Tensegrity Structres

7/26/2019 Tensegrity Structres

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CONTENTS

FIGURE LIST………………………………………………...…………………………….…….…..IV

1.INTRODUCTION……………………………………………………………………………………1

2,.TENSION………………………………………………………………………………………...…2

2.1 Definition Of Tension…………..…………………………………………………….……..…2

2.2 Tension Members……………………………………………………………………….…..……

!. TENSEGRIT"………………………………………………………………………………...……#

!.1 Definition $n% &rin'i()es Of Tense*rit+ …………………………….…………………….…#

!.2 istor+ Of Tense*rit+ …………………………………………………….......………….……..-

!.2.1 Ori*ins Of Tense*rit+……………………………………………………....................….-

!.! $(()i'tions Of Tense*rit+…………………………………………………………………... 1

!. C/r'teristi's Of Tense*rities…………………………………………...……………..…..10

!.0 $%nt*es Of Tense*rit+ Oer Conention) Contin3o3s4

Str3't3res……………………………………………………………………………….……….… 15

!.5 Dis%nt*es Of Tense*rit+ Oer Conention) Contin3o3s4 Str3't3res

………………………………………………………………………………………..…1#

!.# To(o)o*i') C)ssifi'tion Of E)ementr+ Ce))s Of Tense*rit+ Str3't3res

………………………………………………………………………………..……….…16

!.#.1 R/ombi' 'onfi*3rtion…………………………………………………………….….…..16

!.#.2 Cir'3it 'onfi*3rtion………………………………………………………….…………...1-

!.#.! 78 t+(e9 'onfi*3rtion…………………………………………………………….……....2:

!.6 T+(es Of Tense*rities…………………………………………………………..………....….21

!.6.1 Tense*rit+ (rism T;(rism4…………………………………………………….……...…..22



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!.6.2 Dimon% tense*rit+…………………………………………………………….…...…...2

!.6.! 8i*;<* tense*rit+……………………………………………………………………….2#

.=E$VING > MOTER OF TENSEGRIT"…………………………………………….....….26

.1 Intro%3'tion …………………………………………………………………………………...26

.2 Ri*/t e)i? $n% Left e)i?……………………………………………….…………………..!:

.! E?m()es of =ein* in T/e Tense*rit+ S+stem……………………………………...….!1

0.TENSEGRIT" E@$M&LES ………………………………………………….…….…….35

0.1 S3s(ension Ari%*e……………………………………………………………………………!0

5.2 The Skylon Tower……………………………………………………………………...36

5.3 Roof Structures…………………………………………………………………………37

5.4 Child’s Bloon………………………………………………………………………….3!

5.5 "u#n Body……………………………………………………………….………...…3$

REFERENCES…………………………………………………………………………………….:



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LIST OF FIGURES

2.1 Tension n% Com(ression…………………………………………….….……..2

2.2 T+(es of Members………………………..……………………………….….…

!.1 Com(rison betBeen t/e G)ei'/*eBi'/tonstr3tion or Str3't3re;

S'3)(t3re……………………………………………………………………...…......1:

!.2 Sim()e? b+ Sne)son, sim()est tense*rit+ s+stem ……………….................11

!.! @;'o)3mn b+ Sne)son …………………………………………..……….…...12

!. 4 $ssemb)+ of r/ombi' 'onfi*3rtion n% b4 its (ttern ………………...16

!.0 4 Cir'3it 'onfi*3rtion of C3bo't/e%ron tense*rit+ /in* non;

to3'/in* trin*3)r 'ir'3its n% b4 its (ttern …………………………….……...1-

!.5 4 Tr3n'te% Tetr/e%ron T;tetr/e%ron4 3sin* 8 t+(e 'onfi*3rtion,

b4 its (ttern ……………………………………………………….…....…….2:

!.# =oo% @;mo%3)e ………………………………………………………….……21

!.6 ite frme s/(e in rio3s (ro(ortions ………………………………...….22

!.- Dimon% Confi*3rtion of T;(rism ……………………………………….....2!

!.1: 4 T;i'os/e%ron n% b4 its 'orres(on%in* trnsformtion from n%

b' to %o3b)e%;3( o't/e%ron ……….................................................20

!.11 4 O't/e%r) str3't3re b4 ()nr ieB of 'orres(on%in* !;str3ts

sin*)e )+er tense*rit+ s+stem …………………………………..........….20

!.12 &)nr ieB of 5;str3ts tBo )+er tense*rit+ s+stem ……………….…...25

!.1! &)nr ieB of -;str3ts t/ree;)+er tense*rit+ s+stem …………..……...25



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!.1 T;Tetr/e%ron 8 t+(e 'onfi*3rtion ……….………………………….…2#

.1 T/e Common SH3re =ee e?*on ……………………………..………26

.2 T/ree =+ Trin*)e =ee……………………………………………..…...…26

.! Cross tBo (en'i)s ………………………………………………………………..2-

. Ri*/t n% Left e)i? ………………………………………………………..……!:

.0 Ri*/t n% Left e)i?es ………………………………………………..…………!1

.5 *ome T/ree;=+ Aset =ee.…………………………. ………....……!1

.# *ome T/ree;=+ Aset =ee…………………………………......…….!2

.6 E?m()es of =ein* in Tense*rit+ …………………………………….…..…!!

0.1 Go)%en Gte Ari%*e, Sn Frn'is'o, C)iforni …………………...…………!0

0.2 S+)on ToBer Lon%on, En*)n% ………………………………………..……!5

0.! $ %ome %esi*ne% b+ Robert Le Ri'o)is …………………………….…..……!#

0. C/i)%9s A)oon …….……………………………………………………..……....!6

0. 3mn bo%+ tense*rit+ mo%e) …………………………………………….…...!-



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1. INTRODUCTION

T/e te'/niH3e 3se% in 'onstr3'tions b+ r'/ite'ts ro3n% t/e Bor)% is bse% on

/o)%in* t/e str3't3re Bit/ t/e /e)( of its Bei*/t n% 'ontin3it+ of stresses in%3'e%

bsi'))+ in 'om(ression. For e?m()e, e'/ 'om(onent of stone %ome or bri%*e is

(3))e% b+ tension 'tin* %oBnBr% t/ro3*/ t/e str3't3re, b3t t/e 'om(ressie'ontin3it+ is sti)) in '/r*e of s3stinin* most of t/e )o%. On t/e ot/er /n%,

tense*rit+ r'/ite't3re re(resents tot))+ %ifferent (rin'i()e Bit/ tension 'ontin3it+

n% 'om(ression %is'ontin3it+. Tense*rities re(resent s+stem of 7eH3i)ibrte%

omni%ire'tion) stresses9 n% t/e+ %on9t nee% n+ s3((ort n% re se)f;eH3i)ibrte%

s Be)) s (re;stresse%. T/e t/eor+ of tense*rit+ str3't3res is Be)) noBn in 'ii)

en*ineerin* or stt3r+ B/i)e in ot/er en*ineerin* brn'/es t/e (otenti) of t/ese

str3't3res is not +et f3))+ e?()ore%.



