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THEARUPJOURNALCommonBoundary.2 PlantElemintiSupportVol 1, No. 1 Published January 1967 byOve Arup & Partners, Consulting Engineers13 Fitzroy Street, London, W . l .laSimple foldedplate structureEditor: Rosemary DevineArt Editor: Desmond WyethContentsThe cover, front and back,shows folded plates,especially drawn by Poul BeckmannF O L D E D P L A T E ROOFSDavid Dowrick15 FENCHURCH S T R E E TJohn AndersonlbHopperFolded plate roofs"David Dowrick Editorial note:D.V.,this article will bedefended by David Dowrick at the secondTechnical Staff Meeting on 8 February.Everyone is welcome to attendand contribute to the discussion.GENERALWhat is a folded plate? If we answer this quite truthfullythe answer is almost any structure apart from a columnthat we care to name.lcNorth light roofFOLDED PLATE RECIPEMinimum ingredients1. Two flat structural elements (capable of taking shear intheir own plane).2. One common boundary between them.3.One rigid support.Making Procedure1 . Place the two elements together, but not in the sameplane.2. Join the two elements firmly together along the commonboundary.3.Attach both parts of the resulting 3D structure firmlyto the support.4. Allow to stand, and observe.If what you are looking at is similar to figure 1 (a) you nowhave a simple folded plate structure.From this simple beginning a great variety of structurescan be built up including silos, north-light and non-prismaticroofs, box beams for bridges (figs, lb - l e ) . By way ofIdBox beamleNon prismatic roofF i g s . l a - l e RightSome folded plate structures2

Figs. 2a-bFolded plates v shellsFolded Platedefinition, a prismatic roof is one composed of rectangularplates joined together, such that each plate is parallel to acommon longitudinal axis. The variations of folded platestructures are numerous and this discussion will be limitedto roofs.Because of the simple physical concept and the almostunlimited geometric configurations, this medium can bevery popular with architects. The inherent plasticpossibilities and the creation of various types of internaland external space are great attractions to them and as theroofs can be made to span long distances without columns,free planning is facilitated. Added to the spatial freedomsare those of surface texture, as the structure can be madefrom various materials, concrete, steel or timber.The engineer also enjoys the use of folded plates, thoughnot all of the reasons are altruistic. On occasions he isable to span large spaces. The spaces and analysis may beintriguing and in some offices folded plates will be a changefrom routine. It may also involve him in an unfamiliarmaterial and new detailing techniques.Fig.2aShell VaultFolded PlateAs for the client he also may have reasons for satisfaction.1. Economy Folded plates tend to be efficient structurallyand simple to fabricate (plane surfaces) though neitheris necessarily true.2. Functional suitability. He may very well get his shareof what Ove Arup calls 'commodity , whether designedby Arups or not!3. Visual and environmental pleasure. Such a roof mayprovide relief from monotony or even positiveexcitement.On the negative side of the argument, folded plates can betreated in a gimmicky fashion, by any of the perpetrators,be they architect, engineer or client. Let us not use themtoo facilely. Economy and commodity should always besatisfied. Unfortunately they won't always.Folded plate roofs are popular for industrial buildings,churches, schools, exhibition halls and various places ofassembly, for all of which they are well suited. Themodern theory is only about 40 years old, started byGerman engineers particularly Craemer (2), but for somerather obscure reasons they seem more popular in the NewWorld than elsewhere. They are widely used in the UnitedStates and various Commonwealth countries, especially inAfrica. In the United States labour costs are high, in theother countries mainly low, so the reason for the New Worldpartiality to folded plates is not a simple economicdifference from Europe.Simulation in ShellsFig.2bThere is also an interesting paper on reinforcement ofreinforced concrete plates by Guralnick (5).Shell roofs and folded plate structures are closely related,just as a circle can be considered as the limit case of aseries of short straight lines (fig.2a). For prismaticstructures, attempts have been made to treat shells asfolded plates and vice versa. Gibson (4) at Manchesterhas developed very promising computerized solutions forvarious folded plate vaults treated as a series of largeradius interconnected shells (fig. 2b).1CONSTRUCTION IN CONCRETEPerhaps the most adaptable material for folded plates isconcrete and a considerable range of constructionaltechniques is available whether in situ or precast,prestressed or plain reinforced concrete. Spans rangingfrom 30 to 120 ft. are commonly employed, while the largestknown to me is nearly 190 ft.IN SITU OR PRECASTIn many cases the final appearance of the roof will not differmuch whether in situ or precast, so the choice will often beinfluenced more by economics, the type of site and contract,and the preferences of the engineer and contractor, ratherthan by the architect and his concern for surface finish orarticulation. Precasting is popular in the United States,which no doubt results from their high degree of mechanization,especially cranage, and a constant dollar-inspired desire toreduce time on site.Prismatic roofs are generally precast in complete bays, eachbay being an isolated folded plate for its dead load (fig.3)although complex roofs are sometimes made from planeelements stitched together (fig. 14c).We have broad experience in folded plate roofs,principallydue to our African practice. If I may dare to mention acompetitor, Felix Samuely seems to have done quite a lotin Britain. Nervi sometimes does them to perfection.STRUCTURAL ANALYSISFear not! I won't trouble you with detail. One or two notvery inspiring textbooks exist, of which Born'sO) i worthlooking at, together with a welter of post-war mathematicalargument in technical magazines, mainly American. Moststudy the classical concept of the load being resolved intothe planes of the plates which span mainly in their ownplane, interacting with their neighbours with shears alongtheir common boundary - see recipe. The load componentnormal to the plates is carried in lateral bending spanningbetween folds. As most techniques involve solving a set ofsimultaneous equations, the computer comes timely to ouraid.Amongst the published papers on folded plate analysis aresome which advocate simple beam analogy but these shouldbe treated with some suspicion. The best place to lookfor a recommendation on design methods is the AmericanSociety of Civil Engineers' report on folded plateconstruction ' ' published in December 1963.sPRESTRESSINGBoth post- and pre-tensioning are used. One American firmwas selling so many standard roof units that they were ableto set up a long-line pre-tensioning bed (fig. 4). An exampleof the finished products is shown in figure 3. (8)Prestressing, as with other structures, assists in long spans.It is used with both precast and in situ work, though the lattercase is less popular because of inherent difficulties in transferof load to the supports, in allowing for movements of the roofdue to shortening under prestress and in correct distributionof prestress throughout the structure. Perhaps the mostambitious example of a folded plate roof is that for the new3

