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# Xviii stairs

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### Xviii stairs

1. 1. T.Chhay NPIC XVIII. CeNþIr Stairs 1> esckþIepþIm Introduction RKb;GKarTaMgGs; TaMgTab nigx<s;EtgEtmanCeNþIr eTaHbICamanCeNþIreyagRKb;RKan;k¾eday. CeNþIrpSMeLIgeday kMBs;kaM (rise), CMhankaM (run or tread) nigfasCeNþIr (landing)¬rUbTI 18>1¦. karKNnasMrab;kMlaMgrmYl 534
2. 2. T.Chhay NPIC TMhMFmμtarbs;kMBs;kaM nigCMhankaMenAkñúgGKarEdlTak;Tgnwg empirical rule xøH. Rise + run = 430mm 2Rise + run = 635mm Rise × run = 0.05m 2 kMBs;kaMGaRs½ynwgRbePTGKar. ]TahrN_ sMrab;GKarsaFarN³ kMBs;kaMKWRbEhl 15cm b:uEnþsMrab;GKarsñak;enAvaERbRbYlcenøaH 15cm eTA 19cm . CMhankaMKWRbEhl 25cm enAkñúgGKar saFarN³ nigERbRbYlcenøaH 23cm eTA 32cm sMrab;GKarsñak;enA. CaTUeTA kMBs;kaMminRtUvFMCag 20cm nigminRtUvtUcCag 10cm ehIycMnYnkMBs;kaM)anBIkarEckTMhMCan;eTACan;rbs;GKarnwgkMBs;kaM snμt;. kargarbegðIyrbs;kaMCeNþIrman fμdus (troweling Alundum grit) kar:U asphalt kar:U terrazzo kar:U marble b¤RBM. bEnßmBIelIbnÞúkefr CeNþIrRtUv)anKNnasMrab;bnÞúkGefrGb,brma 4.8kN / m 2 . 2> RbePTCeNþIr Types of Stairs eKmanCeNþIrCaeRcInRbePTEdlGaRs½yCacMbgeTAnwgRbePT nigtYnaTIrbs;GKar nigGaRs½y eTAelItMrUvkarsßabtükmμ. RbePTCeNþIrFmμtabMputmandUcxageRkam³ !> Single-flight stair³ kareFVIkarrbs;rcnasm<n§½éntYCeNþIrRsedogeTAnwgkMralxNÐ½mYyTisEdl RtUv)anRTenAcugsgçag. kMralrbs;kMralRtUv)aneKehAfa waist ¬rUbTI 181¦. enAeBltY CeNþIrmanfas eKRtUvdak;FñwmenARtg; B nig C edIm,IlkçN³esdækic© ¬rUbTI 18>2¦. RbsinebI FñwmTaMgBIrenHminRtUv)andak; enaHRbEvgElVgCeNþIrnwgekIneLIgedaysarTTwgrbs;fasBIrEdl latsn§wgcenøaH A nig D . enAkñúgGKarsñak;enATTwgfasKWsßitenAcenøaH1.2m eTA1.8m ehIy cMgaysrubcenøaH A nig D KWRbEhl 6m . viFIepSgeTotkñúgkarRT Single-flight stair KWRtUveRbI stringer b¤Fñwmxag (edge beam) enARCugBIrtambeNþayCeNþIr. kaMRtUv)anRtedayFñwm ¬rUbTI 18>3¦. @> Double-flight stair³ GñkeRbInwgmanlkçN³gayRsYlkñúgkareRbIR)as;GKarEdlman double- flight stair. RbePTEdlRtUv)aneRbIR)as;CaTUeTAKWRbePT quarter-turn ¬rUbTI 18>4¦nig closed-well stair b¤ open-well stair dUcbgðajenAkñúgrUbTI 18>5. sMrab;karviPaKeRKOgbgÁúM CeNþIr tYmYy²RtUv)anKitdUc single-flight ehIyRtUv)anBicarNaedayRTenAelIFñwmBIr b¤eRcIn dUcbgðajenAkñúgrUbTI 18>2. fasCeNþIrlatsn§wgkñugTisedATTwgcenøaHTMrBIr ehIyRtUv)an karKNnasMrab;kMlaMgrmYl 535
