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

9. T.chhay
dUckrNIssrEdr PaBKμanlMnwgGacmann½yCalkçN³srub b¤Gacmann½yCalkçN³edaytMbn;.
karekagrbs;Ggát;RtUv)anbgðajenAkñúgrUbTI 5>9 a. enAeBlFñwmekag tMbn;rgkarsgát; ¬EpñkxagelI
GkS½NWt¦ manlkçN³ nigkareFVIkarRsedognwgssr ehIyvanwg buckle RbsinebIEpñkrbs;muxkat;man
lkçN³RsavRKb;RKan;. EtvamindUcssr edaysartMbn;rgkarsgát;rb;muxkat;RtUv)anTb;edayEpñk
EdlrgkarTaj ehIyPaBdabmkxageRkA (flexural buckling) RtUv)anbegáIteLIgeday twisting
(torsion). karbegáItnUvPaBKμanlMnwgenHRtUv)aneKehAfa lateral-torsional buckling (LTB).
eKGacbgáar Lateral-torsional buckling )aneday lateral bracing tMbn;rgkarsgát; CaBiesssøab
Edlrgkarsgát; CamYynwgcenøaHRKb;RKan;. karBRgwgenHRtUv)anbgðajlkçN³nimitþsBaØaenAkñúgrUbTI
5>9 b. dUcGVIEdleyIg)aneXIj moment strength GaRs½yeTAnwgRbEvgEpñkEdlmin)anBRgwgEdlCa
cMgayrvagcMnucénTMrxag (lateral support) .
eTaHbICaFñwmGacTTYlm:Um:g;RKb;RKan;edIm,IeFVIeGayvaeTAdl;lkçxNÐ)aøsÞiceBjelj vak¾RtUv
GaRs½yfaetIva)anrkSa cross-sectional integrity b¤Gt;. vanwg)at;bg; integrity RbsinebIEpñkrgkar
sgát;NamYyrbs;muxkat; buckle. RbePT buckling GacCa compression flange buckling Edl
eKehAfa flange local buckling(FLB) b¤ buckling énEpñkrgkarsgát;rbs;RTnug EdleKehAfa web
local buckle (WLB). dUcEdl)anerobrab;enAkñúgCMBUk 4 RbePT local buckling epSgeTotekIteLIg
edayGaRs½ynwg width-thickness ratio rbs;Epñkrgkarsgát;rbs;muxkatt;.
rUbTI 5>10 bgðajBIT§iBlrbs; local and lateral-torsional buckling. FñwmR)aMdac;eday
ELkRtUv)anbgðajenAkñúgRkaPicénbnÞúk-PaBdab. ExSekagTI ! CaExSekagbnÞúk-PaBdabrbs;FñwmEdl
KμanlMnwg ¬edayviFINak¾eday¦ ehIy)at;bg;lT§PaBRTbnÞúkrbs;vamuneBlvaeTAdl; first yield ¬rUbTI
5>3 b¦. ExSekag @ nig # RtUvKñanwgFñwmEdlGacRTbnÞúkedayqøgkat; first yield bu:Enþmin)anyUrRKb;
122 Fñwm

10. T.chhay
RKan;edIm,IbegáItsnøak;)aøsÞic nigTTYl)an plastic collapse. RbsinebIvaGaceTAdl; plastic collapse
enaHExSekagbnÞúk-PaBdabnwgmanlkçN³dUcExSekag $ b¤ %. ExSekag $ sMrab;krNIm:Um:g;esμIenAeBj
RbEvgFñwmTaMgmUl ehIyExSekag % sMrab;FñwmEdlrgm:Um:g;ERbRbYl (moment gradient) . eKGac
TTYl)ankarKNnaRbkbedaysuvtßiPaBCamYynwgFñwmEdlRtUvKñanwgExSekagNamYyénExSekagTaMgenH
b:uEnþExSekag ! nig @ bgðajBIkareRbIsMPar³edayKμanlkμN³RbsiT§PaB.
5>4> cMNat;fñak;rbs;rUbrag Classification of Shapes
AISC cat;cMNat;fñak;rUbragmuxkat;Ca compact, noncompact b¤ slender GaRs½ynwgtMél
rbs; width-thickness ratios. sMrab; I- nig H-shapes pleFobsMrab;søab (unstiffened element) KW
b f / 2t f ehIypleFobsMrab;RTnug (stiffened element) KW h / t w . eKGacrk)ankarcat;cMNat;fñak;
rbs;muxkat;enAkñúg Section B5 of the specification, “Local Buckling” in Table B5.1. vanwg
RtUv)ansegçbdUcxageRkam. edayyk
λ = width-thickness ratio
λ p = upper limit for compact category
λr = upper limit for noncompact category
enaH RbsinebI λ ≤ λ p ehIysøabP¢ab;eTAnwgRTnugCab;Kμandac; enaHrUbragmanlkçN³ compact.
RbsinebI λ p < λ ≤ λr enaHrUbragmanlkçN³ uncompact.
RbsinebI λ > λr enaHrUbragmanlkçN³ slender.
cMNat;fñak;RtUvQrelI width-thickness ratio rbs;muxkat;EdlmantMélFMCag. ]TahrN_ RbsinebI
RTnugCa compact ehIysøabCa noncompact enaHrUbragRtUv)ancat;cMNat;fñak;Ca noncompact .
123 Fñwm

