Bending Analysis.pdf

8/13/2019 Bending Analysis.pdf

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CMBUk- karviPaKbegag

GnuelamtambTdanACI 318-M08

karkMnt;muxkat;nigPaBFn;begsMrab;Fwm


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karkMnt;muxkat;sMrab;PaBFn; KWCakarKNnarkvimaRxkat;eday eGayEeFV Ikardl;Edn)a:sIk rW ebtugeFVIkardl;Ebk.

bnkcugeRkay CabnkEdl)anBIkarKuNbnkCak;Esg bn kefr/ bnKuNnwgemKuNbnk.

bn keRkAbgeGayman m:Um:g;Bt;begag/ kMlaMgkat;TTwg/ m: Um:g;rmYlt

Cak;EsgnviFIGnuvtbn k. karkMnt;muxkat;RtUveFV Iy:agNa eGaygrbs;vaFMCag rWes InwgkMlaMgeRkA.

1- esckIepIm (Introduction)


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muxkat;ebtugGaem: KWCamuxkat;minesIsac; eRBaHvaeFVIeLIgBIrUbFatuBIrepSgKa dUecH eyIgRtUvmankarsntxHkgkarKNnarkmuxkat;.

virUbkmrbs;ebtug nigEdkes IKaenAelIkMritkMBs;dUcKa PaBbnSRKb;RKan

virUbkm smamaRtlIenEGCamYynwgRbEvgBITIRbCu MTMgn;. muxkat;Rtg; nwgbnRtg;eRkayeBlxUcRTg;RTayedaybegag.

PaBFn;Tajrbs;ebtugminKitkgkarKNnaeRBaH PaBFnes Inwg10%

nPaBFn;sgt;. muxkat;eRbHminKitCaRbsiTiPaB ehIymuneBleRTaMgmUl Camuxkat;RbsiTPaB.

2- esckIsnt(Assumption)


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viFIviPaKeGLas Ic KWminGnuvt cMeBaHlkNenARKb;kMritkMlaMgsMBaFpeT. sMrab;kMlaMgsMBaFpx


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3- RbePTEbkedaybegag

eRkamGMeBInkMlaMgbegag karEbkneRKOgbg Mman4RbePTmaNPaKrynEdkEdleRbIk gmuxkat;.

1-muxkat;tulkm (balanced failure section)KWCakarEbkedaysar ebtugEbkRsbeBlEdlEdkcab;ep I )a:sIkkm.

ebtugEbkeBlvirUbkmesInwge

cu= 0.003

rWEdkeFVI) :as IkkmeBlEdlvirUbkmRtg;TIRbCu MTMgn;rbs;EdkTajesInnwgey .


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2-muxkat;BRgwgRCul (compression-controlled section)KWkarEbkedaysaebtug eBlEdlEdkenAEK

)a :s Ikkm eBalKW virUbkmrbs ;EdkenAEKm et < ey. brimaNEdkeRcInehIyeFVIkarkgeGLas Ic muxkat;manlkNRsYy.

3-muxkat;BRgwgtic (tension-controlled section)KWkarEbkedaysaEdk eBlEdlEdkenAEKm)a :sIkkm eBalKW

virUbkmrbs;EdkenAEKm et 0.005 . brimaNEdktic ehIy

EdkeFV Ikarkg)a:s Ic muxkat;manlkNsV it.


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4-muxkat;BRgwgmFm(transition failure section)KWkarEbkedaysaebtug eBlEdl EdkenAEKmeRkArUbkmrvag

ey nig0.005 eBalKW ey < et < 0.005 . muckat;enHmanlkNrvagmuxkat;BRgwgtic nigmuxkat;BRgwgRCul eBalKWman lkNBak;kNalRsYy.


