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