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npOKQt(lCllcpoundUff IUI-I~tox-il at 1 nOTlCOOjLICl tuv~6phl 2 AWlCOIVroo-fllt elt 10 Bov Il)viaPIOV ti~ 6lrOvOI) t Ev6x1utx rtjgtuPOlfolia~ lC(I1 bOlud)v fpyOlv do Nwv middotyop Mt)olt rp F I P 110 AIPC tfllt AI PCA M6vljLOV jLCMl~ dl( tltllPonilt aBlOjUilV fflt F IP Ana toC 1959 lilofTlp1 rpoqlElov MEAngtv d 311Cllv 16XVllCgtV PlIO Mt)UTlTi)lt t1t 2a ampc 10V 1(00jLOV Kal Elt 16 dlio~ TTIlt rEqJvpat Totupvo~ (UV1pIKOV aVOIljLCl 1 It1PQ tK olCup06tjLo1(X) EXEI lt5T1jLOoIBUOE 611middotmiddot00o~ oU110 l1POBVU1ojLtvO oupuliejLa (al IftIPCl)WtlI(Ot ~PIUIoQ~ ellt 1 )alolo 101) Epyo(ITlPioU toC EM n

ISO MIlpTlo 1969

22 MoetPi dO~l-toU

E~ to ax I poundtval crxEOHl(1)leVOV to 61l0iWIJIl Co 61toiov uno K1i ~KQ 150 drtEIIOviC1 tOy 1tp(1y~u-ru6v Ipopeu roO 61toioo 61JooC a( ow-tO)Lol (6p90yoov lu i 1tAQKOOOKOL K)n) Exouv

avaxO ell icrooUVQIJOUC 6peoyrovllca~ ltltXOOl O25~1 1tOI de olatoOltQc txooo~ ttl auCilv pcmTtV 65poveac KQi f6v Cliltov KEvTpo~apuc6v a~ova 1tpOJ tac 1tpay)LQCIK6C

H avo)urytl oitn lW1poundOtl1 anapai-tnCoc 01011 to uAncov CoO

~--~L ------~------------- LLe

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I lt7 bull

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a

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1

o ~ o gt bull 0o x o 0 _ c

laquo E -J VI

I

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0- ~

gt 0W

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o

X Oc 0 bull

W ltl laquo T~

_------- pound--- -t- ------------------- 0 eL

I----------------------------------- ltGO--------------~I

MapTIOS 1969 lSI

oOIClJJiou 1tpOCnpEpEtaL EU dOKIlI 1tOXO~ I ix crUVE1tltlC TO OO dIJIOV OEOV 1tQVfOn va hu t6 CUJTO 1tOXOe poundV ovngecrEt npO~ TOV 1tpaYJJaTIICOV qlopea OOtU t tEt 1tUXI1 Ete IJpoundV TO toishyxooJJa 025 JJ d~ oE TCu ll1toMgti1to~ 9toEle 060 -010 JJ

AUl OtaKEKOJJJJiv11c ypajJ)Ifc eE 0 aUTO cn~J1a EXEl crXEolashycr9i TO TtEpiypajJjJa toO 1tpaYJumKol) tpopewc

3

22

L1 ot oLn I - I

npaYJ1atlKn OtaTOIJTi

nMuooOlr~ J = 778104 EKt

(to l1t6cnacrte tol) KtVTPOU ql(JvEiae Tf]e 1ttaKOe)

IooouvalJ~ OtoTO)lit op90Ywvuol 25 X 155 EK

L1laTop r 2 - 2

npaY)ICImctl 6IaroJJTj

44 3

5 5

6 6

to = 386 EI(

Popoue OTtO Tfie ~c(l)Tepll(ile E1tIshy

1[AaKOOOl~ J = ID I ()4 EIC4 10 = 220 BJ(

la05uvu)Ior OlatO)ITj Op90ywvu-n 2S x 94 EIC

LhaT O f-~ 3-3

npu))laTlJ(Tt Olato~ui

TUClKOOOK Oc J = 14OCUOt EICmiddot If = 575 EIC

laoouvu)lOC lha ToJJit op90YOOVIK1 25 x J89 eIC

dar olo t) 4-4

npa)lJanKTt OtUTO)li nAUICobOKOc J = 407104 EIC4 lo = 300 EIC

lcroouvalJ~ olatO)lli op90)OOVLIC1 25 x 125 EK

L1tar o p1 5 -j

npaYlJatucll OIQtojJi) nAaICooolC6i J = 28510 EIC 4 0 = 264 EK

lOoouvajJ~ OtatO)l 6pe01lVtK~ 25 x III

dta-rout) 6-6

npaY)IatlICtl IhaTO)lit Op90YWVlK1 60 x 60 EK

Tcroouvaj1Ot OtaTO)li] Op90yooVlloi 25 X 80 EK

BOOEI tGlv OVOHtpcu eupE9ElOampV a oO vnjloov olato)l(i)v poundaxe~ Olelae11 tIC TOO npay)lCltlKOU 1POptM (pt olatocrm jJll (v11v de ax J) to mpiypo)l)lO TOn 001C11l10U

23 K)fa~E middot 17EteapaH~ L1lcirae-

Of UAIKOV tOU 00K1IJiou poundxP1101jJOTtOT911 to Araldil IClr K)oltpOPOl)v do to pound1J1tOPIOV lmO 1l0PqlTlv 1tAaICwv nUxolll 1 EK Ent npoTurrou Oo KljJiou 2 x It EK poundIJEtpi]9TlOClV nCPOOtOEAClshyOTlKtl Ota9Epo S KClI to IJEtpov tAaOTTK6tTlt0t E tOO UAIKOO toO OOKI)ltOU Kat eUpe911

S = 10 (xYP euro K2jTOtIV) EK E = 30500 XYPEKmiddot

E~EAt(T KArlJ tl~ )l11KGlV 150 H KAT)Iat nOXotX npoKigt1ttEL eurox toO nOXotx d - 25 EK toO 1005uvtlJloU qlOP~ Kal tIC toO 1tltIXOOe d = J EK t~ JtlalCoe AraJdit luveTtWc EXO)UV

I KatamceD11 50 A ~ 7 =-1shy6Jlo im~u

d KaTMICEu1l 25 t= d = - 1shy6J1o iwllCt

poundKJiyU(U oE

ICAT)I~ TOcrEC1lv

BOOEI tWV v6IJoov ti)~ J1TJxaVlKilt O)lOIOT11tOt breOAOyi~EtClI IJOVOTilJw t nAtov fJ O1tOIJEVOOOCl ICAijJat Tj (L1tClpa(t11T~ 516 t1v nClpOn(J1lV tpmgtvav i]t01 1 KAtJ1a~ oovolJeoov

bull P Ko taOKEUTuUVCljJEIDV p = lIZ 6

p 110(001Jo

1250= 1050middot25 = - 1shy

AtCllPOOvramp Ta cpopTia PI Kal Pwto dVacpEpO)leva Ele tTtv 1tCl pc)ypaqgtov 21 oui tilt KAijJaKoe OOV6IJEooV p = 1250 EUmiddot piOICOI1EV tCu Brei tOG OOK l)liou poundqlaplJootealt ltpOpticrEtc r Kat II

PI p p P PeP 4

ltlgt6pnm I 47 50 62 68 6laquo 52shy

ltlgt6 II 52 50 88 46 104 52

TO QVfDTtpoo QlOll tLa ~~altncoOvtal enl tOO 00K lj1100 de 8Eow tJItpal vo)ltva~ d t T6 ox I JJi04gt 6 WPOAOYICtICltIV 5uvCt)lolJtshytpwv E~ ro 11j1tw tfk 1tAaK~ OPOI4gtilc Kat KaTa ti]v 6ptCovshytlav EvvOlnv ~t01tOeCnW11 crtitPtY)Ja 10 o1toTov it11oltpOhlaE eft to OjJOiW)1Cl 6P L~OVtjav OKlv11a[av roo ciXPlPGIc toiYto OUIJshypoi VEt de TOV 1tpaY)JollKoV qJop~a 16 14gt tf)lt ouwpyaoialt t (l)v T01Xoo)laTooVtOn lOO)ElOU Ilna tfle n)alolootitc KCtTocrK6Uf]lt ete Tponov WltTTS to 1tAaiOlCt va OOVCtVtol vo 8poundOOPTl900v dx TOIClOm o)UTo9ETWV K6)1 Poov

MEta~U T(i)v OIEOTCIUPOO)lpoundVWV 1tOAootlK(UV 191JltIv T~e Q1JOKEUfle tpw10taaeO)lEtpiae (TonoeeTf911 to qlopno)Jtvov OOIC[)IIOV I(ai ~iilqJeToav oui ti)v qJOptlOlv 1000 l(itPlvOV )lOVOXPwjJCtshytllCOV pUle al Ele t6 oxi]lJotD 3 Kal4 tjlqlCtlVOIJpoundVCtI ql(JltoypashyqliCIl lOoxpoo~v oKpoundpaiat 101 tl)lICtKEpaiae tacewc Kat 6)loiwe oUI nlv CPOptlOlV II ai qgtWtoypocpiCtl t(l)v OX11JlOtooV 5 KCli 6 laOxPOlllot EIVCII Ctf ypaJJIlCti ICato )I~ KOt TltIv 6Ttoicuv 1 Otoshycpopa lCupirov taoE(J)v 0 1 - cr~ elvat 0tCl9EPci Kat LO1) np6lt

nlt I5EuvuEtQ de t6c poundil(ovCllt t(i)v (croxPOOIJWV de talt atmiddot XIJ6lt tol) nEptypci)l)1Oto- TOO ltPOPClllt JqllotaTat crucrcroopEUOIe tUOEooV AiCtv 5UO)lEv1lt l)ui ttV Oa(jluAElaV tfle KataoKEui1lt Alo tOOTO poundAT1q1e11 1tp6VOla de TTlV lCataOlCEUT)V ooOtpound al 0) shyACt)ai olfl)9uvopound(il~ toO 1tpoundPlypU)I)latOt v6 KUTaowOv 6)laA6r tEpCtl oui T~lt napeIlPOAij r hltXfl~ tvl(nOOEOO~ d e Tp6nov ampOtE f) )Iulipnolgt t(i)v TuaCtov pound1( TOO ev6~ cnUouo ttie ywshyvialt de t6 etepo va I(OO[Otattll 6J1llcottpa pt Q1tOttMcJ)Ja TfiV lJe(ooOlV Til cnryKWlPOOE(Ufi nov 1UOamp00 cit Tfl V crtXJmiddotnv

