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X. connections for prestressed concrete element
 

X. connections for prestressed concrete element

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    X. connections for prestressed concrete element X. connections for prestressed concrete element Document Transcript

    • Department of Civil Engineering NPIC X. tMNsMrab;Ggát;ebtugeRbkugRtaMg Connections for Prestressed Concrete Elements 10.1. esckþIepþIm Introduction tYnaTIrbs;tMNKWkarepÞrbnÞúk nigkugRtaMgBIEpñkmYyrbs;rcnasm<½n§eTAEpñkEdlenAEk,rRbkb edaylkçN³esdækic© ehIypþl;nUvesßrPaBdl;RbB½n§eRKOgbgÁúM. bnÞúkEdleFVIGMeBIRtg;tMNminRtwmEt ekItecjEtBIbnÞúkTMnajb:ueNÑaHeT vak¾GacekItBIbnÞúkxül; T§iBlrBa¢ÜydI karpøas;bþÚrmaDEdlekIteLIg edaysar long-term creep nig shrinkage/ differential movement rbs;kMral nigT§iBlrbs; sItuNðPaB. edaysartMNCacMnuctP¢ab;EdlmanlkçN³exSayCageKenAkñúgRbB½n§eRKOgbgÁúMTaMgmUl dUcenH vaRtUvman nominal design strength FMCag nominal design strength rbs;Ggát;EdlvaRtUvtP¢ab;. em KuNbnÞúkbEnßmy:agehacNas; 1.3 RtUv)aneKeRbIenAkñúgkarsikSaKNnakartP¢ab; EtelIkElgkrNI insensitive connection dUcCa pad sMrab; column base. eKsikSaKNnatMNTaMgGs;sMrab;kMlaMgTaj tamTisedkGb,brma 0.2 dgénbnÞúkefrbBaÄr elIkElgEteKRtUveRbI bearing pad Edl)ansikSa KNnad¾RtwmRtUv. krNIEdlRtUv)aneKKitBicaNasMrab;ersIusþg;enAkñúgkarsikSaKNnatMNmandUcxageRkam³ !> Load transfer mechanism @> emKuNbnÞúk (load factors) #> karpøas;bþÚrmaD (volumetric changes) $> PaBsVit (ductility) %> PaBrwgmaM (Durability) ^> karTb;Tl;nwgGKÁIP½y (fire resistance) &> kMritGt;eGan nigRbeLaHtMrUvkar (required tolerance and clearance) *> karBicarNaEdlTak;TgnwgkargartMeLIg (erection-related consideration) (> karBicarNaEdlTak;TgnwgGakasFatuekþA nigGakasFatuRtCak; !0> esdækic©énkarlMGittMN (economics of the details of the connection) tMNsMrab;Ggát;ebtugeRbkugRtaMg 639
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa 10.2. kMritGt;eGan Tolerance eKRtUvkMNt;)a:n;RbmaNRbeLaHrvagGgát;tamPaBCak;Esþg. eKRtUvkMNt;TItaMgEdlmankMrit Gt;eGanx<s;RtUv)anGnuBaØat nigkEnøgEdlkMritlMeGanminRtUv)anGnuBaØat ehIyeKk¾KitbBa©ÚlRbeLaH sMrab;ktþaTaMgenH. xageRkamCakMritlMeGanEdlENnaMsMrab;TMhMlMgakenAkñúgFñwm ssr nig spandrel panel³ !> karERbRbYlkñúgbøg;BITItaMgEdl)ankMNt;enAkñúgbøg;³ ± 0.5in. sMrab;ssr b¤Fñwm @> kargakecjenAkñúgbøg;BIbnÞat;Rtg;EdlRsbeTAnigG½kSGaKar³ 1 / 40in. kñúg 1 ft RKb;FñwmEdl xøICag 20 ft b¤KMlatrbs;ssrBIrEdlenAEk,rKñatUcCag 20 ft / 0.5in. sMrab;KMlatssr EdlXøatq¶ayBIKña 20 ft . Connections for Prestressed Concrete Elements 640
    • Department of Civil Engineering NPIC #> PaBxusKñaén relative position rbs;ssrEdlenAEk,rBI relative position Edl)ankMNt;³ 0.5in. enARtg;nIv:UkMral (deck level). $> lMgakBIkUnRbeyal (plumb)³ ± 0.25in. sMrab;ral;kMBs; 10 ft / GtibrmaRtwm 1in. sMrab; kMBs;TaMgmUl. %> PaBERbRbYlénkMritkMBs;rbs; bearing surface BIkMritkMBs;Edl)ankMNt;³ ± 0.5in. sMrab; ssr nigFñwmTaMgGs; nigsMrab;RKb;TItaMg. ^> lMgakEpñkxagelIrbs; spandrel BIkMritkMBs;Edl)ankMNt;³ 0.5in. / sMrab;RKb; spandrel &> lMgakénkMritkMBs;rbs; bearing surface BIExSRsbeTAExSrnIv:UEdl)ankMNt;³ 1 / 40in. kñúg 1 ft sMrab;RKb;FñwmxøICag 20 ft