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RbePTmuxkat;BRgwgtic

b

As d

f c

f y

N.A

ec=0.003

ey=f y/Es

b

As dt

f c

f s


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4- viFIKNna nigtMrUvkarPaBFn;

GaRsytamACI 318M-05

4>1 viFIKNnaPaBFn;(Strength Design Method)viFIKNnaPaBFn;tMrUveGayPaBFn;KNnanFatubg MenARtg;RKb;muxk

KYrEtesI rWFMCagPaBFn;RtUvkar Edl)anKNnaedayemKuN k. CaTUeTAPaBFn;KNna PaBFn;dac;xat(U) rW f Sn U

EdlPaBFn;KNna= emKuNkat;bnyPaBFn;(f ) PaBFn;edIm f = mKuNkat;bnyPaBFn; EdlmanEcgk gcMnuc 4>4 xageRk


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PaBFn;edIm= PaBFn;nFatubg M rWmuxkat; EdlKNnaedayeRbIesckI sntnigsmIkarPaBFn;rbs;vIFIKNnaPaBFn;.

PaBFn;dac;xat= emKuNbnk \TiBlbnkeRbIR)as;. PaBFn;RvkarRtUv)anrkedayGaRsytamkarbnSMbnk.

emKuNbnk= emKuNbEnmbn k EdlbNalmkBIkarERbRbkeRbIR)as;.

bnkeRbIR)as;= bn kbgajedaybTdansagsg;TUeTA minKitemKuN


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karkMNt;(Notation)

PaBFn;dac;xat(Require Strength)Mu = m:Um:g;dac;xat PaBFn;Bt;begagRtUvkarPu = kMlaMgcMpitdac;xat PaBFn;bnkcMpitRtUvkarVu = kMlaMgkat;dac;xat PaBFn;kat;RtUvkarTu = m: Um:g;rmYldac;xat PaBFn;rmUlRtUvkar

PaBFn;edIm(Nominal Strength)Mn = PaBFn;Bt;begagedIm M b = PaBFn;Bt;begagedIm enAlkxNvirUbkmtulkal Pn = PaBFn;kMlaMgcMpitedIm enAeBlmancMNakpt


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Po = PaBFn;kMlaMgcMpitedIm enAeBlcMNakpitesIsUnP b = PaBFn;kMlaMgcMpitedIm enAlkxNvirUbkmtVn = PaBFn;kat;edIm Vc = PaBFn;kat;edIm Edlpl;edayebtugVs = PaBFn;kat;edIm Edlpl;edayEdk Tn = PaBFn;m: Um:g;rmYledIm PaBFn;KNna(Design Strength)f Mn = PaBFn;Bt;begagKNnaf Pn = PaBFn;kMlaMgcMpitKNa enAeBlmancMNakpit f Vn = PaBFn;kMlaMgkat;KNna= f (V c + V s)


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f Tn = PaBFn;m: Um:g;rmYlKNna4>2 tMrUvkarPaBFn;(Strength Requirement)lkxNmUldansMrab;karKNnaPaBFn; manbgajdUcxageRPaBFn;KNna PaBFn;RtUvkar

emKuNkat;bnyPaBFn

PaBFn;edIm

emKuNbnk

\TBlbnkeRral;Fatup Mrbs;eRKOgbg M nigral;muxkat;TaMgGs; RtUvEtGnuvtlkxN xage eRkamlkxNkarbnSMbn kcMeBaHRKb;GMeBI Bt;begag/ bn kcMpit/kMlaMgkat;/>>>.l.

un

un

un

V V

P P M M

f

f f

)1.2(


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4>3 PaBFn;dac;xat(Require Strength)edIm,ITTYl)annUvPaBFn;dac;xat bnkcugeRkayRtUvy

karbnSMbnkmandUcxageRkam

)79.(6.10.19.0)69.(6.16.19.0

)59.(2.00.10.12.1

)49.()(5.00.16.12.1)39.()8.00.1()(6.12.1

)29.()(5.0)(6.1)(2.1

)19.()(4.1

Eq ACI H E DU Eq ACI H W DU

Eq ACI S L E DU

Eq ACI Ror S or L LW DU Eq ACI W or L Ror S or L DU

Eq ACI Ror S or L H LT F DU

Eq ACI F DU

r

r

r


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kgenaHD = bnkefr E = \TiBlbn krBa ydIF = bnkbNalBITMgn; nigsMBaFvtravH = bnkbNalBITMgn; nigsMBaFdIL = bn kGefr Lr = bn kGefrdMbUl R =

bn kTwkeP gS = bnkRBil T = \TiBlsItuNPaB/ karrYjmaD/ karRskmaD


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W = bn kxl;karBicarNaepSg EdlTak;TgnwgkarbnSMbnk mandUcxage

