Xiii footings

Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa

XIII. eCIgtag
FOOTINGS

1> esckþIepþIm Introduction
eCIgtagebtugGarem:CaGgát;éneRKOgbgÁúMEdlRtUv)aneRbIedIm,IRTssr nigCBa¢aMg nigmannaTI
bBa¢Ún ehIynigBRgaybnÞúkrbs;vaeTAdI. karKNnaKWQrelIkarsnμt;faeCIgtagmanlkçN³rwg dUcenH
bMErbMrYlsMBaFdIEdlenABIeRkameCIgtammanlkçN³CabnÞat; (linear). eKTTYl)ansMBaFdImanlkçN³
esμIenAeBlEdlbnÞúkssrRtYtsIuKñaCamYynwgTIRbCMuTMgn;rbs;eCIgtag. ebIeTaHbICakarsnμt;enHGac
TTYlyk)ansMrab;eCIgtagrwg Etkarsnμt;enHkøayeTACaminsUvsuRkitenAeBlEdleCIgtagkøayeTACa
manlkçN³Tn; (flexible) xøaMg. karKNnad¾RtwmRtUvrbs;eCIgtagtMrUveGay³
- minRtUvFMCaglT§PaBRTRTg;bnÞúkrbs;dI.
- RtUveCosvagsMrutFM sMrutDIepr:g;Esül (differential settlement) b¤mMurgVil.
- RtUvmanemKuNsuvtßiPaBRKb;RKan;Tb;nwgkarrGil (sliding) nig¼b¤ karRkLab; (overturning).
RbePTeCIgtagEdlmanlkçN³TUeTAbMputenAkñúgsMNg;RtUv)aneRbIKW single footing nig wall
footing ¬rUbTI13>1 nig 13>2¦. enAeBlEdlbnÞúkssrRtUv)anbBa¢ÚneTAdIedayeCIgtag enaHdIrg

karsgát;. brimaNénsMrutGaRs½ynwgktþaCaeRcIn dUcCa RbePTdI GaMgtg;sIuetbnÞúk CMerABIeRkamnIv:UdI
RbePTeCIgtag. RbsinebIrcnasm<n§½EtmYymaneCIgtagxusKña enaHvanwgmansMrutxusKña ehIykugRtaMg
fμInwgekItmanenAkñúgeRKOgbgÁúM. sMrutDIepr:g;EsülFMnwgbgáeGayGgát;enAkñúgsMNg;EdlminEmnCaeRKOg
bgÁúMrgeRKaHfñak; b¤EpñkxøHEdlrgplb:HBal;Gac)ak;.
CaTUeTAbnÞúkbBaÄrRtUv)andak;enAcMTIRbCMuTMgn;rbs;eCIgtag. RbsinebIkMlaMgGnuvtþn_pÁÜbminRtYt
sIunwgTIRbCMuTMgn;rbs;eCIgtag enaHm:Um:g;Bt;ekItman. kñúgkrNIenH sMBaFenABIeRkameCIgtagmçagFMCag
sMBaFenABIeRkameCIgtagmçageTot.
RbsinebIlT§PaBRTRTg;bnÞúkrbs;dIxusKñaenAeRkameCIgtagepSgKña enaHsMrutDIepr:g;Esülnwg
ekItman ¬]TahrN_ RbsinebIeCIgtagénGKarxøHQrelIdI ÉxøHeTotQrelIfμ¦. enAkñúgkrNIEbbenH
eKKYreFVIkarEcksMNg;enHCaBIrEpñkedaytMN edIm,IGnuBaØateGayvaRsutedayÉkraCBIKña.
CMerAeCIgtagBIeRkamnIv:UdIKWCaktþad¾sMxan;kñugkarKNnaeCIgtag. CMerAKYrRtUv)ankMNt;BIkarBi
esaFn_dI Edl)anpþl;nUvBt’mand¾KYreGayTukcitþBIlT§PaBRTRTg;rbs;dId¾mansuvtßiPaBeTAtamRsTab;dI

Footing 274

T.Chhay NPIC

epSgKñaBIeRkamnIv:UdI. r)aykarN_BIkarBiesaFn_dIkMNt;nUvlT§PaBRTRTg;GnuBaØatedIm,IeRbIkñúgkarKNna.
enAtMbn;RtCak;EdlmanFøak;RBil frost action GacnwgekIneLIg b¤fycuH. dUcenHeKcaM)ac;RtUvdak;eCIg
tagBIeRkam freezing depth edIm,IeCosvagkarmanclna.
2> RbePTeCIgtag Types of Footings
eKmaneCIgtagCaeRcInRbePTEdleRbIsMrab;RTssr b¤CBa¢aMg. eCIgtagEdleKeRbICaTUeTAman
dUcxageRkam³
- Wall footings RtUv)aneRbIedIm,IRT structural wall EdlRTbnÞúkBIkMralxNÐ½ b¤edIm,IRT
nonstructural walls. vamanTTwgkMNt; nigmanRbEvgCab;KñaenABIeRkamCBa¢aMg ¬rUbTI13>1¦. Wall

footings Gac mankMras;EtmYy Gacmanfñak; b¤GacmanCMral.

Footing 275


- b¤ single footings RtUv)aneRbIedIm,IRTssreTal ¬rUbTI13>2¦. vaGacmanragkaer
Isolated,

ctuekaNEkg b¤rgVg;. mþgeTot eCIgtammankMras;esμI manfñak; b¤manCMral. vaCaRbePTeCIgtagEdl
manlkçN³snSMsMécbMput negvaRtUv)aneRbIenAeBlssrmanKMlatq¶ay. RbePTEdleKcUlcitþeRbI
CageKKWmanragkaer b¤ctuekaNEkgCamYykMras;esμI.
- Combined footing ¬rUbTI13>3¦CaTUeTARTssrBIr b¤ssrbIEdlminenACYrEtmYy. ragrbs;

eCIgtagkñúgbøg;GacCactuekaNEkg b¤ctuekaNBñay GaRs½ynwgbnÞúkssr. Combined footings
RtUv)aneRbIenAeBlssrBIrenACitKñaEdleCIgtag single footings minGaceRbI)an b¤enAeBlssrmYy
sßitenAelI b¤enAEk,r property line.

Footing 276

T.Chhay NPIC

- ¬rUbTI13>4¦ rYmmaneCIgtag single footings BIrP¢ab;edayFñwm
Cantilever or strap footings

mYy b¤ strap mYy nigRTssreTalBIr. vaRtUv)aneRbIenAeBlEdleCIgtagmYyRTssrcakp©it ehIy
eCIgtagmYysßitenAEk,rmancMgayKMlattUc. RbePTeCIgtagenHCMnYs combined footings nigeBlxøH
manlkçN³snSMsMécCag.
- Continuous footings ¬rUbTI13>5¦ RTnUvssrmYyCYrEdlmancMnYncab;BIbIeLIg. vamanTTwg

kMNt; nigCab;KñaBIeRkamssrTaMgGs;.

Footing 277


- Raft or mat foundations ¬rUbTI13>6¦ pSMeLIgedayeCIgtagmYy CaTUeTARtUv)andak;enABI
eRkamtYGKarTaMgmUl nigRTssrGKar. vaRtUv)aneRbIenAeBl
a. lT§PaBRTRTg;rbs;dItUc

b. bnÞúkssrFM

c. Single footings minGaceRbI

d. Piles minRtUv)aneRbI

e. sMrutDIepr:g;EsülRtUv)ankat;bnßytamry³RbBn§½RKwHTaMgmUl

- Pile caps ¬rUbTI13>7¦ CakMralxNÐ½Rkas;EdlRtUv)aneRbIedIm,IcgP¢ab;RkumssrRKwHCamYyKña

nigedIm,IRT nigbBa¢ÚlbnÞúkssreTAssrRKwH.

3> karBRgaysMBaFdI Distribution of soil pressure
rUbTI 13>8 bgðajBIeCIgtagEdlRTssreTal. enAeBlbnÞúkssr P RtUv)andak;enABIelITI
RbCMuTMgn;eCIgtag enaHsMBaFesμIRtuv)ansnμt;ekItmanenAelIépÞdIBIeRkamépÞeCIgtag. b:uEnþkarBit kar
BRgaysMBaFdIBitR)akdminesμIeT vaGaRs½ynwgktþaCaeRcIn CaBiessGaRs½ynwgFatupSMrbs;dI
(composition of the soil) nigkMritTn;rlas; (degree of flexibility) rbs;eCIgtag.

]TahrN_ karBRgaysMBaFenAelIdIEdlKμanPaBs¥it (cohesionless soil) b¤dIxSac;enABIxag
eRkameCIgtagrwg (rigid footing) RtUv)anbgðajenAkñúgrUbTI 13>9. sMBaFmantMélGtibrmaenABIxag
eRkamGkS½eCIgtag ehIyfycuHenAxagcugeCIgtag. dIEdlKμanPaBs¥it)ancl½tecjBIcugéneCIgtag
begáIteGaymankarkat;bnßysMBaF b:uEnþsMBaFekIneLIgenAmþúMGkS½edIm,IbMeBjlkçxNÐlMnwg. RbsinebI
Footing 278

T.Chhay NPIC

eCIgtagsßitenABIelIdIs¥it (cohesive soil) dUcCadIdæ sMBaFenABIxageRkamcugeCIgtagFMCagenARtg;
GkS½rbs;eCIgtag ¬rUbTI 13>10¦. dIdæEk,rcugRKwHmanPaBs¥itxøaMgCamYynwgdIdæenAEk,rEdlBT§½CMu
vijeCIgtag begáIt)anCakarBRgaysMBaFminesμI.
CaTUeTAsMBaFdIRTRTg;GnuBaØat qa RtUv)ankMNt;ecjBIkarBiesaFn_dI. sMBaFdIRTRTg;GnuBaØat
enHERbRbYleTAtamRbePTdI BItMélx<s;bMputsMrab;RsTab;fμ (rocky bed) eTAtMélTabbMputsMrab;Rs
Tab;dIl,b; (silty soil). ]TahrN_ qa sMrab; sedimentary rock esμI 1450kN / m 2 / sMrab;
compacted gravel esμI 400kN / m 2 / sMrab; well-graded compacted sand esμI 300kN / m 2 / nig

sMrab; silty-gravel esμI 150kN / m 2 .

eyagtamrUbTI 13>8 enAeBlEdlbnÞúk P manGMeBI EpñkéneCIgtagBIeRkamssrrkklnwg
RsutcuHeRkam. eCIgtagnwgyknUvTMrg;ExSRtg;esμI EdlbegáItCasMBaFbukeLIgelIvijedIm,ITb;Epñkén

