1. T.chhay
V. Fñwm
Beams
5>1> esckþIepþIm Introduction
FñwmCaGgát;rbs;eRKOgbgÁúMEdlRTbnÞúkTTwg dUcenHehIy)aneFVIeGayvargnUvkarBt; (flexural or
bending). RbsinebImanvtþmanbnÞúktamGkS½kñúgbrimaNmYyFMKYrsm vanwgRtUv)aneKehAvafa beam-
column ¬EdlnwgRtUvbkRsayenAkñúgCMBUkTI6¦. enAkñúgGgát;eRKOgbgÁúMxøHEdlmanvtþman axial load
kñúgtMéltictYc EtT§iBld¾sþÜcesþIgenHRtUv)aneKecalenAkñúgkarGnuvtþn_CaeRcIn ehIyeK)ancat;
TukvaCa beam. CaTUeTAFñwmRtUv)aneKdak;kñúgTisedk nigrgnUvbnÞúkbBaÄr EtvamincaM)ac;EtkñúgkrNIEbb
enHeT. Ggát;eRKOgbgÁúMEdlRtUv)aneKcat;TukCa beam RbsinebIvargnUvbnÞúky:agNaEdleFVIeGayva
ekag (bending).
rUbragmuxkat; (cross-sectional shape)EdlRtUv)aneKeRbICaTUeTArYmman W-, S- nig M-
shapes. eBlxøH chanel shape k¾RtUv)aneRbIdUcCaFñwmEdlpSMeLIgBIEdkbnÞH kñúgTMrg; I-, H- b¤ box
shape. Doubly symmetric shape dUcCa standard rolled W-, M- nig S-shape CarUbragEdlman
RbsiT§PaBCaeK.
CaTUeTA rUbragEdl)anBIkarpSMrbs;EdkbnÞHRtUv)aneKKitCa plate girder b:uEnþ AISC
Specification EbgEck beam BI plate girder edayQrelIpleFobTTwgelIkMras; (width-thickness
ratio) rbs;RTnug. rUbTI 5>1 bgðajTaMg hot-rolled shape nig built-up shapeCamYynwgTMhMEdlRtUv
eRbIsMrab; width-thickness ratios. Rbsin
t
h 2555
≤
F
¬xñat IS¦ th ≤ 970 ¬xñat US¦
F
w y w y
Ggát;eRKOgbgÁúMRtUv)aneKcat;TUkCa beam edayminKitfavaCa rolled shape b¤Ca built-up. EpñkenH
RtUv)anerobrab;enAkñúg chapter F of the Specification, “Beams and Other Flexural Members”
ehIyvak¾CaRbFanbTEdlRtUvykmkniyayenAkñúgCMBUkenH. RbsinebI
114 Fñwm
2. T.chhay
h 2555
tw
>
Fy
¬xñat IS¦ h
tw
≤
970
Fy
¬xñat US¦
enaHGgát;eRKOgbgÁúMRtUv)aneKcat;TukCa plate girder nwgRtUv)anerobrab;enAkñúg Chapter G of the
specification, “Plate Girders”. enAkñúgesovePAenHeyIgnwgniyayBI plate girder kñúgCMBUkTI 10.
edaysarEt slenderness rbs;RTnug plate girder RtUvkarBicarNaBiessenABIelI nigBIeRkamEdlcM)ac;
sMrab;Fñwm.
RKb; standard hot-rolled shape EdlGacrk)anenAkñúg Manual KWsßitenAkñúgRbePT beams.
Built-up shape PaKeRcInRtUv)ancat;cMNat;fñak;Ca plate girder b:uEnþ built-up shape xøHRtUv)ancat;
TukCaFñwmedaykarkMNt;rbs; AISC.
sMrab; beams/ TMnak;TMngeKalrvagT§iBlbnÞúk (load effects) nig strength KW
M u ≤ φb M n
Edl Mu = bnSMénm:Um:g;emKuNEdlFMCageK
φb = emKuNersIusþg;sMrab;Fñwm = 0.9
M n = nominal moment strength
Design strength, φb M n enAeBlxøHRtUv)aneKehAfa design moment.
5>2> kugRtaMgBt; nigm:Um:g;)øasÞic Bending Stress and the Plastic Mement
edIm,IGackMNt; nominal design strength M n dMbUgeyIgRtUvBinitüemIlkarRbRBwtþeTA
(behavior) rbs;Fñwmtamry³énkardak;bnÞúkRKb;lkçxNÐ taMgBIbnÞúktUcrhUtdl;bnÞúkEdlGaceFVIeday
Fñwm)ak;. BicarNaFñwmEdlbgðajenAkñúgrUbTI 5>2 a EdlRtUv)andak;edayeFVIy:agNaeGayvaekag
eFobnwgGkS½em ¬GkS½ x − x sMrab; I- nig H-shape¦. sMrab; linear elastic material nigkMhUcRTg;
RTaytUc karBRgaykugRtaMgBt;RtUv)anbgðajenAkñúg rUbTI 5>2 b CamYynwgkugRtaMgEdlRtUv)an
snμt;faBRgayesμItamTTwgrbs;Fñwm. ¬kMlaMgkat;RtUv)anBicarNaedayELkenAkñúgEpñkTI 5>7¦. BI
elementary mechanics of materials/ kugRtaMgRtg;cMNucNamYyGackMNt;)anBI flexural formula³
fb =
My
Ix
¬%>!¦
Edl M CamU:m:g;Bt;enAelImuxkat;EdlBicarNa/ y CacMgayEkgBIbøg;NWt ¬neutral plane) eTAcMnuc
Edlcg;dwg nig I x Cam:Um:g;niclPaBénmuxkat;EdleFobnwgGkS½NWt. sMrab; homogeneous material
115 Fñwm
3. T.chhay
GkS½NWtRtYtsIuKñanwgGkS½TIRbCMuTMgn;. smIkar %>! KWQrenAelIkarsnμt;fa karBRgay strain man
lkçN³CabnÞat;BIelIdl;eRkam Edlmüa:geToteyIgGacsnμt;fa muxkat;Edlrab (plane) munrgkarBt;
enArkSarabdEdleRkaykarBt;. el;IsBIenH muxkat;FñwmRtUvEtmanGkS½sIuemRTIbBaÄr ehIybnÞúkRtUvEt
sßitenAkñúgbøg;EdlmanGkS½sIemRTIenaH. FñwmEdlminbMeBjtamklçxNÐTaMgenHRtUv)anBicarNaenAkñúg
EpñkTI 5>13. kugRtaMgGtibrmanwgekItenAsrésEpñkxageRkAbMput Edl y mantMélGtibrma. dUc
enHvamantMélGtibrmaBIrKW kugRtaMgsgát;GtibrmarnAsrésEpñkxagelIbMput nigkugRtaMgTajGtibrma
enAsrésEpñkxageRkambMput. RbsinebIGkS½NWtCaGkS½sIuemRTI kugRtaMgTaMgBIrenHnwgmantMélesμIKña.
sMrab;kugRtaMgGtibrma smIkar %>! GacsresrkñúgTMrg;
f max =
Mc
Ix
=
M
=
M
Ix / c Sx
¬%>@¦
Edl c CacMNayEdkBIGkS½NWteTAsrésrEpñkxageRkAbMput ehIy S x Cam:UDulmuxkat;eGLasÞicénmux
kat; (elastic section modulus) . sMrab;RKb;rUbragmuxkat; section modulus mantMélefr. sMrab;mux
kat;minsIuemRTI S x nwgmantMélBIr³ mYysMrab;srésEpñkxagelIbMput nigmYyeTotsMrab;srésEpñkxag
eRkambMput. tMélrbs; S x sMrab; standard rolled shape RtUv)andak;kñúg dimension and properties
table enAkñúg Manual.