153 M6pnol) 1969

EIlt TnV nopoOOov lpcoV(l- npICtaOrU16v dt T6v nPOO010PIshyaJl6v 161V lQcrWlV J16vov tnl TOO ntplYpaJlIlOtOlt 1)pdaGnllev TOOltltTtIV pound1lt to oi l(100V TaV loOXprollwV TamWV 00 600v d C tei aT))Uta tOO ncptypOIJIJOtOlt J1t 02 = 0 trouv at - 0 = = a Kat a = 8 Sd Suva~t9a S~kaSIl t K lt1lt n~~c S lt~lt laoXPwJ1aTIK1)lt T~poundrot va ~XWfJev 11)v TIIlV Tf)lt ciYVcUoTOO ICVptalt toatoolt a bull

~ QvtltPtp9T) ellt t1v 1tapif)p(l(pOV 23 Elval

a ICatooKroli = 10 7 olloiwJ1o

61(1 t6 GVro nEpi)p0)1110 loll T01X~OT0I9 nPOKlmTpoundl T61C laOLt tcpEAKOaJ1oi) 0 = 3 x 10 = JO lYP tKmiddot 6llt at avc~vfto n~ napa)olnv T1)C t ICQIIVcw KaTanOVnaerolt 100 T01X6r J10tOt 119EVtQI 74gt20 d~ T1Iv 6vw naPEU~lv Etc Tar ICOTOshyICOPUltPOolt nOPUQlt toll 10IXOOIIOTOC ell tJl4lQvl~6J1Ev(u 9)shy1tt1Knl TcWUlt Stv lmEppotvouv lQ 8 x 10 = 80tYPCIC nposhyCKTelVOVTnI OlVE1tGgtlt ~tJ)t Tne paactJgtC TOO TOIXOO)JOTOC ot 6shy1tAIO)JO TCUV tIC t(L)v avoo il1tootllAw)Jat(J)v

Ett Tillt 1tapuclt toC 10IxOO)JOt0e TtOclal 61tAIO)J6e l)1O 1O amptlt toxap~ om)6( 6 01tololt ICplvamplCU tnaplCt)c Sla lllv noposhyAOPnV TaV laaEWV de tae 9taamp TauT~ n A1Iv Tilt dKOVOlt T6lV taacwv de TO toX(J~ TOC ltAatolou tAnrp9T) oopaplblt un 6VIV ICal 11 dKOOV T6lV looXptuJ1(JV toC cpoptcoc amp1lt t11V t01toget110W TOC mOTlPOO OnAIO)JOC

AI napOVOlapoundO)1ampVOl taEampllt de to im6A011tOV cpoppoundo 1tAllv

toO TOll(oJ1atalt ilOlPOIVtQl itU toU A6you ~ tv90 ii naplshyI

(HQ tnv anOa1amv toO ICcVtpopaplKol) a~ovolt TfIe iU1t0IlfiC an6 tol UpIYPlaquo4tllatOe liui tOv laooovollOV laquopO pta ICal V Sui t6V npoYJ1alllC6v q)Opta

l nouwpo+ov 616upo - nocnuAwpa

31 AJlrt1ltelJleuroVov nl~ iQeu1l

TO jlaatK6v tlnt~KG)I tltavao)Jpavo)Jevov 6(lt 6A1V tllv nep[shy)JEtpOV tav ICT1)PlWV imOOtUMo)1a (xpiatOtal crxeoOv tll1ttIC11V cpOpTtOlv Anoteittal t iuo OICEA(i)V tf ti)v t6 IJ~V 1tPc) t6 toWtepllCOv tOC ICtf(piou IlIKp(i)V OIwrrrtcrEWv poundYKIPWT[shy~6ta l de tOV 1tEPLJ1poundtPIKOV tEWteplK6v Toixov to St J1eyoAushytepov 1t)~Prolt OPlltOV tv TO 1tPOOOVEI IC(1ta tnV )JOPltPllv lAy npocrapJl6lEt(11 E1( teu apXltElCtOV~ICdlt analti)oEtlt KatQ TQ~ pamKW 1i10(JTaow 6)Jw~ )10pcpoCtal tv 0loptll0Et np6lt tllv JleyioT1)v KQTan6v11alv tOU etc tOUpound ICa9 uilDI OpOqgtOlk

- ------

15-4 H6pTIO~ 1969

toO KtTlP ioo T o IIIKp61 cnctUo toO igtnoatu)(i)lJau~ tyKI P(a)shytl~JOV el( t Oy 1lCPljJltpuc6v t o iXov t oi) KtllP(ou ~Opoundl vn hu 1tlQtO~ Qlixl jJpoundya)nepov tli)y J S h Cltoo t c1rv 11tO I oUxi IJElaAUt epOv 100 nuxouc tau neplJIEtpiKOU 1o[xoo tll nposhy06vEmc To Ap(lltTHlD dr t6 6noiov to69n anQvtlatC t1C tii~ qgtrot06shy)aatIKi~ SlCppounduvflOel~ to 6 Ka90ptoj10c t~V 1COOcxnG)V d t UX6 VtQ 6po~ov btl t oO OlcrKpoundAo~ moOtuM1gtiJat~ toO O1lHlat~ 7 6Ol(oojJeV ll t 6An(~c Kata~op(xpou qlopti shya poundWr 16 6no[a aVUAu)lPQvEL rKcitcpov Ol(Hor Kui 5il poundI OAoOl tO~ KCItel OpoundlpOV UJtoKEqlevOlX 6p6pouC

aJGHOEIA1TIKH E PE Y N A

(2)

r- I

I

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8

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rshy

lts CJ) A~3t I I

) 30t 1m ~I I reg3~)xPF I

o II)

ai

r-

I

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To umxCT(OAoOV ti JlCic np6pgtTlIlD ooVata l vii ge(j)pl9~ ~nlshymoov KaS 000 fJ oeonooooa rv1Ctal~ toD IpOptwlt bmptshyn pound1 nlv napaApoundVLV febv 6p9ampv Cal olaqllltllCGlv Suvqu~wv tlilv op6Jali)v d e tru to)J~ t~ Itapa))i))oult 1tP~ 16 binEshySo woO ox 7 6141 1tlV lCutamceuiv lCut t iv ql6PU01V 101) 6-shy~OlW~U1()~ hJH)OLl101tOlT1 8)lCQV oL V6~0l Tf ~1)xQvufJ~ 6shy~o16t Tl1CX ICU90P108pound10WV Pelotl toamptrov llllv ) lllalCwv ~TJshyJ(wv 1tUXOIlt lllivri ~pound6lV KU rtapa~OpqlltbceolV OUTrot ~CJtpound 1t pOaOloplltO~tvll c 1tpoundlpa~Utl 1Clil( 1fC tv 141 OOK1~ (41 tV1ashyae~ vei 1tPOlCU4OUV p6ael tti)v lJl6Krov TOlrt(J)V a1 T6OE I~ Kat YE V1KGx n tVlaltT1lt ti~ KaacrKEuf~

EN TA IE 01 ynOITYIOMATOI

~ ~~~ -~-~-=-~1~A~shy==-====~ ~+shy==+=~-I I

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+

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o-~- -=-=-=-=__=__=-_== I I I I I I Iw I I I I

nPArMA Tl KH AIATOMHo

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---- ----------shybull

-------- 40----------~

+- 00

j 1II0AYNAM Or ca AIATOMH

+25- -shy

2 A I AT OM H a - 8

ltiii n pOp l-IOTlllri bellO ~ 3 PTI(JlV EoMqd o u

r)(HMA 7

155 MlapTlot 1969 T~XYIKa XpOYIICQ

32 MOQqrYJ roV r50(~llwv

Ett to crX 7 ElvaL OXEOl(lO~eVOv to 6~oi(J)jla anEIICovl~ov TOV npIlYjlIlTLKltW cpoPeuroIl lmO l)ijlul(u 1 50 TOO 6notou 6jloor ai OWTOjllli (op60yoovlIcai TCAaKOOOICO ICA1t) ExOUV ampvax6fj dt tcroouv~~o~ op60YOOVLIUr 1t6TO~ 25 bc fjtOL dr OW~ to~ar txo~crcu TtiV aimv poreT a8pavEiar Kat E1tLTtpocr9E shyoor COv aUTOV IEVTpOpapLIOV 6~ola 1tp6r T~ npay~aTllclr rOLQTE~~ Olcx T6 Aim6vod)or toO UTtOOTUAOOjlaTOr TO OTtotov poundXEl OWOTaOtV ICa6ET~ T4) t1tl1ttOq) TOU ax 7 IOllV rtp6r 35 EK ll clvayrorll EYEVEtO ATlCP9tVTor KOTo OlWIlVtlKOV pCl8~ov UTt 6yenEL ltIx KPIHIPiou tfio OTO npootYYIOlV io6tTlshytOr tli)v poundmcpavEIli)v TOOV 8ulToJli)v

AvayUYf1 olaTojWv

Ae1ttov unOOTUAOOjla

npnYlJatlK1 otllToJlil 35 x 15 EI F = 525 ampK8 J = 9900 EIC~ too00va~0r OLatOIJ-n 25 x 18 EK F = 450 J = 12400

aOKOr uyro~ator

1tpay~aTUcll OlOCO~ti nAaKOOOIOlt amplr eir oXn~a 7 tooo0vn~0r OlOtOIJi1 op60yoovln 8la0~ 64 X 25 EIC