3. 3. T.Chhay NPIC KNnadUc one-way slab. kñúgkrNI open-well stair EpñkkNþalrbs;fasCeNþIrRTbnÞúkeBj cMENkÉsgçagBIrRTbnÞúkEtBak;kNþal dUcbgðajenAkñúgrUbTI 18>5 d. bnÞúkBak;kNþaleTot RtUv)anRTenAkñúgTisbeNþayedaytYCeNþIr ¬muxkat; A-A nig B-B¦. #> Three or more flight of stair³ kñúgkrNIxøH EdlTMhMTaMgmUlrbs;CeNþIrRtUv)ankMNt; three or more flight of stair GacRtUv)anTTYlyk ¬rUbTI 18>6¦. tYCeNþIrmYy²RtUv)anKitdac;eday ELkBIKñadUckñúgkrNI double-flight staircase. karKNnasMrab;kMlaMgrmYl 536
4. 4. T.Chhay NPIC \$> Cantilever stair³ RtUv)aneRbICaTUeTAsMrab;CeNþIr fire-escape stair ehIyvaRtUv)anRTeday CBa¢aMg b¤Fñwmebtug. CeNþIrRbePTenHGac full-flight EdltYCeNþIrQrelIEtCBa¢aMgmçag nigGac half-flight EdltYCeNþIrQrelICBa¢aMgsgçag b¤RbePT semispiral dUcbgðajenAkñúgrUbTI 18>7. enAkñúgCeNþIrRbePTenH kaMnImYy²eFVIkarCaFñwm cantilever ehIyEdkemRtUv)andak;enAkñúgtMbn; rgkarTajénCMhankaM nigEdkRtUv)anf<k;eTAkñúgCBa¢aMgebtug. EdkTb;sItuNðPaB nigkarrYmmaD RtUv)andak;kñúgTisedATTwg. TMrg;epSgeTotrbs;CeNþIr cantilever stair KWeRbI open-riser step EdlRTedayFñwm kNþaldUcbgðajenAkñúgrUbTI 18>8. FñwmmanCMraldUctYCeNþIr ehIyEpñkxagelIrbs;Fñwm GnuBaØateGaykaMCeNþIrKgelI. kñúgkrNICaeRbI kaMebtugGaem:rcak;eRscGacRtUv)aneRbI CamYy nwgkarpþl;BiesssMrab;rwtb‘ULúgedIm,IP¢ab;kaMeTAnwgFñwm. karKNnasMrab;kMlaMgrmYl 537
5. 5. T.Chhay NPIC %> Precast flights of stair³ el,Ónkñúgkarsagsg;enAkñúgKMeragxøHtMrUveGayeRbI precast flights of stair ¬rUbTI 18>8¦. tYCeNþIrGacRtUv)ancak;edayELk ehIybnÞab;mkRtUv)anP¢ab;eTAnwgfas CeNþIrEdlcak;enAnwgkEnøg. kñúgkrNIepSgeTot tYCeNþIrrYmTaMgfasCeNþIr RtUv)ancak;nig bnÞab;mkdak;enAelICBa¢aMg b¤FñwmTMr. vaRtUv)anKNnaCakMralxNÐ½mYyTisEdlmanTMrsamBaØ karKNnasMrab;kMlaMgrmYl 538
6. 6. T.Chhay NPIC CamYynwgEdkemenA)at waist rbs;CeNþIr. brimaNEdkRKb;RKan;RtUv)andak;enAelItMN dUc bgðajenAkñúgrUbTI 18>9. TMBk;RtUv)aneKeFVIedIm,IkargarelIkdak; nigtMeLIg. EdkBiessRtUvdak;enARtg; muxkat;eRKaHfñak; edIm,ITb;nwgkugRtaMgTajEdlekItmanenAkñúgCeNþIrkñúgdMNak;karelIkdak;. ^> Free standing stair³ sMrab;CeNþIrRbePTenH fasCeNþIrsßitenAkñúgxül;edayKμanTMrenA xagcug ¬rUbTI 18>10¦. CeNþIreFVIkarkñúglkçN³Cakþaelat (springboard) EdlbegáItCakugRtaMg rmYlenAkñúgkMralxNÐ½. karKNnasMrab;kMlaMgrmYl 539
