THEARUPJOURNAL

Cover: East elevation of shell structure

Introduction

Jack Zunz

For some years we have considered writing theOpera House story. We have never done any-thing about it-perhaps it was lack of time, will,motivation or even the doubt that the buildingwould ever be completed. Now, nearly 15years after construction commenced, theQueen will officially open it on 20 October.Instead of the book we didn'twrite we thoughtthat the best thing to do would be to celebratethe end of the saga with a special issue of TheArup Journal. It contains some of the relativelyfew technical papers which have been writtenabout the job as well as some selected photo-graphs.It is difficult to believe that the festivities whichwill mark the opening ceremonies take place16 years since we started work on the job.After the unending technical, human andpolitical problems, after spending over £50m,we may well ask, was it all worthwhile?It is probably too early to say, but not too earlyto make some observations. Probably the mostsignificant feature of the whole story is theastonishing reality that in a modern society,with all its checks and balances, its account-ants and accountability, its budgets andbudgetary controls, a folly on this scale couldbe contemplated. In other words, it is nothingshort of miraculous that it happened at all.In concept it is not a building of this age. It hasthe romanticism of formereras when autocraticpatronage made great follies possible. Yet,when Utzon's scheme was chosen from morethan 200 competition entries, when thePremier of New South Wales was hell-bent onstarting the job without drawings, and whenall those associated with Utzon caught someof the euphoria of creating one of the greatbuildings of the age, it looked as though theimprobable would come about after all.Much has been said and written about Utzon's

2 concept of the Opera House. He is a man of

Vol. 8 No. 3 October 1973Published byOva Arup Partnership13 Fitzroy Street, London, W1 P 6BO

Editor: Peter HaggettArt Editor: Desmond Wyeth FSIAEditorial Assistant: David Brown

immense imaginative gifts. I n those early yearshe inspired all who came under his magic spell,and although there were great difficulties, theywere gradually solved one by one and by1963-64 the situation began to look quitehopeful.But then the going got rougher and Litton waspressed to produce drawings for the interiors.He didn't, couldn't, wouldn't, have it whichway you will, and he resigned in 1966, leavingbehind hard feelings, chaos, controversy, butabove all a shattered dream.Whatever judgement posterity makes aboutUtzon's resignation and the subsequentfurore.no-one will deny his poetic, conceptual andvisionary gifts and that his inability (for what-ever reason) to complete the project is atragedy. The truth is that he did walk out wheninformation for the interiors and the glass wallswas virtually non-existent. Hall, Todd andLittlemore were appointed by the New SouthWales Government to the unenviable task ofcompleting the job.They were faced with the now fixed para-meters of the distinctive roof shape, with verydefinite accommodation requirements whichcould hardly be fitted in, and above all with ahalf-finished work of art - and Utzon's OperaHouse has an artistic quality with a capital A.Some of its critics have often said that therewas too much art and too little commodity.Unfortunately, Utzon is not at the finishingpost to prove whether they were right orwrong and half-finished works of art can neverbe wholly satisfactorily finished by others.Why did Utzon resign - did he jump or was hepushed? My guess is that he jumped. Hisbehaviour, his letters, his interviews, all pointto a path of self-destruction. He ditched hisfriends and collaborators for footling or noreasons at all and literally overnight left Austra-lia never to return - at least not yet. AlthoughUtzon's Opera House was the stuff that dreamsare made of, although his use of shapes,materials, textures and colours was individualand introduced us to unique technical prob-lems. I don't think that he ever really under-stood the complexity of the problems he wascreating. Nor do I believe that he understood

