V alternative design methods

T.Chhay NPIC

V. viFIKNnaepSgeTot
Alternative Design Methods

1> esckþIepþIm Introduction

enAkñúgemeronTI3 nigTI4 karviPaK nigkarKNnaGgát;ebtugBRgwgEdkRtUv)anBnül;edayQrelIeKal
karN_Edlpþl;eGayeday ACI Code 318-05. viFIKNnad¾éTRtUv)anbgðajenAkñúg]bsm<n§½ Appendix B én
ACI Code edayeyageTAtamemKuNbnÞúkEdleGayenAkñúg]bsm<n§½ Appendix C. viFIKNnaepSgeTotenH

KWCaeKalkarN_énkarviPaK nigkarKNnaenAkñúg ACI Code 318-99. vamanlkçN³RsedogKñaxøHeTAnwg viFI
Edl)anBnül;BImun elIkElgEtvaeRbIemKuNbnÞúk nigemKuNkat;bnßyersIusþg; φ xusKña. smIkarviPaK nig
smIkarKNnaeKalEdlmanenAkñúgemeronmun nwgRtUv)aneRbIenATIenH. enAeBleKeRbI Appendix B edIm,I
KNna eKRtUvCMnYsnUvGVIEdlRtUvKñaenAkñúg Code enaH.
2> emKuNbnÞúk Load Factors

RbsinebIersIusþg;tMrUvkar required strength RtUv)antageday U ehIykMlaMgxül; nigkMlaMgrBa¢ÜydI
RtUv)antageday W nig E erogKña enaHtam ACI Code, Appendix C ersIusþg;tMrUvkar U KYrEtCatMélEdl
FMCageKkñúgcMeNambnSMbnÞúkxageRkam³
1> sMrab;krNIbnÞúkefr bnÞúkGefr nigbnÞúkxül;
U = 1 .4 D + 1 .7 L (5-1a)
U = 0.75(1.4 D + 1.7 L) + (1.6W b¤ 1.0E ) (5-1b)

U = 0.9 D + (1.6W b¤ 1.0E ) (5-1c)

2> enAeBlbnÞúkxül; W minRtUv)ankat;bnßyedayemKuNTisedA directionality factor 1.3W Gac
RtUv)aneRbICMnYs 1.6W . enAeBlEdlbnÞúkrBa¢ÜydIRtUv)anQrenAelIbnÞúkeFVIkar service forces enaH
1.4 E GacRtUv)aneRbICMnYseGay 1.0 E .

3> kñúgkrNIEdlbnÞúksMBaFdI H RtUv)anbBa©ÚleTAkñúgkarKNna
U = 1 .4 D + 1 .7 L + 1 .7 H (5-2a)
enAeBlEdlbnÞúkefr D nigbnÞúkGefr L kat;bnßyT§iBlrbs; H enaH
U = 0 .9 D + 1 .7 H (5-2b)
sMrab;bnSMbnÞúkén D / L b¤ H
U = 1 .4 D + 1 .7 L
4> RbsinebITMgn; nigbnÞúksMBaFEdl)anmkBIsarFaturav F RtUv)anbBa©ÚleTAkñúgkarKNna
viFIKNnaepSgeTot 73

Department of Civil Engineering viTüasßanCatibhubec©keTskm<úCa
U = 1 .4 D + 1 .7 L + 1 .4 F (5-3a)
enAeBlEdlbnÞúkefr D nigbnÞúkGefr L kat;bnßyT§iBlrbs; F enaH
U = 0.9 D + 1.4 F (5-3b)
sMrab;bnSMbnÞúkén D / L b¤ F
U = 1 .4 D + 1 .7 L
sMBaFbBaÄrénsarFaturavKYrRtUv)anKitCabnÞúkefr.
5> enAeBlEdlT§iBlTgÁic impact effects RtUv)anrab;bBa©Úl enaHvaRtUv)anKitbBa©ÚleTAkñúgbnÞúkGefr.
6> enAeBlEdl structural effects T énsMrut differential settlement, creep, karrYmmaD shrinkage b¤
bNþÚrsItuNðPaB mantMélFM vaKYrRtUv)anrab;bBa©ÚleTAkñúgbnSMbnÞúkén
U = 0.75(1.4 D + 1.4T + 1.7 L) (5-4a)
U = 1.4 D + 1.4T (5-4b)
smIkar (5-1a) RtUv)aneRbICaTUeTA. emKuNbnÞúkefresμInwg 1.4 nigemKuNbnÞúkGefresμInwg 1.7 .
sMrab;bnÞúkefr nigbnÞúkGefrcMcMnuc PD nig PL enaHbnÞúkcMcMnucemKuN PU = PD + PL dUcKña
M U = M D + M L Edl M D nig M L m:Um:g;bnÞúkefr nigm:Um:g;bnÞúkGefrerogKña.

