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I. basic concepts

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  • 1. NPIC I. KMniteKal Basic Concepts 1> esckþIepþIm Introduction ebtugmanersIusþg;xøaMgkñúgkarsgát; b:uEnþmanersIusþg;exSaykñúgkarTaj ¬EdlenAcenøaHBI 8% eTA 12% énersIusþg;sgát;¦. edaysarersIusþg;rgkarTajtUcEbbenH sñameRbHEdlekItBIkarBt;nwgekIt manenAdMNak;kaldMbUgénkardak;bnÞúk. edIm,Ikat;bnßy b¤karBarmineGaymansñameRbHenH eKRtUv GnuvtþkMlaMgcMp©it b¤cakp©ittamTisbeNþayrbs;Ggát;eRKOgbgÁúM. dUcenHkMlaMgenH)anbegáInersIusþg; kñúgkarBt; ersIusþg;kñúgkarkat; nigersIusþg;kñúgkarrmYlrbs;muxkat;. bnÞab;mkmuxkat;GaceFVIkarCa lkçN³eGLasÞic ehIymuxkat;manersIusþg;rgkarsgát;esÞIrEteBjenAeBlEdlbnÞúkTaMgGs;manGMeBI mkelIeRKOgbgÁúM. eKal KMnit 1
  • 2. T.Chhay kMlaMgEdleKGnuvtþtamTisbeNþayenHRtUv)aneKeGayeQμaHfa kMlaMgeRbkugRtaMg (prestres- sing force). kMlaMgeRbkugRtaMgCakMlaMgsgát;tamTisbeNþayrbs;Ggát;EdleFVIeGaymuxkat;rg kugRtaMgmunnwgGgát;rgbnÞúkefr nigbnÞúkGefr. eKkMNt;RbePTkMlaMgeRbkugRtaMg nigGaMgtg;sIuetrbs; vaedayQrelIRbePTénsMNg; RbEvgElVg nigPaBrlas; (slenderness). rUbTI 1>1 bgðajBITMrg;rbs; kMlaMgeRbkugRtaMgBIrRbePT. k> eRbobeFobCamYynwgebtugGarem: Comparison with Reinforced Concrete EdkenAkñúgebtugGarem:min)anGnuvtþkMlaMgrbs;vaeTAelIGgát;eT EdlpÞúyBIGMeBIrbs;EdkeRbkug RtaMg. enAeBlEdlkugRtaMgTajedaykarBt;FMCagersIusþg;Tajrbs;ebtug ebtugeRbkugRtaMgcab;epþIm eFVIkarCaebtugGarem:. edayRKb;RKgbrimaNrbs;kMlaMgeRbkugRtaMg eKGaceFVIrcnasm<½n§Ca flexible b¤ rigid eday minmanT§iBlelIersIusþg;rbs;vaeT. eKBi)aknwgTTYl)annUvlkçN³ flexible enAkñúgebtugGarem:Nas; RbsinebIeKcg;TTYl)anlkçN³esdækicx<s;. x> lkçN³esdækic©rbs;ebtugeRbkugRtaMg Economics of Prestressed Concrete Ggát;ebtugeRbkugRtaMgmankMBs;TabCagGgát;ebtugGarem:sMrab;RbEvg niglkçxNÐénkardak; bnÞúkdUcKña. CaTUeTAkMBs;rbs;Ggát;ebtugeRbkugRtaMgsßitenAcenøaH 65% eTA 80% énkMBs;rbs;ebtug Garem:. dUcenHvaRtUvkarebtugticCagGgát;ebtugGarem:BI 20% eTA 35% EtkarsnSMsMécbrimaNeb- tugenHmantulüPaBCamYynwgtMéld¾x<s;rbs;sMPar³EdlmanKuNPaBl¥EdlRtUvkarkñúgkarrgeRbkug- RtaMg. edaysarragFrNImaRt