Department of Civil Engineering                                                              NPIC




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T.Chhay                                                                     viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                NPIC




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T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                               NPIC




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T.Chhay                                                                      viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                        NPIC




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T.Chhay                                                                       viTüasßanCatiBhubec©keTskm<úCa
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Department of Civil Engineering                                                                          NPIC




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T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering               NPIC




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T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                               NPIC




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T.Chhay                                                                               viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering               NPIC




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T.Chhay                                                                             viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                          NPIC




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T.Chhay                                                                                   viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




Prestressed Concrete Circ...
Department of Civil Engineering               NPIC




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T.Chhay                                                                        viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                              NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




Prestressed Concrete Circ...
Department of Civil Engineering                                                             NPIC




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T.Chhay                                                                viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                        NPIC




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T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                            NPIC




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T.Chhay                                                                viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                             NPIC




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T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa
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Department of Civil Engineering                                                               NPIC




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T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                           NPIC




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T.Chhay                                                                     viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                          NPIC




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T.Chhay                                                                        viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                            NPIC




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T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering                                                           NPIC




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T.Chhay                                                               viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                           NPIC




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T.Chhay                                                                           viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering                                                           NPIC




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T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                             NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




Prestressed Concrete Circ...
Department of Civil Engineering                                                           NPIC




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T.Chhay                                                                   viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                     NPIC




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T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                   NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




Prestressed Concrete Circ...
Department of Civil Engineering               NPIC




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T.Chhay                                                       viTüasßanCatiBhubec©keTskm<úCa




Prestressed Concrete Circ...
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
Xi. prestressed concrete circular storage tanks and shell roof
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Xi. prestressed concrete circular storage tanks and shell roof

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Xi. prestressed concrete circular storage tanks and shell roof