116 Fñwm
4. T.chhay
smIkar %>! nig %>@ mantMéleTA)ankñúgkrNIbnÞúktUclμmEdlsMPar³enAEtsßitenAkñúg linear
elastic range. sMrab;eRKOgbgÁúMEdk vamann½yfakugRtaMg f max minRtUvFMCag f y ehIymann½yfa
m:Um:g;minRtUvFMCag
M y = Fy S x
Edl M y Cam:Um:g;Bt;EdleFVIeGayFñwmeTAdl;cMnuc yielding.
enAkñúgrUbTI 5>3 FñwmTMrsamBaØCamYynwgbnÞúkcMcMnucenAkNþalElVgRtUv)anbgðajnUvkardak;
bnÞúktamdMNak;kalCabnþbnÞab;. enAeBl yielding cab;epþIm karBRgaykugRtaMgenAelImuxkat;Elg
manlkçN³CabnÞat; ehIy yielding nwgrIkralBIsrésEpñkxageRkAeTAGkS½NWt. kñúgeBlCamYyKña
117 Fñwm
5. T.chhay
tMbn;Edlrg yield nwglatsn§wgtambeNþayFñwmBIGkS½kNþalrbs;FñwmEdlm:Um:g;Bt;mantMélesμInwg
M y enATItaMgCaeRcIn. tMbn;Edlrg yield enHRtUv)angðajedayépÞBN’exμAenAkñúgrUbTI 5>3 c nig d.
enAkñúgrUbTI 5>2 b yielding eTIbnwgcab;epþIm. enAkñúgrUbTI 5>2 c yielding )anrIkralcUleTAkñúgRTnug
ehIyenAkñúgrUbTI 5>2 b muxkat;TaMgmUl)an yield. eKRtUvkarm:Um:g;bEnßmkñúgtMélCamFüm vaesμIRb
Ehl 12% én yield moment edIm,InaMFñwmBIdMNak;kal (b) eTAdMNak;kal (d) sMrab; W-shape .
enAeBleKeTAdl;dMNak;kal (d) RbsinebIenAEtbEnßmbnÞúkeTotFñwmnwg)ak; enAeBlEdlFatuTaMgGs;
rbs;muxkat;)aneTAdl; yield plateau rbs; stress-strain curve ehIy unrestrict plastic flow nwg
ekIteLIg. Plastic hing RtUv)aneLIgRtg;GkS½rbs;Fñwm ehIysnøak;enHCamYnnwgsnøak;BitR)akdenA
xagcugrbs;FñwmbegáIt)anCa unstable machanism . kñúgeBl plastic collapse, mechanism motion
RtUv)anbgðajenAkñúgrUbTI 5>4. Structural analysis EdlQrelIkarBicarNa collapse mechanism
RtUv)aneKehAfa plastic analysis. karENnaMBI plastic analysis nig design RtUv)anerobrab;enAkñúg
Appendix A kñugesovePAenH.
lT§PaBm:Um:g;)aøsÞic EdlCam:Um:g;EdlRtUvkaredIm,IbegáItsnøak;)aøsÞic GacRtUv)anKNnay:ag
gayRsYlBIkarBicarNakarBRgaykugRtaMgRtUvKña. enAkñúgrUbTI 5>5 ers‘ultg;kugRtaMgsgát; nigkug
RtaMgTajRtUv)anbgðaj Edl Ac CaRkLaépÞmuxkat;Edlrgkarsgát; nig At CaRkLaépÞmuxkat;Edl
rgkarTaj. RkLaépÞTaMgenHCaRkLaépÞEdlenABIxagelI nigBIxageRkamGkS½NWt)aøsÞic (plastic
neutral axis) EdlmincaM)ac;dUcKñanwgGkS½NWteGLasÞic. BIsßanPaBlMnwgrbs;kMlaMg eyIg)an
C =T
Ac Fy = At Fy
Ac = At
dUcenHGkS½NWt)aøsÞicEckmuxkat;CaBIcMENkesμIKña. sMrab;rUbragEdlsIemRTIeFobnwgGkS½énkarBt;
GkS½NWteGLasÞic nigGkS½NWt)aøsÞicKWdUcKña. m:Um:g;)aøsÞic M p Ca resisting couple EdlbegáIteLIg
edaykMlaMgBIresμIKña nigmanTisedApÞúyKña b¤
⎛ A⎞
M p = Fy ( Ac )a = Fy ( At )a = Fy ⎜ ⎟a = Fy Z
⎝2⎠
118 Fñwm
6. T.chhay
Edl A= RkLaépÞmuxkat;srub
a = cMgayrvagGkS½NWtrbs;RkLaépÞBak;kNþalTaMgBIr
⎛ A⎞
Z = ⎜ ⎟a = m:UDulmuxkat;)aøsÞic (plastic section modulus)
⎝2⎠
]TahrN_ 5>1³ CamYynwg built-up shape EdlbgðajenAkñúgrUbTI 5>6 cUrkMNt; ¬k¦ elastic section
modulus S nig yielding moment M y nig ¬x¦ plastic section modulus Z nig plastic moment
M p . karekageFobnwgGkS½ x ehIyEdkEdleRbIKW A572 Grade 50 .
dMeNaHRsay³
¬k¦ edaysarvamanlkçN³sIuemRTI enaH elastic neutral axis ¬GkS½ x ¦ sßitenABak;kNþalmuxkat;
¬TItaMgrbs;TIRbCMuTMgn;¦. m:Um:g;niclPaBrbs;muxkat;GacRtUvkMNt;)anedayeRbIRTwsþIbTGkS½
Rsb (parallel axis theorem) ehIylT§plénkarKNnaRtUv)ansegçbenAkñúgtarag 5>1.
tarag 5>1
Component I A d I + Ad 2
Flange 260417 5000 162.5 132291667
Flange 260417 5000 162.5 132291667
Web 28125000 - - 28125000
Sum 292.71×106
119 Fñwm
7. T.chhay
Elastic section modulus KW
I 292.71 ⋅10 6 292.71 ⋅10 6
S= = = = 1.67 ⋅10 6 mm 3
c 25 + (300 / 2 ) 175
Yield moment KW
M y = Fy S = 345 × 1.67 = 576.15kN .m
cMeLIy³ S = 1.67 ⋅106 mm3 nig M y = 576.15kN .m
¬x¦ edaysarrUbragenHmanlkçN³sIuemRTIeFobnwgGkS½ x / enaHGkS½enHEckmuxkat;CaBIrcMEnkesμIKña
ehIyGkS½enHk¾Ca plastic neutral axis Edr. TIRbCMuTMgn;rbs;épÞBak;kNþalxagelIRtUv)an
kMNt;edayeRbI principle of moment. Kitm:Um:;g;eFobGkS½NWténmuxkat;TaMgmUl ¬rUbTI 5>6¦
ehIykarKNnaRtUv)anerobCatarag 5>2.
tarag 5>2
Component A y Ay
Flange 5000 162.5 812500
Web 1875 75 140625
Sum 6875 953125
y=∑
Ay 953125
= = 138.64mm
∑A 6875
rUbTI 5>7 bgðajfaédXñas;m:Um:g;rbs;m:Umg;KUrEdlekItmanenAxagkñúgKW
:
a = 2 y = 2(138.64) = 277.28mm
ehIy plastic section modulus KW
⎛ A⎞
Z = ⎜ ⎟a = 6875 × 277.28 = 1.906 ⋅10 6 mm 3
⎝2⎠
Plastic moment KW
M p = Fy Z = 345 × 1.906 = 657.6kN .m
120 Fñwm
8. T.chhay
cMeLIy³ Z = 1.906 ⋅106 mm3 nig M p = 657.6kN .m
]TahrN_ 5>2³ KNna plastic moment, M p sMrab; W 10 × 60 rbs;Edk A36 .
