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FOLDABLE GRIDS OF COUPLED ARCHES
Félix Escrig. Prof. of the School 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.
Figure1. Model folded and deployed of an spherical X-Frame grid.
1. INTRODUCTION
In the former designs we have used the good good properties properties of bundles of X-frames to build in a few days complexes structures as shown in Figures 1 and 2. Figure 2. Structure build for shadow (8x8 s qm.)
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).
Figure 3. Three different stages of deploying deploying of the cover oz St. St. Pablo swimming of Sevilla.
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 4. Rhombic deployable plane mesh.
Figure 5. Cylindrical projection of a rhombic deployable 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 the length “li” that must be the same in any case as shown in the figure 6. Figure 6. Change of width for a rhombic mesh.
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 assemblie on wheels.
Figure 7 . Two coupled arches and position of the hinges.
Fig Figure 8. The deploying of two coupled arch rches.
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 9. Th The ne necessa ssary dis disp placement of of th the tw two coupled arches is named “d”
Figure 10. Design of a deployable cover by means of coupled arches.
Figure 11. Reduced scale model of the previous des ign.
We can use any curve for the arches with the only restriction that the hinge is placed at the half of the height.
Figure 12. External view of a deployable cover.
If we connect several of the coupled arches we can achieve a longitudinal construction as shown in the Figure 10.
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. Figure 13. Internal view of a deployable cover.
The Fig 12 and 13 shows different different views of the building and the Figure 14 some constructive details.
Figure 14. The main constructive details of the previous design.
This design is covered covered with a transparent fabric to collect directly the solar radiation 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 t esting 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 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.
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 f abric 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 19. Details of the driving system.
Figure 20. Details of the momented driving system.
Figure 21. Views of the reduced scale model of the whole.
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.