2

2. TENSION

2.1 Definitions Of Tension

Tension for'e is for'e t/t is e?erte% eH3))+ on bot/ en%s of 'b)e, '/in, ro(e,

Bire or ot/er 'ontin3o3s obJe't n% is trnsmitte% betBeen t/e en%s b+ t/tobJe't. On mi'ros'o(i' )ee), obJe'ts 3n%er tension /e se(rtion betBeen

mo)e'3)es t/t 'retes (otenti) ener*+ in t/eir bon%s.

It reH3ires for'e to (3t n obJe't 3n%er tension, b3t te'/ni'))+, tension itse)f is not

for'e for s )on* s t/e sit3tion is stb)e. Nonet/e)ess, (/+si'ists mes3re t/e

tension in s+stem in 3nits of for'e. On'e some (rt of t/e s+stem be*ins moin*,s3'/ s B/en one en% of ro(e 3n%er tension is re)ese%, t/e (otenti) ener*+

betBeen t/e mo)e'3)es of t/e ro(e is 'onerte% to me'/ni') ener*+, n% t/e

tension is 'onerte% to for'e. $s )on* s n obJe't 3n%er tension is stri*/t, t/e

tension is 'onstnt for its entire )en*t/.

$ for'e is n+ (3s/ or (3)) 'tin* 3(on n obJe't s res3)t of its inter'tion Bit/

not/er obJe't. Tension for'es re one of t/e 'ont't for'es, B/i'/ re t/e for'es

(resent B/en tBo obJe'ts re in 'ont't Bit/ one not/er. T/ere re )so non;'ont't

for'es, s3'/ s *rit+, m*neti' for'e n% e)e'tri') for'e, B/i'/ 't t %istn'e.

K1

Com(ression, %e'rese in o)3me of n+ obJe't or s3bstn'e res3)tin* from (()ie%

stress. Com(ression m+ be 3n%er*one b+ so)i%s, )iH3i%s, n% *ses n% b+ )iin*

s+stems. In t/e )tter, 'om(ression is mes3re% *inst t/e s+stem9s o)3me t t/e

stn%r% (ress3re to B/i'/ n or*nism is s3bJe'te%e.*., t/e (ress3re of t/etmos(/ere t se )ee) is t/e stn%r%, or referen'e, for most )n% nim)s, b3t t/e



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stn%r% for %ee(;se fis/es n% simi)r s(e'i)i<e% forms is t/e norm) (ress3re of

t/eir enironment. Tension is t/e o((osite of 'om(ression. Fi*.2.14

Figure 2.1 Tension n% Com(ression



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2.2 Tension Members

T/e tension member 'onsi%ere% for t/e %esi*n is )iner member B/i'/ 'rries n

?i) (3)). T/e members 3n%er*o e?tension %3e to t/is ?i) (3)). T/is is one of t/e

'ommon t+(es of for'e trnsmitte% in t/e str3't3r) s+stem. Tension members re

er+ effi'ient sin'e t/e entire 'ross se'tion 'rries 3niform stress 3n)ie f)e?3r)

members. T/e tension members %o not b3')e een B/en stresse% be+on% t/e

e)sti' )imit. en'e t/e %esi*n is not effe'te% b+ t/e t+(e of se'tion 3se% i.e., &)sti',

Com('t or Semi;'om('t. Some of t/e 'ommon e?m()es of tension members in

str3't3res re Aottom '/or% of (in Jointe% roof tr3sses, bri%*es, trnsmission )ine

n% 'omm3ni'tion toBers, Bin% br'in* s+stem in m3)ti;store+ b3i)%in*s, et'. T/e

obJe'tie of t/is e?er'ise is to %etermine t/e tensi)e stren*t/ of *ien member

/in* s(e'ifie% en% 'onne'tion. T/e stren*t/ of t/ese members is inf)3en'e% b+

seer) f'tors s3'/ s t/e )en*t/ of 'onne'tion, t+(e of 'onne'tion b+ bo)ts or

Be)%s4, 'onne'tion e''entri'it+, si<e n% s/(e of fsteners, net re of 'ross;se'tion

n% s/er )* t t/e en% 'onne'tion. K2

2.2.1 Types of Tension Members

Figure 2.2 T+(es of Members



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T/e tension members m+ be m%e of sin*)e str3't3r) s/(es. T/e stn%r%

str3't3r) s/(es of t+(i') tension members re Fi*.2.24

4 Ro%s n% Ars b4 Cb)es n% =ires '4Sin*)e n% %o3b)e n*)es

%4Ro))e% =;n% S;se'tion e4 Str3't3r) Tee f4 A3it;3( Ao? Se'tions

Ros !n "!rs#T/e sH3re n% ro3n% brs re s/oBn in Fi*3re;2 re H3ite often

3se% for sm)) tension members. T/e ro3n% brs Bit/ t/re%e% en%s re 3se% Bit/

(in;'onne'tions t t/e en%s inste% of t/re%s.

T/e en%s of re'tn*3)r brs or ()tes re en)r*e% b+ for*in* n% bore% to form e+e

brs. T/e e+e brs re 3se% Bit/ (in 'onne'tions. T/e ro%s n% brs /e t/e

%is%nt*e of in%eH3te stiffness res3)tin* in noti'eb)e s* 3n%er t/e se)f

Bei*/t.

$ires !n C!b%es#T/e Bire t+(es re 3se% for /oists, %erri's, ri**in* s)in*s, *3+

Bires n% /n*ers for s3s(ension bri%*es.

Sing%e Stru&tur!% S'!pes !n (%!tes#T/e sin*)e str3't3r) s/(es, i.e. n*)e

se'tions n% tee;se'tions s s/oBn in Fi*3re;2 re 3se% s tension members. T/e

n*)e se'tions re 'onsi%erb)+ more ri*i% t/n t/e Bire ro(es, ro%s n% brs. =/en

t/e )en*t/ of tension member is too )in*, t/en t/e sin*)e n*)e se'tion )so be'omes

f)e?ib)e.

T/e sin*)e n*)e se'tions /e t/e %is%nt*e of e''entri'it+ in bot/ ()nes in

riete% 'onne'tion.

T/e '/nne) se'tion /s e''entri'it+ in one ?is on)+. Sin*)e '/nne) se'tions /e

/i*/ ri*i%it+ in t/e %ire'tion of Beb n% )oB ri*i%it+ in t/e %ire'tion of f)n*e.



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O''sion))+, I;se'tions re s3e% s tension members. T/e I;se'tions /e more

ri*i%it+, n% sin*)e I;se'tions re more e'onomi') t/n b3i)t 3( se'tions.

"ui%t)up "o* Se&tions#TBo or more t/n tBo members re 3se% to form b3i)t 3(

members. =/en t/e sin*)e ro))e% stee) se'tion 'n not f3rnis/ t/e reH3ire% re, t/en

b3i)t;3( se'tions re 3se%.

T/e %o3b)e n*)e se'tions of 3neH3) )e*s s/oBn in t/e fi*3re re e?tensie)+ 3se%

s tension members in t/e roof tr3sses. T/e n*)e se'tions re ()'e% b' to b'

on tBo si%es of *3sset ()te. =/en bot/ t/e n*)e se'tions re tt'/e% on t/e

sme si%e of t/e *3sset, t/en b3i)t;3( se'tion /s e''entri'it+ in one ()ne n% is

s3bJe'te% to tension n% ben%in* sim3)tneo3s)+. T/e tBo n*)e se'tions m+ be

rrn*e% in t/e str s/(e i.e. t/e n*)es re ()'e% %i*on))+ o((osite to e'/

ot/er Bit/ )e* on o3ter si%es4.