Sydney Opera House Special Issue

Contents

Introduction, 2by J. Zunz

Sydney Opera House,by Ova Arup and J. Zunz

4

Design of the Concourse, 22by Ova Arup and R. Jenkins

The glass walls, 30by D. Croft and J. Hooper

Grouting prestressing ducts, 42by J. Nutt

Adhesives for structural jointing, 48by T. O'Brien and J. Nutt

Influence of corrosion on the design, 52by J. Nutt

Sydney Opera House Awards, 54

Credits

Editor's note

the problem-solving processes which ensuedwhen new technology had to be developed oreven when existing technology had to beadapted for new and untried forms. It is justpossible that, in his seeming blindness to seethat his collaboration with us was vital for thetechnical success of the scheme, lies anotherfactor in his urge to leave the job.However, these are personal opinions. Despitethe know-ails who have written and lecturedon the subject, no-one will ever really find thetruth. What is truth anyway? Whatever it is itwill remain tucked away in men's minds.Post-Utzon, the affair became more orderly,though cost estimates still kept on rocketing,but control was a little tighter and problemsbecame more easily soluble. However, thewhole thing was none-the-less just a shadeduller.What about Arups? What has the job done tous or for us, if anything ? Again, it is probablytoo early to see it in perspective, but there aresome facts and some pointers.Firstly the facts -we stretched ourselves to thelimits of our skills. In extending ourselves andmaking that extra effort we developed ourknow-howjust that little bit more. We use thisknowledge in otherfields. When we have beenextended as much as we have, it makes ourordinary jobs easier and we hope to do thembetter. We have had a good deal of publicity,some critical, but mostly complimentary: wehave received the Queen's Award for Industryand, if travelling broadens the mind, many ofus have had opportunities for mind -stretching.As for the more speculative consequences -we were and still are in the middle of a greatcontroversy. Our name is inextricably linkedwith the building. and while its success will belinked with Utzon and his successors, itsfailure will reflect on us. We became unwillingpawns in the controversy. On the one hand wewanted to help Utzon and do what was bestfor the job, on the other we wanted to acthonourably towards a client who had treatedus well and fairly. Whatever we did was boundnot to please everybody. So we did all andsometimes more than was asked of us andwhat we thought was best for the job.

The evolution anddesign of theConcourse at theSydney OperaHouse

Ove Arup andRonald Jenkins

This paper first appeared in the Proceedings ofthe Institution of Civil Engineers, April 7968.It is reproduced hereby kind permission of theCouncil of the Institution of Civil Engineers.

The structure discussed in this paper generallyknown as 'the Concourse' or 'the folded slabforms a small part of the Sydney Opera House.The architect for the scheme was Jern Utzon,of Hellebaak, Denmark, and the structuralengineers were Ova Arup & Partners, Con-sulting Engineers, London. The structure has asomewhat unusual shape, which was deter-mined more by architectural than by structuralconsiderations. As a rule authors of engineeringpapers only touch lightly on the developmentof a design and the aesthetic intention behind,it, confining themselves strictly to the struc-tural, constructional and perhaps functionalaspects, In the present case, however, theauthors felt that this approach would be toonarrow, because it would not explain why thestructure was given this form. Certainly,func-tional and structural reasons alone would nothave produced it, although they had a consid-erable influence on it. The first part of the paperwill therefore try to explain how the designwas produced by the joint effort of architectand engineers.

IntroductionFigs. 3 and 4 (p. 5) show two of theoriginal competition drawings submitted by thearchitect, on which the location of the Con-course is indicated. In the following an attemptwill be made to describe the progression ofarchitectural and structural considerations putforward by the architect and the engineerswhich led to the chosen design.In Fig.4(p. 5) it will be seen that the architecthad originally shown the Concourse supportedon a number of columns at midspan. However,when this structure was first discussed betweenthe architect and engineers, the architect askedwhether it would not be possible to do withoutthese columns. A typical question, whichreceived the typical answer, that of course itwas possible, but would cost a lot of money,and as the columns did not obstruct anythingthis expenditure might not be justified. Thearchitect then explained that his conceptdemanded that the architecture should beexpressed through the structure. in fact thestructure in this case was the architecture; itshould be bold, simple, on an impressive scaleand of a form which combined sculpturalquality with a clear expression of the forcesacting on it. This achieved, finishes could besimple: the concrete itself would speak. Thearea covered by the Concourse was the placewhere people would arrive by car to the OperaHouse. and the impact of this vast unsupportedroof would be spoilt by centre columns, evenif they did not hinderthe traffic. Hefeltjustifiedin achieving the desired architectural effect byspending the money on a bolder structurerather than on expensive finishes.The solution proposed bythe engineers to meetthese aspirations was based on the boreholedata supplied by the client, according to which

22 firm sandstone would be found 3-4.6 in below

ground level, an assumption which much laterwas proved not to hold good for the crucialsouthern end of the site. It was also designedto solve the problem of draining this vast area(approximately 7000m2). The architect wan-ted the surface of the Concourse roof to beabsolutely level, without the customary falls todrain off the water. Instead, the jointsbetween the proposed 1.83x1.22m sand-stone paving slabs would be left open to allowthe water to seep through. This meant that itwould not be necessary, and in fact not desir-able, to provide a solid slab at the top; thesupporting structure should be formed as,aseries of channels leading the water towardsthe two ends of the Concourse but providingsupport for the sandstone paving slabs alongline spaced 1.83m apart. Fig. 1 indicates therestrictions placed on the cross-section:(a) Support for paving slabs every 1.83m.(b) Channels in-.between(c) Total depth of structure should be uniform

over the full length of the span, and thisdepth should be as'small as possible.

Fig. 2 shows the longitudinal layout of oneportion of the final structure.

