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. 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§½éntYCeNþIrRsedogeTAnwgkMralxNнmYyTisEdl
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. 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. 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. 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)anKNnaCakMralxNнmYyTisEdlmanTMrsamBaØ
karKNnasMrab;kMlaMgrmYl 538

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 rmYlenAkñúgkMralxNн.
karKNnasMrab;kMlaMgrmYl 539

7. T.Chhay NPIC
RbBn§½énkardak;bnÞúkbIRbePT RtUv)anykmkBicarNakñúgkarKNnaCeNþIrRbePTenH
edayKitBicarNafam:Um:g;rmYlnwgekItmanenAkñúgkMralRKb;lkçxNн³
- 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. T.Chhay NPIC
biTCit enABak;kNþalTTwgrbs;CeNþIr. srésEdklMGitRtUv)anbgðajenAkñúgrUbTI
18>13.
sßabtükrcUlcitþCeNþIrRbePTenH ehIyCeNþIrRbePTenHeBlxøHRtUv)aneKehAfa pliers-
shaped staircase b¤ jackknife staircase.
karKNnasMrab;kMlaMgrmYl 541

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. 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. 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. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 545

13. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 546

14. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 547

15. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 548

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. 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. 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. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 552

20. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 553

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. 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;kMralxNнGb,brmasMrab;karBarPaBdabKW
= 0.208m ¬sMrab;kMralxNнTMrsamBaئ
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. 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. 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. 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. T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 559