T/e str s/(e n*)e se'tions m+ be 'onne'te% b+ btten ()tes. T/e btten ()tes

re )terntie)+ ()'e% in tBo (er(en%i'3)r %ire'tions.

$ b3i)t;3( se'tion m+ be m%e of tBo '/nne)s ()'e% b' to b' Bit/ *3sset in

betBeen t/em. S3'/ se'tions re 3se% for me%i3m )o%s in sin*)e ()ne;tr3ss. In

tBo;()ne tr3sses, tBo '/nne)s re rrn*e% t %istn'e Bit/ t/eir f)n*e t3rne%

inBr%. It sim()ifies t/e trnserse 'onne'tions n% )so minimi<es )'in*. T/e

f)n*es of tBo '/nne)s re e(t o3tBr%s, s in t/e 'se of '/or% members or )on*

s(n *ir%ers, in or%er to /e *reter )ter) ri*i%it+.

T/e /e+ b3i)t;3( tension members in t/e bri%*e *ir%er tr3sses re m%e of n*)es

n% ()tes. S3'/ members 'n resist 'om(ression in reers) of stress tes ()'e.



7



8

+. TENSERIT-

+.1 Definition n (rin&ip%es Of Tensegrity

$nt/on+ &3*/ *ies t/e fo))oBin* %efinition of tense*rit+> $ tense*rit+ s+stem is

estb)is/e% B/en set of %is'ontin3o3s 'om(ressie 'om(onents inter'ts Bit/

set of 'ontin3o3s tensi)e 'om(onents to %efine stb)e o)3me in s('e. Tense*rit+

str3't3res re %istin*3is/e% b+ t/e B+ for'es re %istrib3te% Bit/in t/em. T/e

members of tense*rit+ str3't3re re eit/er )B+s in tension or )B+s in

'om(ression. In t/e str3't3res %is'3sse% in t/is boo, t/e tensi)e members re

3s3))+ 'b)es or ro%s, B/i)e t/e 'om(ression members re se'tions of t3bin*. T/e

tensi)e members form 'ontin3o3s netBor. T/3s tensi)e for'es re trnsmitte%

t/ro3*/o3t t/e str3't3re. T/e 'om(ression members re %is'ontin3o3s, so t/e+ on)+

%o t/eir Bor er+ )o'))+. Sin'e t/e 'om(ression members %o not /e to trnsmit

)o%s oer )on* %istn'es, t/e+ re not s3bJe't to t/e *ret b3')in* )o%s t/e+ Bo3)%

be ot/erBise, n% t/3s t/e+ 'n be m%e more s)en%er Bit/o3t s'rifi'in* str3't3r)

inte*rit+. In t/e re)m of /3mn 'retion, (ne3mti' str3't3res re tense*rities. For

instn'e, in b))oon, t/e sin is t/e tensi)e 'om(onent, B/i)e t/e toms of ir insi%e

t/e b))oon s3(()+ t/e 'om(ressie 'om(onents. T/e sin of t/e b))oon 'onsists of

toms B/i'/ re 'ontin3o3s)+ )ine% to e'/ ot/er, B/i)e t/e toms of ir re /i*/)+

%is'ontin3o3s. If t/e b))oon is (3s/e% on Bit/ fin*er, it %oesn9t 'r' t/e

'ontin3o3s, f)e?ib)e nettin* forme% b+ t/e b))oon9s sin %istrib3tes t/is for'e

t/ro3*/o3t t/e str3't3re. $n% B/en t/e e?tern) )o% is remoe%, t/e b))oon ret3rns

to its ori*in) s/(e. T/is resi)ien'e is not/er %istin*3is/in* '/r'teristi' of

tense*rit+ str3't3res. $not/er /3mn rtif't B/i'/ e?/ibits tense*rit+ H3)ities is

(restresse% 'on'rete. $ (restresse% 'on'rete bem /s intern) stee) ten%ons B/i'/,

een Bit/o3t t/e (resen'e of n e?tern) )o%,



9

re stron*)+ in tension B/i)e t/e 'on'rete is 'orres(on%in*)+ in 'om(ression. T/ese

ten%ons re )o'te% in res so t/t, B/en t/e bem is s3bJe'te% to )o%, t/e+

bsorb tensi)e for'es, n% t/e 'on'rete, B/i'/ is not effe'tie in tension, remins in

'om(ression n% resists /e+ 'om(ressie for'es e)seB/ere in t/e bem. T/is

H3)it+ of (restresse% 'on'rete, t/t for'es re (resent in its 'om(onents een B/en

no e?tern) )o% is (resent, is )so er+ '/r'teristi' of tense*rit+ str3't3res. In t/e

nt3r) re)m, t/e str3't3r) frmeBor of non;Boo%+ ()nts re)ies 'om()ete)+ on

tense*rit+ (rin'i()es. $ +o3n* ()nt is 'om()ete)+ 'om(ose% of 'e))s of Bter B/i'/

be/e m3'/ )ie t/e b))oon %es'ribe% boe. T/e sin of t/e 'e)) is f)e?ib)e inter;

)in*e of toms /e)% in tension b+ t/e for'e of t/e Bter in t/e 'ontine% 'e)). $s t/e

()nt is stret'/e% n% bent b+ t/e Bin%, rin n% ot/er nt3r) for'es, t/e for'es re%istrib3te% t/ro3*/o3t t/e ()nt Bit/o3t %ist3rbn'e to its str3't3r) inte*rit+. It 'n

s(rin* b' to its 3s3) s/(e een B/en, in t/e 'o3rse of t/e nt3r) 3(/e)s it

3n%er*oes, it fin%s itse)f %istorte% fr from t/t s/(e. T/e essenti) str3't3r) 3se t/e

()nt mes of Bter is es(e'i))+ seen B/en t/e ()nt %ries o3t n% t/erefore Bi)ts.

K!



10

+.2 /istory Of Tensegrity

Tense*rit+ is %ee)o(in* n% re)tie)+ neB s+stem bre)+ more t/n 0: +ers o)%4

B/i'/ 'retes m<in*, )i*/tBei*/t n% %(tb)e fi*3res, *iin* t/e im(ression of

')3ster of str3ts f)otin* in t/e ir. $s it is e?()ine% in Gme< PQ3re*3i K1, it is not

'ommon)+ noBn t+(e of str3't3re, so noB)e%*e of its me'/nism n% (/+si')

(rin'i()es is not er+ Bi%es(re% mon* r'/ite'ts n% en*ineers. oBeer, one of

t/e most '3rio3s n% (e'3)ir s(e'ts of tense*rit+ is its ori*in 'ontroers+ n%

(o)emi' Bi)) )B+s be (resent B/en r*3in* bo3t its %is'oer+. K

+.2.1 Origins Of Tensegrity

T/ree men /e been 'onsi%ere% t/e inentors of tense*rit+> Ri'/r% A3'minster

F3))er, Di% Geor*es Emmeri'/ n% ennet/ D. Sne)son. $s (re'3tion, t/ese

nmes /e been mentione% in '/rono)o*i') or%er of t/eir *rnte% (tents> F3))er;

1! No 1-52 Emmeri'/;26 Se( 1-5 Sne)son;15 Feb 1-504. $)t/o3*/ )) of t/e

t/ree /e ')ime% to be t/e first inentor, R. Motro mentions t/t Emmeri'/ re(orte%t/t t/e first (roto;tense*rit+ s+stem, '))e% G)ei'/*eBi'/tonstr3tion, Bs 'rete%

b+ 'ertin r) Io*nson some 3t/ors ')) /im Po/nsen4 in 1-2: Fi*3re !.14.