Footing 279


eCIgtag. EpñknImYy²mannaTICa cantilever nigRtUv)anKNnasMrab;TaMgm:Um:g;Bt; nigkMlaMgkat;TTwg.
karKNnaeCIgtagnwgRtUv)anBnül;y:aglMGitenAeBleRkay.
4> karBicarNakñúgkarKNna Design Consideration
eCIgtagRtUv)anKNnaedImI,RTbnÞúkssr nigbBa¢nbnÞúkssreTAdIy:agsuvtßiPaB. viFIsaRsþkñúg
Ú
karKNnaRtUvEtykersIusþg;caM)ac;xageRkammkBicarNa³
- RkLaépÞeCIgtagQrelIlT§PaBRTRTg;dIGnuBaØat
- kMlaMgkat;mYyTis one-way shear
- kMlaMgkat;BIrTis two-way shear b¤kMlaMgpug punching shear
- m:Um:g;Bt; nigbrimaNEdkRtUvkar
- lT§PaBRTRTg;rbs;ssrenA)atrbs;va nigEdk dowel caM)ac;
- RbEvgf<k;rbs;Edk
- sMrutDIepr:g;Esül
ersIusþg;caM)ac;TaMgenHnwgRtUvBnül;enAkñúgEpñkxageRkam.
4>1> TMhMeCIgtag Size of Footing

RkLaépÞeCIgtagGacRtUv)anKNnaBIbnÞúkxageRkABitR)akd ¬m:Um:g; nigbnÞúkKμanemKuN¦Edl
minFMCaglT§PaBRTRTg;rbs;dI. CaTUeTA sMrab;bnÞúkQr
RkLaépÞeCIgtag = total service load (including selfq- weight)
allowable soil pressure,
¬!#>!¦
a

b¤ Area = P(total )qa
Edl bnÞúkeFVIkarsrubCabnÞúkKNnaKμanemKuN. enAeBlEdlRkLaépÞRtUv)ankMNt; sMBaFdI
emKuNRtUv)anTTYledayEckbnÞúkemKuN Pu = 1.2D + 1.6L eday®kLaépÞeCIgtag. kareFVI
EbbenHedIm,IKNnaeCIgtagtamviFIKNnaersIusþg; (strength design method) .
qu =
Pu
area of footing
¬!#>@¦
sMBaFdIGnuBaØat qa RtUv)anTTYlBIkarBiesaFn_dI nigQrelIlkçxNÐbnÞúkeFVIkar (service
load) .

Footing 280

T.Chhay NPIC

4>2> kMlaMgkat;mYyTis ¬kMlaMgkat;Fñwm¦ Vu1 One-Way Shear (Beam
Shear)
sMrab;eCIgtagCamYynwgkMlaMgBt;mYyTis muxkat;eRKaHfñak;sßitenAcMgay d BIépÞmuxrbs;ssr.
kMlaMgTajGgát;RTUgenAmuxkat; m − m kñúgrUbTI13>11 GacRtUv)anBinitüemIldUcGVIEdl)aneFVIsMrab;
Fñwm. kMlaMgkat;TTwgGnuBaØatenAkñúgkrNIenHesμInwg³
2
φVc = φ f 'c bd
12
¬ φ = 0.75 ¦ ¬!#>#¦
Edl b = TTwgrbs;muxkat; m − m . kMlaMgkat;TTwgemKuNenAmuxkat; m − m GacRtUv)an
KNnadUcxageRkam³
⎛L C ⎞
Vu1 = qu b⎜ − − d ⎟
⎝2 2 ⎠
¬!#>$¦
RbsinebIEdkkMlaMgkat;TTwgminRtUv)aneRbI enaH d GacRtUv)anKNna edaysnμt; Vu = φVc ³
d=
12Vu1
2φ f ' b
¬!#>%¦
c

4>3> kMlaMgkat;BIrTis ¬kMlaMgpug¦ Vu1 Two-Way Shear (Punching
Shear)

Footing 281


kMlat;kat;BIrTisCargVas;énkMlaMgTajGgát;RTUgEdlbNþalmkBIT§iBlénbnÞúkssrenAelI
eCIgtag. sñameRbHeRTt GacekIteLIgenAkñúgeCIgtagenAcMgay d / 2 BImuxépÞssrenARKb;RCug. eCIg
tagnwg)ak;enAeBlEdlssrBüayamTMluHEpñkéneCIgtag ¬rUbTI13>12¦.
ACI Code, Section 11.12.2 GnuBaØatersIusþg;kMlaMgkat;TTwg Vc enAkñúgeCIgtagEdlKμanEdk

kMlaMgkat;TTwgsMrab;GMeBIkMlaMgkat;BIrTis esμInwgtMéltUcCageKbMputén
Vc1 =
4
12
f 'c bo d ¬!#>^¦
⎛ 4 ⎞ f ' c bo d
Vc 2 = ⎜ 2 + ⎟
⎜ β ⎟ 12
¬!#>&¦
⎝ ⎠
⎛α d ⎞ f ' c bo d
Vc3 = ⎜ s + 2 ⎟
⎜ b ⎟ 12 ¬!#>*¦
⎝ o ⎠
Edl β= pleFobRCugEvgelIRCugxøIrbs;ssr
bo = brimaRténmuxkat;eRKaHfñak;EdlenAcMgay d / 2 BIRkLaépÞbnÞúk ¬muxkat;ssr¦

emIlrUbTI 13>12
d = kMBs;RbsiT§PaBrbs;eCIgtag

Footing 282

T.Chhay NPIC

sMrab;tMél Vc1 nig Vc2 eyIgeXIjfa Vc1 lb; ¬tUcCag Vc2 ¦ enARKb;eBlEdl β ≤ 2 b:uEnþ
Vc 2 lb; ¬tUcCag Vc1 ¦ enARKb;eBlEdl β > 2 . enHbgðajeGayeXIjfakMlaMgkat;TTwgGnuBaØat

Vc RtUv)ankat;bnßysMrab;eCIgtagEvgxøaMg. bMErbMrYlsMBaFdIBitR)akdtambeNþayRCugEvgCamYynwg

karekIneLIgén β . sMrab;rUbragdéTeToteRkABIctuekaN β KWCapleFobrvagTMhMEvgCageKbMputénRk
LaépÞbnÞúkRbsiT§PaBkñúgTisedAEvg elITTwgFMCageKbMputkñúgTisedAxøI ¬EkgnwgTisedAEvg¦.
sMrab;smIkar ¬!#>*¦ α s RtUv)ansnμt;esμI 40 sMrab;ssrenAkNþal/ esμI 30 sMrab;ssrenA
xag nigesμI 20 sMrab;ssrenARCug. ersIusþg;kMlaMgkat;TTwgrbs;ebtug Vc3 bgðajBIT§iBlénkMeNIn
bo elI d . sMrab;pleFobx<s;én bo / d enaH Vc3 nwglb;.

QrelItMélTaMgbIxagelIrbs; Vc kMBs;RbsiT§PaB d EdlcaM)ac;sMrab;kMlaMgkat;BIrTisKW)an
mkBItMélEdlFMCageKkñúgcMeNamrUbmnþxageRkam ¬ φ = 0.75 ³
d1 =
3Vu 2
φ f' b
¬Edl β ≤ 2 ¦
c o

¬!#>(¦
b¤ d1 =
⎛
12Vu 2
4⎞
¬Edl β > 2 ¦ ¬!#>!0¦
φ ⎜ 2 + ⎟ f ' c bo
⎜
⎝ β⎟⎠
d2 =
⎛α d
12Vu 2
⎞
¬!#>!!¦
φ ⎜ s + 2 ⎟ f ' c bo
⎜ b ⎟
⎝ o ⎠
kMlaMgkat;TTwgBIrTis Vu 2 nigkMBs;RbsiT§PaB d caM)ac; ¬RbsinebIEdkkMlaMgkat;TTwgmin
RtUv)aneRbI¦GacRtUv)anKNnadUcxageRkam ¬eyagtamrUbTI 13>12¦³
a. snμt; d

b. kMNt; bo ³ bo = 4(c + d ) sMrab;ssrkaer EdlRCugesμI c .

bo = 2(c1 + d ) + 2(c 2 + d ) sMrab;ssrctuekaN EdlmanRCugesμInwg c1 nig c 2

c. kMlaMgkat;TTwg Vu 2 eFVIGMeBIenAelImuxkat;EdlmanbeNþay bo = 4(c + d ) b¤ bo = 2(c1

+ d ) + 2(c 2 + d ) nigkMBs; d . muxkat;enHrgnUvkMlaMgbBaÄrcuHeRkam Pu nigkMlaMg

bBaÄreLIgelI qu ¬smIkar !#>@¦. dUcenH
Vu 2 = Pu − qu (c + d ) 2 sMrab;ssrkaer ¬!#>!@a¦
Vu 2 = Pu − qu (c1 + d )(c 2 + d ) sMrab;ssrctuekaNEkg ¬!#>!@b¦

Footing 283


d. kMNt; d FMbMput ¬én d1 nig d 2 ¦. RbsinebI d EdlrkeXIjminmantMélEk,rtMél
d Edl)ansnμt; eFVIkarsnμt;nigedaHRsayeLIgvij.

4>4> ersIusþg;Bt; nigEdkeCIgtag Flexural Strength and Footing
Reinforcement
muxkat;eRKaHfñak;sMrab;m:Um:g;Bt;ekItmanenABImuxépÞssr ¬muxkat; n − n / rUbTI 13>13¦.
eKRtUvBinitüemIlm:Um:g;Bt;enAelITisnImYy²rbs;eCIgtag nigdak;brimaNEdkRKb;RKan;. sMrab;eCIgtag
kaer nigssrkaer m:Um:g;Bt;mantMélesμIKñaTaMgBIrTis. edIm,IkMNt;muxkat;EdkcaM)ac; eKRtUveRbIkMBs;
rbs;eCIgtagTaMgBIrTis. edaysarEtEdkenAkñúgTismYysßitenAelIEdkenAkñúgTismYyeTot kMBs;Rb
siT§PaB d ERbRbYleTAtamGgát;p©itrbs;EdleRbI. tMélmFümrbs; d GacRtUv)anykmkeRbI. tMél
sMrab;karGnuvtþn_ d RtUv)ansnμt;esμI h − 110mm .

