X. connections for prestressed concrete element

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


#> 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



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



-
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


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



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



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 .



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.


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¤



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


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



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 )


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


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 ) .



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.



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



(
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



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 ⎣ ⎝ ⎠ ⎝ ⎠⎦



=
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.



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.


X. connections for prestressed concrete element

More Related Content

What's hot

Viewers also liked

Similar to X. connections for prestressed concrete element

More from Chhay Teng

X. connections for prestressed concrete element