dMeNaHRsay³ BI dimensions and properties tables enAkñúg Part1 of the Manual
A = 17.6in 2
A 17.6
= = 8.8in
2 2
TIRbCMuTMgn;sMrab;RkLaépÞBak;kNþalGacrk)anBIkñúgtaragsMrab; WT-shapes EdlRtUv)ankat;
ecjBI W-shapes. rUbragEdlRtUvKñarbs;vaKW WT 5× 30 ehIycMgayBIépÞxageRkAbMputrbs;søab
eTATIRbCMuTMgn;KW 0.884in dUcbgðajenAkñúgrUbTI 5>8.
a = d − 2(0.884 ) = 10.22 − 2(0.884 ) = 8.452in
⎛ A⎞
Z = ⎜ ⎟a = 8.8(8.452) = 74.38in 3
⎝2⎠
lT§plEdlTTYl)anenHmantMélRbhak;RbEhlnwgtMélEdleGayenAkñúg dimensions and
properties tables ¬PaBxusKñabNþalmkBIkarKitcMnYnxÞg;eRkayex,ós¦
cMeLIy³ M p = Fy Z = 36(74.38) = 2678in. − kips = 223 ft − kips
5>3> lMnwg Stability
RbsinebIFñwmGacrkSalMnwgrbs;va)anrhUtdl;vasßitkñúglkçxNÐ)aøsÞiceBjelj enaH nominal
moment strength RtUv)aneKKitfamantMélesμInwg plastic moment capacity Edl
Mn = M p
pÞúymkvij M n < M p .
121 Fñwm
14. T.chhay
eTaHbICakarRtYtBinitüsMrab; M p ≤ 1.5M y RtUv)aneFVIenAkñúg]TahrN_xagelI b:uEnþvamincaM)ac;
sMrab; I- nig H-shape ekageFobGkS½xøaMg ehIyvaminRtUv)aneFVIdEdl²enAkñúgesobePAenHeT.
rbs; compact shape CaGnuKmn_nwg unbraced length, Lb EdlRtUv)ankM
Strength moment
Nt;CacMgayrvagcMnucénTMrxag b¤karBRgwg. enAkñúgesovePAenH bgðajcMnucénTMrxageday “X” dUc
bgðajenAkñúgrUbTI 5>12. TMnak;TMngrvag nominal strength M n nig unbraced length RtUv)an
bgðajenAkñúgrUbTI 5>13 . RbsinebI unbraced length minFMCag L p FñwmRtUv)anBicarNamanTMr
xageBj ehIy M n = M p . RbsinebI Lb FMCag L p b:uEnþtUcCag b¤esμI)a:ra:Em:Rt Lr enaHersIusþg;nwg
QrelI inelastic LTB . RbsinebI Lb FMCag Lr enaHersIusþg;nwgQrelI elastic LTB .
eKGacrksmIkarsMrab; enAkñúg
theorical elastic lateral-torsional buckling strength
Theory of Elastic Stability (Timoshenko and Gere, 1961) nigCamYykarpøas;bþÚrnimitþsBaØaxøH
smIkarenHmanragdUcxageRkam³
127 Fñwm
15. T.chhay
2
π ⎛ πE ⎞
Mn = EI y GJ + ⎜ ⎟ I y C w
⎜L ⎟ ¬%>#¦
Lb ⎝ b⎠
Edl Lb = unbraced length
G = shear modulus = 77225MPa b¤ = 11200ksi sMrab;eRKOgbgÁúMEdk
J = torsional constant
C w = warping constant ( mm 6 )
RbsinebIm:Um:g;enAeBlEdl lateral-torsional buckling ekIteLIgFMCagm:Um:g;EdlRtUvKñanwg first yield
enaH strength QrenAelI inelastic behavior. m:Um:g;EdlRtUvKñanwg first yield KW
M r = FL S x (AISC Equation F1-7)
Edl FL CatMélEdltUcCageKkñúgcMeNam ( Fyf − Fr ) nig Fyw . enAkñúgsmIkarenH yield stress enA
kñúgsøabRtUv)ankat;bnßyeday Fr kugRtaMgEdlenAsl; (residual stress) . sMrab; nonhybrid
member, F yf = Fym = Fy ehIy FL EtgEtesμInwg F y − Fr . teTAmuxeTotenAkñúgCMBUkenH eyIg
CMnYs FL eday Fy − Fr . Ca]TahrN_ eyIgsresr AISC Equation E1-7 Ca
(
M r = Fy − Fr S x ) (AISC Equation F1-7)
EdlkugRtaMgEdlenAsl; Fr = 10ksi = 69MPa sMrab; rolled-shapes nig Fr = 16.5ksi = 114MPa
sMrab; welded built-up shapes. dUcbgðajenAkñúgrUbTI 5>13 RBMEdnrvag elastic behavior nig
inelastic behavior KW unbraced length Lr EdltMélrbs; Lr RtUv)anTTYlBIsmIkar %># enAeBl
Edl M n RtUv)andak;eGayesμI M r . eKTTYl)ansmIkarxageRkam³
Lr =
ry X 1
(Fy − Fr ) ( )
1 + 1 + X 2 Fy − Fr 2 (AISC Equation F1-6)
Edl
π EGJA
X1 =
Sx 2
2
(AISC Equation F1-8 and F1-9)
4C w ⎛ S x ⎞
X2 = ⎜ ⎟
I y ⎝ GJ ⎠
dUckrNIssrEdr inelastic behavior rbs;FñwmmanlkçN³sμúKsμajCag elastic behavior
CaTUeTAeKeRcIneRbIrUbmnþEdl)anmkBIkarBiesaFn_ (empirical formulas). CamYynwgkarEktMrUvd¾tic
tYc AISC )aneGayeRbIsmIkarxageRkam³
128 Fñwm
16. T.chhay
⎛ Lb − L p ⎞
(
Mn = M p − M p − Mr ⎜ ) ⎟
⎜ Lr − L p ⎟
¬%>$¦
⎝ ⎠
790ry 300ry
Edl Lp =
Fy
¬xñat ¦
IS Lp =
Fy
¬xñat US¦ (AISC Equation F1-4)
Nominal bending strength rbs; compact beam RtUv)anbgðajedaysmIkar %># nig %>$ rgnUv
upper limit M p sMrab; inelastic beam RbsinebIm:Um;g;EdlGnuvtþBRgayesμIelI unbraced length Lb .
RbsinebIdUcenaHeT vaman moment gradient ehIysmIkar %># nig %>$ RtUv)anEksMrYledayemKuN
Cb . emKuNenHRtUv)aneGayeday AISC F1.2 kñúgTMrg;
12.5M max
Cb = (AISC Equation F1-3)
2.5M max + 3M A + 4 M B + 3M C
Edl M max = tMéldac;xatrbs;m:Um:g;GtibrmaenAkñúg unbraced length (including the end points)
M A = tMéldac;xatrbs;m:Um:g;enAcMnucmYyPaKbYnén unbraced length
M B = tMéldac;xatrbs;m:Um:g;enAcMnucBak;kNþalén unbraced length
M C = tMéldac;xatrbs;m:Um:g;enAcMnucbIPaKbYnén unbraced length
enAeBlm:Um:g;Bt;BRgayesμI tMél Cb esμInwg
12.5M
Cb = = 1.0
2.5M + 3M + 4M + 3M
]TahrN_ 5>4³ kMNt; Cb sMrab;FñwmTMrsamBaØRTbnÞúkBRgayesμICamYyEtnwgkarTb;xagenAxagcug
b:ueNÑaH.
