"Gothic" Construction in Ancient Greece Author(s): Jacques Heyman Reviewed work(s): Source: Journal of the Society of Architectural Historians, Vol. 31, No. 1 (Mar., 1972), pp. 3-9 Published by: University of California Press on behalf of the Society of Architectural Historians Stable URL: http://www.jstor.org/stable/988722 . Accessed: 30/01/2012 03:56

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http://www.jstor.org "Gothic" Construction in Ancient Greece

JACQUES HEYMAN University of Cambridge

THE FACT THAT ancientGreek and Gothicarchitecture are,visually, so obviouslydistinct leads to the ideathat the masonrystructure behaves in differentways in the two styles.However, an examinationof the mechanicsof ma- sonryconstruction does not supportthis assumption. This is not to imply thatancient Greek and Gothicarchitects had thesame view of theirbuildings; indeed, neither is likelyto havethought of structurein a way thata modernstructural engineerwould considerrelevant. Ruskinobserved "that the principal distinctions between existingstyles of architecturedepend on theirmethods of roofingany space,as a window or door for instance... ; thatis to say, that the characterof Greekarchitecture ... dependson its roofinga spacewith a singlestone laid from Fig. I. Stone lintel (from Ruskin). side to side ... ; and the characterof Gothicarchitecture dependson its roofingspaces with pointedarches ."* Thetype of "Greek"lintel Ruskin had in mindis illustrated... by his own sketch(Fig. I). Ruskinseems to makea in Although comparison purely Fig. 2. A brick plate-bande(from visualterms between Greek and Gothic,it is cleara little Ruskin). laterthat he is thinkingalso of the structuralfunctions of thetwo Otherwriters make a more "transla- styles. explicit contrast,of course,a Gothicarch thrusts aswell as fromvisual to structural for sideways tion" interpretation; example, down. Fletcherdefines and Gothic HenriFocillon writes that (Banister Romanesque "theGreeks opposed the action as arcuated traceable to the of in styles, finally Etruscans.) gravity thevertical direction only."2 Banister Fletcher Ruskininsists that: givesa full statementof structuralfunction when he writes that"Greek architecture was columnarand tra- theGreek system, considered merely as a pieceof construction,is essentially weakand with beated a Thusthe massivestone lintels barbarous,compared thetwo others[Roman and (trabs= beam)."3 of, Forinstance, in thecase of a windowor door, such for a Greek are to act as beams Gothic]. large example, temple supposed asfig. I, if youhave at your disposal a single large and long stone betweenadjacent columns, and to transmitpurely vertical you mayindeed roof it in theGreek manner, as you have done loadsto thosecolumns and thenceto the foundations.By here,with comparative security; but it is alwaysexpensive to ob- tainand to raiseto theirplace stones of thislarge size, and in many J. Ruskin,Lectures on Architectureand Deliveredat Edin- placesnearly impossible to obtainthem at all: and if youhave not I. Painting such andstill insist the in the Greek burghin November1853 (London, 1907), p. II. stones, uponroofing space 2. H. Focillon, TheArt of the West,2 vols. (London, 1963), I, 67. way,that is to say,upon having a squarewindow, you must do it 3. SirBanister Fletcher, A Historyof Architectureon the ComparatiPe bythe miserably feeble adjustment of bricks ... [Fig.2]; you can- Method,17th ed. (London, 1961), p. 93. notbut see in a momentthat this cross bar is weakand imperfect. 