1997-2 A New Geometry for Cylindrical Deploy Able

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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, the difficulty of stiffening them and the great size of the end walls are not

the smaller of them.

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

The cylindrical meshes are produced by the packa-

ge of scissors with the same length arms in which

some of them have the eccentric joint.

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).

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 to the

stretching of the diagonals (Fig. 6).

The problem in this case is that the stiffeners notoperate during the deployment.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5



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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 coverswith rigid parallels because their weigh increases

considerably and this limits the mobility. Fig. 8

shows different states of this movement.

In practice, for small structures the angular restriction of the knots permits a controlled deployment.

But it can not be supposed for large dimensions.

Other solution is to use three way grids (Fig. 9 and 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

Fig. 6

Fig. 7

Fig. 8

Fig. 9 Fig. 10



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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 introducedenergy maintains up the structure.

Something do not alluded yet is that these 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 use very deployed scissors. For this, in spite

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.

The problem is that if we surpass the alignment angle

the set will be unable to come back to fold an it willbe blocked.

In the case of cylindrical grids 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 simple geometry.

As cited before the great dimension of end walls canbe considered an inconvenient (Fig. 16).

Fig. 13Fig. 12 Fig. 14

Fig. 15

Fig. 16

Fig. 11



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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 DIA-

GONAL STIFFNERS.

Instead of the complex solution of the Fig. 11 we

use some 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 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.

This has at the same time two advantages, reduces the size of the end wall and stabilizes the angular

deformations without need of diagonals.

Fig. 17

Fig. 18

Fig. 19



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Let us to explain of what consist this geometry.

We make a spherical partition of parallel and meridian

(Fig. 20) and we substitute each segment by a scissor

(Fig. 21). So that it will be possible the folding, each

length near each knot must fulfil the property of be

the same. This means analytically (Figs. 22 and 23).

1

1

1

3

1

3

1

2

11

2

sinsin1

cossintg

.....................................

sinsin1

cossintg

sin1

cossin

tg

α α

α α α

α α

α α α

α

α α

α

T

T n

n

T

T

+

=

+

=

+=

[1]

in which

)...(2

2

121

21

3

−+++=

+=

n

n

T

T

α α α α

α α α

[2]

)cos(

sinR

i

i

α δ

α

−

=l [3]

Fig. 20 Fig. 21

Fig. 22

Fig. 23

Fig. 24



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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]

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. 25

Fig. 26

Fig. 27



7

Fig. 29

Fig. 28



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4. REFERENCES

1.- CALATRAVA, S.; ESCRIG, F. & VALCARCEL, J.P.«Arquitectura Transformable».

E.T.S.A. de Sevilla. 1993. ISBN 84-600-8583-X

2.- ESCRIG, F. & VALCARCEL, J. P.«Estructuras Espaciales Desplegables Curvas».Informe de la Construcción, nº 383. Madrid. 1987 ISSN 0020-0883

3.- ESCRIG, F. 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 otrosStructural Analysis and Design of Deployable Structures.

Computer & Structures Vol. 32 nº 3/4. 1989 PP 661-669

5.- ZEIGLER, T.Collapsable Self-Supporting StructuresU.S. Patent nº 4.437.275. 1981

1997-2 A New Geometry for Cylindrical Deploy Able

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