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