Ggát;ebtugeRbkugRtaMgmanBum<sμúKsμajCagebtugGarem:. eTaHbIvamantMélbEnßmCaeRcInk¾eday EtRbsinebIeKplitvaeRcIntMélrbs;vaminsUvCaxusKñaeT. eRKOgbgÁúMebtugeRbkugRtaMgRtUvkartMEhTaMticCaeRKOgbgÁúMebtugGarem: edaysarkarRtYtBinitüKuNPaB ebtug)anl¥Cag nigRKwHrbs;vaRTnUvTMgn;pÞal;tUcCag. enAeBlEdlFñwmebtugGarem:manRbEvgFMCag 21m vanwgmanTMgn;pÞal;FMNas; EdleFVIeGayva manPaBdabry³eBlyUr nigsñameRbHFM. dUcenHsMrab;FñwmEdlmanRbEvgEvg eKniymeRbIebtugeRbkug RtaMg edaysarFñwmragFñÚmantMéléføkñúgkarsagsg; nigmü:aeTotvaeFVIkarmin)anl¥edaysarvargnUv Basic Concept 2
  • 3. NPIC long-term shrinkage nig creep. sMrab;s<anEdlmanElVgEvg²dUcCa segmental bridge b¤ cable- stayed bridge eKeRbIEtebtugeRbkugRtaMgb:ueNÑaH. 2> Rbvtþirbs;ebtugeRbkugRtaMg Historical Development of Prestressing ebtugeRbkugRtaMgminEmnCabec©keTsfμIeT enAqñaM 1872 visVkr P. H. Jackson EdlmkBI California TTYl)annUvnIyb½RttkákmμsMrab;karrkeXIjRbB½n§eRbkugRtaMgedayeRbI tie rod edIm,I begáItFñwm b¤FñÚBIdMubøúkdac;²BIKña ¬emIlrUbTI 1>1 a¦. enAqñaM 1888 visVkrsBa¢atiGaLWm:g; C. W. Doehring TTYl)annIyb½RttkákmμsMrab;kareRbIRbB½n§eRbkugRtaMgenAkñúgkMraledayeRbI metal wire. b:uEnþsMrab;kareRbIR)as;elIkdMbUgenHminsUvTTYl)aneCaKC½yeT edaysarkMhatbg;eRbkugRtaMgGaRs½y nwgeBl. eRkaymkenAedImstvtSTI20 J. Lund mkBI Norway nig G.R. Steiner mkBIshrdæ)an BüayamedIm,IedaHRsaybBaðaenH EtminTTYl)anlT§pleT. kñúgGMLúgeBld¾yUrCamYynwgkarvivDÆd¾tictYcedaysarminTan;rkeXIjnUvEdlersIusþg;x<s;Edl GacykQñHkMhatbg;eRbkugRtaMg R. E. Dill )anrkeXIjnUvT§iBlrbs; shrinkage nig creep rbs;ebtugeTAelIkMhatbg;rbs;eRbkugRtaMg. dUcenHKat;)anrkeXIjnUv post-tensioning én unbonded rod EdlGacTUTat;nwgkMhatbg;kugRtaMgGaRs½ynwgeBlenAkñúgEdk EdlekItBIkarkat;bnßy RbEvgrbs;Ggát;edaysar creep nig shrinkage. enAedImTsvtS 1920 W. H. Hewett )anbegáIt nUveKalkarN_ circular prestressing EdleRbICamYynwgGagsþúkTwk b¤vtßúravEdlmanragmUl. visVkr)araMg Eugene Freyssinet )anesñInUvkareRbIR)as; high-strength steel nig high- ductility steel edIm,IykQñHnUvkMhatbg;eRbkugRtaMgkñúgcenøaHqñaM 1926 dl; 