3> emKuNkat;bnßyersIusþg; Strength-Reduction Factor φ

ersIusþg; nominal strength énmuxkat;RtUv)ankat;bnßyedayemKuN φ edIm,IKitsMrab;kar)at;bg;
ersIusþg;enAkñúgsMPar³d¾tictYc small adverse variations in material strength karplitEdleFIVeLIgedayéd
artisanry TMhMxñat karRKb;RKg nigkMriténkarRtYtBinitü. emKuN φ CaEpñkmYyénemKuNsuvtßiPaB.

bTdæan ACI Code, Section C.3 (Appendix C) kMNt;nUvtMélxageRkamedIm,IeRbIR)as;³
- sMrab;muxkat;rgkarTaj φ = 0.90
- sMrab;muxkat;rgkarsgát;
k> CamYyEdkkgvNÐ φ = 0.70
x> CamYyEdkkgFmμta φ = 0.65
- sMrab;kMlaMgkat; nigkMlaMgrmYl φ = 0.75
- sMrab;RTnab;enAelIebtug φ = 0.65
- sMrab;karBt;enAelIebtugsuT§ b¤enAelIebtugEdlmanbrimaNEdkGb,brma 1.4 / f y ³ φ = 0.65
sMrab;muxkat;EdlsßitenAkñgtMbn; transition region rvagmuxkat;rgkarTaj tension-controlled
section nigmuxkat;rgkarsgát; compression-controlled section enaH φ GacnwgekIneLIgCabnÞat;rhUtdl;

0 .9 .

Alternative Design Method 74

T.Chhay NPIC

eKk¾GaceRbIemKuNkat;bnßyersIusþg; φ sMrab;ssr ¬b¤muxkat;Edlman ε t < 0.005 ¦ edayvaErbRbYl
eTAtamkrNIxageRkam³
1> enAeBlEdl Pu = φPn ≥ 0.1 f 'c Ag enaH φ = 0.7 sMrab;ssrEdkkgFmμta nig φ = 0.75 sMrab;
EdkkgvNÐ½. krNIekIteLIgCaTUeTAsMrab;muxkat;rgkarsgát; compression control.
Ag Camuxkat;eBj.

2> rvagtMél 0.1 f 'c Ag b¤ φPn ¬mYyNaEdltUcCag¦ nigsUnü ehIy Pu sßitenAkñúgtMbn;Taj
tension control zone nig φ FMCag 0.7 ¬b¤ 0.75 ¦. ACI Code, Section C3.2 kMNt;fa sMrab;

Ggát;Edlman f y minFMCag 400MPa CamYyEdksIuemRTI nigCamYycMgayrvagEdkrgkarsgát;
nigkarTaj (d − d ' ) minRtUvticCag 0.7h ¬ h =kMBs;srubrbs;muxkat;¦ nig d = h − d s enaHtM
él φ RtUv)anekIneLIgCabnÞat;eTArk 0.9 .
sMrab;tMbn; transition region, φ RtUv)ankMNt;edayviFan linear interpolation rvag 0.7 ¬b¤
0.75 ¦ nig 0.9 . rUb 5>1 bgðajBIbMErbMrYlrbs; φ sMrab;Edk 400 MPa . smIkarbnÞat;mandUc xageRkam³

φ = 0.57 + 67ε t sMrab;muxkat;EdkkgFmμta (5-5)

φ = 0.65 + 50ε t sMrab;muxkat;EdkkgvNÐ½ (5-6)

mü:agvijeTot φ enAkñúgtMbn; transition region GacRtUv)ankMNt;CaGnuKmn_eTAnwg (dt / c)
sMrab;Edk 400MPa dUcxageRkam³
⎛d ⎞
φ = 0.37 + 0.20⎜ t ⎟ sMrab;muxkat;EdkkgFmμta (5-7)
⎝ c ⎠
viFIKNnaepSgeTot 75

⎛ dt ⎞
φ = 0.50 + 0.15⎜ sMrab;muxkat;EdkkgvNÐ½
⎝ c ⎠
⎟ (5-8)

Edl c CakMBs;GkS½NWtenAersIusþg; normal strength.
4> muxkat;ctuekaNEkgCamYyEdkrgkarTaj Rectangular Sections with Tension
Reinforcement
BIkarviPaKénmuxkat;ctuekaNEkgEdkrgkarTaj smIkarxageRkamRtUv)anbMEbk Edl f 'c nig fy

KitCa MPa ³
f 'c ⎛ 600 ⎞
⎜ ⎟
ρb = 0.85β1
f y ⎜ 600 + f y ⎟
⎝ ⎠
RbsinebIPaKryEdkGtibrmaRtUv)ankMNt; 0.75ρb enaH
f 'c ⎛ 600 ⎞
ρ max = 0.75ρb = 0.6375β1 ⎜ ⎟ (5-9)
fy ⎜ 600 + f y ⎟
⎝ ⎠
enHbgðajfa ρmax = 0.75ρb FMCag ρmax = 0.634ρb Edl)aneGayenAkñúgemeronTI3 sMrab;Edk
400 MPa .