11. T.chhay
tarag 5>3 RtUv)andkRsg;ecjBI AISC Table B5.1 nigman width-thickness ratio sMrabmuxkat;
hot-rolled I- nig H-shape.
tarag 5>3 Width-thickness parameters*
λp λr
Element λ
IS US IS US
bf 170 65 370 141
Flange
2t f Fy Fy Fy − 69 Fy − 10
h 1680 640 2550 970
Web
tw Fy Fy Fy Fy
* sMrab; hot-rolled I- nig H-shape rgkarBt;
5>5> Bending Strength of Compact Shapes
FñwmGac)ak;edayvaTTYlm:Um:g; M p ehIyvakøayCa)aøsÞiceBjelj b¤k¾vaGac)ak;eday
!> lateral-torsional buckling (LTB), eday elastically b¤ inelastically
@> flange local buckling (FLB), eday elastically b¤ inelastically
#> web local buckling (WLB), eday elastically b¤ inelastically
RbsinebIkugRtaMgBt;Gtibrma (maximum bending stress) tUcCagEdnsmamaRt
(proportional limit) enAeBlEdl buckling ekIteLIg failure enHRtUv)aneKehAfa elastic. RbsinebI
minGBa©wgenH vaCa inelastic. ¬sUmemIlkarbkRsayEdlTak;TgenAkñúgEpñk 4>2 rbs;emeronTI 4 .¦
edIm,IgayRsYl CadMbUgeyIgcat;cMNat;fñak;FñwmCa compact, noncompact b¤ slender. kar
erobrab;enAkñúgEpñkenHGnuvtþcMeBaHFñwmBIrRbePT³ ¬!¦ hot-rolled I-nig H-shape ekageFobGkS½xøaMg
ehIyEdlbnÞúkenAkñúgbøg;énGkS½exSay ehIy ¬2¦ channels ekageFobGkS½xøaMg ehIybnÞúkdak;tam
shear center b¤k¾RtUv)anTb;RbqaMgnwgkarrmYl. ¬ Shear center CacMnucenAelImuxkat; EdltamcMnuc
enHbnÞúkTTwgRtUv)ankat;tam RbsinebIFñwmekagedayKμankarrmYl.¦ vanwgekItmancMeBaH I-nig H-
Shapes. eKminBicarNaGMBI Hybrid beam ¬Edlsøab nigRTnugrbs;vamanersIusþg;epSgKña¦eT ehIy
smIkar AISC xøHnwgRtUv)anEkERbbnþicbnþÜcedIm,IeqøIytbeTAnwgkarkMNt;enH edayeKCMnYs Fyf nig
Fyw EdlCa yield strength rbs;søab nigRTnugeday Fy .
124 Fñwm

12. T.chhay
eyIgcab;epþImCamYynwg compact shape EdlRtUv)ankMNt;CarUbragEdlRTnugrbs;vaRtUv)an
P¢ab;eTAsøabCab;tdac; ehIyEdlbMeBjnUvtMrUvkar width-thickness ratio xageRkamsMrab;søab nig
RTnug³
bf
2t
≤
170
F
nig th ≤ 1680 ¬xñatCa IS ¦ 2btf ≤ 65 nig th ≤ 640 ¬xñatCa IS ¦
F F F
f y w y f y w y
sMrab;RKb; standard hot-rolled shape Edl)anrayeQμaHenAkñúg Manual )aneKarBlkçxNÐxag
elI dUcenHeKRtUvkarBinitüEtpleFobsøabb:ueNÑaH. rUbragPaKeRcInk¾bMeBjtMrUvkarrbs;søabEdr dUcenH
vaRtUv)ancat;cMNat;fñak;Ca compact. RbsinebIFñwmCa compact ehIymanTMrxagCab; b¤ unbraced
length xøI enaH nomina’moment strength, M n Ca plastic moment capacity eBjrbs;rUbrag M p .
sMrab;Ggát;EdlminmanTMrxagRKb;RKan; moment resistance RtUv)ankMNt;eday lateral-torsional
buckling strength EdlmanlkçN³Ca elastic b¤ inelastic .
RbePTTImYy (laterally supported compact beam) CakrNIEdlFmμta nigsamBaØCageK.
AISC F1.1 eGay nominal strength Ca
Mn = M p (AISC Equation F1.1)
Edl M p = F y Z ≤ 1 .5 M y
tMélkMNt;eday 1.5M y sMrab; M p KWedIm,IkarBarbnÞúkEdleFVIkarelIslb; nigRtUv)anbMeBj
enAeBlEdl
F y Z ≤ 1 .5 F y S b¤ Z ≤ 1.5
S
sMrab; I- nig H-shape ekageFobGkS½xøaMg enaH Z / S EtgEttUcCag 1.5 Canic©. ¬b:uEnþsMrab; I- nig H-
shape ekageFobGkS½exSay enaH Z / S nwgminEdltUcCag 1.5 eT.¦
]TahrN_ 5>3³ FñwmEdlbgðajenAkñúgrUbTI 5>11 CaEdl A36 EdlmanrUbrag W 16 × 31 . vaRTkM
ralxNнebtugGarem:Edlpþl;nUv continuous lateral support dl;søabrgkarsgát;. Service dead
loadKW 450lb / ft . bnÞúkenHRtUv)andak;BIelIFñwm vaminRtUv)anKItbBa©ÚlbnÞúkpÞal;rbs;FñwmeT. Service
live load KW 550lb / ft . etIFñwmenHman moment strength RKb;RKan;b¤eT?
125 Fñwm