129 Fñwm
17. T.chhay
dMeNaHRsay³ edaysarlkçN³suIemRTI m:Um:g;GtibrmasßitenAkNþalElVg dUcenH
1
M max = M B = wL2
8
dUcKña edaysarlkçN³sIuemRTI m:Um:g;enAcMnucmYyPaKbIesμIm:Um:g;enAcMnucbIPaKbYn. BIrUbTI 5>14
wL ⎛ L ⎞ wL ⎛ L ⎞ wL 2 wL2 3
M A = MC = ⎜ ⎟− ⎜ ⎟= − = wL2
2 ⎝4⎠ 4 ⎝8⎠ 8 32 32
12.5M max 12.5(1 / 8)
Cb = = = 1.14
2.5M max + 3M A + 4 M B + 3M C 2.5(1 / 8) + 3(3 / 32) + 4(1 / 8) + 3(3 / 32)
cMeLIy³ Cb = 1.14
rUbTI 5>15 bgðajBItMélrbs; Cb sMrab;krNIFmμtaCaeRcInénkardak;bnÞúk nigTMrxag.
sMrab; unbraced cantilever beams, AISC kMNt;tMél Cb = 1.0 . tMél 1.0 CatMéltUc
¬edayminKitBIrrUbragrbs;Fñwm nigkardak;bnÞúk¦ b:uEnþkñúgkrNIxøHvaCatMélEdltUcEmnETn. karkMNt;
TaMgGs;én nominal moment strength sMrab; compact shapes GacRtUv)ansegçbdUcxageRkam³
130 Fñwm
18. T.chhay
sMrab; Lb ≤ L p /
M n = M p ≤ 1.5 M y (AISC Equation F1-1)
sMrab; L p < Lb ≤ Lr /
⎡ ⎛ −L ⎞⎤
(
M n = Cb ⎢ M p − M p − M r )⎜ Lb − L p ⎟⎥ ≤ M p
⎜L ⎟
(AISC Equation F1-2)
⎢
⎣ ⎝ r p ⎠⎥
⎦
sMrab; L p > Lr /
M n = M cr ≤ M p (AISC Equation F1-12)
2
π ⎛ πE ⎞
Edl M cr = Cb EI y GJ + ⎜
⎜ L ⎟ I y Cw
⎟ (AISC Equation F1-13)
Lb ⎝ b⎠
2
C S X 2 X1 X 2
= b x 1 1+
Lb / ry (
2 Lb / ry 2 )
tMélefr X1 nig X 2 RtUv)ankMNt;BImun ehIyRtUv)anrayCataragenAkñúg dimensions and
properties tables in the Manual.
T§iBlrbs; Cb eTAelI nominal strength RtUv)anbgðajenAkñúgrUbTI5>16. eTaHbICa strength
smamaRtedaypÞal;eTAnwg Cb k¾eday EtRkaPicenH)anbgðajy:agc,as;BIsar³sMxan;rbs; upper
limit M p edayminKitBIsar³sMxan;rbs;smIkarEdlRtUveRbIsMrab; M n .
]TahrN_ 5>4³ kMNt; design strength φb M n sMrab; W 14 × 68 rbs;Edk A242 Edl³
k> TMrxagCab;
x> unbraced length = 20 ft / Cb = 1.0
131 Fñwm
19. T.chhay
K> unbraced length = 20 ft / Cb = 1.75
dMeNaHRsay³
k> BI Part 1 of the Manual /W14 × 68 KWsßitenAkñúg shape group 2 /dUcenHvaGacman yield stress
F y = 50ksi / kMNt;faetIrUbragenHCa compact, noncompact b¤ slender.
bf 65
= 7.0 <
2t f 50
rUbragenHKW compact dUcenH
M n = M p = Fy Z x = 50(115) = 5750in. − kips = 479.2 ft − kips
cMeLIy³ φb M n = 0.9(479.2) = 431 ft − kips
x> Lb = 20 ft nig Cb = 1.0 . KNna L p nig Lr ³
300ry 300 × 2.46
Lp = = = 104.4in. = 8.7 ft
Fy 50
BI torsion properties tables in Part 1 of the Manual,
J = 3.02in 4 nig C w = 5380in 6
eTaHbICa X1 nig X 2 RtUv)anerobCataragenAkñúg dimensions and properties table in part 1 of
the Manual eyIgnwgKNnavaenATIenHsMrab;bgðaj
π EGJA π 29000(11200)(3.02)(20)
X1 = = = 3021ksi
Sx 2 103 2
2 2
C ⎛S ⎞ ⎛ 5380 ⎞⎛ 103 ⎞ −2
X 2 = 4 w ⎜ x ⎟ = 4⎜ ⎟⎜ ⎟ = 0.001649ksi
I y ⎝ GJ ⎠ ⎝ 121 ⎠⎝ 11200 × 3.02 ⎠
ry X 1
Lr = 1 + 1 + X 2 ( Fy − Fr ) 2
( Fy − Fr )
2.46(3021)
= 1 + 1 + 0.001649(50 − 10 )2 = 316.8in = 26.40 ft
(50 − 10)
edaysar L p < Lb < Lr strength QrelI inelastic LTB nig
(
M r = Fy − Fr S x = ) (50 − 10)(103) = 343.3 ft − kips
12
⎡ ⎛ Lb − L p ⎞⎤
M n = Cb ⎢ M p − M p − M r ⎜ ( ⎟⎥
⎜ Lr − L p ⎟⎥
)
⎢
⎣ ⎝ ⎠⎦
⎡ ⎛ 20 − 8.7 ⎞⎤
= 1.0⎢479.2 − (479.2 − 343.3)⎜ ⎟⎥
⎣ ⎝ 26.4 − 8.7 ⎠⎦
132 Fñwm
20. T.chhay
cMeLIy³ φb M n = 0.90(392.4) = 353 ft − kips
K> Lb = 20 ft nig Cb = 1.75 . Design strength sMrab; Cb = 1.75 KWesμInwg 1.75 dgén Design
strength sMrab; Cb = 1.0 . dUcenH
M n = 1.75(392.4) = 686.7 ft − kips > M p = 479.2 ft − kips
Nominal strength minGacFMCag M p / dUcenHeRbI nominal strength M n = 479.2 ft − kips
cMeLIy³ φb M n = 0.90(479.2) = 431 ft − kips
Part 4 of the Manual of Steel Construction, “Beam and Girder Design,” mantaragmanRbeyaCn_
CaeRcInsMrab;viPaK nigKNnaFñwm. Ca]TahrN_ Load Factor Design Selection Table raynUvrUbrag
EdleRbICaTUeTAsMrab;Fñwm EdlRtUv)anerobCalMdab;én Z x . edaysar M p = Fy Z x rUbragk¾RtUv)an
erobCalMdab;én design moment φb M p . tMélefrdéTeTotEdlmanRbeyaCn_k¾RtUv)anerobCatarag
EdlrYmman L p nig Lr ¬EdlCaEpñkmYyEdlKYreGayFujRTan;kñúgkarKNna¦.
Plastic Analysis
enAkñúgkrNICaeRcIn m:Um:g;emKuNGtibrma M u nwgRtUv)anTTYlBI elastic structural analysis
edayeRbIbnÞúkemKuN. eRkamlkçxNÐc,as;las; ersIusþg;EdlcaM)ac; (required strength) sMrab;rcna
sm<n§½EdlminGackMNt;edaysþaTic (statically inderteminate structure) RtUv)anrkedayeRbI plastic
analysis. AISC GnuBaØateGayeRbI plastic analysis RbsinebIrUbrag compact nigRbsinebI
Lb ≤ L pd
24800 + 15200(M 1 / M 2 )
Edl L pd =
Fy
ry ¬xñat SI ¦ (AISC Equation F1-17)
m:Um:g;EdltUcCageKkñúgcMeNamm:Um:g;cugTaMgBIrsMrab; unbraced segment
M1 =
M 2 = m:Um:g;EdlFMCageKkñúgcMeNamm:Um:g;cugTaMgBIrsMrab; unbraced segment
pleFob M1 / M 2 viC¢manenAeBlEdlm:Um:g;begáIt reverse curvature enAkñúg unbraced
segment. enAeBlenH Lb Ca unbraced length EdlenACab;nwgsnøak;)aøsÞicEdlCaEpñkmYyén failure
mechanism. b:uEnþRbsinebIeKeRbI plastic analysis, nominal moment strength M n EdlenACab;nwg
133 Fñwm
21. T.chhay
snøak;cugeRkayEdlminenAEk,rsnøak;)aøsÞicRtUv)anKNnatamviFIdUcKñasMrab;FñwmEdlviPaKedayviFIeG
LasÞic ehIyvaRtUvEttUcCag M p .