3 4 Thus Ruskin is making structural as well as aesthetic judgments, although his statementthat the Greek system is weak and the plate-bandemiserably feeble is, in fact, mere assertion. The square form offends Ruskin's eye and the form that of a it. pointed (as, explicitly, leaf) delights Fig. 3. Iron "reinforcement"of Viollet le Duc expressesvery similar structuralviews in architraveof Propylaea, Athens his dictionary; he devotes half a page to the plate-bande, (after Dinsmoor, "Structural Iron..."). twice calling it an "appareilvicieux."4 This, however, is by contrastwith the Greeklintel: "LesGrecs n'admettaient pas l'arc, et s'ils avaient"i franchir un espace entre deux piliers, deux pieds-droits ou deux colonnes, ils posaient sur les points d'appuiverticaux un monolithe horizontal."Viollet le Duc is particularlyupset by the dishonesty of the late eighteenth- and nineteenth-centurypractice of concealing iron barswithin the masonry to form the true and effective structure (e.g., the Madeleine, the Panth6on): "Les archi- tectes du moyen age, on le comprend, ne pouvaient s'as- treindre"a mentir de cette sorte aux principesles plus vrais et les plus naturelsde la construction,et c'est pour cela que plusieursles considererentcomme des gens naifs." However, the Greeks did, in fact, themselves use con- cealed iron in their masonry,5 although the use was only occasional.The matterhas given rise to some controversy,6 but it seems fairly clearthat the Greekiron cannot properly be considered as reinforcement in the modern sense. In Fig. 4. Propylaea,Athens, reconstructed (photo: author). some instances it may have slightly relieved stresses (but does so no longer, since it has long since rustedaway); more This form of construction is as ingenious as it is mis- usually it served some sort of simplifying constructional directed. Although the stressesresulting from the bending function, from a of simple keying together masonry (the moment would be reduced, tensile stresseswould still be Theban treasury,Delphi) to a kind of permanentfalsework present,and stone is a materialweak in tension. In the pres- (as at the Temple of Zeus, Agrigento; see below). ent state of the Propylaea (Fig. 4) it will be seen that, de- The Propylaea at Athens (Mnesicles,437 B.C.)is one of spite the precautions, at least two of the architravesare the buildings which originally had concealed iron. Each broken right through at their centers of span. To be sure, architraveis composed of two marble beams 5o cm thick this fracturemay have occurredas a result of the iron rust- and 8o cm high, spanning typically about 3.6 m between ing away, with the load of the marble ceiling beams thus the centers of supporting columns; the clear span between being imposed directly on the architraves.The history of abaci is, of course, less than 3.6 m. These twin architraves the fracturesis, however, unimportant;and, as will be seen, were channelled out on their top faces, and an iron bar, the fracturesthemselves are not of structuralimportance. about m and of section about 75 mm X mm 1.6 long IIS Ruskin notes a similar fracture in Edinburgh, and de- was apparentlyinserted to spreadthe load (Fig. 3). Suppos- scribes "the great church with the dome, at the end of ing the structuralaction of the architraveto be that of a George Street," whose "huge horizontal lintel above the beam in bending, then the introduction of the iron bars door is alreadysplit right through." It might be naturalto would reduce the value of the maximum bending moment suppose that such splits are a sign of danger, or to believe in the marble beams to one-half. something approaching with Pol Abraham that cracks are "signes avant-coureurs in 4. E. E. Viollet le Duc, Dictionnaireraisonne' de l'architecturefranfaise de la ruine,"7but these beliefs are not supported any way du XIe au XVIe siecle,Io vols. (Paris,1858-1868), vrI, 207. by modern structuralanalysis. Indeed, I have recently ar- 5. W. B. Dinsmoor, "StructuralIron in Greek Architecture," gued "that the crackedstate is the naturalstate of masonry, AmericanJournalof Archaeology (2nd ser.), xxvI (1922), 148. 6. R. A. Jewett, "StructuralAntecedents of the I-beam, I8oo- 185o," Technologyand Culture, vim (1967), 346. For a discussionby H. Dorn, see Technologyand Culture, Ix (1968),415, with a response 7. Pol Abraham, Violletle Duc et le rationalismemedieval (Paris, by Jewett, 419, and rejoinderfrom Dorn, 427. 1934), p. 8. :5

Fig. 6. Collapsemechanism for voussoirarch.