Support for paving slab every 6 ft

I is is

chann<t rof mlmum and uniform

collet depth over full

ninv,aco length of span

Fig.1Basic requirements for cross-section

E Max. negative moment

Substructure

101 ft

Fig. 2Basic longitudinal layout

Max. negative moment

I e

162 ft

There are two variants of this layout in otherparts of the final structure, with different spansand different depth of structure, and beforethese dimensions could be fixed the designwent through numerous variations, whichhowever did not depart essentially from Fig. 2.It will be seen that if it is assumed that horizon-tal forces could be absorbed at A by the under-lying sandstone, and at C by the substructure,which included a series of reinforced concreteboxes or longitudinal walls, then C-B and B-Acould be strutted against each other, creatingcompression in both struts but reducing themoments. There would be maximum externalnegative moments at B and C and a maximumexternal positive moment somewhere inbetween. A glance at the shape of the 'arch'C-B-E shows that the angle CBA is critical; ifit is too large the compression forces will beexcessive, and the strains produced by theseforces, by the stressing of the cables in thesetwo members, and by creep and temperaturestresses, could produce movements whichmight approach a critical stage. However, afterthe engineers' proposal had received the bless-ing of the architect, a preliminary investigationon the basis of the layout as it was then, provedthat the proposal was structurally sound.

Confining ourselves now to the main sectionC-B the task was to design a 'slab' or a seriesof beams, which would, as economically aspossible, meetthe requirements in Fig. 1 whichcould take the negative moments at B and Cand the positive at midspan, and which in adramatic or sculptural way would reflect thevariation in the external forces along the spanand indicate how they were resisted at eachpoint.

Fig. 3Cross-sections of various schemes (a)-(d)

Max. positive moment

This aspiration to have the structure 'truthfullydisplayed', to achieve 'structural honesty', is ofcourse very familiar to students of architecturaltheory. It is a declared architectural ideal oflong standing, and rightly so. But it must notbe taken too literally. Geoffrey Scott showed50 years agothatthis requirement was psycho-logical rather than factual. It has nothing to dowith choosing the most efficient structure.The spectator does not in fact understand thesubtleties of a modern concrete structure,whose strength in any case may be hiddenfrom the eye in the form of reinforcement orcables. It is not so much a question of how thestructure really acts, but rather of how thespectator thinks it acts, or whether he can relateit to some simple structural facts which liewithin his experience. Thus he may be able toappreciate the strength of an arch springingfrom solid abutments, a cantilever which isstrong at its root, a simply-supported 'fish-belly' beam or a fixed beam with haunchesproducing an arching effect, and this may givehim an impression of structural 'rightness'.More subtle effects would be lost on him; theywould not form part of his architecturalexperience.

In this particular case the most economicalanswer would probably have been a series ofbox-sections or I-beams spaced 1.83m apart,uniform over the whole length, with prestress-ing cables catering for the variations in themoment. But this would obviously not havemet the architect's request at all. It seemednatural to the engineers, therefore, to seek thesolution by exploiting a typical and by nowvery familiar reinforced concrete form, theT-beam. This can be said to be the best shapeto take positive moments in reinforced con-crete. And the same shape, only upside-down,is the best shape for negative moments. In thisway the desired expression of the variation inthe external moments could be obtained byvarying the shape from a series of inverted T-beams at the supports to T-beams at midspan- or from section 1 to section 5 in Fig. 3.

Such a solution would make structural sensein reinforced concrete if the formwork could bemade reasonably simple, and full use made ofthe repetitive nature of the job. It would also beappropriate for prestressed concrete if the liveload were small compared with the dead load,which was thought to be the case at the time.As it happened, due to the exigencies of theprogramme, it was not practical to place thepaving slabs before prestressing, and these hadtherefore to be counted in with the live load,making the two about even. This considerablyreduced the structural usefulness of the chang-ing concrete sections, and made it impossibleto justify the design on economic grounds. Butit met the architectural requirements and therewas no question of going back to a straight-forward box-section.

The question then was howgradually to mergesection 1 into section 5 (Fig, 3) in a mannerwhich(a) Produced a sculpturally interesting soffit(b) Produced the lightest possible structure

for the given depth, i.e. least redundantmaterial

(c) Was easy to construct.

Fig. 3 shows four ways of doing this. In (a)the slab is simply raised through successivesectionsfrom 1 to 5. In (b) the walls are movedsidewaysfrom 1 through 2, 3,4and 5, graduallyextending the top slab and contracting thebottom slab. In (c) the walls are graduallytwisted, inclining more and more towards eachother and reducing the area of the bottom slabuntil both slabs reach the same minimum, thentwisted the other way, thereby increasing thearea of the top slab until this covers the wholearea, when section 5 is reached.

