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EXPANDABLE srnUC'IURf..s

': , ESCRIG Dr. Architect,

11 Profesor de la Escuela Tcnica Superiorde Arquitectura db Sevilla. Sl'AIN.

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. Instead o "corrtJination" of planar linear structures lI'e canuse ' ~ d d i t i o n of polyhedrals whose edges are struts lI'ithIPartiallY or totally triangulated faces. 5ee Fig 9 to givcFig 3 or Fig 10 to give Fig 6 and othcr more, likc Fig 11land 12, to obtain less convcntionaJ structures.III!

Possibilitics to combine deformable modulus composcd of crossed bars with an spatial joint at theirhalf are studied in this paper to obtain expandnble plnne structures. Spatial grids ables to be foldcdand exp:mded ar e systernatized in thei . main families. ChallgCS in the basie ar e introduced also toobtain curved grids. faced surfaces and archs. G r a p h i ~ s aOO pictures give us cIcar idea of the spatia!configuraron of cach nndel. :

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aplanar clement as shown in Fig 1> "combinedl' in(fig 2) , is able to cover a surface with astructure working as a whole (Fig 3) .

s.:une applies if we "coniline" IIn elernent as shown inig 4 in two dircctions (Fig S) to follow the wholeructure of Fig 6.

Fig 3lements rom Fig 1 and 4 may be "combined" in threerections to give more rigid structures (Fig 7 and B). Wen change a150 these elernents by others that increase

possibilities aOO even introduce substantialthat nllow us to gcneratc almost a11 the moreual structures (Ref 3) .

may considCT conventional plana. structures of bars asby cumularan of a ser of basie elements with

struts that, by "combinaron" or "addition",the required space.

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OF smI.ICIURAL SYSTEMS

Fig 14,IiThis elernent is isostatic if "h" is fixed and is no t aItriangulated structure, thereforc i ts struts are working inflexiono But i ts calculus is easy and i ts util i ty:satisfactory for light loads.lIf we plane to l'corrbine" several elements like these te getla whole like i t is shown in Fig 3, we obtain the structurelshown in Fig IS, in whic all struts have the same lcnght

"'l" a n d , t h c r e f o r ~ . there is g e o m e t r i c ~ l c o r n p a t i b i l i ~ y . t otake different Slzes in plan by changlng ' 'h '' f ran mWlIll.Irn!to "1" (F:i:g 16).I[Fi; 10

h a ll these cases wc have began fran rigid elements tohighly hyperestatic systems by joining ene cIernent to

even those alements no l heing rigid by thenselves.struc:tures, as shown in Fig 3, necd boundary conditions

control angular dcformations in their p l a n ~ . But, ~ o r r e c !designed, a11 these structures have an opt1mal resistent

this rescarch. however, 'ole have planed the possibilityfinding unstable structures in which th e degrees oE

IIl3ke them deformable and, consequently, able totheir posilion, area or Com.

mech81lisrns should be vcry userul i f 'ole could controldeformability and f ix their pesition with sorne

tional elenent stiffening th e whole in th e desired

achieve that 'ole ar e going to use the same "combination""addition" methods before explained.

we s tar t with a deformable truss like the one shownn Fig 13. This longitudinal planar elernent has no t been

as structure hecause i t has one degree of freedanch makes i t unstable. Nevertheless, if height ' 'h ' 'is fi.xed,shown in Fig 14. it is able to carry 1000s acting in i ts '

f ''11'' is variable with mechanical procedures "L" mayfran l i tUe values to another arbitrari1y high

accordingly with number of crosses.

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111, ; , "metu", th " .. "'Y ' ,b" EXpANllAllLE TIPE J. " '"the sarne rigidity conditions than tfie Fig 3 ene and will beIstable i f completed with sorne aid to fi x angular change inplan. PiS 17. 18 and 19 ShCM three different sUites o thesame lOOdel.

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.... J.II f basical Pig 13 is "coobined" according te configuration; shoio.'n in Fig 6, thc vi'sual aspect is more canplex and lessintuitive bu t i t wilI be proved !hat in Fig 20 is obtained

IEXPANOABLE TYPE n. PiS ZI, 2Z and Z3 show three differcntIstates o the IOOdcl .,

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