7. 7. T.Chhay NPIC RbBn§½énkardak;bnÞúkbIRbePT RtUv)anykmkBicarNakñúgkarKNnaCeNþIrRbePTenH edayKitBicarNafam:Um:g;rmYlnwgekItmanenAkñúgkMralRKb;lkçxNÐ½³ - enAeBlbnÞúkGefreFVIGMeBIEtenAelItYCeNþIrxagelI nigBak;kNþalfas ¬rUbTI 18>12¦ tYCeNþIrxagelInwgrgnUvkMlaMgTajbEnßmBIelIm:Um:g;Bt; EttYCeNþIrxageRkamnwgrgnUv kMlaMgsgát; EdlGacbegáItCakMlaMgPøat; (buckling) enAkñúgkMral . - enAeBlbnÞúkGefreFVIGMeBIEtenAelItYCeNþIrxageRkam nigBak;kNþalfas tYCeNþIrxag elInwgrgkMlaMgTaj EttYCeNþIrxageRkamnwgrgm:Um:g;Bt; nigkMlaMgsgát;. - enAeBlbnÞúkGefreFVIGMeBIenATaMgelItYCeNþIrxagelI nigxageRkam kardak;bnÞúkenAelI tYCeNþIrmYynwgbNþaleGaytYrCeNþIrmYyeTotrmYl. kugRtaMgrmYlekItenAkñúgCeNþIr TamTarsrésEdkRKb;RKan;enAkñúgépÞTaMgsgçagrbs;CeNþIr nigfas. srésEdkTTwg enAkñúgkMral nigfasRtUv)andak;enAkñúgépÞTaMgsgçagrbs;ebtugkñúgTMrg;CaEdlGkSr U karKNnasMrab;kMlaMgrmYl 540
8. 8. T.Chhay NPIC biTCit enABak;kNþalTTwgrbs;CeNþIr. srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>13. sßabtükrcUlcitþCeNþIrRbePTenH ehIyCeNþIrRbePTenHeBlxøHRtUv)aneKehAfa pliers- shaped staircase b¤ jackknife staircase. karKNnasMrab;kMlaMgrmYl 541
9. 9. T.Chhay NPIC &> Run-riser stair³ CaRbePTCeNþIrEdlpSMeLIgedaycMnYn kMBs;kaM nigCMhankaMCaeRcInEdl P¢ab;KñaedaypÞal;y:agrwgedayKμankMral waist ¬rUbTI 18>14 a¦. CeNþIrRbePTenHTTYl karcab;GarmμN_edaysßabtükredaysarrUbragxageRkArbs;va. karviPaKeRKOgbgÁúMrbs; run-riser stair GacRtUv)ansMrYledaysnμt;faT§iBlrbs;kMlaMgtamGkS½RtUv)anecal nig snμt;fabnÞúkenAelICMhankaMnImYy²RtUv)anRbmUldak;enAxagcugrbs;CMhankaM ¬rUbTI 18> 14 b¦. sMrab;karviPaKéntYCeNþIrEdlRTedayTMrsamBaØ edayBicarNatYCeNþIrsamBaØén CMhankaMBIr ABC EdlrgnUvbnÞúkcMcMnuc P enARtg;cMnuc B’ ¬rUbTI 18>14 b¦. edaysartM N B nig B’ CatMNrwg m:Um:g;enARtg;tMN B esμIm:Um:g;enARtg;tMN B’ b¤ M B = M B' = PS / 2 Edl S CaTTwgrbs;CMhankaM. m:Um:g;enAkñúgkMBs;kaM BB' mantMélefr ehIyesμI nwg PS / 2 . enAeBlEdlKμankMBs;kaM CeNþIr ABC eFVIkarCaFñwmTMrsamBaØ ehIym:Um:g;Bt;Gtibrma EdlekItmanenAkNþalElVgCamYytMél