$s Emmeri'/ e?()ins> Cette curieuse structure, assemblée de trois barres et de

sept tirants, était manipulable à l'aide d'un huitième tirant detendu, l'ensemble étant

déformable. Cette configuration labile est très proche de la protoforme autotendante

à trois barres et neuf tirants de notre invention.



11

Figure +.1 Com(rison betBeen t/e G)ei'/*eBi'/tonstr3tion or Str3't3re;S'3)(t3re

T/is mens it Bs str3't3re 'onsistin* of t/ree brs, seen 'or%s n% n ei*/t/

'b)e Bit/o3t tension serin* to '/n*e t/e 'onfi*3rtion of t/e s+stem, b3t

mintinin* its eH3i)ibri3m. e %%s t/t t/is 'onfi*3rtion Bs er+ simi)r to t/e

(roto;s+stem inente% b+ /im, t/e E)ementr+ EH3i)ibri3m, Bit/ t/ree str3ts n%

nine 'b)es Fi*3re !.24.

$)) t/e sme, t/e bsen'e of (re;stress, B/i'/ is one of t/e '/r'teristi's of

tense*rit+ s+stems, %oes not ))oB Io*nsons s'3)(t3re;str3't3re to be 'onsi%ere%

t/e first of t/is in% of str3't3res.



12

Figure +.2 Sim()e? b+ Sne)son, sim()est tense*rit+ s+stem

T/e most 'ontroersi) (oint /s been t/e (erson) %is(3te, )stin* more t/n t/irt+

+ers, betBeen R. A. F3))er Mss'/3setts, 16-0;1-6!4 n% . D. Sne)son Ore*on,

1-2#4. $s t/e )tter e?()ins in )etter to R. Motro, %3rin* t/e s3mmer of 1-6, F3))er

Bs neB (rofessor in t/e A)' Mo3ntin Co))e*e Nort/ Cro)in, US$4, in %%ition

to bein* '/rismti' n% non'onformin* r'/ite't, en*ineer, mt/emti'in,

'osmo)o*ist, (oet n% inentor re*isterin* 20 (tents %3rin* /is )ife4. Sne)son Bs

n rt st3%ent B/o tten%e% /is )e't3res on *eometri' mo%e)s, n% fter t/t

s3mmer, inf)3en'e% b+ B/t /e /% )ernt from F3))er n% ot/er (rofessors, /e

strte% to st3%+ some t/ree;%imension) mo%e)s, 'retin* %ifferent s'3)(t3res Fi*3re

!.!4.



13

Figure +.+ @;'o)3mn b+ Sne)son, /is first tense*rit+ rt (ie'e.I))3strtion %onte% b+ t/e rtist.

$s t/e rtist e?()ins, /e '/iee% neB in% of s'3)(t3re, B/i'/ 'n be 'onsi%ere%

t/e first tense*rit+ str3't3re eer %esi*ne%. =/en /e s/oBe% it to F3))er, sin* for

/is o(inion, t/e (rofessor re)i<e% t/t it Bs t/e nsBer to H3estion t/t /e /%

been )ooin* for, for so mn+ +ers. In F3))er9s Bor%s>

“For twentyone years, before meeting !enneth "nelson, # had been ransac$ing the

%ensegrity concepts. &( )espite my discovery, naming and development of both the

multidimensional vectorial geometry and the three dimensional %ensegrity, # had

been unable to integrate them, thus to discover multidimensional four, five and si*

a*es symmetrical %ensegrity.+

In 'ontrst to ot/er 3t/ors, n% serin* s n i))3strtion of /oB im(ortnt it Bs

'onsi%ere%, /e )B+s Brote Tense*rit+ strtin* Bit/ '(it) T.



14

$t t/e sme time, b3t in%e(en%ent)+, Di% Geor*es Emmeri'/ Debre'en;3n*r+,

1-20;1--54, (robb)+ ins(ire% b+ Io*nsons str3't3re, strte% to st3%+ %ifferent in%s

ofstr3't3res s tensi)e (risms n% more 'om()e? tense*rit+ s+stems, B/i'/ /e

'))e%str3't3res ten%3es et 3toten%nts, tensi)e n% se)f;stresse% str3't3res. $s

res3)t, /e %efine% n% (tente% /is rese3? 3toten%nts, B/i'/ Bere e?'t)+ t/e

sme in% of str3't3res t/t Bere bein* st3%ie% b+ F3))er n% Sne)son.



15

+.+ pp%i&!tions Of Tensegrity

T/e H3)ities of tense*rit+ str3't3res B/i'/ me t/e te'/no)o*+ ttr'tie for /3mn

3se re t/eir resi)ien'e n% t/eir bi)it+ to 3se mteri)s in er+ e'onomi') B+.

T/ese str3't3res er+ effe'tie)+ '(it)i<e on t/e eer in'resin* tensi)e

(erformn'e mo%ern en*ineerin* /s been b)e to e?tr't from 'onstr3'tion

mteri)s. In tense*rit+ str3't3res, t/e et/ere) +et stron*4 tensi)e members

(re%ominte, B/i)e t/e more mteri);intensie 'om(ression members re

minimi<e%. T/3s, t/e 'onstr3'tion of b3i)%in*s, bri%*es n% ot/er str3't3res 3sin*

tense*rit+ (rin'i()es 'o3)% me t/em /i*/)+ resi)ient n% er+ e'onomi') t t/e

sme time. In %omi') 'onfi*3rtion, t/is te'/no)o*+ 'o3)% ))oB t/e fbri'tion of er+ )r*e;s')e str3't3res. =/en 'onstr3'te% oer 'ities, t/ese str3't3res 'o3)%

sere s frmeBors for enironment) 'ontro), ener*+ trnsformtion n% foo%

(ro%3'tion. T/e+ 'o3)% be 3sef3) in sit3tions B/ere )r*e;s')e e)e'tri') or

e)e'trom*neti' s/ie)%in* is ne'essr+, or in e?tr;terrestri) sit3tions B/ere

mi'rometeorite (rote'tion is ne'essr+. $n%, t/e+ 'o3)% (roi%e for t/e e?')3sion or

'ontinment of f)+in* nim)s oer )r*e res, or 'ontin %ebris from e?()osions.

T/ese %omes 'o3)% en'om(ss er+ )r*e res Bit/ on)+ minim) s3((ort t t/eir (erimeters. S3s(en%in* str3't3res boe t/e ert/ on s3'/ minim) fo3n%tions

Bo3)% ))oB t/e s3s(en%e% str3't3res to es'(e terrestri) 'onfines in res B/ere

t/is is 3sef3). E?m()es of s3'/ res re 'on*este% or %n*ero3s res, 3rbn

res n% %e)i'te or r3**e% terrins. In s(/eri') 'onfi*3rtion, tense*rit+ %esi*ns

'o3)% be 3sef3) in n o3ter;s('e 'onte?t s s3(erstr3't3res for s('e sttions. T/eir

e?treme resi)ien'e me tense*rit+ str3't3res b)e to Bit/stn% )r*e str3't3r)

s/o's )ie ert/H3es. T/3s, t/e+ 'o3)% be %esirb)e in res B/ere ert/H3esre (rob)em. 0+



16

+. C'!r!&teristi&s Of Tensegrities

C/r'teristi's of tense*rities 'n be s3mmri<e% s fo))oBs >

+..!3 T/e+ /e /i*/er )o%;berin* '('it+ Bit/ simi)r Bei*/t.