1928. bc©úb,nñeKeRbIebtugeRbkugRtaMgsMrab;sMNg;GaKar sMNg;dI s<anEdlmanElVgEvg².l. 3> eKalKMniténebtugeRbkugRtaMg Basic Concepts of Prestressing k> esckþIepþIm Introduction kMlaMgeRbkugRtaMg P EdlbMeBjlkçxNÐragFrNImaRt niglkçxNÐdak;bnÞúkrbs;Ggát;RtUv)an kMNt;edayeRbIeKalkarN_emkanik nigTMnak;TMngkugRtaMg-sac;lUteFob ¬rUbTI 1>2¦. eBlxøHeKRtUv karsnμt;eGayFñwmebtugeRbkugRtaMgCa homogeneous nigeGLasÞic. eKal KMnit 3
  • 4. T.Chhay enAkñúgrUbTI 1>2 (a) bgðajBIFñwmctuekaNTMrsamBaØrgnUvkMlaMgeRbkugRtaMgcMp©it P . muxkat; FñwmrgnUvkugRtaMgsgát;esμIKW P f =− (1.1) Ac Edl Ac = bd CaRkLaépÞrbs;muxkat;FñwmEdlmanTTwg b nigkMBs;srub d . sBaØadkRtUv)aneRbI sMrab;kugRtaMg b¤kMlaMgsgát; nigsBaØabUksMrab;kugRtaMg b¤kMlaMgTaj. RbsinebImankMlaMgTTwgG½kS (transverse load) GnuvtþeTAelIFñwm enaHkugRtaMgEdl)anm:Um:g; Gtibrma M EdlekItmanenAkNþalElVgKW P Mc ft =− − (1.2a) Ac I g Basic Concept 4
  • 5. NPIC nig fb = − P Mc + Ac I g (1.2b) Edl ft = kugRtaMgenAsrésxagelIbMput f b = kugRtaMgenAsrésxageRkambMput c = h sMrab;muxkat;ctuekaN 1 2 3 m:Um:g;niclPaBrbs;muxkat;TaMgmUl ¬sMrab;muxkat;ctuekaN = bh ¦ Ig = 12 BIrUbTI 1>2 (b) eyIgeXIjfaersIusþg;rgkarsgát;rbs;FñwmedIm,ITb;nwgkMlaMgxageRkARtUv)ankat; bnßyedaykMlaMgeRbkugRtaMgcMp©it. edIm,Ikat;bnßykugRtaMgTajenAsrésxagelIbMput eKRtUvdak; prestressing tendon BIeRkamG½kSNWtsMrab;muxkat;kNþalElVg ¬rUbTI 1>2 (c) nig (d)¦ . RbsinebIeK dak; tendon enAcMNakp©it e BITIRbCMuTMgn;rbs;muxkat; eKTTYl)anm:Um:g; Pe eFobnwgG½kS cgc ehIy kugRtaMgenAkNþalElVgkøayCa P Pec Mc ft =− + − (1.3a) Ac Ig Ig nig fb = − P Pec Mc Ac − Ig + Ig (1.3b) edaysarmuxkat;enARtg;TMrsamBaØminrgm:Umg;Edl)anBIbnÞúkTTwgG½kSxageRkA enaHsrésxag : elIbMputrbs;muxkat;GacrgkugRtaMgTajFMedaysarkMlaMgeRbkugRtaMgcakp©it. edIm,IkMritkugRtaMgenH eKRtUvdak; prestressing tendon CamYynwgcMNakp©ittUcCagcMNakp©itenAkNþalElVg b¤GacsßitenAelI G½kS cgc . x> Basic Concept Method enAkñúg basic concept method eKkMNt;kugRtaMgénsrésxageRkAbMputrbs;muxkat;ebtug eRbkugRtaMgedaypÞal;BIkMlaMgeRbkugRtaMgEdlGnuvtþtambeNþayG½kS nigbnÞúkTTwgG½kS. RbsinebI Pi CakMlaMgeRbkugRtaMgedImmunkMhatbg; nig Pe CakMlaMg eRbkugRtaMgRbsiT§PaBeRkaykMhatbg; enaH Pe γ= Pi Edl γ = emKuNeRbkugRtaMgenAsl; (residual prestress factor). edayCMnYs r 2 = I g / Ac ¬Edl r CakaMniclPaBénmuxkat;TaMgmUl¦ enaHeyIg)ansmIkardUcxageRkam³ a. manEtkMlaMgeRbkugRtaMg eKal KMnit 5