! IF i g . 3 abovePrecast production line units, Florida(reproduced with permission fromAmerican Concrete Institute Journal)F i g . 4 belowLong line pretensioning of roof units, Florida(reproduced with permission fromAmerican Concrete Institute Journal)town hall in Marl in the Ruhr, West Germany (figs. 5 to 8).This is in situ, post-tensioned and spans almost 190 ft. Thebuilding is built to take mining subsidence and its portalframe has pins and a sliding support making it staticallydeterminate. Apart from the advantage this has in earthmovements, it also avoids complications due to movementunder prestress but it is a pity that the sequence ofstressing was not described in the technical paper(7)asthis poses interesting problems. The whole roof, comprising1400 cubic yards of concrete, was poured continuously in an80 hour period, a quarter of the prestress was applied twodays later, presumably to control shrinkage cracking.This building, while ambitious in scale, seems to use farthicker plates in the roof than necessary.Another post-tensioned structure is shown in figure 10.WATERPROOFING AND DRAINAGEFolded plate roofs, almost by definition, provide naturalvalleys to guide water to the supports and concrete onessometimes need little other than a screed giving extra fallin the valleys to give adequate watertightness (fig. 9b). Asthe concrete mixes tend to be stiff and therefore fairlydense they are naturally reasonably waterproof but only iflow tensile stresses exist in the concrete. In Africa, wequite frequently u s e l / 2 i n . cover to top steel in in situ roofslabs poured on a slope without any top shutter, e.g.Salisbury Market Hall. This type of roof is then generallywaterproofed with bituminous felt. Feldman's Warehousein Vereeniging was given a top membrane of waterproofpaint. Occasionally no waterproofing membrane is used,but more than l / 2 i n . top cover would obviously be calledfor.In concrete construction the roof water is typically ledaway in downpipes cast into the columns (fig. 9a). It is aswell to provide overspills in case the downpipe entrancebecomes clogged. Sometimes the geometry of the roof issuch that water could fill up to the ridges should the drainsbecome blocked. This loading should be allowed for in thedesign at a suitably reduced load factor.There are, of course, various sealants which may be appliedto concrete roofs, some not very good. A good moderntreatment consists of a layer of neoprene covered by afinishing coat of HYPALON. Of this type of roof coating,generally termed elastomeric, a trade name to rememberis CASCO-DUR. It seems durable and comes in variousFig. 5Town Hall, M a r l , W.Germany. Top shutter(reproduced with permission fromBeton-und-Stahlbetonbau)

Fig. 6Town Hall, M a r l , W.Germany(reproduced with permission from Beton-und-Stahlbetonbau)S0,00m 1Sirzungssalsp-OJt/m*SO/95Wondelhalltp-QSt/m'P- Roum fur hvdraulischt PttssenFig.7Town Hall, Marl, W.Germany. Longitudinal section dimensions in metres(reproduced with permission from Beton-und-Stahlbetonbau)1 Fatten zujc *f,00m1si11*1 F 4AhschiutS-wand u VO50/35uu1*0-solosinS sofss[1k:UO tOO4 - — - 8,00Fig.8Town Hall, Marl, W.Germany. Cross section, dimensions in metres(reproduced with permission from Beton-und-Stahlbetonbau)f[ 32bptOO-J