13. T.chhay
dMeNaHRsay³ Service dead load srub edayrYmbBa©ÚlTaMgTMgn;rbs;FñwmKW
wD = 450 + 31 = 481lb / ft
sMrab;FñwmTMrsamBaØrgbnÞúkBRgayesμI m:Um:g;Bt;GtibrmaekItmanenAkNþalElVgesμInwg
1
M max = wL2
8
Edl w CabnÞúkEdlmanxñatkMlaMgelIÉktþaRbEvg ehIy L CaRbEvgElVg. enaH
1 2 0.481× 30 2
M D = wL = = 54.11 ft − kips
8 8
0.55 × 30 2
ML = = 61.88 ft − kips
8
edaysar dead load tUcCag live load min)an 8 dg enaHbnSMbnÞúk A4-2 nwgmantMélFMCageK³
M u = 1.2M D + 1.6M L = 1.2 × 54.11 + 1.6 × 61.88 = 164 ft − kips
müa:gvijeTot bnÞúkGacRtUv)anKitemKuNmun
wu = 1.2wD + 1.6wL = 1.2 × 0.431 + 1.6 × 0.550 = 1.457kips / ft
1 1.457 × 30 2
M u = wu L2 = = 164 ft − kips
8 8
RtYtBinitü compactness ³
bf
2t
= 6.3 ¬BI Part 1 of the Manual ¦
f
65
Fy
=
65
36
= 10.8 > 6.3 dUcenH søabCa compact .
h
tw
<
640
Fy
¬sMrab;RKb;rUbragenAkñúg Manual ¦
dUcenH W 16 × 31 Ca compact sMrab;Edk A36 .
edaysarFñwmCa compact ehIymanTMrxag
M n = M p = F y Z x = 36(54.0 ) = 1944in − kips = 162 ft − kips
RtYtBinitüsMrab; M p ≤ 1.5M y ³
Zx 54
= = 1.15 < 1.5 (OK)
S x 47.2
φb M n = 0.90(162) = 146 ft − kips < 164 ft − kips (NG)
cMeLIy³ Design moment tUcCagm:Um:g;emKuN dUcenH W 16 × 31 minRKb;RKan;.
126 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

22. T.chhay
]TahrN_ 5>6³ FñwmTMrsamBaØmYymanRbEvg 40 feet RtUv)anTb;xagenAxagcugrbs;va ehIyvargnUv
service load dUcxageRkam³
Dead load = 400lb / ft ¬edayrYmbBa©ÚlTaMgTMgn;Fñwm¦
Live load = 1000lb / ft
RbsinebIeKeRbI AISC A572 Grade 50 etI W 14 × 90 RKb;RKan;b¤Gt;?
dMeNaHRsay³ bnÞúkemKuN nigm:Um:g;emKuNKW
wu = 1.2wD + 1.6 wL = 1.2(0.40) + 1.6(1.00) = 2.08kips / ft
1 2.08(40 )2
M u = wu L2 = = 416.0 ft − kips
8 8
kMNt;lkçN³rUbragmuxkat; ¬faetICa compact, noncompact b¤ slender¦³
bf
λ= = 10.2
2t f
65 65
λp = = = 9.19
Fy 50
141 141
λr = = = 22.3
F y − Fr 50 − 10
eday λ p < λ < λr dUcenHrUbragenHKW noncompact. RtYtBinitülT§PaBRTRTg;edayQrelIsßanPaB
kMNt;rbs; flange local buckling³
50(157 )
M p = Fy Z x = = 654.2 ft − kips
12
Mr ( )
= F y − Fr S x = (50 − 10)
143
12
= 476.7 ft − kips
⎛ λ − λp ⎞
Mn (
= M p − M p − Mr ⎜ ) ⎟ = 652.4 − (654.2 − 476.7 )⎛ 10.2 − 9.19 ⎞ = 640.5 ft − kips
⎜ λr − λ p ⎟ ⎜ ⎟
⎝ ⎠ ⎝ 22.3 − 9.19 ⎠
Design strength EdlQrenAelI FLBdUcenH
φb M n = 0.9(640.5) = 576 ft − kips
RtYtBinitülT§PaBRTRTg;EdlQrelIsßanPaBkMNt;rbs; lateral-torsional buckling. BI Load
Factor Design Selection Table³
L p = 15 ft nig Lr = 38.4 ft
Lb = 40 ft > Lr
dUcenHvanwg)ak;edayeGLasÞic LTB.
135 Fñwm

