Transactions on Information and Communications Technologies vol 12, 1995 WIT Press, ISSN

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1 Visualization of expandable structures with self-folding roofing plates J.P. Valcarcel,* F. Escrig/ E. Martin," J.A. Vazquez" " Department of Technology of Construction, E.T.S. Architecture La Coruna, Spain * Department of Structures, E.T.S. Architecture, Sevilla, Spain Abstract The expandable structures of bars are a very useful solution for the problem of covering an area with a structure which is able to be removed when the conditions of use requires it. Our team has been studying a lot of solutions for several years and many proposals had been made. Usually the roofing of such structures has been solved with textile cover. Recently our team have studied several interesting solutions with selffolding rigid plates for vaults and domes. The visualization of these structures is a basic tool in order to design the correct folding of complicated systems of roofing plates. In this paper the main problems of design and roofing of these grids will be studied, as well as the experiences of our team on this field. 1 Introduction Recently, a new transformable architecture is arising. Its most important achievements are the mobile structures which can cover an area when necessary, or be removed, thus leaving this enclosure in the open air. In sport areas like stadiums, swimming-pools, football fields, spectator generally prefer to be out in the open, weather permitting. However, in adverse climatological conditions, it becomes necessary to cover the whole area, or at least the areas where people is seated. Any solution that offers these two options will represent a good architectonical solution.

2 192 Visualization and Intelligent Design in Engineering Lately, significant achievements have dealt with this problem by using large elements witch can be displaced. Important examples, such as the Sky dome in Toronto or the Ariake Colosseum in Tokyo come to mind. We are more interested in another possible solution to this problem that lies in the use of expandable space bar structures. These consist of modular bar units, made up of mobile bundles or scissors joined at ends and at an inner joint. They can be folded up to form a compact package or unfolded to cover a large enclosure. They are quite simple structures, the main difficulty of which lies in finding an adequate system for covering them, since it is very difficult that the roofing elements adapt to the strong folding allowed by the bars of the structure. A good example could be the swimming-pools. People prefers to be at open air in summer, but if they are not cover during the winter they are unable to use. Even a good design of the cover let improve the heating, with an important reduction of maintenance costs. In the research line developed by our team, there are some interesting proposals about modulus with self-folding textile cover, even used in a recent cover for a swimming- pool in Seville. The reference [5] provides a study of several of our proposal, in which self folding textile covers are employed. Textile covers are very interesting solutions for many structures, but a truly effective cover must be made with rigid elements, usually plates or sandwich panels. These provide adequate protection against the rain and, at the same time, form heat and acoustic insulation. This aspect is worth noting, since covers made up of stiff textile membranes produce a loud noise under heavy rain. For this reason our team has carried out a great deal of research into roofing systems consisting of expandable structures with rigid panels which can either fold and unfold together with the structure. References [6], [7], [8] provides a study of several of our proposals on covering with rigid plates expandable cylindrical vaults or domes with triangular modulus and reference [9] on domes with squared modulus like the swimming-pool of Seville. 2 Foldable rigid plates for covering expandable trusses. The roofing system is solved with plates which fold up by means of an auxiliary crosspiece structure. This is placed over the holding up structure and merely serves as a guide for the unfolding of the panels. It is worth remarking that the auxiliary structure only needs to support the weight of each of the panels and this, only in the unfolding process. Therefore it can be of reduced cross section.

3 Visualization and Intelligent Design in Engineering 193 In figure 1 one can observe the unfolding of a typical module of this system, useful for plane or cylindrical trusses. If the panels are placed so as to fold towards the inside of the truss, it is possible to solve the problems of the point of union in order to prevent water from entering. The reference [7] provides a complete study of these solutions. Fig. 1 When the structure is made up of squared modulus, it is possible to use another system, deploying the roofing plates by the diagonal. In both cases the system allows a nearly complete folding. Of course, there is a limit to the degree of Fig. 2 folding for real structures which is defined by the thickness of the bars and the roofing plates, In this case the sequence of unfolding would be (fig. 2). If the expandable structure of squared modulus is flat the design of roofing plates is simple. The fig 3 shows the process of deploying of a truss of four squared modulus. The top four modulus has been chosen, because folding of plate are more complicated. This process can be generalized, even for structures of great complexity, as is the case of an unfolding dome of squared or triangular modulus, in this situation, the conditions for geometrical compatibility require all modules of each sector to be different, even the bars have the same length, but the angulus between scissors are different in each modulus. Besides this, it is necessary to take into account that when de truss closes up, one must allow the crosspieces of the auxiliary structure to displace laterally to a slight degree, in order to avoid the lower panels running into the upper ones. In practise, this poses no difficulty, since the auxiliary scissors lack lateral stiffness. It would be

