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1 2a

(d)c)b)a)ig 2.

ANALYSIS OF EXPANOABLE SPACE BAR STRUCTURES.FELIX ESCRIS1 ANO JUAN P. VALCARCEL2lHead of the Oepartment of Structures of Escuela Tcnica Superior de Arquitec-tura de Sevil la. Ada. Reina Mercedes s/n. 41012. SEVILLA. SPAIN.2Head of the Department of Structures of Escuela Tcnica Superior de Arquitec-tura de LA CORUA . Castro E l v 1 ~ a . 18000. LA CORUA. SPAIN.

As we see, the structural components are bars articulated at the ends andconnected by means of a joint at an inner point. Each joint will c ~ n n e c t fromtwo to six or even more bars by means of proper devices.

Fig 3a shows a structure made with rigid struts while Fig 3b shows the samestructure completed with a cable chord.

Lying over constructional or functional problems we will to st ab li sh the wayto analyze these structures.

INTROOUCTIONExpandable bar structures are a special kind of art iculated structures that

can achieve several spatial configurations from completely folded, where al lstructural elements are concentrated in a bundle, to widely expanded, coveringa gred area. Fig 1 shows an a r r a n ~ e m e n t of this kind in three different states . These systemsfollow the paterns shown in F i 2. When correctly engaged, thesystem grDWS in one, two or three spatial directions building a complex wholewith the same properties than elemental cells: expandino and folding abilities.

f

Fig. 2. Expandable structure in trhee different states .

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DESIGN ANALYSISStandart programs to solve design of many bar structures are unable to do

i t w1th Expandable Space bar structures because in them each strut is supportednot only at the ends but also at central points as shown aboye. Hence we willdefine a computer program whose characteristic elements are shown in Fio 4.

(3)

(z)

NI EA O O Or u1O EA O O UzZ I2 3EI1L (1)PI O O :-2:"Z o vL1LZ

O O O 3EIZLPz :-2:"ZL1L Z wC O ~ P A T I B I L I T Y HATR IX

From FiQ4 and takin9 y axis paral lel to x'y' plane, transformation systemlaw is

(: c o s ~ cos(31 c.osDl 1OS0(2 cos(3 2 cos12 y'cos0(3 cos(33 cos 13 z'where relat ionships between tWo systems leads te

(: l-eo s e( cost- cos t x'cos f3 ces D y'- sen r - sencosoc'cos Y cos1cost" z'ensen, sen,

(b)

.u. o . -& I.>Z>

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