33 K)lla(tl - nUQafan~~ 6l(fra~tl

Or Kat npotpoundp~v nmiddottx611 amplr UA lKOV TOO 80KI)II00 t1EUrrl to ouovAraldlt KOKAoCPOPOOV dr TO tll1tOPIOV 000 J10Pql1lV 1tQK~V noxour 1 E~ Erri npOTlntOO OOKIJlioo 2 x IJ eK t shy)Ie1Pll8T1oav i) ltpOOtOEAu(JtIKn Otll6Epa S Kat TO jl t tpOV oashy0111C61T)t0t E toO OAII(OO COl) liOKIJliou Kai Eupt61loav

S = 10 (xyplpoundlt I latlV) poundlt E = 30500 xypeK

H JClr~a~ ~~KGgtV ~ln 1 50

H Kitjla~ nclxmx rrpoKumEL poundIe wO mixoult toov 25 EK t oO taoouvCt~Ou 1tpOr tov Ttpay~atlKOV cpopeurooor Kat t OO 1taXOUlt 100 I ampK tfjr nAIlKOr Araldil L~Ve1tampr tXO)lpound V

l ICaTaOlCEl)ll 50 KAfjl1l1 jlTlKWV A = Y = 6)l0~oo~a =-

1 = 50

KlltIlOlCSUT) 25 = - - 25

o~oiw~1l I

H KM)Ial tiUv OUVQ~EWV 1tPOEICUVEV h tfjr QvaYKTI~ QnOKt1)shyOEUX eOKpWOOr poundlICOV~ looxpw~atllCi)v KalmuA(i)v Kat lin nOAunA1l900V oui tilv KaA01EpllV Qno-Ti)1TjOlv Tfir tv 1(i) lio-Killiq) tvtaoewo Outw ~t~61l

- ~ 1 P P KatllOlw1 IlOOOUp =415KMila uuvo)lpoundOOV = - I

P 6jloioojlU 315

B60El tlOv v6~oov tfr jll1XllvIKfjr O)lOIOTI]TOr lntO)OYIEtol )lovotljLU)~ nAtov ~ OltOjlpoundVOUOIl KAr~a~ anapal tlltOo 8 ~a tllv napooollv ~pEuvav rtOL -n KAr~a~ raaeoov

o KOtaOICEutl _ P 1 _ 415 - ~ - 5025 = 033(7 = 6jloioojla

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E~WTEPII(OY oKiAoS

EmcpavELa 10 X 10 = 10 EK

TOL~ looXpro~oov

156

aplpd 6~ 6 ~ 20

OE~lIi 611 0 7~ 35

lISao lip 0 = 275

AvCl)alJ~aVO~Vll DuvaJHe

P 1 = Fmiddot 01= 10275 10 pound 28 XYP

EOLJTpoundPIKOY odAot

EntCjlclvElCl 035 X 10 = 035 EIC~

Toe laoxpoolWlv lISaolt 6p 0 = 55

AvlaquolallJavotttvl SUVClIlU

p = F middot a= 035middot55middot10= 19XYP

lP =28 + 19 =47XYp

P lP = 2847= 060

p lP= 19 47 = 040

R ICCltQVOjLT T6lV TtlcrpoundOJI eli rtie oHno~Qc TllIv SUo OlCe)6)v TOO unOOtoAlh)LClmc Ttupa r0 llEacp tOU UII OUC t(lO lntoatushy~QCOlt elc t6v 20 1 opocpov evm K(j-rCil8~

E~wTlplI(OY adAot

E1ttqlQVElCl 10 X 10 = 10 EIC

TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

Ala)ClIl~alo~vT1 OUVQJHI

P = Fmiddot a= 10 middot 325middot10 33 XYP

EawnplKOV adAot

Emcp6vE1Q 035 X 10 = 035 flC

TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

01 )6-YOt P j1P Kai P~IP Eb Till SUO uvO)teuropw EAampYX8eicraC aT6811oc 68rrroOl de 6 KCltCilTEPUl lIpom)Ylcrtu6v cro)11ltshypOcr)lCl (016t1 OfV TtPETtEl vO Q)V0118f1 on t6 cpoptiov emaAishy811 poundi~ 16v avcigttQtov 6pocpov KClt So TiCo 6v OXl QVa)Karov TtQVTo)( OIc61tl)lOV va EfXpound olpoundppoundu-IlSfI Kat TtpoundpITtCCOOlt cpOPTtshycre~ til tvS1Q~crOV 6pocpov)

6ul T6v aJltcrox iJ1tOlCEi~vov til~ cpoPTfcrpoundiJW opocpov tl CJOJIshy

~TOXl) d Tilv Qvo)IlVlv qloptiwv TOO )leyQAOU Kai CoO Jl1~ lCCOl OKEAOUt dvm 60 lCat 401-gt avtlo[oiXtJgtI tv OLD T6v lmoKpoundJlEVOV OpoqlOV Kat tnt T6 SUOJlEVOtEpOV fCOl tmep dit aOqluAElat Col JllJCPOC UTtOOTOAcigt)lCltOt Kat Ola tOtx euroV (JUVEXpoundiQ lmOICpoundIJltVOUC 6p6cpoVt n ow)Jt1OxTl autl1 ouvoml vO 8eooPTI8-a Om8Epo teal fa11 np(gtt 72 Kat 28

The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

ISO MIlpTlo 1969

22 MoetPi dO~l-toU

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H avo)urytl oitn lW1poundOtl1 anapai-tnCoc 01011 to uAncov CoO

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3

22

L1 ot oLn I - I

npaYJ1atlKn OtaTOIJTi

nMuooOlr~ J = 778104 EKt

(to l1t6cnacrte tol) KtVTPOU ql(JvEiae Tf]e 1ttaKOe)

IooouvalJ~ OtoTO)lit op90Ywvuol 25 X 155 EK

L1laTop r 2 - 2

npaY)ICImctl 6IaroJJTj

44 3

5 5

6 6

to = 386 EI(

Popoue OTtO Tfie ~c(l)Tepll(ile E1tIshy

1[AaKOOOl~ J = ID I ()4 EIC4 10 = 220 BJ(

la05uvu)Ior OlatO)ITj Op90ywvu-n 2S x 94 EIC

LhaT O f-~ 3-3

npu))laTlJ(Tt Olato~ui

TUClKOOOK Oc J = 14OCUOt EICmiddot If = 575 EIC

laoouvu)lOC lha ToJJit op90YOOVIK1 25 x J89 eIC

dar olo t) 4-4

npa)lJanKTt OtUTO)li nAUICobOKOc J = 407104 EIC4 lo = 300 EIC

lcroouvalJ~ olatO)lli op90)OOVLIC1 25 x 125 EK

L1tar o p1 5 -j

npaYlJatucll OIQtojJi) nAaICooolC6i J = 28510 EIC 4 0 = 264 EK

lOoouvajJ~ OtatO)l 6pe01lVtK~ 25 x III

dta-rout) 6-6

npaY)IatlICtl IhaTO)lit Op90YWVlK1 60 x 60 EK

Tcroouvaj1Ot OtaTO)li] Op90yooVlloi 25 X 80 EK

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23 K)fa~E middot 17EteapaH~ L1lcirae-

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S = 10 (xYP euro K2jTOtIV) EK E = 30500 XYPEKmiddot

E~EAt(T KArlJ tl~ )l11KGlV 150 H KAT)Iat nOXotX npoKigt1ttEL eurox toO nOXotx d - 25 EK toO 1005uvtlJloU qlOP~ Kal tIC toO 1tltIXOOe d = J EK t~ JtlalCoe AraJdit luveTtWc EXO)UV

I KatamceD11 50 A ~ 7 =-1shy6Jlo im~u

d KaTMICEu1l 25 t= d = - 1shy6J1o iwllCt

poundKJiyU(U oE

ICAT)I~ TOcrEC1lv

BOOEI tWV v6IJoov ti)~ J1TJxaVlKilt O)lOIOT11tOt breOAOyi~EtClI IJOVOTilJw t nAtov fJ O1tOIJEVOOOCl ICAijJat Tj (L1tClpa(t11T~ 516 t1v nClpOn(J1lV tpmgtvav i]t01 1 KAtJ1a~ oovolJeoov

bull P Ko taOKEUTuUVCljJEIDV p = lIZ 6

p 110(001Jo

1250= 1050middot25 = - 1shy

AtCllPOOvramp Ta cpopTia PI Kal Pwto dVacpEpO)leva Ele tTtv 1tCl pc)ypaqgtov 21 oui tilt KAijJaKoe OOV6IJEooV p = 1250 EUmiddot piOICOI1EV tCu Brei tOG OOK l)liou poundqlaplJootealt ltpOpticrEtc r Kat II

PI p p P PeP 4

ltlgt6pnm I 47 50 62 68 6laquo 52shy

ltlgt6 II 52 50 88 46 104 52

TO QVfDTtpoo QlOll tLa ~~altncoOvtal enl tOO 00K lj1100 de 8Eow tJItpal vo)ltva~ d t T6 ox I JJi04gt 6 WPOAOYICtICltIV 5uvCt)lolJtshytpwv E~ ro 11j1tw tfk 1tAaK~ OPOI4gtilc Kat KaTa ti]v 6ptCovshytlav EvvOlnv ~t01tOeCnW11 crtitPtY)Ja 10 o1toTov it11oltpOhlaE eft to OjJOiW)1Cl 6P L~OVtjav OKlv11a[av roo ciXPlPGIc toiYto OUIJshypoi VEt de TOV 1tpaY)JollKoV qJop~a 16 14gt tf)lt ouwpyaoialt t (l)v T01Xoo)laTooVtOn lOO)ElOU Ilna tfle n)alolootitc KCtTocrK6Uf]lt ete Tponov WltTTS to 1tAaiOlCt va OOVCtVtol vo 8poundOOPTl900v dx TOIClOm o)UTo9ETWV K6)1 Poov