4 194 Visualization and Intelligent Design in Engineering Fig. 3 unnecessary because its only purpose is to guide the unfolding of the roofing plates. The result of this process is shown in next figures. This has been formulated through a calculus program, the results of which have been translated into an AutoCAD environment, using.scr files. 3 Generation of expandable structures through C.A.D. The design and manipulation of expandable spacial structures of bars is too complicated for direct analysis. The best solution is define the coordinates of knots and nodal connection of bars in specific calculation programs and transfer of the generated data to C.A.D. At the same time, the proposed system allows for the study of the folding and unfolding of the truss and the detection of the would-be geometrical incompatibilities that must be taken into account for the calculation. When the modules of the structure are straight their generative laws are simple and can be formed in a CAD environment with not much trouble, creating a module and repeating it by juxtaposition. Nevertheless, for curved structures, the laws of geometrical compatibility will generally force all the modules of the truss to differ. The usual resources of the CAD will no suffice and the handling of such objets would demand such complexity that this would render the method useless.

5 Visualization and Intelligent Design in Engineering 195 It is for this reason that the method developed by our team outlines the advantages of a numerical calculation of a computerized language (in this case QUICKBASIC or C, depending on the routine applied) for the study of the conditions of geometrical compatibility, and the advantages of the CAD environment (in this case AUTOCAD 12.0) for the manipulation of the objets including the auxiliary structure that support the roofing plates and the foldable plates themselves. Once the structure has been fully deployed and completed with the required bars, these data can be recovered and linked with a calculation program of the sort mentioned in the references. Therefore the phases of this process are: Development of the base truss (programming). Transfer of this base truss to a CAD environment and its manipulation. In this phase is possible to detect geometric incompatibilities. Recovering of the complete truss from a programming environment with its consequent calculation and sizing of the same. A new step to a CAD environment in order to obtain then building plans, knots, details, etc. ACKNOWLEDGEMENTS This paper has been made possible by a grant from the XUNTA DE GALICIA through a research project. REFERENCES. 1.- Perez Pinero, E.; Candela, F.; Dalf, S.: "La obra de Perez Pinero". Arquitectura. Madrid n pp Escrig, F.; P.Valcarcel, J.B. "Curved Expandable Space grids". Nonconventional Structures '87. London P.Valcarcel, J.B.; Escrig, F. "Analysis of curved expandable space bar structures" Int. Symposium on 10 Years of Progress in Shell and Spatial Structures. I ASS. Madrid Escrig, F.; P.Valcarcel, J.B.; Gil Delgado, O. "Design of expandable spherical grids" Int. Symposium on 10 Years of Progress in Shell and Spatial Structures. I ASS. Madrid P.Valcarcel, J.B.; Escrig, F. "Expandable Structures with Self-folding Textile Cover". International Conference on Mobile and Rapidly Assembled Structures. MARAS'91. Southampton 1991.

6 196 Visualization and Intelligent Design in Engineering 6.- P. Valcarcel, J.B.; Escrig, F.; Estevez, J.; Martin, E. "Large Span Expandable Domes" Int. Symposium on Large Span Structures. I ASS. Toronto P. Valcarcel, J.B.; Escrig, F.; Martin, E. "Expandable Domes with Incorporated Roofing Elements". Four International Conference on Space Structures. Surrey P. Valcarcel, J.; Escrig, F.; Martin, E. "Expandable structures with incorporated roofing elements". I.A.S.S. Congress on Spatial Lattice and Tension Structures. Atlanta Secuence of deploying for a squared dome

7 Visualization and Intelligent Design in Engineering 197 Secuence of deploying for a cilindrical vault

8 198 Visualization and Intelligent Design in Engineering Secuence of deploying for a triangular modulus dome