sMrab; f ' ≤ 28MPa
c

f 'c ⎛ 600 ⎞
ρ max = 0.542 ⎜ ⎟ (5-10)
fy ⎜ 600 + f y ⎟
⎝ ⎠
β1 = 0.85 sMrab;ebtugEdlmanersIusþg; f ' ≤ 28MPa . c

f ' −28
β = 0.85 − 0.05(
1
c
) sMrab;ebtugEdlmanersIusþg; 28MPa < f ' ≤ 56MPa . c
7
β = 0.65 sMrab;ebtugEdlmanersIusþg; f ' > 56MPa .
1 c

PaKryEdkénmuxkat; balanced section ρb nigPaKryEdkGtibrmaGnuBaØati ρmax GacRtUv)an
KNnasMrab;tMélepSgKñaén f 'c nig f y dUcbgðajenAkñúgtarag 5>1. PaKryEdkKNnaEdlesñIeLIgsMrab;
ρ ≤ ρ max k¾RtUv)anbgðajenAkúñgtarag 5>1.
taragTI5>1³ PaKryEdkEdlRtUv)anesñIreLIg ρ s

f 'c ( MPa) f y (MPa) %ρ s
20 235 1.4
400 1.2
28 400 1.4
500 1.2
35 400 1.4
500 1.2
smIkarm:Um:g;KNnaRtUv)anbMEbkenAkñúgemeronmunmanTMrg;dUcxageRkam³


T.Chhay NPIC

φM n = M u = Ru bd 2 (3-21)
⎛ ρf y ⎞
Edl Ru = φρf y ⎜1 −
⎜ 1.7 f ' ⎟ = φRn
⎟ (3-22)
⎝ c⎠

nig φ = 0.9 . sMrab;muxkat;rgkarTaj tension-controlled section / ε t ≥ 0.005
⎛ As f y ⎞
φM n = M u = φAs f y ⎜ d −
⎜ ⎟ (3-19a)
⎝ 1.7 f 'c b ⎟
⎠
⎛ ρf y ⎞
dUcKña φM n = M u = φf y bd 2 ⎜ d −
⎜ ⎟
1.7 f 'c ⎟
(3-20)
⎝ ⎠
eyIgeXIjfasMrab;eRkABI m:Um:g;emKuN M u / f 'c / f y eKmanGBaØatibIenAkñúgsmIkarenHKW b / d nig
ρ . dUcenHeKminGacedaHRsaysmIkarenH)aneT Tal;EtGBaØatiBIrRtUv)ansnμt;. CaTUeTA eKeRcInsnμt; ρ
¬edayeRbI ρmax ¦ nig b k¾RtUv)ansnμt;Edr. edayQrelIkarBiPakSaBIxagedIm krNIxageRkamRtUv)anbegáIt
eLIgenAeBl M u / f 'c / f y RtUv)ansÁal;³
1> RbsinebI ρ RtUv)ansnμt; enaH Ru GacRtUv)anKNnaBIsmIkar (3-22) EdleGay bd 2
= M u / Ru . GñkKNnaGaceRbI ρ rhUtdl; ρ max EdlbegáItmuxkat;ebtugEdkrgkarTajGb,-

brma. RbsinebIeRbI ρmin vanwgbegáItmuxkat;ebtugGtibrma. RbsinebI b RtUv)ansnμt;bEnßmBI
elI ρ enaH d GacRtUv)anKNnadUcxageRkam³
Mu
d= (5-11)
Ru b

RbsinebI d / b = 2 enaH d = 3 (2M u / Ru ) nig b = d / 2 bgçittMéleTArktMélEdlFM.
2> RbsinebI d nig b RtUv)aneGay PaKryEdkRtUvkar ρ GacRtUv)anKNnaedaysmIkar (3-20)
eKTTYl)an
3> ρ = 0.85 f 'c ⎡1 − 1 − 1.7φfM ubd 2 ⎤
⎢
4
⎥ (5-12)
f y ⎢
⎣ ' c ⎥
⎦
0.85 f 'c ⎡ 2 Ru ⎤
= ⎢1 − 1 − ⎥
fy ⎣ 0.85 f 'c ⎦

nig As = ρbd
Ca]TahrN_/ RbsinebI M u = 275.72kN .m / b = 300mm / d = 450mm / f 'c = 20MPa nig
f y = 400MPa enaH ρ = 0.0154 BIsmIkar (5-12) nig As = ρbd = 0.0154 × 300 × 450 = 2079mm 2 enA

eBlEdleKeGay b nig d eKKYrEtBinitüemIlfaetIeKRtUvkarEdkrgkarsgát;b¤Gt; eRBaHEt d tUc. eKGacedaH
Rsayva)andUcxageRkam³
k> KNna ρmax nig Ru,max = φρmax f y [1 − (ρmax f y / 1.7 f 'c )]