MEta~U T(i)v OIEOTCIUPOO)lpoundVWV 1tOAootlK(UV 191JltIv T~e Q1JOKEUfle tpw10taaeO)lEtpiae (TonoeeTf911 to qlopno)Jtvov OOIC[)IIOV I(ai ~iilqJeToav oui ti)v qJOptlOlv 1000 l(itPlvOV )lOVOXPwjJCtshytllCOV pUle al Ele t6 oxi]lJotD 3 Kal4 tjlqlCtlVOIJpoundVCtI ql(JltoypashyqliCIl lOoxpoo~v oKpoundpaiat 101 tl)lICtKEpaiae tacewc Kat 6)loiwe oUI nlv CPOptlOlV II ai qgtWtoypocpiCtl t(l)v OX11JlOtooV 5 KCli 6 laOxPOlllot EIVCII Ctf ypaJJIlCti ICato )I~ KOt TltIv 6Ttoicuv 1 Otoshycpopa lCupirov taoE(J)v 0 1 - cr~ elvat 0tCl9EPci Kat LO1) np6lt

nlt I5EuvuEtQ de t6c poundil(ovCllt t(i)v (croxPOOIJWV de talt atmiddot XIJ6lt tol) nEptypci)l)1Oto- TOO ltPOPClllt JqllotaTat crucrcroopEUOIe tUOEooV AiCtv 5UO)lEv1lt l)ui ttV Oa(jluAElaV tfle KataoKEui1lt Alo tOOTO poundAT1q1e11 1tp6VOla de TTlV lCataOlCEUT)V ooOtpound al 0) shyACt)ai olfl)9uvopound(il~ toO 1tpoundPlypU)I)latOt v6 KUTaowOv 6)laA6r tEpCtl oui T~lt napeIlPOAij r hltXfl~ tvl(nOOEOO~ d e Tp6nov ampOtE f) )Iulipnolgt t(i)v TuaCtov pound1( TOO ev6~ cnUouo ttie ywshyvialt de t6 etepo va I(OO[Otattll 6J1llcottpa pt Q1tOttMcJ)Ja TfiV lJe(ooOlV Til cnryKWlPOOE(Ufi nov 1UOamp00 cit Tfl V crtXJmiddotnv

153 M6pnol) 1969

EIlt TnV nopoOOov lpcoV(l- npICtaOrU16v dt T6v nPOO010PIshyaJl6v 161V lQcrWlV J16vov tnl TOO ntplYpaJlIlOtOlt 1)pdaGnllev TOOltltTtIV pound1lt to oi l(100V TaV loOXprollwV TamWV 00 600v d C tei aT))Uta tOO ncptypOIJIJOtOlt J1t 02 = 0 trouv at - 0 = = a Kat a = 8 Sd Suva~t9a S~kaSIl t K lt1lt n~~c S lt~lt laoXPwJ1aTIK1)lt T~poundrot va ~XWfJev 11)v TIIlV Tf)lt ciYVcUoTOO ICVptalt toatoolt a bull

~ QvtltPtp9T) ellt t1v 1tapif)p(l(pOV 23 Elval

a ICatooKroli = 10 7 olloiwJ1o

61(1 t6 GVro nEpi)p0)1110 loll T01X~OT0I9 nPOKlmTpoundl T61C laOLt tcpEAKOaJ1oi) 0 = 3 x 10 = JO lYP tKmiddot 6llt at avc~vfto n~ napa)olnv T1)C t ICQIIVcw KaTanOVnaerolt 100 T01X6r J10tOt 119EVtQI 74gt20 d~ T1Iv 6vw naPEU~lv Etc Tar ICOTOshyICOPUltPOolt nOPUQlt toll 10IXOOIIOTOC ell tJl4lQvl~6J1Ev(u 9)shy1tt1Knl TcWUlt Stv lmEppotvouv lQ 8 x 10 = 80tYPCIC nposhyCKTelVOVTnI OlVE1tGgtlt ~tJ)t Tne paactJgtC TOO TOIXOO)JOTOC ot 6shy1tAIO)JO TCUV tIC t(L)v avoo il1tootllAw)Jat(J)v

Ett Tillt 1tapuclt toC 10IxOO)JOt0e TtOclal 61tAIO)J6e l)1O 1O amptlt toxap~ om)6( 6 01tololt ICplvamplCU tnaplCt)c Sla lllv noposhyAOPnV TaV laaEWV de tae 9taamp TauT~ n A1Iv Tilt dKOVOlt T6lV taacwv de TO toX(J~ TOC ltAatolou tAnrp9T) oopaplblt un 6VIV ICal 11 dKOOV T6lV looXptuJ1(JV toC cpoptcoc amp1lt t11V t01toget110W TOC mOTlPOO OnAIO)JOC

AI napOVOlapoundO)1ampVOl taEampllt de to im6A011tOV cpoppoundo 1tAllv

toO TOll(oJ1atalt ilOlPOIVtQl itU toU A6you ~ tv90 ii naplshyI

(HQ tnv anOa1amv toO ICcVtpopaplKol) a~ovolt TfIe iU1t0IlfiC an6 tol UpIYPlaquo4tllatOe liui tOv laooovollOV laquopO pta ICal V Sui t6V npoYJ1alllC6v q)Opta

l nouwpo+ov 616upo - nocnuAwpa

31 AJlrt1ltelJleuroVov nl~ iQeu1l

TO jlaatK6v tlnt~KG)I tltavao)Jpavo)Jevov 6(lt 6A1V tllv nep[shy)JEtpOV tav ICT1)PlWV imOOtUMo)1a (xpiatOtal crxeoOv tll1ttIC11V cpOpTtOlv Anoteittal t iuo OICEA(i)V tf ti)v t6 IJ~V 1tPc) t6 toWtepllCOv tOC ICtf(piou IlIKp(i)V OIwrrrtcrEWv poundYKIPWT[shy~6ta l de tOV 1tEPLJ1poundtPIKOV tEWteplK6v Toixov to St J1eyoAushytepov 1t)~Prolt OPlltOV tv TO 1tPOOOVEI IC(1ta tnV )JOPltPllv lAy npocrapJl6lEt(11 E1( teu apXltElCtOV~ICdlt analti)oEtlt KatQ TQ~ pamKW 1i10(JTaow 6)Jw~ )10pcpoCtal tv 0loptll0Et np6lt tllv JleyioT1)v KQTan6v11alv tOU etc tOUpound ICa9 uilDI OpOqgtOlk

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15-4 H6pTIO~ 1969

toO KtTlP ioo T o IIIKp61 cnctUo toO igtnoatu)(i)lJau~ tyKI P(a)shytl~JOV el( t Oy 1lCPljJltpuc6v t o iXov t oi) KtllP(ou ~Opoundl vn hu 1tlQtO~ Qlixl jJpoundya)nepov tli)y J S h Cltoo t c1rv 11tO I oUxi IJElaAUt epOv 100 nuxouc tau neplJIEtpiKOU 1o[xoo tll nposhy06vEmc To Ap(lltTHlD dr t6 6noiov to69n anQvtlatC t1C tii~ qgtrot06shy)aatIKi~ SlCppounduvflOel~ to 6 Ka90ptoj10c t~V 1COOcxnG)V d t UX6 VtQ 6po~ov btl t oO OlcrKpoundAo~ moOtuM1gtiJat~ toO O1lHlat~ 7 6Ol(oojJeV ll t 6An(~c Kata~op(xpou qlopti shya poundWr 16 6no[a aVUAu)lPQvEL rKcitcpov Ol(Hor Kui 5il poundI OAoOl tO~ KCItel OpoundlpOV UJtoKEqlevOlX 6p6pouC

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32 MOQqrYJ roV r50(~llwv

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AvayUYf1 olaTojWv

Ae1ttov unOOTUAOOjla

npnYlJatlK1 otllToJlil 35 x 15 EI F = 525 ampK8 J = 9900 EIC~ too00va~0r OLatOIJ-n 25 x 18 EK F = 450 J = 12400

aOKOr uyro~ator

1tpay~aTUcll OlOCO~ti nAaKOOOIOlt amplr eir oXn~a 7 tooo0vn~0r OlOtOIJi1 op60yoovln 8la0~ 64 X 25 EIC

33 K)lla(tl - nUQafan~~ 6l(fra~tl

Or Kat npotpoundp~v nmiddottx611 amplr UA lKOV TOO 80KI)II00 t1EUrrl to ouovAraldlt KOKAoCPOPOOV dr TO tll1tOPIOV 000 J10Pql1lV 1tQK~V noxour 1 E~ Erri npOTlntOO OOKIJlioo 2 x IJ eK t shy)Ie1Pll8T1oav i) ltpOOtOEAu(JtIKn Otll6Epa S Kat TO jl t tpOV oashy0111C61T)t0t E toO OAII(OO COl) liOKIJliou Kai Eupt61loav

S = 10 (xyplpoundlt I latlV) poundlt E = 30500 xypeK

H JClr~a~ ~~KGgtV ~ln 1 50

H Kitjla~ nclxmx rrpoKumEL poundIe wO mixoult toov 25 EK t oO taoouvCt~Ou 1tpOr tov Ttpay~atlKOV cpopeurooor Kat t OO 1taXOUlt 100 I ampK tfjr nAIlKOr Araldil L~Ve1tampr tXO)lpound V

l ICaTaOlCEl)ll 50 KAfjl1l1 jlTlKWV A = Y = 6)l0~oo~a =-

1 = 50

KlltIlOlCSUT) 25 = - - 25

o~oiw~1l I

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- ~ 1 P P KatllOlw1 IlOOOUp =415KMila uuvo)lpoundOOV = - I

P 6jloioojlU 315

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o KOtaOICEutl _ P 1 _ 415 - ~ - 5025 = 033(7 = 6jloioojla

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ral t6 rrpoYjlotLKD Kai til 000 KA[~aKa Ent toO 8011)I(ou EmshyPAI18EVtu qgtoptfa