23. T.chhay
BI Part 1 of the Manual/
I y = 362in 4
J = 4.06in 4
C w = 16000in 6
sMrab;FñwmTMrsamBaØRTbnÞúkBRgayesμICamYynwgTMrxagenAxagcugsgçag
Cb = 1.14
AISC Equation F1-13 eGay
2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜ ⎟
⎜ L ⎟ I yCw ≤ M p
Lb ⎝ b⎠
⎡ 2 ⎤
= 1.14 ⎢ π ⎛ π × 29000 ⎞
29000(362)(11200)(4.06 ) + ⎜ ⎟ (362)(16000) ⎥
⎢ 40(12 ) ⎝ 40 × 12 ⎠ ⎥
⎣ ⎦
= 1.14(5412 ) = 6180in. − kips = 515.0 ft − kips
M p = 654.2 ft − kips > 515.0 ft − kips
edaysar 515.0 < 640.5 dUcenH LTB lub ehIy
φb M n = (0.90)515.0 = 464 ft − kips > M u = 416 ft − kips (OK) /
cMeLIy³ eday M u < φb M n enaHFñwmman moment strength RKb;RKan;.
lkçN³kMNt;rbs; noncompact shapes RtUv)ansMrYleday Load Factor Design Selection
Table. Noncompact shapes RtUv)ankMNt;sMKal;eday footnote farUbragCa noncompact sMrab;
F y = 250 MPa = 36ksi b¤ F y = 350 MPa = 50ksi . Noncompact shapes k¾RtUv)anerobcMenAkñúg
taragedaylkçN³xusEbøkKñadUcxageRkam³
!> sMrab; noncompact shapes tMélEdlmanenAkñúgtaragrbs; φb M p CatMélBitR)akdrbs;
design strength EdlQrelI flange local buckling. enAkñúg]TahrN_TI 5>6 eyIg)an
KNnatMélenHesμInwg 576 ft − kips b:uEnþtMélRtwmRtUvenAkñúgtarag φb M p KW
0.90(654.2 ) = 589 ft − kips
@> tMél L p enAkñúgtaragCatMélrbs; unbraced length Edl nominal strength EdlQr
elI inelastic lateral torsional buckling esμInwg nominal strength EdlQrelI flange
136 Fñwm

24. T.chhay
local buckling dUcenH nominal strength sMrab; unbraced length GtibrmaGacRtUv)an
KitCaersIusþg;EdlQrelI web local buckling. ¬rMlwkfa L p sMrab; compact shapes
Ca unbraced length GtibrmaEdl nominal strength GacRtUv)anKitesμInwg plastic
moment¦. sMrab;rUbragenAkñúg]TahrN_5>6 karKNna nominal strength EdlQrelI
FLB eTAersIusþg;EdlQrelI inelastic LTB (AISC Equation F1-2) CamYynwg
Cb = 1.0 ³
⎛ Lb − L p ⎞
M n = M p − (M p − M r )⎜ ⎟ ¬%>%¦
⎜L −L ⎟
⎝ r p⎠
tMélrbs; M r nig Lr RtUv)anTTYlBI]TahrN_ 5>6 ehIynwgminRtUv)anpøas;bþÚr. b:uEnþ
tMélrbs; L p RtUvEt)anKNnaBI AISC Equation F1-4³
300ry 300(3.70 )
Lp = = = 157.0in. = 13.08 ft.
Fy 50
CMnYstMélxagelIkñúgsmIkar %>% eyIgTTYl)an
⎛ L − 13.08 ⎞
640.5 = 654.2 − (654.2 − 476.7 )⎜ b ⎟
⎝ 38.4 − 13.08 ⎠
Lb = 15.0 ft.
enHCatMélbBa©ÚlkñúgtaragCa L p sMrab; W = 14 × 90 CamYynwg Fy = 50ksi . cMNaMfa
300ry
Lp =
Fy
GaceRbIsMrab; noncompact shapes. RbsinebIeFVIEbbenH lT§plEdlTTYl)anenAkñúg
smIkarsMrab; inelastic LTB EdlRtUv)aneRbIenAeBl Lb minmantMélFMRKb;RKan; enaH
ersIusþg;EdlQrelI FLB nwglub.
5>7> Summary of Moment Strength
viFIsaRsþkñúgkarKNna nominal moment strength sMrab; I- nig H-shaped sections Edl
ekageFobnwgGkS½ x nwgRtUv)ansegçbenATIenH. GgÁTaMgGs;EdlmanenAkñúgsmIkarxageRkamRtUv)an
kMNt;rYcehIyBImun ehIyelxsmIkarrbs; AISC minRtUv)anbgðajenATIenHeT. karsegçbenHsMrab;Et
compact shapes nig noncompact shapes Etb:ueNÑaH ¬minmansMrab; slender shapes eT¦.
137 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