M B = PL / 4 = PS / 2 . sMrab;tYCeNþIrEdlpSM eLIgedaykMBs;kaM nigCMhankaMeRcIn viFIdUcKñaRtUv)aneRbI düaRkamm:Um:g;Bt;RtUv)anbgðaj enAkñúgrUbTI 18> 15 a. m:Um:g;enAkñúg BB' mantMélefrsμInwgm:Um:g;enARtg;tMN B b¤ 2PS . dUcKña M C = M 'C = 3PS / M D = M ' D = 3PS nig M E = M ' E = 2PS . RbsinebImanvtþmanfasCeNþIrenAcugmçag b¤cugsgçag bnÞúkenAelIfask¾RtUv)anRbmUl CabnÞúkcMcMnucdUckrNICMhankaMEdr.karviPaKrcnasm<n§½k¾GaceFVIedayBicarNabnÞúkBRgay esμIenAelItYrCeNþIr. m:Um:g;enAkñúgkMBs;kaMTaMgGs;mantMélefr nigTTYl)anBIrdüaRkamm:Um:g; Bt;énFñwmTMrsamBaØEdlrgbnÞúkesμI ¬rUbTI 18>15 b¦. ]TahrN_TI 18>3 bgðajBIkar KNnaCeNþIredayeRbIkarsnμt;BIr KWbnÞúkcMcMnuc nigbnÞúkBRgayesμI. RbsinebItYCeNþIrRtUv)anbgáb; b¤Cab;enAcugmçag b¤cugTaMgBIr m:Um:g;GacRtUv)anTTYl edayeRbIviFIviPaKeRKOgbgÁúMNamYyk¾)an. edIm,IBnül;krNIenH cat;TuktYCeNþIrEdlpSMeLIg edayCMhankaMBIr nigRtUvbgáb;enAcugTaMgBIr ¬rUbTI 18>16 a¦. m:Um:g;enAcugbgáb; A nig B EdlbNþalBIbnÞúkenARtg; B esμInwg PL / 8 = PS / 4 . lT§plenHRtUv)anTTYledaysnμt; faCeNþIrminmankMBs;kaM ABC eFVIkarCaFñwmbgáb;cugEdlrgnUvbnÞúkcMcMnucenAkNþalElVg ¬rUbTI 18>16 b¦. m:Um:g;enAkNþalElVg muxkat; B esμInwg PL PS PS PS −MA = − = 4 2 4 4 karKNnasMrab;kMlaMgrmYl 542
10. 10. T.Chhay NPIC m:Um:g;Bt;éntYCeNþIrEdlmankMBs;kaMmYyRtUv)anbgðajenAkñúgrUbTI 18>16 a. cMNaMfam:Um:g; enAkñúgkMBs;kaM BB' mantMélefr ehIy M B = M ' B = PS / 4 . sMrab;tYCeNþIrEdlmanlkçN³sIuemRTI cugbgáb;TaMgsgçag ehIyrgnUvbnÞúkcMcMnucenA Rtg;cMnucCMhankaM m:Um:g;enAcugbgáb;GacRtUvKNnadUcxageRkam³ M (fixed end ) = PS 2 (n − 1) 12 Edl P= bnÞúkcMcMnucenARtg;cMnucCMhankaM S = TTwgCMhankaM n = cMnYnCMhankaM enAeBl n = 2 enaH M (fixed end) = PS (4 − 1) = PS 12 4 EdllT§pldUcnwglT§plTTYl)anBIxagedIm. RbsinebImanfasCeNþIrenAcugmçag b¤cugsgçag bnÞúkenAelIfasCeNþIrGacRtUv)an dak;CabnÞúkcMcMnucenAKMlat S . *> Helical stair (open-spiral stair)³ CaRbePTeRKOgbgÁúMbITMhM EdlCaTUeTAmanragCargVg;enA kñúgbøg; ¬rUbTI 18>17¦. vaCaRbePTCeNþIrEdleKeRbIenAkñúg entrance hall, theater foyer nigGKarkariyal½yEdlmankMBs;Tab. tMélrbs;vaéføCagCeNþIrRbePTFmμta. CeNþIrGacRtUv)anRTenARCugxøHEdlCab;nwgCBa¢aMg b¤GacKNnaCa free-standing helical staircase