearing elements using survey data might be required in order to improve the knowledge of the behaviour and safety of the building • The model highlighted the interaction between the upper and lower structure • The rib plays a key role in the execution of the difficult intersection between the webs and the efficient distribution of the loads within the entire vault according to a two-way pattern • This FE model can gauge more simplified modelling strategies for the building or parts of it, while more complex loading conditions or the origin of some more specific defects can be examined.
Gothic Architecture: design and history 56
Gothic Architecture: design and history Dimitris Theodossopoulos 28 HA2 Autumn 2005
Summary
• Main design issues and innovations • Structural outline • Chronological development • Classical styles (France) • Outside the canon • Gothic in the UK • Case study: Burgos Cathedral
Gothic Architecture: design and history 57
References
• Acland, J. H. 1972. Medieval structure: the gothic vault. Toronto University Press • Clifton-Taylor, A. (1986). The Cathedrals of England. Thames & Hudson • Fitchen, J. 1961. The construction of Gothic cathedrals. Clarendon Press • Fletcher, B. A history of Architecture. (Background: building techniques and processes) • Leedy, W. C. (1980). Fan vaulting. Scolar press, London. • Stalley, R. 1999. Early medieval architecture. Oxford History of Art, Oxford • Theodossopoulos, D., Sinha, B. P., Usmani, A. S. 2003. Case Study of the Failure of a Cross Vault: Church of Holyrood Abbey. J. Architectural Engrg, ASCE, vol. 9(3), pgs. 109-117. • Theodossopoulos, D. (2004). Structural scheme of the Cathedral of Burgos, Proc. Int. Conf. Struct. Analysis Hist. Constructions, Padua; Modena, Lourenço & Roca eds., Taylor & Francis, London, pgs. 643-652, ISBN 04-1536-379-9
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Gothic Architecture: design and history Dimitris Theodossopoulos 29