b¤ssrEk,rBIrEdlXøatBIKñaticCag 20 ft / GtibrmaRtwm 0.5in. sMrab;RKb;FñwmEvgCag b¤esμI 20 ft b¤ssrEk,rBIrXøatBIKñaeRcInCag b¤esμI 20 ft . *> bMErbMrYlBI bearing length Edl)ankMNt;enAelITMr³ 3 / 4in. . (> bMErbMrYlBI bearing width enAelITMr³ ± 0.5in. . !0> PaBrt;Rtg;rbs;RCugEKm³ 0.25in. tarag 10>1 eGaynUvkMritlMeGogEdlGacGnuvtþsMrab;tMN. 10.3. Ggát;smas Composite Members dUcEdl)anerobrab;lMGitenAkñúgCMBUkTI5 BIEpñkEpñk5>7 eTAEpñk5>11/ eKRtUvFanakarepÞr kMlaMgkat;tamTisedkenARtg;épÞb:HrvagGgát;cak;Rsab; nig situ-cast-topping. ]TahrN_ 5>14 bgðajBIkMlaMgGnþrGMeBI (interaction forces) nig flowchart énEpñk 5>8>2 eGay operational step- by-step design procedure nigsmIkarKNnaEdlGacGnuvtþ)an (applicable design equation). rUbTI 5>18 én]TahrN_ 5>3 ehIykarsikSaKNnapþl;nUvTMhM nigKMlatrbs; dowel EdlmanT§iBldl;kar epÞreBj eljénkMlaMgkat;tamTisedkrvagGgát;EdlP¢ab;Kña. 10.4. RTnab;TMrebtugGarem:enAkñúgGgát;smas Reinforced Concrete Bearing in Composite Members rUbTI 10>1 bgðajBI composite-action dowel reinforcement. edIm,IkarBarebtugEdlb:H bearing edaypÞal;kuMeGaypÞúHEbkedaysarkMlaMgsgát;FelIslub eKRtUvGnuvtþkMlaMgxageRkAeTAelI M bearing EdlmanTMhMFMRKb;RKan;. kareFVIEbbenHkugRtaMgEdlTTYl)anBIsßanPaBkMNt;nwgminFMelIs tMNsMrab;Ggát;ebtugeRbkugRtaMg 641
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa ersIusþg;sgát;rbs;ebtugeT. eKGackMNt; nominal bearing strength rbs;ebtugsuT§tamsmIkarxag eRkam Vn = C r (0.85 f ' c A1 ) A2 / A1 ≤ 1.2 f ' c A1 (10.1) Edl C r = 1 .0enAeBleKdak;EdkBRgwgenAkñúgTisrbs;kMlaMgb:HtamTisedk (horizontal frictional force) N u dUceXIjenAkñúgrUbTI 10>2 b¤enAeBlEdleKyk N u = 0 . eKGackMNt; C r = (S × W / 200) Nu / Vu EdlRkLaépÞ S × W minRtUvFMCag 9.0in.2 ehIyvaRtUv)anbgðaj enAkñúgrUbTI 10>3 . A1 = RkLaépÞ direct bearing A2 = RkLaépÞGtibrmarbs;cMENkénépÞTMrEdlmanragFrNImaRtRsedogKñanwgRkLaépÞrg bnÞúk dUcbgðajkñúgrUbTI 10>3. Design bearing strength KW Vu = φVn Edl φ = 0.70 . edIm,IeCosvagsñameRbH nig spalling EdlekIteLIgedayécdnüenAxagcugrbs; thin- stemmed member, eKENnaMeGayeRbIEdkGb,brmaEdlesμInwg N u / φf y b:uEnþminRtUvtUcCag 1#3 ¬Ggát;p©it 9.52mm ¦ enAeBlEdl bearing area tUcCag 2in.2 (12.9cm 2 ). RbsinebIbnÞúkemKuN Vu FMCag design bearing strength Vu = φVn dUcEdl)anKNnaBI smIkar 10>1/ enaHeKRtUvkarEdkBRgwgenAkñúg bearing area. eKGacsikSaKNnaEdkenHedayRTwsþI Connections for Prestressed Concrete Elements 642
    • Department of Civil Engineering NPIC - shear friction Edlerobrab;enAkñúgCMBUk 5. eKRtUvsikSaKNna reinforced bearing sMrab;Ggát;cak; Rsab;TaMgGs; elIkElgEtkMraltan; nig hollow-core slab edIm,IkarBarsñameRbHtamTisedk nigsñam eRbHtamTisbBaÄrenARtg;EdkxageRkAbMputrbs;FñwmRtg;TMr. eKGacsnμt;PaBeRTtrbs;sñameRbHxag cugedaysuvtßiPaBRbhak;RbEhlnwg 20o dUceXIjenAkñúgrUbTI 10>2. RbsinebI Vu esμInwgkMlaMgkat; emKuN ¬EdlRsbeTAnwgbøg;sñameRbHsnμt;¦ eKKYrkMNt;tMélrbs;kMlaMgkat;dUcbgðajenAkñúgtarag 10>2 sMrab;emKuN shear-friction RbsiT§PaBGtibrma μe . eKGacrkRkLaépÞEdkEdlEkgeTAnwgbøg;sñameRbHsnμt;BIsmIkarxageRkam³ Vup Avf = (10.2) φμe f y Edl Vu / φ = nominal strength Vn f y = yield strength rbs; Avf tMNsMrab;Ggát;ebtugeRbkugRtaMg 643