1> PaBFn;nwg\TiBlrBa y EdlGnuvtrYmbBalCamYybn kGefr.2> sMrutxusKa/ karrYjmaD/ karRskmaD karrIkrUmnkarRskma

karpas;brsItuNPaB BwgEpkelIkarRbmaNR)adkniymmYyBl EdlekItegkgkareRbIR)as;.

3> sMrab;eRKOgbg Ms itenAkgtMbn;TwkCMnn; bn kTwkCMnn; nigkarbnSMb

bTdanASCE 7

nwgRtUveRbI.sMrab;eRKOgbg MCaeRcIn RtUv)anBicarNaelIbnkefr Gefr xl; nigrBa ydI.EdlbnkF, H, R, S, nigT minRtUv)anKit enaHeyIgmansm


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edIm,IbnSMbnkTaMgenHKWmank gtaragTI 2>1.

bn k PaBFn;dac;xat efr nigGefr 1.4D1.2D + 1.6L + 0.5L r efr Gefr nigxl; 1.2D + 1.6L r + 1.0L1.2D + 1.6L r + 0.8W

1.2D + 1.6W + 1.0L + 0.5L r 0.9D + 1.6W

efr Gefr nigrBaydI1.2D + 1.0L + 1.0E0.9D + 1.0E

taragTI 2>1 karbnSMbn ksMrab;PaBFn;dac;xat

4>4 KNk tb P BF


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begag/ karTajcMpit/ begagnigrmYl sVIt 0.90

begag RsYy 0.60

kMlaMgkat; nigrmYl 0.75

PaBRTelIebtug 0.65

sgt;cMpit manrWKanbegageRKOgbg MmanEdkkgvil eRKOgbg MepSgeTot

0.750.70

4>4 emKuNkat;bnyPaBFn;(Strength Reduction Factor)

PaBFn;pal;rbs;muxkat; RtUvbnyedayemKuNkat;byPaBFn; edIm,ItM

PaBminc,as;las; EdlmancMeBaHbMErbMrYl PaBFn;/ muxkat;/ karRtYtBint///.


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sMrab;Edkkgvil ssr0.20

0.70 ( )0.005t y y

f e e e

0.250.65 ( )

0.005t y yf e e

e

sMrab;EdkkgFmta

rUbTI 2>2 karERbRbYlf CamYynwget nigc/d t


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5- karviPaK nigkarkMnt;muxkatk gkarsikSaeRKOgbg MebtugsrsEdk viFIsaRsBIrEdleRbICajwkjab;KW1>karviPaKmuxkat; KWkarkMnt;rklTPaBRTRTgk grbs;muxkat; edIm,IeRbobnwg\TiBlkMlaMgeRkA edaydwgvimaRtmuxkat;ebtug PaBFn;rbs;ebtugnigEdk nbNajEdk.

2>karkMnt;muxkat; KWkarkMnt;rkvimaRtmuxkat; nigbNajEdk edaydwg\T iBlkMlaMg eRkA PaBFn;rbs;Edk nigebtug.


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6- r)aykMlaMgsMBaFpsmmU

r)aykMlaMgpkgebtugeBlEbk GacsntCarag ctuekaNEkg/RbelBIEb:t/ ):ar:abUl rWragepSgeTAtamlTplBiesaFn_.

ebtugmanr)aykMlaMgp0.85 f c rayelItMbn;sgt;edayksNan kMras;nGkSnWRt KWc KitBIEKmsgt;mkdl;GkSnWRt kMras;ntMbn;sgt;KWa=b1c Edl b1 ERbRbYlBI0.65 eTA0.85 .