  1. 1. Department of Civil Engineering NPIC XI. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg Prestressed Concrete Circular Storage Tanks and Shell Roofs 11.1. esckþIepþIm Introduction CaTUeTA GagragmUlebtugeRbkugRtaMgCabnSMd¾l¥bMputénTMrg;eRKOgbgÁúM nigsMPar³sMrab;sþúksar- Faturav nigsarFaturwg. kareFVIkarrbs;vaGs;ry³eBlCagknø³stvtSbgðajfa enAeBlEdleKsikSa KNnavaCamYynwgCMnaj nigkarykcitþTukdak;KYrsm vaGaceFVIkar)an 50qñaM b¤eRcInCagenHedayKμan karEfTaMFMdMueT. kic©xMRbwgERbgdMbUgkñúgkareRbIkMlaMgeRbkugRtaMgvNÐeTAelIeRKOgbgÁúMragmUlKWeFVIeLIgeday W.S. Hewett Edl)anGnuvtþeKalkarN_ tie rod nigeKalkarN_rwtk,al (turnbuckle principle) enAedIm TsSvtSqñaM 1920. b:uEnþEdkBRgwgEdlmanenAeBlenaHman yield strength TabNas; EdlkMNt;nUv kugRtaMgTajGnuvtþn_mineGayFMCag 30,000 psi b¤ 35,000 psi ¬ 206.9 eTA 241.3MPa ¦. CakarBit kMhatbg;eRbkugRtaMgry³eBlEvgd¾FMEdlbNþalBI concrete creep, shrinkage nig steel relaxation swgEtlubbM)at;kMlaMgeRbkugRtaMg. edaysareRkaymk eKrkeXIjEdkEdlmanersIusþg;x<s; enAkñúg TsSvtSqñaM 1940 J.M. Crom )anbegáItedayeCaKC½ynUveKalkarN_rMu high-tensile wire CMuvijCBa¢aMg ragmUlrbs;GagebtugeRbkugRtaMg. taMgBIeBlenaHmk eRKOgbgÁúMsþúkragmUlCag 3,000 RtUv)anksag eLIgedaymanTMhMGgát;p©itepSg². GagsþúkEdlmanTMhMFMCageKmanGgát;p©itrhUtdl; 300 ft (92m) . KuNsm,tþid¾cMbgkñúgkareFVIkar nigesdækic©énkareRbIkMlaMgeRbkugRtaMgvNÐkñúgGagebtugBIelI EdkBRgwgFmμtaKWkarminGnuBaØateGaymansñameRbH. kugRtaMgsgát;vNÐ (circumferential “hugging” hoop stress in compression) Edlpþl;edaykarrMuEdkeRbkugRtaMgBIxageRkACMuvijGagsþúkragmUlKWCa bec©keTsFmμCatisMrab;lubbM)at;sñameRbH enAkñúgCBa¢aMgxageRkAEdlbNþalBIsMBaFrbs;sarFaturwg sMBaF]sμ½n nigbnÞúksarFaturwgEdlGagsþúk. bec©keTsepSgeTotkñúgkareFVIeRbkugRtaMgvNÐedayeRbI tendon mYy²f<k;Cab;eTAnwgCnÞl;RtUv)aneRbIR)as;y:agTUlMTUlayenAGWur:ubCagenAGaemricxageCIg eday sarmUlehtuesdækic©kñúgtMbn; nigbec©keTs. GagsþúkEdleRbIeRbkugRtaMgvNÐ ehIyEdlGaccak;enAnwgkEnøg b¤cak;Rsab;CakMNat;² Edl rYmmanGagsþúkTwk GagTwks¥úy silo GagsþúkeRbg nigsarFatuKImI eRKOgbgÁúMsßanIybUmeRbgenAkNþal smuRT (offshore oil platform structure), cryogenic vessel nig nuclear reactor pressure vessels. eKcat;TukeRKOgbgÁúMTaMgenHCakMralekagesþIg (thin shell) edaysarpleFobd¾EsntUcénkMras;elIGgát; GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 667
  2. 2. T.Chhay viTüasßanCatiBhubec©keTskm<úCa p©itrbs;va. edaysarminGnuBaØateGaymansñameRbHeRkamGMeBIbnÞúkeFVIkar eKrMBwgfa shell eFVIkarCa lkçN³eGLasÞiceRkamGMeBIbnÞúkeFVIkar nigeRkamlkçN³bnÞúkelIs (overload condition). 11.2. eKalkarN_ nigdMeNIrkarsikSaKNna Design Principles and Procedures 11.2.1. kMlaMgxagkñúg Internal Loads BicarNaBIkareFVIkarrbs;GagragmUlEdlBak;B½n§nwgkarBinitüTaMgsMBaFxagkñúgEdlbNþalBI sMPar³EdlpÞúkenAxagkñúgmanGMeBIelImuxkat;kMralCBa¢aMgekagragsIuLaMgesþIg (thin-wall cylindrical shell) nigkMlaMgeRbkugRtaMg radial xageRkA nigeBlxøHkMlaMgeRbkugRtaMgbBaÄrEdleFVIeGaykMlaMgxag kñúgmanlMnwg. sMBaFxagkñúgCasMBaF radial edk b:uEnþERbRbYltamTisbBaÄrEdlGaRs½yeTAnwgRbePT sMPar³EdlpÞúkenAkñúgGag. RbsinebIsMPar³CaTwk b¤CaGgÁFaturav sMBaFbBaÄrBRgayeTAelICBa¢aMgGag manragRtIekaN CamYynwgGaMgtg;sIuetGtibrmaenARtg;)atrbs;CBa¢aMg. sarFatu]sμ½nnwgpþl;sMBaF edkefrelIkMBs;TaMgmUlrbs;CBa¢aMg. karBRgaysMBaFbBaÄrrbs;sMPar³EdlmanlkçN³dMuRKab; dUcCa FüÚgfμ b¤RKab;FBaØCatimanragRsedogKñaniwgkarBRgaysMBaFrbs;]sμ½nmkelICBa¢aMgGagEdr. rUbTI 11>1 bgðajBIkarBRgaysMBaDsMrab;krNIénkardak;bnÞúkTaMgbIenH. Prestressed Concrete Circular Storage Tanks and Shell Roofs 668
  3. 3. Department of Civil Engineering NPIC RTwsþIeGLasÞicmUldæanrbs; cylindrical shell GnuvtþeTAelIkarsikSaviPaK nigeTAelIkarsikSa KNnaCBa¢aMgrbs;GageRbkugRtaMg. kMlaMgkg (ring force) bgákMlaMgTajkg (ring tension) enAkñúg CBa¢aMgsIuLaMgesþIg (thin cylindrical wall) edaysnμt;KμankarTb; (unrestrained) enAxagcugénmuxkat; edknImYy²eT. TMhMrbs;kMlaMgKWsmamaRteTAnwgsMBaFEdlGnuvtþenAxagkñúg nigKμanm:Um:g;bBaÄrekIt mantamkMBs;rbs;CBa¢aMgeT. RbsinebIcugrbs;CBa¢aMgRtUv)anTb; (restrained) TMhMrbs; ring force ERb RbYl ehIym:Um:g;Bt;nwgekItmanenAkñúgmuxkat;bBaÄrrbs;CBa¢aMgGag. dUcenHTMhMrbs; ring force nigm:U m:g;bBaÄrCaGnuKmn_énkMriténkarTb;rbs; cylindrical shell enARtg;RBMEdnrbs;va ehIyvaRtUv)anKNna BIRTwsþkMralekageGLasÞic (elastic shell theory). bnÞúksarFaturavenAelI)atrGiledayesrI Liquid Load on Freely Sliding Base BIemkanicmUldæan (basic mechanics), ring force KW pd F= = pr (11.1a) 2 ehIykugRtaMgkg (ring stress) KW pd pr fR = = (11.1b) 2t t Edl d= Ggát;p©itrbs;sIuLaMg r = kaMrbs;sIuLaMg t = kMras;CBa¢aMg p = sMBaFÉktþaxagkñúgRtg;)atCBa¢aMg = γH γ = TMgn;maDrbs;sMPar³EdlpÞúkenAkñúgGag. Tensile ring stress enARtg;RKb;cMnucBIxageRkamépÞrbs;sMPar³EdlpÞúkenAkñúgGagkøayCa f R = γ (H − y ) = γ (H − y ) d r (11.2a) 2t t Edl H CakMBs;rbs;sarFaturav ehIy y CacMgayBIelI)at. Ring force EdlRtUvKñaKW F = γ (H − y )r (11.2b) dUckñúgsmIkar 11.1b/ Tensile ring stress GtibrmaenARtg;)atrbs;CBa¢aMgEdlrGiledayesrIsMrab; y = 0 køayCa γHd γhr f R (max ) = = (11.2c) 2t t GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 669
  4. 4. T.Chhay viTüasßanCatiBhubec©keTskm<úCa bnÞúk]s½μnenAelI)atEdlrGiledayesrI Gaseous Load on Freely Sliding Base mþgeTotBIeKalkarN_emkanicmUldæan/ tensile ring stress efrKW pd pr fR = = (11.3) 2t t cMNaMfa eKRtUveRbITMhMGgát;p©ittamRTwsþIEdlKitBI centerline EdlmanlkçN³suRkit Etedaysarpl eFob t / d manTMhMtUceBk dUcenHeKGaceRbIGgát;p©itxagkñúg d )an. bnÞúkGgÁFaturav nigbnÞúk]s½μnenAelI)atCBa¢aMgEdlTb; Liquid and Gaseous Load on Restrained Wall Base RbsinebI)atrbs;CBa¢aMgRtUv)anbgáb; b¤ pinned/ enaHeKlubecal ring tension enARtg;)at. edaysarkarbgáb;enARtg;)at enaHeKminGacGnuvtþ simple membrane theory rbs; shell EdlbNþal BIkMhUcRTg;RTayedaysar restraining force enARtg;)atCBa¢aMg. eKcaM)ac;eFVIkarbMElgm:Um:g;Bt;eTACa membrane stress ehIylMgakecj (deviation) rbs; ring tension enARtg;bøg;kNþalrbs;kMBs;CBa¢aMg RtUv)anKitCatMélRbhak;RbEhl nigRtUv)anerobrab;enAkñúgEpñk 11.3. RbsinebIm:Um:g;Bt;bBaÄrenAkñúgbøg;edkrbs;CBa¢aMgenARtg;kMBs;NamYyKW M y / kugRtaMgbegáag (flexural stress) ebtugrgkarsgát; b¤rgkarTajkøayCa M y 6M y ft = f c = = 2 kñúgmYyÉktþakMBs; (11.4) S t karBRgaykugRtaMgbegáagelIkMras;rbs;CBa¢aMgGagRtUv)anbgðajenAkñúgrUbTI 11>2. Prestressed Concrete Circular Storage Tanks and Shell Roofs 670
  5. 5. Department of Civil Engineering NPIC 11.2.2. m:Um:g;Tb; M nigkMlaMgkat; Radial Q enARtg;)atCBa¢aMgEdlrGiledayesrIEdl o o ekItBIsMBaFsarFaturav Restraining Moment M o and Radial Shear Force Qo at Freely Sliding Wall Base Due to Liquid Pressure 11.2.2.1. Membrane Theory karsikSaBIkMlaMg nigkugRtaMgenAkñúgCBa¢aMgGagragmUlKμansñameRbHCakarviPaKkMralragekag sIuLaMgEdleFVIkarCalkçN³eGLasÞic. RbsiinebI shell minxUcRTg;RTayeRkamT§iBlrbs;sMBaFsar- Faturavxagkñúg eKGacGnuvtþsmIkarlMnwg basic membrane )an. kMlaMgtambeNþayÉktþa N y / kMlaMg ÉktþavNÐ (circumferential unit force) Nθ nigkMlaMgkat;ÉktþaRtg;p©it N yθ nig Nθ y RtUv)anbgðaj enAkñúg differential element énrUbTI 11>3 (b). cMNaMfa GBaØtiTaMgbYnenHeFVIGMeBIenAkñúgbøg;rbs; shell. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 671
  6. 6. T.Chhay viTüasßanCatiBhubec©keTskm<úCa smIkarlMnwgmUldæanbIsMrab;kMlaMgÉktþaGBaØtiTaMgbYnenHKW ∂Nθ ∂N yθ +r + pθ r = 0 (11.5a) ∂θ ∂y ∂N y ∂Nθ y r +r + pyr = 0 (11.5b) ∂y ∂θ Nθ + pz = 0 (11.5c) r Edl ∂N yθ = ∂Nθ y KWbNþalmkBIkardak;sIuemRTI. dUcenHcMnYnGBaØtiRtUv)ankat;bnßymkenARtwmbIEdl bgðajBIeRKOgbgÁúMkMNt;edaysþaTicEdlrgEtnwgkMlaMgedaypÞal;. sMrab;kardak;bnÞúk axisymmetic dUc bgðajenAkñúgrUbTI 11>3 (d)/ pθ = p y = 0 ehIy p z = p ⋅ f ( y ) . kardak;bnÞúkEbbenHminGaRs½ynwg θ eT. dUcenH p z = −γ (H − γ ) (11.6) ehIydMeNaHRsayrbs;smirk 11.5 KW N yθ = N y = 0 ehIy Nθ = γ (H − y )r (11.7) 11.2.2.2. RTwsþIbTBt;begáag Bending Theory karENnaMBIkarTb; (restraint) enARtg;RBMEdnrbs;GagnaMeGayman radial horizontal shear nigm:Um:g;bBaÄrenAkñúg shell. dUcenH smIkarkMlaMg membrane EdlbgðajenAkñúgEpñkelIkmunRtUv)an EkERbedaykardak;bEnßmm:Um:g; nigkMlaMgkat;. smIkarEdlEkERbRtUvkMNt;Ca bending theory rbs; circular shell EdlRTwsþIenHKitTaMgtMrUvkarPaBRtUvKñaénbMErbMrYlrageFob (strain compatibility) enA kñúgkMhUcRTg;RTayEdlbgáeLIgedaykarekItmankMlaMgkat; nigm:Um:g;xagelI. m:Um:g;Bt; nig central shear enAkñúgkMralragekagsIuLaMgEdlrgbnÞúk axisymmetric RtUv)an bgðajedayviucT½rkMlaMg nigviucT½rm:Um:g;enAkúñgrUbTI 11>4. FatuGnnþtUc ABCD bgðajBIcMnucGnuvtþn_ nigTisedArbs;m:Um:g;Éktþa M y eFobnwgG½kS x nig M θ eFobG½kS y / circumferential unit moment M yθ nig M θ y / kMlaMgkat;EkgÉktþa Q y EdlmanGMeBIenAkñúgbøg;énkMragekagbBaÄr nigEkgeTAnwg shell axis ehIy unit radial shear Qθ EdlmanGMeBIkat;tamkaM shell enAkñúgbøg;EdlRsbnwg shell. eFVItMrYlplénm:Um:g; nigkMlaMgkat;enAkñúgrUbTI 11>4 eTAelIkMlaMgenAkñúgrUbTI 11>3 (b) begáIt )ansmIkarlMnwgxageRkam³ Prestressed Concrete Circular Storage Tanks and Shell Roofs 672