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa Vup = kMlaMgkat;emKuNGnuvtþn_ EdlkMNt;edaytMélEdleGayenAkñúgtarag 10>2 ehIy 1,000λAcr μ μe = Vup Edl λ = 1 .0sMrab;ebtugTMgn;Rsal/ 0.85 sMrab; sand-lightweight nig 0.75 sMrab; all-lightweight concrete. Acr = RkLaépÞrbs;épÞb:Hbøg;sñameRbH EdleKGacykvaesμInwg l d b Edl l d Ca development length rbs; Avf ehIy b CaTTwgmFümrbs;Ggát;. tarag 10>3 eGay development length ld sMrab;TMhMEdkepSg². eKGackMNt;EdkbBaÄr Ash Edlkat;tamsñameRbHtamTisedkdUcxageRkam Connections for Prestressed Concrete Elements 644
    • Department of Civil Engineering NPIC Ash = (Avf + An ) f y (10.4) μ 'e f ys 1,000λAcr μ Edl μ 'e = ( Avf + An f y) (10.5) ehIy rbs; Ash f ys = yield strength An = RkLaépÞrbs;EdkedIm,ITb;Tl;kMlaMgTajtamG½kS N u enAkñúgrUbTI 10>2 Edl ( ) An = N u / φf y (10.6) Edl Nu = kMlaMgTajtamTisedkGnuvtþn_emKuNEdlEkgeTAnwgbøg;sñameRbHsnμt; φ = emKuNkat;bnßyersIusþg; = 0.75 tMNsMrab;Ggát;ebtugeRbkugRtaMg 645
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa cMNaMfa eKRtUvf<k;EdkBRgwgTaMgGs;enAelIRCugNak¾edayrbs;bøg;sñameRbHsnμt;eGay)an l¥eday development length b¤edaykarpSareTAnwgEdkEkg (angles)/ EdkbnÞH b¤EdkTMBk; (hooks) edIm,IbegáItkMlaMgTb;Tl;Edl)anKNna. KNnaRTnab;TMrebtugGarem: 10.4.1. Reinforced Bearing Design ]TahrN_ 10>1³ FñwmebtugeRbkugRtaMgragctuekaN PCI standard 16RB28 rgkMlaMgkat;emKuNbBaÄr Vu = 90,000lb(400kN ) nigkMlaMgTajtamTisedk N u = 21,000lb(93.4kN ) . FñwmRtUv)anRTenAelI Teflon pad TMhM 4in. × 4in.(10cm × 10cm ) . KNna end reinforcement enAkñúgFñwmEdlGackarBarkar ekItman bearing crack tamTisedk b¤tamTisQr. eKeGayTinñn½yxageRkam³ f 'c = 5,000 psi (34.47 MPa ) ebtugTMgn;Fmμta f y = 60,000 psi sMrab;EdkFmμtaTaMgGs; (413.7 MPa ) θ = 20 o dMeNaHRsay³ EdktamTisedk (Avf + An ) sMrab;karkMNt;EdkBRgwgtamTisedk/ sakl,gEdk #6 kMBs;Fñwm h = 28in. b = 16in. BItarag 10>3/ ld = 29in. Acr = l d b = 29 × 16 = 464in.2 BItarag 10>2/ μ = 1.4 nigBIsmIkar 10.3 1,000λAcr μ 1,000 × 1.0 × 464 × 1.4 μe = Vup = 90,000 = 10.61 > μ e GnuBaØat = 3.4 dUcenHeRbI μe = 3.4 BIsmIkar 10.2 Avf = Vup φf y μ e = 90,000 0.75 × 60,000 × 3.4 ( = 0.59in.2 3.4cm 2 ) N u = 21,000lb N u 21,000 = Vu 90,000 = 0.23 > tMélGb,brma 0.20 dUcenH yk N u = 21,000lb . Connections for Prestressed Concrete Elements 646
    • Department of Civil Engineering NPIC BIsmIkar 10.6/ An = N u / φf y = 21,000 /(0.75 × 60,000) = 0.47in.2 (2.94cm 2 ) Edksrub As = Avf + An = 0.59 + 0.47 = 1.06in.2 (6.63cm 2 ) dUcenH eRbI 3#6 = 1.32in.2 (8.52cm 2 ) EdkbBaÄr ¬ Ash ¦ BItarag 10>3/ ld = development length rbs;Edk #6 = 29in.(74cm) nig Acr = ld b = 29 × 16 = 464in 2 (3,159cm 2 ). BIsmIkar 10.5 1,000λAcr μ 1,000 × 1.0 × 464 × 1.4 μ 'e = (A + A ) f = 0.93 × 60,000 = 11.64 > μe GnuBaØat = 3.4 vf n y dUcenH eRbI μ 'e = 3.4 . BIsmIkar 10.4 Ash = (Avf + An ) f y = 0.93 × 60,000 = 0.27in.2 (1.74cm 2 ) μ 'e f ys 3.4 × 60,000 dUcenH eRbIEdkkg (stirrup) ( = 0.66in.2 4.26cm 2 ) 10.5. Dapped-End Beam Connections - Dapped end beam CaGgát;eRKOgbgÁúMEdlmankarbnßykMBs;FñwmPøam²enAxagcugrbs;vaedIm,I nUv seating b¤ bearing caM)ac;enAelI corbel b¤ bracket edayKμankar)at;bg; clear height rvagkMral. tMNsMrab;Ggát;ebtugeRbkugRtaMg 647