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smmUl Cak;Esg b

Asd

f c

f y

N.A

ec=0.003

ey=f y/Es

0.85f c

C=0.85f cab

T=A sf y

az = a/2

d-z

rUbTI 2>3 r)aykMlaMgsMBaFpsmmUlkgebtug

0 85


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23rUbTI 2>4 tMlb 1 ERbRbYleTAtamPaBFn;ebtug

1.00

0.75

0.50

0.25

0.85

0.65

1 2 3 4 5 6 7 8 ksi28 MPa 56 MPa

1

0.85max min , 0.65' 28

0.85 0.057

c f b

ACI 318M05,section 10.2.7.3

MPa f if MPa f MPaif MPa

MPa f

MPa f if

c

c

c

c

55'65.055'287

28'05.085.0

28'85.0

1 b

7 k bMB k EdkT j


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RbePTmuxkat;tulkmekItmaneBlEdl Edkcab;ep Im):asIkkm sbeBlEdlebtuehIykarEbkenHRbRBwteTAedayrhs. PaKryEdkEdlRtUvnglkxNtulkmKW

bd

balanced A sb

)(

d: KWCacMgayBIEKmsgt;eTATIRbCuMTMgn;nEdkTajEdl b: KWCaTTwgnEpksgt;rbs;eRKOgbgM

ebIsinCa eyIgeRbIEdktUcCaglkxNtulkm enaHmuxkat;CaRbePTmuxkat;BRgwgtEdlEdkeFV I) :asIkkmmuneBlebtugEbk vaCakarEbkyWt nigpl;tMnwgmun.

7- muxkat;bMBak;EdkTaj(Singly Reinforced Beam)


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25rUbTI 2>5 r)aykMlaMgsMBaFprbs;ebtugsmmUlragctuekaNEkg

Ik RKH Mb k iP K igk kMt k t BIM d E k lIlk NlMg


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1/ kMlaMgsgt;RtUvesInwgkMlaMgTaj

smIkarRKwH sMrab;karviPaK nigkarkMnt;muxkat; manBIrsMxan;edayEpkelIlkxNlMgcMeBaHRKb;RbePTbnknigmuxkat;

2/ lTPaBm: Um:g;begagkg esInwgplKuNkMlaMgsgt;nwgdeXaHrbs;va rW esInwg

kMlaMgTajKuNnwgdeXaH

)1.2('85.0 y sc f Aab f T C

2

2'85.0

)2.2(22

ad f A M

ad ab f M

ad T

ad C M

y sn

cn

n

7>1 lk Nb SIiUbk


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or

7>1 lkxNbnSIvirUbkm(Condition of Strain Compatibility) e

seud c

c

es eu d cc

c d

eueu es

e t e u

d t c

c

c dt

e u

e u e tor

)3.2(

)4.2(

7>2 muxkat;tulkm(B l St i C diti )


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28rUbTI 2>6 muxkat;tulkmkgkarBt;begag

7>2 muxkat;tulkm(Balance Strain Condition)


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kMBs;GkSeNWk sMrab;lkxNtulkm

)5.2(003.0003.0

003.0003.0

yt

b

y yu

u

t

b

d c

d c

e

e e e e

lkxNtulkmvirUbkmekIteLIgelImuxkat; enAeBlNaEdlvrUbkm Gtibrmarbs;ebtugenApsgt;xagelIeu = 0.003 CamYyvirUbkmeGL icdMbUges = ey = f y/E s kgEdkTaj.

7>3 muxkat;RsYy (C i C l S i )


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muxkat;RsYYy 0.003

/CCL

t CCL y s

cd c f E

0.0030.003 /

CCL

t y s

cd f E

virUbkmGtibrmasMrab;Bt;begag0.003

0.003 0.004t

c

d 0.429

7>3 muxkat;RsYy (Compression-Control Section)

yt

CCL

d

c

e 003.0

003.0

)6.2(

7>4 muxkat;sVit (T i C l S i )


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muxkat;sVit

10.375TCL

t

ad

b

0.0030.005

TCL

t TCL

cd c

0.0030.375

0.003 0.005TCL

t

cd

7>4 muxkat;sV it (Tension-Control Section)