In these three cases a further variable must bedetermined before the shape of the soffit isdefined, namely the 'speed' of the change in

1

d

(a)

(b)

(c)

(d)

t

2

d3

d4

d5

I3

d1

d4

d

Fig. 4Soffit of various schemes ( a)-(d)

section along the axis of the beam. In order tomake the shape as smooth and flowing aspossible the engineers decided to make thechange in section follow a sinusoidal variation.In scheme (a) this form of variation wouldproduce a series of beams 1.83m apart con-nected by a wavy slab; in (b) there would be'wavy' beams connected in alternate bays byflat top and bottom slabs, and in (c) the wavybeams would be twisted at the same time. InFig.4 (a), (b), (c) and (d) are attemptstoshowhow the soffits would appear. In the engineers'opinion there was a progression from (a) to (c)in aesthestic interest and also in some ways instructural suitability, but unfortunately thecomplexity of formwork was also increasing.However, as the twisted surfaces of (c) con-tained straight lines, these could be producedeasily enough from straight boards or twistedplywood. This was therefore the solution putforward to the architect, but in a slightlymodified form, as indicated in Fig. 3 (d). Itseemed to the engineers that scheme (c), seenfrom below, looked too much like a flat soffitwith certain regular hollows scooped out of it.By connecting the hollows together, i.e. byintroducing a piece of top slab between the'beams' of the same width as the beam at mid-span, the appearance was more of a series ofswelling and undulating beams, and the shapeof the beam soffits was repeated in the under-

Fig.5Proposed round-edged sections

side of the top slab. Another minor modifica-tion was that the beam sides, instead of beingvertical in sections 1 and 5, were slightlyslanted to facilitate withdrawal of the form-work.

Scheme (d) was at once approved by thearchitect, and was the one incorporated in thepreliminary design submitted to the client bythe architect and engineers in April 1958, andapproved. The architect had however intro-duced a further modification in the design,which the engineers were not too happyabout.He insisted that the visible corners betweenthe modulating walls or beams and the soffitsof top slab and beam should be rounded off, asshown in Fig. 5, and explained that this wasvery necessary in order to bring out the sculp-tural quality of the design. The engineers didnot dispute this, but were worried about howto producethese rounded corners, and thoughtit would be very difficult and expensive. It hadbeen their idea that the forms should be madeof straight narrow boards forming the twistedsurfaces, which would therefore show thefamiliar boardmarkings characteristic of struc-tural concrete. However, the architect demon-strated on a small model that these board marksand the sharp corners would be out of scale,and that the desired effect could only beachieved by smooth rounded surfaces.

Ajointvisit paid bythe architect and the engin-eers to the Sydney plywood factory of Messrs.Symonds, who were masters in the manipula-tion of plywood, confirmed that the architect'sideas would be difficult to realize, and on thereturn journ ey from Sydney the designer there-fore considered other and more practical waysof effecting the transition from section 1 tosection 5 in Fig. 3 (d).

It appeared that there were not so many simpleways of effecting this transition, if one observedthe rule that the cross-sections should alwaysbe made up of straight lines, which would thenproduce twisted surfaces which could be madeup of plywood. The method proposed in Fig. 3(c) and (d) seemed to bethe simplest possible,i.e. tilting the side B-C (Fig. 12, p.7), rotatingit round point B until point C coincided with D, 23

then twisting the side back in the other direc-tion, rotating about D until point B coincidedwith F. The next simple method (Fig. 6)seemed to be to rotate the side B-C roundpoint B as before, and simultaneously to rotatepart of the beam soffit D-C round D, in such away that the point of intersection C betweenthe two lines moved on a straight line from Cto its ultimate destination, point F. The result-ing shape of the beam, assuming that the sinu-soidal variation of cross-sections was main-tained, proved to be very interesting and topossess that roundness or voluptuousnesswhich the architect was looking for, in spite ofthe fact that there were no rounded corners.Fig. 13 (p.8) shows some typical cross-sections and Fig. 14 (p.8) a dimensionedsection of the executed scheme.

After considering this new proposal and mak-ing models to judge its effect, the architectwholeheartedly approved of it, adopted it, andhad it passed by the Technical Panel.

The engineers, having concentrated theirattention on obtaining an architecturally-interesting solution which could be producedwith fairly simple formwork, had at that stagepossibly given too little weight to one possibledisadvantage of the last scheme comparedwith that in Fig. 3, namely that the 'kink' in theside walls might increase the internal burstingstresses produced by the bending stressesresulting in an increase of ordinary reinforce-ment, thereby adding to the difficulties of com-pacting the concrete. Butthiswas only a minorsnag compared with many others whichemerged during the detailed design and theexecution of this work. For one thing, theassumptions on which the design was basedunderwent various changes, all for the worse.It was found, for instance, that the underlyingsandstone dipped down at the southern end ofthe site, making it doubtful whether the safebearing which the design called for could beprovided at this end. Then the architect chan-ged, at the Technical Panel's request, the ratiobetween treads and risers of the steps, flatten-ing the slope of A-B (Fig. 2). As pointed outearlier, the angle C-B-A had a vital influenceon the horizontal forces which had to beabsorbed. For these reasons it was found desir-able to introduce tie-beams between thefoundations atA and C. This added to the cost,but put the design on a much sounder basis,and part of the cost was offset by the fact thatthe prestress produced by the cables in the tie-beams made it possible to reduce the numberof cables in the folded slab itself.