  7. 7. Department of Civil Engineering NPIC ∂Nθ ∂N yθ + − Qθ + pθ r = 0 (11.8a) ∂θ ∂y ∂N y ∂Nθ y r+ + pyr = 0 (11.8b) ∂y ∂θ ∂Qθ ∂Q y + r + Nθ + p z r = 0 (11.8c) ∂θ ∂y ∂M y ∂M yθ r+ + Qy r = 0 (11.8d) ∂y ∂y ∂M θ ∂M yθ + r − Qθ r = 0 (11.8e) ∂θ ∂y edaysarPaBsIuemRTIénkardak;bnÞúk/ N yθ = Nθ y = M θ y = M yθ = 0 ehIyeKGacminKit dQθ Edlkat;bnßysmIkarDIepr:g;EsüledayEpñk 11.8 mkCasMnMuénsmIkarDIepr:g;EsülFmμta (ordinary differential equation) dN y r + pyr = 0 (11.9a) dy dQ y r + Nθ + p z r = 0 (11.9b) dy dM y − r + Qy r = 0 (11.9c) dy CamYynwg central membrane forces N y efr ehIyeKykvaesμInwgsUnü enaHeKGacsresrsmIkar EdlenAsl; 11.9b nig 11.9c kñúgTMrg;sMrYldUcxageRkamEdlmanGBaØtibI Nθ / Qy nig M y ³ GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 673
  8. 8. T.Chhay viTüasßanCatiBhubec©keTskm<úCa dQ y 1 + Nθ = − p z (11.10a) dy r dM y − Qy = 0 (11.10b) dy edIm,IedaHRsaysmIkarTaMgenH eKRtUvKitBIbMlas;TI nigsmIkarFrNImaRt. smIkarkMlaMg RbsiebI v nig w CabMlas;TIenAkñúgTis y nig z enaHbMErbMrYlragÉktþaenAkñúgTisTaMgenHKW dv εy = dy ehIy εθ = − w r ehIyeKTTYl)an Ny = Et (ε y + μεθ ) = Et⎛ dv w⎞ ⎜ −μ ⎟=0 ⎜ dy r⎟ (11.11a) 1− μ 2 1− μ ⎝ 2 ⎠ nig Nθ = Et (εθ + με y ) = Et ⎛ w dv ⎞ ⎜− + μ ⎟ ⎜ r dy ⎟ (11.11b) 1− μ2 1− μ2 ⎝ ⎠ Edl pleFobB½rsug μ= t = kMras;rbs;CBa¢aMg BIsmIkar 11.11a dv w =μ (11.12a) dy r BIsmIkar 11.11b w Nθ = − Et (11.12b) r smIkarm:Um:g; edaysarPaBsIuemRTI kMeNagenAkñúgTisvNÐminmanERbRbYleT dUcenH kMeNagenAkñúgTis y RtUv esμInwg − d 2v / dy 2 . edayeRbIsmIkarm:Um:g;dUcKñasMrab;kMraleGLasÞicesþIg (thin elastic plate) eKTTYl )an M θ = μM y (11.13a) d 2w M y = −D (11.13b) dy 2 Edl D = Et 3 / 12(1 − μ 2 ) CaPaBrwgRkajTb;karBt;begáagrbs;kMralekag (shell) b¤kMral (plate) Prestressed Concrete Circular Storage Tanks and Shell Roofs 674
  9. 9. Department of Civil Engineering NPIC bBa©ÚlsmIkar 11.12 nig 11.13 eTAkñúgsmIkar 11.10 eKTTYl)an d 2 ⎛ d 2 w ⎞ Et ⎜D ⎟ + w = pz (11.14) dx 2 ⎜ dy 2 ⎟ r 2 ⎝ ⎠ RbsinebIkMras;CBa¢aMg t efr enaHsmIkar 11.14 køayCa d 4w Et D + w = pz (11.15) dy 2 r2 edayyk β =4 Et = ( 31− μ2 ) 2 4r D (rt )2 smIkar 11.15 køayCa d 4w pz 4 + 4β 4 w = (11.16) dy D smIkar 11.16 RsedognwgsmIkarEdlTTYlsMrab;Ggát;FñwmEdlmanPaBrwgRkaj D EdlRTedayRKwHeG LasÞicCab; nigRbQmnwgGMeBIénGaMgtg;sIuetbnÞúkÉktþa p z . dMeNaHRsayTUeTAénsmIkarenHsMrab; radial displacement kñúgTis z KW w = e βy (C1 cos β y + C2 sin βy ) + e − βy (C3 cos βy + C 4 sin βy ) + f ( y ) (11.17) Edl f (y) CadMeNaHRsayTUeTAénsmIkar 11.16 Ca membrane solution EdleGaynUvbM;las;TI pz r 2 w= Et 11.2.3. smIkarTUeTAénkMlaMg nigbM;las;TI General Equations of Forces and Displacements edayedaHRsaysmIkar 11.17 nigbBa©ÚlnUvnimitþsBaØaxageRkam Φ (βy ) = e − βy (cos β y + sin βy ) Ψ (β y ) = e − βy (cos βy − sin β y ) θ (βy ) = e − βy cos β y ζ (βy ) = e − βy sin βy eKGackMNt;smIkarsMrab; radial deformation tamTis z nigkargakecjbnþrbs;vaRtg;kMBs; y BI)at CBa¢aMgBIsmIkarsMrYlxageRkamCaGnuKmn_énm:Um:g;ÉktþaRtg;)atCBa¢aMg M o nig radial shear Qo ³ PaBdab w = − 2β13 D [βM o Ψ(βy ) + Qoθ (βy )] (11.18a) mMurgVil dw = 2β12 D [2βM oθ (βy ) + QoΦ(βy )] dy (11.18b) GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 675
  10. 10. T.Chhay viTüasßanCatiBhubec©keTskm<úCa d 2w =− 1 [2βM o Φ(βy ) + 2Qoζ (βy )] (11.18c) dy 2 2βD d 3w = 1 [2βM oζ (βy ) − Qo Ψ (βy )] (11.18d) dy 3 D GnuKmn_ shell Φ(βy ) / Ψ(βy ) / θ (βy ) nig ζ (βy ) RtUv)aneGayenAkñúgemKuNT§iBlsþg;dar (standard influence coefficient) éntarag 11>1 sMrab;EdntMél 0 ≤ βy ≤ 3.9 . BIsmIkar 11.18a bMlas;TI radial Gtibrma b¤PaBdabenARtg;)atCBa¢aMgEdlTb;KW (w) y = 0 = − 1 (βM o + Qo ) (11.19a) 2β 3 D ehIyBIsmIkar 11.18b mMurgVil (rotation) Gtibrmarbs;CBa¢aMgRtg;)atkøayCa ⎛ dw ⎞ ⎜ ⎜ dy ⎟ ⎟ = 1 (2βM o + Qo ) (11.19b) ⎠ y = 0 2β D 2 ⎝ Edl M o nig Qo Ca restraining moment nig ring shear enARtg;)atdUcbgðajenAkñúgrUbTI 11>1. sMrab;GagEdlmankMras;CBa¢aMgefr kMlaMgÉktþatamkMBs;CBa¢aMgmandUcxageRkam³ Etw Nθ = − (11.20a) r d 3w Qy = −D 3 (11.20b) dy M θ = μM y (11.20c) d 2w M y = −D (11.20d) dy 2 BIsmIkar 11.18c, 11.18d, 11.20b nig11.20d smIkarsMrab;m:Um:g;bBaÄr nig radial shear tamTisedk enARtg;)atrbs;CBa¢aMg Edl y = 0 køayCa γHrt (M y )y = 0 = M o = ⎛1 − β1 ⎞ ⎜ ⎟ ( ) ⎜ (11.21a) H⎟⎝ ⎠ 12 1 − μ 2 γrt (Q y )y = 0 = Qo = −(2 βH − 1) ( ) (11.21b) 12 1 − μ 2 eKGacTTYl)ansmIkarsMrab;m:Um:g;bBaÄrenARtg;kMBs; y BIelI)atCBa¢aMgBI My = − 1 [βM o Φ(βy ) + Qoζ (βy )] (11.22) β bMErbMrYlkMlaMg ring shear force ΔQ y EdlRtUvniwgbMlas;TI radial wy rbs;CBa¢aMgRtg;kMBs; y BIelI )atenAeBlGagTeT CamYynwgtMélrbs; Qo nig M o EdlbNþalBIkardak;bBa©ÚlsarFaturav nig]sμ½n eBj dUcbgðajenAkñúgrUbTI 11>5. eKGacsresrsmIkarkMlaMgenHCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 676
  11. 11. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 677
  12. 12. T.Chhay viTüasßanCatiBhubec©keTskm<úCa ΔQ y = + Et r ( ) wy b¤ ΔQ y = Et 2rβ 3 D [βM o Ψ (βy ) + Qoθ (βy )] b¤ ΔQ y = ( 61− μ2 ) [βM Ψ(βy) + Q θ (βy )] o o (11.23) β 3rt 2 Ring shear Q yenARtg;bøg; y BIelI)atesμInwgplsgrvag ring force sMrab;)atEdlrGiledayesrI CamYynwg ΔQ y ³ Q y = F − ΔQ y (11.24) Prestressed Concrete Circular Storage Tanks and Shell Roofs 678
  13. 13. Department of Civil Engineering NPIC eKcaM)ac;eKarBtamkarkMNt;sBaØaEdleRbIkñúgdMeNaHRdayTaMgenH. viFIEdlgayRsYlKWKUrragEdlxUc RTg;RTayrbs;CBa¢aMg ehIyeRbIsBaØabUksMrab;lkçxNÐxageRkam³ !> m:Um:g;EdleFVIeGaymankugRtaMgTajenAelIsrésxageRkAbMputénépÞxageRkA. @> kMlaMg Ring tension radial. #> kMlaMg thrust EdlmanTisedAcUlkñúgeTArkG½kSbBaÄr. enATIenH eKeRbITisedAdUcKñasMrab; kMlaMg ring tension edIm,IKUrdüaRkamsMrab;kMlaMgeRbkugRtaMglMnwg (balancing prestressing forces) enAelIRCugdUcKñanwgkMlaMg ring tension sMrab;kareRbobeFob. $> clnaCBa¢aMgxagcUlkñúgeTArkG½kSbBaÄr. %> muMrgVilbRBa©asTisRTnicnaLika. sMBaFsarFaturavmanGMeBIelICBa¢aMgEdlman)atCaTMr Pinned (Pinned Wall Base, Liquid Pressure) enAeBl)atCBa¢aMgmanTMr pinned ehIyrgnUvm:Um:g;bnÞúksarFaturav M o = 0 enARtg;)at 2β 3γH (rt )2 Qo = + ( 12 1 − μ 2 ) 1/ 2 γH ⎛ rt ⎞ b¤ Qo = + 1/ 4 ⎜ 2 ⎟ [12(1 − μ )] (11.25) 2 ⎝ ⎠ eKGacKNnarktMélrbs; shell constant β , β 2 , nig β 4 sMrab;eRbIenAkñúgsmIkarelIkmun)any:aggay BIsmIkarsMrab; β 4 dUcxageRkam³ Et 3( − μ 2 ) 1 β4 = = (11.26a) 4r 2 D (rt )2 β 3 = [3(1 − μ )]2 3/ 4 (11.26b) (rt )3 / 2 β 2 = [3(1 − μ )]2 1/ 2 (11.26c) (rt ) β= [3(1 − μ )] 2 1/ 4 (11.26d) (rt )1/ 2 11.2.4. Ring Shear Qo and Moment β 4 Gas Containment RbsinebIEKmrbs; shell manlkçN³esrIenARtg;)atCBa¢aMg sMBaFxagkñúgbegáItEtkugRtaMg hoop f R = pr / t ehIykaMrbs;sIuLaMgnwgekIneLIgedayTMhM GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 679
  14. 14. T.Chhay viTüasßanCatiBhubec©keTskm<úCa rf R pr 2 w= = (11.27) E Et dUcKña sMrab; full restraint enARtg;)atCBa¢aMg (w) y =0 = 1 (βM o + Qo ) (11.28a) 2β 3 D ⎛ dw ⎞ nig ⎜ ⎜ dy ⎟ ⎟ = 1 (2βM o + Qo ) = 0 (11.28b) ⎠ y =0 2 β D 2 ⎝ edaHRsayrk M o nig Qo eyIgTTYl)an p prt M o = − β 2 Dw = − =− ( ) (11.29a) 2β 2 12 1 − μ 2 p (2rt )1 / 2 nig Qo = +4 β 3 Dw = + p =+ [12(1 − μ )] (11.29b) β 2 1/ 4 sMBaFsarFatu]sμ½nmanGMeBIelICBa¢aMgEdlman)atCaTMr Pinned (Pinned Wall Base, Gas Pressure) RbsinebI)atCBa¢aMgCaTMr pinned ehIyrgm:Um:g;bnÞúk]sμ½n M o = 0 enARtg;)at ⎛ pr 2 ⎞ Qo = 2β 3 D⎜ ⎟ ⎜ Et ⎟ ⎝ ⎠ 1/ 2 ⎛ rt ⎞ b¤ Qo = p ⎜ ⎟ [12(1 − μ )] (11.30) 2 ⎝ ⎠ 1/ 4 2 tarag 11>2 bgðajkarsegçbénsmIkarKNnasMrab;GagsþúksarFaturav ehIytarag 11>3 bgðajBI taragsegçbRsedogKñasMrab;GagpÞúksarFatu]sμ½n. 11.3. m:Um:g; M nig kMlaMg Ring Shear Q enAkñúgGagsþúksarFaturav o o Moment M o and Ring Force Qo in Liquid Retaining Tank ]TahrN_ 11>1³ GagragmUlebtugeRbkugRtaMgRtUv)anTb;eBlelj (full restrained) enARtg;)at CBa¢aMg. vamanGgát;p©itxagkñúg d = 125 ft (38.1m) nigpÞúkTwkEdlmankMBs; H = 25 ft (7.62m) . kMras;CBa¢aMg t = 10in(25cm) . KNna (a) m:Um:g;bBaÄrÉktþa M o nigkMlaMg radial ring force Qo enARtg;)atrbs;CBa¢aMg nig (b) m:Um:g;bBaÄrÉktþa M y enARtg;kMBs; 7.5 ft (2.29m) BIelI)at. eRbIpl eFobB½rsug μ = 0.2 ehIyTMgn;maDrbs;Twk γ = 62.4lb / ft 3 (1,000kg / m3 ) . Prestressed Concrete Circular Storage Tanks and Shell Roofs 680
  15. 15. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 681