Footing 284

T.Chhay NPIC

CaerOy² kMBs;RbsiT§PaBrbs;eCIgtagRtUv)anRKb;RKgedaykMlaMgkat;TTwg EdlcaM)ac;
RtUvkarkMBs;eCIgtagFMCagkMBs;eCIgtagEdlRtUvvkaredaym:Um:g;Bt;. EdkBRgwgkñúgTisedAnImYy²Gac
RtUv)anKNnaenAkñúgkrNIGgát;rgkarBt;dUcxageRkam³
⎛ As f y ⎞
M u = φAs f y ⎜ d −
⎜
⎟
1.7 f ' b ⎟
¬!#>!#¦
⎝ c ⎠
mü:ageTot PaKryEdk ρ GacRtUv)ankMNt;dUcxageRkam ¬smIkar $>@¦
0.85 f ' c ⎡ ⎤
ρ=
fy ⎢
⎢1 − 1 −
2 Ru
⎥
φ (0.85 f ' c ) ⎥
¬!#>!$¦
⎣ ⎦
Edl Ru = M u / bd 2 . enAeBlEdl Ru RtUv)ankMNt; ρ k¾RtUv)anTTYlBIsmIkar !#>!$.
tMrYvkarpleFobEdkGb,brmaenAkñúgGgát;rgkarBt;KWesμInwg 1.4 / f y enAeBl
f 'c < 31MPa nigesμInwg f ' c / 4 f y enAeBl f 'c ≥ 31MPa . b:uEnþ ACI Code, Section 10.5

bgðajfasMrab;kMralxNÐ½ EdlmankMras;esμI RkLaépÞGb,brma nigKMlatGtibrmaénEdkenAkñúgTisedA
énkarBt;KYrRtUvkarEdkrYmmaD nigEdksItuNðPaB. tMrUvkarEdkGb,brmaelIkeRkayenHmantMéltUc
ehIypleFobEdkGb,brmaEdlmantMélFMCagRtUv)anesñIeLIg EtvaminKYrFMCag 1.4 / f y .
EdkenAkñúgeCIgtagmYyTis nigeCIgtagBIrTisRtUvEtBRgayeBjTTwgeCIgtag. kñúgkrNI
eCIgtagctuekaNBIrTis ACI Code, Section 15.4.4 kMNt;faenAkñúgTisedAEvg EpñkénEdksrub γ s l
RtUv)anEbgEckesμIenAelITTwgrbs;eCIgtag. enAkñúgTisedAxøI PaKryBitR)akdrbs;EdksrubenAkñúgTis
edAenHRtUvEt)andak;esμIenAkñúg bandwidth esμInwgRbEvgénRCugxøIéneCIgtagGaRs½ynwg
γs =
2
β +1
¬!#>!%¦
Edl β=
long side of footing
short side of footing
¬!#>!^¦
Bandwidth RtUvEtsßitenAkNþalénGkS½rbs;ssr ¬rUbTI13>14¦. EdkEdlenAsl;enA

kñúgTisedAxøIRtUvEtBRgayesμIBIxageRkA Bandwidth . PaKryEdkenAsl;enHminKYrticCagEdkrYm maD
nigEdksItuNðPaB.
enAeBlEdlssreRKOgbgÁúMGMBIEdk b¤ssrdæRtUv)aneRbI enaHmuxkat;eRKaHfñak;sMrab;m:Um:g;
Bt;enAkñúgeCIgtagRtUv)anykenAcenøaHBak;kNþal nigEKmCBa¢aMgdæ nigcenøaHBak;kNþalépÞssrnig
EKmén steel base plate (ACI Code, Section 15.4.2).

Footing 285


4>5> lT§PaBRTRTg;rbs;ssrenAelIKl; Bearing Capacity of Column at
Base
bnÞúkmkBIssrmanGMeBIelIeCIgtagenAKl;rbs;ssr EdlmanRkLaépÞesIμnwgRkLaépÞmux
kat;ssr. kMlaMgsgát;RtUv)anbBa¢ÚnmkssredaypÞal;eday bearing enAelIebtug. kMlaMgEdlman
GMeBIenAelIebtugenARtg;Kl;énssrminRtUvelIslT§PaBRTRTg;rbs;ebtugEdlkMNt;eday ACI Code,
Section 10.17 ³

lT§PaBRTRTg; N1 = φ (0.85 f 'c A1 ) ¬!#>!&¦
Edl φ = 0.65 nig A = RkLaépÞ bearing énssr. tMélénlT§PaBRTRTg;EdleGay
1

edaysmIkar 13.17 GacRtUv)anKuNedayemKuN A / A ≤ 2.0 sMrab; bearing enAelIeCIgtagenA
2 1

eBlépÞEdlRTFMCagRkLaépÞbnÞúkenARKb;RCug. A enATIenHCaRkLaépÞénEpñkéneCIgtagEdlrUb
2

FrNImaRtdUcKña ehIyRtYtsIuKñaCamYynwgRkLaépÞbnÞúk ¬rUbTI 13>15¦. edaysarEt A > A enaH 2 1

emKuN A / A nwgFMCagmYy EdlbgðajfalT§PaBRTRTg;GnuBaØatekIneLIgedaysarTMrxagénRk
2 1

LaépÞeCIgtagEdlBT§½CMuvijKl;ssr. lT§PaBRTRTg;kMEN modified bearing strength KW³
A
N 2 = φ (0.85 f ' c A1 ) 2 ≤ 2φ (0.85 f ' c A1 )
A
¬!#>!*¦
1

RbsinebIbnÞúkemKuN P FMCag N b¤ N EdkRtUv)andak;edIm,IbBa¢ÚnkMlaMgelIs. eKGac
u 1 2

TTYlva)anedaydak;Edk dowel b¤EdkssrRtUv)andak;bgðÜscUleTAkñúgeCIgtag. kMlaMgelIsKW
Pex = Pu − N1 ehIyRkLaépÞrbs;Edk dowel KW Asd = ( Pex / f y ) ≥ 0.005 A1 Edl A CaRkLaépÞ 1

rbs;muxkat;ssr. y:agehacNas;EdkbYnedImRtUv)aneRbIbYnedImenARCugTaMgbYnrbs;ssr.

RbsinebIkMlaMgemKuNtUcCag N b¤ N enaHeKdak;EdkGb,brma. ACI Code, Section
1 2

15.8.2 bgðajfaRkLaépÞEdkGb,brmarbs;Edk dowel y:agehacNas;esμInwg 0.005 Ag ¬nigminRtUv

Footing 286

T.Chhay NPIC

ticCagbYnedIm¦ Edl A CaRkLaépÞeBj (gross section) rbs;muxkat;ssr. EdkGb,brmak¾RtUv)an
g

eRbIEdrenAeBlEdlkMlaMgemKuNFMCag N b¤ N . Edk dowel RtUv)andak;enARCugTaMgbYnrbs;ssr
1 2

ehIybgðÜscUleTATaMgkñúgssr nigTaMgkñúgeCIgtag. Ggát;p©itEdk dowel minKYrFMCagEdkbBaÄrenAkñúg
ssr 4mm . tMrUvkarenHcaM)ac;edIm,IFanakareFVIkard¾l¥rvagssr nigeCIgtag. Edkb®Ba¢Üsrbs;Edk
dowel RtUv)anBinitüemIledIm,IkMNt;nUvkarbBa¢Únd¾l¥énkMlaMgsgát;eTAkñúgeCIgtag.

4>6> RbEvgEdkRCYs Development Length of the Reinforcing bars
muxkat;eRKaHfñak;sMrab;RtYtBinitüRbEvgEdkbgáb;dUcKñasMrab;m:Um:g;Bt;. RbEvgbgáb;sMrab;
Edksgát;RtUv)aneGayenAkñúgemeronTI7³
0.24 f y d b
l dc =
f 'c
b:uEnþvaenHminRtUvtUcCag 0.044d b f y ≥ 20cm . sMrab;tMélepSgeToteyag tamemeronTI7.
4>7> sMrutDIepr:g;Esül ¬karKNnaeCIgtagkñúglkçxNÐlMnwg¦
Differential Settlement (Balanced Footing Design
CaTUeTAeCIgtagRTnUvbnÞúkdUcxageRkam³
- bnÞúkefrEdl)anmkBIeRKagxageRkam (substructure) nigeRKagxagelI
(superstructure) .

- bnÞúkGefrEdlGnuvtþmkelI
- TMgn;rbs;sMPar³EdleRbIsMrab;cak;bMeBj
- bnÞúkxül;
eCIgtagnImYy²enAkñúgGKarRtUv)anKNnaedIm,IRTbnÞúkGtibrmaEdlGacekItmanenAelIssr
Edl)anBIkarbnSMbnÞúkd¾eRKaHfñak;bMput edayeRbIsMBaFRTRTg;rbs;dIGnuBaØat.

Footing 287


bnÞúkefr nigRbEhlCabnÞúkGefrmYyEpñktUc ¬EdleKehAfa bnÞúkGefrFmμta (usual live
load)¦ GacGnuvtþCab;Gt;dac;mkelIeRKagsMNg;. bnÞúkGefrEdlenAsl;epSgeTot GacekItmanyUr²

mþg ehIymanGMeBImkelIeRKagsMNg;EpñkxøHEtb:ueNÑaH EdlbNþaleGaymanbnÞúkepSg²KñaenAelIssr.
dUcenH sMBaFdIenABIeRkameCIgtagepSgKña nwgERbRbYlGaRs½ynwgbnÞúkenAelIssr ehIysMrutDIepr:g;
EsülnwgekItmanenABIeRkameCIgtagepSgKñaénsMNg;EtmYy. edaysarsMrutedayEpñk (partial
settlement) minGaceCosput enaHbBaðabEgVreGaysMrutDIepr:g;Esülrbs;sMNg;CagGt;eGaneGay)an.

brimaNénsMrutDIepr:g;EsülGaRs½ynwgPaBxusKñaénkMritENnrbs;dI/ kMras;sMPar³EdlGacsgát;)an
enABIeRkamnIv:UeCIgtag nigPaBrwgRkajén combined footing nigsMNg;xagelI. sMrutDIepr:g;EsülFM
eFIVeGayebtugeRbH nigeFVIeGayxUcxatdl;kargarbegðIy (cladding or finishing) CBa¢aMgxNÐ½ nigBidan.
sMrutDIepr:g;EsülGacsMEdgedaykarrmUlrbs;eRKag (angular distortion of structure).
Bjerrum bgðajfakarEdkkMNt;eRKaHfñak;rbs;karrmYlsMrab;lkçxNÐxøHERbRbYlcenøaHBI 1 / 600 eTA

1 / 150 GaRs½ynwgkarxUcxatEdlnwgekItmanenAelIrcnasm<n§½.

sMrab;karGnuvtþn_ eKGacsnμt;fasMBaFdIeRkambnÞúkefrmantMélesμIKñasMrab;RKb;eCIgtag dUcenH
vaeFVIeGaymanbnÞúkesμI. bnÞúkefr ¬b¤bnÞúkFmμta¦ GacRtUv)ansnμt;esμInwgplbUkrvagbnÞúkGefr nig
PaKryénbnÞúkGefrEdlekItmanCaerOy²enAelIeRKagsMNg;. KμankrNIEdllT§PaBRTRTg;dIGnuBaØat
FMCagbnÞúkefrbUknwgbnÞúkGefrGnuBaØatsMrab;eCIgtagnImYy²eT. ]TahrN_TI 13>4 Bnül;BIviFIsaRsþ
sMrab;KNnaRkLaépÞeCIgtag EdlykmkKitBicarNaBIT§iBlrbs;sMrutDIepr:g;Esül.
5> eCIgtagebtugsuT§ Plain Concrete Footings
eCIgtagebtugsuT§GacRtUv)aneRbIedIm,IRTCBa¢aMgdæ b¤bnÞúkRsal nigbBa¢ÚlbnÞúkTaMgenaHeTAdI
Edlva. ACI Code GnuBaØateGayeRbIeCIgtagebtugsuT§enAelIdI RbsinkugRtaMgKNnaminRtUvFMCag
krNIxageRkam³
- kugRtaMgrgkarBt;GtibrmasMrab;karTajRtUvEttUcCagb¤esμInwg 5φ f 'c / 12 ¬Edl
φ = 0.55 ¦
- kugRtaMgGtibrmaenAkñúgkMlaMgkat;TTWgmYyTis (beam action)RtUvtUcCagb¤esμInwg φ f 'c / 9
¬Edl φ = 0.55 ¦
- kugRtaMgGtibrmaenAkñúgGMeBIBIrTisKW