31. T.chhay
dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaBKW 3 / 4 + 1/ 8 = 7 / 8in. .
gross nig net shear areas KW
Agv = (2 + 3 + 3 + 3)t w = 11(0.300) = 3.300in.2
⎛ 7⎞
Anv = ⎜11 − 3.5 × ⎟(0.300) = 2.381in.2
⎝ 8⎠
gross nig net tension areas KW
Agt = 1.25t w = 1.25(0.300) = 0.375in.2
⎛ 7⎞
Ant = ⎜1.25 − 0.5 × ⎟(0.300 ) = 0.2438in.2
⎝ 8⎠
AISC Equation J4.3a eGay
[ ]
φRn = φ 0.6 Fy Agv + Fu Ant = 0.75[0.6(36)(3.3) + 58(0.2438)] = 64.1kips
AISC Equation J4.3b eGay
[ ]
φRn = φ 0.6 Fu Anv + Fy Agt = 0.75[0.6(58)(2.381) + 36(0.3750)] = 72.3kips
tY fracture enAkñúg AISC Equation J4.3b mantMélFMCag ¬Edl 82.86>14.14¦ dUcenHsmIkarenH
mantMélFMCag.
cMelIy³ RbtikmμemKuNGtibrmaEdlQrelI block shear=72.3kips.
5>9> PaBdab Deflection
bEnßmBIelIsuvtßiPaB eRKOgbgÁúMRtUvEt serviceable . eRKOgbgÁúMEdlman serviceable CaeRKOg
bgÁúMEdleFVIkar)anl¥ minbNþaleGayGñkEdleRbIR)as;vamanGarmμN_favaKμansuvtßiPaB. sMrab;Fñwm
edIm,ITTYl)an serviceable eKRtUvkMNt;bMlas;TIbBaÄr b¤PaBdab. PaBdabFMCaTUeTAekItmancMeBaH
flexible beam EdlGacmanbBaðaCamYynwgrMjr½. PaBdabGacbgábBaðaeTAdl;Ggát;d¾éTeTotEdlP¢ab;
144 Fñwm

32. T.chhay
eTAnwgva edaybNþaleGaymankMhUcRTg;RTaytUc. elIsBIenH GñkeRbIR)as;sMNg;nwgeXIjPaB
GviC¢manedaysarPaBdabFM ehIyeFVIkarsnidæanxusfasMNg;KμansuvtßiPaB.
sMrab;krNITUeTArbs;FñwmTMrsamBaØEdlRTbnÞúkBRgayesμIdUckúñrUbTI 5>22 PaBdabbBaÄrGti-
brmaKW³
5 wL4
Δ=
384 EI
eKGacrk)anrUbmnþPaBdabsMrab;FñwmeRcInRbePT niglkçxNÐdak;bnÞúkenAkñúg Part 4, “Beam
and Girder Design,”of the Manual. sMrab;sßanPaBminFmμtaeKGaceRbI standard analytical
method dUcCa method of virtual work CaedIm. PaBdabCa serviceability limit state minEmnCa
sßanPaBkMNt;sMrab;ersIusþg;eT dUcenHCaTUeTAPaBdabRtUv)ankMNt;CamYy service loads.
karkMNt;d¾smrmüsMrab;PaBdabGtibrmaGaRs½yeTAnwgtYnaTIrbs;Fñwm nwgkarRbmaNBIPaB
xUcxatEdlekItBIPaBdab. AISC Specification pþl;nUvkarENnaMtictYcEdlmanEcgenAkñúg Chapter
L, “Serviceability Design Consideration,” faeKRtUvEtRtYtBinitüPaBdab. eKGacrk)ankarkMNt;
d¾smrmüsMrab;PaBdabBI governing building code. tMélxageRkamCaPaBdabGnuBaØatGtibrmasrub
¬service dead load bUknwg service live load¦.
L
Plastered construction:
360
L
Unplastered floor construction:
240
L
Unplastered roof construction:
180
Edl L CaRbEvgElVg.
eBlxøHeKcaM)ac;eRbIkarkMNt;PaBdabCatMélwlx CagkareRbIPaBdabCatMélRbPaK. eBlxøH
karkMNt;RtUv)anKitcMeBaHPaBdabEdlbNþalEtBI live load, edaysarCaerOy² dead load
deflection RtUv)ankarBarkñúgeBlsagsg;.
145 Fñwm

33. T.chhay
]TahrN_ 5>9³ RtYtBinitüPaBdab;rbs;FñwmEdlbgðajenAkñúg rUbTI 5>23. PaBdabGtibrmasrub
GnuBaØatKW 240 .
L
dMeNaHRsay³ PaBdabGtibrmasrubGnuBaØat = 240 = 9100 = 38mm
L
240
Total service load = 7.3 + 8 = 15.3kN / m
5 wL4 5 × 15.3 × 9100 4
Maximum total deflection = = = 32.2mm < 38mm (OK)
384 EI 384 × 2 ⋅105 × 212 ⋅10 6
cMeLIy³ FñwmbMeBjlkçxNÐPaBdab
PondingCaPaBdabmYyEdlb:HBal;dl;suvtßiPaBrbs;eRKOgbgÁúM. vaeRKaHfñak;bMputsMrab;RbBn§½
kMralxNнrabesμIGaceFVIeGayTwkePøógdk;. RbsinebIRbBn§½bgðÚrTwksÞHkñúgGMLúgeBlePøóg TMgn;rbs;Twk
Edldk;elIkMraleFVIeGaykMraldab EdlvabegáIt)anCaGagsMrab;sþúkTwkkan;EteRcIn. RbsinebIkrNI
enHekIteLIgtQb;Qr enaHeRKOgbgÁúMGacnwg)ak;. AISC specification tMrUvfaRbBn§½dMbUlRtUvEtman
PaBrwgRkajRKb;RKan;edIm,IkarBar ponding, elIsBIenH vaerobrab;BIkarkMNt;m:Um:g;niclPaB nig)a:ra:-
Em:Rtd¾éTeTotenAkñúg Section K2, “Ponding”.
5>10> karKNnamuxkat; Design
karKNnamuxkat;FñwmtMrUvkareRCIserIsrUbragmuxkat;EdlmanersIusþg;RKb;RKan; nigbMeBjtMrUvkar
serviceability. enAeBleyIgKitBIersIusþg; flexure EtgEtmaneRKaHfñak;CagkMlaMgkat; dUcenHkar
Gnuvtþn_TUeTAKWeKKNnamuxkat;sMrab; flexure rYcehIyRtYtBinitükMlaMgkat;tameRkay. viFIsaRsþkñúg
karKNnamuxkat;RtUv)anerobrab;xageRkam³
!> kMNt;m:Um:g;emKuN/ M u . vadUcKñanwg required design strength, φb M n . TMgn;rbs;Fñwm
CaEpñkrbs; desd load b:uEnþvaminRtUv)andwgenARtg;cMnucenH. eKGacsnμt;tMélenH b¤k¾eK
ecalvasin bnÞab;mkeKnwgRtYtBinitüvaeLIgvijeRkayeBleKeRCIseIsrUbragehIy.
146 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
149 Fñwm

