A NEW GEOMETRY FOR CYLINDRICAL DEPLOYABLE X-FRAMES
Félix Escrig, Prof. of School of Architecture of Sevilla. Spain José Sánchez, Lecturer of School of Architecture of Sevilla. Spain Juan P. Valcárcel. Prof. of School of Architecture of La Coruña. Spain
SUMMARY
One of the most known applications of deployable meshes of scissors is for geometry of cylindrical type. In this sense there are numerous patent that solve the angular instability problems but that are reduced to small constructions, furniture or panels for exhibitions. For large sizes are produced quite problems that make these structures of scarce application. The large deformations, deformations, the difficulty of stiffening them and the great size of the end walls are not the smaller of them.
Fig. 1
In this paper we make a short revision of proposals known till the moment and we propose alternatives of operation tested in the laboratory and in the full size.
1. INTRODUCTION
Fig. 2
The cylindrical meshes are produced by the package of scissors with the same length arms in which some of them have the eccentric joint.
Fig. 3
Fig. 1 shows the deployment of a curved X-lattice in the plan, while Fig. 2 shows the same for a straight one. Combining both in the form indicated in the Fig. 3 we obtain a spatial mesh that has the particularity of have an alone degree of freedom for the deployment but several degrees of freedom for the angular stability in plan (Fig. 4).
Fig. 4
A way of avoiding it is to locate in some type of structures diagonal stiffeners when deployed (Fig. 5). This same effect can be accomplished by the textile cover in the final state since also puts a limit l imit to the stretching of the diagonals (Fig. 6).
Fig. 5
The problem in this case is that the stiffeners not operate during the deployment. 1
The same effect we would obtain with a rigid fordable cover (Fig. 7) and in this case operates at all times. But not always we go to use covers with rigid parallels because their weigh increases Fig. 6 considerably and this limits the mobility. Fig. 8
Fig. 7
shows different states of this movement. In practice, for small structures the angular restriction restrict ion of the knots permits a controlled deployment.
Fig. 8
But it can not be supposed for large dimensions. Other solution is to use three way grids (Fig. 9 and 10).
Fig. 9
Fig. 10
In this case during the deployment is produced the bend of bars since the plan of the arms is warped, more when more deployed is the structure. We know that the diagonals of a warped 2
quadrilateral not coincide in any intermediate point. A solution used by Ziegler [Ref. 5] and Gantes [Ref. 4] consists of introducing some diagonals scissors (Fig. 11) that have the virtue of increasing much the stiffens and that go through an incompatible phase, what permits that surpassed this, same introduced energy maintains up the structure. Fig. 11
Something do not alluded yet is that these t hese structures tend to collapse if they are not anchored to the
ground. With this solution of abundant diagonals we need joints to connect eight bars with what increases its dimension and by all so produces eccentricities. Other usual problem is that the X-Structures work in flexion what is inconvenient for very slender bars. In this sense a form of diminish the stresses is to t o use very deployed scissors. For this, in spite
Fig. 12
Fig. 13
Fig. 14
of position like shown in Fig. 12 we must use better the Fig. 13 alignment of contiguous bars. We would think that surpassing the alignment angle we can improve the behaviour and in some instances it is, though it is not so for all type of loads, for instance wind forces.
Fig. 15
Fig. 16
The problem is that if we surpass the alignment angle the set will be unable to come back to fold an it will be blocked. In the case of cylindrical grids gri ds this can happen in the curved lattices but not in the strait ones that can not align contiguous bars (Fig. 15). Then they always can return. It is perhaps the only clear advantage of the cylindrical forms in addition to the simplicity of fabric patterns and the t he simple geometry. As cited before the great dimension dimen sion of end walls can be considered an inconvenient (Fig. 16). 3
Fig. 17
We have applied this type of structures reducing their height and attend to take advantages of other properties (Fig. 17). Nevertheless we have better alternatives.
2. CYLINDRICAL GRIDS WITH SIMPLE DIAGONAL STIFFNERS.
Fig. 18
Instead of the complex solution of the Fig. 11 we use some simplest simplest diagonal members (Fig. 18) that in addition to bracing help to connect the fabric to the joints. We save material with respect to the solution of diagonal arms but we have yet complex joints. Advantages of these structures are the cinematic compatibility in any time during
deploying.
Fig. 19
Fig. 19 illustrates this type in several states of folding.
3. CYLINDRICAL GRIDS WITH SPHERICAL EXTREMES
Other solution that we have tested with success is that of to close the ends with spherical segments. segments. This has at the same time two advantages, reduces the size of the end wall and stabilizes the angular deformations without need of diagonals. 4
Fig. 20
Fig. 21
Let us to explain of what consist this geometry. We make a spherical partition of parallel parall el and meridian (Fig. 20) and we substitute substitut e each segment by a scissor (Fig. 21). So that it will be possible the folding, each length near each knot must fulfil the t he property of be the same. This means analytically (Figs. 22 and 23). Fig. 22
tg α 2
=
sinα 1cosα 1 2 1 + sin α 1 3
tg α 3
=
sinα 1cosα T 1 + sinα T sinα 1
[1]
..................................... n
tg α n
=
sinα 1cosα
T
1 + sinα T sinα 1
Fig. 23
in which 3
α T = α 1 + 2α 2 n
α T
l
=
= α 1 +
2 (α 2 + ... + α n 1 )
R sinα i cos(δ − α i )
Fig. 24
5
[2]
−
[3]
Where a1 is determined by the number of subdivisions of the lower parallel an then all the angle values are also given. As it is known from [Ref. 1, 2 and 3]
Fig. 25
However, this is not sufficient condition for the folding since the upper rings hinde the foldability. But it is a good solution as a cap quarter that connected as indicated in the Fig. 25 is compatible with a cylindrical mesh letting the height of the entry so reduced as it is wanted.
Our experiences in models (Fig. 26) an in real constructions (Fig. 27) reveals us what appropriated of the solution since have resisted without problem winds of up to 120 km./h. lacking any lateral stiffning.
Fig. 26
Fig. 27
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Fig. 28
Fig. 29
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4. REFERENCES
1.- CALATRAVA, CALATRAVA, S.; ESCRIG, ESCRIG , F. F. & VALCARCE VALCARCEL, L, J.P. J.P. «Arquitectura Transformable». E.T.S.A. de Sevilla. 1993. ISBN 84-600-8583-X
2.- ESCRIG, F. F. & VALCARCEL, VALCARCEL, J. P. «Estructuras Espaciales Desplegables Curvas». Informe de la Construcción, nº 383. Madrid. 1987 ISSN 0020-0883
3.- ESCRIG, ESCRI G, F. VALCARCEL, VALCARCEL , J.P. & SANCHEZ, J. «Cubiertas de rapido montaje para piscinas al aire libre». R. E. Revista de Edificación Universidad de Navarra Nº 23 Octubre 1996 pp 5-17.
4.- GANTES, C. y otros Structural Analysis and Design of Deployable Structures. Computer & Structures Vol. 32 nº 3/4. 1989 PP 661-669
5.- ZEIGLER, T. Collapsable Self-Supporting Structures U.S. Patent nº 4.437.275. 1981
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