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa rUbTI 10>4 bgðajBIFñwmebtugeRbkugRtaMgEdlman dapped end KMrUenAxagcug. sñameRbHBIrRbePTGac ekItman³ sñameRbHelx @ CasñameRbHkMlaMgkat;edaypÞal; (direct shear crack) cMENkÉsñameRbH elx #/ elx $ nigelx % CasñameRbHkMlaMgTajGgát;RTUgEdlbgáedaykMlaMgTajtamG½kS nigkMlaMg begáagenAkñúgkMBs;FñwmEdlkat;bnßy ehIykugRtaMgRbmUlpþúMenAmþúMkac;RCug. dUcenH eKRtUvdak;RbePT EdkBRgwgxageRkam dUcbgðajenAkñúgrUb³ !> EdkrgkarBt; (flexural reinforcement) A f bUknwgEdkrgkarTajtamG½kS An Edl As = A f + An edIm,IkarBar cantilever bending stresses. @> Shear-friction reinforcement A f + An bUknwgEdkrgkarTajtamG½kS An edIm,IkarBar kMlaMgkat;bBaÄredaypÞal; (direct vertical shear force) enARtg;RbsBVénEpñk dapped nig EpñkEdlmin dapped rbs;FñwmEdlbgáeGaymansñameRbHelx @. #> EdkrgkMlaMgkat; (shear reinforcement) Ash edIm,ITb;Tl;nwgkugRtaMgTajGgát;RTUgEdl ekItmanenARtg;cMnuckac;RCugEdlbgáeGaymansñameRbHelx #. $> EdkrgkMlaMgTajGgát;RTUg (diagonal tension reinforcement) Ah + Av edIm,IkarBarsñam eRbHelx$ EdlekItBIkugRtaMgTajGgát;RTUgenAkñúgEpñk papped rbs;Fñwm. %> Development length As = A f + Ah edIm,IkarBarsñameRbHelx% EdlbNþalBIkugRtaMg TajGgát;RTUg enAkñúgEpñkmin dapped rbs;Fñwm. 10.5.1. karkMNt;EdkBRgwgedIm,ITb;Tl;kar)ak; Determination of Reinforcement to Resist Failure 10.5.1.1. EdkrgkarBt; nigEdkrgkarTajtamG½kS Flexure and Axial Tension sMrab;lMnwgm:Um:g;enAkñúgrUbTI 10>4/ m:Um:g;emKuNsrubEdleFVIGMeBIenAelIEpñk cantilever dapped enARtg;bøg;rbs; As KW M u = Vu a + N u (h + d ) (10.7a) Edl h= kMBs;rbs;Ggát;BIelI dap d = kMBs;RbsiT§PaBrbs; dap eTATIRbCMuTMgn;rbs;EdkBRgwg As a = ElVgkMlaMgkat; (shear span) M u RtUvTb;Tl;edayersIusþg;m:Um:g; nominal M n = M u / φ / b¤ Connections for Prestressed Concrete Elements 648
    • Department of Civil Engineering NPIC Vu a + N u (h − d ) Mn = (10.7b) φ edaysnμt;faédXñas;m:Um:g; jd ≅ 0.9d Vu a + N u (h − d ) Fn = (10.8) 0.9φd Edl φ = 0.90 sMrab;karBt;begáag. edaysar 0.9φ = 0.81 edIm,ICakarsMrYleKeRbItMél φ = 0.85 enA kñúgsmIkar 10.8 edIm,ITTYl)an Vu a + N u (h − d ) Fn = (10.9a) φd V ⎛a⎞ N ⎛h−d ⎞ b¤ Fn = u ⎜ ⎟ + u ⎜ φ ⎝d ⎠ φ ⎝ d ⎠ ⎟ (10.9b) enaHEdkrgkarBt;begáagKW Fn Vu a + N u (h − d ) As = = (10.10) fy φf y d ehIyEdkrgkarTajedaypÞal;EdlbNþalBIkMlaMgTaj Nu KW Nu An = (10.11) φf y BIsmIkar 10.10 nig 10.11/ RkLaépÞsrubrbs;EdkrgkarBt;begáag nigEdkrgkarTajedaypÞal;køayCa 1 ⎡ ⎛a⎞ ⎛ h ⎞⎤ As = A f + An = ⎢Vu ⎜ d ⎟ + N u ⎜ d ⎟⎥ (10.12) φf y ⎣ ⎝ ⎠ ⎝ ⎠⎦ Edl tMélEksMrYlrbs; φ = 0.85 . 10.5.1.2. EdkrgkMlaMgkat;bBaÄredaypÞal; Direct Vertical Shear sñameRbHelx@ EdlekItBIkMlaMgkat;edaypÞal;RtUv)anTb;edaybnSMénEdk As nig Ah enAkñúg rUbTI 10>4. eKGackMNt;EdkBRgwgtamTisedk Ah EdlRtUvkaredIm,ITb;Tl;nwgkMlaMgkat;edaypÞal; tamsmIkarxageRkam Ah = 0.5( As − An ) (10.13) Edl As = 2Vu 3φf y μ e + An (10.14a) Nu An = (10.14b) φFy 1,000λbhμ μe = Vu CamYynwg φ = 0.85 nig μe dUcenAkñúgsmIkar 10.3. dUcenH tMNsMrab;Ggát;ebtugeRbkugRtaMg 649