  • 6. T.Chhay Pi ⎛ ect ⎞ ft =− ⎜1 − 2 ⎟ (1.4a) Ac ⎝ r ⎠ P ⎛ ec ⎞ f b = − i ⎜1 + 2b ⎟ (1.4b) Ac ⎝ r ⎠ Edl ct nig cb CacMgayBITIRbCMuTMgn;rbs;muxkat; (G½kS cgc ) eTAsrésxagelIbMput nig xageRkambMput erogKña. b. kMlaMgeRbkugRtaMgrYmnwgTMgn;pÞal; RbsinebITMgn;pÞal;rbs;FñwmbegáItm:Um:g; M D enARtg;muxkat;EdlBicarNa smIkar 1.4a nig 1.4b køayCa Pi ⎛ ect ⎞ M D ft =− ⎜1 − 2 ⎟ − t (1.5a) Ac ⎝ r ⎠ S P ⎛ ec ⎞ M f b = − i ⎜1 + 2b ⎟ + D (1.5b) Ac ⎝ r ⎠ Sb Edl S t nig Sb Cam:UDulénmuxkat;sMrab;srésxagelIbMput nigxageRkambMput erogKña. rUbTI 1>3 bgðajBIKnøgrbs;EdkeRbkugRtaMg. rUbTI 1>3 (a) bgðajBIKnøgrbs;EdkeRbkugRtaMg kñúgTMrg; harped EdlRtUv)aneKeRbIenAkñúg pretensioned beam nigsMrab;bnÞúkTTwkG½kSmanGMeBIcMcMnuc. rUbTI 1>3 (b) bgðajBIKnøgrbs;EdkeRbkugRtaMgkñúgTMrg; draped EdlRtUv)aneKeRbIenAkñúg post- tensioning beam. Basic Concept 6
  • 7. NPIC bnÞab;BIkarsagsg; nigkartMeLIgkMralehIy eRKOgbgÁúMrgbnÞúkGefrEdlbegáIt)anCam:Um:g; M s . CaTUeTA GaMgtg;sIueteBjeljrbs;bnÞúkenHekItmanbnÞab;BIsMNg;RtUv)ansagsg;rYcral; ehIykMhat eKal KMnit 7
  • 8. T.Chhay bg;GaRs½ynwgeBlkñúgebtugeRbkugRtaMgekIteLIgrYcehIy. dUcenH kMlaMgeRbkugRtaMgCakMlaMgeRbkug RtaMgRbsiT§PaB Pe . RbsinebIm:Um:g;srubEdlbNþalBIbnÞúkTMnajCa M T enaH M T = M D + M SD + M L (1.6) Edl m:Um:g;EdlbNþalBITMgn;pÞal; MD = M SD = m:Um:g;EdlbNþalBIbnÞúkefr M L = m:Um:g;EdlbNþalBIbnÞúlGefr ehIysmIkar 1.5 nwgkøayCa Pe ⎛ ect ⎞ M T ft =− ⎜1 − 2 ⎟ − t (1.7a) Ac ⎝ r ⎠ S P ⎛ ecb ⎞ M f b = − e ⎜1 + 2 ⎟ + T (1.7b) Ac ⎝ r ⎠ Sb rUbTI 1.4 bgðajBIKMrUénkarBRgaykugRtaMgenAelImuxkat;mansøabeRKaHfñak;rbs;Ggát;eRbkug RtaMg. eKminGnuBaØateGaykugRtaMgTajenAkñúgebtugenAelIsrésxageRkAbMputrbs;muxkat;FMCagkug RtaMgGnuBaØatGtibrmaEdleGayedaybTdæaneT ¬dUcCa ft = 0.5 f 'c enAkñúg ACI Code¦. Rb sinebIvaFMCagtMélGnuBaØat