Footing 288

T.Chhay NPIC

⎛1 2 ⎞ 2.66
⎜ 9 9 β ⎟φ f ' c ≤ 12 φ f ' c
⎜ + ⎟ ¬Edl φ = 0.55 ¦
⎝ ⎠
- ersIusþg;kMlaMgsgát;GtibrmaminKYrFMCagkarkMNt;rbs;lT§PaBRTRTg;ebtugGnuBaØat. f 'c
énebtugsuT§minKYrtUcCag 17MPa .
- kMras;Gb,brmarbs;eCIgtagebtugsuT§minKYrtUcCag 20cm .
- muxkat;eRKaHfñak;sMrab;m:Um:g;Bt;KWsßitenAépÞrbs;ssr b¤CBa¢aMg.
- muxkat;eRKaHfñaksMrab;GMeBIénkMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTisKWsßitenAcMgay
d nig d / 2 BIépÞénssr b¤CBa¢aMg erogKña. eTaHbICaeCIgtagebtugsuT§minRtUvkarEdkk¾eday

k¾vaCakarEdlRbesIkñúgkardak;sésEdkrYmmaDsMrab;TisTaMgBIrrbs;eCIgtag.
- kugRtaMgEdlbNþalBIbnÞúkemKuNRtUv)anKNnaedaysnμt;BRgayCaragbnÞat;enAkñúgebtug.
- kMBs;RbsiT§PaB d RtUv)anKitfaesμInwgkMBs;srubdkeGay 75mm .
- sMrab;karBt; nigkMlaMgkat;mYyTis eRbImuxkat;eBj bh b:uEnþsMrab;kMlaMgkat;BIrTis eRbI b h
o

edIm,IKNna φVc .
]TahrN_ 13>1³ KNnaeCIgtagebtugBRgwgedayEdkedIm,IRTCBa¢aMgebtugEdlmanTTwg 50cm Edl
RTbnÞúkefr 379.5kN / m EdlrYmbBa©ÚlbnÞúkpÞal;rbs;CBa¢aMg nigRTnUvbnÞúkGefr 292kN / m . )at
rbs;eCIgtagsßitenACMerA 1.8m BInIv:UdI. eKeGay f ' = 28MPa / f y = 400MPa nigsMBaFdIGnuBaØat
c

0.24MPa = 240kN / m . 2

dMeNaHRsay³
1> KNnasMBaFdIRbsiT§PaB. snμt;kMBs;srubrbs;eCIgtagKW 50cm . TMgn;rbs;eCIgtagKW
0.5 × 25 = 12.5kN / m . edaysnμt;TMgn;maDrbs;dIesμInwg 16kN / m
2 3

enaHTMgn;dIbMeBjBIelIeCIgtagKW 16 × (1.8 − 0.5) = 20.8kN / m .
2

bnÞúkCBa¢aMgEdlbgáb;enAkñúgdIKW 25 × 0.5 × (1.8 − 0.5) /1m = 16.25kN / m .
2

bnÞúkCBa¢aMgebtugbgát;kñúgdIKitCadI 16 × 0.5 × (1.8 − 0.5) /1m = 10.4kN / m .
2

sMBaFdIRbsiT§PaBenA)atrbs;eCIgtagKW 240 − 12.5 − 20.8 − 16.25 + 10.4 = 200.85kN / m . 2

2> KNnaTTwgrbs;eCIgtagsMrab;CBa¢aMgRbEvg 1m
TTwgrbs;eCIgtag = bnÞúksrub ¼ sMBaFdIRbsiT§PaB
total loal
width of footing =
effective soil pressure

Footing 289


379.5 + 292
= = 3.34m
200.85
yk 3.4m
3> sMBaFdIsuT§= bnÞúkemKuN ¼ TTwgeCIgtag ¬sMrab;RbEvg 1m ¦
Pu = 1.2 D + 1.6 L = 1.2 × 379.5 + 1.6 × 292 = 922.6kN / m

sMBaFdIsuT§ æ =
(net upward pressure) q u =
922.6
3.4
= 271.4kN / m 2

4> epÞógpÞat;kMBs;snμt;sMrab;tMrUvkarkMlaMgkat;TTwg. kMras;karBarEdksMrab;eCIgtagKW 75mm
ehIysnμt;eRbIEdk DB25 enaH d = 500 − 75 − 12 = 413mm . muxkat;eRKaHfñak;sMrab;kMlaMg
kat;TTwgmYyTisKWsßitenAcMgay d BIépÞénBa¢aMg³
⎛B c⎞ ⎛ 3400 500 ⎞ −6
Vu = q u ⎜ − d − ⎟ = 271.4⎜ − 413 − ⎟10 = 0.28kN
⎝2 2⎠ ⎝ 2 2 ⎠
kMlaMgkat;TTwgmYyTisGnuBaØat= 0.17 28 = 0.9
d EdlRtUvkar =
Vu 280
= = 415mm
0.17φ f ' b 0.75 × 0.9 × 1
c

kMBs;srubKW 415 + 75 + 12 = 502mm b¤ 500mm . d Cak;EsþgKW 500 − 75 − 12 = 413mm
¬dUckarsnμt;¦.
cMNaMfa eKnwgRtUvkarkarsakl,gmYycMnYnedIm,Isnμt; nigKNnatMél d eGaymantMélEk,r.
5> KNnam:Um:g;Bt; nigEdk. muxkat;eRKaHfñak;KWsßitenAépÞénCBa¢aMg³
2 2
1 ⎛B c⎞ 271.4 ⎛ 3.4 0.5 ⎞
M u = qu ⎜ − ⎟ = ⎜ − ⎟ = 285.3kN .m
2 ⎝ 2 2⎠ 2 ⎝ 2 2 ⎠
M 285.3 ⋅ 10 6
Ru = u = = 1.67 MPa
bd 2 1000 × 413 2
sMrab; Ru = 1.67MPa / f ' c = 28MPa nig f y = 400MPa enaHPaKryEdk
0.85 f ' c ⎡ 2 Ru ⎤ 0.85 × 28 ⎡ 2 × 1.67 ⎤
ρ= ⎢1 − 1 − ⎥= ⎢1 − 1 − ⎥ = 0.0048
fy ⎢
⎣ φ (0.85 f ' c ) ⎥
⎦ 400 ⎣ 0.9 × 0.85 × 28 ⎦

PaKryEdkGb,brmasMrab;Ggát;rgkarBt;
1.4 1.4
ρ min = = = 0.0035
f y 400

PaKryEdkrYmmaDKW 0.18% ¬sMrab; f y = 400MPa ¦. dUcenHeRbI ρ = 0.0048 dUcEdl)an
KNna
As = 0.0048 × 1000 × 413 = 1982.4mm 2 / m

Footing 290

T.Chhay NPIC

eRbIEdk DB25 EdlmanKMlat 225mm ¬ As = 2182mm 2 ¦
6> RtYtBinitüRbEvgEdkbgáb;sMrab;Edk DB25
l d = 48d b = 48 × 25 = 1200mm ¬eyagtamemeronTI 7¦
EdleGay
B c 3400 500
ld = − − 75 = − − 75 = 1375mm
2 2 2 2
7> KNnaEdkrgkñúgTisedAbeNþayeCIgtag³ As = 0.0018 × 1000 × 500 = 900mm 2 / m
eRbIEdk DB16 KMlat 200mm ¬ A = 1005mm ¦. bøg;lMGitRtUv)anbgðajenAkñúgrUbTI
s
2

13>16.

]TahrN_ 13>2³ KNnaeCIgtag single footing edIm,IRTssrebtugeRbIEdkkgFmμtasßitenAxagkñúg
EdleRbI 8DB28 . ssrenHRTnUvbnÞúktamGkS½GefrKμanemKuN 1090kN nigbnÞúkcMGkS½efrKμanem
KuN 890kN . )atrbs;eCIgtagsßitenACMerA 1200mm BInIv:UdI ehIysMBaFdIGnuBaØatKW 240kN / m 2 .
eKeGay f 'c = 28MPa / f y = 400MPa .
dMeNaHRsay³
1> KNnasMBaFdIRbsiT§PaB. snμt;kMras;srubrbs;eCIgtag 600mm . TMgn;eCIgtagKW 0.6 × 25
= 15kN / m . bnÞúkdIenABIelIeCIgtag ¬snμt;TMgn;maDrbs;dIesμInwg 16kN / m ¦ KW 0.6 × 16
2 3

= 9.6kN / m 2
sMBaFdIRbsiT§PaBKW = = 240 − 15 − 9.6 = 215.4kN / m 2

Footing 291


2> KNnaRkLaépÞrbs;eCIgtag
bnÞúkeFVIkar = D + L = 1090 + 890 = 1980kN
RkLaépÞeCIgtag = 215.4 = 9.2m
1980 2

RCugrbs;eCIgtagKW = 3.03m
dUcenHeRbI = 3m ¬rUbTI 13>17¦
3> sMBaFdIsuT§= bnÞúkemKuN ¼ RkLaépÞeCIgtag
Pu = 1.2 D + 1.6 L = 1.2 × 1090 + 1.6 × 890 = 2732kN

sMBaFdIsuT§ æ =
(net upward pressure) q u =
2732
3× 3
= 303.6kN / m 2

4> epÞógpÞat;kMBs;snμt;EdlbNþalmkBIkMlaMgkat;TTwgBIrTis. RbsinebIeKGt;eRbIEdkkMlaMgkat;
TTwg enaHkMlaMgkat;TTwgBIrTiskMNt;kMBs;caM)ac;rbs;eCIgtag. sMrab;kMBs;eCIgtagsrubsnμt;
600mm KNna d eTAGkS½TIRbCMuTMgn;énEdkRsTab;xagelIedIm,Idak;enAkñúgeCIgtagTaMgBIrTis.

eRbIEdk DB15 sMrab;KNna d .
d = 600 − 75 − 37 = 488mm
¬vaCakarRbesIrEdlsnμt; d = h − 112 ¦
bo = 4(c + d ) = 4(450 + 488) = 3752mm

c + d = 450 + 488 = 938mm
Vu 2 = Pu − q u (c + d )2 = 2732 − 303.6(0.450 + 0.488)2 = 2464.9kN
3 × 2464900
d1 caM)ac;=
3Vu 2
φ f ' c bo
=
0.75 × 28 × 3752
¬
= 496.6mm β = 1 smIkar !#>(¦
12 × 2464900
d2 caM)ac;=
⎛αsd
12Vu 2
⎞
=
⎛ 40 × 488 ⎞
= 275.8mm
φ⎜ 0.75⎜ + 2 ⎟ 28 × 3752
⎜ b + 2 ⎟ f ' c bo
⎟ ⎝ 3752 ⎠
⎝ o ⎠
¬ α = 40 sMrab;ssrenAkNþal¦ edaysar d > d snμt; dUcenHeyIgRtUveFVIkarKNnasak
s 1

l,grhUtdl; d nig d mantMélRbEhlKña. eRkayBIkarKNnamkeyIgTTYl)an
1

h = 610mm / d = 498mm / d = 495.5mm . dUcenH kMBs;snμt;elIkeRkay h = 610mm
1

RKb;RKan;.
5> RtYtBinitükMBs;EdlbNþaledaysarGMeBIkMlaMgkat;mYyTis³ muxkat;eRKaHfñak;enAcMgay d BI
épÞssr