EdlTTYlkareBjniymCaeK. eRkamGMeBIrbs;bnÞúk tYCeNþIrGacrgnUvkug RtaMgrmYl. tYCeNþIrxagelInwgrgnUvkugRtaMgTaj ÉcMENkÉkugRtaMgsgÁt;ekItmanenAEpñk xageRkamrbs;CeNþIr. kMlaMgEdleFVIGMeBIenARtg;muxkat;NamYyGacpSMeLIgedaym:Um:g; bBaÄr m:Um:g;edk m:Um:g;rmYl kMlaMgtamGkS½ kMlaMgkat;TTwgEdlkat; waist rbs;CeNþIr nigkM laMg radial horizontal shearing force. EdkbeNþayempSMeLIgedayEdk helical bar Edldak;enAkñúg waist rbs;CeNþIr nigCMhankaMBIfasxagelIeTATMrxageRkam. EdkTTwgRtUv EtmanTMrgCaEdkkgbiTCitedIm,ITb;kugRtaMgrmYl b¤CaTMrg;EdkGkSr U pÁÜbKñadak;enAkNþal TTwgrbs;CeNþIr. karKNnasMrab;kMlaMgrmYl 543
11. 11. T.Chhay NPIC viFIepSgeTotsMrab;pþl;eGay helical stair KWeRbIFñwm helical girder enAkNþalTTwg rbs;CeNþIr. kaMnImYy²RtUv)anKitCaFñwm cantilever ehIyEdkRtUv)andak;enAEpñkxagelI rbs;kaM. karKNnasMrab;kMlaMgrmYl 544
12. 12. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 545
13. 13. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 546
14. 14. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 547
15. 15. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 548
16. 16. T.Chhay NPIC ]TahrN_TI 18>1³ KNnaCeNþIrdUcbgðajenAkñúgrUbTI 18>18 edIm,IRTbnÞúkGefrBRgayesμI 4.8kN / m 2. snμt;kMBs;kaMesμInwg 15cm ehIyCMhankaMesμInwg 30cm . eKeGay f 'c = 21MPa nig f y = 400MPa . dMeNaHRsay³ 1> bnÞúk³ snμt;kMras;kMral ¬waist¦ esμInwg 10cm . TMgn;rbs;kaMmYy = trapezoidal area × 25 ⎛ 0.1118 + 0.2618 ⎞ =⎜ ⎟ × 0.3 × 25 = 1.4kN / m ⎝ 2 ⎠ eyagtamrUbTI 18>18 b snμt;TMgn;kargarbegðIyEdlRKbBIelIkaMCeNþIrKW 0.3kN / m . dUcenHbnÞúkefrsrub D.L. = 1.7kN / m Wu = 1.2 D + 1.6 L = 1.2 × 1.7 + 1.6 × 4.8 × 0.3 = 4.35kN / m karKNnasMrab;kMlaMgrmYl 549
17. 17. T.Chhay NPIC 2> m:Um:g;Bt;GtibrmaenAkñúgmYykaMKW Wu l 2 / 2 4.35 2 Mu = 1.8 = 7.05kN .m 2 ⎛ 11.18 + 26.18 ⎞ kMras;mFümrbs;kaMCeNþIrKW⎜ ⎝ 2 ⎟ = 18.68cm ⎠ . karKNnasMrab;kMlaMgrmYl 550
18. 18. T.Chhay NPIC yk d = 18.68 − 2 − 0.6 = 16.1cm ⎛ a⎞ M u = φAs f y ⎜ d − ⎟ ⎝ 2⎠ snμt; a = 12.5mm 7.05 ⋅10 6 As = = 127 mm 2 ⎛ 12.5 ⎞ 0.9 × 400⎜161 − ⎟ ⎝ 2 ⎠ As f y 127 × 400 RtYtBinitü a= = 0.85 f 'c b 0.85 × 21× 300 = 9.5mm ¬mantMélRbEhlkarsnμt;¦ brimaNEdkGb,brma As = 0.00333(300)(161) = 161mm 2 eRbI 2DB12 sMrab;mYykaM. kMras;kMralGacyktUcCagkarsnμt;enH b:uEnþedIm,IeCosvagPaB dabFM nigPaBrMjr½rbs;CeNþIr eKRtUveRCIserIskMras;kMralsmrmü. 