eKRtUvdak;EdkBRgwgminEmneRbkugRtaMgeTAtamsmamaRtedIm,ITb;Tl;nwg kMlaMgTajsrubEdlmankñúgeKalbMNgRKb;RKgsñameRbHenAdMNak;kalrgbnÞúkeFIVkar. K> C-Line Method sMrab; C-Line method b¤ line-of-pressure concept b¤ thrust concept FñwmebtugeRbkugRtaMg RtUv)aneKsnμt;CaFñwmebtugsuT§eGLasÞic ehIyeKviPaKvaedayeRbIeKalkarN_eKalrbs;sþaTic. eKcat; TukkMlaMgeRbkugRtaMgCakMlaMgsgát;xageRkA CamYynwgkMlaMgTajefr T enAkñúg tendon. eKeRbIsmI- karlMnwg ∑ H = 0 nig ∑ M = 0 edIm,IrkSalMnwgrbs;muxkat;. rUbTI 1>5 bgðajBIkareRbobeFobExSskmμénkMlaMgsgát; C nigkMlaMgTaj T enAkñúgebtug Garem: nigebtugeRbkugRtaMg. édXñas; a sMrab;ebtugeRbkugRtaMgmantMélefr EtvaERbRbYlBIsUnüenA eBlrgeRbkugRtaMgeTAtMélGtibrmaenAeBlEdlvarg bnÞúkxageRkAeBjeljsMrab;ebtugeRbkugRtaMg. BIdüaRkamGgÁesrIrbs;kMNt;FñwmEdlbgðajenAkñúgrUbTI 1>6 eyIg)an M = Ca = Ta (1.8) e' = a − e (1.9a) edaysar C = T / a = M / T eK)an Basic Concept 8
  • 9. NPIC M e' = −e (1.9b) T BIrUbeyIg)an C Ce' ct ft =− − (1.10a) Ac Ig C Ce' cb fb = − + (1.10b) Ac Ig b:uEnþenAkñúg tendon kMlaMg T esμInwgkMlaMgeRbkugRtaMg Pe dUcenH Pe Pe e' ct ft =− − (1.11a) Ac Ig Pe Pe e' cb fb = − + (1.11b) Ac Ig eKal KMnit 9
  • 10. T.Chhay edaysar I c = Ac r 2 enaHeyIgGacsresrsmIkar 1.11a nig b dUcxageRkam Pe⎛ e' ct ⎞ ft =− ⎜1 + 2 ⎟ (1.12a) Ac⎝ r ⎠ P ⎛ e' c ⎞ f b = − e ⎜1 − 2b ⎟ (1.12b) Ac ⎝ r ⎠ smIkar 1.12 a nig b nigsmIkar 1.7 a nig b RtUveGaytMélkugRtaMgenAsrésxageRkAdUcKña. X> Load-Balancing Method eKGacKNna nigviPaKFñwmebtugeRbkugRtaMgedayeRbI load-balancing method EdlbegáIt eday Lin. viFIenHEp¥kelIkareRbIR)as;kMlaMgtamTisQrrbs;EdkeRbkugRtaMgEdlmanTMrg; draped b¤ harped edIm,ITb;Tl;nwgbnÞúkTMnajEdlmanGMeBIelIGgát;. rUbTI 1>7 bgðajBIkMlaMglMnwg (balancing forces) sMrab;FñwmebtugebkugRtaMgEdlmanEdkeRbkugRtaMgTMrg; draped nig harped. kMlaMglMnwg Rbtikmμ R esμInwgbgÁúMkMlaMgbBaÄrrbs;kMlaMgeRbkugRtaMg P . bgÁúMkMlaMgedkrbs;kMlaMgeRbkugRtaMg P mantMélesμInwgkMlaMg P eBjEtmþgsMrab;karKNnakugRtaMgsrésxageRkArbs;ebtugEdlenAkNþal ElVgsMrab;FñwmTMrsamBaØEdlmanRbEvgEvg. sMrab;muxkat;déTeTot eKeRbIbgÁúMkMlaMgedkrbs;kMlaMg P Cak;Esþg. Basic Concept 10