Fig. 7. Stableposition for an imperfectlyfitted plate-bande. Fig. 5. Temple of Zeus, Athens (photo: author). forcesbetween two adjacentportions of masonryare so althoughthe cracksmay be so smallas to be invisible,or be high thatthere is no dangerof slidingfailure; this assump- closedby the elasticityof the stone."' tion will usuallybe satisfied,although it is possibleto find A very visiblefracture is shown in Figure5, wherethe practicalcounterexamples. Further, stresses in masonry architravehas sagged slightly to reveala wedge-shaped constructionare usually so smallthat there is no dangerof crackat the centerof span (Templeof Zeus, Athens,174 crushingof the material. B.C.and later). There is no questionof thisstone architrave Certaintheorems of structuralbehavior can be proved actingin any senseas a lintelbeam. The mode of actionis within the frameworkof theseassumptions. For example, clear;the two halvesof the architravemust thrust against the demonstrationthat it is possibleto find anythrust line, eachother at theirpoint of contactat midspan,and they are which,for a givenloading, lies wholly within the masonry, supportedin some way on the tops of the two columns. gives completeassurance that the structureis stableunder The architraveis, in fact,an elementaryplate-bande consist- that loading,and that there is no possibilityof collapse. ing of two stonesonly, and a more precisedescription of Conversely,to demonstratethat a structureis unstable,it is the structuralforces will be furnishedby a study of the necessaryto determinea correspondingmechanism of col- plate-bande. lapse.Such a mechanismmust involve failure at morethan one point of the structure,as may perhapsbe madeclear froma considerationof the simplevoussoir arch (Fig. 6.) If Elsewhere,I have recently discussed the behavior of masonry thepoint load increases sufficiently in intensity,then hinging structureson theassumption that it is impossibleto transmit actionat four cross-sectionswill permita mechanismmo- tensileforces from one portionof thestructure to thenext.9 tion andlead directlyto collapse. That is, these studieshave been concernedwith what is Fourhinges are necessary for the collapseof anyarchlike essentiallya Gothic type of construction,in whichrelatively structure;three hinges will not permitunrestricted collapse. smallstones are assembledeither dry or with such weak Thusthe plate-bande (Fig. 2) can sagwith perfectsafety to mortarthat tensioncannot be developed.For sucha ma- the positionof Figure7, shouldthe supportingwalls move sonrystructure to be stable,it mustbe capableof develop- apartslightly; this is, of course,the preciseconfiguration of ing a line of thrust,in equilibriumwith its own weightand the architraveof the Temple of Zeus, Athens (Fig. 5). anyexternal loading, which lies wholly within the masonry, Thereis, in fact,no arrangementof hingepoints in the up- so thatcompressive forces alone are transmitted from one per andlower facesof theplate-bande which would consti- stoneto thenext. The assumption is madethat the frictional tutea mechanismof collapse.The conclusionmust be that, no matterwhat the loading, and providing the abutmentsdo not so much as to the whole to 8. J. Heyman, "On the RubberVaults of the Middle Ages, and spread permit plate-bande Other Matters,"Gazette des Beaux-Arts, LxxI (1968), 177. "snapthrough," this miserablyfeeble adjustment of bricks 9. J. Heyman, "The Stone Skeleton,"InternationalJournal of Solids can nevercollapse. Ultimate failure will only occurwhen and "On the Structures,11 (I966), 249;J. Heyman, RubberVaults," the is increasedso enormouslythat p. 177; and J. Heyman, "The Safety of MasonryArches," Interna- superimposedloading tionalJournal of MechanicalSciences, xI (1969), 363. crushingoccurs of the material. 6