37. T.chhay
RkaPic ExSekagenABIelI nigenABIsþaMcMnucenaH RtUvKñanwgFñwmEdlGacTTYlyk)an. RbsinebIeKKitTaMg
ExSekagdac;² enaHExSekagsMrab;rUbragRsalCagsßitenABIelI nigBIxagsþaMExSekagdac;². cMNucenAelI
ExSekagEdlRtUvnwg L p RtUv)anbgðajeday solid circle ehIy Lr RtUv)anbgðajeday open circle.
eKmanExSekagBIrRbePT mYysMrab; Fy = 36ksi = 250MPa nigmYyeTotsMrab; Fy = 50ksi = 350
MPa .
kñúg]TahrN_ 5>10 required design strength ¬EdlrYmbBa©ÚlTaMgTMgn;Fñwmsnμt;¦ KW 913.5
ft − kips ehIyvaman continuous lateral support. sMrab;TMrxagCab; eKGacyk Lb = 0 . BIRkaPic
F y = 36ksi ExSekagRkas;TImYyenABIelI 913.5 ft − kips KW W 30 × 108 EdldUcKñanwgkareRCIserIs
enAkñúg]TahrN_ 5>10. eTaHbICa Lb = 0 minRtUv)anbgðajenAkñúgRkaPicBiessk¾eday k¾tMéltUc
bMputrbs; Lb EdlbgðajKWtUcCag L p sMrab;RKb;rUbragenAelITMBr½enaH.
ExSekagFñwmEdlbgðajenAkñúgrUbTI 5>25 KWsMrab; compact shape dUcenHtMélrbs; φb M n sM
rab;tMéltUcEdlRKb;RKan;rbs; Lb KW φb M p . dUcEdl)anerobrab;enAkñúgEpñk 5>6 RbsinebIrUbragCa
noncompact tMélGtibrma φb M n nwgQrelI flange local buckling. vaCakarBitEdl maximum
unbraced length sMrab; φb M n xagelInwgxusKñaBItMél L p EdlTTYlCamYynwg AISC Equation
F1-4. The moment strength rbs; noncompact shapeRtUv)anbgðajCalkçN³RkaPicenAkñúgrUbTI
5>27 Edl maximum design strength RtUv)ankMNt;sMKal;eday φb M 'n ehIy maximum
unbraced length EdlRtUvnwg φb M 'n xagelIRtUv)ansMKaleday L' p .
150 Fñwm

38. T.chhay
eTaHbICaRkaPicsMrab; compact nig noncompact shapes manlkçN³RsedogKñak¾eday k¾
φb M n nig Lb RtUv)aneRbIsMrab; compact shapes Et φb M 'n nig L' p RtUv)aneRbIsMrab;
noncompact shapes.
]TahrN_ 5>11³ FñwmEdlbgðajenAkñúg rUbTI 5>28 RtUvRTbnÞúkcMcMnucGefrBIrEdlmYy²mantMél
20kips Rtg;cMnucmYyPaKbYn. PaBdabGtibrmaminRtUvFMCag L / 240 . Lateral support RtUv)anpþl;
eGayenAcugrbs;Fñwm. eRbIEdk A572 Grade50 nigeRCIserIs rolled shape.
151 Fñwm

39. T.chhay
dMeNaHRsay³ RbsinebIeKecalTMgn;rbs;Fñwm enaHkMNat;FñwmcenøaHbnÞúkcMcMnucrgnUvm:Um:g;efr.
M A = M B = M C = M max
ehIy Cb = 1.0
eTaHRbsinCaeKKitTMgn;pÞal;rbs;Fñwmk¾eday k¾vaGacRtUv)anecaledayeFobnwgbnÞúkcMcMnuc
ehIy Cb k¾enAEtmantMélesμI 1.0 EdlGnuBaØateGayeKGaceRbIRkaPicedayKμankarEkERb.
edayminKitBITMgn;FñwmbeNþaHGasnñ eyIgTTYl)an
M u = 6(1.6 × 20) = 192 ft − kips
BIRkaPic CamYynwg Lb = 24 ft sakl,g W 15× 53 ³
φb M n = 219 ft − kips > 192 ft − kips (OK)
LÚveyIgKitBITMgn;Fñwm
M u = 192 +
1
(1.2 × 0.053)(24)2 = 197 ft − kips < 219 ft − kips (OK)
8
kMlaMgkat;TTwgKW
1.2(0.053)(24)
Vu = 1.6(20) + = 32.8kips
2
BI factored uniform load tables/
φvVn = 112kips > 32.8kips (OK)
PaBdabGtibrmaGnuBaØatKW
L 24(12 )
= = 1.2in.
240 240
BI Beam Diagrams nig Formulas section in Part 4 of the Manual/ PaBdabGtibrma
¬enAkNþalElVg¦ sMrab;bnÞúkBIresμIKñaEdlRtUv)andak;sIuemRTIKñaKW
Δ=
Pa
24 EI
(
3L2 − 4a 2 . )
Edl P= GaMgtg;sIuetbnÞúkcMcMnuc
a. =cMgayBITMreTAbnÞúk
L = RbEvgElVg
Δ=
20(6 × 12 )
24 EI
[ ]
3(24 × 12 )2 − 4(6 × 12 )2 =
13.69 × 10 6
EI
sMrab;TMgn;pÞal;rbs;Fñwm PaBdabGtibrmak¾sßitenAkNþalElVgEd dUcenH
152 Fñwm