34 n eQUjiutli(Q Ut(JTtUaf070

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E~WTEPII(OY oKiAoS

EmcpavELa 10 X 10 = 10 EK

TOL~ looXpro~oov

156

aplpd 6~ 6 ~ 20

OE~lIi 611 0 7~ 35

lISao lip 0 = 275

AvCl)alJ~aVO~Vll DuvaJHe

P 1 = Fmiddot 01= 10275 10 pound 28 XYP

EOLJTpoundPIKOY odAot

EntCjlclvElCl 035 X 10 = 035 EIC~

Toe laoxpoolWlv lISaolt 6p 0 = 55

AvlaquolallJavotttvl SUVClIlU

p = F middot a= 035middot55middot10= 19XYP

lP =28 + 19 =47XYp

P lP = 2847= 060

p lP= 19 47 = 040

R ICCltQVOjLT T6lV TtlcrpoundOJI eli rtie oHno~Qc TllIv SUo OlCe)6)v TOO unOOtoAlh)LClmc Ttupa r0 llEacp tOU UII OUC t(lO lntoatushy~QCOlt elc t6v 20 1 opocpov evm K(j-rCil8~

E~wTlplI(OY adAot

E1ttqlQVElCl 10 X 10 = 10 EIC

TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

Ala)ClIl~alo~vT1 OUVQJHI

P = Fmiddot a= 10 middot 325middot10 33 XYP

EawnplKOV adAot

Emcp6vE1Q 035 X 10 = 035 flC

TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

01 )6-YOt P j1P Kai P~IP Eb Till SUO uvO)teuropw EAampYX8eicraC aT6811oc 68rrroOl de 6 KCltCilTEPUl lIpom)Ylcrtu6v cro)11ltshypOcr)lCl (016t1 OfV TtPETtEl vO Q)V0118f1 on t6 cpoptiov emaAishy811 poundi~ 16v avcigttQtov 6pocpov KClt So TiCo 6v OXl QVa)Karov TtQVTo)( OIc61tl)lOV va EfXpound olpoundppoundu-IlSfI Kat TtpoundpITtCCOOlt cpOPTtshycre~ til tvS1Q~crOV 6pocpov)

6ul T6v aJltcrox iJ1tOlCEi~vov til~ cpoPTfcrpoundiJW opocpov tl CJOJIshy

~TOXl) d Tilv Qvo)IlVlv qloptiwv TOO )leyQAOU Kai CoO Jl1~ lCCOl OKEAOUt dvm 60 lCat 401-gt avtlo[oiXtJgtI tv OLD T6v lmoKpoundJlEVOV OpoqlOV Kat tnt T6 SUOJlEVOtEpOV fCOl tmep dit aOqluAElat Col JllJCPOC UTtOOTOAcigt)lCltOt Kat Ola tOtx euroV (JUVEXpoundiQ lmOICpoundIJltVOUC 6p6cpoVt n ow)Jt1OxTl autl1 ouvoml vO 8eooPTI8-a Om8Epo teal fa11 np(gtt 72 Kat 28

The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

MapTIOS 1969 lSI

oOIClJJiou 1tpOCnpEpEtaL EU dOKIlI 1tOXO~ I ix crUVE1tltlC TO OO dIJIOV OEOV 1tQVfOn va hu t6 CUJTO 1tOXOe poundV ovngecrEt npO~ TOV 1tpaYJJaTIICOV qlopea OOtU t tEt 1tUXI1 Ete IJpoundV TO toishyxooJJa 025 JJ d~ oE TCu ll1toMgti1to~ 9toEle 060 -010 JJ

AUl OtaKEKOJJJJiv11c ypajJ)Ifc eE 0 aUTO cn~J1a EXEl crXEolashycr9i TO TtEpiypajJjJa toO 1tpaYJumKol) tpopewc

3

22

L1 ot oLn I - I

npaYJ1atlKn OtaTOIJTi

nMuooOlr~ J = 778104 EKt

(to l1t6cnacrte tol) KtVTPOU ql(JvEiae Tf]e 1ttaKOe)

IooouvalJ~ OtoTO)lit op90Ywvuol 25 X 155 EK

L1laTop r 2 - 2

npaY)ICImctl 6IaroJJTj

44 3

5 5

6 6

to = 386 EI(

Popoue OTtO Tfie ~c(l)Tepll(ile E1tIshy

1[AaKOOOl~ J = ID I ()4 EIC4 10 = 220 BJ(

la05uvu)Ior OlatO)ITj Op90ywvu-n 2S x 94 EIC

LhaT O f-~ 3-3

npu))laTlJ(Tt Olato~ui

TUClKOOOK Oc J = 14OCUOt EICmiddot If = 575 EIC

laoouvu)lOC lha ToJJit op90YOOVIK1 25 x J89 eIC

dar olo t) 4-4

npa)lJanKTt OtUTO)li nAUICobOKOc J = 407104 EIC4 lo = 300 EIC

lcroouvalJ~ olatO)lli op90)OOVLIC1 25 x 125 EK

L1tar o p1 5 -j

npaYlJatucll OIQtojJi) nAaICooolC6i J = 28510 EIC 4 0 = 264 EK

lOoouvajJ~ OtatO)l 6pe01lVtK~ 25 x III

dta-rout) 6-6

npaY)IatlICtl IhaTO)lit Op90YWVlK1 60 x 60 EK

Tcroouvaj1Ot OtaTO)li] Op90yooVlloi 25 X 80 EK

BOOEI tGlv OVOHtpcu eupE9ElOampV a oO vnjloov olato)l(i)v poundaxe~ Olelae11 tIC TOO npay)lCltlKOU 1POptM (pt olatocrm jJll (v11v de ax J) to mpiypo)l)lO TOn 001C11l10U

23 K)fa~E middot 17EteapaH~ L1lcirae-

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S = 10 (xYP euro K2jTOtIV) EK E = 30500 XYPEKmiddot

E~EAt(T KArlJ tl~ )l11KGlV 150 H KAT)Iat nOXotX npoKigt1ttEL eurox toO nOXotx d - 25 EK toO 1005uvtlJloU qlOP~ Kal tIC toO 1tltIXOOe d = J EK t~ JtlalCoe AraJdit luveTtWc EXO)UV

I KatamceD11 50 A ~ 7 =-1shy6Jlo im~u

d KaTMICEu1l 25 t= d = - 1shy6J1o iwllCt

poundKJiyU(U oE

ICAT)I~ TOcrEC1lv

BOOEI tWV v6IJoov ti)~ J1TJxaVlKilt O)lOIOT11tOt breOAOyi~EtClI IJOVOTilJw t nAtov fJ O1tOIJEVOOOCl ICAijJat Tj (L1tClpa(t11T~ 516 t1v nClpOn(J1lV tpmgtvav i]t01 1 KAtJ1a~ oovolJeoov

bull P Ko taOKEUTuUVCljJEIDV p = lIZ 6

p 110(001Jo

1250= 1050middot25 = - 1shy

AtCllPOOvramp Ta cpopTia PI Kal Pwto dVacpEpO)leva Ele tTtv 1tCl pc)ypaqgtov 21 oui tilt KAijJaKoe OOV6IJEooV p = 1250 EUmiddot piOICOI1EV tCu Brei tOG OOK l)liou poundqlaplJootealt ltpOpticrEtc r Kat II

PI p p P PeP 4

ltlgt6pnm I 47 50 62 68 6laquo 52shy

ltlgt6 II 52 50 88 46 104 52

TO QVfDTtpoo QlOll tLa ~~altncoOvtal enl tOO 00K lj1100 de 8Eow tJItpal vo)ltva~ d t T6 ox I JJi04gt 6 WPOAOYICtICltIV 5uvCt)lolJtshytpwv E~ ro 11j1tw tfk 1tAaK~ OPOI4gtilc Kat KaTa ti]v 6ptCovshytlav EvvOlnv ~t01tOeCnW11 crtitPtY)Ja 10 o1toTov it11oltpOhlaE eft to OjJOiW)1Cl 6P L~OVtjav OKlv11a[av roo ciXPlPGIc toiYto OUIJshypoi VEt de TOV 1tpaY)JollKoV qJop~a 16 14gt tf)lt ouwpyaoialt t (l)v T01Xoo)laTooVtOn lOO)ElOU Ilna tfle n)alolootitc KCtTocrK6Uf]lt ete Tponov WltTTS to 1tAaiOlCt va OOVCtVtol vo 8poundOOPTl900v dx TOIClOm o)UTo9ETWV K6)1 Poov

MEta~U T(i)v OIEOTCIUPOO)lpoundVWV 1tOAootlK(UV 191JltIv T~e Q1JOKEUfle tpw10taaeO)lEtpiae (TonoeeTf911 to qlopno)Jtvov OOIC[)IIOV I(ai ~iilqJeToav oui ti)v qJOptlOlv 1000 l(itPlvOV )lOVOXPwjJCtshytllCOV pUle al Ele t6 oxi]lJotD 3 Kal4 tjlqlCtlVOIJpoundVCtI ql(JltoypashyqliCIl lOoxpoo~v oKpoundpaiat 101 tl)lICtKEpaiae tacewc Kat 6)loiwe oUI nlv CPOptlOlV II ai qgtWtoypocpiCtl t(l)v OX11JlOtooV 5 KCli 6 laOxPOlllot EIVCII Ctf ypaJJIlCti ICato )I~ KOt TltIv 6Ttoicuv 1 Otoshycpopa lCupirov taoE(J)v 0 1 - cr~ elvat 0tCl9EPci Kat LO1) np6lt

nlt I5EuvuEtQ de t6c poundil(ovCllt t(i)v (croxPOOIJWV de talt atmiddot XIJ6lt tol) nEptypci)l)1Oto- TOO ltPOPClllt JqllotaTat crucrcroopEUOIe tUOEooV AiCtv 5UO)lEv1lt l)ui ttV Oa(jluAElaV tfle KataoKEui1lt Alo tOOTO poundAT1q1e11 1tp6VOla de TTlV lCataOlCEUT)V ooOtpound al 0) shyACt)ai olfl)9uvopound(il~ toO 1tpoundPlypU)I)latOt v6 KUTaowOv 6)laA6r tEpCtl oui T~lt napeIlPOAij r hltXfl~ tvl(nOOEOO~ d e Tp6nov ampOtE f) )Iulipnolgt t(i)v TuaCtov pound1( TOO ev6~ cnUouo ttie ywshyvialt de t6 etepo va I(OO[Otattll 6J1llcottpa pt Q1tOttMcJ)Ja TfiV lJe(ooOlV Til cnryKWlPOOE(Ufi nov 1UOamp00 cit Tfl V crtXJmiddotnv

