Department of Civil Engineering                                             viTüasßanCatiBhubec©keTskm<úCa



            ...
T.Chhay                                                                                  NPIC




epSgKñaBIeRkamnIv:UdI. r...
Department of Civil Engineering                                       viTüasßanCatiBhubec©keTskm<úCa


    -             b...
T.Chhay                                                                               NPIC




     -                     ...
Department of Civil Engineering                                           viTüasßanCatiBhubec©keTskm<úCa


    -     Raft ...
T.Chhay                                                                                  NPIC




eCIgtagsßitenABIelIdIs¥i...
Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


eCIgtag. EpñknImY...
T.Chhay                                                                               NPIC




          4>2> kMlaMgkat;mY...
Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


        kMlat;kat...
T.Chhay                                                                                     NPIC




        sMrab;tMél Vc...
Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


          d. kMNt...
T.Chhay                                                                                    NPIC




           CaerOy² kMB...
Department of Civil Engineering                                                 viTüasßanCatiBhubec©keTskm<úCa


         ...
T.Chhay                                                                                      NPIC




ticCagbYnedIm¦ Edl A...
Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


         bnÞúkefr...
T.Chhay                                                                                  NPIC



          ⎛1   2 ⎞       ...
Department of Civil Engineering                                                    viTüasßanCatiBhubec©keTskm<úCa

       ...
T.Chhay                                                                                   NPIC




        eRbIEdk DB25 Ed...
Department of Civil Engineering                                               viTüasßanCatiBhubec©keTskm<úCa


    2> KNna...
T.Chhay                                                                                                        NPIC




  ...
Department of Civil Engineering                                                 viTüasßanCatiBhubec©keTskm<úCa


         ...
T.Chhay                                                                                    NPIC




]TahrN_ 13>3³ KNnaeCIg...
Department of Civil Engineering                                            viTüasßanCatiBhubec©keTskm<úCa

               ...
T.Chhay                                                                              NPIC




          2 DB 20  ¬ As = 62...
Department of Civil Engineering                                       viTüasßanCatiBhubec©keTskm<úCa


]TahrN_ 13>4³ KNnaR...
T.Chhay                                                                                         NPIC




                 ...
Department of Civil Engineering                                          viTüasßanCatiBhubec©keTskm<úCa


          kMNt;k...
T.Chhay                                                                                  NPIC




enACitCageK begáIt)anCa ...
Department of Civil Engineering                                      viTüasßanCatiBhubec©keTskm<úCa


        viFId¾samBaØ...
T.Chhay                                                                                 NPIC




        bnÞúkeFVIkarsrub ...
Department of Civil Engineering                                              viTüasßanCatiBhubec©keTskm<úCa


            ...
T.Chhay                                                                                   NPIC




        EdkRtUv)andak;b...
Department of Civil Engineering                                        viTüasßanCatiBhubec©keTskm<úCa


                  ...
T.Chhay                                                                                 NPIC




7> eCIgtageRkambnÞúkssrca...
Department of Civil Engineering                                 viTüasßanCatiBhubec©keTskm<úCa


             q min =
    ...
T.Chhay                                                                                   NPIC



                        ...
Department of Civil Engineering                                        viTüasßanCatiBhubec©keTskm<úCa


        cMNaMfa ku...
T.Chhay                                                                                   NPIC




     2> LÚvviFIsaRsþKNn...
Department of Civil Engineering                                   viTüasßanCatiBhubec©keTskm<úCa




9> kMralxNнelIdI Sla...
T.Chhay                                                                                   NPIC




     - bnÞúkcMcMnuc b¤b...
Department of Civil Engineering                                    viTüasßanCatiBhubec©keTskm<úCa


(pile cap)  RtUv)anKNn...
Upcoming SlideShare
Loading in...5
×

Xiii footings

564

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
564
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Xiii footings