  16. 16. T.Chhay viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ (a) enARtg;)atCBa¢aMg r = × 125 = 62.5 ft (19m ) 1 2 t = 10in. = 0.83 ft (0.25m ) BIsmIkar 11.26d β= [3(1 − μ )] 2 1/ 4 = [3(1 − 0.2 × 0.2)]1 / 4 = 0.181 (rt )1 / 2 (62.5 × 0.83)1 / 2 BIsmIkar 11.21a ⎛ 1 ⎞ γHrt ⎜ βH ⎟ M o = −⎜1 − ⎝ ⎟ ⎠ 12 1 − μ 2 ( ) ⎛ 1 ⎞ 62.4 × 25 × 62.5 × 0.83 = −⎜1 − ⎟× ⎝ 0.181× 25 ⎠ 12(1 − 0.04) = −18,574 ft. − lb / ft (7.68kN .m / m ) BIsmIkar 11.21b γrt Qo = +(2 β H − 1) 12 1 − μ 2 ( ) 62.4 × 62.5 × 0.83 = +(2 × 0.181× 25 − 1) 12(1 − 0.04 ) = +7,677lb / ft (112kN / m ) (b) enARtg;kMBs; 7.5 ft BI)atCBa¢aMg y = 7.5 ft kMBs;Twk = (H − y ) = 25 − 7.5 = 17.5 ft (5.33m) pleFobkMBs; = ⎛1 − H ⎞ = 1 − 7.5 = 0.7 ⎜ ⎝ y ⎟ ⎠ 25 βy = 0.181 × 7.5 = 1.36 BIsmIkar 11.22 My = + 1 [βM o Φ(βy ) + Qoζ (βy )] β BItarag 11.1 sMrab; β y = 1.36 Φ = 0.311 ζ = 0.252 Prestressed Concrete Circular Storage Tanks and Shell Roofs 682
  17. 17. Department of Civil Engineering NPIC My = + 1 (− 0.181 × 18,574 × 0.311 + 7,677 × 0.252) 0.181 = +4,912 ft − lb / ftt 11.4. kMlaMg Ring Shear Q enARtg;Bak;kNþalkMBs;rbs;CBa¢aMg y Ring Force Q y at Intermediate Heights of Wall ]TahrN_ 11>2³ KNna radial ring force Q enAkñúg]TahrN_ 11>1 Rtg; (a) y = 7.5 ft (2.29m) y nig (b) y = 10 ft (3.05m) BIxagelI)atrbs;CBa¢aMg sMrab;CBa¢aMgrGiledayesrI. dMeNaHRsay³ kMlaMg ring force enARtg;)atEdlrGilesrI F = γHr = 62.4 × 25 × 62.5 = 97,500lb / ft (1,423kN / m ) . BIsmIkar 11.23/ bMErbMrYlkMlaMg ring force KW 6(1 − μ ) ΔQ y = + [βM o Ψ (βy ) + Qoθ (βy )] β 3 rt 2 BIsmIkar 11.1/ β = 0.181 . dUcenH β 3 = 0.0059 (a) Q y enARtg; 7.5 ft BIelI)atCBa¢aMg βy = 0.181× 7.5 = 1.36 BItarag 11.1 sMrab; βy = 1.36 Ψ (βy ) = −0.1965 θ (βy ) = +0.0543 6(1 − 0.04 ) ΔQ y = + [0.181(− 18,574)(− 0.1965) + 7,677(+ 0.0543)] 0.0059 × 62.5(0.83)2 = 24,431lb / ft (356kN / m ) BIsmIkar 11.2b/ ring force F = γ (H − y )r = 62.4 × (25 × 7.5) × 62.5 = 68,250lb / ft . dUcenH Q7.5 = F − ΔQ y = 68,250 − 24,431 = 43,819lb / ft (705kN / m ) dUcbgðajenAkñúgrUbTI 11>6(a). (a) enARtg;kMBs; 7.5 ft BI)at (b) enARtg;kMBs; 10 ft BI)at. (b) Q y enARtg;kMBs; 10 ft BI)atrbs;CBa¢aMg βy = 0.181 × 10 = 1.81 BItarag 11>1 sMrab; βy = 1.81 / GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 683
  18. 18. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Ψ (β y ) = −0.1984 θ (β y ) = −0.0387 6(1 − 0.04 ) ΔQ y = [0.181(− 18,574)(− 0.1984) + 7,677(− 0.0387 )] 0.0059 × 62.5(0.83)2 = 8,387lb / ft kMlaMg ring force F = γ (H − y )r = 62.4(25 − 10) = 62.5 = 58,500lb / ft . dUcenH Q10 = F − ΔQ y = 58,500 − 8,387 = 50,113lb / ft (731kN / m ) dUcbgðajenAkñúgrUbTI 11>6 (b). eRbobeFobCamYynwg tMél Q y = 50,115lb / ft EdlTTYl)anedayeRbI membrane coefficient enAkñúg]TahrN_ 11>3. 11.5. Cylindrical Shell Membrane Coefficients eKGackMNt;m:Um:g;Bt;enARtg;kMBs;Nak¾edayBI)atrbs;GagragsIuLaMgBIsmIkarm:Um:g;Bt;sMrab; Fñwmkugs‘ul (cantilever beam). eKTTYl)ansmIkarenHedayKuNm:Um:g; cantilever edayemKuNEdl TMhMrbs;vaCaGnuKmn_eTAnwgTMhMFrNImaRtrbs;Gag ehIyRtUv)aneGayeQμaHfa membrane coeffi- cients. eKGacerobcMsmIkarm:Um:g;mUldæanEdl)anbegáItenAkñúgEpñk 11.2 sMrab;GagsþúkragmUleLIg vijedaybBa©ÚlemKuN H 2 / dt EdltMNageGayragFrNImaRt nigemKuN γH 3 b¤ pH 2 EdltMNag eGayT§iBl cantilever sMrab;kardak;bnÞúksarFaturav nigsarFatu]sμ½n. Prestressed Concrete Circular Storage Tanks and Shell Roofs 684
  19. 19. Department of Civil Engineering NPIC tMélefr β enAkñúgsmIkar 11.26d CaGnuKmn_én rt b¤ dt Edl d CaGgát;p©itGag. edayeRbI pleFobB½rs‘ug μ ≅ 0.2 sMrab;ebtug eyIg)an β= [3(1 − μ )] 2 1/ 4 = 1.30 = 1.84 (rt ) 1/ 2 (rt ) 1/ 2 (dt )1 / 2 eKGacsresremKuN 1 / βH EdleRbIenAkñúgsmIkarm:Um:g;Bt;begáagmUldæanénEpñk 11.2 edayeRbItY (dt / H 2 )1 / 2 edaysar β = 1.84 /(dt )1 / 2 . eKk¾GacsresrplKuN βy eLIgvijedayeRbItY λ (H 2 / dt ) edayeRbI y = λH Edl y CakMBs;BI)at. 1/ 2 dUcenH eKGacbgðajm:Um:g; M y énsmIkar 11.22 enAkñúgmuxkat;CBa¢aMgEdlmancMgay y BI)at edayeRbIemKuNrag (form factor) H 2 / dt CamYynwgemKuN cantilever γH 3 b¤ pH 2 dUcxageRkam³ M y = numerical variant × form factor × cantilever facotor b¤ ⎡ M y = ⎢ variant × H2⎤ ⎥ × γH or pH 3 2 ( ) (11.31) ⎢ ⎣ dt ⎥ ⎦ emKuNrag (form factor) H 2 / dt CatMélefrsMrab;eRKOgbgÁúMCak;lak;. dUcenH plKuNén variant nig form factor begáIt)an membrane coefficient C dUcenH smIkar 11.31 køayCa M y = CγH 3 (11.32a) sMrab;bnÞúksarFaturav ehIy M y = CpH 2 (11.32b) sMrab;bnÞúksarFatu]sμ½n. tarag 11>4 dl; 11>16 bgðajBI membrane coefficient C sMrab; form factor H 2 / dt Ca mYynwglkçxNÐRBMEdnEdlniymeRbICageK niglkçxNÐbnÞúkepSg². vakat;bnßykarKNnaCaeRcInEdl TamTarCaTUeTAenAkñúgkarKNna nigkarviPaK shell edayminman)at;bg;suRkitPaBénlT§pleT. eday eRbI membrane coefficient sMrab;dMeNaHRsayénkMlaMg nigm:Um:g;GagragmUl vanwgpþl;lT§plRsedog KñanwglT§plEdlTTYl)anBIdMeNaHRsaym:Um:g;Bt;EdlbgðajenAkñúgEpñk 11>2 nigsMnMuénsmIkarEdl manenAkñúgtarag 11>2 nig 11>3 . GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 685
  20. 20. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 686
  21. 21. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 687
  22. 22. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 688
  23. 23. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 689
  24. 24. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 690
  25. 25. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 691
  26. 26. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 692
  27. 27. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 693
  28. 28. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 11.6. Prestressing Effects on Wall Stresses for Fully Hinged, Partially Sliding and Hinged, Fully Fixed, and Partially Fixed Bases sarFaturav b¤]sμ½nEdlsþúkenAkñúgGagragsIuLaMgGnuvtþsMBaF radial ecjeRkA γh b¤ p enAelI CBa¢aMgGag EdlbegáIt ring tension enAkñúgmuxkat;edknImYy²Rtg;srésxageRkAbMputrbs;CBa¢aMgEdl begáItCasñameRbHEdlminGacGnuBaØat)an. edIm,Ikat;bnßysñameRbHTaMgenHEdlbNþaleGayRCab nig eFVIeGayeRKOgbgÁúMeFVIkarminl¥ eKRtUvGnuvtþkMlaMgeRbkugRtaMgedkxageRkAEdlbegáIt radial thrust cUl kñúgEdlGaceFVIeGay radial tension ecjeRkAmanlMnwg. elIsBIenH edIm,IkarBarkarekItmansñameRbH enAelIépÞxagkñúgrbs;CBa¢aMgenAeBlGagTwkTeT eKRtUvbBa©ÚlkMlaMgeRbkugRtaMgbBaÄredIm,Ikat;bnßykug RtaMgTajEdlenAsl; (residual tension) eGayenAkñúgEdnénm:UDuldac;rbs;ebtug nigedIm,IbMeBjlkç- xNÐemKuNsuvtßiPaB. edIm,IFanakarRbqaMgnwgkarekItmansñameRbHenAépÞxageRkArbs;CBa¢aMgGag eKKYrGnuvtþkMlaMg eRbkugRtaMgedkFMCagkMlaMgEdlvaRtUvkarbnþicedIm,IeFVIeGaykMlaMg radial ecjeRkAEdlbgáedaysar- Faturav b¤]sμ½nxagkñúgmanlMnwg GBa©WgehIyvabegáIteGaymankugRtaMgsgát;EdlenAesssl; (residual compression) enAkñúgGagenAeBlvaeBj. karekIneLIgénkMlaMgeRbkugRtaMgvNÐ (circumferential prestressing forces) tamry³kareRbIEdkeRbkugRtaMgedkbEnßm nigeBlxøHmanEdkbBaÄrFmμtak¾RbqaMg nwgT§iBlrbs;sItuNðPaB nigbMErbMrYlsMeNIm (moisture gradient) Edlqøgkat;kMras;CBa¢aMgkñúgbrisßan minl¥pgEdr. 11.6.1. )atCBa¢aMgrGiledayesrI Freely Sliding Wall Base enAeBllkçxNÐRBMEdnén)atrbs;CBa¢aMgGacrGiledayesrI enaHeBlGagrgbnÞúkxagkñúg vanwg minmanm:Um:g;enAkñúgCBa¢aMgbBaÄrEdlbNþalBIbnÞúksarFaturav b¤k¾bNþalBIkMlaMgeRbkugRtaMg eTaHbIenA eBlGageBjdl;kMBs; H k¾eday. manEt nominal moment d¾tUcb:ueNÑaHekItmanenAeBlGagmineBj b¤rgeRbkugRtaMgedayEpñk b¤k¾TeT ehIyvaminRtUvkarkMlaMgeRbkugRtaMgbBaÄreT. rUbragxUcRTg;RTay rbs;GagEdlrGiledayesrIRtUv)anbgðajenAkñúgrUbTI 11>7. enAeBlEdlkarrGiledayesrICalkçxNÐd¾l¥Edlpþl;nUveRKOgbgÁúMkMNt;edaysþaTic ehIyman lkçN³esdækic©CaeK b:uEnþeKBi)aknwgTTYl)ankñúgkarGnuvtþCak;Esþg. kMlaMgkkit (frictional force) EdlekItmanenARtg;)atCBa¢aMgeRkayeBlEdleKdak;eGayGagdMeNIrkareRbIR)as; dUcenHCMerIsenHmin GaceRbIkar)aneT. Prestressed Concrete Circular Storage Tanks and Shell Roofs 694
  29. 29. Department of Civil Engineering NPIC 11.6.2. )atCBa¢aMgCaTMrsnøak; Hinged Wall Base sMrab;CBa¢aMgEdlmantMNsnøak;enA)at kMlaMg radial force GtibrmaEdlbNþalBIsarFaturav EdlvapÞúk ehIyeRbkugRtaMgenARtg;muxkat;eRKaHfñak;Rtg;cMgay y BIelI)atswgEtesμInwgeRbkugRtaMgkñúg krNI)atrGiledayesrIRtg;kMBs; y Edr. b:uEnþeKRtUvbBa©Úlm:Um:g;bBaÄr ehIykMlaMgeRbkugRtaMgbBaÄr køayCacMa)ac;edIm,Ikat;bnßykugRtaMgTajenAkñúgebtugenARtg;épÞCBa¢aMgxageRkA. rUbragxUcRTg;RTayrbs;CBa¢aMgEdlmanTMr hinged RtUv)anbgðajenAkñúgrUbTI 11>8. cMNaMfa muxkat;eRKaHfñak;sMrab; ring force mincaM)ac;enARtg;kMBs;dUcKñanwgmuxkat;eRKaHfñak;sMrab;m:Um:g;eT. edIm,Ikat;bnßysñameRbHEdlGacekItmanrhUtdl;cMnYnGb,brma/ eKcaM)ac;RtUvkar residual ring compression EdlmantMélGtibrma 200 psi(1.38MPa ) sMrab; wire-wrapped presstressed tank Edlminman diaphragm nigmantMélGtibrma 100 psi (0.7 MPa ) sMrab;GagEdlman continuous metal diaphragm. kugRtaMgTajGtibrmaenAépÞxagkñúgrbs;CBa¢aMgminRtUvFMCag 3 f 'c eRkamGMeBIbnÞúk eFVIkar (working load) dUcEdleGayenAkñúgtarag 11>17 enAkñúgEpñkxagmux. rUbragxUcRTg;RTay rbs;GacCBa¢aMg nigbMErbMrYlkugRtaMgenAkñúgebtugEdlkat;tamkMras;rbs;muxkat;enAeBlGagTeT nigenA eBlvaeBj dUcbgðajenAkñúgrUbTI 11>8. sMrab;GagEdlrgeRbkugRtaMgCamYynwg pretensioned tendon nig post-tensioned tendons kugRtaMgsgát;EdlenAesssl;Gb,brmaKYrmantMéldUcGVIEdlerobrab;enA kñúgEpñk 11.10. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 695
