I. THE ARCHITECTURAL DESIGN OF LE CORBUSIER AND XENAKIS Bound... · 2 PHILIPS TECHNICAL REVIEW VOLUME 20 '. loudspeakers, and to the technical devices and methods used. The articles

2 PHILIPS TECHNICAL REVIEW VOLUME 20

'. loudspeakers, and to the technical devices and methods used. Thearticles in the present issue are devoted to the pavilion itself.

. From the outset this pavilion, designed by Le Corbusier and hiscollaborator Y. Xenakis, has aroused considerable interest inthe world of architecture' because of its extraordinary conceptionand advanced desig';' as a shell structure. The building is entirelycomposed of shçlls háving the form of hyperbolic paraboloids. Themethod of const;:';ction in prestressed concrete, proposed and trans-lated into reality by Dr. H. C. Duyster, director of the contractingfirm N. V. "Strabed~' and a specialist in this field, is remarkablefor its originality and elegance. Before plunging into this ad-venture - as Mr. Duyster himself put it - N.V. "Strobed"approachetl Professor C. G. J. Vreedenburgh of the Delft Tech-nische Hogeschool for advice concerning the stresses that mightaccu'; i~ the' shells wh~rt'loaded by their own weight, and by windand snow loads. To"satisfy N.V. Strobed as to the feasibility ofthe proposed scheme of construction and supply data for the actualstructure, tests on scale models were made by Mr. A. L. Bouma

. and Mr. F. K. Ligienberg in the "T.N.D." Institute ai Rijswijk(Netherlands) and the Stevin Laboratoryat Delft.

These aspects are treated in the four articl.es printed in thisissuè: the architect's conception, the mechanical principles, themodel tests and the actual construction of the building., 'As regards thefirst article it should be mentioTJed that Y. Xena-

kis, the architect largely responsible for designing the shape ofthe pavilion, has placed at our disposal a description of the wayin which the architectural design of the building was evolved .. In ~ur opinion, however, there was little point in attempting torender the author's French text faithfully into English or otherlanguages, for translation tvould do less than justice to the elo-quence of the artist's highly individual style and risk distortingthe sentiments of the original. It was therefore decided to confinethe English rendering of his article to a reproduetion. of the factualcontents *).

The second article in this series also calls for some comment.Although Professor Vreedenburgh has kindly taken great painsto make the train of thought in his text as comprehensible as possi-ble to the readers of this Review, we cannot disguise thefact thatmany readers will perhaps have difficulty in following the detailsof his article, lying as it does far outside the range of subjectsnormally dealt witfJ, in these pages. On the other hand, the article

. should be of particular interest to the specialist, since it providesfor the first time in published form certain formulae and resultsconcerning hyperbolic-paraboloidal shells which can be turned topractical architectural use.

*) For those readers who would like to have a copy of theoriginal French text, reprints will be available of the articlepublished in the French edition of this Review.

I. THE ARCHITECTURAL DESIGN OF LE CORBUSIER AND XENAKIS

after Y. XENAKIS t). 061.41(493.2) : 725.91

. ' A report is given below of the ideas embodied inthe architectural conception of the Philips pavilionand of the various stages through which the designpassed before the pavilion acquired its final shape.This report is an authorized shortened version ofan article by Y. Xenakis, who also provided thedrawings illustrating the evolution of the design.These drawings are' the main feature of the article.When L~ Corbusier, in' the béginning of 1956,

agreed to undertake the design of the Philips pavilion,he had' in mi~d a structure to enclose a space ofunconventional form and to be materialized by

. casting cement on a metal-gauze framework sus-pended from scaffolding. The structure would havea roof and surf~ces on which pictures, colours andfilm scenes c~uld he projected for performing aspectacle in light a~d sound - a so-titled "Elec-trÓnic Poem". In October 1956, Y. Xenakis, underthe direction of Le Corbusier, entered upon a de-

t) Paris, 35 rue de Sèvres.

tailed study of the project 1). The result was adesign based entirely on the use of ruled surfaces.This result, to which artistic intuition as well as

practical considerations contributed, will be eluci-dated in the following page!,.

The first design

The ground-plan of the pavilion was fairly simplyestablished, being dictated by the requirements forthe performance of the "Electronic Poem". Eachperformance was to last 8 to 10 minutes and to beattended by some 600 or 700 persons, uniformlydistributed over the whole :floor surface of thepavilion. A space of more or less circular plan wastherefore' needed, with an area of 400 or 500 m2

and with two large "spouts" as entrance and exitchannels.