viFIKNnaepSgeTot 77

x> KNna φM n,max = Ru,maxbd 2 = ersIusþg;m:Um:g;Gtibrmarbs;muxkat;EdkrgkarTaj.
K> RbsinebI M u < φM n,max enaHvaminRtUvkarEdkrgkarTajeT. KNna ρ nig As BIsmIkar (5-
12)
X> RbsinebIeKsÁal; ρ nig b KNna Ru ³
⎛ ρf y ⎞
⎜ 1 .7 f ' ⎟
Ru = φρf y ⎜1 − ⎟
⎝ c⎠

KNna d BIsmIkar (5-11)
d=
Mu
Rb
nig As = ρbd
u

]TahrN_TI1³
kMNt;muxkat;EdkcaM)ac;sMrab;muxkat;EdlmanTTwg b = 250mm nigkMBs;srub d = 700mm ¬rUbTI5>2¦
RbsinebIvargnUvm:Um:g;emKuNxageRkA 312kN.m . eKeGay f 'c = 28MPa nig f y = 400MPa .

dMeNaHRsay
1> snμt;eRbIEdk DB25 mYyRsTab; ¬epÞógpÞat;enAeBleRkay¦ d = 700 − 50 = 650mm .
2> RtYtBinitüemIlfaetImuxkat;RtUvkarEdksgát;b¤Gt;. eRbobeFobersIusþg;m:Um:g;KNnaénmuxkat; ¬eday
eRbI ρmax ¦ CamYym:Um:g;KNna. sMrab; f 'c = 28MPa nig f y = 400MPa / ρmax = 0.02276 .
⎛ ρ max f y ⎞
Ru = φρmax f y ⎜1 −
⎜ ⎟ = 6.63MPa
⎝ 1 .7 f 'c ⎟
⎠
ersIusþg;m:Um:g;KNnaénmuxkat;ebtugEdkrgkarTajKW
φM n, max = Ru / maxbd 2 = 6.63 × 250 × 6502 × 10−6 = 700.3kN .m > 312kN .m
dUcenH ρ < ρmax enaHvaCamuxkat;EdlmanEtEdkrgkarTaj.


T.Chhay NPIC

3> KNna ρ BIsmIkar (5-12) edIm,ITTYl)an ρ = 0.0089 / As = ρbd = 0.0089 × 250 × 650
= 1446mm 2 eRbIEdk 3DB 25 (As = 1472mm 2 ). muxkat;cugeRkayRtUv)anbgðajenAkñúgrUbTI 5>2.

4> epÞógpÞat; ε t ³
1472 × 400
a= = 98.96mm
0.85 × 28 × 250
a
c= = 116.4mm
0.85
d −c
εt = t 0.003 = 0.0137 > 0.005 φ = 0.9
c

5> muxkat;ctuekaNCamYynwgEdkrgkarsgát; Rectangular Sections with
Compression Reinforcement
muxkat;ebtugEdkrgkarTaj singly reinforced section EdlmanersIusþg;m:Um:g;GtibrmaenAeBlEdl
ρ max rbs;EdkRtUv)aneRbI. RbsinebIm:Um:g;emKuNFMCagersIusþg;m:Um:g;kñúg ¬krNImuxkat;RtUv)ankMNt;¦ enaHeK
RtUvkarmuxkat;EdkDub doubly reinforced section edaybEnßmEdkTaMgenAkñúgtMbn;sgát; nigtMbn;Taj. viFI
saRsþsMrab;KNnamuxkat;ctuekaNEkgCamYyEdksgát; enAeBlEdleKsÁal; M u / f 'c / b / d nig d '
Rtuv)ansegçbenAkñúgemeronTI4. karEdlxusKñamanEtmYyKW ρmax = 0.75ρb RtUv)aneRbIenAkñúgkarKNnaenH³
f 'c ⎛ 600 ⎞
⎜ ⎟
ρ max = 0.6375β1 (5-9)
f y ⎜ 600 + f y ⎟
⎝ ⎠
dUcKña RtUvepÞogpÞat; ε t ≥ 0.005 sMrab; φ = 0.9 .
]TahrN_TI2³ muxkat;FñwmRtUv)ankMNt;eday b = 300mm nigkMBs;srub h = 500mm ehIyrgnUvm:Um:g;emKuN
M u = 447.5kN .m . kMNt;muxkat;EdkcaM)ac;edayeRbI f 'c = 28MPa nig f y = 400MPa . ¬eyagtamrUb

5>3¦.