40. T.chhay
5 wL4 5 (0.053 / 12 )(24 × 12 )4 0.04 × 10 6
Δ= = =
384 EI 384 EI EI
PaBdabsrub
13.69 × 10 6 0.04 × 10 6 13.73 × 10 6
Δ= + = = 1.114in. < 1.2in. (OK)
EI EI 29000(425)
cMeLIy³ eRbI W12 × 53 .
eTaHbICaRkaPicQrelI Cb = 1.0 k¾eday b:uEnþeKk¾GaceRbIvay:agRsYledIm,IKNnamuxkat;enA
eBlEdl Cb minesIμnwg 1.0 edayEck required design strength eday Cb munnwgdak;vaeTAkñúgRka
Pic. ]TahrN_ 5>12 nwgbgðajBIbec©keTsenH.
]TahrN_ 5>12³ eRbIEdk A36 ehIyeRCIserIs rolled shapes sMrab;FñwmenAkñúg rUbTI 5>29. bnÞúkcMcM
nucCa service live load ehIybnÞúkBRgayesμIKW 30% CabnÞúkefr nig 70% CabnÞúkGefr. Lateral
bracing RtUv)anpþl;eGayenAcug nigkNþalElVg. vaminmankarkMNt;sMrab;PaBdabeT.
dMeNaHRsay³ edaysnμt;TMgn;FñwmesμI 100lb / ft. enaH
wD = 0.30(3) + 0.10 = 1kips / ft.
wL = 1.2(1.0 ) + 1.6(0.7 × 3) = 4.560kips / ft.
Pu = 1.6(9) = 14.4kips
bnÞúkemKuN nigRbtikmμRtUv)anbgðajenAkñúgrUbTI 5>30.
m:Um:g;EdlcaM)ac;sMrab;KNna Cb ³ m:Um:g;Bt;enAcMgay x BIcugxageqVgKW
⎛ x⎞
M = 61.92 x − 4.590 x⎜ ⎟ = 61.92 x − 2.280 x 2
⎝2⎠
¬sMrab; x ≤ 12 ft ¦
sMrab; x = 3 ft / M A = 61.92(3) − 2.280(3)2 = 165.2 ft − kips
153 Fñwm

41. T.chhay
sMrab; x = 6 ft / M B = 61.92(6) − 2.280(6)2 = 289.4 ft − kips
sMrab; x = 9 ft / M C = 61.92(9) − 2.280(9)2 = 372.6 ft − kips
sMrab; x = 12 ft / M max = M u = 61.92(12) − 2.280(12)2 = 414.7 ft − kips
12.5M max
Cb =
2.5M max + 3M A + 4 M B + 3M C
12.5(414.7 )
= = 1.36
2.5(414.7 ) + 3(165.2 ) + 4(289.4) + 3(372.6)
bBa©ÚleTAkñúgRkaPicCamYynwg unbraced length Lb = 12 ft nigm:mU:g;Bt;KW
M u 414.7
= = 305 ft − kips
Cb 1.36
sakl,g W 21× 62 ³
φb M n = 343 ft − kips ¬sMrab; Cb = 1 ¦
edaysar Cb = 1.36 design strength BitR)akdKW
φb M n = 1.36(343) = 466 ft − kips
b:uEnþ design strength minRtUvelIs φb M p EdlesμIRtwmEt 389 ft − kips ¬TTYl)anBIRka
Pic¦ dUcenH design strength BitR)akdRtUvEtesμInwg
φb M n = 389 ft − kips < M u = 414.7 ft − kips (N.G.)
sMrab;rUbragsakl,gbnÞab; eyIgRtUvrMkileLIgelIeTArkExSekagCab;Rkas;bnÞab;enAelIRkaPic
eyIgTTYl)an W 21× 68 . sMrab; Lb = 12 ft design strength Edl)anBIRkaPicKW 385 ft − kips sMrab;
Cb = 1.0 . ersIusþg;sMrab; Cb = 1.36 KW
φb M n = 1.36(385) = 524 ft − kips > φb M p = 432 ft − kips
dUcenH φb M n = φb M p = 432 ft − kips > M u = 414.7 ft − kips (OK)
TMgn;FñwmKW 68lb / ft EdltUcCagTMgn;snμt; 100lb / ft . (OK)
kMlaMgkat;TTwgKW
Vu = 61.92kips
¬lT§plBitR)akdnwgtUcCagenHbnþic edaysarTMgn;pÞal;rbs;FñwmtUcCagbnÞúksnμt;¦
BI factored uniform load table
φvVn = 177kips > 61.92kips (OK)
cMeLIy³ eRbI W 21× 68
154 Fñwm