1) A brief account of this study has already been published:Y. Xenakis, Le Corbusier's "Elektronisches Gedicht" undder Philips Pavillon, Gravesaner Blätter 3, 47-54, 1957(No. 9).

r195'/59, No. 1 PHILlPS PAVILIONAT BRUSSELS,I I'In order to be able to produce various fantastic paraboloid (hypar) is also produced by moving a

effects, locally changing colours, shifts of light and straight line such that it always remàins parallelI

shade, etc. in the projection of pictures or colour to a given plane, but in this case it slides along two.slides, the enclosing walls (or at least part of them) skew straight lines (rectilinear direc\!·ixes). Thehad to he curved surfaces, so that they would receive static stress distribution in a shell having the formthe light from divergent angles. All uniformity was of a hyperbolic paraboloid can, to a certain extent,to be avoided, even the uniformity of curvature be calculated: such a shell _is found tol-possess re-found in spherical and cylindrical vaults. This led markable properties of strength -and stilbility (seeto the idea of having surfaces with differing radii article II in this series). Moreover, thtse surfaces

- .

Fig. 1. The church Notre Dame de la Solitude at Coyoacan, Mexico, having a concreteshell roof in the form of a hyperbolic paraboloid, designed by the architect Felix Candela.(Illustration from: F. Candela, Les voûtes minces et l'espace architectural, L'architec-ture d'aujourd'hui 27, 22-27, March 1956.)

of curvature. Such surfaces also seemed suitablefor meeting the acoustic requirements. To allowêomplete freedom for creating a wide variety ofspatial impressions with the aid of loudspeakers,the aim was to avoid as far as possible the uncontrol-led acoustic contributions due to reflections fromthe walls and which are audible either as isolatedechos or as reverberation. It is known that parallelflat walls are dangerous in this respect, because ofrepeated reflections; parts of spherical surfaces areequally inappropriate, since they can give rise tolocalized echos.

Having turned his thoughts to surfaces withwidely varying radii of curvature, Xenakis was lednaturally to consider saddle surfaces, and in parti-cular the ruled surfaces that come into this cat-egory. Through the work of Laffaille and other pio-neers in this field, the architect was familiar withsimple. ruled surfaces, such as the hyperbolic para-boloid and the conoid. The conoid is obtained byletting a straight line (a generator) slide along twonon-intersecting lines (directrixes), one a straightline and the other an arbitrary curve, such that itremains parallel to a given plane. The hyperbolic

,I

produced by straight lines readily lend, themselvesto construction in straight wooden beaxhsor in con-crete (see article IV). These attractive propertieshave led to an incrcasing use of such' shell struc-tures in various countries, particularly for roofconstructions ( fig. 1). :The Philips pavilion offered the architect a unique,-

opportunity to build a structure entirely from theseruled surfaces, and in this way to create a homo-geneous three-dimensional envelope in the sensethat the three dimensions would each really playan independent role, as opposed to conventionalarchitecture in which, usually, the form of theground-plan is still manifest in every section of thebuilding high above the ground.

The working-out of this novel architcctural idea,however, was necessarily a process involving artistic. intuition and a feeling for form rather than a ques-tion of reasoning. The series of sketches, figs. 2-10,allow the architect to show how he arrived at hisfirst design.This design (fig. 1:0)contains a conoid E, a surface

consisting mainly of two conoids A and D, twohyperbolic paraboloids K and G,'a con:t;tectingcone

4 PHILlPS TECHNICAL REVIEW VOLUME 20

Photo Lucien Hervé

Fig. 11. The first model. The "stomach" is set out on the baseof the model; the strings indicate the ruled surfaces. The inter-sections of the ruled surfaces are represented by spokes ofpiano wire. Their bent-over ends have no structural signifi-cance.

L and two open triangles as entrance and exit. Thetwo peaks, produced from the oblique straight linesarising out of one of the channels (fig. 6) arecounterbalanced by a third peak projecting abovethis channel.

Fig. 11 shows a model of the first design. Theribs in which the surfaces interseet are formed inthis model by spokes of piano wire, the bent endsbeing anchored in a wooden base. The surfaces areproduced by spanning strings between the ribs.

The second design

At this stage, engineers of a Parisian firm ofcontractors were consulted by the architects regard-ing the system of construction.

With a view to soundproofing, Philips had speci-fied a wall weight of 120 kg/m2 (concrete or cementabout 5 cm thick). There was therefore no questionof building the pavilion in the form of a tent,whether or not with metal-reinforced "canvas". Theengineers consulted believed that in these circum-stances the pavilion would have to be constructedon a fairly heavy metal skeleton, after the mannerof the wire spokes in the model and with supportingstanchions corresponding to the vertical bent wiresin the model. At all events they thought it desirableto change from conoids to hyperbolic paraboloidsso as to make it possible to specify more easily theexact curvature of all surfaces and simplify thecalculation of static stresses as well as the work oferection.