5>6> Bending Strength of Noncompact Shapes
dUckarkt;cMNaMBImun standard W-, M-, nig S-shapes PaKeRcInCa compact sMrab;
F y = 250 MPa nig F y = 350MPa . cMnYntictYcb:ueNÑaHCa noncompact edaysar width-
thickness ratio rbs;søab b:uEnþKμanrUbragmYyNaCa slender eT. edaysarmUlehtuTaMgenH AISC
Specification edaHRsay noncompact nig slender flexural member enAkñúg]bsm<n§½ (Appendix
F). enAkñúgesovePAenH eyIgnwgBicarNa slender flexural member enAkñúgCMBUkTI10.
CaTUeTA FñwmGac)ak;eday lateral-torsional buckling, flange local buckling b¤ web local
buckling. RKb;RbePTénkar)ak;GacsßitenAkñúgEdneGLasÞic b¤ inelastic range. RTnugrbs;RKb;
rolled shapes enAkñúg Manual Ca compact dUcenH noncompact shapes CaRbFanbTsMrab;Etsßan
PaBkMNt; (limit states) én lateral-torsional buckling nig flange local buckling. ersIusþg;EdlRtUv
nwgsßanPaBkMNt;TaMgBIrRtUv)anKNna ehIyeKyktMélEdltUcCageK. BI AISC Appendix F CamYy
bf
λ=
2t f
RbsinebI λ p < λ ≤ λr / enaHsøabCa noncompact ehIy buckling Ca inelastic eyIgnwgTTYl)an
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜ )⎟
⎜ λr − λ p ⎟
(AISC Equation A-F1-3)
⎝ ⎠
Edl λp =
170
Fy
IS ¬sMrab; ¦
λp =
65
Fy
¬sMrab; US ¦
λr =
370
F y − Fr
¬sMrab; IS ¦ λr =
141
F y − Fr
¬sMrab; US ¦
(
M r = F y − Fr S x )
kugRtaMgEdlenAesssl; = 69MPa = 10ksi sMrab; rolled shapes
Fr =
¬GgÁenHRtUv)ankMNt;sMrab; nonhybrid beam¦
134 Fñwm
25. T.chhay
!> kMNt;faetIrUbrag compact b¤Gt;
@> RbsinebIrUbrag compact, RtYtBinitüsMrab; lateral-torsional buckling dUcxageRkam³
RbsinebI Lb ≤ L p vaminEmn LTB ehIy M n = M p
RbsinebI L p < Lb ≤ Lr / vaman inelastic LTB ehIy
⎡ ⎛ −L ⎞⎤
(
M n = Cb ⎢ M p M p − M r )⎜ Lb − L p ⎟⎥ ≤ M p
⎜L ⎟
⎢
⎣ ⎝ r p ⎠⎥
⎦
RbsinebI Lb > br / vaman elastic LTB ehIy
2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜ ⎟ I y C w ≤ M p
⎜L ⎟
Lb ⎝ b⎠
#> RbsinebIrUbrag noncompact edaysarsøab/ RTnug b¤TaMgBIr enaH nominal strength nwgCa
tMéltUcCageKénersIusþg;EdlRtUvKñanwg flange local buckling, web local buckling nig
lateral-torsional buckling.
k> Flange local buckling³
RbsinebI λ ≤ λ p vaminman FLB.
RbsinebI λ p < λ ≤ λr søabCa noncompact, ehIy
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜
⎜ λr − λ p
) ⎟≤Mp
⎟
⎝ ⎠
x> Web local buckling³
RbsinebI λ ≤ λ p vaminman WLB.
RbsinebI λ p < λ ≤ λr RTnugCa noncompact, ehIy
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜
⎜ λr − λ p
) ⎟≤Mp
⎟
⎝ ⎠
K> Lateral-torsional buckling³
RbsinebI Lb ≤ L p vaminman LTB.
RbsinebI L p < Lb ≤ Lr / vaman inelastic LTB ehIy
⎡ ⎛ −L ⎞⎤
(
M n = Cb ⎢ M p M p − M r )⎜ Lb − L p ⎟⎥ ≤ M p
⎜L ⎟
⎢
⎣ ⎝ r p ⎠⎥
⎦
RbsinebI Lb > br / vaman elastic LTB ehIy
138 Fñwm
26. T.chhay
2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜ ⎟ I y C w ≤ M p
⎜L ⎟
Lb ⎝ b⎠
5>8> ersIusþg;kMlaMgkat;TTwg Shear Strength
ersIusþg;kMlaMgkat;rbs;FñwmRtUvEtRKb;RKan;edIm,IbMeBjTMnak;TMng
Vu ≤ φvVn
Edl Vu = kMlaMgkat;TTwgGtibrmaEdll)anBIkarbnSMbnÞúkemKuNFMCageK
φv = emKuNersIusþg;sMrab;kMlaMgkat;TTwg = 0.9
Vn = nominal shear strength/
BicarNaFñwmsamBaØenAkñúgrUbTI 5>17. enAcMgay x BITMrxageqVgnigsßitenAelIGkS½NWtrbs;
muxkat; sßanPaBrbs;kugRtaMgRtUv)anbgðajenAkñúgrUbTI 5>17 d . edaysarFatuenHsßitenAelIGkS½
NWt vaminrgnUvkugRtaMgBt;eT. BI elementary mechanics of materials/ kugRtaMgkMlaMgkat;TTwg
(shearing stess) KW
fv =
VQ
Ib
¬%>^¦
139 Fñwm
27. T.chhay
Edl fv =kugRtaMgkMlaMgkat;TTwgbBaÄr nigedkenARtg;cMnucEdleyIgBicarNa
V = kMlaMgkat;TTwgbBaÄrenARtg;muxkat;EdlBicarNa
Q = m:Um:g;RkLaépÞTImYyeFobGkS½NWt rvagcMnucEdlBicarNanwgEpñkxagelIb¤EpñkxageRkam
rbs;muxkat;
I = m:Um:g;niclPaBeFobnwgGkS½NWt
b = TTwgrbs;muxkat;enAcMnucEdlBicarNa
smIkar %>^ KWQrelIkarsnμt;fakugRtaMgmantMélefreBjelITTwg b dUcenHvapþl;tMélsuRkit
sMrab;Et b mantMéltUc. sMrab;muxkat;ctuekaNEkgEdlmankMBs; d nigTTwg b tMéllMeGogsMrab;
d / b = 2 KWRbEhl 3% . sMrab; d / b = 1 tMéllMeGogKW 12% nigsMrab; d / b = 1 / 4 tMéllMeGogKW
100% (Higdon, Ohlsen, and Stiles, 1960). sMrab;mUlehtuenH smIkar %>^ minGacGnuvtþ)ansMrab;
søabrbs; W-shape dUcKñasMrab;RTnugrbs;va.