)7.2(

7>5 PaKryEdk(St l R ti )


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eyIgman7>5 PaKryEdk(Steel Ratios)

As

b d

As

f y

b d f y

0.85f'c a b

b d f y 0.85 b1

f'c

f y c

d 0.85 b1

f'c

f y c

dt

dt

d

0.85 b1

f'c

f y

eu

eu es 0.85 b

1

f'c

f y

eu

eu et

dt

d

1> PaKryEdktulkm(Balance steel ratio)eyIgman

f c f'c f s f y es eyf y

Es

b 0.85 b1f'c

f y

eueu ey

0.85 b1f'c

f y

600MPa

600MPa f y

)8.2(

)9.2(

2> PaKryEdkGtibrma(Maximum steel ratio)


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2> PaKryEdkGtibrma(Maximum steel ratio)

- bTdanACI 318-99

- bTdanACI 318-02 nig05max 0.75 b

max et 0.85 b1f'

cf y

eueu et

CamYy et 0.004

enAeBl e

u 0.003

Es 2 105

MPanigey

f y

Es0.002

max

b

eu eyeu 0.004

5

7 0.714

max

b

eu eyeu 0.005

5

8 0.625

10.2(

cMeBaH

cMeBaH f y 400MPa

et 0.005cMeBaH

et 0.004

3> PaKryEdkGb brma(Minimum steel ratio)


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3> PaKryEdkGb,brma(Minimum steel ratio)

)11.2(min

3 f'c

f y

200

f y

(in psi)

min0.25 f 'c

f y

1.4

f y(in MPa)

7>6 m: Um:g;lTPaBRTRTg;(Flexural Strength)TajecjBIsmIkar(2.1) eyIg)an

yksmIkar(2.12)

CYsk gsmIkar(2.2)

)12.2('85.0 b f

f Aa

c

y s

)13.2('

59.0

'7.1

b f

f Ad f A M

b f

f Ad f A M

c

y s y sn

c

y s

y sn

CY k Ik As )12(9012 y f bdf


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CYs kgsmIkar(2.13)bd s )14.2(

'59.012

c y

yn f bd f M

tag dUecH smIkar(2.14)

kayCa' y

c

f

f

)15.2()()95.01(' 22 ncn k bd bd f M

Edl

t e

dUcenH m:Um:g;lTPaBRTRTg;KWEdl nig CaGnuKmn_

n M f

et eudt c

c

f f e t

f max min1.45 250 et

30.9

0.65

)95.01( nk

8 P BRKb RK k


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8- PaBRKb;RKan;nmuxkat;muxkat;mYyGacCamuxkat;RKb;RKan; luHRtaNalTPaBm:Um:g;begagk grbs;

muxkat;enaH FMCag rWesInwgm:Um:g;eRkAdac;xat Mu .

)2

( a

d f A M y sn f f

1.2 1.6u D L M M M

un M M f

1/ KNnam:Um:g;Bt;begageRkAdac;xat

3/ ep gpat;fa

maxmin BinitemIlPaKryEdk 2/ KNnam:Um:g;begagk g rWm: Um:g;lTPaBRTRTg;

D M 4.1

rk eRbsmIkar (2.15)

]T h NTI1


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]TahrN_TI 1

250cm

epgpat; faetImuxkat;RKb;RKan; rWeTsMrab;RTbn k?

edaydwgfaLL=10kN/m; DL= 22kN/m f c= 27 MPa; f y= 400 MPa; A s= 11.61cm 2

As45cm40cm

20cm

rUbTI 2>7 muxkat; nigvimaRtrbs;Fwmly

]TahrNTI2


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]TahrN_TI 2

600cm

KNnabn kGefrEdlmanGMeBIelIFwm edaydwgfaLL=?; DL= ? f c= 25 MPa; f y= 400 MPa; A s= 15.2cm 2