dMeNaHRsay³

viFIKNnaepSgeTot 79

1> kMNt;ersIusþg;m:Um:g;KNnaénmuxkat;EdkeTal. snμt; ρ = 0.018 . dUcenH Ru = 5.5MPa . sMrab;
EdkBIrRsTab; d = 500 − 90 = 410mm
M u1 = Ru bd 2 = 5.5 × 300 × 410 2 × 10 −6 = 277.4kN .m
m:Um:g;KNnaKW M u = 447.5kN .m > 277.4kN .m dUcenHeKRtUvkarEdksgát;
2> KNna As1 / M u 2 / As2 nig As
As1 = ρbd = 0.018 × 300 × 410 = 2214mm 2

M u 2 = M u − M u1 = 447.5 − 277.4 = 170.1kN .m
M u 2 = φAs 2 f y (d − d ' ) snμt; d ' = 50mm
170.1 ⋅ 106 = 0.9 As 2 400(410 − 50) As 2 = 1312.5mm 2
As = As1 + As 2 = 2214 + 1312.5 = 3526.5mm 2 ¬ 6DB28 ¦
3> epÞógpÞat;PaB yield rbs;Edkrgkarsgát;. Edkrgkarsgát; yield RbsinebI
f 'c ⎛ d ' ⎞⎛ 600 ⎞
ρ − ρ ' ≥ K = 0.85β1 ⎜ ⎟⎜ ⎟
fy ⎝ d ⎠⎜ 600 − f y
⎝
⎟
⎠
28 ⎛ 50 ⎞⎛ 600 ⎞
K = (0.85) 2 ⎜ ⎟⎜ ⎟ = 0.0185
400 ⎝ 410 ⎠⎝ 600 − 400 ⎠
A 2214
ρ − ρ ' = s1 = = 0.018 < K
bd 300 × 410
dUcenH Edkrgkarsgát;Gt; yield ³ f 's < f y
4> KNna f 's ³ f 's = 600[(c − d ') / c] ≤ f y /
kMNt; As1 ³ As1 = 2214mm2
As1 f y 2214 × 400
a= = = 124mm
0.85 f 'c b 0.85 × 28 × 300
a 124
c= = = 145.9mm
β1 0.85
145.9 − 50
f 's = 600 = 394.4 MPa < 400MPa
145.9
5> KNna A's BI M u 2 = φA's f 's (d − d ' )
170.1 ⋅ 106 = 0.9 A's 394.4(410 − 50)
dUcenH A's = 1331mm2 b¤KNna A's BI A's = As 2 ( f y / f 's ) = 1331mm2 ¬ 3DB25 ¦
6> epÞógpÞat;
⎛ dt − c ⎞
εt = ⎜ ⎟0.003
⎝ c ⎠
d t = h − d ' = 500 − 50 = 450mm


T.Chhay NPIC

⎛ 450 − 145.9 ⎞
εt = ⎜ ⎟0.003 = 0.006 > 0.005 φ = 0.9
⎝ 145.9 ⎠
c 145.9
= = 0.324 < 0.375 (OK)
dt 450
7> epÞógpÞat; φM n cugeRkay/ As = 3694.5mm2 / A's = 1472.6mm2 /
As1 = 2221.9mm 2 / a = 124.5mm nig c = 146.5mm
⎛ 124.5 ⎞
M n = 2221.9 × 400⎜ 410 − ⎟ + 1472.6 × 394.4(410 − 50) = 518.15kN .m
⎝ 2 ⎠
epÞógpÞat; ε t / dt = 450mm
⎛ dt − c ⎞
εt = ⎜ ⎟0.003 = 0.006 > 0.005
⎝ c ⎠
φ = 0.9
φM n = 0.9 × 518.15 = 466.3kN .m > 447.5kN .m

6> karKNnamuxkat;GkSret Design of T-Section

kñúgkarKNnamuxkat;GkSret enAeBlEdleKsÁal;m:Um:g;emKuN M u kMras;søab T TTwg b RtUv)ankM
Nt;BIkarKNnakMralxNÐ ehIykarkMNt;rbs; ACI Code sMrab;TTwgsøabRbsiT§PaB b RtUv)aneGayenAkñúg
emeronTI3. kMras;RTnug bw GacRtUv)ansnμt;edayERbRbYlBI 200 → 500mm TMhMEdlRtUv)aneRbIKWsßitenA
cenøaH 300 → 400mm . GBaØatiBIrRtUvkarkMNt;CacaM)ac;KW d nig As . CMhanéjkarKNnaRtUv)ansegçbenA
kñúgemeronTI4.
]TahrN_TI3³ muxkat;FñwmGkSret RtUv)anbgðajenAkñúgrUbTI4 manTTwgRTnug bw = 250mm TTwgsøab b = 1m
kMras;søab t = 100mm nigkMBs;RbsiT§PaB d = 370mm . kMNt;muxkat;EdkcaM)ac;RbsinebIm:Um:g;emKuN
420kN.m . eKeGay f 'c = 28MPa nig f y = 400MPa .