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa 1 ⎛ 2Vu ⎞ As = ⎜ 3μ + N u ⎟ ⎜ ⎟ (10.15) φf y ⎝ e ⎠ tMélrbs; As EdleRbIenAkñúgsmIkar 10.13 KYrFMCagtMélTaMgBIrEdlTTYl)anBIsmIkar 10.12 nig 10.15. eKRtUvbgðÚtEdk As edaytMélGb,brma 1.7ld kat;tamcMnuccugénEpñk dap b¤ ld kat;sñameRbH elx% ehIyf<k;enAxagcugrbs;FñwmedaypSarP¢ab;eTAnwg cross bar/ angle b¤ plates. ekRtUvbgðÚtEdk tamTisedk Ah dUcKña ehIyEdkbBaÄr Ash nigEdkbBaÄr b¤EdkeRTt Av k¾RtUv)anf<k;edayTMBk; (hook) tamkarTamTarrbs; ACI Code. ersIusþg;kMlaMgkat; nominal rbs; dap end RtUv)ankMNt;Rtwm Vn ≤ 0.30 f 'c bd ≤ 1,000bd (10.16a) sMrab;ebtugTMgn;Fmμta/ ⎛ 0.07a ⎞ Vn ≤ ⎜ 0.20 − ⎟ f 'c bd (10.16b) ⎝ d ⎠ ⎛ 280a ⎞ b¤ Vn ≤ ⎜ 800 − ⎝ d ⎠ ⎟bd (10.16c) sMrab; sand-lightweight b¤ all-lightweight concrete, edayykmYyNaEdltUcCag Edl a Ca shear span nig d CakMBs;RbsiT§PaBrbs;Fñwm. 10.5.1.3. EdkrgkMlaMgTajGgát;RTUgRtg;kac;RCug Diagonal Tension at Reentrant Corner eKTTYl)anEdkBRgwgEdlRtUvkaredIm,ITb;Tl;nwgsñameRbHedaysarkMlaMgTajGgát;RTUgeRTtE dlralBIp©iténkugRtaMgRbmUlpþúMenARtg;kac;RCugeTAkan;EpñkEdlmin dapped BIsmIkarxageRkam Vu Ash = (10.17) φf y Edl φ = 0.85 ehIy f y Ca yield strength rbs;EdkBRgwg Ash . 10.5.1.4. EdkrgkMlaMgTajGgát;RTUgenAkñúg Dapped end Diagonal Tension in the Dapped end edIm,IkarBarsñameRbHGgát;RTUgelx$ enAkñúg dapped end/ eKRtUvdak;EdkbEnßm As y:agNa edIm,IeGayersIusþg;kMlaMgkat; nominal srub Vn bMeBjsmIkar Connections for Prestressed Concrete Elements 650
    • Department of Civil Engineering NPIC Vu Vn = = Av f y + Ah f y + 2λbd f 'c (10.18) φ y:agehacNas;k¾eKRtUvdak;EdkBak;kNþalénEdkBRgwgenHbBaÄr dUcenHsmIkar 10.18 eGay 1 ⎛ Vu ⎞ Av, min = ⎜ − 2λbd f 'c ⎟ ⎜φ ⎟ (10.19) 2 fy ⎝ ⎠ cMNaMfa karKitBIkareFVIkarTamTardUcxageRkam³ !> kMBs;rbs; dapped end y:agehack¾esμIBak;kNþalénkMBs;Fñwm elIkElgkMBs;FñwmFMCag tMrUvkar. @> RbsinebIkugRtaMgBt;begáagEdlKNnasMrab;kMBs;eBjelj (full depth) rbs;muxkat;eday eRbIbnÞúkemKuN nig gross section propertied FMCag 6 f 'c Pøam²BIeRkay dap/ eKKYrdak; EdkBRgwgbeNþaybEnßmenAkñúgFñwmedIm,IbegáItersIusþg;Bt;begáagtMrUvkar. #> eKRtUvdak;EdkrgkarTajGgát;RTUg Ash eGaykan;EtEk,rkac;RCug. EdkBRgwgenHCaEdk bEnßmeTAelIEdkrgkMlaMgkat;KNna (design shear reinforcement) EdlRtUvkarsMrab;mux kat;FñwmEdlmankMBs;eBj. 10.5.2. KNnatMNrbs; Dapped end Beam Dapped-End Beam Connection Design ]TahrN_ 10>2³ FñwmebtugeRbkugRtaMg PCI standard 16RB28 Edl dapped enAxagcugsMrab; bearing enAelI column corbel/ rgnUvkMlaMgkat;TMnajemKuNenAxagcug Vu = 110,000lb(489kN ) nigkMlaMgTajtamG½kStamTisedk Nu = 20,000lb(97.9kN ) . KNnaEdkrgkarBt;begáag Edkrg kMlaMgkat;edaypÞal; nigEdkrgkarTajGgát;RTUg As / Ash / Ah nig Av EdlRtUvkarsMrab;karBarsñam eRbH EdlbNþalBI dapping énFñwmxagcug. Tinñn½yEdleKeGayman f 'c = 5,000 psi(34.5MPa) ebtugTMgn;Rsal ehIy f y = 60,000 psi(414Mpa) . dMeNaHRsay³ snμt;fa shear span a = 6in.(152mm) / kMBs;RbsiT§PaB dapped-end d = 16in.(406mm) nig h = 18in.(457mm) . EdkrgkarBt; nigEdkrgkarTajtamG½kS As Nu 20,000 = = 0.18 < 0.20 Vu 110,000 dUcenH N u = 0.20 ×110,000 = 22,000lb(97.9kN ) tMNsMrab;Ggát;ebtugeRbkugRtaMg 651