The forces acting on a plate-bandemay be determined havior of the monolith. The thrust line of Figure 8(b) is a from the sketch of Figure 8(a); the overall depth of the arch most unlikely state for an unbroken architrave,but it is a is D, and it spans between two rigid abutment walls dis- possibleequilibrium state. Providing that the thrustH can be tance L apart.A parabolicthrust line is shown lying wholly developed (by adjacent architraves,but see below), then within the masonry;this shapeof thrustline will equilibrate just as the plate-bandecan never collapse, so also can the ar- the uniform self-weight W of the arch, for any value of the chitrave never collapse. The state of Figure 8(b) is not so rise h of the parabola.Simple staticalconsiderations for this foolish or unlikely should the architravebe broken (Fig. 5). thrustline lead immediately to the equation H - WL/8h. The argumentsof the previous paragraphsreally state no That is, the plate-bandemust be supportedoff the abutment more than that it would be wise, in analyzing the stability walls by vertical forces W/2 as shown, and also by horizon- of a Greek trabeatedstructure, to assume that all the ma- tal thrustsH, whose value is inversely proportional to the sonry is cracked.If a complete and satisfactoryanalysis can height h of the parabola.Thus the plate-bandepresses down be made for the cracked structure,then this is a complete on its supports and also thrustsoutwards. proof that the original structure, cracked or not, is also If the supports give way slightly under the thrust, then stable. hinges will open (Fig. 7). Since the thrust must still be transmittedwithin the masonry, the thrust line must pass through the hinge points, and its position is determined With the Temple of Aphaia, Aegina, 490 B.C. (Figs. 9, Io), uniquely, Figure 8 (b); the correspondingvalue of the hori- a "safe"system of forceswill firstbe derivedfor the existing zontal component H of the abutment thrust is the smallest possible to maintain equilibrium (since the height h of the parabolais the largest possible). This thrust line must, of necessity, be that obtaining in the broken architraveof the Temple of Zeus, Athens (Fig. 5). For an unbroken architrave,there is, of course, the possi- bility of some tension being developed; the architrave might actually behave as a beam in bending, and exhibit nothing correspondingto the thrustline for the plate-bande of Figure 8 (b). It is at this point that the structuraltheorems concernedwith masonry can be introduced,in order to ob- tain a safe analysis for the architrave. Figure 8(b) will be taken to representa monolithic architrave,but which has been cut, hypothetically, into parallel voussoirs; for the of the monolith has been a purpose analysis, replaced by Fig. 9. Temple of Aphaia, Aegina (photo: author). geometrically similarplate-bande. Since the plate-bandehas been shown to be a safe structure,in the sense that it can stably supportits own weight and any superimposedloads, then a fortiori the original monolith is also safe. The cuts turning the architraveinto a flat arch can only have weak- ened the original structure. Thus it is not necessary (although it may be of interestin other connections) to determine the actual mode of be-

w w

H ~~ h D/D H H w/.4

L 7L (a) (b)

Fig. 8. Theplate-bande: (a) possibleline of thrust,and (b) limiting Fig. io. Temple of Aphaia,Aegina. Restoredeast elevation (from line of thrust. BanisterFletcher). 7 structure.It will be seen from the dimensions noted (Fig. The corner columns are clearly the most critical; Figure i i) that the intercolumniationis reducedfor the end span;as 13(a) shows the column on the southeast corner, and an a result, the last architravespans only about 1.25 m clear assessmentwill be made of its tendency to overturn. The between abaci ratherthan the 1.43 m of the internal spans. weight of the column, together with the "dead"weight of Assuming the architravesto be cracked,then lines of thrust the portion of the architravesupported directly from the for the unsupportedmasonry can be sketched (Fig. 12). The abacus,is about 8.3 t. The plan view shows the two thrusts architravesmeasure approximately 850o mm x 850omm (and acting at abacuslevel, one from the architraveon the east are, as usual, in two halves); the weights of unsupported elevation, and one from the south elevation. Thus the cor- plate-bande(Fig. 12) have been calculatedassuming a unit ner column is acted upon by a combined horizontal thrust weight for the limestone of 2000 kg/m3. of 0.33 42= 0.47 t in the southeasterlydirection. The horizontal thrustsin Figure 12 are the values of the Due to this thrust, the vertical reaction at the column quantity H= WL/8D shown in Figure 8 (b). It will be seen base (io.i t) will shift through some distance,say e. When that, of the six columns in the east elevation, the central the value of e just reachesthat of the radius of the column two are exactly in balance, since the horizontal thrusts of (0.54 m), then the column will be on the point of over- 0.43 t (I tonne equalsiooo kg) canceleach other. (Had there turning; if e is less than this value, the column will be stable. been eight columns in the elevation, as in the Parthenon, The overturning tendency is partiallycounteracted by the then the four central columns would have been exactly in vertical loads (0.90 t) from the architraves,acting at an balance,providing that the intercolumniationswere equal.) effectiveleverarm of o.58 /2= 0.41 m. By taking moments The first internal column on either side, however, has a about the base of the column, the value of e may be found slight out-of-balance horizontal thrust at abacus level of from the equation o.Io t. The corner columns are the worst in this respect; an Io.I e = (0.47) (5.26) - 2(0.90) (0.41) out-of-balance force of o.33 t is shown (Fig. 12). - 2.47-0.74, Providing these horizontal thrustscan be developed, the or e = 0.17 m. architravesthemselves will be completely safe. Stability of Thus the line of thrustfor the corner column lies very com- the whole structurewill be assured,therefore, if it can be fortably within the column, being eccentricby only 17 cm shown that the columns can resistthe out-of-balance forces. at the base where the radius is 54 cm.