  30. 30. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 696
  31. 31. Department of Civil Engineering NPIC 11.6.3. )atCBa¢aMgrGiledayEpñk nigmanTMrsnøak; Partially Sliding and Hinged Wall Base edIm,ITTYl)an partially slinging and hinged wall-base system eKRtUveFVIrn§enAkñúgkMralRT )atCBa¢aMgy:agNaedIm,IeGayCBa¢aMgGacrGilkñúgGMLúgeBlrgeRbkugRtaMg. eRkayeBlrgeRbkugRtaMg nigkMhatbg;eRbkugRtaMgedaysar creep, shrinkage nig relaxation, eKRtUvbiTrn§ ehIyCBa¢aMgGageFVI karCa hinged eRkamGMeBIlkçxNÐ service load. eKRtUvRKb;RKgTMhMénkarrGil eTaHbIvaCa full sliding b¤ partial sliding k¾eday edIm,IeGayvasßitkñúgkMritGnuBaØatmunnwgeKTTYl)anTMr hinged. karrGil edayEpñkRbEhl 50% énkarrGileBjelj nigedaymansnøak;enAxagcugrbs;CBa¢aMg vapþl;RbeyaCn_ dl;clnarbs;eRKOgbgÁúMTaMgsMrab;)atrGileBjelj nigTaMgsMrab;)atmansnøak; ehIykarbiTrn§enARtg; tMN pinned Rtg;)atCBa¢aMgRbqaMgnwgkarelcRCabénsarFaturav b¤]sμ½nKWvakan;EtGaRs½yeTAnwgkMrit rGil EdleKGnuBaØatcMeBaH full sliding CagcMeBaH anchorage. rUbragxUcRTg;RTayrbs;CBa¢aMgkñúg GMLúgdMeNIrkarGnuvtþeRbkugRtaMg rYmCamYynwg ring force/ m:Um:g;bBaÄr nigbMErbMrYlkugRtaMgebtugkñúg kMras;CBa¢aMg RtUv)anbgðajenAkñúgrUbTI 11>9. eRbkugRtaMgbBaÄrEdlRtUvkarsMrab;krNI partial slide- pinned mantMéltUcCagkrNI fully pinned EdlminmankarrGileRcInNas;. 11.6.4. )atCBa¢aMgbgáb;eBlelj Fully Fixed Wall Base PaBbgáb;eBjeljrbs;CBa¢aMgenARtg;)atmann½yfaTb; (restraint) mineGayvilTaMgRsugenA Rtg;)atCBa¢aMg. eKGacTTYl)anlkçxNÐenH RbsinebIkMNat;TabCageKrbs;CBa¢aMgRtUv)ancak;kñúgeBl CamYyKñanwgkMral ehIymankarf<k;)any:agl¥eTAkñúgkMral)atEdlmanPaBrwgRkajdUcKña. b:uEnþeKBi)ak nwgTTYl)anRbB½n§minkMNt;EbbenHNas; ehIyvak¾minmanlkçN³esdækic©pg edaysarépÞ)atGagman TMhMFM ehIyPaBbgáb;edayEpñkkøayCacaM)ac;. kMlaMg radial tamTisedkEdl)anBIkMlaMgeRbkugRtaMg nig)anBIsMBaFxagkñúgminmankarERbRbYlBIragRtIekaNsMrab;sarFaturag ragctuekaNsMrab;]sμ½n nigrag ctuekaNBñaysMrab;GgÁFatuRKab;eT. b:uEnþ restraint EdlbegáItedaykMral)atEkERb ring force nig bBa©Úlm:Um:g;bEnßmeTAkñúgmuxkat;bBaÄrrbs;CBa¢aMg. edaysarPaBbgáb;enARtg;)at vanwgminmanbMlas; TIekItmanenARtg;)at b¤kMBUlrbs;CBa¢aMgeT ehIykarERbRbYlénkMeNagrbs;kMBs;CBa¢aMgekItmanenA eBlGagTeT dUcbgðajenAkñúgrUbTI 11>10. cMNaMfa eKKYrsikSaKNnaCBa¢aMgeGayQrRtg; CamYynwg kugRtaMgsgát;Edlesssl;Gb,brmaEdlbNþalBIkMlaMgeRbkugRtaMg 200 psi dUckñúgkrNIelIkmun. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 697
  32. 32. T.Chhay viTüasßanCatiBhubec©keTskm<úCa eRbkugRtaMgbBaÄrEdlRtUvkarsMrab;GagEdlman)atCBa¢aMgbgáb;eBjeljmantMélFMCagsMrab;krNI lkçxNÐRBMEdkdéTeTotxøaMgNas;. eKcaM)ac;eFVIeGaymanbMErbMrYlkugRtaMgTajenAkñúg)atCBa¢aMgRtg;épÞ xageRkAEdlbNþalBIm:Um:g;GviC¢mand¾FMenARtg;)ateGaymantMélFM ¬emIlrUbTI 11>10 a nig b¦ ehIy bRBa©askMeNagEdlenAEk,rva. eBlxøH vamanlkçN³esdækic©CagedayeRbIEdkBRgwgFmμtaenAEpñkxag eRkamrbs;CBa¢aMgbEnßmBIelIEdk eRbkugRtaMg edIm,IGaceRbIeRbkugRtaMgbBaÄrtUcCag nigeGayEdkBRgwg FmμtaTTYlnUvm:Um:g;GviC¢mand¾FMenaH. eKk¾Gackat;bnßykugRtaMgTajenAkñúgebtugedayeRbIkMlaMgeRbkug RtaMgbBaÄrcakp©itCamYynwgcMNakp©itsmrmü rYmCamYynwgEdkBRgwgFmμtabEnßm. b:uEnþ EdkeRbkugRtaMg Prestressed Concrete Circular Storage Tanks and Shell Roofs 698
  33. 33. Department of Civil Engineering NPIC bBaÄrEdleRbIenAkñúgGagsþúkmantMéléfø edaysartMrUvkar anchorage enAxagcug nig)atrbs;CBa¢aMg Gag. dUcenH eKRtUvkarkat;bnßyeRbkugRtaMgbBaÄrkñúgkarsikSaKNnaedIm,IbEnßmlkçN³esdækic©dl; karsikSaKNna RbB½n§eRKOgbgÁúMGagTaMgmUl. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 699
  34. 34. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 11.6.5. )atCBa¢aMgbgáb;mineBjelj Partially Fixed Wall Base 11.6.5.1. karTb;nwgkarvil Rotational Restraint dUckarbgðajBIxagedIm eKBI)akkñúgkareFVIeGay)ankarTb;eBleljRbqaMgnwgkarvilenARtg;)at CBa¢aMgNas;. mUlehtusMxan;manbI³ ¬!¦ eKRtUvpþl;nUvPaBrwgRkajcaM)ac;enAkñúgkMral)atGagRtg;kEnøg RbsBVCamYyCBa¢aMgedIm,ITTYl)ankarbgáb;eBjelj. ¬@¦ clnarbs;dIxageRkamCBa¢aMgGacbgákarvil rbs;)atCBa¢aMg. nig ¬#¦ eKTamTarkarRb mUlpþúM anchorage sMrab;TaMgeRbkugRtaMgbBaÄr nigTaMgeRb kugRtaMgvNÐedkrbs;kMNat;CBa¢aMg-)at edaysarCBa¢aMg nig)atrgeRbkugRtaMgdac;edayELkBIKña. edaysarkMral)atmanépÞFM T§iBlénkarTb; b¤kareFVIeGayrwgrbs;vaRtUv)ankMNt;RtwmbrievN toe d¾tUcceg¥ótEdleFVIkarCalkçN³ cantilever BI)atCBa¢aMg. CMerIsd¾RtwmRtUvénTTwgrbs; toe b¤ base ring kMNt;nUvPaBRtwmRtUvéntMélPaBrwgRkajkñúgkarKNnaEdl)anBIdWeRkénkarbgáb;snμt;rbs;)at CBa¢aMg. rUbTI 11>11 bgðajBIT§iBlénTTwg base ring eTAelImMurgVilrbs;CBa¢aMg nigbMlas;TIrbs; ring. Epñk (c) rbs;rUbbgðajBIsßanPaBlMnwgEdlcugrbs; ring sßitenAelInIv:UdUcKñanwg)atrbs;CBa¢aMg b:uEnþlkçxNÐEdlbgðajenAkñúgEpñk (a) nig (b) Bak;B½n§nwgbMlas;TIBIxageRkam)atrbs;CBa¢aMg ehIyva min)anbMeBjlkçxNÐeT. Prestressed Concrete Circular Storage Tanks and Shell Roofs 700
  35. 35. Department of Civil Engineering NPIC eKGacTTYl)anrUbmnþkñúgkaredaHRsayrkTTwg ring base eRKaHfñak;tamry³kareRbIeKalkarN_ tMrYtpl (superposition) edaybUkbBa©ÚlkrNIénCBa¢aMgviledayesrI (freely rotating wall) CamYYynwg krNICBa¢aMgbgáb;eBjelj dUcbgðajenAkñúgrUbTI 11>12. eKyk M o = m:Um:g;bgáb;eBjeljtamRTwsþIenARtg;)atCBa¢aMg M p = m:Um:g;edayEpñkenARtg;)atCBa¢aMgEdlbNþalBI loaded cantilever toe θ1 = mMurvilesrIrbs;)atCBa¢aMgsMrab;EtTMr pinned EdlRtUvnwgPaBdab Δ1 rbs; stiff unloaded toe θ2 = mMurgVil)atCBa¢aMgEdlbNþalBI restraining moment M p EdlRtUvnwgPaBdab Δ 2 én straight unloaded toe θ3 = mMurgVileFobxagcugén stiffening toe EdlmanlkçN³Ca cantilever eRkamGMeBIbnÞúkbBaÄr EdlRtUvnwgPaBdab Δ3 rbs;cug toe EdlbNþalBIbnÞúkbBaÄr. L = TTwgrbs; stiffening toe. q = bnÞúkÉktþaEdlGnuvteTAelI stiffening toe = γH Edl H CakMBs;rbs;Gag EdlGgát;p©it rbs;vaesμInwg d / kMras;CBa¢aMgrbs;vaesμInwg t ehIykMras;kMralrbs;vaesμInwg h . GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 701
  36. 36. T.Chhay viTüasßanCatiBhubec©keTskm<úCa eKTTYl)anmMurgVilÉktþaθ rbs;CBa¢aMgRtg;)atrbs;vaEdlbNþalBIm:Um:g; M o b:uEnþminmanbMlas; TI radial BIsmIkar 11.18a edayeGay w = 0 edIm,ITTYl)an Q = −βM . smIkar 11.18b sMrab;mMurgVil ÉktþakøayCa Mo Mp θ1 = θ2 = (11.33) 2βD 2βD dUcenH eyIg)an LM o LM p Δ1 = Δ2 = (11.34) 2βD 2βD RbsinebIeKcat;Tuk stiffening wall toe Ca cantilever Edlrg transverse load γH / Cantilever moment Gtibrma M p ehIyPaBdabEdlRtUvKña Δ 3 KW γHL2 3γHL4 Mp = Δ3 = (11.35) 2 2 Eh 3 eKGacTTYl)anm:Um:g;enARtg;)atCBa¢aMgEdlbgáb;edayeRbI membrane coefficient C BItarag 11>4 sMrab; form factor H 2 / dt nigRbePTbnÞúk. sMrab;bnÞúksarFaturag M o = CγH 3 (11.36) BIsmIkar 11.12(c) rUbragEdlxUcRTg;RTayedaysarbnÞúkeBjKW Δ1 = Δ 2 + Δ 3 snμt; μ = 0.2 nig β = 2 / dt edayCMnYs Δ 2 nig Δ 3 BIsmIkar 11.34 eTAkñúgsmIkar 11.35 nig 11.36 enaHeyIg)an 2CH 2 L2 = (11.37) 1+ (t / h )3 (L = 1) (dt )1 / 2 γHL2 nig Mo = 2 (11.38) yktY S= (t / h )3 (11.39) (dt )1 / 2 tY S énsmIkar 11.39 enHRtUv)aneKeGayeQμaHfa modifying factor sMrab;karbgáb;edayEpñk. em KuNenHCaTUeTAmantMéltUc ehIybgðajnUvplsgrvagm:Um:g;bgáb;srub M o nigm:Um:g;Tb;edayEpñk (partial restraint moment) M p . dUcenH M p = M o (1 − S ) (11.40) tMélrbs; L enAkñúgPaKEbgénsmIkar 11.37 RtUv)ansnμt;esμInwg 1 sMrab;karsMrYlenAkñúgkarEkERb emKuN S . Prestressed Concrete Circular Storage Tanks and Shell Roofs 702
  37. 37. Department of Civil Engineering NPIC RbsinebItMélrbs; S tUcEmnETn dUckñúgkrNIGagEdlmanGgát;p©itFM ¬Ggát;p©itFMCag 125 ft eTA 150 ft ¦ smIkarkarsMrab; L nig M p køayCasmIkrsMrab;karbgáb;eBjelj L2 = 2CH 2 nig M p = CγH 3 11.6.5.2. Base Radial Deformation kMhUcRTg;RTay radial Δ s én base ring EdlrgkMlaMg radial enAkñúgbøg;rbs;vaGacTTYlBIRTwsþI rbs;kMralmUlEdlmanRbehagcMp©it. smIkarsMrab;PaBdabrbs;kMralEdlbgðajenAkñúgrUbTI 11>13 (a) KW d oQ ⎛ d o + d 2 ⎜ 2 ⎞ Δs = − μ⎟ (11.41) 2hE ⎜ d o − d 2 ⎝ 2 ⎟ ⎠ Edl μ = pleFobB½rs‘ug ~ 0.2 sMrab;ebtug ehIy E Cam:UDuleGLasÞic. kMlaMg radial edkÉktþaEdl RtUvkarsMrab;begáItbMlas;TIÉktþaenAkñúgkMlagmYltan;KW GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 703
