bending analysis.pdf
TRANSCRIPT
-
8/13/2019 Bending Analysis.pdf
1/64
1
CMBUk- karviPaKbegag
GnuelamtambTdanACI 318-M08
karkMnt;muxkat;nigPaBFn;begsMrab;Fwm
-
8/13/2019 Bending Analysis.pdf
2/64
2
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)
-
8/13/2019 Bending Analysis.pdf
3/64
3
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)
-
8/13/2019 Bending Analysis.pdf
4/64
4
viFIviPaKeGLas Ic KWminGnuvt cMeBaHlkNenARKb;kMritkMlaMgsMBaFpeT. sMrab;kMlaMgsMBaFpx
-
8/13/2019 Bending Analysis.pdf
5/64
5
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 .
-
8/13/2019 Bending Analysis.pdf
6/64
6
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.
-
8/13/2019 Bending Analysis.pdf
7/64
7
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.
-
8/13/2019 Bending Analysis.pdf
8/64
8
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
-
8/13/2019 Bending Analysis.pdf
9/64
9
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
-
8/13/2019 Bending Analysis.pdf
10/64
10
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
-
8/13/2019 Bending Analysis.pdf
11/64
11
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
-
8/13/2019 Bending Analysis.pdf
12/64
12
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)
-
8/13/2019 Bending Analysis.pdf
13/64
13
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(
-
8/13/2019 Bending Analysis.pdf
14/64
14
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
-
8/13/2019 Bending Analysis.pdf
15/64
15
kgenaHD = bnkefr E = \TiBlbn krBa ydIF = bnkbNalBITMgn; nigsMBaFvtravH = bnkbNalBITMgn; nigsMBaFdIL = bn kGefr Lr = bn kGefrdMbUl R =
bn kTwkeP gS = bnkRBil T = \TiBlsItuNPaB/ karrYjmaD/ karRskmaD
-
8/13/2019 Bending Analysis.pdf
16/64
16
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
-
8/13/2019 Bending Analysis.pdf
17/64
17
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
-
8/13/2019 Bending Analysis.pdf
18/64
18
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///.
-
8/13/2019 Bending Analysis.pdf
19/64
19
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
-
8/13/2019 Bending Analysis.pdf
20/64
20
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.
-
8/13/2019 Bending Analysis.pdf
21/64
21
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 .
-
8/13/2019 Bending Analysis.pdf
22/64
22
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
-
8/13/2019 Bending Analysis.pdf
23/64
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
-
8/13/2019 Bending Analysis.pdf
24/64
24
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)
-
8/13/2019 Bending Analysis.pdf
25/64
25rUbTI 2>5 r)aykMlaMgsMBaFprbs;ebtugsmmUlragctuekaNEkg
Ik RKH Mb k iP K igk kMt k t BIM d E k lIlk NlMg
-
8/13/2019 Bending Analysis.pdf
26/64
26
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
-
8/13/2019 Bending Analysis.pdf
27/64
27
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 )
-
8/13/2019 Bending Analysis.pdf
28/64
28rUbTI 2>6 muxkat;tulkmkgkarBt;begag
7>2 muxkat;tulkm(Balance Strain Condition)
-
8/13/2019 Bending Analysis.pdf
29/64
29
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 )
-
8/13/2019 Bending Analysis.pdf
30/64
30
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 )
-
8/13/2019 Bending Analysis.pdf
31/64
31
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 )
-
8/13/2019 Bending Analysis.pdf
32/64
32
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)
-
8/13/2019 Bending Analysis.pdf
33/64
33
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)
-
8/13/2019 Bending Analysis.pdf
34/64
34
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
-
8/13/2019 Bending Analysis.pdf
35/64
35
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
-
8/13/2019 Bending Analysis.pdf
36/64
36
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
-
8/13/2019 Bending Analysis.pdf
37/64
37
]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
-
8/13/2019 Bending Analysis.pdf
38/64
38
]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
-
8/13/2019 Bending Analysis.pdf
39/64
39
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)
-
8/13/2019 Bending Analysis.pdf
40/64
40
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'
-
8/13/2019 Bending Analysis.pdf
41/64
41
)17.2(e seu
c d'
c
e' s euc d'
c
c d'eu
eu e' s
9>2 PaKryEdk(Steel Ratios)
-
8/13/2019 Bending Analysis.pdf
42/64
42
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;.
-
8/13/2019 Bending Analysis.pdf
43/64
43
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
-
8/13/2019 Bending Analysis.pdf
44/64
44
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
-
8/13/2019 Bending Analysis.pdf
45/64
45
rUbTI 2>9 r)aykugRtaMnigvirUbkmrbs;muxkat;EdkDubEdkTajnigsgt;
9>4 Edksgt;eFV I) : as Ikkm(Compression Steel is yield)
-
8/13/2019 Bending Analysis.pdf
46/64
46
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
-
8/13/2019 Bending Analysis.pdf
47/64
47
rUbTI 2>10 r)aykugRtaMgnigvirUbkmrbs;muxkat;EdkDub enAeBlEdksgt;eFVI):as ikkm
]- KNnam:Um:g;lTPaBRTRTg;rbs;F wmEdlbgajkgrUbTI 2>11 xage
-
8/13/2019 Bending Analysis.pdf
48/64
48
] 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)
-
8/13/2019 Bending Analysis.pdf
49/64
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
-
8/13/2019 Bending Analysis.pdf
50/64
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
-
8/13/2019 Bending Analysis.pdf
51/64
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
-
8/13/2019 Bending Analysis.pdf
52/64
52
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
-
8/13/2019 Bending Analysis.pdf
53/64
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
-
8/13/2019 Bending Analysis.pdf
54/64
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
-
8/13/2019 Bending Analysis.pdf
55/64
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
-
8/13/2019 Bending Analysis.pdf
56/64
56
rUbTI 2>14 r)aykMlaMgsMBaFp nigvirUbkmrbs;F wmGkSet
bz=a/2
0 003
-
8/13/2019 Bending Analysis.pdf
57/64
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
-
8/13/2019 Bending Analysis.pdf
58/64
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
-
8/13/2019 Bending Analysis.pdf
59/64
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
-
8/13/2019 Bending Analysis.pdf
60/64
60
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
-
8/13/2019 Bending Analysis.pdf
61/64
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;
-
8/13/2019 Bending Analysis.pdf
62/64
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
-
8/13/2019 Bending Analysis.pdf
63/64
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
-
8/13/2019 Bending Analysis.pdf
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