Footing 292

T.Chhay NPIC

cMgayBIcugeCIgtag = ⎜ L − 2 − d ⎞ = 777mm
⎛
⎝2
c
⎟
⎠
Vu1 = 303.6 × 0.777 × 3 = 707.7kN
kMBs;caM)ac;sMrab;kMlaMgkat;TTwgmYyTisKW
Vu1 707700
d= = = 350mm < 498mm
0.75 × 0.17 f ' c b 0.75 × 0.17 28 × 3000
6> KNnaEdk nigm:Um:g;Bt;. muxkat;eRKaHsßitenAépÞssr. cMgayBIcugeCIgtagKW
⎛L c⎞
⎜ − ⎟ = 1500 − 225 = 1275mm
⎝ 2 2⎠
2
1 ⎛L c⎞ 1
M u = q u ⎜ − ⎟ b = 303.6 × 1.275 2 × 3 = 740.3kN .m
2 ⎝ 2 2⎠ 2
M 740.3 ⋅ 10 6
Ru = u = = 0.995MPa
bd 2 3000 × 498 2
BIsmIkar !#>!$ eyIg)an ρ = 0.0028
As = ρbd = 0.0028 × 3000 × 498 = 4183.2mm 2
AsGb,brma ¬EdkrYmmaD¦ = 0.0018 × 3000 × 498 = 2689.2mm < 4183.2mm 2 2

A Gb,brma ¬EdkrgkarBt;¦ = 0.0033 × 3000 × 498 = 4930.2mm
s
2

dUcenH eyIgyk As = 4930.2mm 2 . eRbI 13DB22 ¬ As = 4941.7mm 2 ¦ KMlat rbs;EdkKW
s = (3000 − 150) / 12 = 237.5mm enAkñúgTiwedATaMgBIr.

7> RtYtBinitükugRtaMgRT (bearing stress)
a. ersIusþg;RT (bearing strength) N enA)atrbs;ssr ¬ A1 = 450 × 450mm 2 ¦KW
1

N1 = φ (0.85 f ' c A1 ) = 0.65 × 0.85 × 28 × 450 × 450 × 10 −3 = 3132.7 kN
b. ersIusþg;RT (bearing strength) N enAépÞxagelIrbs;eCIgtag ¬ A
2 2 = 3 × 3m 2 ¦ KW
A2
N 2 = N1 ≤ 2N1
A1

A2 = 9000000mm 2 A1 = 202500mm 2
9000000
= 6.67 > 2
202500
dUcenH N 2 = 2 N1 = 6265.4kN . edaysar Pu = 2732kN < N1 enaHkugRtaMgRTKWRKb;
RKan;. RkLaépÞGb,brmaénEdk dowel caM)ac;KW 0.005 A = 0.005 × 450 × 450
1

Footing 293


= 1012.5mm 2 . cMnYnEdkGb,brmaKW 4 dUcenHeRbIEdk DB25 dak;enARCugTaMgbYnrbs;
ssr.
c. RbEvgbgáb;rbs;Edk dowel enAkñúgkMlaMgsgát;³
0.24d b f y 0.24 × 25 × 400
l dc = = = 453.5mm
f 'c 28
Gb,brma = 0.044d b f y = 440mm > 200mm . dUcenHeRbIEdk dowel DB25 4edIm
l dc

RbEvg 455mm dak;kñúgssrnigeCIgtag. cMNaMfa l dc < d = 498mm RKb;RKan;.
8> RbEvgbgáb;rbs;EdkemenAkñúgeCIgtagsMrab; DB22 KW l d = 48 × 22 = 1056mm ¬eyagtamem
eronTI 7¦. RbEvgbgáb;BitR)akdenAkñúgeCIgtagKW l = L / 2 − c / 2 − 75 = 1500 − 225 − 75
d

= 1200mm . bøg;lMGitrbs;eCIgtagRtUv)anbgðajenAkñúgrUbTI 13>17.

Footing 294

T.Chhay NPIC

]TahrN_ 13>3³ KNnaeCIgtagragctuekaNsMrab;ssrén]TahrN_TI13>2 RbsinebIRCugmYyrbs;
eCIgtagRtUv)ankMNt;esμI 2.6m .
dMeNaHRsay³
1> viFIsaRsþKNnasMrab;eCIgtagctuekaNmanlkçN³RsedogKñanwgkarKNnaeCIgtagkaer eday
KitBicarNaGMeBIrbs;kMlaMgmkelIeCIgtagtmaTisnImYy²dac;edayELkBIKña.
2> BI]TahrN_mun RkLaépÞcaM)ac;rbs;eCIgtagKW 9.2m 2

beNþayeCIgtag = 9..2 = 3.54m
26
dUcenHyk 3.6m ¬rUbTI 13>18¦. TMhMeCIgtagKW 2.6 × 3.6m 2

3> Pu = 2732kN . dUcenH sMBaFdIsuT§ æ (net upward pressure) KW
2732
qu = = 291.9kN / m 2
2.6 × 3.6
4> RtYtBinitükMBs;EdlbNþalBIkMlaMgkat;TTwgmYyTis. muxkat;eRKaHfñak;sßitenAcMgay d BIépÞ
rbs;ssr. sMrab;TisedAEvg
⎛L c ⎞
Vu1 = ⎜ − − d ⎟ × q u b
⎝2 2 ⎠
⎛ 3.6 0.45 ⎞
=⎜
⎝ 2
−
2
− 0.498 ⎟ × 291.9 × 2.6 = 817.4kN
⎠
kMlaMgkat;TTwgenHlb;
sMrab;TisedAxøI V = 606.3kN ¬mineRKaHfñak;¦
u1

6 × 817.4 ⋅ 10 3
d caM)ac; =
6Vu1
= = 475mm
φ f ' b 0.75 28 × 2600
c

EdleRbI = 498mm > 475mm
d

5> RtYtBinitüGMeBIkMlaMgkat;TTwgBIrTis ¬kMlaMgkat;pug (punching shear)¦. muxkat;eRKaHfñak;
enAcMgay d / 2 BIépÞssrTaMgbYnRCug.
bo = 4(450 + 498) = 3792mm

(c + d ) = 450 + 498 = 948mm
3.6
β= = 1.38 < 2
2.6
eRbI Vu = φ f ' c bo d / 3

Vu 2 = Pu − q u (c + d ) 2 = 2732 − 291.9 × 0.948 2 = 2469.7kN

Footing 295


3Vu 2 3 × 2469700
d1 = = = 492mm
φ f ' c bo 0.75 × 28 × 3792

d 2 = 271.5mm
6> KNnaEdkenAkñúgTisedAEvg. muxkat;eRKaHfñak;enAnwgépÞénTMr. cMgayBIcugéneCIgtagKW
L c 3600 450
− = − = 1575mm
2 2 2 2
1
M u = 291.9 × 1.575 2 × 2.6 = 941.3kN .m
2
M 941.3 ⋅ 10 −3
Ru = u = = 1.46MPa
bd 2 2.6 × 0.498 2
GnuvtþtamsmIkar !#>!$ eyIgTTYl)an ρ = 0.0042
As = 0.0042 × 2600 × 498 = 5438.2mm 2
As Gb,brma ¬EdkrYmmaD¦ = 0.0018 × 2600 × 610 = 2855mm 2
As Gb,brma ¬EdkrgkarBt;¦ = 0.0033 × 2600 × 498 = 4273mm 2

eRbI As = 5438.2mm 2 . eRCIserIs 10DB28 ¬ As = 6157.5mm 2 ¦ KMlatEdkKW
S = (2600 − 150 ) / 9 = 272mm
7> KNnaEdkenAkñúgTisedAxøI. cMgayBIépÞssreTAcugeCIgtagKW
2600 450
− = 1075mm
2 2
1
M u = 291.9 × 1.075 2 × 3.6 = 607.2kN .m
2
M 607.2 ⋅ 10 −3
Ru = u = = 0.68MPa
bd 2 3.6 × 0.498 2
GnuvtþeTAkñúgsmIkar !#>!$ eK)an ρ = 0.0019
As = 0.0019 × 3600 × 498 = 3406mm 2
As Gb,brma ¬EdkrYmmaD¦ = 0.0018 × 3600 × 610 = 3953mm 2
As Gb,brma ¬EdkrgkarBt;¦ = 0.0033 × 3600 × 498 = 5916mm 2

tMélrbs; As EdlRtUveRbIRtUvEtFMCagb¤esμI 3953mm 2 . eRbI 18DB20 ¬ As = 5655mm 2 ¦
2 2
γs = = = 0.84
β + 1 3 .6
+1
2 .6
cMnYnEdkenAkñúgcMerokRbEvg 2.6m KW 18 × 0.84 = 15 edIm. cMnYnEdkenAsl;sMrab;RCug mçag²KW
(18 − 15) / 2 = 2 edIm. dUcenHdak;Edk 15DB 20 enAkñúgcMerokRbEvg 2.6m ehIydak;

Footing 296

T.Chhay NPIC

2 DB 20 ¬ As = 628mm 2 ¦ enAelIRbEvg 0.5m enAelIRCugnImYy²sgçagcMerok 2.6m .
cMnYnEdksrubKW 19 edIm. enAkñúg]TahrN_enH EdkRtUv)anBRgayedayKMlatesμI²Kña elIRbEvg
3.6m / S = (3600 − 150 ) / 18 = 192mm . bøg;lMGitsésrEdkRtUv)anbgðajenAkñúg

rUbTI !#>!*.
8> RtYtBinitükugRtaMgRTenA)atssr dUcEdl)anBnül;enAkñúg]TahrN_mun. eRbIEdk dowel
DB 25 cMnYn 4 edIm.