ot 0-90 t O*90t I IB8t '033t 1-25 1?l-51-43 I•*t 116-0333t c'J 8-3t 9-8t

242 20 260 1'08 (a) (b)

I •r

Fig. 11. Temple of Aphaia,Aegina. Leadingdimensions. 13*4t 033t I-81t 2.07t 0-O33t

\i 0O33t1 Si/ 'O*33t \43t o4t 0-58 1*25 I*-43 Fig. 13. Temple of Aphaia,Aegina: (a) forces on Fig. 12. Temple of Aphaia,Aegina. Possibleforces in existing southeastcolumn, and (b) forcesdue to full archi- architrave. trave. 8

This analysisgives a safe estimate of the presentbehavior would be assuredfinally only becausethey could act also as of the southeastcorner column (Fig. 9). The addition of a plate-bandestransmitting purely compressive forces. second course of masonry to make up the frieze can only There is, in fact-and purely from the point of view of improve the safety of the structure (some of the frieze is in structural action-no clear distinction between what is place at the northeastcorner). From the analysisof the p late- thought of as Greek architectureand what is thought of as bande(Fig. 8), it will be seen that, if the depth D is doubled, Gothic. Greek appearsto be monolithic, but is stable only then the value H of the horizontal thrust will remain un- because the monoliths can be safely broken into Gothic- changed, since the value of the self-weight W is also dou- sized building blocks. Any structuraldefinition of Gothic bled. Thus in Figure 13(b) the vertical loads are increased might therefore be expected to apply also to Greek con- comparedwith those markedin Figure 13(a), but the hori- struction. zontal thrustsare the same. The new equation for comput- Choisy defines Gothic in terms of the rib vault and the ing the eccentricity e of the thrust line at the base of the. flying buttress,and rejectsthe pointed arch as unimportant; column is characteristically,he startshis discussionby noting that the 13.4 e = 2.47 - 1.49, materialsavailable (as for Romanesque) were small pieces " or e = 0.07 m; of Stone: "c'est l'aide de moellons et de pierres presque that is, the thrust line is eccentric by a mere 7 cm. toujours de petit 6chantillon que furent 6levies nos cath6- The final addition of cornicesand pediment will improve drales."'0Thus Gothic is the art of building large structures the situation still further, and it is likely that a final thrust out of small fragments. line could be found which was almost truly concentric at Now a structurebuilt of small stones must of necessity the base.The reductionof the intercolumniationfor the end achieve stabilityby some sort of arching action; if a space is spanscertainly helps here, but, in fact, the corner columns vaulted, then the resulting structurewill thrust sideways, at Aegina would have been quite stable under a horizontal and will requirebuttressing. The rib is a visual reflection of thrust of 0.43 t (Fig. 12) instead of the reduced value of the lateralthrust of the vault; the flying buttressis the effec- 0.33 t. However, the visual impressionof stabilityconferred tive counterbalanceto this thrust. The presence of flying by a reduction in intercolumniation for the end spans is buttresseswill always indicate a masonry ratherthan a tim- certainly confirmed by the structuralanalysis, and the de- ber vault ("voyez Notre-Dame du c6t6 du chevet: qui donc vice was often used (e.g., the Parthenon). pourra dire que ce n'est pas la un monument 6taye?").11 A purely visual use of the device may be found in the However, Choisy's twin essencesneed not be insisted doubled end pilastersof the Banqueting House, Whitehall upon too