All these changes naturally delayed the com-pletion of the detailed drawings which wereurgently needed on site, and further aggravatedthe almost impossible situation which wascreated by the client's insistence that workshould begin on site early in 1959, long beforethe brief - let alone any finished and dimen-sioned drawings - had been completed. Thesituation was not improved by the contractor'sinsistence that his programme demanded anearly start on exactly this particular part of thejob. Add to this the difficult nature of the job,complicated or unusual formwork, narrow sec-tions packed with steel, etc., and the contrac-tor's unfamiliarity with prestressed concrete.and it is no wonderthat the atmosphere on thejob deteriorated and the workmanship suffered.

A description of the snags which developedand of how they were overcome would per-haps be useful but falls outside the scope ofthis paper. But it may be of interest to mentionanother complication which was happilyavoided, because it concerns the design, and itthrows some light on the somewhat differentpoints of view of architect and engineers.

It arose from the fact that a part of the Con-course slab (the part and er the restaurant) wasraised a few steps over the rest. It was part ofthe architect's philosophy - to use a now

24 popular phrase - that the structure, i.e. the

Fig. 6Isometric view of executed scheme

Fig. 7Cross-section through proposed slab

Fig. 8Cross-section through executed slab

shape of the slab as seen from below, shouldregister this fact: one should be aware of whathappened above, just as one should be awareof the forces acting on the slab. The cross-section in Fig. 7 shows what the architectwanted to do: the beams under the higherportion are lifted up and there is a gradualtransition to the normal level, more or lessfollowing the steps above. It was difficult toargue that this could not be done, although itposed tremendous problems, because the fivespecial beams were unsymmetrical in cross-section and the prestressing would createtorsional movements which would have to beabsorbed by the adjoining, already fully-stressed, beams. This would require structuraladditions and might even prove to be almostimpossible - apart from the fact that it wouldupset the whole arrangement of stressing twoadjoining beams at a time, and would requirefive sets of special and more complicatedforms, thereby invalidating the excuse of repe-titive formwork.

The engineers' view was that even if the archi-tect was correct in preferring his solution froman aesthetic point of view-which they did notdispute - the very considerable cost, and thedisturbance itwould cause in an alreadycriticalsituation, would be too high a price to pay forsomething which after all would not be missed

by anybody. However, the architect was insis-tentand the engineers were bracing themselvesto attempt a solution to the problem when theheating engineers intervenedwith ademandforspace overtheslab in whichthey could accom-modate their pipes and other services. Thisclinched the matter: by keeping the beams atthe same level as in Fig. 8, the desired spacewould automatically be created and everybodywas satisfied!Figs. 9 and 10 show the appearance of theConcourse slab from underneath and from theside, and Fig. 11 is an aerial view of thefinish edslab without the pavement.

This account of the development of the designis necessarily brief and deals only with thetypical case. Amongst otherthings it leaves outthe considerable difficulties in creating thecorrect boundary conditions, especially for thecross-beams spanning the openings in thesupporting wall at the north end, but these aredealt with in the next part of the paper.

Structural designThe Concourse is a folded-plate structure inprestressed concrete and the analysis was quiteconventional. Some unusual features werepresent, however, because it was not simply abridge but had also to have the architecturalattributes already described.

The depth/span ratios were low and the shapewas not ideally suited to prestressing. Thestructural design was. thus, mainly concernedwith keeping withintheworking stresses underall conditions. The cross-sections continuouslyvaried according to geometrical rules. For thismain reason most of the numerical work wasprogrammed for the electronic digital com-puter. The analysis was done and the workingdrawings prepared in 1959.The remarkable feature was the extremely flatangle of 191° of the leg from A to B (Fig. 11,p.7 ). This madethe portal part of the structure(A, B, C), very sensitive to the phenomena ofconcrete movements. Time, temperature andload gave many combinations to investigateand reinforced the case for computer working.A general description of the whole structurewill now be given.The part denoted by RC substructure in Figs.10 and 11 (p.7) consisted of two-storey box-like structures which received the prestressedtie-beams in a floor at that level. The com-pression in the tied portal due to the thrust atthe foot, A, was taken up at the other end byshear walls in the substructure.The couple thus imposed on the substructurerequired special measures forstability, but wasa greatly reduced problem compared with theoriginal idea of thrusting against the rock,because the indicated rock level was wellbelow the tie level.The substructure was not there just for thestructural purpose described. The shear-wallspacings were determined by the various usesof the rooms. A certain amount of structuralirregularity was a small thing compared withthe large spaces required for main stairwayentrances and especially for the service road,1 2.8 m wide, which entered the Opera Houseattie-beam level atthecentreof the Concourse.These boundary conditions at the north side ofthe portal are shown diagrammatically in Fig.10 (p.7).The upper reaches of the Concourse showntypically from C, D to E in Fig. 11 (p.7), weresubject to several varieties of spans, slopes andflats. The figure indicates that where visible tothe public, the architect required the 1.83mwide, varying section, folded slabs to flowcontinuously into the upper reaches. Becauseof the reduced depth the most critical pointwas found in the upper sloping part.For an ordinary continuous beam one wouldhave introduced something like a concretehinge overthe intermediate support at C. How-ever, the vertical reaction at C was combinedwith a horizontal reaction of the order of203 tonnes/1.83m wide Concourse beam. Ahinge under these conditions would haverequired costly mechanical devices. It wasdecided to make the beams monolithic with theshear walls, which in the region of C had thusto receive the vertical reaction, the portal com-pression and a couple equal to the differencebetween the end moment of the portal part andthat of the upper part of the Concourse.