  38. 38. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 2.5hE Q2 = (11.42) do ehIytMélRtUvKñaén radiant thrust EdlGnuvtþeTAelI ring xageRkAKW 2hE Q3 = (11.43) do K ⎛d2 + d2 ⎞ Edl K =⎜ o ⎜ d2 − d2 − μ⎟ ⎟ ⎝ o ⎠ ehIy d = Ggát;p©itxagkñúgrbs; base ring = (do − 2L) . eKkMNt;PaBrwgRkaj relative rbs;CBa¢aMgedayeRbItYénkMlaMgEdlRtUvkarsMrab;begáItbMlas;TI ÉktþaenAkñúgCBa¢aMg nigkMral)atBIeKalkar virtual work dUcEdlbgðajenAkñúgrUbTI 11>13 (b) nig (c). kar BRgayfamBleRbkugRtaMgcenøaHCBa¢aMg nig base slab ring CaGnuKmn_én relative radial stiffness rbs;va dUcenHeKcaM)ac;RtUvkMNt;PaBrwgRkaj relative. b:uEnþ eKRtUvdwgfa PaBrwgRkajrbs; base ring enAkñúgGageRbkugRtaMgEdlmankugRtaMgsgát; radial enAkñúgbøg;rbs;vamantMélFMCagPaBrwg RkajénCBa¢aMgsIuLaMgrbs;GageRkamsMBaF radial xagkñúg. dUcenH kMhatbg;eRbkugRtaMgBIPaBxusKña énPaBrwgRkajminsMxan;eTsMrab;GagGgát;p©itFM EteKRtUvBicarNavasMrab;GagGgát;p©ittUc. eKGacTTYlbMlas;TIÉktþa Δ EdlbNþalBIkMlaMg radial Q' EdlminmanmMurgVilenARtg;)at CBa¢aMgBIsmIkar 11.8 b edayeRbI 2βM = −Q sMrab;mMurgVil dw / dy = 0 . PaBdabÉktþa Δ enAkñúg smIkar 11.18a køayCa Q3 Δ= 4β 3 D b¤ Δ= Q' 4β 3 D (11.44) Et 3 Edl D= ( ) 12 1 − μ 2 edayeRbI μ ~ 0.2 / smIkar 11.44 sMrab;bMlas;TI radial Éktþarbs;CBa¢aMgenARtg;)atCBa¢aMgEdlmin manmMurgVilkøayCa 3/ 2 ⎛t⎞ Q ' = 2 .2 E ⎜ ⎟ (11.45) ⎝d ⎠ Edl E Cam:UDuleGLasÞicrbs;ebtug. BIsmIkar 11.42/ kMlaMg radial EdlRtUvkarsMrab;begáItbMlas;TI radial ÉktþaenAkñúgkMlagragmUltan;KW ⎛ h ⎞ Q2 = 2.5 E ⎜ ⎟ ⎜d ⎟ (11.46) ⎝ o⎠ Prestressed Concrete Circular Storage Tanks and Shell Roofs 704
  39. 39. Department of Civil Engineering NPIC edaybUk Q' nig Q2 enaHkMlaMgsrubEdlmanGMeBIenARtg;kEnøgRbsBVrvagCBa¢aMg nig)atRtUv)anEbg EckeTACBa¢aMg nigeTA)atedayQrelIsmamaRténfamBl relative EdlRtUvkarsMrab;begáItbMlas;TI ÉktþanImYy². smamaRténkMlaMgsrub Q'+Q2 EdlRtUv)anRTedayCBa¢aMgKW Q' R= Q'+Q2 edayyk R= 1 1 + S1 kMNt; S1 edayCMnYssmIkar 11.45 nig11.46 eTAkñúgsmIkarxagelI eyIg)an 2.5(h / d ) S1 = 2.2(t / d )3 / 2 edaysnμt; d ~ do / b¤ 1/ 2 ⎛h⎞ ⎛d ⎞ S1 = 1.1⎜ ⎟ × ⎜ ⎟ (11.47) ⎝t⎠ ⎝t ⎠ RbsinebI S1 tUc enaHeKGacyksmamaRténkMlaMgedkEdlepÞrBI)atkMraleTACBa¢aMg ¬suRkitRKb;RKan;¦ 100 R= % (11.48) S1 enAeBlEdl ring xageRkArbs;kMralrgkugRtaMgsgát;eday radial thrust enARtg;EKm eKRtUvEksMrYl tMélrbs; Q2 EdlTTYlBIsmIkar 11.42 ehIy S1 enAkñúgssmIkar 11.48køayCa 1/ 2 1 ⎛h⎞ ⎛d ⎞ S1 = ⎜ ⎟ × ⎜ ⎟ (11.49) K⎝t⎠ ⎝t ⎠ Edl BIelIkmun ⎛ do + d 2 2 ⎞ ⎜ K= 2 −μ⎟ ⎜d −d2 ⎟ ⎝ o ⎠ EdlkñúgenaH d CaGgát;p©itxagkñúgrbs; slab ring = d o = 2L ehIy d o CaGgát;p©itxageRkA. 11.7. Recommended Practice for Situ-Cast and Precast Prestressed Concrete Circular Storage Tanks 11.7.1. kugRtaMg Stresses eKalkarN_ENnaMTUeTAsMrab;GagsþúkragmUlebtugeRbkugRtaMgEdlcak;enAnwgkEnøgRtUv)anpþl; eGayeday Prestressed Concrete Institute/ American Concrete Institute nig Post-Tensioning Institute sMrab;eRCIserIskugRtaMgGnuBaØat/ karkMNt;TMhM kMras;CBa¢aMgGb,brma nigdMeNIrkardMeLIg nig GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 705
  40. 40. T.Chhay viTüasßanCatiBhubec©keTskm<úCa sagsg;. kugRtaMgGnuBaØatenAkñúgebtug nig shotcrete RtUv)aneGayenAkñúgtarag 11>17. kugRtaMg GnuBaØatenAkñúgEdkBRgwgRtUv)aneGayenAkñúgtarag 11>18. 11.7.2. emKuNbnÞúk nigersIusþg;tMrUvkar Required Strength Load Factors eRKOgbgÁúM rYmCamYynwgrcnasm<½n§rbs;va nigeCIgtag KYrRtUv)ansikkSaKNnay:agNaeGay ersIusþg;KNna (design strength) FMCagT§iBlrbs;bnSMbnÞúkemKuNEdlkMNt;eday ACI 318, ANSI/ ASCE 7-95 b¤GaRs½yelIkarEksMrYledayvisVkrEdlQrelIkarviPaKd¾smehtupl CamYynwglkçxNÐ xageRkam³ Prestressed Concrete Circular Storage Tanks and Shell Roofs 706
  41. 41. Department of Civil Engineering NPIC smIkarersIusþg;m:Um:g; nominal M n RsedogKñanwgsmIkarEdleRbIsMrab; linear prestressing ⎛ a⎞ M n = A ps f ps ⎜ d p − ⎟ (11.50a) ⎝ 2⎠ ⎛ a⎞ ⎛ a⎞ b¤ M n = A ps f ps ⎜ d p − ⎟ + As f y ⎜ d − ⎟ ⎝ 2⎠ ⎝ 2⎠ (11.50b) enAeBlEdleKeRbI As ehIy Edl Aps = EdkeRbkugRtaMgbBaÄrkñúgTTwgmYyÉktþa f ps = kugRtaMgenAkñúgEdkeRbkugRtaMgRtg;ersIusþg; nominal f y = yield strength rbs;EdkFmμta 11.7.3. tMrUvkarGb,brmakñúgkarKNnaCBa¢aMg Minimum Wall-Design Requirements 11.7.3.1. kMlaMgvNÐ Circumferential Forces sarFaturav kMlaMgedIm Fi = γr (H − γ ) ff pi (11.51a) ps karcak;bMeBj (backfill) kMlaMgedIm Fbi = p(r + t ) (11.51b) Edl t CakMras;CBa¢aMgsrub. 11.7.3.2. kMras; nigkugRtaMg Thickness and Stresses kMras;CBa¢aMg (Core Wall Thickness) Fi t co = (11.52) f ci GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 707
  42. 42. T.Chhay viTüasßanCatiBhubec©keTskm<úCa b:uEnþminRtUvtUcCagkMras;CBa¢aMgGb,brmaEdlmanerobrab;enAkñúgEpñk 11.7.3.6. kugRtaMgcugeRkayEdlbNþalBIkarcak;bMeBj nigeRbkugRtaMgedIm Fbi Fi f pe f = + (11.53) t t co f pi 11.7.3.3. PaBdab Deflections PaBdab radial eGLasÞicedImrbs;CBa¢aMgEdlbNþalBIkMlaMgeRbkugRtaMgedImKW Fi r Δi = (11.54) t co Ec Edl kaMxagkñúgrbs;Gag r= t co = kMras;rbs;CBa¢aMgenAxagcug xag)atrbs;CBa¢aMg Ec = 57,000 f 'c psi (4,700 f 'c MPa ) sMrab;ebtugTMgn;Fmμta nig shotcrete. PaBdab radial cugeRkay Δf GacmantMélesμInwg1.5 eTA3dgénPaBdabdMbUg. sMrab;lkçxNÐ eKGacykPaBdab radial EdlGnuBaØatcugeRkaydUcxageRkam Δf = 1.7 Δ i (11.55) 11.7.3.4. T§iBlTb; Restraint Effects m:Um:g;Bt;bBaÄrGtibrmarbs;CBa¢aMgEdlbNþalBIkMlaMgkat; radial M f = 0.24Qo rt co (11.56a) m:Um:g;enHekItmanenAcMgay y = 0.68 rt co (11.56b) BI)at b¤cugEKm kMlaMgkat; radial sMrab;)atEdlcak;rYmKñaEdlsnμt;favaCatMNsnøak; t co Qo = 0.38 Fi (11.57) r RbePTénkarlMGitenaHRtUv)aneRbIsMrab;EtGagsþúkEdlcak;enAnwgkEnøgEdlsagsg;edayman diaphragm enAkñúgCBa¢aMgrbs;vab:ueNÑaH. 11.7.3.5. EdkFmμtasMrab;karf<k;enA)at Mild Steel for Base Anchorage RbsinebIeKeRbI diaphragm/ eKRtUvbgðÚtEdkxagkñúgEdlmanragGkSr UTaMgGs;cMgay Prestressed Concrete Circular Storage Tanks and Shell Roofs 708
  43. 43. Department of Civil Engineering NPIC y1 = 1.4 rt co (11.58a) BIelI)at. RbsinebIeKmineRbI diaphragm eKRtUvbgðÚtvacMgay y2 = 1.8 rtco (11.58b) BIelI)at. cMNaMfa eKRtUvbUkbEnßmRbEvgf<k; (anchorage length) BIelI y1 b¤ y2 . RkLaépÞGb,brma rbs;EdkbBaÄr nominal enARtg;tMbn;)atKW As = 0.005t co (11.59) ehIyeKRtUvbgðÚtvaBI)atnUvcMgay 3 ft b¤ y3 = 0.75 rt co (11.60) edayykmYyNaEdlFMCag. 11.7.3.6. kMras;CBa¢aMgGb,brma Minimum Wall Thickness CBa¢aMgcak;enAnwgkEnøg CBa¢aMgcak;Rsab; eKRtUvcMNaMfa sMrab;GagEdlrgeRbkugRtaMgCamYynwg tendon, eKENnaMkMras;CBa¢aMgminRtUvtUc Cag 9in. sMrab;kargarGnuvtþn_. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 709
  44. 44. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 11.8. RKb;RKgsñameRbHenAkñúgCBa¢aMgrbs;GagebtugeRbkugRtaMgragmUl Crack Control in Walls of Circular Prestressed Concrete Tanks nig Preston ENnaMsmIkarxageRkamedayQrelIkargarrbs; Nawy sMrab;TMhMsñameRbH Vessy GtibrmaenAépÞxageRkArbs;CBa¢aMgGageRbkugRtaMg³ wmax = 4.1 ⋅10 −6 ε ct E ps I x (11.61) Edl ε ct = bMErbMrYlrageFobrbs;épÞrgkarTaj (tensile surface strain) enAkñúgebtug 8 ⎛ s 2 s1tb ⎞ I x = grid index = ⎜ ⎟ π ⎜ φ1 ⎝ ⎟ ⎠ s2 = KMlatEdkkñúgTiselx “2” s1 = KMlatEdkkñúgTisEkgelx “1” ¬Tisedk¦ tb = kMras;karBarEdkKitdl;G½kSEdk φ1 = Ggát;p©itEdkkñúgTisem “1” eKGacKNnabMErbMrYlrageFobrgkarTajBI α t f pi ε ct = (11.62) E ps Edl αt = )a:ra:Em:RtkugRtaMg (stress parameter) ≅ f p / f pi f p = kugRtaMgCak;EsþgenAkñúgEdkeRbkugRtaMg f pi = eRbkugRtaMgedImmuneBlkMhatbg; sMrab;GagEdlsþúksarFaturav TMhMsñameRbHGnuBaØaGtibrmaKW 0.004in. 11.9. karsikSaKNnadMbUg Roof Design dMbUlsMrab;GagEdlsagsg;kñúgTMrg;ekag (shell dome) b¤ CadMbUlrabesμIEdlRTenAelIssr xagkñúg. CaTUeTA tMélrbs;dMbUlRbEhlCamYyPaKbIéntMéleRKOgbgÁúMTaMgmUl. kñúgkrNIdMbUlrabesμI ¬eTaHcak;Rsab; b¤cak;enAnwgkEnøg¦ karKNnaeFVItameKalkarN_KNnaRbB½n§kMralebtugGarem: b¤ebtug eRbkug RtaMgmYyTis b¤BIrTisFmμta dUcEdlerobrab;enAkñúg ACI 318 Code. RbsinebI dMbUlCaRbePT ebtugeRbkugRtaMgcak;Rsab; ehIyGgát;p©itGagminFM enaHeKmincaM)ac;eRbIssrxagkñúgeT. ebIminGBa©wg eT tMélrbs;ssrxagkñúgbEnßm nigeCIgtagrbs;vaGacbegáIntMélrbs;eRKOgbgÁúMTaMgmUl. dMbUlekagmanRbeyaCn_sMrab;GagEdlmanGgát;p©itminFMCag 150 ft edaysarvaminRtUvkar ssrTMrxagkñúg nigehIyvamanlkçN³esdækic©sMrab;GagEdlbgáb;eRkamdIkñúgkarTb;Tl;nwgbnÞúkcak;bM Prestressed Concrete Circular Storage Tanks and Shell Roofs 710