+..b3 T/e+ re )i*/t Bei*/t in 'om(rison to ot/er str3't3res Bit/ simi)r resistn'e.

+..&3 T/e+ %on9t nee% to be n'/ore% or /e to )en n+ s3rf'e s t/e+ %on9t

%e(en% on t/eir Bei*/t or *rit+. T/e+ re stbi)i<e% in n+ (osition b+ eH3i)ibri3m of

'om(ressie for'es in str3ts Bit/ tension) for'es in (restresse% 'b)es. &restrin in

t/e 'b)es 'n be trnsforme% into (restress on)+ if t/e str3't3re is stti'))+

in%eterminte.+..3 T/e+ re enntiomor(/i' i.e. e?ist s ri*/t n% )eft;/n%e% mirror (irs.

+..e3 E)ementr+ tense*rit+ mo%3)es 'n be 3se% s3'/ s msts, *ri%s, ro(es,

rin*s et'.4 to me more 'om()e? tense*rit+ str3't3res.

+..f3 i*/er t/e (re;stress, stiffer t/e str3't3re Bo3)% be, i.e. its )o% berin*

'('it+ in'reses Bit/ t/e in'resin* (re;stress. T/e %e*ree of tension of t/e (re;

stresse% 'om(onents is %ire't)+ (ro(ortion) to t/e mo3nt of s('e t/e+ o''3(+.

+..g3 In tense*rit+ str3't3re t/e 'om(ressie members re s/ort n%%is'ontin3o3s, /en'e t/e+ %o not 3n%er*o b3')in* esi)+ n% no torH3e is *enerte%

in t/em.

+..'3 T/e resi)ien'e %e(en%s on t/e str3't3re ssemb)+ n% mteri) 3se%.

+..i3 T/e+ Bor s+ner*i'))+ i.e. t/eir be/io3r 'nnot be (re%i'te% b+ 'onsi%erin*

t/e be/io3r of n+ of t/eir 'om(onents se(rte)+.

+..43 T/e+ re sensitie to ibrtions 3n%er %+nmi' )o%in*. S)i*/t '/n*e in )o%

'3ses t/e stress to re%istrib3te in t/e B/o)e str3't3re Bit/in no time n% t/3s, t/e+/e t/e bi)it+ to res(on% s B/o)e. 4 enner intro%3'e% term 7E)sti'

M3)ti()i'tion9 for t/e tense*rit+ str3't3res. It is (ro(ert+ of tense*rit+ str3't3re

B/i'/ %e(en%s on t/e %istn'e betBeen tBo str3ts. If tBo str3ts re se(rte% b+

'ertin %istn'e t/e e)on*tion of ten%ons tensi)e members4 tt'/e% to t/em is

m3'/ )ess 'om(re% to t/is %istn'e.

+..%3 T/e %eformtion res(onse of entire tense*rit+ str3't3re to )o% is non;)iner s

its stiffness in'reses r(i%)+ Bit/ in'resin* )o%, )ie t s3s(ension bri%*e.



17

+..m3 T/e tense*rities re 'ommon)+ mo%e))e% Bit/ fri'tion)ess Joints, n% t/e se)f;

Bei*/t of 'b)es n% str3ts is ne*)e'te%. %6&

+.5 6!nt!ges Of Tensegrity O6er Con6ention!% 7Continuous3 Stru&tures

+.5.!3 $s t/e )o% is %istrib3te% in B/o)e str3't3re t/ere re no 'riti') (oints of

Beness.

+.5.b3 T/e+ %on9t s3ffer n+ in% of torsion n% b3')in* %3e to s('e rrn*ement

n% s/ort )en*t/ of 'om(ression members.

+.5.&3 For'es re trnsferre% nt3r))+ n% 'onseH3ent)+, t/e members (ositiont/emse)es (re'ise)+ b+ )i*nin* Bit/ t/e )ines of for'es trnsmitte% in t/e s/ortest

(t/ to Bit/stn% t/e in%3'e% stress.

+.5.3 T/e+ re b)e to ibrte n% trnsfer )o%s er+ r(i%)+ n% /en'e, bsorb

s/o's n% seismi' ibrtions B/i'/ mes t/em (()i'b)e s sensors or 't3tors.

+.5.e3 T/e+ 'n be e?ten%e% en%)ess)+ t/ro3*/ %%in* e)ementr+ str3't3res.

+.5.f3 Constr3'tion of str3't3res 3sin* tense*rit+ (rin'i()e mes it /i*/)+ resi)ient

n%, t t/e sme time, er+ e'onomi'). K0



18

+.8 Dis!6!nt!ges Of Tensegrity O6er Con6ention!% 7Continuous3 Stru&tures

+.8.!3 If t/e str3't3re be'omes too )r*e it f'es (rob)em of br 'on*estion i.e. t/e

str3ts strt r3nnin* into or to3'/in* e'/ ot/er4.

+.8.b3 T/e+ s/oB re)tie)+ /i*/ %ef)e'tions n% )oB mteri) effi'ien'+ s 'om(re%

to Bit/ 'onention) 'ontin3o3s str3't3res.

+.8.&3 Fbri'tion 'om()e?it+ is mJor brrier in %ee)o(in* f)otin* 'om(ression

str3't3res.

+.8.3 $%eH3te %esi*n too)s re not i)b)e for t/eir %esi*n, softBre 7Tense*rite

2:::9 %ee)o(e% b+ R. Motro et ).4 is t/e most %n'e% too) i)b)e to %esi*n

tense*rit+ str3't3res.

+.8.e3 $t )r*e 'onstr3'tions t/e str3't3re 'nnot Bit/stn% )o%s /i*/er t/n t/e

'riti'), re)te% to its %imensions n% (restress. K5



19

+.9 Topo%ogi&!% C%!ssifi&!tion Of E%ement!ry Ce%%s Of Tensegrity Stru&tures

+.9.1 R'ombi& &onfigur!tion

T/e nme of tense*rit+ (tterns is bse% on t/e B+ t/e+ re 'onstr3'te% ten%on

(tterns4. In Fi*. !., e'/ str3t of s+stem re(resents t/e )on*est %i*on) of

r/omb3s forme% b+ fo3r 'orres(on%in* ten%ons n% 'n be fo)%e% fo))oBin*

t/ese %i*on). Gener))+, t/is 'onfi*3rtion 'orres(on%s to t/e %imon% tense*rit+.

T;(rism se'tion !.6.14 n% T;i'os/e%ron se'tion !.6.24 tense*rities re Be)) noBne?m()es of t/e r/ombi' 'onfi*3rtion B/ere r/omb3s re(resents non;()nr

H3%ri)ter) forme% b+ ten%ons. K0

Figure +. 4 $ssemb)+ of r/ombi' 'onfi*3rtion n% b4 its (ttern



20

+.9.2 Cir&uit &onfigur!tion

In t/is s+stem, t/e 'om(resse% members re forme% b+ ')ose 'ir'3its see Fi*.

