Sakiyama Takeshi

Nagasaki University's Academic Output SITE: NAOSITE

28 TRANSACTIONSOFJSCE,Vol.5,1973Ol tleElasticBlCkling ofTwo-】lingcdCircllarAl･ChesTalieshiSAT(lYAMAPublShedinikeProc.ofJSCE,No,217,SePlember1973.779 1-10(InJapanese),M Eng.,AssocLatePro/essor,Del,w LmentofStJuCiuyalEngmeermg,NagrlSallUnlyerSly,NagtJSahllrLtrOdtlCもioltThe bucklng behavlOr Oftwo-hinged cilCularalChesisstudledconslderlngtheextenslOnalityofalChaxISandtheshealdeformation.Intheanaly-sュs,tleload lSCOlSldeledtocontinuetOact10l･malyasalChbucltls.TheanalystsCanbeappledtothearcheswithanyhelglttOSPanlatlO.BasicEqtlatiorLTheequlbriuIlequatiolSCOnCerllngthedefolruedelementofcirculararchale晋 ･N･(Il苦 )pR-0 ･(1la)晋 -臥 (1一昔 )qR-0- (1･b)哩d¢一QR-0 (1C)1Vlele 〟:bendilgllOment,N. axlalfoICe.R. 1adllSOfculVature,Q. slearlngfoICe,β: deflectlOnang一e,¢･ polarcooldlnate,p,a: normalandtangentlalcomponentsofloadpetunltlengH10ftledeforlledalChlfuanduJaretheradialandtangentialcomponentsofdlSPlacelnentOftileClCulalalChand¢thede･Election angleduetobendlngdeformation,βotheFrom the Eqs･(1･a)-(1･C)and (2･aト(2･d),thebasICdlfereltlalequat10nSCOlCelnlng tleelastlCbucklngOfclrCulalalChesaleIntroduced asfoillows.･ra2(% -aE7)+/lBaB(貰 +α晋 一昔 )-1意 (a瑠 一α晋 )-o･ ,.(3･a)a2(晋 一環 )- aB(芸 十- )･ 岩 (α瑠 -α晋 )-o ･(3･b)貰 ･p2a2(計 - )-0 - ･(3･C)wheledワニlQ/α,li-u/I-,{u-W/L,FL2-G/〟E,a2-AL2/Iα,I,:archarlgleandlengthofclCulalarchBlCklinB･ColdltiolSWeconsidelthetwo･hingedclCulalalCh sub-JeCted to uniform nolmal_:∴load p shown ln Fig.1.When the load may le･11ain nor11alto tle de-folmedalCh,thesolutionsoft7,れ andM conslder-1ngtheleftendconditlOnS,Fig.1 Two-hlnged 17(0)-zb(0)-M(0)-0,aleaSArch. follows.･7(q)-C⊥･ull(り)+C2･u12(ヮ)+ca･ulS(7/)-uH(り)･(4･a)lJv(甲)-Cl.Wll(甲)+C2･W12(q)+cB･WAS(甲)一肌4(7)･･(4･b)去･M(q)--晋 sin% tc2･aesln掌･C8･Pcos告 ･sil告) ･(4lC)FIOm thelightendcondltiorlSt7(1)-ib(1)-M(1)-0,folowlngtwotypesOfbucl(llngCOndltlOnSCande8ectlOnangleduetosheardefolmation,E the beobtalled･Yotngsm0dulus,C theshearmodulus,∫thel110-mentofInertiaofarea,Atheareaofcross･sectlOn,･LtleShearcoemcientdependingOn theshapeoftheGloss-Section,tleIWeget0-4･Po-i(争 W)･ ･(2la,M-一昔 署 -･ ･(21b)･-筈 (憲 一l)･ ,I(2･C)O-誓 βO-誓 ‡封 昔 +中 卜 (2･d)(1) SymmetrlCbucklngCOndltlOn2中 .a2-β2-即 諾 =̀当･sin号 cos昔-2aa(pZ･aZ･昔 )･cos言sin昔･qpaQ(lr-β3)cos号C恥昔-o(5)wleleβ2-了瑞 賢 ･ 〝2-意 ,a2-竿 , 那-蛋When theshealdefolmat10n Can bc neglectedI(.SAKIYAMA(G/〟E-∞),thesymmehlCbucklng COndition (5)becomes2P3(2g2･a2-β2)sln号cos書-2a3(Pz･a2)･cos号 sin昔･aβa2(α2一βりcos号 cos昔-o＼ (6)(2) AsymmetllCbucklIlgCOnditions,ni-0,･･ (7)Fl'Om thecondltion(7),theeigeIValueAofasym-mehlCblCklnglS･C2-了豊 蒜 (～-1･2,･日, ･(8,Byneglectllgthesheardefolmation,theasynlmet-1lCbucklingcondition(8)becomesTc皇-(2nTl)2-α2 (n-1,2,-)･ (9)Thebuckling condition(9)wastlStObtainedbyTimoshenkoNumel･icalRe別ltsFlg 2Showstilebucklingloadsandbucklngu･modesoftwo･hlngedclCularalChsubjectedtotletniform loadnormaltothearchaxis. ThedottedFIE.2 CliticalLoadsandDucklingModes.Fig.3 AfectionofSlendelneSSRatlO,lIneSmeanthecasesofneglectilgtleSheardefol･nation.Flg.3givestherelatlOl0felgenValtlehandalChangle α folthefoLu CasesOfslendemeSS lat1050,100,150and200. 1meachcasetheslealdefor･matlOnWasneglected.ThearchalgleαoforthelntelSeCtlngPOlntSOfk-αculVeSOffirstsymmetricandasymmetrlCbtlCklmgAL2//- 502:Al.2/I=loo宅jlL2/I-150巳:AL2/I-2002:Flg 4ShowstlereglOnmetricbucklng.aleα0-22.00,α｡-ll.00,α0- 7.30,α0- 5.59.0fsymmetllCandasym･Fig.4 TypeofFilStBucl(ling.

On the elastic buckling of two-hinged circular arches.

Sakiyama, Takeshi

Nagasaki university's Academic Output SITE

http://naosite.lb.nagasaki-u.ac.jp/dspace/bitstream/10069/16677/1/jsce_5.pdf

On the elastic buckling of two-hinged circular arches.

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