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa 1 ⎡ ⎛a⎞ ⎛ h ⎞⎤ As = ⎢Vn ⎜ d ⎟ + N u ⎜ d ⎟⎥ φf y ⎣ ⎝ ⎠ ⎝ ⎠⎦ 1 ⎡ 6 18 ⎤ = ⎢110,00 × 16 + 22,000 × 16 ⎥ = 1.46in. 2 0.75 × 60,000 ⎣ ⎦ EdkrgkMlaMgkat;edaypÞal; As nig Ah BItarag 10>2 / μ = 1.4λ Edl λ = 1.0 . bnÞab;mk BIsmIkar 10.14c Edl b sMrab;muxkat; 16RB28 esμInwg 16in. 1,000λbhμ 1,000 × 1.0 × 16 × 18 × 1.4 μe = = = 3.67 > μ e GnuBaØatGtibrma = 3.4 Vu 110,000 dUcenH eRbI μe = 3.4 . bnÞab;mk BIsmIkar 10.5 1 ⎛ 2Vu ⎞ 1 ⎛ 2 × 110,000 ⎞ As = ⎜ ⎜ 3μ + N u ⎟ = 0.75 × 60,000 ⎜ 3 × 3.4 + 22,000 ⎟ = 0.96in. ⎟ 2 φf y ⎝ e ⎠ ⎝ ⎠ )anmkBIelImun < As = 1.46in.2 dUcenH eRbI As = 1.46in.2 (9.1cm2 ) . enaHEdk 3#7 = 1.80in.2 EdlRKb;RKan;. BIsmIkar 10.4b = 0.49in.2 (3.0cm 2 ) N 22,000 An = u = φf 0.75 × 60,000 y BIsmIkar 10.13/ EdkrgkMlaMgkat;tamTisedkkat;tamkMBs;rbs;FñwmKW Ah = 0.5( As − An ) = 0.5(1.29 − 0.43) = 0.43in.2 (2.77cm 2 ) . dUcenH sakl,gEdk 2#3 = 2(2 × 0.11) = 0.44in.2 (2.84cm 2 ) EdleKRtUvepÞógpÞat;vaCabnþbnÞab;. tamkarRtYtBinitüBIsmIkar 10.16a ersIusþg;kMlaMgkat; nominal KW Vn EdlGacekItman = 800bd = 800 ×16 ×16 = 204,800lb Vn tMrUvkar = u = V 110,000 = 146,667lb < 204,800lb O.K. φ 0.75 EdkBRgwgbBaÄrrgkarTajGgát;RTUgenAkac;RCug BIsmIkar 10.19 = 2.45in.2 (15.3cm 2 ) V 110,000 Ash = u = φf 0.75 × 60,000 y dUcenH sakl,gEdkkgbiTCit #4 / As = 2 × 0.20 = 0.40in.2 . cMnYnrbs;Edkkg 2.16 / 0.4 = 5.4 dUcenHeRbI 6#4 EdlRtUv)anRbmUlpþúMenAmþúMkac;RCug. EdkBRgwgkarTajGgát;RTUg Av enAkñúg Dapped End BIsmIkar 10.19 Connections for Prestressed Concrete Elements 652
    • Department of Civil Engineering NPIC 1 ⎛ Vu ⎞ Av = ⎜ − 2λbd f 'c ⎟ 2 fv ⎜ φ ⎝ ⎟ ⎠ ersIusþg;kMlaMgkat; nominal rbs;ebtugsuT§KW 2λbd f 'c = 2 × 1.0 × 16 × 16 5,000 = 36,204lb ⎛ 110,000 ⎞ bnÞab;mk Av = 1 ⎜ 2 × 60,000 ⎝ 0.75 − 36,204 ⎟ = 0.92in.2 ⎠ sakl,gEdkkgGkSr U 4#4 = 4(2 × 0.20) = 1.60in.2 . BIelIkmun/ Ah = 0.44in.2 . dUcenH BIsmIkar 10.18 ersIusþg; kMlaMgkat; nominal srubrbs;muxkat;KW Vn EdlGacekItman = Av f y + Ah f y + 2λbd f 'c = 1.60 × 60,000 + 0.44 × 60,000 + 36,034 V = 158,434 > u = 146,667lb O.K. φ RtYtBinitütMrUvkar Development Length sMrab;karf<k; EdkBRgwg As KW 3#7 . BItarag 10>3/ sMrab;Edk #7 / f 'c = 5,000 psi nig ld = 42in. . kMBs;FñwmEdlmin dapped = 2 ft 4in. = 28in. ehIy development length srub = 28 − d + ld = 28 − 16 + 42 = 54in. . edaysar development length Gb,brma l d = 42in. eRbI l d = 54in. = 4 ft 6in.(108cm ) . tMNsMrab;Ggát;ebtugeRbkugRtaMg 653
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa EdkBRgwg Ah KWEdkGkSr U #4 . dUcenHBItarag 10>3/ 1.7ld = 32in.(81cm) BIeRkayFñwm dap. rUbTI 10>5 bgðajBIkarlMGitEdksMrab;tMNFñwm dapped. 10.6. Brackets nig Corbel ebtugGarem: Reinforced Concrete Brackets and Corbels Corbel CaFñwm cantilever xøI EdlpleFob shear span elIkMBs; a / d minRtUvFMCag 1.0 . varg kMlaMgkat;edaypÞal; Vu nigkMlaMgTajtamTisedk N u . Epñk 5.14 enAkñúgCMBUk5/ design flowchart enAkñúgEpñk 5.14.4 nig]TahrN_ 5>7 bgðajBIkMlaMgsgát; nigkarGnuvtþénRTwsþI shear-friction enAkñúg karsikSaKNna corbel. karlMGitsrésEdkrbs;tMNCakargard¾sMxan;mYyedIm,ITTYleCaKC½ykñúgkar sikSaKNna corbel edayKitBIlT§PaBrbs;vaedIm,ITb;Tl;nwgGnuvtþkMlaMgGnuvtþn_. srésEdklMGit rbs; corbel KMrURtUv)anbgðajenAkñúgrUbTI 10>6. Connections for Prestressed Concrete Elements 654