dMeNaHRsay³

viFIKNnaepSgeTot 81

1> KNnaTItaMgTItaMgGkS½NWt Edlmuxkat;GacmanragctuekaN. snμt;kMBs;rbs;bøúksgát; a = 100mm
Edl a = t = 100mm enaH
⎛ t⎞
φM n = φ (0.85 f 'c )bt ⎜ d − ⎟ = 685.44kN .m > 420kN .m
⎝ 2⎠
m:Um:g;KNnaEdlsøabebtugGacRT)anFMCagm:Um:g;emKuNEdlmanGMeBIelIva. dUcenH muxkat;eFVIkar
manragctuekaN.
2> kMNt;muxkat;EdkTaj edayKitmuxkat;manragctuekaNEdl b = 1000mm
Mu 420000000
Ru = = = 3.06 MPa
bd 2
1000 × 370 2
BIsmIkar (5-12) sMrab; Ru = 3.07MPa nig ρ = 0.0092
As = ρbd = 0.0092 × 1000 × 370 = 3404mm 2
eRbI 6DB28 / As = 3694.5mm2 ¬BIrRsTab;¦
3> epÞógpÞat;fa ρ w = As / bwd ≥ ρmin / ρ w = 3404 /(250 × 375) = 0.0363 > ρ min = 0.00333
4> epÞógpÞat; ε t = ⎛ dt c− c ⎞0.003 dt = 375mm
⎜
⎝
⎟
⎠
3404 × 400 57.21
a= = 57.21mm c= = 67.3mm
0.85 × 28 × 1000 0.85
ε t = 0.0135 > 0.005 φ = 0.9

7> viFI strut and tie Strut and Tie Method

1> esckþIepþIm Introduction

ACI Code, Appendix A / ENnaMnUvviFImYyepSgeTot eRkABIviFIEdl)anBnül;BIxagedImenAkñúgem
eronTI 3. viFIenHeKeGayeQμaHfa strut and tie model. viFIepSgenHRtUv)anGnuvtþy:agmanRbsiT§PaBenAkñúg
tMbn;Edldac; discontinuity enAkñúgeRKOgbgÁúM dUcCatMbn;TMr tMbn;EdlbnÞúkGnuvtþ b¤tMbn;Edlmuxkat;FrNI
maRtpøas;bþÚrPøam²dUcCa brackets nig portal frames. enAkñúgtMbn;TaMgenH muxkat;rabesμIminrkSaenArabesμI
eRkayeBlrgkarBt; ¬dUcGVIEdl)ansnμt;enAkñgemeronTI3¦ ehIyvaRtUv)aneKeGayeQμaHfa tMbn; D (D-
region) ¬rUbTI5>5 a¦. tMbn;epSgeTotebs;Fñwmsþg;da RTwsþIbTFñwmmUldæan nigTMnak;TMng linear strain

relationshipRtUv)anGnuvtþ. tMbn;TaMgenHRtUv)aneKeGayeQμaHfa tMbn; B (B-region) ¬rUbTI5>5 a¦.

edayQrelIeKalkarN_ St. Venant PaBdac;KñaenAkñúgkarEbgEckkugRtaMgenAkúñgtMbn; D ¬Edl
bNþalmkBIragFrNImaRt b¤lkçxNÐbnÞúk¦bgðajfakugRtaMgbNþalmkBIbnÞúktamGkS½ nigm:Um:g;Bt; kar
BRgaykugRtaMgesÞIrEtmanlkçN³CabnÞat;enAcMgayRbEhlnwgkMBs; h rbs;Ggát;BIcMnucdac; ¬rUbTI5>5 b nig


T.Chhay NPIC

c¦. RbsinebItMbn; D BIrCan;Kña b¤CYbKña BYkvaGacRtUv)anKitCatMbn; D EtmYy. pleFobrvagRbEvgGtibrma
nigkMBs;esμInwg 2 EdlbegáItmMuGb,brma 26.5o rvag strut and tie ¬b¤RbEhl 25o ¦.

enAkñúgKMrU strut and tie ¬rUbTI5>6¦ cMnucEdlkMlaMgbICYbKñaenAtMN D RtUv)aneKeGayeQμaHfa cMnuc
node nigmaDebtugEdlenACMuvijcMnuc node RtUv)anehAfatMbn;cMnuc nodal zone. kMlaMgEdlmanGMeBIenAelI

cMnuc node GacERbRbYleTAtamkMlaMgTaj nigkMlaMgsgát;énbnSMepSg² dUcCa C − C − C / C − C − T /
C − T − T / T − T − T ¬rUbTI 5>7¦. rUbTI5>8 bgðajBIRbePTtMbn;cMnuc typical nodal zone sMrab;kar

Gnuvtþn_bnÞúkepSg² cMENkÉrUbTI 5>9 bgðajBI extended nodal zone sMrab;sésrEdkmYy b¤eRcInRsTab;.
2> KMrU strut and tie Strut and Tie Model