  45. 45. Department of Civil Engineering NPIC eBj (backfill). dUcenH TMrg; shell nigtMNrbs;vaeTAnwgCBa¢aMgGagmanT§iBly:agxøaMgeTAelItMél. CakareBjniym dMbUl shell RtUv)anRTedayCBa¢aMgGagCamYynwgtMNEdlman flexible completely ebImindUecñaHeT eKRtUvEksMrYlkarKNnaTaMgCBa¢aMgGag nigTaMg roof dome EdlTak;TgnwgdWeRkénkar Tb; nigPaBrwgRkaj relative CamYynwgtMélsagsg;bEnßmkñúgeBlCamYyKña. dMbUlekagragEsV‘rEdlman rise-to-diameter ratio h' / d tUc eKeRcInyktMélRbEhl 1/ 8 . dMbUlekagEbbenH b¤ axisymmetrical shell begáItkMlaMgedkEdlmanTisecjeRkAenARtg; springing EdlvaRtUv)anTb;Tl;eday ring beam eRbkugRtaMgEdlKNnay:agRtwmRtUvenARtg;TMr. RbePT ring beam kMNt;RbtikmμelIs nigm:Um:g;elIsEdlbNþalBIkugRtaMgbEnßmedaypÞal; nigkugRtaMgBt;enARtg; cugbgáb;enAkñúg shell Ek,r springing. eKGacniyaymüa:geTotfa membrane solution RtUvbMeBjkar EkERbedaydak;vabEnßmBIelIT§iBlm:Um:g;Bt;EdlkMNt;edaytMrUvkar strain compatibility én bending theory. 11.9.1. Membrane Theory of Spherical Domes 11.9.1.1. Shell of Revolution smIkarlMnwg membrane sMrab;kMlaMgedaypÞal;enAkñúg shell of revolution dUcEdlbgðajenA kñúgrUbTI 11>14 RtUveRbIsMrab;kMNt; kMlaMg meridional Éktþa Nφ / kMlaMg tangential Éktþa Nθ nig kMlaMg central Éktþa Nφθ nig Nθφ edayeRbItYbnÞúkTMnaj pφ / pθ nig p z . smIkarTaMgenHman³ Meridional: ( ∂ Nφ ro )− N ∂r ∂Nθφ + r1 + pφ ro r1 = 0 (11.63a) θ ∂φ ∂φ ∂θ ∂Nθ ∂ro ∂Nθφ Tangential: r1 + Nθφ + + po ro r1 = 0 (11.63b) ∂θ ∂φ ∂φ N φ Nθ Tis z ³ r1 + r2 + pz = 0 (11.63c) edaysarbnÞúkmanlkçN³sIuemRTI/ RKb;tYTaMgGs;EdlTak;Tgnwg ∂θ RtUv)anbM)at; ehIyeKGacsresr tYEdlTak;Tgnwg ∂φ eLIgvijCaDIepr:gEsülsrub dφ edaysarKμantYNamYyERbRbYlGaRs½ynwgtY θ . ehIybgÁúM circumferential load pθ = 0 edaysarkMlaMgpÁÜbkMlaMgkat;RtUv)anbM)at;tambeNþay meridional nigrgVg;EdlRsb. dUcenH eKGacsresrsmIkar 11.63 eLIgvijCa d dφ ( ) Nφ ro − Nθ r1 cos φ + p y r1ro = 0 (11.64a) N φ Nθ + + pz = 0 (11.64b) r1 r2 GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 711
  46. 46. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 11.9.1.2. dMbUlekagragEsV‘r Spherical Dome smIkarlMnwgrbs; Membrane Analysis dMbUlekagragEsV‘rmankMeNagefr. dUcenH r1 = r2 = ro . edaysnμt;fa kaMrbs;EsV‘resμInwg a enaH ro = a sin φ enAkñúgrUbTI 11>14(c) ehIyedayyk p z = wD sMrab;bnÞúkpÞal; enaHsmIkarlMnwg Prestressed Concrete Circular Storage Tanks and Shell Roofs 712
  47. 47. Department of Civil Engineering NPIC TUeTA 11.64 køayCa ⎛ 1 ⎞ ⎜ 1 + cos φ − cos φ ⎟ Nθ = awD ⎜ ⎟ (11.65a) ⎝ ⎠ nig Nφ = − awD 1+ cos φ (11.65b) Edl wD CaGaMgtg;sIuetrbs;bnÞúkpÞal;kñúgmYyÉktþaépÞ. eyIgeXIjy:agc,as;BIsmIkar 11.65 b fa kMlaMg meridional Nφ nwgGviC¢manCanic©. dUcenH kMlaMgsgát;nwgekItmantambeNþay meridian ehIyvanwgekIneLIgenAeBlEdlmMu φ ekIneLIg³ enAeBl φ = 0 / Nφ = −awD / 2 ehIyenAeBlEdl φ = π / 2 / Nφ = −awD . kMlaMg tangential Nθ mantMélGviC¢man ¬kMlaMgsgát;¦ sMrab;EttMélkMNt;énmMu φ b:ueNÑaH. edayyk Nθ = 0 enAkñúgsmIkar 11.65a/ 1/(1 + cosφ ) − cosφ = 0 eKTTYl)an φ = 51o 49' . kar kMNt;bgðajfa sMrab; φ > 51o 49' kugRtaMgTajekItmanenAkñúgTisEkgnwg meridian. karEbgEckkug RtaMg meridional Nφ ehIykarEbgEckkugRtaMg tangential Nθ sMrab;TaMgbnÞúkpÞal; wD nigbnÞúk GefrxageRkA wL RtUv)anbgðajenAkñúgrUbTI 11>15. RbsinebIbnÞúkxageRkAefr ¬bnÞúkRBil¦ EdleGayGaMgtg;sIuet wL / kMlaMg meridional Nφ RtUv)anTTYlBIlMnwgénGgÁesrIedayeGaybnÞúkxageRkAesμInwgkMlaMg meridional xagkñúg mann½yfa − π (d / 2)2 wL = 2π (a sin φ )Nφ . edaysar d / 2 = a sin φ eyIgTTYl)an wL a Nφ = − (11.66a) 2 dUcenH Nφ CatMélefrelIkMBs; shell TaMgmUl dUcEdleXIjenAkñúgrUbTI 11.15. Nθ EdlbNþalBIbnÞúkGefr wL KW awL ⎛1 ⎞ awL Nθ = −awL cos 2 φ + = awL ⎜ − cos 2 φ ⎟ = cos 2φ (11.66b) 2 ⎝2 ⎠ 2 sMrab;krNI Nθ = 0 / mMu φ = 45o . dUcenH kugRtaMg shell EdlbNþalBIkMlaMg tangential Nθ sMrab; φ < 45o CakugRtaMgsgát; Edlkat;bnßysñameRbH. BIkarEbgEckkugRtaMg tangential Nθ eKGacsnñi- dæan)anfadMbUlrbs;GagsþúkmanlkçN³ flat ¬pleFob h' / d enAkñúgrUbTI 11>15(b) minRtUvFMCag 1 / 8 ¦ EdlebtugTaMgGs;nwgrgkugRtaMgsgát;EdlbNþalBI Nφ nig Nθ enAeBlEdlmMu φ < 51o 49' sMrab;kMlaMg meridianal nig 45o sMrab;kMlaMg tangential. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 713
  48. 48. T.Chhay viTüasßanCatiBhubec©keTskm<úCa dUcEdl)anerobrab;BIxagedIm RbePTTMrenARtg; springing ¬RbsinebIva restrained¦vanwgbegáIt RbtikmμminkMNt;EdlbgáeGayekItmankugRtaMgedaypÞal; nigkugRtaMgBt;enAkñúg shell Ek,r springing. dUcenH eKGacGnuvtþ bending theory sMrab; plate nig shell edIm,IkMNt;kugRtaMgBt;. xageRkamenH Cakarerobrab;BIkarsikSaKNna ring beam eRbkugRtaMgenARtg; springing edIm,IRbqaMgnwgbgÁúMkMlaMg sgát; meridional edk Nφ EdkeFVIeGayEKmrbs; dome cl½tcUlkñúg. Prestressed Concrete Circular Storage Tanks and Shell Roofs 714
  49. 49. Department of Civil Engineering NPIC BIsmIkar 11.65b nig11.66a eKGacsresrkMlaMg meridional Nφ sMrab;bnÞúkpÞal; wD kñúgmYy ÉktþaépÞ nigbnÞúkGefrBRgayesμI wL kñúgmYyÉktþaépÞRbeyal (unit projected area) ⎛ wD wL ⎞ N φ = − a⎜ ⎜ 1 + cos φ + 2 ⎟ ⎟ (11.67) ⎝ ⎠ Edl a = d / 2 sin φ CakaMrbs; sheall. cMNaMfakMlaMg (thrust) Nφ køayCakMlaMgbBaÄrRtg; springing ¬ φ = π / 2 ¦ én hemisphe- rical dome nigesμInwg W = a / 2(2 wD + wL ) kñúgmYyÉktþaTTwg. cMeBaHtMélepSgeTotrbs; φ / Nφ manlkçN³eRTt ehIyeKRtUvtMélénbgÁúMedkrbs;vasMrab;karsikSaKNna ring beam eRbkugRtaMgenA Rtg; springing EdleKGacehAfa shell rim. bgÁúMkMlaMgedkenHKW p = Nφ cosφ . RbsinebI P Ca kMlaMgeRbkugRtaMgkñúgmYykMBs;FñwmenAkñúg ring beam enaHBIsmIkar 11.1a P = pd / 2 ehIy P= d 2 ( Nφ cos φ ) (11.68) Cak;Esþg RbsinebIeKGacGnuvtþ P edaypÞal;eTAelI dome rim enaHeKGackMNt;kugRtaMgenA kñúg dome edaysmIkar 11.67. CaTUeTA vamingayRsYleT edaysareKRtUvkarEdkeRbkugRtaMgkñúg brimaNd¾eRcIn Edl P minGacsßitenAkñúgkMras;d¾esþIgrbs;CBa¢aMg)an ehIykugRtaMgenAkñúgebtugRtg; tMbn; rim GacmantMélx<s;Nas;. dUcenH eKRtUvkardak; edge beam EdlbMElg shell eGayeTAeRKOg bgÁúMkMNt;edaysþaTic kMraldMbYlekagminkMNt;edaysþaTiceRbkugRtaMg lkçxNÐRBMEdnd¾samBaØbMputEdlTTYl)anenAeBlEdlRbtikmμ edge beam manTisbBaÄr nig TMrminman restraint dUcbgðajenAkñúgrUbTI 11>16 Edl dome thrust Nφ qøgkat;TIRbCMuTMgn;rbs;Fñwm. RbsinebIeKkat;vatamExS A − A kMlaMgedk Nφ cosφ eFVIeGayEKm dome cl½tcUlkñúg)ancMgay Δs = d 2 Et ( Nθ − μNφ ) (11.69) Edl μ= pleFobB½rs‘ug ~ 0.2 sMrab;ebtug d = ElVg shell (shell aspan) GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 715
  50. 50. T.Chhay viTüasßanCatiBhubec©keTskm<úCa ehIyeKTTYl)ankMlaMgÉktþa tangential BIsmIkar 11.65 dUcxageRkam wD d ⎛ ⎞ wL d ⎜ 1 + cos φ − cos φ ⎟ − 4 sin φ (cos 2φ ) 1 Nθ = ⎜ ⎟ (11.70) 2 sin φ ⎝ ⎠ Rcasmkvij kMlaMg meridional Nφ eFVIeGay ring beam cl½tecjeRkA)ancMgay Nφ (cos φ )d 2 Δb = (11.71) 4 Ebh dUcenHeKRtUvmankMlaMgeRbkugRtaMgRKb;RKan;edIm,Icl½t ring beam cUlkñúgCamYynwgcMgaysrub ΔT = Δ s + Δ b dUcenHkMlaMgsrubEdlmanGMeBIelImuxkat; ring beam KW P= bh t ( Nθ − μNφ + 2 ) ( d Nφ cos φ ) (11.72) Edl h CakMBs; ring beam srub. kareRbobeFobrvagsmIkar 11.72 nig 11.68 bgðajfakMlaMgeRbkug RtaMgRbsiT§PaBEdlRtUvkarelIkmunmantMélFMCagkMlaMgeRbkugRtaMgRbsiT§PaBEdlRtUvkarelIkeRkay. TMhMénkarekIneLIgenHmanRbEhlBI 5% eTA10%. lkçxNÐdUcKñamanlkçN³Bit sMrab; dome EdlExS Prestressed Concrete Circular Storage Tanks and Shell Roofs 716
  51. 51. Department of Civil Engineering NPIC rbs;kMlaMgBI dome minkat;tamTIRbCMuTMgn;rbs; ring beam ehIyFñwmRtUv)anP¢ab;y:agrwgeTAnwgCBa¢aMg dUcenAkñúgrUbTI 11>17 (a). eKGacTTYltMélRbhal;RbEhlrbs;kMlaMgeRbkugRtaMgtMrUvkar P eday begáIntMélrbs; P enAkñúgsmIkar 11.68 cMnYn 10%. kñúgkrNIEbbenH kugRtaMgenAkñúg shell Rtg;tMbn; springing GacxusBIkugRtaMgEdlTTYl)anBI membrane solution y:agxøaMg ehIyeKRtUveFVIkarEktMrUv bending solution. RbsinebIkMlaMgeRbkugRtaMg radial edkenAkñúg ring beam mantMélFMCagtMrUvkar enaHkMhUcRTg; RTayedaysarkarBt;d¾FMnwgekItmanenAkñúg shell beam dUcbgðajenAkñúgrUbTI 11>17 (b) CamYynwg karekIneLIgéntMélrbs;kMlaMg tangential Nθ y:agxøaMg ebIeRbobeFobCamYynwgkarekIneLIgénkMlaMg meridional Nφ . CalT§pl kugRtaMgBt;enAkñúgebtugenARtg;tMbn;EdlT§iBlGacelIskugRtaMgGnuBaØat GtibrmaeRkamGMeBI service load. RbsinebI kMlaMgeRbkugRtaMgedImmuneBlrgkMhatbg;KW Pi enaHRk- LaépÞrbs;muxkat;FñwmKW Pi Ac = (11.73) fc Edl Pi = kMlaMgeRbkugRtaMgedIm P / γ GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 717
  52. 52. T.Chhay viTüasßanCatiBhubec©keTskm<úCa kugRtaMgsgát;GnuBaØatenAkñúgebtug fc = γ = PaKrykugRtaMgEdlenAesssl;. eKcg;rkSaeGaytMélrbs; f c mantMélTab Rbhak;RbEhlnwg 0.2 f 'c nigminelIs 800 psi eTA 900 psi eT edIm,IeFVIeGaybMErbMrYlrageFobd¾FMEdlekItmanenAkñúg edge ring beam mantMélGb,- brma EdlRtLb;mkvijeKGacbegáItkugRtaMgFMenAkñúg shell Rtg;tMbn; springing. RkLaépÞrbs;EdkeRbkugRtaMgenAkñúg dome ring KW Pi A ps = (11.74b) f pi Edl CakugRtaMgGnuBaØatenAkñúgEdkrgeRbkugRtaMgmuneBlxatbg;. RbsinebIeKminRtUvkarkMNt; f pi A ps CatMélsuRkit enaHeKGacykRkLaépÞEdkeRbkugRtaMg W cot φ A ps = (11.74b) 2πf pe Edl W= bnÞúkefr nigbnÞúkGefrsrubenAelI dome EdlbNþalBI wD + wL f pe = eRbkugRtaMgRbsiT§PaBeRkayeBlkMhatbg; eKGacykkMras;Gb,bramrbs; dome EdlRtUvkaredIm,ITb;Tl; buckling dUcxageRkam 1.5 pu hd = a (11.75) φβ i β c Ec Edl a= kaMrbs; dome shell pu = sMBaFKNnaÉktþaBRgayesμI ultimate EdlbNþalBIbnÞúkefr nigbnÞúkGefr = (1.2 D + 1.6 L ) / 144 φ= emKuNkat;bnßyersIusþg;sMrab;sMPar³EdlrgkugRtaMgsgát; = 0.65 β i = emKuNkat;bnßy buckling sMrab;bMErbMrYlrbs;épÞragEsV‘rEdlbNþalBIPaBminl¥ β i = (a / ri )2 / Edl ri ≤ 1.4a β c = emKuNkat;bnßy buckling sMrab; creep/ sMPar³Edl nonlinearity nigsñameRbH = 0.44 + 0.003WL / b:uEnþminFMCag 0.53 . Ec = m:UDuleGLasÞicedImrbs;ebtug = 57,000 f 'c psi (4,700 f 'c MPa ) Prestressed Concrete Circular Storage Tanks and Shell Roofs 718