  • 11. NPIC A. Loading-Balancing Distributed Loads and Parabolic Tendon Profile BIrUbTI 1>8 eyIgGacsresrGnuKmn_)a:ra:bUldUcxageRkamsMrab;tMNageGayTMrg;rbs; tendon Ax 2 + Bx + C = y (1.13) sMrab; x = 0 eyIgman y = 0 dUcenH C = 0 ehIy dy = 0 dUcenH B = 0 dx sMrab; x = l / 2 eyIg)an y = a dUcenH A = 42a l ∂ y 2 eyIgman q =T 2 ∂x (1.14) eFVIDIepr:g;EsülBIrdgeTAelIsmIkar 1.13 ehIyCMnYs ∂ 2 y / ∂x 2 eTAkñúgsmIkar 1.14 eyIg)an 4a 8Ta q =T 2 ×2 = (1.15a) l l2 ql 2 b¤ T= 8a (1.15b) ql 2 Ta = (1.15c) 8 dUcenH RbsibebI tendon manTMrg;)a:ra:bUlehIykMlaMgeRbkugRtaMgRtUv)ansMKal;eday P enaH balanced-load Edl)anBIsmIkar 1.15a køayCa 8 Pa wb = (1.16) l2 BIrUbTI 1>9 bnÞúkTTwgG½kS wb BIrEdlmantMélesμIKña TisedApÞúyKña)anTUTat;KñaGs; dUcenHmin mankugRtaMgBt;ekIteLIgeT. edaysar T = C dUcenHeyIgGacCMnYs C eTAkñúg T )an. eday sarKμanm:Um:g;Bt; FñwmenArkSaPaBRtg; edayminmanragekag b¤ptenAépÞxagelIbMput. kugRtaMgsrésxageRkAbMputrbs;ebtugeBjkMBs;rbs;muxkat;EdlenAkNþalElVgKW eKal KMnit 11
  • 12. T.Chhay P' C f bt = − =− (1.17) Ac Ac kugRtaMgenHmantMélefr ehIykMlaMg P' = P cos θ . rUbTI 1>10 bgðajBIplbUkkugRtaMgedIm,I TTYl)an net stress. cMNaMfakMlaMgeRbkugRtaMgenAkñúg load-balancing method RtUvmanGMeBIenARtg; TIRbCMuTMgn; (cgc) rbs;muxkat;Rtg;TMrsMrab;FñwmTMrsamBaØ nigenARtg; cgc rbs;muxkat;cugTMenrrbs;Fñwm cantilever. eKRtUvdak;lkçxNÐEbbenHedIm,IkarBarm:Um:g;EdlKμanlMnwgcakp©it (eccentric unbalanced moment). enAeBlEdlbnÞúkTTwgG½kSFMCag balancing load wb dUcenHbnÞúkKμanlMnwgbEnßm (additional unbalanced load) wub begáIt)anm:Um:g; M ub = wubl 2 / 8 enAkNþalElVg. kugRtaMgsrésxageRkA EdlRtUvKñanwgkrNIenHRtg;kNþalElVgkøayCa Basic Concept 12
  • 13. NPIC P' M ub c f bt = − m (1.18) Ac Ig eKGacsresrsmIkar 1.18 CaBIrsmIkardUcxageRkam P' M ub ft =− − t (1.19a) Ac S nig fb = − P' M ub Ac + Sb (1.19b) smIkar 1.19 nwgeGaytMélkugRtaMgsrésdUcKñanwgsmIkar 1.12 nigsmIkar 1.7 Edr. cMNaMfa eKyk P' = P enARtg;muxkat;kNþalElVgeRBaHkMlaMgeRbkugRtaMgmanTisedkenARtg;muxkat; enaH Edl θ = 0 . 