As50cm 45cm

25cm

rUbTI 2>8 muxkat; nigvimaRtrbs;FwmTMrsamB

9 k bMB k EdkD bEd


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9- muxkat;bMBak;EdkDubEd(Doubly Reinforced Beam)

kalNalTPaBm: Um:g;Bt;begagkgrbs;muxkat;enaH tUcCag m:Um:g;eRkA

Edksgt; nigEdkTajRtUvEtdak;bEnmelIbrimaNEdkGtibrman

1/ Edksgt;eFVI):as Ikkm2/ Edksgt;yWtk geGLas c

eBlKNnamuxkat;BRgwgsgxagEdkDub eyIgmanBIrkrNIKW

9>1 lkxNbnSIvirUbkm(Condition of Strain Compatibility)


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or

( p y)

eseu

d c

c

es eud c

c

c d

eueu es

e t e u

d t c

c

c dt

e u

e u e tor

)3.2()16.2(

e' d'


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)17.2(e seu

c d'

c

e' s euc d'

c

c d'eu

eu e' s

9>2 PaKryEdk(Steel Ratios)


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y

)18.2(

1> PaKryEdksgt;

'A'

s b d

2> PaKryEdkTaj

' f sf y

As b d

As f y b d f y

0.85f'c a b A' s f y b d f y

0.85 b f'c cf y d

)19.2(3> PaKryEdkTajGtibrma

t.max max 'f s

f y )20.2(

t.max ebtug PaBFn;nmuxkat; KWRKb;RKan;.


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eBl

4> PaKryEdkTajGb,brma

)22.2(

0.85 b1f'c c

f y d

'f s

f y

0.85 b1f'c

f y

d'eu

eu e' s

d

'f s

f yf s f y

t.max

g ;; ; ;

ebtug PaBFn;nmuxkat; KWminRKb;RKan;.

cy 0.85 b

1

f'c

f y

eueu ey

d'

d'

Edksgt;eFVIkar):asikkm cy f's f y


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g ; ) cy

y

f's f yEdksgt;mineFV Ikar):asikkm

1> lMnwgnkMlaMg

2> lMnwgnm:Um:g;

9>3 viPaKelIPaBFn;(Strength Analysis)

T C Cs C 0.85f .c a bCs A' s f s

T A s f y

Mn Mn1 Mn2

Mn1 Cs d d'( ) A' s f's d d'( )

Mn2 C d a2 0.85f'c a b d a2

Mn2 T Cs d a

2

As f y A' s f's d a

2


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rUbTI 2>9 r)aykugRtaMnigvirUbkmrbs;muxkat;EdkDubEdkTajnigsgt;

9>4 Edksgt;eFV I) : as Ikkm(Compression Steel is yield)


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enAeBlEdksgt;eFVI):asIkkm KWmannyfa .g; )

f's f y

a As f y A' s f y0.85f' c b

PaBFn;m: Um:g;edIm(Nominal moment strength)Mn As A' s f y d a2 A' s f y d d'

)23.2(

)24.2(

PaBFn;nwgkarBt;begag(Flexual strength)

)'('

2')( 21 d d f Aad f A A M M M y s y s snnn f f f


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rUbTI 2>10 r)aykugRtaMgnigvirUbkmrbs;muxkat;EdkDub enAeBlEdksgt;eFVI):as ikkm

]- KNnam:Um:g;lTPaBRTRTg;rbs;F wmEdlbgajkgrUbTI 2>11 xage


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] g; g; ;gj g gsMParHeRbIR)as; f c= 30 MPa f y= 400 MPa

CMhanndMeNaHRsay 1-epgpat;)a:sIkkmrbs;Edksgt;2-epgpat;PaBsV it 3-KNnam:Um:g;

b=30cm

d=54.5cm

d=6cm

As=38.82cm 2

A s=7.74cm 2

N.A.

c =9cm

1

' ' 0.003' 0.85

0.003 /c

y y s

f d K

f d f E b

)'('

2121 d d f A

ad f A M M M y s y snnn f f

10.375TCL

t t

aad d

b

rUbTI 2>11 muxkat;F wmbMEdk

9>5 Edksgt;mineFV I) : as Ikkm(Compression Steel is not yield)


