SpaCf¡ Structures 1 (1985) 79-91

Expandable Space Structures

Felix Escrig

Escuela Técnica Superior de Arquitectura de Sevilla, Ada. Reina Mercedes s/n, Sevilla 41012, Spain

(Received: 11 October, 1984)

Abstract: Expandable space structures are of great value in situations whereprimary functional requirements inelude transportability and ease of erection. Afamily of expandable space structures are described in the present paper, wheretheir practical applications and constructional aspects as well as their geometric andstatical analyses are discussed.

1. Introduction

Let us begin by considering aplane assembly,composed of crosses (Fig. 1). This assembly isdefonnable by pushing or pulling from the ends, whileits shape changes by increasing the height when thelength decreases and vice versa (Fig. 2).

In technical literature this is called a mechanism,with its use as a structure being restricted, because ofits mobility which makes it unable to carry loads. Butlet us suppose that, by means of an additional bar orsupports we fix the height H or the length L (Figs 3 and4). Then this assembly would be able to resist loads.

H

~~ --..:L=-- ~

Fig.l.

H'

Fig.2.

79

Fig.3.

Fig.4.

2. Generation of basic structures

1. Let us now consider an aggregate of twoassemblies, as shown above, placed perpen­dicular to one another (Fig. 5). Ifwe deform oneof them the other will take the same defonnationand it suffices to change the height H to expandor contract the couple,

By making use of this property, let us carry onto build an aggregate with a number of these

Space Structures 0266-3511/85/$03·30 © Elsevier Applied Science Publishers Ud, England, 1985. Printed in Northem Ireland

Expandable space structures

~ ..... ~""L-\ __ .JH

Fig.l0. YJg.12.

81

Fig.ll.

By joining elements in this way we obtainstructures such as those shown in Figs 11, 12 and13 at three degrees of expansiono

3. By combining basic elements obliquely 4 x 4, asrepresented in Fig. 14, and increasing the com­plexity of this configuration, we can createstructures such as those shown in Figs 15-17 inthree different states.

4. By combining basic elements oblíquely 3 x 3 asshown in Fig. 18, we may obtain expandablestructures such as shown in Fígs 19-21.

Fig.13.

Fig.14.

Expandable space structures

Fig.19.

Fig.20.

83

Hg. 21.

Hg. 22.

Hg. 23.

Fig.24.

Fig.25.

Expandable space structures 85

Flg.38.

Fig.37.

.--·.·.·--.--- .. -0·---·-···----·····.

4. Practical applications

Fig.35.

Possibilities of design from pattems described aboveare enormous and sorne cases are presented asexamples.

Figure 36 shows a hexagonal expaodable umbrellawith triangular modulation and supported on a centralmasto

Figure 37 shows a cylindrical barrel vault withrectangular modulation and supported 00 two sides.

Figure 38 shows an arch with triangular m~ulatioowith hioges at two eods.

Figure 39 shows a spherical dome with quadrilateralmodulation supported at four comers.

Figure 40 shows a perfect hemispherical domemade with bars oí the same leogth.

(d) Systems with more than one level of crossesmay be used with the same modifications asdiscussed aboye (Figs 32-35).

Restrictions to be imposed are difficult togeneralize io more irregular cases.

Flg.36. Fig.39.

Expandable space structures

Fig.41.

Figure 41 shows a quadrilateral expandableumbrella supported on a central mast with inwardsslope for drainage.

5. Architectonical aspects

To be useful in architectonical applications, thesestructures may be presented in their own right, tocreate movable structural systems for various usesinduding creation of enclosures.

In many cases there will be a need for a surface coverto protect spaces from rain, sun or wind, incor-

Fig.42.

87

porating a textile fabric tied at upper or lower nodes,and this will be expanded and folded with the structureto give a tense and continuous surface. This cover willbe used to give rigidity to the frame and to add to thestrength of the whole structure.

This cover may be repeated, one on the top jointsand the other under the bottom joints, to achieve athermal insulation layer and to improve functionalcomfort (Fig. 42).

The fabric cover may be arranged with auxiliarydevices to force the folding as shown in Fig. 43, inwhich strings of length m induce the surface to foldinwards (Fig. 44).

~lmFig.43.

1m

FIg.44.

6. Constructional aspects

As in conventional space structures, design of joints isthe basis of the whole designo

Figs 45-54 show sorne particular solutions used inreduced scale models and architectonical designs,while Figs 55-61 define sorne connections betweenstruts and joint elements.

Another major problem relates to folding andexpanding mechanical devices. Figures 62~ showthree different solutions.

In Fig. 62 an electric motor forces, by means of ascrew, the movement of the opposite joints duringexpansion or folding.

In Fig. 63 a hydraulic system separates the oppositejoints whilst gravity helps the reverse process.

In Fig. 64 a rope connecting distant joints by meansof a tensor engine forces the folding whilst gravityhelps the expansiono

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Expandable space structures

Fig.66.

Fig.67.

Figure 66 shows bending moment diagrams with

MI = Pln M2 = (PI + P2)n M3 = (PI + P2+ P3)n

91

Fig.68.

Figure 67 shows shear force diagrams with

QI = P¡sina Q2 = (PI + P2)sina

Q3 = (PI + P2 + P3)sina

Figure 68 shows axial force diagrams with

NI = PIcosa N2 = (PI + P2 + P3)cosa

N3 = (PI + P2 + P3)cosa

Torsional rigidity may be of great importanceparticularly in non-syrnmetrical structures.

When strength of the fabric cover is to be taken intoaccount, analysis becomes more complicated.