!.044 B/i'/ %o not 'om()+ Bit/ stn%r% %efinition of tense*rit+. T/is 'n be

'onstr3'te% b+ ')osin* t/e r/omb3s *enerte% b+ str3ts n% ten%ons of t/e %imon%

(ttern tense*rit+, s3'/ s T;i'os/e%ron see Fi*. 1.124. K0

Figure +.5 4 Cir'3it 'onfi*3rtion of C3bo't/e%ron tense*rit+ /in* non;to3'/in* trin*3)r 'ir'3its n% b4 its (ttern



21

+.9.+ :; type< &onfigur!tion

$ 7<i*;<*9 'onfi*3rtion )so bein* n enntiomor(/i'4 is obtine% from t/e r/ombi'

'onfi*3rtion s t/e bsi' str3't3re. Aot/ en%s of n+ str3t s/o3)% be 'onne'te% b+

t/ree non;)i*ne% ten%ons rrn*e% to form 789 s/(e. Tr3n'te% tetr/e%ron see

Fi*. !.54 is ')ssi' e?m()e of 8 t+(e 'onfi*3rtion obtine% from tr3n'te%i'os/e%ron B/i'/ be)on*s to t/e ')ss of r/ombi' 'onfi*3rtions. K0

Figure +.8 4 Tr3n'te% Tetr/e%ron T;tetr/e%ron4 3sin*8 t+(e 'onfi*3rtion, b4 its (ttern



22

+.= Types Of Tensegrities

T/e tense*rit+ str3't3res re Bi%e)+ ')ssifie% s (restresse% n% *eo%esi'

str3't3res. T/e+ re %ii%e% into t/ree min 'te*ories> Tense*rit+ (rism, Dimon%

tense*rit+ n% 8i*;<* tense*rit+. T/e @;mo%3)e see Fi*. !.#4 b3i)% b+ Sne)son /%

*ien birt/ to tense*rit+ (rin'i()e. T/is sim()e tense*rit+ str3't3re 'onsists of tBo @;

s/(e% Boo%en str3ts s3s(en%e% in ir b+ stret'/e% n+)on 'b)es. T/e sim()e itefrme is t/e bsi' (restresse% tension'om(ression 'e)) of @;mo%3)e tense*rit+

str3't3re. It 'onsists of tBo 'rosse% str3ts firm)+ /e)% to*et/er b+ *irt/ of fo3r

tension members, be'3se t/e e'tor4 s3m of 'om(ression for'es (3s/in* o3t

eH3)s to t/e s3m of tension for'es (3))in* in. $s s/oBn in Fi*. !.6, t/e

'/n*e in )en*t/ of bot/ str3ts n% ten%ons i.e. '/n*e in (ro(ortion of frme is

re)te% to t/e rition in %istrib3tion of for'es, bot/ tension n% 'om(ression. %5&



23

Figure +.9 =oo% @;mo%3)e



24

Figure +.= ite frme s/(e in rio3s (ro(ortions

It is H3si;tense*rit+ str3't3re be'3se it is ()nr 2D4, n% t/e str3ts to3'/ e'/

ot/er. If n+ one of t/e ten%ons is remoe%, t/en t/e b)n si%e Bi)) Bor s

'om(resse% 'om(onent t/is is '))e% s 7str3t effe't9. T/is bsi' (rin'i()e is reH3ire%

to %esi*n rio3s e)ementr+ 'om(onents of tBo )+er n% t/ree )+er tense*rit+

s+stems. T/e )en*t/s of t/e fo3r ten%ons n% t/e )en*t/s of t/e tBo str3ts %etermine

t/e s/(e of t/e ite frme see Fi*. !.64.

+.=.1 Tensegrity prism 7T)prism3

$)so noBn s 7T/ree str3ts T;(rism9 Bs inente% b+ r) Io*nson in Mos'oB in

1-21. It is t/e sim()est n% t/erefore one of t/e most instr3'tie members of t/e

tense*rit+ fmi)+. T/e T;(rism /s - ten%ons n% ! str3ts see Fi*. !.-4 n% be)on*s

to s3b')ss of (rismtoi%s. It /s been '))e% tense*rit+ (rism or T;(rism s it 'n

be 'onsi%ere% s tBiste% (rism 'onsistin* of tBo trin*3)r f'es tBiste% Bit/

res(e't to e'/ ot/er. Gener))+, t/ese tense*rit+ str3't3res re %esi*ne% b+ ee(in*

t/e )en*t/s of one set of ten%ons n% str3ts 'onstnt, n% %eterminin* t/e )en*t/s of

not/er set of ten%ons. =/en one en% of t/e (rism is tBiste% re)tie to t/e ot/er, t/e

re'tn*3)r si%es of t/e (rism be'ome non;()nr H3%ri)ter)s. T/3s, tBo o((osite

n*)es of e'/ H3%ri)ter) be'ome obt3se n% '3te. For str3't3re to be stb)e n%



25

(restresse%, t/e (rism is tBiste% in s3'/ B+ t/t t/e %istn'e betBeen t/e obt3se

n*)es is )est n interme%ite st*e of tBistin*4 n% /en'e, 'om()ete)+ stb)e T;

(rism is forme%.

Figure +.> Dimon% Confi*3rtion of T;(rism



26

+.=.2 Di!mon tensegrity

T/e tense*rit+ i'os/e%ron )so noBn s T;i'os/e%ron %e(i'te% in Fi*. !.1:4 is

')ssi' e?m()e of %imon% tense*rit+. T/ese tense*rities re '/r'teri<e% b+ t/e

f't t/t e'/ trin*)e of ten%ons is 'onne'te% to t/e %J'ent one i str3t n% tBo

inter'onne'tin* ten%ons. It Bs first e?/ibite% b+ A3'minster F3))er in 1-- n% is

one of feB tense*rities B/i'/ e?/ibit mirror s+mmetr+. T/is tense*rit+ is ')ssifie%

s 7%imon%9

t+(e be'3se e'/ of its str3ts is s3rro3n%e% b+ %imon% form of fo3r ten%onsB/i'/ re s3((orte% b+ tBo %J'ent str3ts min* t/em %istin't from 8i*;<*

tense*rit+. It /s 5 str3ts n% 2 ten%ons Bit/ ten%on to str3t )en*t/s rtio of :.51!.

If t/e H3%ri)ter)s neste% Bit/ str3ts re '/n*e% to sH3res t/en t/e ten%ons form

'3bo't/e%ron netBor. Fi*. !.1:b4 i))3strtes t/e '/n*e in s+stem of ten%ons

from n o't/e%r) rrn*ement Bit/ e'/ str3t %o3b)e%;3( b+ (resen'e of tBo

str3ts in t/e i%enti') (osition4 to '3bo't/e%ron n% b'. Sm)) rroBs in%i'te t/e

%ire'tion of moement of t/e str3ts n% of t/e 'orres(on%in* (ir of o((osite (ointsof t/e H3%ri)ter) s t/e ten%on s+stem *oes t/ro3*/ trnsformtions.