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49

eBlEdkmineFV I)a :s Ikkm/ kMlaMgpCak;EsgRtUvykkmeRbIedayKNtamrUbmndUcxageRkam

yu s s s s f cd c

E E f ''.' e e

cd c

u s'' e e

c,ab;lMnwgnkMlaMg eyIgman

g )

)25.2('

''85.0c

d c E Aab f f A u s sc y s e

)26.2(0'')'('85.0

0'

''85.0

1112 d f Aa f A f Aba f

f Ac

d c E Aab f

s y s sc

y su s sc

b

e

Edl MPa E f u s 6001 e


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50

b f c'85.0EcksmIkar(2.26) nwg eyIg)an

0'85.0

'''85.0

)'(

0'85.0

'')'('85.0

1112

111

2

b f d f A

ab f

f A f Aa

b f d f Aa f A f Aba f

c

s

c

y s s

c

s y s sc

b

b

tagb f

f A f A p

c

y s s

'85.0

)'(

21 1

b f d f A

qc

s

'85.0'' 11 b nig

)27.2(022 q paa

edaHRsaysmIkardWeRkTI2n(2.27) eyIgTTYl)an


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51

CMerAGkSNWkc GacKNna

nig q p paq p pa 2221

1 b ac

PaBFn;m: Um:g;edIm(Nominal moment strength)

)28.2(

PaBFn;nwgkarBt;begag(Flexual strength)

)'(''2')( 21 d d f Aa

d f A A M M M s s y s snnn f f f

)'(''2

')( 21 d d f Aad f A A M M M s s y s snnn

]- KNnam:Um:g;lTPaBRTRTg;rbs;F wmEdlbgajkgrUbTI 2>12 xage


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sMParHeRbIR)as; f c= 35 MPa f y= 400 MPa

b=35cm

d= 6cm

d= 5cm

As=49.2 cm 2

A s=15.2 cm 2

N.A.

c =9cm

rUbTI 2>12 muxkat;FwmbMBak;Edk

10- karviPaKmuxkat;ragT-I


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53

10 karviPaKmuxkat;rageRkamGMeBInkMlaMgBt;begag EpkxHnkMralrgkMlaMgsgt;.EpknkMralEdleFV IkarCamYyF wmehAfasabF wm.

S

CL (b-b w)/2

b

bw

(b-b w)/2

hf

xx

rUbTI 2>13 TTwgsabRbsiTPaB

10>1 TTwgRbsiTPaBnmuxkat;ragT-I


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54

TTwgRbsiTPaBrbs;sabTak;Tgnwg

- KMlatFwm/ TTwgtYFwm/ kMras;kMral/ lkxNTMrrbs;F wm/ Tisnkk TTwgRbsiTPaBkMnt;yktUck gcMeNamtMlTaMgbI EdlKNnadUcteTA

1-GaRsynwgRbEvgFwm 2- GaRsynwgkMras;F wmnigTTwgtYFwm 3-GaRsynwgKMlatrvagF wm

4

Lb

w f bhb 16

S b

b KWCaTTwgRbsiTPaBrbs;Fwm L KWCaRbEvgF wm

bw KWCaTTwgtYF wm hf KWCakMras;kMral

10>2 muxkat;ragT-I eFV IkardUcCactuekaN


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55

muxkat;et nigGu IeFV Ikar dUcCamuxkat;ctuekaN kalNakMras;ntMbn;sgt;sitenAkgsabnmuxkat;.

dUecH eyIg)an

m: Um:g;kgrbs;muxkat;KW

2a

d f A M y sn f f

f ha

b f

f Aa

c

y s

'85.0

min d b A

w

sw

10>3 karviPaKmuxkat;ragT-I


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56

rUbTI 2>14 r)aykMlaMgsMBaFp nigvirUbkmrbs;F wmGkSet

bz=a/2

0 003


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57

hf d

a

( d

- z )

bw

e=0.003

C

T=A s.f y

= +

z =a w/2

( d

- z

)