9> RbEvgbgáb;rbs;Edkem l d = 960mm sMrab; DB20 nig l d = 1344mm sMrab; DB28 .
⎛ 3600 450 ⎞
l d Edldak; ¬TisEvg¦ = ⎜ − − 75 ⎟ = 1500mm
⎝ 2 2 ⎠
l d Edldak; ¬TisxøI¦ = 1000mm

Footing 297


]TahrN_ 13>4³ KNnaRkLaépÞeCIgtagcaM)ac;sMrab;sMrutesμIKña ¬karKNnaeCIgtagEdlmanlMnwg
(balanced footing design) ¦ RbsinebIbnÞúkGefrFmμta (usual live load) esμI 20%
sMrab;RKb;eCIgtagTaMgGs;. eCIgtagrgnUvbnÞúkefr nigbnÞúkGefrdUcbgðajenAkñúgtaragxageRkam.
sMBaFdIsuT§GnuBaØat (allowable net soil pressure) esμI 287kN / m 2 .
elxeCIgtag
1 2 3 4 5

bnÞúkefr 535kN 800kN 620kN 845kN 935kN

bnÞúkGefr 670kN 980kN 890kN 755kN 1070kN

dMeNaHRsay³
1> kMNt;eCIgtagEdlmanpleFobbnÞúkGefrelIbnÞúkefrFMCageK. enAkñúg]TahrN_enH eCIgtag
elx 3 manpleFob 1.44 FMCagpleFobdéT.
2> KNnabnÞúkFmμtasMrab;RKb;eCIgtagTaMgGs;. bnÞúkFmμtaKWCabnÞúkefr nigEpñkénbnÞúkGefr
EdlmanGMeBIrCaTUeTAenAelIeRKagsMNg;. enAkñúg]TahrN_enH
bnÞúkFmμta = D.L + 0.2( L.L)
tMélénbnÞúkFmμtaRtUv)anbgðajenAkñúgtaragxageRkam.
3> kMNt;RkLaépÞrbs;eCIgtagEdlmanpleFob L.L / D.L
D.L + L +
RkLaépÞeCIgtagelx 3 = allowable soilL.pressure = 620287890 = 5.26m 2
sMBaFdIFmμtaeRkameCIgtagelx 3 KW
Usual load 798
= = 151.7 kN / m 2
Area of footing 5.26
4> KNnaRkLaépÞcaM)ac;sMrab;eCIgtagnImYy²edayEckbnÞúkFmμtarbs;vaedaysMBaFdIenAeRkam
eCIgtagelx 3 . RkLaépÞrbs;vaRtUvbgðajenAkñúgtaragxageRkam. ]TahrN_ eCIgtagelx 1
RkLaépÞcaM)ac;rbs;vaesμI 669 / 151.7 = 4.41m 2 .
5> KNnasMBaFdIGtibrmaeRkameCIgtagnImYy²
D+L
q max = ≤ 287kN / m 2 ¬sMBaFdIGnuBaØat¦
area

Footing 298

T.Chhay NPIC

elxeCIgtag
1 2 3 4 5
Dead load
Live load 1.25 1.225 1.44 0.89 1.14

bnÞúkFmμta = D.L + 0.2( L.L) (kN ) 669 996 798 996 1149

RkLaépÞcaM)ac; = Usual load (m 2 )
151.7
4.41 6.57 5.26 6.57 7.57

sMBaFdIGtibrma = D + L (kN / m 2 )
area 273.2 270.9 2.87 243.5 264.9

]TahrN_ 13>5³ KNnaeCIgtagebtugsuT§edIm,IRTCBa¢aMgebtugEdlmankMras; 400mm . bnÞúkEdl
manGMeBIelICBa¢aMgrYmmanbnÞúkefr 233.5kN / m ¬rYmbBa©ÚlbnÞúkpÞal;rbs;CBa¢aMgrYc¦ nigbnÞúkGefr
146kN / m . )atrbs;eCIgtagsßitenACMerA 1200mm BInIv:UdI. eKeGay f 'c = 20MPa nigsMBaFdI

GnuBaØat 240kN / m 2 .
dMeNaHRsay³
1> KNnasMBaFdIRbsiT§PaB. snμt;kMBs;srubeCIgtagKW 710mm
TMgn;rbs;eCIgtag = 0.71× 24 = 17kN / m 2
edaysnμt;TMgn;maDdIesμI 16kN / m 3 enaHTMgn;rbs;dIenAelIeCIgtagesμI (1.2 − 0.71) × 16
= 7.84kN / m 2 .

sMBaFdIRbsiT§PaBKW 240 − 17 − 7.84 = 215.16kN / m 2 .
2> KNnaTTwgeCIgtagsMrab;CBa¢aMgRbEvg 1m ¬ b = 1m ¦
total load
width of footing =
effective soil pressure
233.5 + 146
=
215.16
= 1.76m yk 1.8m ¬rUbTI 13>19¦
3> U = 1.2D + 1.6L = 1.2 × 233.5 + 1.6 × 146 = 513.8kN / m
sMBaFdIsuT§ (net upward pressure) esμI qu = 513.8 / 1.8 = 285.4kN / m 2
4> RtYtBinitükugRtaMgBt;. muxkat;eRKaHfñak;KWsßitenAépÞCBa¢aMg. sMrab;RbEvg1m énCBa¢aMg
nigeCIgtag
2 2
1 ⎛L c⎞ 1 ⎛ 1 .8 0 .4 ⎞
M u = qu ⎜ − ⎟ = 285.4⎜ − ⎟ = 69.9kN .m
2 ⎝ 2 2⎠ 2 ⎝ 2 2 ⎠

Footing 299


kMNt;kMBs;RbsiT§PaB d esμI 710 − 75 = 635mm edaysnμt;fa)at 75mm KμanRb siT§PaB.
bd 3 1000 × 6353
Ig = = = 2.13 ⋅ 1010 mm 4
12 12
M c 69.9 ⋅ 10 6 ⎛ 635 ⎞
kugRtaMgTajedaykarBt;KW fr = u = ⎜
⎝ 2 ⎠
⎟ = 1.04MPa
I 2.13 ⋅ 1010
kugRtaMgTajedaykarBt;GnuBaØatKW 0.415φ f 'c = 0.415 × 0.55 20 = 1.02MPa ¬Ek,r¦
5> RtYtBinitükugRtaMgkMlaMgkat;TTwg³ muxkat;eRKaHfñak;sßitenAcMgay d = 635mm BIépÞCBa¢aMg
⎛L c ⎞ ⎛ 1.8 0.4 ⎞
Vu = qu ⎜ − − d ⎟ = 285.4⎜ − − 0.635 ⎟ = 18.55kN
⎝2 2 ⎠ ⎝ 2 2 ⎠
f ' c bd 0.55 20 × 1000 × 635 × 10 −3
φVc = φ = = 173.5kN
9 9
dUcenH muxkat;manlkçN³RKb;RKan;. vaCakarRbesIrEdleRbIbrimaNEdkGb,brmasMrab;TaMg
BIrTis.

6> Combined Footings

enAeBlEdlssrmanTItaMgsßitenAEk,rRBM enaHEpñkéneCIgtag single footing GaclycUl
eTAkñúgRBMGñkCitxag. edIm,IeCosvagsßanPaBEbbenH eKGacdak;ssrenAelIRCugEKméneCIgtag
begáIt)anCabnÞúkcakp©it. eKminGaceRbIdMeNaHRsayenHsMrab;lkçxNÐxøH nigeBlxøHvaCadMeNaHRsay
EdlminsnSMsMéc. karKNnad¾l¥GacTTYledalbBa©ÚleCIgtagCamYynwgeCIgtagssrxagkñúgEdlsßit

Footing 300

T.Chhay NPIC

enACitCageK begáIt)anCa combined footing . TIRbCMuTMgn;rbs; combined footing RtYtsIuKñaCamYy
nwgkMlaMgpÁÜbénssrTaMgBIr.
krNIepSgeTot Edl combined footing caM)ac;RtUv)aneRbIKWenAeBlEdldImanlkçN³exSay
ehIyeCIgtagssrmYyKgelIeCIgtagenAEk,r. ragrbs;eCIgtag combined footing GacCactuekaN
Ekg b¤ctuekaNBñay ¬rUbTI 13>20¦. enAeBlEdlbnÞúkssrxagenAEk,rRBMmantMélFMCagbnÞúkssr
kñúg eCIgtagmanragctuekaNBñayGacRtUv)aneRbIedIm,IrkSaTIRbCMuTMgn;eCIgtagenAelIExSCamYynwgbnÞúk
pÁÜbénssrTaMgBIr. CaTUeTA eKcUlcitþeRbIeCIgtagragctuekaNEkg.

beNþay nigTTwgrbs;eCIgtagRtUv)aneRCIserIsedaykMeNInmþg 75mm EdlGacbNþaleGay
sMBaFBRgayesμIenAeRkameCIgtagERbRbYltUc. sMrab;sMBaFBRgayesμIeLIgelI (uniform upward
pressure) eCIgtagnwgdabdUcbgðajenAkñúgrUbTI 13>21. ACI Code, Section 15.10 min)anpþl;nUvviFI

KNnalMGitsMrab; combined footing eT. CaTUeTA karKNnaQrelIkarviPaKeRKOgbgÁúM (structural
analysis).

Footing 301


viFId¾samBaØénkarKNnaKWcat;TukeCIgtagdUcFñwmenAkñúgTisedAEvg EdlRTnUvsMBaFBRgayesμI
eLIgelI (uniform upward pressure) qu . sMrab;TisedATTwg eKsnμt;fabnÞúkssrRtUv)anBRgay
eBjTTwgenABIeRkamssrEdlesμInwgTTwgssrbUknwg d énRCugnImYy². mü:agvijeTot bnÞúkssrman
GMeBIelIFñwmenAeRkamssrCamYynwgeCIgtagEdlmanTTWgGtibrma c + 2d nigbeNþayesμInwgRCugxøI
rbs;eCIgtag ¬rUbTI 13>22¦. eKk¾GaceRbITTwgEdlmantMéltUcCagrhUtdl; c + d .

]TahrN_ 13>6³ KNnaeCIgtag combined footing ragctuekaNEkgedIm,IRTssrBIrdUcbgðajkñúg
rUbTI 13>23. ssrxagelx I manmuxkat; 400 × 400mm nigRTnUv D.L. 800kN nig L.L 535kN .
ssrxagkñúgelx II manmuxkat; 500 × 500mm nigRTbnÞúk D.L. 1115kN nig L.L 625kN . sMBaF
dIGnuBaØatKW 240kN / m 2 ehIy)atrbs;eCIgtagsßitenACMerA 1.5m BInIv:UdI. KNnaeCIgtagedayeRbI
f 'c = 28MPa / f y = 400MPa nigviFIKNnaersIusþg; ACI.

dMeNaHRsay³
1> kMNt;TItaMgkMlaMgpÁÜbénbnÞúkssr. Kitm:Um:g;CMuvijGkS½énssrxagelx I ³
(1115 + 625) × 4900
x= = 2772.7m BIssr I
(1115 + 625) + (800 + 535)
cMgayBIkMlaMgpÁÜbmkExSRBMKW 2772.7 + 600 = 3372.7mm . RbEvgrbs;eCIgtagKW
3372.7 × 2 = 6745.4mm yk 6750mm . kñúgkrNIenHkMlaMgpÁÜbrbs;ssrRtYtsIuKñaCamYy

nwgkMlaMgpÁÜbrbs;sMBaFdIEdlmanGMeBIelIeCIgtag.
2> kMNt;RkLaépÞrbs;eCIgtag. snμt;kMBs;eCIgtagsrub 920mm ¬ d = 920 − 115 = 805mm ¦

Footing 302

T.Chhay NPIC

bnÞúkeFVIkarsrub = 800 + 535 + 1115 + 625 = 3075kN ¬Total actual (working)load¦
sMBaFdIfμI = 240 − 0.92 × 25 − 0.58 × 16 = 207.72kN / m 2 ¬New upward pressure¦
¬snμt;TMgn;maDdI 16kN / m 3 ¦
RkLaépÞcaM)ac; = 207.72 = 14.8m 2 ¬Required area¦
3075

TTwgeCIgtag = 1475 = 2.19m ¬Width of footing¦
6.
.8

ykTTwgeCIgtagesμI 2.2m . dUcenHTMhMeCIgtagKW 6.75 × 2.2m ¬RkLaépÞ 14.85m 2 ¦
3> kMNt;sMBaFdIemKuN ¬factored soil pressure¦ edayeRbIbnÞúkemKuN³
Pu1 ¬ssrelx I¦ = 1.2 × 800 + 1.6 × 535 = 1816kN