  1. 1. 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
  2. 2. 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 EdlRTbnÞúkBIkMralxNн b¤edIm,IRT nonstructural walls. vamanTTwgkMNt; nigmanRbEvgCab;KñaenABIeRkamCBa¢aMg ¬rUbTI13>1¦. Wall footings Gac mankMras;EtmYy Gacmanfñak; b¤GacmanCMral. Footing 275
  3. 3. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - 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
  4. 4. 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
  5. 5. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - 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¦ CakMralxNнRkas;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
  6. 6. 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
  7. 7. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  8. 8. 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
  9. 9. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  10. 10. 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
  11. 11. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  12. 12. 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;kMralxNн 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
  13. 13. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  14. 14. 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
  15. 15. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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¢aMgxNн 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
  16. 16. 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
  17. 17. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  18. 18. 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
  19. 19. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  20. 20. 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
  21. 21. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa = 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
  22. 22. 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
  23. 23. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  24. 24. 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
  25. 25. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ]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
  26. 26. 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
  27. 27. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  28. 28. 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
  29. 29. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  30. 30. 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
  31. 31. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa = 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 ¬!#>!$¦ PaKryEdkKW ρ = 0.0032 ≈ 0.0033(ρ min ) As = 0.0033 × 2200 × 805 = 5844.3mm 2 As Gb,brma ¬rYmmaD¦ = 0.0018 × 2200 × 920 = 3643.2mm 2 As = 5844.3mm 2 lb;. eRbI 10DB 28 ¬ As = 6157.5mm 2 ¦ KMlatEdk = 22009−(no. of spacing) = 228mm 150 (concrete cover) Footing 304
  32. 32. T.Chhay NPIC EdkRtUv)andak;bgðÚtenAcenøaHssrenAEpñkxagelIeCIgtagCamYykMras;karBarEdk 75mm . dak;EdkGb,brmaenA)atrbs;eCIgtagedIm,ITb;nwgm:Um:g;viC¢man. RtYtBinitüRbEvgbgáb; ld BIépÞ ssr. EdkGb,brmaKW As = 3643.2mm 2 . eRbI 8DB25 ¬ As = 3927mm 2 ¦. RbEvgEdkbgáb;caM)ac;sMrab;EdkemxagelIKW 1.3ld = 1.3 × 48 × d b = 1747mm RtUv)andak; ecjBIcMnucm:Um:g;Gtibrma. RbEvgEdkbgáb;Edldak;enARtg;ssrTaMgBIrKWRKb;RKan;. 9> sMrab;EdkenAkñúgTisedAxøI. karKNnam:Um:g;Bt;enAkñúgTisedAxøI ¬TisedATTwg¦ maklkçN³ dUcKñakñúgkrNI single footing. EdkenAeRkamssrnImYy² RtUv)andak;enAkñúgcMerokTTwg (bandwidth) EdlesμInwgplbUkTTwgssrnigkMBs;RbsiT§PaB d BIrdg ¬rUbTI !#>@$¦. 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
  33. 33. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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 !#>@$. RbEvgbgáb;rbs;Edk DB 25 enAkñúgTisedAxøI KW 1.2m . Footing 306
  34. 34. T.Chhay NPIC 7> eCIgtageRkambnÞúkssrcakp©it Footings under Eccentric Column Loads enAeBlEdlssrbBa¢ÚnEtkMlaMgtamGkS½ enaHeKGacKNnaeCIgtagEdlmanbnÞúkeFVIGMeBIcMTIRb CMuTMgn;rbs;eCIgtag EdlbegáIt)anCasMBaFBRgayesμIeRkameCIgtag. b:uEnþ enAkñúgkrNIxøHssrbBa¢ÚnkM laMgcMGkS½ nigm:Um:g;Bt; dUckñúgkrNIeCIgtageRKagbgáb;cug (fixed-end frame). sMBaF q EdlekItman enAelIdInwgminBRgayesμI EdlGackMNt;BIsmIkarxageRkam³ q= ± P Mc A I ≥0 ¬!#>!(¦ Edl A nig I CaRkLaépÞ nigm:Um:g;niclPaBéneCIgtag erogKña. eKmanlkçxNÐdIxusKñaEdl GaRs½ynwgtMél P nig M / nig sMBaFdIGnuBaØat. lkçxNÐKNnaxusKñaRtUv)anbgðajenAkñúgrUbTI 13> 25 nigRtUv)ansegçbdUcxageRkam³ 1> enAeBl e = M / P < L / 6 sMBaFdImanragctuekaNBñay P Mc q max = + A I = P 6M LB + 2 ¬!#>@0¦ BL Footing 307
  35. 35. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa q min = P Mc A − I = P 6M − LB BL2 ¬!#>@!¦ 2> enAeBl e = M / P = L / 6 sMBaFdImanragctuekaNEkg q max = P 6M 2 P + = LB BL2 LB ¬!#>@@¦ q min =0= P 6M − LB BL2 b¤ P = 6M LB BL2 ¬!#>@#¦ 3> enAeBlEdl e > L / 6 sMBaFdImanragRtIekaN L− y L x= = −e 3 2 Footing 308
  36. 36. T.Chhay NPIC ⎛ 3x ⎞ P = q max ⎜ ⎟ B ⎝ 2⎠ q max = 2P = 4P 3xB 3B ( L − 2e) ¬!#>@$¦ 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
  37. 37. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 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
  38. 38. 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
  39. 39. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 9> kMralxNнelIdI Slabs on Ground kMralxNнebtugEdldak;pÞal;elIdIGacnwgrgnUv³ - bnÞúkBRgayesμIenAelIépÞrbs;va EdlbegáIt)anCakMlaMgkñúgtUc² Footing 312
  40. 40. T.Chhay NPIC - bnÞúkcMcMnuc b¤bnÞúkBRgayminesμIEdlbegáItm:Um:g;Bt; nigkMlaMgkat;. kugRtaMgkMlaMgTajekIt eLIg ehIysñameRbHnwgekItmanEpñkxøHrbs;kMralxNн. kugRtaMgTajCaTUeTAekItmanedaybnSMén³ - karrYj (contraction)EdlbNþalmkBIsItuNðPaB nigkarrYmmaD EdlbgçaMgedaykMlaMgkkit rvagkMralxNн nig subgrade begáItCakugRtaMgTaj. - karxUcragmuxkat;rbs;kMralxNнedaykarmYl (warping of the slabe). - lkçxNнénkardak;bnÞúk - sMrut tMN contraction joint RtUv)anbegáIteLIgedIm,Ikat;bnßykugRtaMgTajenAkñúgkMralxNн. tMN expansion joint RtUv)andak;kMralxNнesþIgEdlmankMras;rhUtdl; 250mm . kMralxNнCan;eRkamdIéneRKagsMNg;GKarsñak;enAGacCaebtugGarem:EdlmankMras;BI 100mm eTA 150mm EdlBRgwgedaysMNaj;Edk. sMrab;XøaMg kMralxNнGacmankMras;BI 150mm eTA 300mm GaRs½yelIbnÞúkenAelIkMralxNн. kMralxNнCan;eRkamdIRtUv)anKNnaedIm,ITb;nwgsMBaFdI eLIgelI nigsMBaFTwk. RbsinebIkMralxNнsßitenAelIdIEdlmanlkçN³esßrPaB b¤ENn (incompressible soil) enaHsMrutDIepr:g;EsülRtUv)anecal. kñúgkrNIenH kMras;kMralxNнGacGb, brmaRbsinebIKμanRsTab;TwkeRkamdI. RbsinebIsMrutDIepr:g;EsülFM enaHkMralxNнRtUv)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
  41. 41. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa (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

×