This advice was accepted by Le Corbusier andXenakis, especially since they themselves felt thatthe first design had certain aesthetic weaknesseswhich in any case called for modification.Xenakis set about converting the surfaces by

experiment. His method was simple: he used twostraight metal spokes joined by a system of elasticstrings fixed at equidistant points along each spoke.The strings formed the ruling lines of a hypar,whose geometry was determined by the distancebetween the spokes, the angle between them andthe positioning of two arbitrary strings. Othervariables determine the position of the hypar withrespect to ground level. To select each of the pavilionsurfaces the architect had to proceed by trial anderror, simultaneously varying all the above varia-bles; as soon as he found a satisfactory form for aparticular surface, he immediately put it down onpaper in the form of an orthogonal projection 2).For this purpose it is sufficient to give horizontaland vertical projections showing the positions ofthe two spokes and of two pairs of correspondingpoints thereon (e.g. the end points of the two outer-most strings on the spokes; see jigs. 12 and 13).This done, all pairs of corresponding points are fixed,each pair defining a ruling line. The points at whichthe ruling lines meet the horizontal plane give theintersection of this plane with the part of the hyparsurface involved (jig. 14). This intersection can bepart of a hyperbola or of a parabola (this is the casewhen one of the spokes is below the horizontal plane),or it can be a straight line (one of the spokes lies inthe horizontal plane), or, in special cases, it can bea single point. There are also some hypar shellsin the design, of which the part of the surface useddoes not touch the ground at all.The first step in revising the original design was

to change the position in space of the three peaksso as to obtain more harmonious proportions. Thedifference between the second and third peak hadto be accentuated, and the middle cone L widened.The architect now fixed the height of the peaks at21 m, 13 m, and 18 m respectively. He then proceed-ed, by alternately experimenting with the spokeand string model and drawing the surfaces found,to establish the hyperbolic paraboloidal surfacesthat both gave an aesthetically satisfying form andyielded intersections with the ground level whichwere as much as possible in keeping with the originalground-plan.

2) It is clear that it would hardly be convenient to define thehypar surfaces in terms of the numerical values of thecoefficients in the appropriate equation of the surface(see 11).

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Figs. 2-4.. Development of the ground-plan.

Fig. 2. Circular space with two "spouts" asentrance and exit channels.

Fig. 3. Further development of the plan form;partly from its shape and partly because ofits function, the architect' refers to it suc-cinctly as "l'estomac".

Fig. 4. The ground-plan forming the basis ofthe first design.

Figs. 5-10. Stages in the development of thefirst design.

Fig. 5. Ground profile of the left half of the"stomaeh". The intention was to build overthe ground-plan a shell composed of as fewruled surfaces as possible. A eonoid (E) isconstrueted through the ground profile curve;this wall is bounded by two straight lines,viz. the straight directrix (rising from theleft extremity of the ground profile) and theoutermost ruling line (passing through theright extremity of the ground profile). Thisproduces the first "peak" of the pavilion.

Fig. 6. A ruled surface, but eonsisting of twoconoids,A andD, is alsolaid through the curvebounding the right half of the "stomach".The straight directrix of D passes through,the first peak, and the outermost ruling lineat this side forms with that of E a triangularexit. The straight direetrix of A passesthrough a second peak and is joined by anare to that of D.This basic form is that used in the first

design and was retained, with some modifi-cations, in the final strueture. The mainproblem of the design was to establish anaesthetic balance between the two peaks.

.Fig. 7. Attempt to close the space betweenthe two ruled surfaces of the first design byflat surfaces (which might serve as projeetionwalls).

Fig. 8. Another attempt. Above the entrancechannel a small triangular opening is formed,flanked by two hyperbolie paraboloids (laterdenoted by Gand K), and the whole is coveredwith a horizontal top surfaee.

Fig. 9. Elaboration of fig. 8. The third peakbegins tentatively to take shape.

Fig. 10. The first design completed (seealsothe first model, fig. 11). There are no longerany flat surfaces. The third peak is fullydeveloped and ereates, with its opposingsweep, a counterbalance for the first twopeaks. The heights of the three peaks have.been established. The third peak and thesmall are eonneeting the straight directrixesof conoidsA and D (see fig. 6) form, respec-tively, the apex and the base of a part of acone L. ,. .

1958/59, No. 1

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PHILlPS PAVILION AT BRUSSELS, I 5

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By December 1956 the second design had beencompletely worked out in this way and set downon paper (figs. 15 and 16). From this design a newmodel was made (fig. 17).