Pu 2 ¬ssrelx II¦ = 1.2 × 1115 + 1.6 × 625 = 2338kN

sMBaFdIemKuNsuT§KW qu = (1816 + 2338) / 14.85 = 279.73kN / m 2 ¬net factored soil
pressure¦

4> KUrdüaRkamkMlaMgkat;TTwgemKuNsMrab;FñwmEdlmanRbEvg L = 6750mm EdlenAelIssrBIr
nigrgnUvsMBaFdI 279.73 × 2.2 = 615.4kN / m ¬kñúgRbEvgeCIgtag 1m ¦
Vu ¬enAépÞxageRkArbs;ssr I ¦ = 615.4 × (0.6 − 0.2) = 246.16kN

Vu ¬enAépÞxagkñúgrbs;ssr I ¦ = 1816 − 615.4(0.6 + 0.2 ) = 1323.68kN

Vu ¬enAépÞxageRkArbs;ssr II ¦ = 615.4 × (1.25 − 0.25) = 615.4kN

Vu ¬enAépÞxagkñúgrbs;ssr II ¦ = 2338 − 615.4 × (1.25 + 0.25) = 1414.9kN

5> KUrdüaRkamm:Um:g;emKuNedayKiteCIgtagCaFñwmEdlman L = 6750mm RTedayssrBIr.
sMBaFdIBRgayesμI 615.4kN / m
0.4 2
M u1 ¬enAépÞxageRkAssr I ¦ = 615.4 × = 49.2kN.m
2
12
M u2 ¬enAépÞxagkñúgssr II ¦
= 615.4 × = 307.7kN.m
2
m:Um:g;GtibrmaekItmanenAkMlaMgkat;TTwgesμIsUnü
M u Gtibrma¬KNnaBIssr I ¦ = 1816(2.15 + 0.2) − (2.15 + 0.2 + 0.6)2
615.4
2

= 1589.84kN .m
Mu Gtibrma¬KNnaBIssr II ¦ = 2338(2.3 + 0.25) − 615.4 (2.3 + 0.25 + 1.25)2
2

Footing 303


= 1518.7 kN .m
m:Um:g;EdlKNnaBIRCugTaMgBIréneCIgtagRtUvmantMélRbhak;RbEhlKña. kñúgkrNIenH
eyIgyk M u max = 1589.84kN.m . bMErbMrYltMélrbs;m:Um:g;GaRs½yCacMbgCamYynwgRbEvg
nigTTwgrbs; eCIgtag.
6> RtYtBinitükMBs;sMrab;kMlaMgkat;mYyTis. kMlaMgkat;TTwgGtibrmaekItmanenAcMgay
d = 805mm BIépÞssrxagkñúg II ¬rUbTI 13>23¦.

Vu1 = 1414.9 − 615.4 × 0.805 = 919.5kN
Vu1 919500
d= = = 619.5mm
φ 0.17 f 'c b 0.75 × 0.17 × 2200 × 28
kMBs;RbsiT§PaBEdleGayKW d = 805mm > 619.5mm dUcenHeCIgtagmanlkçN³RKb;RKan;.
7> RtYtBinitükMBs;sMrab;kMlaMgTTwgBIrTis ¬kMlaMgkat;pug¦. sMrab;ssrxagkñúg
bo = 4(c + d ) = 4(500 + 805) = 5220mm

(c + d ) = (500 + 805) = 1305mm
kMlaMgkat;TTwg Vu 2 enAmuxkat; d / 2 BIRKb;RCugrbs;ssresμI
Vu 2 = Pu 2 − qu (c + d ) 2 = 2338 − 279.73 × 1.305 2 = 1861.6kN
3Vu 2 3 × 1861600
d= = = 269.6mm < 805mm
φ f 'c bo 0.75 28 × 5220
ssrxageRkARtUv)anRtYtBinitünigbgðajfaminmaneRKaHfñak;.
8> RtYtBinitükMBs;sMrab;m:Um:g; nigkMNt;sésrEdkcaM)ac;enAkñúgTisEvg
m:Um:g;Bt;Gtibrma = 1589.84kN.m
Mu 1589.84 ⋅ 10 6
Ru = = = 1.115MPa
bd 2 2200 × 805 2
GnuvtþkñúgsmIkar ¬!#>!$¦ PaKryEdkKW ρ = 0.0032 ≈ 0.0033(ρ min )
As = 0.0033 × 2200 × 805 = 5844.3mm 2
As Gb,brma ¬rYmmaD¦ = 0.0018 × 2200 × 920 = 3643.2mm 2
As = 5844.3mm 2 lb;. eRbI 10DB 28 ¬ As = 6157.5mm 2 ¦

KMlatEdk = 22009−(no. of spacing) = 228mm
150 (concrete cover)

Footing 304

T.Chhay NPIC

EdkRtUv)andak;bgðÚtenAcenøaHssrenAEpñkxagelIeCIgtagCamYykMras;karBarEdk 75mm .
dak;EdkGb,brmaenA)atrbs;eCIgtagedIm,ITb;nwgm:Um:g;viC¢man. RtYtBinitüRbEvgbgáb; ld BIépÞ
ssr.
EdkGb,brmaKW As = 3643.2mm 2 . eRbI 8DB25 ¬ As = 3927mm 2 ¦.
RbEvgEdkbgáb;caM)ac;sMrab;EdkemxagelIKW 1.3ld = 1.3 × 48 × d b = 1747mm RtUv)andak;
ecjBIcMnucm:Um:g;Gtibrma. RbEvgEdkbgáb;Edldak;enARtg;ssrTaMgBIrKWRKb;RKan;.
9> sMrab;EdkenAkñúgTisedAxøI. karKNnam:Um:g;Bt;enAkñúgTisedAxøI ¬TisedATTwg¦ maklkçN³
dUcKñakñúgkrNI single footing. EdkenAeRkamssrnImYy² RtUv)andak;enAkñúgcMerokTTwg
(bandwidth) EdlesμInwgplbUkTTwgssrnigkMBs;RbsiT§PaB d BIrdg ¬rUbTI !#>@$¦.

a. EdkenABIeRkamssr I³
Bandwidth = 400 (column width) + 400 (on exterior side of column) + 805

= 1605mm
eRbI 1.6m . sMBaFdIeLIgelIsiT§enAkñúgTisedAxøIeRkamssr I KW
Pu1 1816
= = 825.5kN / m
width of footing 2.2
cMgayBIcugTMenreTAépÞssrKW 2200 400
2
−
2
= 900mm

Mu ¬enAépÞénssr ¦I =
825.5 2
2
0.9 = 334.3kN.m

M 334.3 ⋅ 10 6
Ru = u = = 0.32MPa
bd 2 1600 × 805 2
PaKryEdk ρ tUcCagPaKryEdkGb,brmasMrab;EdkrYmmaD 0.0018 .
As min = 0.0018 × 1600 × 920 = 2649.6mm 2
eRbI 6DB25 ¬ As = 2945.2mm 2 ¦ dak;enAkñúg bandwidth RbEvg 1.6m .
b. EdkenABIeRkamssr II³
Bandwidth = 500 + 805 + 805 = 2110mm
eRbI 2100mm . sMBaFdIeLIgelIsiT§enAkñúgTisedAxøIeRkamssr II KW
Pu 2 2338
= = 1062.7kN / m
width of footing 2.2
cMgayeTAépÞssrKW 2200 500
2
−
2
= 850mm

Mu ¬enAépÞénssr kñúgTisedAxøI¦
II =
1062.7
2
0.85 2 = 383.9kN.m

Footing 305


Mu 383.9 ⋅ 10 6
Ru = = = 0.28MPa
bd 2 2100 × 805 2
PaKryEdk ρ tUcCagPaKryEdkGb,brmasMrab;EdkrYmmaD 0.0018 .
As min = 0.0018 × 2100 × 920 = 3477.6mm 2
eRbI 8DB25 ¬ As = 3927mm 2 ¦ dak;enAkñúg bandwidth RbEvg 2.1m BIeRkamssr
II dUcbgðajenAkñúgrUb !#>@# nig !#>@$. RbEvgbgáb;rbs;Edk DB 25 enAkñúgTisedAxøI

KW 1.2m .

Footing 306

T.Chhay NPIC

7> eCIgtageRkambnÞúkssrcakp©it Footings under Eccentric Column Loads
enAeBlEdlssrbBa¢ÚnEtkMlaMgtamGkS½ enaHeKGacKNnaeCIgtagEdlmanbnÞúkeFVIGMeBIcMTIRb
CMuTMgn;rbs;eCIgtag EdlbegáIt)anCasMBaFBRgayesμIeRkameCIgtag. b:uEnþ enAkñúgkrNIxøHssrbBa¢ÚnkM
laMgcMGkS½ nigm:Um:g;Bt; dUckñúgkrNIeCIgtageRKagbgáb;cug (fixed-end frame). sMBaF q EdlekItman
enAelIdInwgminBRgayesμI EdlGackMNt;BIsmIkarxageRkam³
q= ±
P Mc
A I
≥0 ¬!#>!(¦
Edl A nig I CaRkLaépÞ nigm:Um:g;niclPaBéneCIgtag erogKña. eKmanlkçxNÐdIxusKñaEdl
GaRs½ynwgtMél P nig M / nig sMBaFdIGnuBaØat. lkçxNÐKNnaxusKñaRtUv)anbgðajenAkñúgrUbTI
13> 25 nigRtUv)ansegçbdUcxageRkam³
1> enAeBl e = M / P < L / 6 sMBaFdImanragctuekaNBñay
P Mc
q max = +
A I
=
P 6M
LB
+ 2 ¬!#>@0¦
BL

Footing 307


q min =
P Mc
A
−
I
=
P 6M
−
LB BL2
¬!#>@!¦
2> enAeBl e = M / P = L / 6 sMBaFdImanragctuekaNEkg
q max =
P 6M 2 P
+ =
LB BL2 LB
¬!#>@@¦
q min =0=
P 6M
−
LB BL2
b¤ P
=
6M
LB BL2
¬!#>@#¦

3> enAeBlEdl e > L / 6 sMBaFdImanragRtIekaN
L− y L
x= = −e
3 2

Footing 308

T.Chhay NPIC

⎛ 3x ⎞
P = q max ⎜ ⎟ B
⎝ 2⎠
q max =
2P
=
4P
3xB 3B ( L − 2e)
¬!#>@$¦
4> enAeBleCIgtagRtUv)anrMkilcMgay e BIGkS½énssredIm,IbegáItsMBaFdIBRgayesμI
enAeRkameCIgtag. m:Um:g;GtibrmaekItmanenAmuxkat; n − n
M = M '− Hh nig e =
M
P

8> eCIgtageRkamm:Um:g;BIrTis Footings under Biaxial Moment
enAkñúgkrNIxøH eCIgtagGacrgnUvkMlaMgtamGkS½ nigm:Um:g;Bt;BIrTisCMuvijGkS½ x nigGkS½ y dUc
krNIm:asIunsÞÚcEdlbgVilxøÜn)an 360o . enaHeCIgtagRtUv)anKNnasMrab;bnÞúkeRKaHfñak;.
tamrUbTI 13>26 RbsinebIbnÞúkcMGkS½ P manGMeBIenAcMgay ex BIGkS½ y nig e y BIGkS½ x .
enaH³
M x = Pe y nig M y = Pex
sMBaFdIenARCug ! KW qmax = P + MIx c y + MIy c x
A x y