153 M6pnol) 1969

EIlt TnV nopoOOov lpcoV(l- npICtaOrU16v dt T6v nPOO010PIshyaJl6v 161V lQcrWlV J16vov tnl TOO ntplYpaJlIlOtOlt 1)pdaGnllev TOOltltTtIV pound1lt to oi l(100V TaV loOXprollwV TamWV 00 600v d C tei aT))Uta tOO ncptypOIJIJOtOlt J1t 02 = 0 trouv at - 0 = = a Kat a = 8 Sd Suva~t9a S~kaSIl t K lt1lt n~~c S lt~lt laoXPwJ1aTIK1)lt T~poundrot va ~XWfJev 11)v TIIlV Tf)lt ciYVcUoTOO ICVptalt toatoolt a bull

~ QvtltPtp9T) ellt t1v 1tapif)p(l(pOV 23 Elval

a ICatooKroli = 10 7 olloiwJ1o

61(1 t6 GVro nEpi)p0)1110 loll T01X~OT0I9 nPOKlmTpoundl T61C laOLt tcpEAKOaJ1oi) 0 = 3 x 10 = JO lYP tKmiddot 6llt at avc~vfto n~ napa)olnv T1)C t ICQIIVcw KaTanOVnaerolt 100 T01X6r J10tOt 119EVtQI 74gt20 d~ T1Iv 6vw naPEU~lv Etc Tar ICOTOshyICOPUltPOolt nOPUQlt toll 10IXOOIIOTOC ell tJl4lQvl~6J1Ev(u 9)shy1tt1Knl TcWUlt Stv lmEppotvouv lQ 8 x 10 = 80tYPCIC nposhyCKTelVOVTnI OlVE1tGgtlt ~tJ)t Tne paactJgtC TOO TOIXOO)JOTOC ot 6shy1tAIO)JO TCUV tIC t(L)v avoo il1tootllAw)Jat(J)v

Ett Tillt 1tapuclt toC 10IxOO)JOt0e TtOclal 61tAIO)J6e l)1O 1O amptlt toxap~ om)6( 6 01tololt ICplvamplCU tnaplCt)c Sla lllv noposhyAOPnV TaV laaEWV de tae 9taamp TauT~ n A1Iv Tilt dKOVOlt T6lV taacwv de TO toX(J~ TOC ltAatolou tAnrp9T) oopaplblt un 6VIV ICal 11 dKOOV T6lV looXptuJ1(JV toC cpoptcoc amp1lt t11V t01toget110W TOC mOTlPOO OnAIO)JOC

AI napOVOlapoundO)1ampVOl taEampllt de to im6A011tOV cpoppoundo 1tAllv

toO TOll(oJ1atalt ilOlPOIVtQl itU toU A6you ~ tv90 ii naplshyI

(HQ tnv anOa1amv toO ICcVtpopaplKol) a~ovolt TfIe iU1t0IlfiC an6 tol UpIYPlaquo4tllatOe liui tOv laooovollOV laquopO pta ICal V Sui t6V npoYJ1alllC6v q)Opta

l nouwpo+ov 616upo - nocnuAwpa

31 AJlrt1ltelJleuroVov nl~ iQeu1l

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15-4 H6pTIO~ 1969

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aOKOr uyro~ator

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l ICaTaOlCEl)ll 50 KAfjl1l1 jlTlKWV A = Y = 6)l0~oo~a =-

1 = 50

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156

aplpd 6~ 6 ~ 20

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lP =28 + 19 =47XYp

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p lP= 19 47 = 040

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TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

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TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

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The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

153 M6pnol) 1969

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~ QvtltPtp9T) ellt t1v 1tapif)p(l(pOV 23 Elval

a ICatooKroli = 10 7 olloiwJ1o

61(1 t6 GVro nEpi)p0)1110 loll T01X~OT0I9 nPOKlmTpoundl T61C laOLt tcpEAKOaJ1oi) 0 = 3 x 10 = JO lYP tKmiddot 6llt at avc~vfto n~ napa)olnv T1)C t ICQIIVcw KaTanOVnaerolt 100 T01X6r J10tOt 119EVtQI 74gt20 d~ T1Iv 6vw naPEU~lv Etc Tar ICOTOshyICOPUltPOolt nOPUQlt toll 10IXOOIIOTOC ell tJl4lQvl~6J1Ev(u 9)shy1tt1Knl TcWUlt Stv lmEppotvouv lQ 8 x 10 = 80tYPCIC nposhyCKTelVOVTnI OlVE1tGgtlt ~tJ)t Tne paactJgtC TOO TOIXOO)JOTOC ot 6shy1tAIO)JO TCUV tIC t(L)v avoo il1tootllAw)Jat(J)v

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15-4 H6pTIO~ 1969

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The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

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15-4 H6pTIO~ 1969

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1 = 50

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- ~ 1 P P KatllOlw1 IlOOOUp =415KMila uuvo)lpoundOOV = - I

P 6jloioojlU 315

B60El tlOv v6~oov tfr jll1XllvIKfjr O)lOIOTI]TOr lntO)OYIEtol )lovotljLU)~ nAtov ~ OltOjlpoundVOUOIl KAr~a~ anapal tlltOo 8 ~a tllv napooollv ~pEuvav rtOL -n KAr~a~ raaeoov

o KOtaOICEutl _ P 1 _ 415 - ~ - 5025 = 033(7 = 6jloioojla

H tK tfjlt poundV 0PlOVtlq) poundTtIJtEOQ) aXEtnfjr aU~~tpia toov KashytaKOplxpOlV cpep6vtwv atOIIEOOV toO Ktllpiou Kal OtClltEpWr II poundK tflr (mapiecor taxuplOv tOtXw~6toov euromJaA AO)ltVTl oleshyHK1 aKwllcrio toO EpeUVW~tvou lmootOAW~atCk dr tar OT6shy8~cu troY 1tAoKampV tampv 6pocpQ)V til~ KllTaaKEUf)r t~1lOlpoAiae1) pound1r to 80Ki~lov 010 tOOV OtllpiiEWV (4) (5) (6) Kui (7) TO ltpopTill TO OOlCouaeva dr tar OiOElr (I) Kai ( ) lthr lipaapoundl~ tOOV eurotKapaiux 1tP~ TO nAIlIOiooJ1a toO ax 7 blllKoocrroV 80shyK(i)V t1tEnAfl61loav UltO tilv npOEIPIlJ1poundVTjV KAiJlal(a ouvCtlJEwv Jlioq) amplpoA01laKwv liuvopo~hpwv euroqgtapjloo13euroV1oov Efc tar Ulnar euront (00 OOKlJliou eeoElr eurovtj) to 6~OlOjlOpqgtov poptiov tfjr oOKoD (2) (3) (4) CtvtLKatEOt661l lrJtO tvo~ dr to )lEaov tfjr OOKOU (2) (4) uno toi) 8uVIl~o)lftpou (3) )lE)lOVOOlJtvwr oOlCOUIJEVOU popt(ou ~e)teOl)r ltPOOOlOPUO~EVOU euro1rl tfj PaOEl tGgtv KavovOlv avtllCatoOTaaEWr Err to ax 7 OELKV00vshy

ral t6 rrpoYjlotLKD Kai til 000 KA[~aKa Ent toO 8011)I(ou EmshyPAI18EVtu qgtoptfa

34 n eQUjiutli(Q Ut(JTtUaf070

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AI T~EIr Ti)V (OOXpw~wv t01lJ1Elro61lOaV oui AeUKfjC )IEAUVllr Efr TTlV lpW(oypoqgtillv toO ox 8

3 gtA~w1lOrJalr TW) JTE~QauaHi(w) Mousaucl7wv

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ArravTTOtV 6~UX poundlr TO Kupi~ QnooxoAo()V 11v f peuvav tOVt1lV tprot1l~Il fitm TO() npoo010PIOJlO() t(i)v ltOOootO)v avaA1lVEWr Ka11l1C0pUqlWV OUVCtJ1EWV O1tO tK01tpou t~V OKEshyAlbv TOO U1tQOtI)AroJlaTOr 1tappoundXEI 11 tv croVEXEiQ 01tOUOll t1i~ evtoOEWr t(i)v 8tatoJlWv tOOV lt1lltEA(i)V tOUtWv pound~ t6c 0T6shy6~ar tG)v Jttowv t(i)v uyenwv troy op6qgtO)v 0i51~ err t6 ~toov tOU unocmgtAro~atOlt toO tpiTou 6pOqgt01l toO Ol 8 11 KOTllVO~ t(i)v taaampwv Ei~ tar OlaWjlIlr tUlV QUO OKeAWV tOO 6nOOtlA(i)~at0r e[val tl Kat0l6

E~WTEPII(OY oKiAoS

EmcpavELa 10 X 10 = 10 EK

TOL~ looXpro~oov

156

aplpd 6~ 6 ~ 20

OE~lIi 611 0 7~ 35

lISao lip 0 = 275

AvCl)alJ~aVO~Vll DuvaJHe

P 1 = Fmiddot 01= 10275 10 pound 28 XYP

EOLJTpoundPIKOY odAot

EntCjlclvElCl 035 X 10 = 035 EIC~

Toe laoxpoolWlv lISaolt 6p 0 = 55

AvlaquolallJavotttvl SUVClIlU

p = F middot a= 035middot55middot10= 19XYP

lP =28 + 19 =47XYp

P lP = 2847= 060

p lP= 19 47 = 040

R ICCltQVOjLT T6lV TtlcrpoundOJI eli rtie oHno~Qc TllIv SUo OlCe)6)v TOO unOOtoAlh)LClmc Ttupa r0 llEacp tOU UII OUC t(lO lntoatushy~QCOlt elc t6v 20 1 opocpov evm K(j-rCil8~