rUbTI 5>18 bgðajBIkarBRgaykugRtaMgkMlaMgkat;sMrab; W-shape. ExSdac;CakugRtaMgmFüm
V / Aw EdlBRgayenAkñúgRTnug ehIytMélenHminxusKñaBIkugRtaMgGtibrmaenAkñúgRTnugeRcIneT. eyIg
eXIjc,as;ehIyfa RTnugnwg yield y:agyUrmunnwgsøabc,ab;epþIm yield. edaysarbBaðaenH yielding
rbs;RTnugsMEdgnUvsßanPaBlImItkMNt;mYy. edayyk shear yield stress esμInwg 60% én tensile
yield stress eyIgGacsresrsmIkarsMrab;kugRtaMgenAkñúgRTnugenAeBl)ak;Ca
V
f v = n = 0.60 F y
Aw
Edl Aw = RkLaépÞmuxkat;rbs;RTnug. dUcenH nominal strength EdlRtUvKñanwgsßanPaBkMNt;enHKW
Vn = 0.6 F y Aw
140 Fñwm
28. T.chhay
ehIyvaGacCa nominal strength in shear RbsinebIRTnugminman shear buckling. RbsinebIvaekIt
eLIgvanwgGaRs½ynwgpleFob width-thickness ratio h / t w rbs;RTnug. pleFob h / t w rbs;RTnug
EdlRsavxøaMgmantMélFMNas; enaHRTnugGacnwg buckle in shear eday inelastic b¤ elastic. TMnak;TM
ngrvag shear strength nig width-thickness ration manlkçN³RsedogKñanwgTMnak;TMngrvag flexural
strength nig width-thickness ratio ¬sMrab; FLB b¤ WLB¦ nigrvag flexural strength nig unbraced
length ¬sMrab; LTB¦. TMnak;TMngRtUvbgðajenAkñúgrUbTI 5>19 nigRtUv)aneGayenAkñúg AISC F2.2 dUc
xageRkam³
sMrab; h / t w < 418 / Fy ¬sMrab; US¦/ h / t w < 1100 / Fy ¬sMrab; IS¦ RTnugmanesßrPaB
Vn = 0.6 F y Aw (AISC Equation F2-1)
sMrab; 418 / Fy < h / t w ≤ 523 / Fy ¬sMrab; US¦/ 1100 / Fy ≤ h / t w < 1375 / Fy
¬sMrab; IS¦ enaH inelastic web buckling GacnwgekIteLIg
418 / Fy
Vn = 0.6 Fy Aw
h/t
¬sMrab; US¦ Vn = 0.6Fy Aw 1100//t Fy ¬sMrab; IS¦
h
w w
(AISC Equation F2-1)
sMrab; 523 / Fy < h / t w ≤ 260 ¬sMrab; US¦/ 1375 / Fy ≤ h / t w < 260 ¬sMrab; IS¦ enaH
sßanPaBkMNt;KW elastic web buckling
Vn =
132000 Aw
¬sMrab; US¦ Vn = 910 Aw2 ¬sMrab; IS¦ (AISC Equation F2-1)
(h / t w )
2
(h / t w )
Edl Aw = RkLaépÞmuxkat;rbs;RTnug = dt w KitCa ¬ mm 2 ¦
d = kMBs;srubrbs;Fñwm
Vn = nominal strength ¬KitCa KN ¦
RbsinebI h / t w > 260 enaHeKRtUvkar web stiffener ehIyvaRtUv)anbriyayenAkñúg
Appendix F2 ¬b¤ Appendix G sMrab; plate girder ¦.
AISC Equation F2-3 KWQrelI elastic stability theory, ehIy Equation F2-2 CasmIkar
Edl)anBIkarBiesaFn_sMrab;tMbn; inelastic Edlpþl;nUvkarpøas;bþÚrrvagsßanPaBkMNt; web yielding
nig elastic web buckling.
kMlaMgkat;CabBaðaEdlkMrekItmansMrab; rolled steel beams karGnuvtþn_TUeTAKWbnÞab;BIKNna
FñwmsMrab; flexural ehIyeyIgnwgRtYtBinitümuxkat;EdlTTYl)ansMrab;kMlaMgkat;TTwg.
141 Fñwm
29. T.chhay
]TahrN_ 5>7³ RtYtBinitüFñwmenAkñúg]TahrN_ 5>6 sMrab;kMlaMgkat;TTwg.
dMeNaHRsay³ BI]TahrN_ 5>6/ wu = 2.080kips / ft nig L = 40 ft . Edk W 14 × 90 CamYynwg
F y = 50ksi RtUv)aneRbI. sMrab;FñwmTmrsamBaØRTbnÞúkBRgayesμI kMlaMgkat;GtibrmaekItmanenA
elITMr ehIyesμInwgkMlaMgRbtikmμ
w L 2.080(40)
Vu = u = = 41.6kips
2 2
BI dimensions and properties tables in Part 1 of the Manual, web width-thickness ratio rbs;
W 14 × 90 KW
h
= 25.9
tw
418 418
= = 59.11
Fy 50
edaysar h / t w < 418 / Fy enaHersIusþg;RtUv)anRKb;RKgeday shear yielding rbs;RTnug
Vn = 0.6 Fy Aw = 0.6 Fy (dt w ) = 0.6(50 )(14.02 )(0.44 ) = 185.1kips
φvVn = 0.90(185.1) = 167kips > 41.6kips (OK)
cMeLIy³ Shear design strength FMCagkMlaMgkat;emKuN dUcenHFñwmmanlkçN³RKb;RKan;.
tMél φvVn EdlRtUv)anerobCataragenAkñúg factored uniform load table enAkñúg part 4 of
the Manual dUcnHkarKNnarbs;vaminmanRbeyaCn_sMrab; standard hot-rolled shapes.
,
142 Fñwm
30. T.chhay
Block Shear
Block shear Edl)anBicarNasMrab;tMNenAkñúgGgát;rgkarTaj k¾GacekItmanenAkñúgRbePTxøH
rbs;tMNenAkñúgFñwmEdr. edIm,IsMrYlkñúgkartP¢ab;BIFñwmmYyeTAFñwmmYyeTot edayeGaynIv:UsøabxagelI
esμIKña enaHRbEvgd¾xøIrbs;søabxagelIrbs;FñwmmYyRtUvEtkat;ecj b¤ coped. RbsinebI coped beam
RtUv)antP¢ab;edayb‘ULúgdUckñúgrUbTI 5>20 kMNt; ABC cg;rEhkecj. bnÞúkEdlGnuvtþenAkñúgkrNI
enHnwgCaRbtikmμbBaÄrrbs;Fñwm dUcenHkMlaMgkat;nwgekItenAtamExS AB ehIynwgekItmankMlaMgTaj
tam BC . dUcenH block shear strength nwgCatMélEdlkMNt;rbs;Rbtikmμ.
eyIg)anerobrab;BIkarKNna block shear strength enAkñúgCMBUkTI3rYcehIy b:uEnþeyIgnwgrMlwk
vaeLIgvijenATIenH. kar)ak;GacekIteLIgedaybnSMén shear yielding nig tendion fracture b¤eday
shear fracture nig tension yielding. AISC J4.3, “Block Shear Rupture Strength,” eGaysmIkar
BIrsMrab; block shear design strength³
[
φRn = φ 0.6 Fy Agv + Fu Ant ] (AISC Equation J4.3a)
φRn = φ [0.6 Fu Anv + F y Agt ] (AISC Equation J4.3b)
Edl φ = 0.75
Agv = gross area rgkMlaMgkat; ¬enAkñúgrUbTI 5>20 RbEvg AB KuNnwgkMras;RTnug¦
Anv = net area rgkMlaMgkat;
Agt = gross area rgkMlaMgTaj ¬enAkñúgrUbTI 5>20 RbEvg BC KuNnwgkMras;RTnug¦
Ant = net area rgkMlaMgTaj
smIkarEdlmanlT§plFMCagKWCasmIkarEdlmantY fracture FMCag.
]TahrN_ 5>8³ kMNt;RbtikmμemKuNGtibrma EdlQrelI block shearEdlGacRTFñwmdUcbgðajkñúg
rUbTI 5>21.
143 Fñwm
34. T.chhay
@> eRCIserIsrUbragEdlbMeBjnUvtMrUvkarersIusþg;enH. eKGacGnuvtþtamviFImYykñúgcMeNamviFIBIr
xageRkam³
k> eRkayeBlsnμt;rUbragEdk KNna design strength rYcehIyeRbobeFobvaCamYy
nwgm:Um:g;emKuN. epÞogpÞat;eLIgvijRbsinebIcaM)ac;. eKGaceRCIserIsrUbragsnμt;
y:aggayRsYlEtenAkñúgsßanPaBkMNt;mYycMnYn ¬]TahrN_ 5>10¦.
x> eRbI beam design charts in Part 4 of the Manual. eKcUlcitþviFIenH ehIyva
RtUv)anBnül;enAkñúg]TahrN_ 5>10 xageRkam.