Transom beams, in one case of considerablesize.were introduced acrossthewide openingsmentioned above.

The transoms were in a state of vertical andhorizontal bending and torsion. The torsionarose from the beam end moment differenceswhich depended on the combinations of tem-perature and loading. The minimum would beobtained if maximum clockwise and anticlock-wise moment differences were numericallyequal. By preloading and other devices theupper spans were made as far as possible tobring about this optimum condition.

The stresses in the transoms resulted in deflec-tions and rotations, but these were of a smallenough order not to influence the assumedfixed end condition of the Concourse. Onemeets a parallel case in the edge beam of acylindrical shell. When the beam is of normalsize it makes no material difference if one takes

into account its torsional rigidity or assumes itdoes not twist.

The portal part of the Concourse contained 47folded slab units, 1.83 an wide. The slabs were178mm thick: therewere 21 units 50m in spanand 1.37m deep; the remainder were 41.5min span and 1.14m deep. Both types weredesigned in a similar way. The longer span hasbeen selected for description in the paper.

With the sloping leg at such a flat angle, astructure with unusual sensitivity to concretemovements seemed to provide a good oppor-tunity for correlating calculated and measuredstrains and deflections. The distance fromLondon, where the design was done, made thesite measurements less extensive and accuratethanwas desirable forthe exercise. The authorsdo not believe that the results add anything topresent knowledge (a common finding unlessthe instrumentation is good) and the correla-tion will not be given in this paper.

Long-term movements were important. Theconstruction of the portals was begun inNovember 1960, and finished in January 1963.The laying of paving slabs, which are a perma-nent superimposed load, may not commenceuntil 1968/9. The application of full live loadwill be a rare and short-term event.

Ultimately the concrete of the portals will beshielded from direct sunlight by the paving.The average temperature condition will bewhen the temperature of the portal concrete isthe same as that of the tie concrete. Long-termfactors are that the paving should be quite flatat average temperature when there are fewpeople on it and the possibility of further creepdueto changes of stress from the weight of thepaving.

Fig. 9Completed structure 1

The control devices used to make these struc-tures largely independent of concrete move-ments not accurately known will be described.However, for the sake of the correlation thedesigners made some research into publishedexperimental information and made use ofwhat they thought was the latest at the time,not very different from that given in the BritishStandard Code of Practice (CP115:1959).A pair of connected folded slab units 3.66mwide, were cast at a time. A gap, to be filled inlater, was left between one pair and the nextpair. In this way stressing operations could becarried out on a pair of connected units withoutdisturbing the adjacent units.The pairof ties corresponding to a pairof foldedslab beams passed on opposite sides of theT-sectionsatAand were connected bya cross-head. Hydraulic ship jacks of 203 tonnes pres-sure were introduced into the gap between thecross-head and the foot of the portal. Twoship jacks were used and oneotherwas keptasa standby in case of breakdown. Also in thegap was a pair of steel wedge assemblies. Thedetails of the jack and wedge apparatus areshown in Figs. 11 (p.7) and Fig. 15 (p.8).The former also shows the profiles of the 28.6mm diameter strand post-tensioning cables.Load cells or dynamometers were used withthe hydraulic jacks and the prestressing jacksso as to obtain more accurate force measure-ments than could be relied upon from pressuregauges. The order of prestressing and jackingwas carefully worked out so that the structurecould be converted from an unstressed, inertstate supported by soffit props to a fully-stressed free-standing condition without atany stage exceeding the permissible designstresses attransfer. Creep and shrinkage lossesin the portals were made good by periodic

Fig.10Completed structure 2

F1g.11Aerial photograph of site showing Concourse area

25

rejacking, which meant moving the ship jacksaround quite a lot.

The folded slabs were cast to true final shape.The knee at B could be maintained to correctheight by the ship jacking and geometricalnon-linearity could thus be avoided. The jack-ing was not simplyto allow for concrete move-ments. The calculated force obtained optimumstress conditions in the portals. The jacks were,in fact, a second method of prestressing.

