1999-3 foldable grids of coupled arches

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FOLDABLE GRIDS OF COUPLED ARCHES

Félix Escrig. Prof. of the School of Architecture of Seville.

José Sanchez. Prof. of the School of Architecture of Seville.

Juan Perez Valcarcel. Prof. of the School of Architecture of La Coruña.

SUMMARY

In our recent works we have used

extensively spatial expandable grids

build by connecting straight bars

connected by means of hinges that

move in three dimensions. We

consider that this system is very

useful in almost all cases in which

we can use elevation devices. But in

other cases it is enough with plane

grids that can be curved on any two

dimensional space.

Thus we achieve a new type of

structures that we have defined

geometrically and we have used to

design some important buildings as

cited in this paper.

1. INTRODUCTION

In the former designs we have used

the good properties of bundles of

X-frames to build in a few days

complexes structures as shown in

Figures 1 and 2.

Figure1. Model folded and deployed of an spherical

X-Frame grid.

Figure 2. Structure build for shadow (8x8 sqm.)

We have published this application for the Sa. Pablo Swimming Pool in Sevilla. (Reference 1).

The gread advantage is that the complete cover can be folded in a little parcel (Figure 3).



We have continued our research in foldable structures by developing two dimensional grids on

curved surfaces. The Figure 4 shows the principles of a new invention. It consist in curve a

rhombic hinged mesh on any surface. By the moment we have developed the projection on a

cylindrical one as explains the figure 5.

Figure 3. Three different stages of deploying of the cover oz St. Pablo swimming of Sevilla.

Figure 4. Rhombic deployable plane mesh.



This solution can not be packed in a bundle

and then it is not portable as the X-Frames

are. But for fixed installations it is easier

of be moved only by pushing or pulling it.

The system, based on the figure 4, if is

curved needs to achieve a solution for thelength “li” that must be the same in any

case as shown in the figure 6.

The figure 7 shows a basic component

formed by two arches hinged at two

intermediate points placed at half of the

height.

The deploying and folding is produced

from the basis motorising the assemblieon wheels.

We have some complications in solving

the hinges because the diameter of the

pipes obliges to displace the position of

the supposed axis (Figure 9) and then the

deploying or folding can not be complete

and it is limited by the corbelling of a tube

upon the other. The separation “d”

controlles the capacity of deploying but

introduces some deflections on the arch.

Figure 5. Cylindrical projection of a rhombic deployable mesh.

Figure 6. Change of width for a rhombic mesh.

Figure 7 . Two coupled arches and position of the hinges.

Figure 8. The deploying of two coupled arches. Figure 9. The necessary displacement of the twocoupled arches is named “d”



We can use any curve for the

arches with the only restriction

that the hinge is placed at the

half of the height.

If we connect several of the

coupled arches we can achieve

a longitudinal construction as

shown in the Figure 10.

Figure 11. Reduced scale model of the previous design.

Figure 13. Internal view of a deployable cover.

Figure 10. Design of a deployable cover by means of coupled arches.

2. TO COVER A SWIMMING POOL WITH COUPLED ARCHES.

Our first design was for a swimming pool with

a covered area of 18x30 sqm.

We solved the system by means of six coupled

arches drove on wheels and managed by hand.

The Figure 10 shows the proposal tested at

first in a reduced scale model as shown in the

Figure 11.

The Fig 12 and 13 shows different views of the

building and the Figure 14 some constructive

details.

Figure 12. External view of a deployable cover.



This design is covered with a transparent fabric to collect directly the solar radiation making

possible a saving in energy of 50%. And even to avoid to use complementary external power.

The test carried on a similar solution build with X-Frames confirmed this extreme. The temperature

of water arrived till 19 º C in winter when the daily average temperature was of 5ºC and the

sunny days were of 80%. The temperature of water arrived till 37ºC when the external temperature

average was of 18ºC. (Figure 15).

Figure 15. Transparent cover used for testing of a system for energy saving.

3. TO COVER AN AUDITORIUM WITH FOLDABLE COUPLED ARCHES.

In this case the span to cover was of 41 m. and we chose a solution as shown in the figure 16,

tested at reduced model in the Figure 17 and in full scale in the Figure 18.

Figure 14. The main constructive details of the previous design.



We used arches made with pipes of D400.6 hinged in five points and powered by means of tour

motors of 2HP wheeled on chains. The Figures 19 and 20 show some details of the solution and

the Figure 21 different aspects of the assemble.

At difference of the solution for the swimming pool, in this case the fabric hangs from the pipes

presenting inside a continuous cylindrical surface.

All the analysis has been done by means of the SAP-90 and tested in laboratory. The Figures 22

to 25 shows some details of the building during the construction.

Figure 16. Design to cover an Auditorium in the folded and deployed positions.

Figure 17. Reduced scale model of this structure.

Figure 18. Full scale model of the two coupled arches.



Figure 19. Details of the driving system.

Figure 21. Views of the reduced scale model of the whole.

Figure 20. Details of the momented driving system.



Figure 22. General view of the construction.

Figure 23. View of the coupled arches. Figure 24. View of the scene.

Figure 25. Erecting the fabric cover. Figure 26. Erecting the fabric cover.

4. REFERENCES.

ESCRIG, F. Ed. “Mobile and Rapidly Assembled Architecture”. STAR. “Structural Architecture”.

Sevilla, 1997.

CHILTON, John. Ed. 3rd. SMG Colloquium “Structural Morphology Towards the new

millenium”. Nottingham, 15-17 August 1997.

ISHII, Kazuo. “Structural Design of Retractable Roof Structures”. WIT. Southampton. To be

published in Sept. 1999.

DOMBERNOWSKY & TURE WESTER Ed. “Engineering a New Architecture”. Aams School

of Architecture. May 26-28, 1998.

1999-3 foldable grids of coupled arches

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