3> KNnakMlaMgkat;enAcMgay d BIépÞTMr Vu = 4.35(1.8 − 0.161) = 7.13kN 21(300 × 161) ⋅10 − 3 = 27.7kN 0.75 0.75 φVc = f 'c bd = 6 6 edaysarEt Vu < φVc / 2 dUcenHeKminRtUvkarEdkkgeT. b:uEnþeKRtUvdak;Edkkg DB10 @100 edIm,IcgCamYyEdkembeNþay. 4> CeNþIrRtUvrkSalMnwgedayTMgn;rbs;CBa¢aMg b¤edayFñwmebtugGarem:enAkñúgCBa¢aMg. kñúgkrNI enH FñwmrgnUvm:Um:g;rmYl 7.05kN .m / m . 5> srésrEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>18. ]TahrN_TI 18>2³ KNnaCeNþIrdUcbgðajenAkñúgrUbTI 18>19 EdlRTbnÞúkGefrBRgayesμI 5.7kN / m 2 . snμt;kMBs;kaMesμInwg 18cm ehIyCMhankaMesμInwg 27.5cm . eKeGay f 'c = 21MPa nig f y = 400MPa . dMeNaHRsay³ 1> RbBn§½eRKOgbgÁúM³ RbsinebIeKmineRbIFñwm stringer enaH eKGacTTYlykdMeNaHRsaymYykñúgcM eNam dMeNaHRsaybYnEdl)anbgðajenAkñúgrUbTI 18>2. enAeBlTMrkNþalminRtUv)aneRbI tYCeNþIrRtuv)anRTenAxagcugénfasCeNþIrxagelI nigxageRkam. RbBn§½rcnasm<n§½enHRtUv)an ykmkeRbIkñúg]TahrN_enH. karKNnasMrab;kMlaMgrmYl 551
19. 19. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 552
20. 20. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 553
21. 21. T.Chhay NPIC 2> bnÞúk³ snμt;kMras;kMral (waist) KW 20cm TMgn;rbs;kaMmYy = trapezoidal area × 25 ⎛ 0.239 × 2 + 0.18 ⎞ =⎜ ⎟0.275 × 25 = 2.26kN / m ⎝ 2 ⎠ TMgn;rbs;tYCeNþIr= 2.26 0.275 = 8.2kN / m 2 TMgn;fasCeNþIr = 0.2 × 25 = 5kN / m 2 edaysnμt;kargarbegðIyRKbelICeNþIrKW 1kN / m 2 . Wu (on stair ) = 1.2(8.2 + 1) + 1.6 × 5.7 = 20.16kN / m 2 Wu (on landing) = 1.2(5 + 1) + 1.6 × 5.7 = 16.32kN / m 2 edayKNnaCeNþIrkñúg 1m TTwgrbs;CeNþIrdUcenH Wu (on stair ) = 20.16kN / m Wu (on landing ) = 16.32kN / m edaysarbnÞúkenAelIfasCeNþIrRtUv)anRTBIrTis dUcenHbnÞúkBak;kNþalRtUv)anKitenAkñúgTis mYy². 3> KNnam:Um:g;Bt;Gtibrma nigEdkBRgwg ¬rUbTI 18>19 d¦³ a. m:Um:g;enAkNþalElVgKW 1.12 M u = 34.42 × 2.6 − 8.16 × 1.5 × 1.85 − 20.16 × = 54.65kN .m 2 yk d = 200 − 20 − 6 = 174mm b. M u = φAs f y (d − a / 2); edaysnμt; a = 20mm 54.65 ⋅10 6 As = = 926mm 2 0.9 × 400 × (174 − 10) As f y 926 × 400 RtYtBinitü a= = 0.85 f 'c b 0.85 × 21× 1000 = 20.75mm c = 24.4mm brimaNEdkGb,brma As = 0.0033 ×1000 ×174 = 574mm2 < 926mm2 eRbIEdk DB12 @120 ¬ As = 942mm2 ¦. sMrab;CeNþIrTTwg 1.5m eRbI 13DB12 . d t = 174mm c = 24.4mm bMErbMrYlrageFobTajsuT§ (net tensile strain) ⎛d −c⎞ εt = ⎜ t ⎟0.003 = 0.0184 > 0.005 dUcenH φ = 0.9 ⎝ c ⎠ karKNnasMrab;kMlaMgrmYl 554