KMrU strut and tie GacRtUv)anbgðajedayKMrU truss CamYynwgkMlaMgeFVIGMeBIenAelIcMnucepSg². LÚv
BicarNanUv truss EdkEdl)anbgðajenAkñúgrUbTI 5>10. edaysarEtvamanlkçN³sIuemRTI RbtikmμenAcMnuc
A nig B esμIKña R A = RB = 20kN nigBIlMnwgéntMNr A nig D kMlaMgTajenAkñúg AB = 20kN enAeBlEdl

kMlaMgsgát;enAkñúg AD b¤ BD = 28.3kN . Ggát; AB RtUv)anKitCa tie cMENkÉ AD nig BD RtUv)ancat;Tuk
Ca strut. kMlaMgenAkñúgGgát;epSg²eTotesμIsUnü. edayeRbobeFob truss enHCamYyFñwmbtugenAkñúgrUbTI 5>6a
eyIgGaceXIjfaRkLaépÞPaKeRcInén ACD nig BED nigRkLaépÞEdlenABIxageRkam nodal zone D min
manRbsiT§PaB nigeFVIkarCa filler. kMlaMgenAkñúg strut sMrab;lkçxNÐbnÞúkenH FMCagkMlaMgenAkñúg tie. kñúg
krNIenH vamanRkLaépÞebtugRKb;RKan;edIm,IeFVIkarCa strut ¬rUbTI5>6a¦. eKRtUvkarCacaM)ac;nUvsésrEdk
viFIKNnaepSgeTot 83

edIm,IeFVIkarCa tie sMrab; AB . karcgP¢ab;d¾RtwmRtUvrbs; tie mansar³sMxan;Nas;sMrab;karKNnaRbkbeday
suvtßiPaB. karcgP¢ab;KYreFVIeLIgenAtMbn; nodal zone.


T.Chhay NPIC

3> viFIsaRsþKNnatam ACI ACI Design Procedure

edayQrelI ACI Code, Section A.2 karKNnatMbn; D-region rab;bBa©ÚlnUvCMhanxageRkam³
- kMNt; nigbMEbknUvtMbn;nImYy²
- kMNt;kMlaMgpÁÜbEdlmanGMeBIelIEdndMbn; D-region nImYy²
- eRCIserIsKMrU truss edIm,IbBa¢ÚnkMlaMgpÁÜbenAkñúgtMbn; D-region. GkS½én strut nig tie KYrRtYtsIuKñaCa
mYynwgtMbn;sgát; compression field nigtMbn;Taj tension field.
- kMNt;TTwgRbsiT§PaBrbs; struts nig nodal zones edayQrelIersIusþg;ebtug ersIusþg;Edk nigKMrU
truss Edl)aneRCIserIs.

viFIKNnaepSgeTot 85

- epÞógpÞat;lkçxNÐeFVIkar serviceability condition EdleyageTAtamtMrUvkarrbs; ACI Code.
PaBdabrbs;Fñwmx<s; deep beam GacRtUv)anKNnaedayeRbIkarviPaKeGLasÞic elastic analysis.
lkçxNÐRKb;RKgsñameRbHén ACI Code, Section 10.6.4 KYrRtUv)anepÞógpÞat;edaysnμt;fa tie
RtUv)aneRsabenAkñúgRBIsebtug eyagtam RA.4.2 .


T.Chhay NPIC

4> tMrUvkarsMrab;karKNna Design Requirement

tMrUvkarKNnasMrab; struts nig tie GacRtUv)ansnμt;dUcxageRkam³
1> KNna struts, ties nigtMbn; nodal zone
φFn ≥ Fu (5-13)
Edl Fu = kMlaMgenAkñúg struts, ties nigtMbn; nodal zone Edl)anBIbnÞúkemKuN
Fn = ersIusþg; nominal strength rbs; struts, ties nigtMbn; nodal zone

φ = 0.75 sMrab;TaMg struts nig tie
2> ersIusþg;rbs; struts ³ ersIusþg;sgát; nominal compressive strength rbs; struts EdlKμanEdk
beNþay Fns KYrEttUcCagtMél Fns enAcugTaMgBIrrbs; struts ³
Fns = f ce Acs (5-14)
Edl Acs = RkLaépÞmuxkat;enAcugmçagrbs; struts
f ce = ersIusþg;sgát;RbsiT§PaBrbs;ebtugEdltUcCagenAkúñg struts b¤ nodal zone.
f ce = 0.85β s f 's (5-15)
Edl sMrab; struts manrUbragCaRBIs
βs =
β s = sMrab; struts EdlTTwgRtg;muxkat;kNþalGgát;FMCag TTwgenAcMnuc node
(bottle-shaped struts) CamYybrimaNEdkRKb;;RKan;edIm,ITb;nwg kugRtaMgTaj

tamTTwg.
β s = 0.6λ dUcGVIEdl)anerobrab;xagelI edayKμanbrimaNEdkRKb;;RKan;edIm,ITb;nwg
kugRtaMgTajtamTTwg ¬ λ = 1.0 sMrab;ebtugTMgn;Fmμta normal-weight
concrete, 0.85 sMrab; ebtugxSac;TMgn;Rsal sand-lightweight concrete nig

0.75 sMrab;ebtug TMgn;RsalTaMgGs; lightweight concrete¦.

