Fig. 1. Retractable membrane roof by Frey Otto.

Fig. 2. Roof of the Montreal Olympic Stadium.

ABSTRACT

Mobility and Deployability are characteristic that arerequested for many purposes and mainly an Architectonicasrequirements.

Many cultural and sports buildings have a circular planthat is very attractive to be covered with deployable roofs.

This paper is related with the subject.

1. INTRODUCTION.

During the last years a lot of research and constructionshave been done to cover spaces with systems that allows to beextended or folded in a short time. They are the movable roofs.

At the same time papers, books or articles in Journalshave been published making the subject avalaible to thearchitects or engineers that have used the mobility to solvesports and cultural facilities in the most examples upon arectangular area [Ref. 1 and 2].

Therefore in this text we want to study different typesof roofing for every perimeter, specially with radial plan bysystematizing and catalloging builded and proyected structures.

We only include in this selection movable roofs withthe restriction of being polygonal or circular in plan and withoutinterior mast or supports. Then we propose the nextclassification.

2. FLEXIBLE ROOFS.

2.1. TENSIONED.

We include examples in wick the roofing textile can bepacked in a parcel.

They are basically two solutions. Folding to a centralsuspensed point or folding around a radial edge.

From the first one we have very important achievements,so early as the sixties. Several desings where builded byTailibert and Otto (Fig. 1). The Montreal Stadium in 1.976 isthe most representative of this type (Fig. 2, 3 and 4).

Fig. 3. Roof of the Montreal Olympic Stadium.

MOBILE STRUCTURES COVERING CIRCULAR AREAS.

By Sánchez, José School of Architecture of Sevilla

Escrig, Félix School of Architecture of Sevilla

Valcárcel, Juan School of Architecture of La Coruña

Fig. 4. Roof of the Montreal Olympic Stadium.

Fig. 7. The Zaragoza bull-ring.

Figs. 10. Helium-supported hanger by Wagner and Kröping.

Figs. 11. Helium-supported hanger by Wagner and Kröping.

Fig. 8. Proyec of cover the Innsbruck Stadium.

Fig. 9. Proyec of cover the Innsbruck Stadium

In the next years have been builded other roofs likethese. The Zaragoza bull-ring by Bergerman 1.995 (Fig. 5, 6and 7) is a recent realization.

If we use circular trusses or arches that slides upon theperimeter we can package the roofing in a line (Fig. 8 and 9).

2.2. INFLATED.

With inflated roofs the solutions are varied andinteresting innovations have been presented in recentConferences, as the idea introduced by Wagner and Kröpingin 1.994 [Ref. 3] that is shown in Figs. 10 and 11. In this case22 cones filled with helium close the roof stayed with cables.

Fig. 6. The Zaragoza bull-ring.

Fig. 5. The Zaragoza bull-ring.

Fig. 12. Deployable Structure by Pérez Piñero

Fig. 13. Cover of swimmingpool by Escrig. Fig. 14

Fig. 16

Fig. 17

Figs. 16 to18. Cover the Innsbruck Stadium byValcarcel and Escrig.

3. DEPLOYABLE STRUCTURES.

3.1. X-FRAMES.

The first proposal was introduced by Pérez Piñero,student of last course of Architecture as a participation in theVI International Competition of UIA in London in 1.961. Fig.12 shows this deployable mesh with 32 m. in span, 11 in heightand a weight of 3 tons. able to be transported on a truck [Ref.4]

The authors proposed in 1.990 a deployable roof with60 m. span, 15 m. height to shadow a swimmingpool, [Ref. 5].The parcel could be stored suspended from the central arch.

After several experiences in reduced scale model weconcluded with other proposal by sliding the deployablestructure below two arches to expand and fold it (Fig. 15.).This solution was proposed to cover the Innsbruck Stadium[Ref. 6] with 120 span and 30 m. height. We obtain twoadvantages. To support the roof during the deploying processhanged of three not alliguet points and to store the parcel hiddenat the ground where arches are clamped (Figs. 16. 17. and 18).

Fig.15. Sequence of the ploying of a hexagonal deployable structure.

Fig. 18

Fig. 20. Diafragma Dome by Pérez Piñero.

Fig. 22. Iris Dome by Hobermann.

Fig. 21. Iris Dome by Hobermann.

Fig. 23. Iris Dome by Sánchez-Cuenca.

Fig. 24 Rombic Dome by Escrig and Sanchez.

Fig. 19. Element of Pérez Piñero Diafragma dome.

3.2. DIAFRAGMA TRUSSES.

Their behaviour is similar to the diafragma of a lenscamera. Theis are circular or polygonal roofing that deploysfrom the key apex. to the border.

Fig. 20 shows a patentfrom Emilio Pérez Piñerocalled «diafragma dome» basedon elements like shown in Fig.19.

Hobermann took some success in 1.992 with his Irisdome shown in Fig. 21 and with applications like in Fig. 22.[Ref. 8].

Hobermann proposal is very flexible because is a singlelayer grid and them is mustable for long spans.

Sánchez-Cuenca corrected this problem with twoinnovations. Struts with transversal sttitres and a sophisticatedjoint.

The authors also proposed a new application with X-Frames based in a rombic polyhedra [Fig. 24).

The particular advantage is that in this case the jointson the border are fixed and not change its position. Fig. 25shows the adaptation to a bull-ring.

Many other researchers and groups are improving jointsand mechanisms to make available these structures [Ref. 8 ]

Fig. 26. The Dome of Civit Arena by Michell & Ritchey.

Fig. 27. The Dome of Civit Arena by Michell & Ritchey.

Fig. 29. The Fukuoka Dome by Takenaka.

Fig. 31. The Fukuoka Dome by Takenaka.