22. 22. T.Chhay NPIC c. EdkTTwgRtUv)andak;edIm,ITb;karrYmmaD As = 0.0018 × 1000 × 200 = 360mm 2 eRbIEdk DB12 EdlmanKMlat 300mm ¬ As = 377mm 2 ¦ d. RbsinebICeNþIrnigFñwmEdlRTvaRtUv)ancak;CamYyKña EdkbEnßmRtUv)andak;enAEpñkxagelI nigEpñkxageRkamrbs;fasCeNþIr. srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>19. 4> kMras;kMralxNÐ½Gb,brmasMrab;karBarPaBdabKW = 0.208m ¬sMrab;kMralxNÐ½TMrsamBaØ¦ L 5.2 = 25 25 kñúgkrNIEdlbgðajenATIenH edaysarcugkMraltYCeNþIrRtUv)ancak;CamYynwgFñwmEdlRTva ehIymandak;EdkbEnßmsMrab;m:Um:g;GviC¢man enaHkMras;kMralGb,brmaGacRtUv)ansnμt;esμInwg = 0.186m < 0.2m Edl)aneRbI L 28 5> KNnafasCeNþIr³ edayBicarNafasCeNþIrkñúgRbEvgTTwg 1m bnÞúkenAelIfasCeNþIRtUv)an bgðajenAkñúgrUbTI 18>20. EpñkkNþal 0.6m RTbnÞúkeBj EtEpñksgçag 1.5m RTbnÞúkEtBak; kNþal. 0.6 2 m:Um:g;Bt; = 17.15 ×1.8 − 8.16 ×1.5 ×1.05 − 16.32 × 2 = 15.08kN.m edaysarEdkenAkñúgfasCeNþIrRtUv)andak;enABIelIEdkCeNþIrem enah d = 200 − 20 − 12 − 0.6 = 167.4mm edaysnμt; a = 10mm 15.08 ⋅10 6 As = = 258mm 2 < As (min) = 574mm 2 0.9 × 400 × (167.4 − 5) eRbIEdk DB12 KMlat 180mm ¬ As = 628mm 2 ¦ 6> FñwmTTwgenAcugfasCeNþIrRtUv)anKNnaedayeGayRTbnÞúkBICeNþIr 34.42kN / m bEnßmBIelI bnÞúkpÞal;rbs;va nigbnÞúkrbs;CBa¢aMgEdlenABIelIva. 7> RtYtBinitükMlaMgkat;dUcFmμta. karKNnasMrab;kMlaMgrmYl 555
23. 23. T.Chhay NPIC ]TahrN_TI 18>3³ KNnaCeNþIr run-riser stair EdlRTedayTMrsamBaØdUcbgðajenAkñúgrUbTI 18>21 sMrab;RTbnÞúkGefrBRgayesμI 5.7kN / m 2 . eKeGay f 'c = 21MPa nig f y = 400MPa . dMeNaHRsay³ 1> bnÞúk³ snμt;kMras;rbs;CMhankaM nigkMBs;kaMesμInwg 15cm . bnÞúkcMcMnucenAelICMhankaMnImYy²RtUv)anKNnadUcxageRkam ¬eyagtamrUbTI 18>21 a ¦. edayKitkñúg 1m TTwgrbs;CeNþIr PD = (0.15 × 0.4 + 0.025 × 0.15) × 25 = 1.6kN cMNaMfa bnÞúkefrcMcMnucenAelIfasCeNþIrmantMéltUcCag 1.6kN buEnþvaGacRtUv)ansnμt;esμI nwg PD edaykarKNnay:agsMrYl. KitbnÞúkGefrenAelITTwgCeNþIr 1m ehIyRbmUlvaCabnÞúk cMcMnuc enaHeK)an PL = 5.7 × 0.25 = 1.425kN karKNnasMrab;kMlaMgrmYl 556
