Weitere ähnliche Inhalte Ähnlich wie Xi. prestressed concrete circular storage tanks and shell roof (16) Xi. prestressed concrete circular storage tanks and shell roof1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
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. 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. 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
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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 686
22. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 688
24. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 690
26. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 692
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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 696
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 720
56. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 722
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. 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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 728
64. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Prestressed Concrete Circular Storage Tanks and Shell Roofs 730