Comparing the second with the first design, wesee that the hypars G and K (which form the mostimportant surfaces for the proj eetion of pictures)have been retained, but the cone L has been widen-ed and the conoids A, E and D changed into fivehypars A, E and B, N, D. In addition, two newhypars C and F appear. Surface F, which abutson E, provides the necessary space for certain in-stallations (air-conditioning plant, toilets, controlroom) and for the extensive equipment needed forautomatically performing, several times an hour,the spectacle of light and sound.

Final modiflcations

Most of the contracting firms .approached byPhilips at this stage of the design had only more orless conventional schemes of construction to propose,

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Fig. 12. Isometric drawing to indicate how the ortho,?onal pro-jection (fig. 13) of a hyperbolic paraboloid may be coàatructed,The two directrixes A, B are projected on to a horizontal plane(A', B') and on to a vertical plane (A", B"); tw6 pairs ofpoints, viz. the end points of A and B, and their corréspondingprojections are shown. i.Fig. 13. Horizontal and vertical projections of the ~rectrixesof a hyperbolic paraboloid from fig. 12. Also ~p.ow~are theprojections X'X' and X"X" of an arbitrary generator lineconnecting two corresponding points X, X on tlie·dh;ectriies.This generator passes through the horizontal plane atroint XO.

Fig. 14. The intersection of a hyperbolic paraboloidwith thehorizontal plane is constructed from the points at: which aseries of generator lines interseet this plane.

which were conspicuously out of keeping with therevolutionary style of the structure. Double-walledshells were suggested, having a total thic~ness of

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6 PHILIPS TECHNICAL REVIEW VOLUME 20

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Fig. 16. The second design. All surfaces of the first design, ex-cept cone L, have now been converted into hyperbolic para-boloids, and two new hyperbolic paraboloids (F and C) havebeen introduced. Compared with fig. 10, the design is seen herefrom the opposite side, as can be seen from cone L, the apexof which appears top right in this sketch. The first peak is herein the foreground.

80 cm and made of wood, metal or plaster carriedby fairly complex skeleton structures. The onlyproposal that was really in unisonwith the architect'sintentions, while being at the same time reasonablein price, came from the Belgian contracting firmN.V. "Strabed", directed by Dl'. H. C. Duyster.Mr. Duyster's plan was to build the pavilion as ashell structure of prestressed concrete 5 cm thick,which would be largely self-supporting, i.e. onlya few stanchions would be used merely to give thewalls some additional support. The intention wasto follow closely the form of the second design, withonly one minor modification. The latter arose froma misunderstanding of the architect's drawing, inwhich the hyperbolic paraboloids that did not touchthe ground were indicated only summarily, leadingMr. Duyster to interpret the cone L and the hyparN (fig. 16) as parts of a single hypar (denoted Mbelow). In fact, this simplification improved thegeometrical purity of the structure. The elegantmethod by which MI'. Duyster proposed to con-struct the ruled surfaces of the pavilion in concreteis described in the fourth article of this series.

Finally, another modification was decided on,which, though a minor one in its effect on the strengthof the structure, was of the utmost importance asregards the overall architectural effect. The designstill envisaged supporting stanchions, one of whichwas actually inside the enclosed space, and as such

was a nuisance. The architect Xenakis now proposeda slight change in the new hypar M and in B inorder to make it possible to dispense with the stan-chions entirely. The reasoning was that the edgemembers (ribs) at the relevant shell intersectionsought to be able to take over, at least for the greaterpart, the supporting function of the stanchions.

Photo Lucion Hcrvé

Fig, 17, Second model, seen from the side which now forms theentrance; the third peak is in the foreground.

The model tests (see article Ill) confirmed that inthe design so modified the stanchions were super-fluous. The structure was thus made entirely self-supporting, that is to say it no longer containedsupporting elements that were not embodied in

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1958/59, No. 1 PHILIPS PAVILION AT BRUSSELS, I 7

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the wall surfaces. To strengthen the third peak,which slopes at a very oblique angle, the hypar C. was made convex at its foot instead of concave,and finally the two triangular openings were partly

closed with extra hypars abutting on the existingones. In this way the definitive form of the pavilionwas arrived at, as illustrated in the plans of figs .18 and 19.

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8 PHILIPS TECHNICAL REVIEW VOLUME 20

Fig. 20. Photograph of part of the interior of the pavilion. The prestrossing wires on theconcrete, which enhance the plastic form of the structure, are unfortunately concealed inthe finished pavilion by a surfacing required for the projection of colours and pictures.

Fig. 20 shows a photograph of the interior madebefore the concrete's prestressing wires were con-cealed by the internal surfacing. This photograph

and the title photograph (and also fig. 12 III IV)give an impression of the remarkable plasticfiguration of the building.