#> RtYtBinitü shear strength.
$> RtYtBinitüPaBdab.
]TahrN_ 5>10³ eRCIserIs standardhot-rolled shape of A36 sMrab;FñwmEdlbgðajenAkñúg rUbTI
5>24. FñwmenHmanTMrxagCab; ehIyRtUv)anRT uniform service live load 5kips / ft . PaBdab
GtibrmaGnuBaØatsMrab;bnÞúkGefrKW L / 360 .
dMeNaHRsay³ snμt;TMgn;FñwmesμI 100lb / ft .
wu = 1.2 wD + 1.6 wL = 1.2(0.10) + 1.6(5.00) = 8.120kips / ft
1 8.12(30 )2
M u = wu L2 = = 913.5 ft − kips = requiredφb M n
8 8
snμt;farUbrag compact. sMrab;rUbrag compact ehIymanTMrxagCab;
M n = M p = Z x Fy
BI φb M n ≥ M u /
φb F y Z x ≥ M u
Mu 913.5(12)
Zx ≥ = = 338.3in.3
φb Fy 0.90(36)
CaFmμta Load Factor Design Selection Table erob rolled shapes EdlRtUv)aneRbICaFñwmedaytM
él plastic section modulus fycuH. elIsBIenH RtUv)andak;CaRkumedayrUbragenAxagelIeKenAkñúg
147 Fñwm
35. T.chhay
Rkum ¬GkSrRkas;¦ rUbragEdlRsalCageKEdlman section modulus RKb;RKan;edIm,IbMeBj section
modulus EdlfycuHenAkñúgRkum. kñúg]TahrN_enH rUbragEdlmantMélEk,rnwg section modulus
requirement KW W 27 × 114 CamYynwg Z x = 343in.3 b:uEnþrUbragEdlRsalCageKKW W 30 × 108 Ca
mYynwg Z x = 343in.3 . edaysar section modulusminsmamaRtedaypÞal;nwgRkLaépÞ karEdlman
section modulus FMCamYynwgRkLaépÞtUc dUcenHTMgn;k¾GacRsaleTAtamRkLaépÞ.
sakl,g W 30 ×108 . rUbrag compact dUcEdl)ansnμt; ¬noncompact shapesRtUv)ankM
Nt;cMNaMenAkñúgtarag¦ dUcenH M n = M p dUcEdl)ansnμt;.
TMgn;rbs;vaF¶n;Cagkarsnμt;bnþic dUcenHeKRtUvKNna required strength eLIgvij eTaHbICa
W 30 × 108 manlT§PaBRTRTg;FMCaglT§PaBRTRTg;tMrUvkaredayrUbragsnμt;k¾eday EtvaPaKeRcInEtg
EtmanlT§PaBRTRTg;FMCaglT§PaBRTRTg;tMrUvkaredayrUbragsnμt;.
wu = 1.2(1.08) + 1.6(5.00) = 8.130kips / ft
8.130(30 )2
Mu = = 914.6 ft − kips
8
BI Load Factor Design Selection Table,
φb M p = φb M n = 934 ft − kips > 914.6 ft − kips (OK)
CMnYseGaykareRCIserIsrUbragEdlQrelI required section modulus, eKGaceRbI design strength
φb M p edaysarvasmamaRtedaypÞal;nwg Z x ehIyvak¾RtUv)anrayenAkñúgtarag. bnÞab;mkeTot
epÞógpÞat;kMlaMgkat;
w L 8.13(30 )
Vu = u = = 122kips
2 2
BI factored uniform load tables /
φvVn = 316kips > 122kips (OK)
cugeRkaybMput epÞógpÞat;PaBdab. PaBdabGtibrmaGnuBaØatsMrab;bnÞúkGefrKW L / 360
L 30 × 12
= = 1in.
360 360
5 wL L4 5 (5.00 / 12 )(30 × 12 )4
Δ= = = 0.703in. < 1in. (OK)
384 EI x 384 29000(4470 )
cMeLIy³ eRbI W 30 × 108 .
148 Fñwm
36. T.chhay
Beam Design Charts
eKmanRkaPic nigtaragCaeRcInsMrab;visVkrEdlGnuvtþn_ ehIyRkaPic nigtaragCMnYyTaMgenHCYy
sMrYly:ageRcIndl;dMeNIrkarKNnamuxkat;. vaRtUv)aneKeRbIy:agTUlMTUlayenAkñúg design office b:uEnþ
visVkrRtUvEteRbIvaedayRbytñ½. enAkñúgesovePAenHmin)anENnaMnUvRkaPic nigtaragTaMgGs;enaHlMGit
Gs;eT b:uEnþRkaPic nigtaragxøHmansar³sMxan;kñúgkarENnaM CaBiessKW ExSekag design moment
versus unbraced length EdleGayenAkñúg Part 4 of the Manual.
ExSekagenHRtUv)anbgðajenAkñúgrUbTI 5>25 EdlbgðajBIRkaPic design moment φb M n Ca
GnuKmn_én unbraced length Lb sMrab; particular compact shape. eKGacsg;RkaPicEbbenHsMrab;
muxkat;epSg²CamYynwgtMélCak;lak;én Fy nig Cb edayeRbIsmikarsmRsbsMrab; moment
strength.
Manual chart rYmmanRKYsarénExSekagsMrab; rolled shapes CaeRcIn. ExSekagTaMgenHRtUv)an
begáIteLIgCamYy Cb = 1.0 . sMrab;ExSekagepSgeTotrbs; Cb KuN design moment Edl)anBIta
rageday Cb . RtUvcaMfa φb M n minGacFMCag φb M p ¬b¤ sMrab; noncompact shapes φb M n QrelI
local buckling¦. bMerIbMras;rbs;RkaPicRtUv)anbgðajbgðajenAkñúgrUbTI 5>26 EdlExSekagEbbenHBIr
RtUv)anbgðaj. cMNucNak¾edayenAelIRkaPicenH dUcCacMnucCYbKñaénExSdac;BIr bgðajBI design
moment nig unbraced length. RbsinebIm:Um:g;Ca required moment capacity enaHExSekagEdlenABI
elIcMnucenaHRtUvKñanwgFñwmEdlman moment capacity FMCag. ExSekagEdlenAxagsþaMKWsMrab;FñwmEdl
man required moment capacity Cak;lak; eTaHbIsMrab; unbraced length FMCagk¾eday. dUcenH enA
kñúgkarKNnamuxkat; RbsinebIeyIgdak; unbraced length nig required design strength cUleTAkñúg
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50. T.chhay
rUbTI 5>34 bgðajfa joist xageRkambMeBjnUvtMrUvkarénbnÞúkxagelI³ 12K 5 TMgn;RbEhl 7.1lb / ft /
14K 3 TMgn;RbEhl 6lb / ft nig 16K 2 TMgn;RbEhl 5.5lb / ft . edayminmankarkMNt;sMrab;kMBs;
dUcenHeyIgerIsnUv joist NaEdlRsalCageK.
cMeLIy³ eRbI 16K 2 .