E~wTlplI(OY adAot

E1ttqlQVElCl 10 X 10 = 10 EIC

TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

Ala)ClIl~alo~vT1 OUVQJHI

P = Fmiddot a= 10 middot 325middot10 33 XYP

EawnplKOV adAot

Emcp6vE1Q 035 X 10 = 035 flC

TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

01 )6-YOt P j1P Kai P~IP Eb Till SUO uvO)teuropw EAampYX8eicraC aT6811oc 68rrroOl de 6 KCltCilTEPUl lIpom)Ylcrtu6v cro)11ltshypOcr)lCl (016t1 OfV TtPETtEl vO Q)V0118f1 on t6 cpoptiov emaAishy811 poundi~ 16v avcigttQtov 6pocpov KClt So TiCo 6v OXl QVa)Karov TtQVTo)( OIc61tl)lOV va EfXpound olpoundppoundu-IlSfI Kat TtpoundpITtCCOOlt cpOPTtshycre~ til tvS1Q~crOV 6pocpov)

6ul T6v aJltcrox iJ1tOlCEi~vov til~ cpoPTfcrpoundiJW opocpov tl CJOJIshy

~TOXl) d Tilv Qvo)IlVlv qloptiwv TOO )leyQAOU Kai CoO Jl1~ lCCOl OKEAOUt dvm 60 lCat 401-gt avtlo[oiXtJgtI tv OLD T6v lmoKpoundJlEVOV OpoqlOV Kat tnt T6 SUOJlEVOtEpOV fCOl tmep dit aOqluAElat Col JllJCPOC UTtOOTOAcigt)lCltOt Kat Ola tOtx euroV (JUVEXpoundiQ lmOICpoundIJltVOUC 6p6cpoVt n ow)Jt1OxTl autl1 ouvoml vO 8eooPTI8-a Om8Epo teal fa11 np(gtt 72 Kat 28

The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

155 MlapTlot 1969 T~XYIKa XpOYIICQ

32 MOQqrYJ roV r50(~llwv

Ett to crX 7 ElvaL OXEOl(lO~eVOv to 6~oi(J)jla anEIICovl~ov TOV npIlYjlIlTLKltW cpoPeuroIl lmO l)ijlul(u 1 50 TOO 6notou 6jloor ai OWTOjllli (op60yoovlIcai TCAaKOOOICO ICA1t) ExOUV ampvax6fj dt tcroouv~~o~ op60YOOVLIUr 1t6TO~ 25 bc fjtOL dr OW~ to~ar txo~crcu TtiV aimv poreT a8pavEiar Kat E1tLTtpocr9E shyoor COv aUTOV IEVTpOpapLIOV 6~ola 1tp6r T~ npay~aTllclr rOLQTE~~ Olcx T6 Aim6vod)or toO UTtOOTUAOOjlaTOr TO OTtotov poundXEl OWOTaOtV ICa6ET~ T4) t1tl1ttOq) TOU ax 7 IOllV rtp6r 35 EK ll clvayrorll EYEVEtO ATlCP9tVTor KOTo OlWIlVtlKOV pCl8~ov UTt 6yenEL ltIx KPIHIPiou tfio OTO npootYYIOlV io6tTlshytOr tli)v poundmcpavEIli)v TOOV 8ulToJli)v

AvayUYf1 olaTojWv

Ae1ttov unOOTUAOOjla

npnYlJatlK1 otllToJlil 35 x 15 EI F = 525 ampK8 J = 9900 EIC~ too00va~0r OLatOIJ-n 25 x 18 EK F = 450 J = 12400

aOKOr uyro~ator

1tpay~aTUcll OlOCO~ti nAaKOOOIOlt amplr eir oXn~a 7 tooo0vn~0r OlOtOIJi1 op60yoovln 8la0~ 64 X 25 EIC

33 K)lla(tl - nUQafan~~ 6l(fra~tl

Or Kat npotpoundp~v nmiddottx611 amplr UA lKOV TOO 80KI)II00 t1EUrrl to ouovAraldlt KOKAoCPOPOOV dr TO tll1tOPIOV 000 J10Pql1lV 1tQK~V noxour 1 E~ Erri npOTlntOO OOKIJlioo 2 x IJ eK t shy)Ie1Pll8T1oav i) ltpOOtOEAu(JtIKn Otll6Epa S Kat TO jl t tpOV oashy0111C61T)t0t E toO OAII(OO COl) liOKIJliou Kai Eupt61loav

S = 10 (xyplpoundlt I latlV) poundlt E = 30500 xypeK

H JClr~a~ ~~KGgtV ~ln 1 50

H Kitjla~ nclxmx rrpoKumEL poundIe wO mixoult toov 25 EK t oO taoouvCt~Ou 1tpOr tov Ttpay~atlKOV cpopeurooor Kat t OO 1taXOUlt 100 I ampK tfjr nAIlKOr Araldil L~Ve1tampr tXO)lpound V

l ICaTaOlCEl)ll 50 KAfjl1l1 jlTlKWV A = Y = 6)l0~oo~a =-

1 = 50

KlltIlOlCSUT) 25 = - - 25

o~oiw~1l I

H KM)Ial tiUv OUVQ~EWV 1tPOEICUVEV h tfjr QvaYKTI~ QnOKt1)shyOEUX eOKpWOOr poundlICOV~ looxpw~atllCi)v KalmuA(i)v Kat lin nOAunA1l900V oui tilv KaA01EpllV Qno-Ti)1TjOlv Tfir tv 1(i) lio-Killiq) tvtaoewo Outw ~t~61l

- ~ 1 P P KatllOlw1 IlOOOUp =415KMila uuvo)lpoundOOV = - I

P 6jloioojlU 315

B60El tlOv v6~oov tfr jll1XllvIKfjr O)lOIOTI]TOr lntO)OYIEtol )lovotljLU)~ nAtov ~ OltOjlpoundVOUOIl KAr~a~ anapal tlltOo 8 ~a tllv napooollv ~pEuvav rtOL -n KAr~a~ raaeoov

o KOtaOICEutl _ P 1 _ 415 - ~ - 5025 = 033(7 = 6jloioojla

H tK tfjlt poundV 0PlOVtlq) poundTtIJtEOQ) aXEtnfjr aU~~tpia toov KashytaKOplxpOlV cpep6vtwv atOIIEOOV toO Ktllpiou Kal OtClltEpWr II poundK tflr (mapiecor taxuplOv tOtXw~6toov euromJaA AO)ltVTl oleshyHK1 aKwllcrio toO EpeUVW~tvou lmootOAW~atCk dr tar OT6shy8~cu troY 1tAoKampV tampv 6pocpQ)V til~ KllTaaKEUf)r t~1lOlpoAiae1) pound1r to 80Ki~lov 010 tOOV OtllpiiEWV (4) (5) (6) Kui (7) TO ltpopTill TO OOlCouaeva dr tar OiOElr (I) Kai ( ) lthr lipaapoundl~ tOOV eurotKapaiux 1tP~ TO nAIlIOiooJ1a toO ax 7 blllKoocrroV 80shyK(i)V t1tEnAfl61loav UltO tilv npOEIPIlJ1poundVTjV KAiJlal(a ouvCtlJEwv Jlioq) amplpoA01laKwv liuvopo~hpwv euroqgtapjloo13euroV1oov Efc tar Ulnar euront (00 OOKlJliou eeoElr eurovtj) to 6~OlOjlOpqgtov poptiov tfjr oOKoD (2) (3) (4) CtvtLKatEOt661l lrJtO tvo~ dr to )lEaov tfjr OOKOU (2) (4) uno toi) 8uVIl~o)lftpou (3) )lE)lOVOOlJtvwr oOlCOUIJEVOU popt(ou ~e)teOl)r ltPOOOlOPUO~EVOU euro1rl tfj PaOEl tGgtv KavovOlv avtllCatoOTaaEWr Err to ax 7 OELKV00vshy

ral t6 rrpoYjlotLKD Kai til 000 KA[~aKa Ent toO 8011)I(ou EmshyPAI18EVtu qgtoptfa

34 n eQUjiutli(Q Ut(JTtUaf070

MEta~U t6lv OLooTaUpOl)~tvrov 1tOMuHKGlV -n6Jl(i)v tnr OUCSKeOf~ cprotoaaeo~eurotpicu hcn09ET1l611 TO qlOPllO~tvov OOK(JlIOV Kat poundA1lCP91) ono KiTptVOV ~ovoxPltO~aTtICOV qlGX n EIt TO OX 8 tJlqlalvo~tvll qgtwToypaqlia looxpro~wv QKEpaiac ttLle~

AI T~EIr Ti)V (OOXpw~wv t01lJ1Elro61lOaV oui AeUKfjC )IEAUVllr Efr TTlV lpW(oypoqgtillv toO ox 8

3 gtA~w1lOrJalr TW) JTE~QauaHi(w) Mousaucl7wv

Or OEtKVUEt1ll dr tllv (ponoypacplav tGgtv tOOIPro~oov tOO oxmiddot 8 cruYKfVtpooalr Tacruov El~ cl1tOtO~OUlt 6)Aayll~ 01Eu80vshyOEOOo (yoovLar) tOO nEpypcl~)lator toO qgtopewr Elval OlljlavnshyKr aLD toOtO euroA1lltp61l cppovti~ E~ t1lv KataOlCwtlv at yrovim autcH KatD to ouvatov va ci~puveoov 810 tir lill~loopy la r Aolfjr euroVLOXIJcrEOOr Kai OUYlPovror va 6nAt060()v OIl~avTIK6)r