    • Department of Civil Engineering NPIC 10.7. Epñklyecjrbs;FñwmebtugGarem: Concrete Beam Ledges eKeRbI beam ledge edIm,IRTbnÞúkcMcMnuccugFñwmebtugeRbkugRtaMgcak;Rsab;tamTisTTwg ehIyva eFVIkarkñúgTMrg;RsedogKñanwg corbel Edr. kM;laMgedaypÞal;EdleFVIGMeBIelI ledge GacbgáeGaymansñam bBaÄrdUcbgðajenAkñúgrUbTI 10>7. RbsinebIbnÞúkCabnÞúkminCab; ehIymkBIRCugmçag/ ledge beam kñúg TMrg;GkSr L eFVIGMeBIdUc spandrel beam nigrgm:Um:g;rmYlbEnßmBIelIkMlaMgkat;edaypÞal;. karKNna ledge beam KWGnuvtþtamkarsikSaKNna nig]TahrN_enAkñúgCMBUk5. enAkñúgemeronenHbgðajBIkar sikSaKNnaEdkrgkMlaMgkat;sMrab; cantilevering ledge EdlCaTUeTAmanpleFob shear span elI kMBs; l p / d tUcCag b¤esμInwg 0.5 . eKRtUvkMNt;esIusþg;kMlaMgkat; nominal rbs; ledge Rtg;kac;RCugedaytMéltUcCageKkñúg cMeNamtMélEdlTTYlBIsmIkar nigeRkamlkçxNÐEdleKeGaydUcxageRkam !> s > b + h tMNsMrab;Ggát;ebtugeRbkugRtaMg 655
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa ( Vn = 3hλ f 'c 2l p + b + h ) (10.20a) ( Vn = hλ f 'c 2l p + b + h + 2d e ) (10.20b) @> s < b + h nigbnÞúkcMcMnucesμIKña ( Vn = 1.5hλ f 'c 2l p + b + h + s ) (10.21a) ⎛ b+h ⎞ Vn = hλ f 'c ⎜ l p + + de + s ⎟ (10.21b) ⎝ 2 ⎠ Edl RbEvglyecjrbs; ledge lp = b = TTwgrbs; bearing area h = kMBs;rbs; ledge s = KMlaténbnÞúkcMcMnuc d e = cMgayBIG½kSénbnÞúkeTAcugFñwm RbsinebI ledge RTbnÞúkCab; b¤bnÞúkcMcMnucEdlmanKMlatEk,rKña eKkMNt;ersIusþg;kMlaMgkat; nominal rbs;muxkat; ledge BI Vn = 24hλ f 'c (10.22) Edl Vn CakMlaMgkat;kñúgmYyÉktþaRbEvg. y:agehacNas; eKRtUveGayersIusþg;KNna Vu esμInwgkM laMgemKuN Vu = φVn sMrab; φ = 0.85 . RbsinebIbnÞúkemKuNGnuvtþn_ Vu FMCagersIusþg;KNna dUc EdlkMNt;BIsmIkar 10.20, 10.21 b¤ 10.22/ eKRtUvdak;EdkBiessEdlKNnaRsedogKñaeTAnwgEdk EdlRtUvkarenAkñúgcug dapped beam dUcEdl)anerobrab;enAkñúgEpñk 10.5. enAkñúgkrNIenH eKRtUv kMNt;EdkrgkarBt; As BIsmIkar 10.12/ EdkBRgwgrgkarTajGgát;RTUgbBaÄr (hanger) Ash BI smIkar 10.17 ehIyEdkBRgwgbEnßm At Edldak;enAsrésxagelI nigsrésxageRkamrbs; ledge BI 200l p d At = (10.23) fy Edl At CaRkLaépÞrbs;EdkbeNþayenAkñúg ledge. eKdak;EdkBRgwg Ash edayKMlatesμIKñaelITTwg 6h énRCugnImYy²rbs; bearing b:uEnþminRtUvFMCagBak;kNþalcMgayeTAkan;bnÞúkbnÞab;. KMlatEdkmin RtUvFMCagkMBs; ledge h b¤ 18in. ehIy Ash RtUv)ansikSaKNnasMrab; ledge EdlminRtUvbEnßmeTAelI EdkrgkMlaMgkat; nigEdkrgkMlaMgrmYlrbs; ledge beam srub. karKNnatMNFñwmlyecj 10.7.1. Design of Ledge Beam Connection ]TahrN_ 10>3³ eRKOgbgÁúMkMralGaKarcMNtrfynþRtUv)anpSMeLIgBI 10 ft -wide double-T RtUv)an Connections for Prestressed Concrete Elements 656
    • Department of Civil Engineering NPIC RTenAmuxkat;FñwmGkSr L sþg;dar. eKRtUvdak;eCIgrbs; double-T y:agNaenAelIRKb;cMnucTaMgGs;enA elI ledge. kMlaMgkat;emKuNbBaÄrxagcug Vu = 24,000lb(107kN ) kñúgeCIgmYy nigkMlaMgTajtamTis edk Nu = 5,000lb(22.4kN ) kñúgeCIgmYy. KNnaersIusþg;kMlaMgkat; nominal rbs; ledge nigsikSa KNnaEdkRbsinebIcaM)ac;. eKeGay b = 4in. h = 12in. d = 10.5in. l p = 6in.(15cm ) s = 48in.(122cm ) f 'c = 5,000 psi (34.5MPa ) ebtugTMgn;Rsal f y = 60,000 psi (414MPa ) dMeNaHRsay³ Vu = 24,000lb N u = 5,000lb s = 48in. b + h = 4 + 12 = 16in. tMélGb,brmarbs; d e = 1 b = 2in. 2 2l p + b + h = 2 × 6 + 4 + 12 = 28in. edaysar s > b + h nig d e < 2l p + b + h ehIyGnuvtþsmIkr 10.20b ehIyersIusþg;kMlaMgkat;Edl GacekItman Vn = hλ f 'c (2l p + b + h + 2de ) = 12 ×1.0 5,000 (2 × 6 + 4 + 12 + 2 × 2) = 27,153lb (120.8kN ) . dUcenHersIusþg;kMlaMgkat;KNna Vu = φVu = 0.75 × 27,153 = 20,365lb < kMlaMgkat;em KuN Vu = 24,000lb ehIyeyIgRtUveRbIEdkBRgwgEdlKNnadUcEdkBRgwgsMrab;muxkat; dapped Edr. EdkrgkarBt;begáag As Shear span a ≅ 3l p / 4 + 1.5 = 3 × 6 / 4 + 1.5 = 6in.(15cm ) edaysar Nu / Vu = 5,000 / 24,000 = 0.21 > 20% dUcenHeKeRbI Nu = 5,000lb . BIsmIkar 10.12 1 ⎡ ⎛a⎞ ⎛ h ⎞⎤ As = ⎢Vu ⎜ d ⎟ + N u ⎜ d ⎟⎥ φf y ⎣ ⎝ ⎠ ⎝ ⎠⎦ tMNsMrab;Ggát;ebtugeRbkugRtaMg 657