O(enin* t/e o't/e%r) str3't3re 'ref3))+ from one en% *ies sin*)e )+er %imon%

str3't3re s %e(i'te% Fi*. !.114. NeB tense*rit+ str3't3res Bit/ s(/eri') s+mmetr+

'n be *enerte% b+ %%ition of neB )+ers of str3ts n% ten%ons n% Joinin* bot/

en%s of e'/ )+er. &)nr ieBs of tense*rit+ s+stems bse% on t/is ((ro'/ re

%e(i'te% in Fi*. !.12 n% Fi*. !.1!.



27

Figure +.1? 4 T;i'os/e%ron n% b4 its 'orres(on%in* trnsformtion

from n% b' to %o3b)e%;3( o't/e%ron

Figure +.11 4 O't/e%r) str3't3re b4 ()nr ieB of 'orres(on%in*

!;str3ts sin*)e )+er tense*rit+ s+stem



28

Figure +.12 &)nr ieB of 5;str3ts tBo )+er tense*rit+ s+stem

Figure +.1+ &)nr ieB of -;str3ts t/ree;)+er tense*rit+ s+stem



29

+.=.+ ;ig)@!g tensegrity

T/e tense*rit+ tetr/e%ron )so noBn s T;tetr/e%ron4 %e(i'te% in Fi*. !.1 is

')ssi' e?m()e of %imon% tense*rit+ %ee)o(e% b+ Frn'es'o %e)) S) in 1-0!.

T/e T;tetr/e%ron is t/e <i*;<* 'o3nter(rt of t/e %imon% T;i'os/e%ron see Fi*.

!.1:4. $)t/o3*/ bot/ str3't3res /e 5 str3ts, t/e mJor %ifferen'e is t/t T;

tetr/e%ron /s fo3r ten%on trin*)es, B/eres t/e T;i'os/e%ron /s ei*/t of t/em.

Figure +.1 T;Tetr/e%ron 8 t+(e 'onfi*3rtion4

In *ener), <i*;<* str3't3res Bit/ 8 t+(e 'onfi*3rtion re sim()er n% )ess ri*i% %3e

to t/eir )oBer n3mber of ten%ons t/n t/eir %imon% 'o3nter(rts Bit/ r/ombi'

'onfi*3rtion.



30

. $EAIN# MOT/ER OF TENSERIT-

.1 Introu&tion

T/e n'ient inention of Bein* %is()+s t/e bsi' (ro(erties of nt3r) str3't3re>

mo%3)r;re(etition, )eft n% ri*/t /e)i') s+mmetr+ n% t/e ')ose sso'ition betBeen

*eometr+ n% (/+si') str3't3re.

TBo n% on)+ tBo f3n%ment) fbri' Bee str3't3res e?ist> t/e stn%r% tBo;B+

()in Bee m%e 3( of sH3res Fi*..14, n% t/e t/ree;B+ trin*)e/e?*onBee Fi*..24 3se% most often in bsetr+. T/o3*/ t/ere re mn+ ritions s3'/

s 'riss;'rossin*, %o3b)in*, et'. t/ese tBo re t/e on)+ (rimr+ forms.

Figure .1T/e Common SH3re =ee Figure .2T/ree;=+ Trin*)e

e?*on =eeIn $si> It '))e% $GOME4



31

$ sin*)e Bein* eent, tBo fi)ments 'rossin* n% in 'ont't Bit/ one not/e

Fi*..!4, e'/ Br(in* t/e ot/er B/ere t/e+ (ress in 'ont't is, in itse)f, n

e)ementr+ str3't3re. $t t/e (oint of 'rossin* t/e tBo t/re%s 'rete %3) /e)i') ?esone ')o'Bise, ri*/t;rottin* n% t/e ot/er 'o3nter')o'Bise, )eft;rottin*. K#

Figure .+Cross tBo (en'i)s. &)'e t/3mb n% in%e? fin*er on t/e (en'i)s n% s)i%e

toBr% t/e 'enter. "o3r /n% Bi)) ten% to rotte eit/er ')o'Bise or 'o3nter')o'Bise



32

.2 Rig't /e%i* n Beft /e%i*

Figure . Ri*/t n% Left e)i?

P3st s t/e in%ii%3) 'rossin*s of fi)ments /e )terntin* /e)i') ?es so e'/

sH3re in ()in Bee )terntes Bit/ its nei*/bors )ie '/ess bor% sH3res. In

or%er to (roe B/et/er Bee 'e)) is ri*/t or )eft /n%e%, im*ine +o3r fin*ers

s)i%in* in 'ont't Bit/ t/e frme of 'e)). "o3r /n% Bi)) moe %oBn;/i)) in

')o'Bise 'o3nter')o'Bise sense ''or%in* to t/e 'e))s rottion.Fi*..4,Fi*..04



33

Figure .5 Ri*/t n% Left e)i?es

Figure .8 *ome T/ree;=+ Aset =ee

In t/ree;B+, or *ome Bein*, /e?*ons )ternte Bit/ trin*)es. If t/e /e?*ons

/e ')o'Bise /e)i? t/e trin*)es re 'o3nter')o'Bise. If t/e /e?*ons re'o3nter')o'Bise t/e trin*)es re ')o'Bise.Fi*..54,Fi*..#4



34

Figure .9 *ome T/ree;=+ Aset =ee

.+ E*!mp%es of $e!6ing in T'e Tensegrity System



35

Figure .= E?m()es of =ein* in Tense*rit+

=ein* n% tense*rit+ s/re t/e (rin'i()e of )terntin* /e)i') %ire'tions, of

)eft;to;ri*/t, of b+(sses ')o'Bise n% 'o3nter')o'Bise.

In t/e to( roB boe re fie (rimr+ Bee fi*3res. Ae)oB t/em re t/e

eH3i)ent tense*rit+ mo%3)es. In%ii%3) tension )ines strin*s, Bires or ro(e re

tt'/e% to t/e en%s of t/e str3ts s s/oBn so t/t e'/ ssemb)+ is ')ose% s+stem

m%e of tension n% 'om(ression (rts. E'/ tension )ine 'onne'ts in%ii%3))+ to

t/e en%s of tBo str3ts. T/e+ %o not t/re% t/ro3*/ )ie strin* of be%s. T/e tension

)ines m3st be %J3ste% for ti*/tness s Bit/ t3nin* strin*e% instr3ment or inf)tin*

'r tire.

Ti*/tenin* t/e tension s+stem stores bot/ tension n% 'om(ression for'es in

eH3) mo3nts, stte t/t en*ineers ')) (restressin*. T/e ener*+ remins store%

insi%e t/e str3't3re 3nti) it is %isssemb)e%.

In t/e fi*3res boe, on)+ t/e 2;str3t ?;mo%3)e n% t/e !;str3t (rism /e tension

netBors Bit/ tot) trin*3)tion. T/e netBors of t/e sH3re (rism, t/e (ent*on

(rism n% t/e /e?*on (rism re not 'om(ose% of trin*)es. In tense*rit+ str3't3res

trin*3)tion in t/e tension netBor is si*nifi'nt be'3se it %etermines if t/e

str3't3re Bi)) be firm or not. Tense*rit+ str3't3res re en%ose)et), s re /3mns n%

ot/er mmm)s B/ose tension m3s')es re e?tern) to t/e 'om(ression members9 bones.