4> Computation of Fiber Stresses in a Prestressed Beam by the Basic Method ]TaheN_ 1>1³ rUbTI 1>11 bgðajBIragFrNImaRtrbs;Fñwm pretensioned dpble T 10LDT24 EdlRT edayTMrsamBaØmanRbEvg 64 ft (19.51m) . vargnUvbnÞúkTMnajefrWSD nigbnÞúkGefrWL Edlmanpl bnÞúksrub 420 plf (6.13kN / m) . kMlaMgeRbkugRtaMgedImmunkMhatbg;KW f pi ≅ 0.70 f pu = 189ksi (1300MPa ) . ehIykMlaMgeRbkugRtaMgeRkaykMhatbg;KW f pe = 150ksi(1034MPa ) . KNnakugRtaMg srésxageRkAbMputenAkNþalElVgEdlbNþalmkBI a. kMlaMgeRbkugRtaMgedImTaMgmUl nigKμanbnÞúkTMnajxageRkA b. lkçxNÐbnÞúkeFVIkarcugeRkayenAeBlEdlkMhatbg;eRbkugRtaMgekItmanehIy. kugRtaMgGnuBaØatmandUcxageRkam³ f 'c = 6ksi TMgn;Rsal (41.4 MPa ) f pu = 270ksi stress relieved (1860 MPa ) = specified tensile strength rbs; tendon f py = 220ksi(1520MPa ) = specified yield strength rbs; tendons f t = 12 f 'c = 930 psi (6.4MPa ) = kugRtaMgTajGnuBaØatGtibrmaenAkñúgebtug f 'ci = 4.8ksi(33.1MPa ) = kugRtaMgsgát;rbs;ebtugenAeBlrgeRbkugRtaMgedIm f ci = 0.6 f 'ci = 2.88ksi(19.9MPa ) = kugRtaMgGnuBaØatGtibrmaenAeBlrgeRbkugRtaMgedIm f c = 0.45 f 'c = kugRtaMgGnuBaØatGtibrmaenAkñúgebtugenAeBleFVIkar snμt;eRbI seven-wire-strand Ggát;p©it 0.5in.(12.7mm) cMnYndb;. Ac = 449in.2 (2897cm 2 ) eKal KMnit 13
  • 14. T.Chhay ( I g = 22469in.4 935346cm 4 ) ( r 2 = I g / Ac = 50.04in.2 323cm 2 ) cb = 17.77in.(451mm ) ct = 6.23in.(158mm ) ec = 14.77in.(375mm ) ee = 7.77in.(197.4mm ) ( Sb = 1264in.3 20713cm3 ) St = 3607in. (59108cm ) 3 3 WD = 359 plf (5.24kN / m ) dMeNaHRsay³ a. lkçxNÐdMbUgenAeBlrgeRbkugRtaMgedIm Aps = 10 × 0.153 = 1.53in.2 (990mm 2 ) Pi = Aps f pi = 1.53 × 189000 = 289170lb(1287kN ) Pe = 1.53 × 150000 = 229500lb(1020kN ) Basic Concept 14
  • 15. NPIC m:Um:g;Edl)anBIbnÞúkpÞal;enAkNþalElVg WD l 2 359(64 )2 MD = = × 12 = 2205696in. − lb(249kN .m ) 8 8 BIsmIkar 1.5 nig 1.7 eyIg)an ⎛ ect ⎞ M D Pi ft =− ⎜1 − 2 ⎟ − t ⎝Ac r ⎠ S 289170 ⎛ 14.77 × 6.23 ⎞ 2205696 =− ⎜1 − ⎟− 449 ⎝ 50.04 ⎠ 3607 = +540.3 − 611.5 ≅ −70 psi (C )(0.5MPa ) P ⎛ ec ⎞ M f b = − i ⎜1 + 2b ⎟ + D Ac ⎝ r ⎠ Sb 289170 ⎛ 14.77 × 17.77 ⎞ 2205696 =− ⎜1 + ⎟+ 440 ⎝ 50.04 ⎠ 1264 = −4022.1 + 1745 ≅ −2277 psi (C )(15.8MPa ) ≤ f ci = −2880 psi