5>13> bnÞHRTFñwm nigbnÞH)atssr Beam Bearing Plates and Column Base Plate
viFIKNnabnÞHRTssrmanlkçN³RsedogKñanwgviFIKNnabnÞHRTFñwm ehIyedaysarmUlehtu
enH eyIgnwgBicarNavaCamYyKña. elIsBI karkMNt;kMras;rbs;bnÞH)atssrtMrUveGaymankarBicarNa
BI flexure dUcenHvaRtUv)anelIkykmkerobrab;enATIenH EdlminEmnenAkñúgCMBUk 4. kñúgkrNITaMgBIr
tYnaTIrbs;bnÞHEdkKWEbgEckbnÞúkEdlRbmUlpþúM (concentrated load) eTAsMPar³EdlRTva.
bnÞHRTFñwmmanBIrRbePTKW³ mYysMrab;bBa¢ÚnRbtikmμrbs;FñwmeTATMr dUcCaCBa¢aMgebtug nigmYy
eTotsMrab;bBa¢ÚnbnÞúkeTAsøabxagelIrbs;Fñwm. dMbUg BicarNaTMrFñwmEdlbgðajenAkñúgrUbTI 5>35 .
eTaHbICaFñwmCaeRcInRtUv)antP¢ab;eTAssrb¤eTAFñwmepSgeTotk¾eday EtRbePTénTMrEdlbgðajenATIenH
RtUv)aneRbICaerOy² CaBiessenARtg; bridge abutments. karKNnaBIbnÞHRT rYmmanbICMhan³
!> kMNt;TMhM N EdleKGackarBar web yielding nig web crippling.
@> kMNt;TMhM B EdlRkLaépÞ B × N manTMhMRKb;RKan;edIm,IkarBarsMPar³EdlRT ¬CaTUeTAKW
ebtug¦ BIkarEbk.
#> kMNt;kMras; t EdlbnÞHRTman bending strength RKb;RKan;.
karBN’naBI Web yielding and web crippling manenAkñúg Chapter K of AISC Specifica-
tion, “Strength Design Consideration”. ÉcMENk bearing strength rbs;ebtugRtUv)anniyayenA
kñúg Chapter J, “Connections, Joints, and Fasteners”.
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51. T.chhay
Web Yielding
Web yielding KWCakarpÞúHEbkedaykarsgát; (compressive crushing) rbs;RTnugFñwmEdl
bNþalBIkarGnuvtþn_kMlaMgsgát;edaypÞal;eTAsøabEdlenABIxagelI b¤BIxageRkamRTnug. kMlaMgenH
GacCakMlaMgRbtikmμBITMrénRbePTdUcbgðajkñúg rUbTI 5>35 b¤vaGacCabnÞúkEdlbBa¢ÚneTAsøabeday
ssr b¤FñwmepSgeTot. Yielding ekIteLIgenAeBlEdlkugRtaMgsgát;enAelImuxkat;edktamry³RTnug
xiteTArkcMnuc yield. enAeBlbnÞúkRtUv)anbBa¢Úntamry³bnÞHEdk web yielding RtUv)ansnμt;faekIt
manenAEk,rmuxkat;EdlmanTTwg t w . enAkñúg rolled shape muxkat;enARtg;cugénBitekag (toe of the
fillet) EdlmancMgay k BIépÞxageRkArbs;søab ¬TMhMenHRtUv)anerobCatarag enAkñúg dimensions
and properties tables in the Manual). RbsinebIbnÞúkRtUv)ansnμt;faEbgEckxøÜnvaeday slope
1 : 2.5 dUcbgðajenAkñúg rUbTI 5>36 RkLaépÞenARtg;TMrrgnUv yielding KW (2.5k + N )t w . edayKuN
RkLaépÞenHnwg yield stress eGay nominal strength sMrab; web yielding enARtg;TMr³
Rn = (2.5k + N )Fy t w (AISC Equation K1-3)
The bearing length N enARtg;TMrmikKYrtUcCag k .
enARtg;bnÞúkxagkñúg beNþayrbs;muxkat;rgnUv yielding KW
2(2.5k ) + N = 5k + N
The nominal strength KW
Rn = (5k + N )Fy t w (AISC Equation K1-2)
The design strength KW φRn , Edl φ = 1.0
Web Cripplimg
Web cripplingCa buckling rbs;RTnugEdlbNþalBIkMlaMgsgát;EdlbBa¢Úntamry³søab.
sMrab;bnÞúkxagkñúg nominal strength sMrab; web crippling KW³
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52. T.chhay
⎡ 1.5 ⎤
⎛N ⎞⎛ t w ⎞ ⎥ Fy t f
Rn = 135t w ⎢1 + 3⎜
2
⎟⎜ ⎟ (AISC Equation K1-4)
⎢ ⎝ d ⎠⎜ t f ⎟
⎝ ⎠
⎥ tw
⎢
⎣ ⎥
⎦
sMrab;bnÞúkenARtg; b¤Ek,rTMr ¬minFMCagBak;kNþalkMBs;FñwmBIcug¦ nominal strength KW³
⎡ 1.5 ⎤
⎛N ⎞⎛ t w ⎞ ⎥ Fy t f
Rn = 68t w ⎢1 + 3⎜
2
⎢
⎟⎜ ⎟
⎝ d ⎠⎜ t f ⎟ ⎥ tw
sMrab; N ≤ 2
d
(AISC Equation K1-5a)
⎢
⎣ ⎝ ⎠ ⎥
⎦
⎡ 1.5 ⎤
2⎢ ⎛ N ⎞⎛ t w ⎞ ⎥ Fy t f
b¤ Rn = 68t w 1 + ⎜ 4 − 0.2 ⎟⎜ ⎟
⎢ ⎝ d ⎠⎜ t f ⎟ ⎥ t w
sMrab; N > 2
d
(AISC Equation K1-5b)
⎢
⎣ ⎝ ⎠ ⎥ ⎦
emKuNersIusþg;sMrab;sßanPaBkMNt;enHKW φ = 0.75
Concrete Bearing Strength
sMPar³EdleRbIsMrab;RTFñwmGacCa ebtug dæ b¤sMPar³epSg²eTot b:uEnþCaTUeTAvaCaebtug.
sMPar³enHRtUvEtTb;nwg bearing load EdlGnuvtþedaybnÞHEdk. The nominal bearing strength
EdlbBa¢ak;enAkñúg AISC J9 dUcKñaenAkñúg American Concrete Institute’s Building Code (ACI,
1995). RbsinebI plate RKbeBjelIépÞrbs;TMr enaH nominal strength KW
Pp = 0.85 f 'c A1 (AISC Equation J9-1)
RbsinebI plate minRKbeBjelIépÞrbs;TMreT enaH nominal strength KW
Pp = 0.85 f 'c A1 A2 / A1 (AISC Equation J9-2)
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53. T.chhay
Edl ersIusþg;rgkarsgát; 28éf¶rbs;ebtug
f 'c =
A1 = bearing area R
A2 = full area rbs;TMr
RbsinebI A2 mincMCamYy A1 enaH A2 KYrmantMélFMCag A1 EdlvamanragFrNImaRtRsedog
Kñanwg A1 dUcbgðajenAkñúgrUbTI 5>37. AISC tMrUveGay
A2 / A1 ≤ 2
The design bearing strength KW φc Pp Edl φc = 0.60 .
Plate Thickness
enAeBlEdlbeNþay nigTTwgrbs;bnÞHTMrRtUv)ankMNt;ehIy bearing pressure mFümRtUv)an
KitCabnÞúkBRgayesμIeTAelI)atén plate EdlRtUv)ansnμt;RTedayTTwg 2k EdlenAkNþalFñwmnig
beNþay N dUcbgðajenAkñúgrUbTI 5>38. bnÞab;mkeTotbnÞHRtUv)anBicarNafaekageFobGkS½RsbeTA
nwgElVgFñwm. dUcenH bnÞHRtUv)anKitCa cantilever EdlmanRbEvgElVg n = (B − 2k ) / 2 nigTTwg N .
edIm,IgayRsYl TTwg 1in. RtUv)anBicarNa CamYynwgbnÞúkBRgayesμIKitCa lb / in. EdlesμInwg bearing
pressure EdlKitCa lb / in.2 .
BIrUbTI 5>38 m:Um:g;GtibrmaenAkñúgbnÞHKW
Ru n R n2
Mu = ×n× = u
BN 2 2 BN
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