  53. 53. Department of Civil Engineering NPIC 11.10. GagebtugeRbkugRtaMgEdlmanEdkeRbkugRtaMgvNÐ Prestressed Concrete Tanks with Circumferential Tendons CMnYseGaykarrMuEdkeRbkugRtaMg (wire or strand) dUcEdl)aneFVIenAkñúg preload system eKeRbI EdkeRbkugRtaMg (tendons) edkxagkñúg b¤xageRkA. kabeRbkugRtaMgTaMgenHrgkugRtaMgeRkayeBleK dak;BYkvaenAkñúgCBa¢aMg. Edk post-tensioning bBaÄrRtUv)aneKeRbIkñúgCBa¢aMgCaEpñkmYyénEdkBRgwg bBaÄr. CBa¢aMgebtugGaccak;enAnwgkEnøg b¤cak;Rsab; ehIyeKcat;TuksñÚlCBa¢aMgCaEpñkmYyénCBa¢aMg ebtugEdlrgeRbkugRtaMgvNÐ. RbePTsMNg;enHminmaneRbIEdk diaphragm dUcRbePTGagEdlrMuEdk eRbkugRtaMg ( wrapped-wire prestressing) EdlCBa¢aMgGagGacman b¤k¾KμanEdk diaphragm. EdkEdlrgeRbkugRtaMgxagkñúgRtUv)ankarBaredaykMras;ebtugkarBardUctMrUvkarrbs; ACI 318 ehIyeKRtUvbMeBjkñúgbMBg; (duct or sheathing) CamYynwgsMPar³EdlkarBarERcH b¤ grouted. eKRtUv karBarEdk bonded post-tensioned eday portland cement grout dUckarTamTarenAkñúg ACI 318 ehIyeKRtUvkarBarkabeRbkugRtaMgxageRkACamYynwg shotcrete cover EdlmankMras;Gb,brma 1in. (25mm ) . dMeNIrkarsikSaKNnaCBa¢aMgmanlkçN³RsedogKñanwgkarsikSaKNnaGagragmUlEdlrgeRbkug RtaMgedaykarrMuEdkeRbkugRtaMg ehIyvaTamTarnUvkarRtYtBinitüsñameRbHdUcKña. eKRtUvykkugRtaMg sgát;esssl;Gb,brmaenAkñúgebtugCBa¢aMgeRkayeBlrgkMhatbg;eRbkugRtaMgTaMgGs;esμInwg 200 psi (1.4MPa ) kñúgkarsikSaKNna enAeBlEdlGagRtUv)anbMeBjdl;nIv:UKNna. RbsinebIGagKμanKMrb eK RtUvykkugRtaMgesssl;enAcugCBa¢aMgesμInwg 400 psi(2.8MPa ) Edlkat;bnßyCaragbnÞat;rhUtdl; tMélmYyEdlmintUcCag 200 psi enAcMgay 0.6 Rh BIcugénnIv:UsarFaturav. RbePT)atCBa¢aMg nigtMNdMbUgragekag BIkarerobrab;xagelI eyIgeXIjy:agc,as;falkçxNÐRBMEdnenARtg;)atrbs;GageRbkugRtaMgrag mUl nigenARtg; ring beam support sMrab;dMbUgragekagkMNt;nUvlkçN³énkarGnuvtþ lkçN³esdækic© nigeCaKC½yénkarsikSaKNnaTaMgmUl. Cavi)ak bTBiesFn_CaeRcInEdlTTYl)anBIkarbegáIttMNeRkam lkçxNÐTaMgenHKWmantMélxøaMgNas;. karlMGitBItMNRtUv)anbgðajenAkñúgrUbTI 11>18 dl;TI 11>22. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 719
  54. 54. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 720
  55. 55. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 721
  56. 56. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 722
  57. 57. Department of Civil Engineering NPIC 11.11. Step-by-Step Procedure for the Design of Circular Prestressed Concrete Tanks and Dome Roofs viFIsakl,g nigEktMrUv (trial-and adjustment procedure) RtUv)anENnaMsMrab;karsikSaKNna GagragmUlebtugeRbkugRtaMg nigdMbUg shell³ !> eRCIserIsRbB½n§eRbkugRtaMg RbePTEdkeRbkugRtaMg ersIusþg;ebtug nigRbePTTMr EdleyIgGac rk)anenAkñúgtMbn;. @> kMNt;sMBaFsMPar³EdlsþúkkñúgGagmanGMeBIelICBa¢aMg γH sMrab;sarFaturav nig p sMrab;sarFatu GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 723
  58. 58. T.Chhay viTüasßanCatiBhubec©keTskm<úCa ]sμ½n. eRbIkarBRgayragctuekaNBñaysMrab;GgÁFaturwgEdlpÞúkenAxagkñúgGag. kMNt;kMlaMg ring Éktþa F = γ (H − y )r sMrab;)atrGileBjelj Edl r CakaMGag nig y Ca cMgayBI)at. #> BItarag 11>4 dl; 11>16 eRCIserIsemKuNm:Um:g;bBaÄreTAtamRbePTbnÞúk niglkçxNÐ restraint rbs;)atEdlbNþaledaysMBaFsarFaturav My =+ 1 [βM oφ (βy ) + Qoζ (βy )] β nigkMNt;kMlaMgTaj ring radial edk γrt Qo = +(2 βH − 1) ( ) 12 1 − μ 2 ehIy Q = (F − ΔQ ) EdlbMErbMrYlén y y 6( − μ ) 2 ΔQ = + 1 y (βM Ψ (βy ) + Q θ (βy )) o o β 3 rt 2 nig β = [3(1 − μ )] 2 1/ 4 (rt )1 / 2 Edl μ = 0.2 sMrab;ebtug. $> kMNt;emKuN membrane C BItarag 11>4 rhUtdl; 11>16. KNnakMlaMg ring F = CγHr . %> KNnam:Um:g;bBaÄreRKaHfñak;enAkñúgCBa¢aMgEdleRbIemKuN membrane C . smIkarsMrab;m:Um:g; EdlbNþalBIbnÞúksarFaturavKW M y = C (γH 3 + pH 2 ) b¤ M y = CpH 2 EdlbNþalBIbnÞúk]sμn½. KNnam:Um:g;enARtg;)at nigRtg;cMnuceRKaHfñak;EdlmancMgay y BI)at. ^> eRCIserIskMlaMgeRbkugRtaMgbBaÄr. &> KNnakugRtaMgebtugkat;tamkMras;rbs;CBa¢aMgsMrab;lkçxNÐGagTeT nigsMrab;GageBj. eKGnuBaØatkugRtaMgsgát;tamG½kSesssl;Gtibrma f cv = 200 psi eRkamGMeBIr service load ehIykugRtaMgTajGtibrma f t = 3 f 'c dUcbgðajenAkñúgtarag 11>17. *> sikSaKNnaEdkeRbkugRtaMgedk nigEdkeRbkugRtaMgbBaÄrEdlkugRtaMgkMNt;manenAkñúgtarag 11>18. (> KNnam:Um:g;emKuN M u EdleRbIemKuNbnÞúkEdleGayenAkñúgEpñk 11.7.2. m:Um:g;tMrUvkar M n = M u / φ Edl φ = 0.9 . KNnaersIusþg;m:Um:g; nominal EdlGacman M n = A ps f ps (d p − a / 2 ) Prestressed Concrete Circular Storage Tanks and Shell Roofs 724
  59. 59. Department of Civil Engineering NPIC b¤ M n = Aps f ps (d p − a / 2)+ As f y (d − a / 2) . m:Um:g;EdlGacman M n RtUvEtFMCag b¤esμInwg m:Um:g;tMrUvkar M n . !0> sikSaKNnaRbEvg L rbs; ring enARtg;)atrbs;CBa¢aMgBIsmIkar 2CH 2 L = 2 1+ (t / h )3 (dt )2 Edl t CakMras;rbs;CBa¢aMg nig h CakMras;rbs;kMral)at. !!> KNnaPaKryrbs;eRbkugRtaMgenAkñúg)atEdlRtUvepÞreTACBa¢aMgBIrUbmnþ 1 R= 1+ S Edl S = 1.1(h / t )× (d / t )1 / 2 . enAeBlEdl rim xageRkArbs; slab ring rgkMlaMgsgát;edaykMlaMg radial Rtg; rim enaHtMél rbs; S RtUv)anEksMrYleTACa 1/ 2 1 ⎛ h ⎞⎛ d ⎞ S1 = ⎜ ⎟⎜ ⎟ K ⎝ t ⎠⎝ t ⎠ ⎛d2 +d2 ⎞ Edl K =⎜ o ⎜d −d 2 2 −μ⎟ ⎟ ⎝ o ⎠ EdlkñúgenH Ggát;p©itxagkñúg do = d = Ggát;p©itkMral ring xagkñúg = d o − 2 L . !@> RtYtBinitütMrUvkarkMras;CBa¢aMgGb,brma nigKNnaPaBdab radial eGLasÞicedImEdlKμanTb; (unrestrained initial elastic radial deflection) Fi r Δi = t co Ec E;dl ( Ec = 57,000 f 'c psi 4,700 f 'c MPa ) t co = kMras;rbs;sñÚlCBa¢aMgenARtg;cug b¤)atrbs;CBa¢aMg d r= 2 PaBdab radial cugeRkay Δ f = 1.7Δ i . !#> f<k;EdkBI)ateTACBa¢aMgEbbNaedayeGayEdkbgðÜscUleTAkñúgCBa¢aMgcMgay y2 = 1.8 rtco b¤ 3 ft.(0.9m) edayykmYyNaEdlFMCag. dUcKña eKRtUvFanafaEdkbBaÄr nominal Gb,brma enARtg;tMbn;)atKW GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 725
  60. 60. T.Chhay viTüasßanCatiBhubec©keTskm<úCa As = 0.005t co !$> epÞógpÞat;TMhMsñameRbHGtibrma wmax = 4.1×10−6 ε ct E ps I x Edl ε ct = bMErbMrYlrageFobépÞrgkarTajenAkñúgebtug = (λt f p )/ E ps f p = kugRtaMgCak;EsþgenAkñúgEdk f pi = eRbkugRtaMgedImmuneBlxatbg; λt ~ f p / f pi 8 ⎛ s 2 s1tb ⎞ I x = grid index = ⎜ ⎟ π ⎜ φ1 ⎝ ⎟ ⎠ KMlatEdkkñúgTis “1” s1 = φ1 = Ggát;p©itrbs;EdkenAkñúgTis “1” s 2 = KMlatEdkkñúgTis “2” tb = kMras;karBarEdkEdlKitdl;p©itrbs;Edk cMNaMfa TTwgsñameRbHGnuBaØatGtibrma wmax = 0.004in. sMrab;GagsþúksarFaturav. !%> sikSaKNnadMbUgragekageRkaykareRCIserIsRbePTtMNenARtg;cugrbs;CBa¢aMgGag. kMNt;pl eFobénkMBs;rbs;dMbUgragekag h' elI)at d rbs;vay:agNamineGay h' / d > 1/ 8 . KNnakMlaMgeRbkugRtaMg radial tamTisedktMrUvkar P sMrab; edge beam BIsmIkar bh P= (Nθ − μNθ ) + φ d N cos φ ( )] t 2 w d ⎡ 1 ⎤ w d Edl Nθ = D ⎢ 2 sin φ ⎣1 + cos φ − cos φ ⎥ − L (cos 2φ ) ⎦ 4 sin φ ⎛ wD wL ⎞ N φ = − a⎜ ⎜ 1 + cos φ + 2 ⎟ ⎟ ⎝ ⎠ nig kMBs;srubrbs;Fñwm rim h= b = TTwgFñwm rim wD = GaMgtg;sIueténbnÞúkpÞal;rbs; shell kñúgmYyÉktþaépÞ ¬bnÞúkefr¦ wL = GaMgtg;sIuetrbs;bnÞúkGefrRbeyal !^> KNnamuxkat; ring-edge beam Pi Ac = fc Prestressed Concrete Circular Storage Tanks and Shell Roofs 726
  61. 61. Department of Civil Engineering NPIC Edl kMlaMgeRbkugRtaMgedIm = P / γ Pi = γ = PaKrykugRtaMgesssl; f c = kugRtaMgsgát;GnuBaØatenAkñúgebtug ¬minRtUvFMCag 0.2 f 'c ¦ b:uEnþminRtUvFMCag 800 ~ 900 psi enAkñúg edge beam. !&> KNnaRkLaépÞrbs;EdkeRbkugRtaMgrbs; edge beam Pi A ps = f si Edl f si CakugRtaMgGnuBaØatenAkñúgEdkeRbkugRtaMgmuneBlxatbg; b¤ W cot φ A ps = 2πf pe RbsinebIeKminviPaKedaysuRkit. kñúgtYcugeRkay W CabnÞúksrubefr nigGefrenAelIdMbUgrag ekag EdlbNþalBI wD + wL nig f pe CaeRbkugRtaMgRbsiT§PaBeRkayeBlxatbg;. !*> RtYtBinitükMras;kMraldMbUgekagGb,brmaEdlRtUvkaredIm,ITb;Tl;nwg buckling 1 .5 p u hd = a φβ i β c Ec Edl a= kaMrbs; dome shell pu = sMBaFKNnaÉktþaBRgayesμI ultimate EdlbNþalBIbnÞúkefr nigbnÞúkGefr = (1.2 D + 1.6 L ) / 144 φ= emKuNkat;bnßyersIusþg;sMrab;sMPar³EdlrgkugRtaMgsgát; = 0.65 β i = emKuNkat;bnßy buckling sMrab;bMErbMrYlrbs;épÞragEsV‘rEdlbNþalBIPaBminl¥ β i = (a / ri )2 / Edl ri ≤ 1.4a β c = emKuNkat;bnßy buckling sMrab; creep/ sMPar³Edl nonlinearity nigsñameRbH = 0.44 + 0.003WL / b:uEnþminFMCag 0.53 . Ec = m:UDuleGLasÞicedImrbs;ebtug = 57,000 f 'c psi (4,700 f 'c MPa ) rUbTI 11>23 bgðajBI step-by-step flowchart sMrab;CMhanEdlENnaMkñúgkarsikSaKNnaGag ebtugeRbkugRtaMgragmUl nigdMbUgragekagrbs;va. GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 727
  62. 62. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 728
  63. 63. Department of Civil Engineering NPIC GagsþúkragmUl nigdMbUlekagebtugeRbkugRtaMg 729
  64. 64. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Prestressed Concrete Circular Storage Tanks and Shell Roofs 730

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