β s = 0.4 sMrab; struts enAkñgGgát;Taj b¤søab
β s = 0.6 sMrab;krNIepSgeTotTaMgGs;
3> EdkExVg struts ¬rUbTI5>11¦³ sMrab; f 'c ≤ 35MPa tMél β s = 0.75 GacRtUv)aneRbIRbsinebI
GkS½rbs; struts RtUv)anExVgedayRsTab;Edk
Asi
∑ sin γ i ≥ 0.003 (5-16)
bs si
Edl Asi = RkLaépÞmuxkat;EdksrubenAKMlat si enAkñúgRsTab;TI i Edlkat; strut enAmMu
α i CamYyGkS½rbs; strut.
si = KMlatEdkenAkñúgRsTab;TI i Edlkat; strut enAmMu α i CamYyGkS½rbs; strut .

viFIKNnaepSgeTot 87

bs =TTwgGgát;
α1 = mMurvagGkS½rbs; strut nigr)arenAkñúgRsTab;TI i énr)arEdlkat;Kñaeday strut.

4> Edkrgkarsgát;enAkñúg struts ³ Edkrgkarsgát;GacRtUv)aneRbIedIm,IbegáInersIusþg;rbs; strut
Fns = f ce Acs + A's f 's (5-17)
Edl Fns = ersIusþg;én strut BRgwgedayEdkbeNþay
A's = RkLaépÞénEdksgát;enAkñúg strut

f 's = kugRtaMgenAkñúg A's ¬ f 's = f y sMrab; 400 → 500 MPa ¦

5> ersIusþg;rbs; tie ³ersIusþg; nominal strength én tie, Fnt KW³
Fnt = Ats f y + Atp ( f se + Δf p ) (5-18)

Edl Ats = RkLaépÞEdkminrgeRbkugRtaMgenAkñúg tie
Atp = RkLaépÞEdkeRbkugRtaMg

f se = kugRtaMgRbsiT§PaBeRkayeBl)at;bg;enAkñúgEdkrgeRbkugRtaMg

Δf p = karbegáInkugRtaMgeRbkugRtaMgEdlbNþalmkBIbnÞúkemKuN

Atp = 0 sMrab;Ggát;minrgeRbkugRtaMg
( f se + Δf p ) ≤ f py (5-19)

eKGacGnuBaØatieGayyk Δf p = 400MPa sMrab; bonded prestressed reinforced b¤
Δf p = 70MPa sMrab; unbonded prestressed reinforced . dUcKña EdnkMNt;x<s;énkarGnuvtþsMrab;

TTwgrbs; tie GacRtUv)anykdUcxageRkam
wt , max = Fnt /( f cebs ) (5-20)


T.Chhay NPIC

6> ersIusþg;rbs;tMbn; nodal zones³ ersIusþg; nominal compression strength éntMbn; nodal zones
Fnn KYrEtesμI
Fnn = f ce Anz (5-21)
Edl RkLaépÞxagebs; nodal zone b¤muxkat;rbs; nodal zone EdlEkgeTAnwgkM
Anz =

laMgpÁÜbenAelImuxkat;
7> karbgçaMgenAkñúgtMbn; nodal zones: y:agehacNas;EdkbgçaMgRtUv)anpþl;eGayenAkñúgtMbn; nodal
zone nigT§iBlrbs;vaRtuv)anKaMRTedaykarBiesaFn_ nigkarviPaK enaHkugRtaMgrgkarsgát;RbsiT§

PaBKNnaenAelIépÞéntMbn; nodal zone EdlbNþalmkBIkMlaMg strut nigkMlaMg tie minKYrelIsBI
tMélxageRkam³
f ce = 0.85β n f 'c (5-22)
Edl β n = 1.0enAkñúgtMbn; nodal zone EdlP¢ab;eday strut b¤ bearing areas b¤TaMgBIr
¬ C − C − C node¦.
β n = 0.8 enAkñúgtMbn; nodal zone Edlf<k;P¢ab; tie mYy ¬ C − C − T node¦.
β n = 0.6 enAkñúgtMbn; nodal zone Edlf<k;P¢ab; tie BIr b¤eRcIn ¬ C − T − T node¦.
karGnuvtþn_énviFI strut and tie method sMrab;Fñwmx<s;manenAkñúgemeronTI8 ]TahrN_TI6.

viFIKNnaepSgeTot 89

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