The tie-beam had been previously prestressedto a concrete compression of about 9 N/mm2.Thus the operation of the jacks decompressedthe concrete. Data of creep recovery for theintended correlation were found to be tooscanty for consideration.

A case could be made for the use of Freyssinetflat jacks throughout in place of the ship jacksand wedges. Th e ship jacks were ordered whenit was thought the jacking might be againstrock instead of ties. The jack travel might thenhave been quite large to an extent that couldnot be predetermined.

To deal with the possibility of extra creep dueto the paving load the intention is to stack thepaving slabs in transverse lines across theConcourse. The jacks will then be put intoposition again and used to compensatefor anyloss of thrust and maintain the correct level atB. The jacking gap will be concreted in wheneverything has settled down and the gap leftbetween every pair of units will be made good.The paving will then be laid true to level at aperiod of average temperature.

It should be mentioned that since there was anodd number of folded slab units of the longspan type, one unit had to be made by itselfwith a gap on each side.

MaterialsConcreteThe fine aggregate was a uniformly-gradedCronulla sand with approximately 4 per centmoisture content. The coarse aggregate wasProspect Blue Metal, a crusher run aggregate,uniformly graded with a maximum size of22 mm. A concrete mix was designed whoseproportion by weight was 1 :1.19:2.43. Thewater/cement ratio was 0.39. An additive,Darex WRDA, was included at the rate of2.2 kg/ma of concrete mixed.

Theauthors' specification called fora minimumcube strength of 48.3N/mm2 at 28 days, andprestressing was allowed to begin whenfield cubes reached an average strength of41.4 N/mm2.

The permissible working concrete stressesadopted in design, were:

N/mm2

Bending compression 1 5.5

Bending tension 1.5

Shear stress 1.2

Local bond stress 1.2

Average bond stress 0.8

Principal tensile stress 1.1

The prestressing strand was augmented withmild steel reinforcement where tensile stresseswere found.

The coefficients assumed for calculatingdeflections were:Young's modulus at transfer 34.5 kN/mmzLong-term Young's modulus 17.2 kN/mm2Young's modulus in tie 34.5 kN/mm2Shrinkage strain 0.03%

PrestressingThe prestressing equipment for 28.6 mm diam-eterstrandwas by Gifford-Udal and a dynamo-meter of Swedish construction was added foraccurate measurement of stress. The 28.6 mmdiameter prestressing strand, which had thenbeen only recently marketed, had a guaranteedminimum tensile strength of 82 tonnes. It was26

Fig. 12Construction sequence

housed in Kopex ducting with an inside diam-eter of 38 mm.

The mechanical properties of the strand,assumed in design were:

Young's modulus, tangent 1 65 kN/mm2

Secant modulus at 63 tonnes 131 kN/mm2

Friction constant betweencable and ducting p=0.30

Wobble constant K=0.0010

The use of the calibrated dynamometers at thelive end and dead end of several cablesshowedK=0.0013 and p=0.25,. It was found that thechange of these constants from those assumeddid not materially affect the analysis.

Loss of prestressThe relaxation of the strand cables was deter-mined by experiments carried out at theUniversity of Sydney.

Loss of prestress partly depended on the dis-tance from anchorages, the angle turnedthrough and the concrete stress at the centroidof the cables, under dead load conditionswith-

0

c-FOLDED SLAB CENTROID

Fig. 13Diagram for analysis with one unknown

FOLDED SLAB CENTROID

^71E

Fig. 14Diagram for analysis with two unknowns

out paving. The loss at transfer was distin-guished from the ultimate loss after severalyears under dead load.

The ultimate loss averaged about 33 per cent.The approximate average contributions were19 per cent due to friction, 5 per cent due tocreep and shrinkage, 5 per cent due to anchor-age slip and elastic shortening and 4 per centdue to relaxation of the strand. The latter wasreduced from 6 per cent by holding the maxi-mum force of 63 tonnes for five minutes beforewedging-off. The high friction loss was partlydue to the large proportion of cables stressedfrom one end only through restrictions in fittingstressing jacks into position at both ends. Therestrictions arose from having all theanchoragein the upper hollowed-out part of the beams,for the visible undersides could not be marredby the making good of anchorage pockets. Theelastic shortening mainly arose from the thrustof the ship jacks. The prestressing cables weregrouted before the ship jacks were broughtinto full operation.