UniH3e to tense*rit+, t/e 'om(ression str3ts re se(rte% one from not/er, non;

to3'/in* Bit/in t/eir tension ene)o(e. T/e e?'e(tion is t/e tBo;str3t ?;mo%3)e, or tr%ition) ite frme. T/is essenti))+ f)t fi*3re9 )'s 'om(ression for'e in t/e <



36

%ire'tion. In or%er to se(rte t/e 'rosse% str3ts t/ir% str3t or e)se n %%ition) @;

mo%3)e, m3st be %%e% to (3)) t/e tBo str3ts (rt.Fi*..64

5. TENSERIT- EM(BES ND ((BICTIONS



37

5.1 Suspension "rige

T/is is non;se)f;s3ffi'ient tense*rit+. It is n'/or*e %e(en%ent. =/en it is

s3((orte% b+ (+)ons B/i'/ re ri*i%)+ 'onne'te% to t/e *ro3n%, t/e (+)ons s/o3)% be

'onsi%ere% (rt of t/e n'/or*e, n% t/e bri%*e s/o3)% be 'onsi%ere% 'om(osite

str3't3re, on)+ t/e non;(+)on (rt of B/i'/ is tense*rit+. If t/e (ro(er f3n'tion of t/e

bri%*e %e(en%s on t/e *rit+ fie)% 'omin* from one B+ rt/er t/n not/er, s

seems )ie)+ *ien t/e %Je'tie s3s(ension, b3t some )o') fstenin*s Borin* Bit/

*rit+, s mi*/t be %esirb)e for Bin% n% ert/H3e resistn'e, Bo3)% firm)+

restore its tense*rit+;/oo% n% s3s(ension bri%*e Bo3)% not 'om()ete)+ 3)nerb)eto %isinte*rtion in t/e bsen'e of *rit+, s o((ose% to t/e 'se of t/e Romn r'/

be)oB B/i'/ Bo3)% be.Fi*.0.14 %!&

Figure 5.1 Go)%en Gte Ari%*e, Sn Frn'is'o, C)iforni



38

5.2 T'e Sy%on Toer

In 1-01, J3st t/ree +ers fter t/e offi'i) %is'oer+ of tense*rit+, t/e Festi) of

Aritins So3t/ An E?/ibition too ()'e in Lon%on. In t/t o''sion, 'om(etition

Bs or*nise% to ere't Verti') Fet3re, st()e of interntion) e?/ibitions

*ro3n%s. &/i)i( &oBe)) n% i%)*o Mo+ /e)(e% n% ins(ire% b+ t/eir former Fe)i?

Sm3e)+4 %esi*ne% t/e S+)on , B/i'/ Bs se)e'te% s t/e best (ro(os) n% b3i)t

ner t/e Dome of Dis'oer+. Some 3t/ors Cr3i's/n, 1--0 A3rstoB, 1--54 stte

t/t t/is nee%)e )ie str3't3re Bs mon3ment Bit/o3t n+ f3n'tion) (3r(ose, b3t it

be'me s+mbo) for t/e festi), be'on of te'/no)o*i') n% so'i) (otenti)ities

n%, fin))+, referen'e for f3t3re en*ineers n% r'/ite'ts. T/e !:: foot /i*/ s(ireBs 'i*r;s/(e% )3mini3m;')% bo%+ s3s(en%e% )most inisib)+ b+ on)+ t/ree

'b)es, n% seeme% to f)ot : feet boe t/e *ro3n%.Fi*.0.24 %!&

Figure 5.2 S+)on ToBer Lon%on, En*)n%



39

5.+ Roof Stru&tures

$n im(ortnt e?m()e of Tense*rit+ bein* em()o+e% in roof str3't3res is t/e st%i

t L &)t $r*entin4, bse% on (ri<e Binnin* 'on'e(t %ee)o(e% b+ r'/ite't

Roberto Ferreir. T/e %esi*n %(ts t/e (tente% Tenstr Tense*rit+ roof 'on'e(t to

t/e tBin (e 'onto3r n% t/e ()n 'onfi*3rtion, n% 'onseH3ent)+, it is more simi)r

to 'b)e;%ome str3't3re t/n to 'onention) roof str3't3re. T/e first st3%ies for

t/e %esi*n of Tense*rit+ *ri%s Bere 'rrie% o3t b+ Sne)son, b3t its (()i'tions Bere

)imite%. For t/e (st feB +ers, t/e min fo'3s /s been in t/e %ee)o(ment of

%o3b)e;)+er Tense*rit+ *ri%s n% fo)%b)e Tense*rit+ s+stems. T/is in% of *ri% /sits most fesib)e (ossibi)ities in t/e fie)% of B))s, roofs n% 'oerin* str3't3res.

Fi*.0.!4 %!&

Figure 5.+ $ %ome %esi*ne% b+ Robert Le Ri'o)is



40

5. C'i%<s "!%oon

$not/er 'ommon e?m()e of tense*rit+ is '/i)%9s b)on. T/e r3bber sin of t/e

b))oon &ontinuous%y pu%%s B/i)e t/e in%ii%3) mo)e'3)es of ir

re is&ontinuous%y pus'ing *inst t/e insi%e of t/e b))oon ee(in* it inf)te%. $))

e?tern) for'es striin* t/e e?tern) s3rf'e re imme%ite)+ n% 'ontin3o3s)+

%istrib3te% oer t/e entire s+stem. T/is mes t/e b))oon er+ stron*.Fi*.0.4

Mo)e'3)es of ir %is'ontin3o3s)+ (3s/in* *inst t/e 'ontin3o3s)+ (3))in* r3bber sin

of t/e b))oon. In t/is e?m()eTense*rit+ is b)n'e of 'ontin3o3s (3)) n%

%is'ontin3o3s (3s/. %!&

Figure 5. C/i)%9s A)oon



41

5.5 /um!n "oy

T/e m3s')es, ten%ons n% )i*ments re t/e (3re)+ tensi)e 'om(onents B/i'/ bin%

to*et/er t/e bones n% 'rti)*eFi*. 0.04. T/ese sttements 'o3)% (robb)+ 3se t/e

ttention of someone better erse% in ntom+. &)nts, f3n*i, sin*)e;'e)) 'ret3res

n% ot/er nim)s s/o3)% be 'onsi%ere% for in')3sion in t/e tense*rit+ 'te*or+ on

'se;b+;'se bsis. %!&

Figure 5. 3mn bo%+ tense*rit+ mo%e)



42

REFERENCES

%'& htt()**www.sk.co#*science*tension+force+5d'7$244f$3,3d-5

%2& htt()**theconstructor.or*structurl+en*ty(es+of+tension+#e#,ers*4!--*

%3& $ &r'ti') G3i%e to Tense*rit+ Desi*n 2n% e%ition Co(+ri*/t 2::;2::6 b+

Robert =i))im A3r/r%t

%4& Controersi) Ori*ins of Tense*rit+ b+ V)entn GME8 PUREGUI

%5& En*ineerin* MEC$NICS, Vo). 21, 2:1, No. 0, (. !00!5#

%6& OerieB of Tense*rit+ I> Asi' Str3't3res b+ Anso% ".D. et ).

%7& Tense*rit+ , =ein* $n% T/e Ainr+ =or)% b+ ennet/ Sne)son

%!& http://bobwb.tripod.com/synergetics/tenseg



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Tensegrity Structres