24. 24. T.Chhay NPIC bnÞúkemKuN Pu = 1.2PD + 1.6PL = 1.2 ×1.6 + 1.6 ×1.425 = 4.2kN 2> KNnam:Um:g;Bt;enAkNþalElVg³ bnÞúkenAkñúg]TahrN_enHmanlkçN³sIuemRTIeFobnwgkNþal ElVgRtg;muxkat; B . RbtikmμenARtg;cMnuc A 15 RA = 4.2 = 31.5kN 2 m:Um:g;enARtg;cMnuc B = R A (8S ) − 7 Pu (4S ) = 31.5(8 × 0.25) − 7 × 4.2(4 × 0.25) = 33.6kN.m 3> KNnasrésEdkcaM)ac;enARtg;muxkat;kNþalElVg³ sMrab; h = 15cm / d = 150 − 25 = 125 Mu 33.6 × 10 6 Ru = = = 2.15MPa bd 2 1000 × 125 2 sMrab; f 'c = 21MPa / nig Ru = 2.15 enaHPaKryEdkKW f y = 400MPa ρ = 0.0064 < ρ max = 0.0135 / ¬ φ = 0.9 ¦ As = 0.0064 × 1000 × 125 = 800mm 2 eRbIEdk DB12 nigmanKMlat 14cm ¬ As = 807mm 2 ¦ tamTisedk nigTisQrkñúgTMrg;Edk kgbiTCit. sMrab;Edkrg eRbIPaKryEdkGb,brmasMrab;Tb;nwgsItuNðPaB nigkarrYmmaD ρ = 0.0018 As = 0.0018 × 400 × 150 = 108mm 2 eRbIEdk DB10 manKMlat 15cm ¬ As = 209.3mm 2 ¦. dak;Edk DB10 enARCugmYy²rbs; kaM ¬ As = 235.5mm 2 ¦ dUcbgðajenAkñúgrUbTI 18>21 c. 4> m:Um:g; nigsrésEdkEdlcaM)ac;sMrab;muxkat;muxkat;epSgeTotRtUv)aneFVICataragdUcxageRkam³ TItaMg A 1 2 3 4 5 6 7 8 0 7.88 14.7 20.48 25.2 28.88 31.5 33.08 33.6 B.M .(kN .m) 0 0.5 0.94 1.31 1.61 1.85 2.02 2.12 2.15 Ru (MPa) 0 0.14 0.27 0.38 0.47 0.55 0.60 0.63 0.64 ρ (% ) ( As mm 2 ) 0 175 338 475 588 688 750 788 800 eRbIEdk DB12 @ 200 sMrab;fas nig DB12 @150 sMrab;kaMCeNþIr. sMrab; As = 588mm 2 eRbIEdk DB12 @ 200 enAkñúgfasCeNþIr. karlMGitsrésEdkRtUv)anbgðaj enAkñúgrUbTI 18>21 c. karKNnasMrab;kMlaMgrmYl 557
25. 25. T.Chhay NPIC 5> RtYtBinitübrimaNEdkcaM)ac;enAkñúgTisTTwgrbs;fas³ bnÞúkenAelIfaskñúgmYyÉktþaRbEvgKW = 16.8kN / m dUcenH 4.2 0.25 16.8 Mu = × 3.6 2 = 27.2kN .m 8 27.2 ⋅10 6 Ru = = 1.74 MPa 1000 × 125 2 ρ = 0.0051 As = 638mm 2 eRbIEdk DB12 @175 As = 646mm 2 6> RbsinebIbnÞúkBRgayesμIRtUv)ansnμt;famanGMeBIelItYCeNþIr eKnwgTTYl)anlT§plRsedogKña. ]TahrN_ bnÞúkemKuNcMcMnucEdl)anKNnaKW 4.2kN manGMeBIelITTwgCMhankaM 0.25m . dUc enHbnÞúkkñúgmYyÉktþaRbEvgKW 4.2 / 0.25 = 16.8kN / m . m:Um:g;GtibrmaenAkNþalElVgRtg; muxkat; B ³ 16.8 2 Mu = × 4 = 33.6kN .m 8 m:Um:g;enAmuxkat;déTEtotGacRtUv)anKNnay:agRsYl ehIykarKNnaGacRtUv)anerobcMCata ragdUcBnül;kñúgCMhan 4. karKNnasMrab;kMlaMgrmYl 558
26. 26. T.Chhay NPIC karKNnasMrab;kMlaMgrmYl 559