ThermometersThetemperature difference between the folded

B

I H . KNOWN

V, UNKNOWN T

B

H

to

V,UNKNOWN i

UNKNOWN

Fig. 15Relaxation/time curves

tR 300

sso

10

s o

NUMBER OF DAYS AFTER PRESTRESSING C LOS SCALE I

10

E is constant throughout, which would be thecase if creep is proportional to stress, it doesnot enter into load analysis because its valuecomes in the denominator on both sides of theequation of relative movements due to loadsand those due to the unknowns (redundants).In fact, influence coefficient methods amountto finding the redundants by this equation. Ifthere is more than one redundant, the equa-tions are simultaneous, as in the second case.When there was a relative temperature changewhile the horizontal thrust was held on thewedges, the second case of two unknowns

lac , arose. Further, in this case there were relativemovements in the released system which com-prised the change of vertical height of thesloping leg and the relative changes of hori-zontal length of folded slab to the tie-beam.which had to be eliminated to restore continuityby redundant actions, It is therefore evidentthat the value of Ecomes into only one side ofthis equation and can not be cancelled. Thefolded slabs were exposed to the air and the tiebeams were not. The daily alterations of tem-perature were small, but there were sometimeslarger the same signover pee ods of severe le days to a

ofweek or more.

The temperature differentials were regarded asshort-term events, and the E value used was34.5 kN/mm2. Thus, in the judgement of thedesigners, creep due to temperature stresseswas ignored.As regards the application of the permanentpaving load, the structure will still be under thewedge and jack apparatus, and any furthercreep will still betaken up. If it is presumed thatcreep will take place where the compressivestress is increased but notwhere it is decreased,the creep will be resisted by peculiar stressdistributions overthe cross-sections, unless thecreep recovery factor is equal to that of creepstrain which seems unlikely. These are stresshistory matters on which published researchwas entirely lacking.The loadings taken for design were:

kg/m per unit

100

Fig. 16Diagram for structural analyses

Fig.17Gain or loss of thrustdue to temperature

400

Na_

FOLDED SLAB

COLDER THAN - 350

FOLDED SLAB

WARMER THAN

TIE BEAM TIE BEAM

xr

300

-25

PArRT'.sue WL, S

in v raceo

-10 t0 +10

TEMPERATURE DIFFERENTIAL IN DEGREE FAHRENHEIT

slab and the tie had an influence, as will beexplained, on the forces applied by the shipjacks. Eight thermometers were located in eachpair of tie beams. The thermometers wereimmersed in water in specially constructedtemperature pockets and read just before thejacking operation. The temperature range usedin the structural design was ±14°C.Portal designThe portal foot at A rested on a foundationthrough lubricated sliding plates.Two cases of statically indeterminate structureswere analysed by the influence coefficientmethod. The analyses were programmed fortheelectronic digital computer to eight significantfigures. In view of this the simplest releasedsystem was adopted, that of cantilevering thewhole folded slab structure from C. Bendingand direct strain were taken into account, butnot shear strain. However, the program wasarranged to give shear forces. Part of the datawas the prestressing tensions and their slope,which were taken into account for resultantshear on the concrete.

Dead load or selfweight 23127 5 x area of section

Paving = 171 kgLive = 272 kgIn plan these are:

Dead loadPavingLive

kg/m2= 1025 average= 308= 488

Integrations for the analysis were performednumerically in the computer by summing

.25 according to repeated Simpson's rule, Thesewere both total integrals over the whole struc-ture and integrals from A to the interval points.

Thefirst case is shown diagrammatically in Fig.13. At A, the horizontal thrust is known and thevertical reaction is the unknown. The secondcase is shown in Fig. 14.The unknowns arethevertical and horizontal reactions at A. Thedesigners had to consider the effects of con-crete movements on these indeterminate struc-tures. In the first case, the horizontal thrustwasto be brought up from time to time to a knownforce over a period of several years.

There was no doubt that shrinkage, creep,elastic tie extension, and the loss of the hori-zontal component of folded slab compressionwould be taken up by jack travel, The verticalcomponent of the compression in the slopingleg, naturally, came into the analysis. When itcame to rejacking, it was found, as expected,that when the thrust was just taken up therehad been a loss. Fig. 15 shows two plots forloss of initial thrust against days on a logarith-mic scale. The differences in the curves weredue to differences in time from casting theconcrete to stressing operations.Itis well known that if the modulus of elasticity

Cross-sections were drawn to scale at eachinterval (numbered 0-27 on Fig. 16), to pro-vide dimensions for the two purposes of mak-ing the formwork and a computer run to givethe area A, the moment of inertia / and thedistance of the centroid. { in the figure, fromthe straight reference lines, AB, BC, at eachcross-section. Due to certain changes afterthecross-sections had been drawn, some unequalintervals appeared, which required modifica-tiontotheSimpson coefficients in their regions.From this preliminary program, the co-ordinates

'of the true axial line (centroid) at each intervalwere given, denoted by y, z in Fig. 16.

The graph used on the site to determine theappropriate jacking force at various tempera-ture differentials is shown in Fig. 17.

Computer runs, for the two spans, were madefor 19 conditions. These comprised transfer,self-weight and paving, and live load; maxi-mum and minimum temperature differences;and jack thrusts ranging from 203 to 376tonnes. The latter were for determining howmuch loss of thrust could be tolerated and towhat extent over-jacking could be employedto compensate for future losses. 27

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