ArravTTOtV 6~UX poundlr TO Kupi~ QnooxoAo()V 11v f peuvav tOVt1lV tprot1l~Il fitm TO() npoo010PIOJlO() t(i)v ltOOootO)v avaA1lVEWr Ka11l1C0pUqlWV OUVCtJ1EWV O1tO tK01tpou t~V OKEshyAlbv TOO U1tQOtI)AroJlaTOr 1tappoundXEI 11 tv croVEXEiQ 01tOUOll t1i~ evtoOEWr t(i)v 8tatoJlWv tOOV lt1lltEA(i)V tOUtWv pound~ t6c 0T6shy6~ar tG)v Jttowv t(i)v uyenwv troy op6qgtO)v 0i51~ err t6 ~toov tOU unocmgtAro~atOlt toO tpiTou 6pOqgt01l toO Ol 8 11 KOTllVO~ t(i)v taaampwv Ei~ tar OlaWjlIlr tUlV QUO OKeAWV tOO 6nOOtlA(i)~at0r e[val tl Kat0l6

E~WTEPII(OY oKiAoS

EmcpavELa 10 X 10 = 10 EK

TOL~ looXpro~oov

156

aplpd 6~ 6 ~ 20

OE~lIi 611 0 7~ 35

lISao lip 0 = 275

AvCl)alJ~aVO~Vll DuvaJHe

P 1 = Fmiddot 01= 10275 10 pound 28 XYP

EOLJTpoundPIKOY odAot

EntCjlclvElCl 035 X 10 = 035 EIC~

Toe laoxpoolWlv lISaolt 6p 0 = 55

AvlaquolallJavotttvl SUVClIlU

p = F middot a= 035middot55middot10= 19XYP

lP =28 + 19 =47XYp

P lP = 2847= 060

p lP= 19 47 = 040

R ICCltQVOjLT T6lV TtlcrpoundOJI eli rtie oHno~Qc TllIv SUo OlCe)6)v TOO unOOtoAlh)LClmc Ttupa r0 llEacp tOU UII OUC t(lO lntoatushy~QCOlt elc t6v 20 1 opocpov evm K(j-rCil8~

E~wTlplI(OY adAot

E1ttqlQVElCl 10 X 10 = 10 EIC

TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

Ala)ClIl~alo~vT1 OUVQJHI

P = Fmiddot a= 10 middot 325middot10 33 XYP

EawnplKOV adAot

Emcp6vE1Q 035 X 10 = 035 flC

TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

01 )6-YOt P j1P Kai P~IP Eb Till SUO uvO)teuropw EAampYX8eicraC aT6811oc 68rrroOl de 6 KCltCilTEPUl lIpom)Ylcrtu6v cro)11ltshypOcr)lCl (016t1 OfV TtPETtEl vO Q)V0118f1 on t6 cpoptiov emaAishy811 poundi~ 16v avcigttQtov 6pocpov KClt So TiCo 6v OXl QVa)Karov TtQVTo)( OIc61tl)lOV va EfXpound olpoundppoundu-IlSfI Kat TtpoundpITtCCOOlt cpOPTtshycre~ til tvS1Q~crOV 6pocpov)

6ul T6v aJltcrox iJ1tOlCEi~vov til~ cpoPTfcrpoundiJW opocpov tl CJOJIshy

~TOXl) d Tilv Qvo)IlVlv qloptiwv TOO )leyQAOU Kai CoO Jl1~ lCCOl OKEAOUt dvm 60 lCat 401-gt avtlo[oiXtJgtI tv OLD T6v lmoKpoundJlEVOV OpoqlOV Kat tnt T6 SUOJlEVOtEpOV fCOl tmep dit aOqluAElat Col JllJCPOC UTtOOTOAcigt)lCltOt Kat Ola tOtx euroV (JUVEXpoundiQ lmOICpoundIJltVOUC 6p6cpoVt n ow)Jt1OxTl autl1 ouvoml vO 8eooPTI8-a Om8Epo teal fa11 np(gtt 72 Kat 28

The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)

156

aplpd 6~ 6 ~ 20

OE~lIi 611 0 7~ 35

lISao lip 0 = 275

AvCl)alJ~aVO~Vll DuvaJHe

P 1 = Fmiddot 01= 10275 10 pound 28 XYP

EOLJTpoundPIKOY odAot

EntCjlclvElCl 035 X 10 = 035 EIC~

Toe laoxpoolWlv lISaolt 6p 0 = 55

AvlaquolallJavotttvl SUVClIlU

p = F middot a= 035middot55middot10= 19XYP

lP =28 + 19 =47XYp

P lP = 2847= 060

p lP= 19 47 = 040

R ICCltQVOjLT T6lV TtlcrpoundOJI eli rtie oHno~Qc TllIv SUo OlCe)6)v TOO unOOtoAlh)LClmc Ttupa r0 llEacp tOU UII OUC t(lO lntoatushy~QCOlt elc t6v 20 1 opocpov evm K(j-rCil8~

E~wTlplI(OY adAot

E1ttqlQVElCl 10 X 10 = 10 EIC

TC~ aoxpoo~wv

cPtEpa 61 Ii = 30

6~a 61lt Ii = 35

~ao 6p 0 = 325

Ala)ClIl~alo~vT1 OUVQJHI

P = Fmiddot a= 10 middot 325middot10 33 XYP

EawnplKOV adAot

Emcp6vE1Q 035 X 10 = 035 flC

TQ~lt taoxp~v

lISa ap 0 = 37

bullAVQAaI-lj3avO)lSVTl OUVQJH

P= Fmiddot a= 03537middot10= 13 np

lP = 33 -j 3 - 46 np

PI EP =- 3346 - 072

P lP - JJ46 =028

01 )6-YOt P j1P Kai P~IP Eb Till SUO uvO)teuropw EAampYX8eicraC aT6811oc 68rrroOl de 6 KCltCilTEPUl lIpom)Ylcrtu6v cro)11ltshypOcr)lCl (016t1 OfV TtPETtEl vO Q)V0118f1 on t6 cpoptiov emaAishy811 poundi~ 16v avcigttQtov 6pocpov KClt So TiCo 6v OXl QVa)Karov TtQVTo)( OIc61tl)lOV va EfXpound olpoundppoundu-IlSfI Kat TtpoundpITtCCOOlt cpOPTtshycre~ til tvS1Q~crOV 6pocpov)

6ul T6v aJltcrox iJ1tOlCEi~vov til~ cpoPTfcrpoundiJW opocpov tl CJOJIshy

~TOXl) d Tilv Qvo)IlVlv qloptiwv TOO )leyQAOU Kai CoO Jl1~ lCCOl OKEAOUt dvm 60 lCat 401-gt avtlo[oiXtJgtI tv OLD T6v lmoKpoundJlEVOV OpoqlOV Kat tnt T6 SUOJlEVOtEpOV fCOl tmep dit aOqluAElat Col JllJCPOC UTtOOTOAcigt)lCltOt Kat Ola tOtx euroV (JUVEXpoundiQ lmOICpoundIJltVOUC 6p6cpoVt n ow)Jt1OxTl autl1 ouvoml vO 8eooPTI8-a Om8Epo teal fa11 np(gtt 72 Kat 28

The use of the photoelastic method to obtain the

stresses in the structural members of two unusually

shaped buildings and the conclusions derived thereof y rhtarcho1 s IltonoMOu

SumMary

We believe that the most accfssible and rapid experishymenta] method to dtltcrmine the s tress of two-dimenshysional s tructural fram es or such in space where the predominating s tress can be donsid r rQ( plane is the photoelastic nwthod rt means naturally that the deshyfinition of the stress is required especially on the perishymeter of the frame whe the definition of the strt n refeItli to a Single rtlading of the value 0 of the isochromatic frin ge order Ri nce one of Lhe main stresses rectugular on this perimeter is rqual to l ro This Cfl r as known is the most prescntlble in pracLice because the g eatest fl Lrains of the material or which the derinition is requishy

red are shown on the perimeter of the frame

In the prosn t publication two charactcri s ti c Examples of complica tl1d structural memhcrs arc given Thei r Rtress at the extre mely strained pOSitions of the perimeter are derined by the photoeluoltic method Th e magnitude or the str~~s concentration at the roints or the perimeshyters discontinuity which is doriole in the first of the above exuHlpl ~s is Rurriciently high and mus t be taken into consideration on similar s tructural members

From the second exampit it is concluded that more care mos t be taken about the determination or the columns loadc Aspeciany in tht case of tall buildings and highly in-flexible jl)ining beams

Born 10 ALllefJs 1936 Graduate o r Ihe Natio naJ T ecbnkal U nlshy-crsi1 y or Alhens l V59 Army Gorp of E ngill etn U1l ~ 1961 W orked on til t de-ian 01 Ute RtOdBhulg IlIOO I 1M noallna dock If ~Ibc and t he rrou- M rU h_Ue IH-ll 10 Oenn an 5lt AM I ~ aIiL to prorettOr of StaU~JiI IHI R OIIIIlIlltke rcsiitaot d(llgn 11 Nat Ttth On lv 1i 61 - 1938 f)oc tor l l1iuf rr Nat Tech Unlv 19 fU [J e shyUverCll leclortt III Ortlece Wetl Ot n na ny 31U Llhya Speake r at 1I1 C Sem iliaftl Uf P n SlrClI cd COfWt6t~ and PrNalirieatloll Attenshyded III 1 Interna llonal structural Conferences and niade 2 CUf-

Irlhu Uonl to the 8tb ConferCncl or thtl International Brldae Comshym Ulee in New York lf em llr or Lhe f-ar UHl ulIke COIlIll lt lfe or rh e fo IP Me~mb~r or th FlP Alp e AI PC A Sln(middot 1 9~ tl hi ConulLing tlnwlnutlng fi rm II ~lJ ILudl ltj IH fW) sP(c~ l Ji rllctu shyrt8 alllOlIQ 111em tile ~1arlla~IIf1 1Igt ~o lld IOll jofl l PII ILIIIRC(I CO ll t roLn rpan In lh~ wnrl Hl~ puh llllUd man~ p~n~ on nrtllshyt r eaatd COl1 er~h~ and WlI cC[l rlll1tn l (ll 1 Worl In LhA N T U lafJorClmiddot 1011 HJt llJluehll t lcily nnd U l t~ uf I1cctnm lc nnal l)l com puler for Ibe 80lu thlJl (I LLlt rf rtJIfTUak(~ rI3I1hIH rtlsl g1I Prtl llltllL)