Fig. 30. The Fukuoka Dome by Takenaka.

Fig. 28. The Fukuoka Dome by Takenaka.

Fig. 25. Rombic Dome to cover a bull-ring.by Escrig and Sanchez.

4. RIGID ROOFS.

4.1. RETRACTABLE ROOFS

We can include in this paragraph any structuralsystems builded with spherical or plane segments that slidealong the border with bogies or other devices. We candistinguish between several designs:

4.2. SUSPENDED SPHERICAL SEGMENTS.

Fig. 26 shows the Pittsburgh Civic Arena buildedin 1.961 by Michell & Ritchey with 125 m. of span, 8 sphericalsegments overlap in one single hanged from a impressivecantilever (Fig. 27)

4.3. SELF SUPPORTED SPHERICAL SEGMENTS.

If we consider three or four segments we can achievethat every one is self-stable. Fukuoka Dome with only threesegments supported in 125º and lenght span 218 m. and 84 m.height (Figs. 28 to 31).

Fig. 33. Komatsu Dome.

Fig. 34. Pulsar Tensegrity Dome by Levy.

Fig. 32 Sliding Dome by M. Apezteguia and Azkue.

Fig. 36. Pulsar Tensegrity Dome by Levy.

Fig. 35. Pulsar Tensegrity Dome by Levy.

4.4. SLIDING SEGMENTS

If parts of the sphere slides upon the surface wecan use varied desings like shown in Fig. 32 build with twolayer grids covering or lightening the central opening. [Ref. 2and 8] Fig. 33 shows a design by Yamashita Sekkei and Ing.Ishii to open central part of the covering on a stadium.

To lighten the weight of this roof the SpaceGroup of Corea and Ing. Matthys Levy have proposed the PulsarDome, a Tensegrity Dome that open the central part 128 m. ofdiameter over a global area of 200 m. span (Figs. 34 to 36.)

Fig. 38. Floating Pavilion by Santiago Calatrava.

Fig. 39. Twistng Trusses by Sanchez.

Fig. 40. Reciprocal Frame by Popovic, Chilton and Choo.

Fig. 37. Folding Trusses by Sanchez.

5. OTHERS.

Many other systems have been proposed and we canonly describe briefly some of them in so short paper.

5.1. FOLDING TRUSSES.

Fig. 37 shows radial trusses that evolve radiallyto fold on an arch. We can use in this solution rigid of flexiblematerial for the cover.

5.2. CANTILEVERS

Santiago Calatrava has done a lot of sketches ofthis kind from Kuwait Pavilion in the Sevilla EXPO’92 on asquare plant to different circular assemblies like FloatingPavilion in Suizerland. Fig. 38 shows the system.

5.3. TWISTING TRUSSES.

The authors have proposed a solution that allowsto cover and to open completely the circular area with rigidtrusses that solve termal insulation, drainage and acousticcontrol (Fig. 39).

5.4. SLIDING STRUTS.

Proposed by Popovic, Chilton and Choo [Ref.10] are geometrical devices that need a lot of mechanicsdetermination to solve the roofing problem and the structuralstability (Fig. 40).

REFERENCES:

[1] ESCRIG, F. & VALCARCEL, J. P.

«Cubiertas rígidas transformables»Hormigón y Aceronº 193. 1994, Madrid. Pp. 85-104

[2] ISHII, K.

‘Structura Design of Retractable roof Structure’ IASSWorking Group Nº 16 1996.

[3] WAGNER, R. and KRÓPLIN, B

«Helium-Supported Hanger for a Small Solar-PoweredAirshap, Proc IASS+ASCE Int. Symposium on Spacial,Lattice and Tension Structures, Atlanta, U.S.A., Abril 1994

[4] PIÑERO, E. P. & ESCRIG, F.

«Las Estructuras de Emilio Pérez Piñero» ArquitecturaTransformable. Textos de Arquit.. E.T.S.A. de Sevilla. 1993

[5] ESCRIG, F. & VALCARCEL, J. P.

‘To cover a Swimming Pool with an ExpandableStructure’ Rapidly Assembled Structures. Ed. P.S. BulsonComputational Mechanics Publications. 1991.ISBN 1-85312-136-3 PP 273-282

[6] ESCRIG, F. & VALCARCEL, J. P.

«Geometrias de las Estructuras Desplegables de Aspas»Arquitectura Transformable. Textos de Arquit.. E.T.S.A. deSevilla. 1993

[7] PIÑERO, E.

Patentes españolas 266.801, 283.201, 311.901U.S. Patent. 3.185.164

5.5. ARTICULATED RODS.

Santiago Calatrava is a master of the mobilestructures that his experiences intensive (Fig. 41) shows thecover for a pool in an urban area.

[8] HOBERMANN, Ch.

«The Art and Science of Folding Structures»SitesArchitectures Nº24 New York 1992.

[9] YOU, Z. & PELLEGRINO, S.

‘Foldable Structures’ International Journal of Solids andStructures Stanford University California 1997

[10] MAR TINEZ APEZTEGUIA, J. & AZKUEARRASTOA J.L.

‘Retractable roof for a multi-purpose center in SanSebastian’ Mobile and Rapidly Assembled Structure II. Ed.P.S. Bulson Computational Mechanics Publications. 1996.ISBN 1-85312.398-6.

[11] POPOVIC, O. CHILTON, J.C. & CHOO, B.S.

‘Rapid construction of modular buildings using the`Reciprocal Farme`’ Mobile and Rapidly Assembled Structure

II. Ed. P.S. Bulson Computational MechanicsPublications. 1996. ISBN 1-85312.398-6.

Fig. 41. Cover for a pool in Alcoy (Spain).