1986-3 Great Size Umbrellas Solved With Expandable Bar Structures

8/7/2019 1986-3 Great Size Umbrellas Solved With Expandable Bar Structures

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GREAT SIZE UMBRELLAS SOLVED WITH EXPANDABLEBAR STRUCTURESESCRIG, F.* and P. VALCARCEL, J.**

*Head of The Department of Structures of School of Architecture (Sevilla)**Head of The Department of Structures of School of Architecture (La Corua)

SUMMARY

After introducing several basical concepts on Expandable Bar Structures anddefining the pat te rns than can be used, a surveying on their applications asroofing is carried out. We propose expandable umbrellas which should be ablefor architectural purposes and discuses their constructional problems andanalysis.

f

INTRODUCTION

In a number of papers already publishedil] ,[2J,[3J and [ 4 ] , we have system-atized and defined the geometry of four

basical patterns that, convenientlyengaged, give tridimensional expandableassemblies that may work as structuresby means of proper mechanic devices.These basical oa tterns are shown inFigs. I throgh' 4 where bars are ableto achieve several movable configur-ations (Fiqs. 5 and 6) and thereforeoccupy more or less surface volume.Something symilar will happen to thearrangements built with these patterns.

For instance in Figs. 7 through 9 wesee different states for the same structure assembled with several regular -prisms like shown in Fig. 4.

Fi g. I

0;:' l.

1 J

Fi g. 5

Fig. 3. Fig. 4


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Fi g. 7 Fig. 8 Fi g. 9

The patterns shown above may be warped and give rise to irregular units to achieveother complex spatial configurations. To this , some compatibility conditions be-tween length of each strut of the whole ha ve to be satisfied. Figs. 10 and 11 showtwo of these structures in folded and expanded positions.

Fi g. 10

Fi g. 11

APPLICATIONSIn this paper we propose architectural solutions that, using the geometrical prop-erties already explained, are able to cover open spaces eventually.Umbrellas with only a central mast provide a good option to be folded or expandedeasily with mechanisms contained in them.


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Fig. Fig. 15 Fi g. 16~ Fig. 17

If we use regular patterns as defined in Figs. 1 through 4 we can obtain structureslike those shown in Figs. 14 through 17, with the same kind of bondary or another,provided that support is placed upon the gravity center of the whole.

Fig 18, Fig. 19These plane assemblies, i f correctly fixed to the supporting mast where foldingmechanism is placed, may be able to ac t as roofs. For that purpose the structuremust be completed with a textil fabric to bring waterfroofing, protection andstrength. Such a roofing material will improve the structural behavior, col labor-ating in tension either by i t se l f or reinforced with cables as shown in Figs. 18and 19. Obviously when these cables act in compression will not be considered inthe analysis.

Fig. 20 Fiq. 21


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Fig. 28

Fig. 29

CONSTRUCTION

The major constructional problems to be sol ved are the design of movable jointsand the mechanical devices of folding and e x p a n d i n g ~

Among other tentative s ol ut io ns fo r joint design we have selected a simple anduseful one, which should be able to ensemble any number of bars with any kind ofmotion (Fig 29).Crossing connections are solved with a bold when two bars are connected (Fig. 30)or with a ring when there are three or more bars (Fig 31).With respect to folding or expanding mechanisms the simplest are those which takeadvantage of their own weight as expanding force while folding is achieved bycables tensed by manual or mechanical devices as shown in Fig. 32.

TABLE 1.

POINT A GOES UP WHENTHE STRUCTURE FOlDSAND GOES DOWN WHENTHE STRUCTURE EXPANDS Fig. 32

FORCES F Ol Dl NG THE STRUCTURE(MECHANICAl ACTlONS)

29 mm. 78 mm. 400 nrn. 68 mm. 41 mm. 100 mm.

Fia.34 Fig.35 Fig.36 Fig.37 Fig.38 Fiq.39UmbrellaMaximal de-flection in

Fi g", 30

Fi 9 31.


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"

,.

ANALYSYS

These structures work in a very different way than other articulated structuresbecause bending moments and shear stresses are of great impbrtance in most cases.Struts have at less two supported ends and a central point of crossing. This im-plies that both stretches of a bar, at every side of the crossing point, are continuous. However the bars are articulated between them. Bending and shear stresseswill be considered clase to axial stresses.To analyze these structures, a computer program has been designed with severaladvantages over other conventional programs, devised to analyze general stressesin ar ticulated structures. The program is described in Reference L 5J . We have usedi t to compare six umbrella designs with the same plane project ion, s imilar el-lements or loads and different height profiles (Figs. 33 through 38). Compressedcables have been removed.Only fo r comparison of umbrella behavior we include in Table 1 the maximal deflec-tions. Inward slope umbrellas are better than plane ones and outward slope um-

brellas are the worst.

Fig. 39

REFERENCES

[1 ] ESCRIG, F. "Expanclable Space Frame Structures". Third International Conferenceon Space Structures. Proceedings. Surrey 1984. Elsevier. pp. 845-850.

[21 ESCRIG, F. "Estructuras espaciales de barras desplegables ll Informes de laConstruccin. IET. Vol 36, n0365. pp. 35-46.

[3 ] ESCRIG, F. "Expancable Space Structures". Space Structures International JOl!r-nal. Vol 1, n02. Elsevier. pp 79-91.

[41 ESCRIG, F. and P. VALCARCEL, J . "Introduccin a la geometra de la s e st ru ct u-ras espaciales desplegables de barras". Boletn Acadmico de la ET5A de LaCorua. n03, Feb. 1986.

[5 ] ESCRIG,F. and P. VALCARCEL, J. "Analysis of Expandable Space Bar Structures".Int. Symposium on Membrane Structures and Space Frames. IASS. Osaka. 1986.

1986-3 Great Size Umbrellas Solved With Expandable Bar Structures

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