P M xc y M y cx
enARCug @ KW q2 =
A
−
Ix
+
Iy
P M xc y M ycx
enARCug # KW q3 =
A
−
Ix
−
Iy
P M xc y M ycx
enARCug $ KW q4 =
A
+
Ix
−
Iy

Footing 309


cMNaMfa kugRtaMgxageRkAminRtUvFMCagsMBaFRTRTg;rbs;dI nigmü:ageTotdIminGacrgkMlaMg
Taj)aneT Edl q ≥ 0 .
]TahrN_ 13>7³ ssrctuekaNEdlmanmuxkat; 300 × 600mm dUcbgðajkñúg rUbTI 13>27 a rgnUv
bnÞúkcMGkS½ PD = 980kN nigm:Um:g; M D = 244kN .m EdlbNþalBIbnÞúkefr nigbnÞúkcMGkS½
PL = 734kN nigm:Um:g; M L = 190kN .m EdlbNþalBIbnÞúkGefr. )atrbs;eCIgtagsßitenACMerA

1.5m BInIv:UdI ehIysMBaFRTRTg;dIGnuBaØatKW 240kN / m 2 . KNnaeCIgtagedayeRbI f 'c = 28MPa /

f y = 400MPa .

dMeNaHRsay³
eCIgtagrgnUvbnÞúkcMGkS½ nigm:Um:g;
P = 980 + 734 = 1714kN

M = 244 + 190 = 434kN .m
cMNakp©itKW e=
M
=
434
P 1714
= 0.253m yk 250mm
eKGacKNnaeCIgtagtmaviFIsaRsþBIrKW³
viFIsaRsþTI1³ rMkilGkS½eCIgtagcMgay e = 250mm BIGkS½ssr. kñúgkrNIenH sMBaFdIRtUv)an
cat;TukfaBRgayesμIenABIeRkameCIgtag ¬rUbTI 13>27 b¦.
viFIsaRsþTI2³ GkS½rbs;eCIgtag nigGkS½rbs;ssrRtYtsIuKña. kñúgkrNIenH sMBaFdImanragCa
RtIekaN b¤ctuekaNBñay ¬rUbTI 13>27 c¦ ehIytMélGtibrma nigGb,brmaRtUv)anKNnadUcbgðaj
enAkñúgrUbTI 13>27.
karGnuvtþn_énviFIsaRsþTaMgBIrsMrab;]TahrN_TI 13>7 GacnwgBnül;y:agsegçbdUcxageRkam³
1> sMrab;viFIsaRsþTI1 snμt;kMBs;eCIgtag 500mm ¬ d = 420mm ¦ nigsnμt;TMgn;maDdIesμI
16kN / m 3
sMBaFdIeLIgelIsuT§KW 240 − 0.5 × 25 − 1× 16 = 211.5kN / m 2
RkLaépÞeCIgtag = 211.5 = 8.1m 2
1714

snμt;TTwgeCIgtagKW 2.7m enaHeCIgtagmanbeNþay 8.1 / 2.7 = 3m . dUcenHeyIgeRCIserIs
eCIgtagEdlmanTMhM 2.7 × 3m nigssrmanTItaMgcakp©itdUcbgðajkñúgrUbTI 13>27 d. GkS½
eCIgtagmancMgay 250mm BIGkS½ssr.

Footing 310

T.Chhay NPIC

2> LÚvviFIsaRsþKNnamanlkçN³RsedogKñanwgkarKNnaeCIgtageTal (single footing).
RtYtBinitükMBs;eCIgtagsMrab;GMeBIkMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis. kMNt;m:U
m:g;Bt;enAépÞssrsMrab;TisxøI nigTisEvg. edaysarcMNakp©itrbs;eCIgtag muxkat;eRKaHfñak;
nwgsßitenAxageqVgénépÞssr dUcbgðajkñúgrUbTI 13>27 d. cMgayeTAcugeCIgtagKW 1450mm
Pu = 1.2 D + 1.6 L = 1.2 × 980 + 1.6 × 734 = 2350.4kN
2350.4
qu = = 290.2kN / m 2
2.7 × 3
1.45 2
m:Um:g;GtibrmaM u = 290.2 × 2.7 ×
2
= 823.7kN .m ¬enAelITTwg 2.7m ¦
1.2 2
enAkñúgTisedAxøI M u = 290.2 × 3 ×
2
= 626.8kN .m

BinitüelIgvijkMBs;eCIgtagEdl)ansnμt;RbsinebIcaM)ac; nigeRCIserIsbrimaNEdkcaM)ac;enAkñúg
TisTaMgBIrrbs;eCIgtag dUcEdl)anBnül;enAkñúg]TahrN_GMBIeCIgtageTal (single footing).
3> sMrab;viFIsaRsþKNnaTI2 KNnaRkLaépÞrbs;eCIgtagtamviFIdUcEdl)anBnül;enAkñúgviFIsaRsþ
TI1 bnÞab;mkKNnasMBaFdIGtibrma nigeRbobeFobvaCamYynigsMBaFdIGnuBaØatEdleRbIbnÞúk
Fmμta
bnÞúksrub P = 1714kN
TMhMrbs;eCIgtag = 2.7 × 3m
edaysarcMNakp©itKW e = 250mm < L / 6 = 3000 / 6 = 500mm karBRgaysMBaFdIeLIgelI
manragCactuekaNBñay. KNnasMBaFdIGtibrma nigGb,brma³
P 6M 1714 6 × 434
q max = + 2 = + = 318.8kN / m 2 > 211.5kN / m 2
LB BL 2.7 × 3 2.7 × 3 2
eCIgtagKμansuvtßiPaB. sakl,g 2.8 × 4m ¬RkLaépÞ = 11.2m 2 ¦
P 6M 1714 6 × 434
q max = + 2 = + = 211.2kN / m 2 < 211.5kN / m 2
LB BL 2.8 × 4 2.8 × 4 2

P 6M 1714 6 × 434
q min = − 2 = − = 94.9kN / m 2
LB BL 2.8 × 4 2.8 × 4 2

5> KNnasMBaFeLIgelIemKuNedayeRbIbnÞúkemKuN bnÞab;mkKNnam:Um:g; nigkMlaMgkat;TTwg dUc
Bnül;kñúg]TahrN_mun.

Footing 311


9> kMralxNÐ½elIdI Slabs on Ground
kMralxNÐ½ebtugEdldak;pÞal;elIdIGacnwgrgnUv³
- bnÞúkBRgayesμIenAelIépÞrbs;va EdlbegáIt)anCakMlaMgkñúgtUc²

Footing 312

T.Chhay NPIC

- bnÞúkcMcMnuc b¤bnÞúkBRgayminesμIEdlbegáItm:Um:g;Bt; nigkMlaMgkat;. kugRtaMgkMlaMgTajekIt
eLIg ehIysñameRbHnwgekItmanEpñkxøHrbs;kMralxNÐ½.
kugRtaMgTajCaTUeTAekItmanedaybnSMén³
- karrYj (contraction)EdlbNþalmkBIsItuNðPaB nigkarrYmmaD EdlbgçaMgedaykMlaMgkkit
rvagkMralxNÐ½ nig subgrade begáItCakugRtaMgTaj.
- karxUcragmuxkat;rbs;kMralxNÐ½edaykarmYl (warping of the slabe).
- lkçxNÐ½énkardak;bnÞúk
- sMrut
tMN contraction joint RtUv)anbegáIteLIgedIm,Ikat;bnßykugRtaMgTajenAkñúgkMralxNÐ½. tMN
expansion joint RtUv)andak;kMralxNÐ½esþIgEdlmankMras;rhUtdl; 250mm .

kMralxNÐ½Can;eRkamdIéneRKagsMNg;GKarsñak;enAGacCaebtugGarem:EdlmankMras;BI 100mm
eTA 150mm EdlBRgwgedaysMNaj;Edk. sMrab;XøaMg kMralxNÐ½GacmankMras;BI 150mm eTA
300mm GaRs½yelIbnÞúkenAelIkMralxNÐ½. kMralxNÐ½Can;eRkamdIRtUv)anKNnaedIm,ITb;nwgsMBaFdI

eLIgelI nigsMBaFTwk. RbsinebIkMralxNÐ½sßitenAelIdIEdlmanlkçN³esßrPaB b¤ENn
(incompressible soil) enaHsMrutDIepr:g;EsülRtUv)anecal. kñúgkrNIenH kMras;kMralxNÐ½GacGb,

brmaRbsinebIKμanRsTab;TwkeRkamdI. RbsinebIsMrutDIepr:g;EsülFM enaHkMralxNÐ½RtUv)anKNnaCa
stiff raft foundation.

10> eCIgtagenAelIssrRKwH Footings on Piles
enAeBlEdlRsTab;dImanlkçN³Tn;enAkñúgkMras;d¾Rkas; ehIylT§PaBRTRTg;rbs;vatUc eKnwg
minENnaMeGaydak;eCIgtagedaypÞal;enAelIdIeT. vaCakarRbesIrkñúgkarbBa¢ÚnkMlaMgtamssrRKwHeTA
RsTab;d¾eRCAEdlmanlkçN³rwgRKb;RKan;edIm,IRTbnÞúk b¤begáItkMlaMgkkitRKb;RKan;CMuvijépÞxagssr
RKwH.
ssrRKwHCaeRcInRbePTRtUv)aneRbIsMrab;RKwH. kareRCIserIsssrRKwHGaRs½yelIlkçxNÐdI/
vtþmanRsTab;TwkeRkamdI/ tYrnaTIrbs;ssrRKwH nigfvikar. ssrRKwHGaceFVIBI ebtug Edk b¤eQI.
CaTUeTA eCIgtagssrRKwH (pile cap) mansar³sMxan;kñúgkarEbgEckkMlaMgBIssreTAk,al
ssrRKwH. eCIgtagssrRKwH (pile cap)RtUvmanTMhMRKb;RKan;edIm,IQrelIssrRKwH. eCIgtagssrRKWH

Footing 313


(pile cap) RtUv)anKNnadUcFñwmEdledkenAcenøaHssrRKwH nigRTbnÞúkcMcMnucBIssr. enA eBlEdl
ssrRtUv)anRTedayssrRKwHBIr eCIgtagssrRKwHGacRtUv)anKNnadUc truss ebtugGarem:ragRtIekaN.
ACI Code, Section 15.2 bgðajfakarKNnam:Um:g; nigkMlaMgkat;TTwgsMrab;eCIgtagelIssr

RKwHRtUv)anQrelIkarsnμt;faRbtikmμmkBIssrRKwHsßitenAcMGkS½ssrRKwH. RkLaépÞeCIgtag b¤cMnYn
ssrRKwHRtUv)ankMNt;BIbnÞúk nigm:Um:g;KμanemKuN.
kMras;ebtugGb,brmasMrab;eCIgtagssrRKwHRtUv)ankMNt;Rtwm 300mm (ACI Code, Section
15.7) . sMrab;karKNnassrRKwH nigeCIgtagssrRKwHlMGit sUmGanesovePAvisVkmμRKwH (books on

foundation engineering) .

Footing 314

Xiii footings

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