O.K. b. lkçxNÐcugeRkayenAeBlrgbnÞúkeFVIkar m:Um:g;kNþalElVgbNþalmkBIbnÞúkbEnßmefr nigGefrKW 420(64 )2 M SD + M L = × 12 = 2580480in. − lb 8 m:Um:g;srub M T = 2205696 + 2580480 = 4786176in. − lb(541kN .m) kugRtaMgenAsrésxagelIbMput Pe ⎛ ect ⎞ M T ft =− ⎜1 − 2 ⎟ − t Ac ⎝ r ⎠ S 229500 ⎛ 14.77 × 6.23 ⎞ 4786176 =− ⎜1 − ⎟− 449 ⎝ 50.04 ⎠ 3607 = +429 − 1327 = −898 psi (C )(6.3MPa ) < f c = 0.45 × 6000 = 2700 psi O.K. kugRtaMgenAsrésxagelIbMput Pe ⎛ ecb ⎞ M T fb = − ⎜1 + 2 ⎟ + Ac ⎝ r ⎠ Sb 229500 ⎛ 14.77 × 17.77 ⎞ 4786176 =− ⎜1 + ⎟+ 449 ⎝ 50.04 ⎠ 1264 = −3192 + 3786 = +594 psi (T )(4.1MPa ) < f t = 12 f 'c = 930 psi O.K. eKal KMnit 15
  • 16. T.Chhay 5> C-Line Computation of Fiber Stresses ]TahrN_ 1>2³ edaHRsay]TahrN_ 1>1 sMrab;lkçxNÐcugeRkayeBlbnÞúkeFVIkar edayeRbI C-line method . dMeNaHRsay³ Pe = 229500lb M T = 4786176in. − lb M 4786176 a= T = = 20.85in. Pe 229500 e' = a − e = 20.85 − 14.77 = 6.08in. BIsmIkar 1.12 Pe ⎛ e' ct ⎞ ft =− ⎜1 + 2 ⎟ Ac ⎝ r ⎠ 229500 ⎛ 6.08 × 6.23 ⎞ =− ⎜1 + ⎟ = −898 psi (C ) 449 ⎝ 50.04 ⎠ P ⎛ e' c ⎞ f b = − e ⎜1 − 2b ⎟ Ac ⎝ r ⎠ 229500 ⎛ 6.08 × 17.77 ⎞ =− ⎜1 − ⎟ = +594 psi (T ) 449 ⎝ 50.04 ⎠ 6> Load-Balancing Computation of Fiber Stresses ]TahrN_ 1>3³ edaHRsay]TahrN_ 1>1 sMrab;lkçxNÐcugeRkayeBlbnÞúkeFVIkareRkayeBlkMhat bg; edayeRbI load-balancing method. dMeNaHRsay³ P ' = Pe = 229500lb enAkNþalElVg enAkNþalElVg a = ec = 14.77in. = 1.231 ft eyIgman balancing load 8 × 229500 × 1.231 = 552 plf (8.1kN / m ) Pa Wb = 8 2 = l 64 2 dUcenHRbsinebIbnÞúkTMnajsrubmanRtwmEt 552 plf FñwmnwgrgkugRtaMg P' / Ac RbsinebIFñwm man tendon TMrg;)a:ra:bUledayminmancMNakp©itenAelITMr. enHedaysarEtbnÞúkTMnajRtUv)an rkSalMnwgeday tendon enAkNþalElVg. dUcenH bnÞúkTMnajsrubEdlFñwmRtUvTTYl = WD + WSD + WL = 359 + 420 = 779 plf Basic Concept 16
  • 17. NPIC Wub = 779 − 552 = 227 plf Wub (l )2 227(64 )2 M ub = = × 12 = 1394688in. − lb 8 8 BIsmIkar 1.19 eyIg)an P' M ub 229500 1394688 ft =− − t =− − Ac S 449 3607 = −511 − 387 = −898 psi (C ) P' M ub 229500 1394688 fb = − + =− + Ac Sb 449 1264 = −511 + 1104 ≅ 594 psi (T ) ≤ f t = 930 psi O.K. eKal KMnit 17