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa = 1 ⎡ 6 12 ⎤ ( ) ⎢24,000 10.5 + 5,000 10.5 ⎥ = 0.38in. 2.45cm 0.85 × 60,000 ⎣ ⎦ 2 2 edaysar 6h = 6 ×12 > s / 2 = 24in. / EbgEckEdkBRgwg s / 2 = 24in. enARCugnImYy²énbnÞúk. TTwgrbs; band sMrab;kardak;EdkrgkarBt;begáag A = 2 × 24 = 48in. ehIyKMlatEdkGti- s brma h = 12in. . dUcenHeRbIEdk 4#3 enAkñúg band width 48in. nImYy² = 0.44in. > EdktMrUvkar 2 0.38in. . dUcenH dak;EdkbEnßmBIrenARtg;cugFñwmedIm,Ipþl;EdksmmUlsMrab;eCIgFñwmEdldak;Ek,r 2 xagcug. EdkbBaÄrrgkarTajGgát;RTUg A sh BIsmIkar 10.17 = 0.53in. (3.42cm ) V 24,000 A = = u 2 2 φf sh 0.75 × 60,000 y elI hand width 48in. . dUcenH Ash / ft = 0.47 / 4 = 0.12in.2 / ft b¤ #3@11in. . Cavi)akeRbIEdkkg biTCit 5#3 enAkñúg bad width 48in. = 0.55in.2 > muxkat;EdktMrUvkar 0.53in.2 . bnÞab;mk sMrab;kargar Gnuvtþn_ eRbIcMnYn nigKMlatdUcKñasMrab;Edk As nig Ash ¬EdkkgbiTCit 5#3 ¦. cMNaMfa manEteCIgmçag rbs;Edkkg Ash RtUv)anKitbBa©ÚleTAkñúgmuxkat;én 5#3 edIm,Ipþl;karRbmUlpþúMtMrUvkarénEdkEk,rkac; RCug. EdkbeNþay Al BIsmIkar 10.23 200l p d 200 × 6 ×10.5 Al = = = 0.21in.2 fy 60,000 sMrab;kargarGnuvtþn_ eRbIEdk #4 mYyenARtg;kac;RCugrbs; ledge edayeGay 4#4 = 0.80in.2 ¬Ggát; p©it 12.7mm ¦ > 0.21in.2 / O.K. CakarBit karKNnaEdlmanlkçN³eBjeljTamTarkarviPaKkMlaMgkat; nigkMlaMgrmYlrbs; muxkat;srubedIm,ITb;Tl;nwgkMlaMgkat;srubEdlbBa¢ÚnedayeCIgrbs; double-T TaMgGs; nigm:Um:g;rmYl EdlekIteLIgedaykarGnuvtþrbs;kMlaMgcakp©itBIeCIgrbs; double-T. karerobrab;BIRkLaépÞEdkBRgwg rbs; ledge Edl)anKNnaenAkñúg]TahrN_enHCaRkLaépÞEdkbEnßmeTAelIelIEdkrgkMlaMgTaj nig Edkrg kMlaMgrmYlEdlTamTarsMrab;Fñwmsrub. rUbTI 10>8 bgðajBIkarlMGitrbs;srésEdksMrab;tMN ledge, b:uEnþmin)anrab;bBa©ÚlEdkrgkM- laMgTaj nigEdkrgkMlaMgrmYlEdlRtUvsikSasMrab;FñwmGkS L TaMgmUl. Connections for Prestressed Concrete Elements 658
    • Department of Civil Engineering NPIC 10.8. lMGittMNEdl)aneRCIserIs Selected Connection Details dUcEdl)aneerobrab;enAkñúgEpñk 10.1 tMNCaeRKOgP¢ab;cMbgenAkñúgRbB½n§eRKOgbgÁúMTaMgmUl Edl kareFVIkarrbs;vakMNt;faeRKOgbgÁúMmansuvtßiPaB nigmanesßrPaB. dUcenH design engineer RtUvmankar Rby½tñy:agxøaMgkñúgkarsikSaKNna nigeRCIserIsnUvmuxkat;EdlsmRsbsMrab;mUlehtu suvtßiPaB nig esdækic©. BIrUbTI 10>9 dl;rUbTI 10>16 manbgðajBIkarlMGiténRbePTtMNEdl)aneRCIserIsCaeRcIn. tMNsMrab;Ggát;ebtugeRbkugRtaMg 659
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa Connections for Prestressed Concrete Elements 660
    • Department of Civil Engineering NPIC tMNsMrab;Ggát;ebtugeRbkugRtaMg 661
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa Connections for Prestressed Concrete Elements 662
    • Department of Civil Engineering NPIC tMNsMrab;Ggát;ebtugeRbkugRtaMg 663
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa Connections for Prestressed Concrete Elements 664
    • Department of Civil Engineering NPIC tMNsMrab;Ggát;ebtugeRbkugRtaMg 665
    • T.Chhay viTüasßanCatiBhubec©keTskm<úCa Connections for Prestressed Concrete Elements 666