literally. King's College Chapel has neither rib (Inigo Jones, I619); these pilastershave no structuralfunc- vaults nor flying buttresses,but is completely and undenia- tion (a comment which can be enlarged to embrace much bly Gothic; the fan vault thrustsout (perhapswith less force of Renaissancearchitecture) but neverthelessdo reflect an than a rib vault),12and the thrustis absorbeddirectly in the original structural purpose. For a Gothic example of a main buttresses.It is the thrust and the counterthrustthat structuralsolution of the problem, we may note the arcades are the inescapable features of masonry construction, of the Doge's Palace at Venice (1309 and later); here, the whether Gothic or Greek. corner column is considerablyenlarged in diameterto con- In small buildings (the Propylaea and the Parthenon at fer stability against the overturning horizontal thrusts,but Athens, the temple at Aegina) the Greek architects used the visual effectis marredby the presenceof tiesbetweenthe monolithic architravesto span between monolithic abaci, arches. and this "standard"form of constructionhas led to the no- tion of certain structuralprinciples to which Greek archi- tects subscribed, among them the idea that the action of These calculationsshow that a building of the proportions gravity is opposed "in the vertical direction only." of the Aegina temple, composed of cracked masonry, In the Temple of Zeus, Agrigento (Theron, 470 B.c., un- would be stable. From the preceding remarks,the conclu- completed), the clearspan between the abaciof the half col- sion must be that the original temple, cracked or not, was umns was over 3.5 m, the columns themselvesbeing at 8 m also stable. Destruction (apartfrom deliberatedestruction) would then be causedonly by decay of the masonry, or by some cataclysm such as a severe earthquake.A mild earth Io. A. Choisy, Histoirede l'architecture, 2 vols. (Paris,1899), II, 259. Elementset theoriede l'architecture,4 4th ed. tremor, some settlement, would do no I . J. Guadet, vols., perhaps causing n.d.), 323. more than crack the stonework. Whether or not the (Paris, m, origi- 12. J. Heyman, "Spiresand Fan Vaults," InternationalJournal of nal architravesacted as beams in bending, their survival Solidsand Structures, m (1967), 243. 9 centers (Fig. I4). The architravewas not a monolith, but was made up of several courses, with a joint in the lowest course at exactly midspan. An iron beam was apparently used (about 100 mm x 200 mm) to span between the abaci and to locate and support the first course during construc- tion; as Jewett points out, the iron could not have been stressedin the completed structureto provide effective re- inforcement. Thus the complete architrave could stand only by arching between columns, with consequent lateral thrusts.In this caseat least, therefore,the Greeksdeliberately used broken lintels, and were clearly not adhering to the trabeatedprinciple ascribedto them. Ruskin, however dimly formulated his own structural was is principles, essentially right: "Stonehenge strong Fig. 14. Temple of Zeus, Agrigento (from Dinsmoor, "Structural enough, but it takessome trouble to build in the mannerof Iron . ."). Stonehenge: and Stonehenge itself is not so strong as an arch of the Colosseum."13 And, we might add, if you choose to build in the mannerof Stonehenge, that is, to rely on stability being assuredby vertical forces only, with no provision for lateralthrust, then all you canbuild is Stone- 13. Ruskin, Lectures,p. 17. henge.