C1

T1=A swf y

(b-b w)/2(b-b w)/2

Asw Asf

z=h f /2

( d

- h

f / 2 )

C2

T2=A sf f y

rUbTI 2>15 karbMEbkkMlaMgrbs;muxkat;F wmGkSret

eBlEdlGMeBIxageRkAkan;EtFM/ r)a:ykMlaMgt;s itenAeRkams


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58

mYycMEnkntYFwmcUlrYmedayRbsiTPaBkgkarTb;nwgm:Um:g;.

kMlaMgsgt;k gtMbn;sgt;KW1-muxkat;ctuekaNdak;Edkmag nigmanbrimaNEdk

sgt; nigkMlaMgTaj sitenAcMgay 2-muxkat;pSMBIsabcMehogTaMgBIr Edlpl;kMlaMgsgt;bEn

nigdeXaHehIyEdksMrab;muxkat;TIBIrenHKW

)('85.0 f w f c habhb f C

f

w hbb

22

y

w f c sf f

bbh f A

)('85.0

d bw sw A

wc ab f C '85.0 y sw f AT )

2( w

ad

2/ f

hd c f w f hbb '85.0)(

eyIg)anmuxkat;EdksrubKW sf sw s A A A


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59

ehIykMras;tMbn;sgt;KW

lTPaBm:Um:g;RTRTg;rbs;muxkat; KWCaplbUkn

2)(

21w

y sf sw

y swnad f A Aad f A M f f

22)( f y sf

w y sf sn

hd f A

ad f A A M f f

22 f

y sf n

hd f A M f

wc

y sf sw b f

f A Aa

'85.0)(

21 nnn M M M f

1-pleFobEdkTajsrubCamYyptYFwmRtUveKarBlkxN


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1 pleFobEdkTajsrubCamYyptYFwmRtUveKarBlkxN

2- PaBsV itrbs;muxkat;min d b

A

w

s

w

375.0t d

c

muxkat;sVit 375.0

t d c muxkat;RsYy

1 b wac Edl

10>4 CMhannkarviPaKmuxkat;ragT-I


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61

1-KNnaTTwgRbsiTPaB nigPaBryEdkGb,brmangEdkGtib,rma

2-ep gpat;lkNmuxkat;GkSet

f ha

maxmin ,

b f f Aa

c

y s

'85.0

b

3-muxkat;eteFVIkarCactuekaNebI4- muxkat;eteFV IkarCaGkSret f ha

k- KNnaEdksMrab;sab y

w f c sf f

bbh f A

)('85.0

x-ep gpat;PaBsVit 375.0t d c

K- KNnam:Um:g;lTPaBRTRTg;


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62

Edl

22)( f y sf

w y sf sn

hd f A

ad f A A M f f

wc

y sf sw b f

f A Aa

'85.0)(

10>5 ]TahrNkarviPaKmuxkat;ragT-I1 bNjF b EdkEdlFIY KMl BIK hI R


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63

1-bNajFwmebtugsrsEdkEdlFwmnImYymanKMlatBIKa ehIyRedayTMrsnak;. RbEvgFwmKW RTkMralmmaRtrb F wmmanbgajk grUbxageRkam/ edaydwg .

cUrKNnam: Um:g;lTPaBRTRTg;rbs;F wm. MPa f c 20'

m4.2mm100

MPa f y 400; m5.4

25 cm

As=15.2 cm 2 2.4m

10cm

2.4m

30.5 cm8 cm

etIm:Um:g;lTPaBRTRTg;esIb:unan RbsinebI As=49.16 cm 2rUbTI 2>16 bNajFwmGkSr

2- cUrKNnam:Um:g;lTPaBRTRTg;rbs;Fwmmuxkat;GkSretbgaj


64/64

64

MPa f c 25' MPa f y 400;

g g g jk grUbTI 2>17 xageRkam.edaydwgfa

25cm

9cm

44cm

90cm

8cm

11cm

13cm

0.85 fc

C

T

As=38.82 cm 2

rUbTI 2>17 muxkat;F wmGkSret

Documents

Bending Analysis.pdf