42. T.chhay
RbsinebItMrUvkarPaBdabRKb;RKgelIkarKNnamuxkat; eKRtUvkMNt;m:Um:g;niclPaBcaM)ac;Gb,-
brma ehIyeKRtUvrkrUbragRsalCageKEdlRtUvnwgtMélenH. kargarenHRtUv)ansMrYly:ageRcIneday
sar moment of inertia selection table in part 4 of the Manual. ]TahrN_ 5>13 nwgbgðajBIkar
eRbIR)as;taragenH ehIynwgBnül;pgEdrBIviFIsaRsþkñúgkarKNnamuxkat;FñwmenAkñúgRbBn§½kMralxNн.
]TahrN_ 5>13³ EpñkénRbBn§½eRKagkMralRtUv)anbgðajenAkñúg rUbTI 5>31. kMralebtugBRgwgeday
EdkmankMras; 4in. RtUv)anRTeday floor beams EdlmanKMlatBIKña 7 ft. . Floor beamsRtUv)anRT
eday girders EdlRtUv)anbnþedayssr. ¬eBlxøH floor beamsRtUv)aneKehAfa filler beams¦.
bEnßmBIelITMgn;rbs;rcnasm<n§½ bnÁÞúkrYmmanbnÞúkGefrBRgayesμI 80 psf nig movable partitions
EdlRtUv)anKitCabnÞúkBRgayesμI 20 psf elIépÞkMral . PaBdabsrubGtibrmaminRtUvelIsBI 1/ 360
énRbEvgElVg. eRbIEdk A36 nigKNnamuxkat;rbs; floor beams. snμt;fakMralpþl;nUv continuous
lateral support rbs; floor beams.
155 Fñwm

43. T.chhay
dMeNaHRsay³
eRbIebtugGarem:TMgn;FmμtaEdlmanTMgn; 150lb / ft 3 sMrab;KNnabnÞúkefr. TMgn;GacRtUv)anKitCabnÞúk
kñúgmYyÉktþaépÞedayKuNTMgn;maDnwgkMras;kMralxNн.
TMgn;kMralxNн = 150⎛⎜⎝ 12 ⎞⎟⎠ = 50 psf
4
snμt;faFñwmnImYy²RTnUvTTwgrgbnÞúk (tributary width) 7 ft. rbs;kMralxNн.
kMralxNн³ 50(7) = 350lb / ft
Partition³ 20(7 ) = 140lb / ft
TMgn;Fñwm³ = 40lb / ft ¬)a:n;sμan¦
srub³ = 530lb / ft ¬ service dead load¦
eTaHbI partition Gacclt½)an b:uEnþ national model building codes KitvaCabnÞúkefr (BOCA,
1996; ICBO, 1997;nig SBCC, 1997). eyIgk¾KitvaCabnÞúkGefrEdrenATIenH.
bnÞúkGefr³ 80(7) = 560lb / ft
ehIybnÞúkemKuNsrubKW
wu = 1.2wD + 1.6wL = 1.2(0.53) + 1.6(0.56) = 1.532kips / ft
kartP¢ab;kMral-Fñwmpþl;nUv no moment restraint ehIyFñwmRtUv)anKitCaFñwmEdlRTedayTMrsamBaØ.
2 1.532(30 )
2
1
M u = wu L = = 172.4 ft − kips
8 8
BI beam design chart CamYynwg Lb = 0 sakl,g W18× 35 ³
φb M u = 179.5 ft − kips > 172.4 ft − kips (OK)
kMlaMgkat;TTwgKW
1532(30)
Vu ≈ = 22.98kips
2
BI factored uniform load tables
φvVn = 103kips > 22.98kips (OK)
PaBdabGtibrmaGnuBaØatKW
L 30(12)
= = 1in.
360 360
5 wL4 5 (0.35 + 0.14 + 0.035 + 0.56)(30)4 (12)3
Δ= = = 1.3in. > 1in. (N.G.)
384 EI 384 29000(510)
edayedaHRsaysmIkarPaBdabsMrab; required moment of inertia TTYl)an
156 Fñwm

44. T.chhay
5wL4 384 5(1.085)(30)4 (12)3
I required = = = 682in.4
384 EΔ required 384(29000)(1)
Moment of Inertia Selection Table RtUv)anerobcMeLIgkñúgviFIdUcKñanwg Load Factor Design
Selection Table dUcenHkareRCIserIsrUbragEdlRsalCageKCamYynwgm:Um:g;niclPaBRKb;RKan;man
lkçN³samBaØ. BI I x Table sakl,g W 21× 44 ³
I x = 843in.4 > 682in.4 (OK)
φb M n = 257.5 ft − kips > 172.4 ft − kips (OK)
TMgn;rbs;rUbragenHFMCagkarsnμt;dMbUgbnþic b:uEnþTMgn;EdlbEnßmenHminGaceRbobeFobnwg moment
capacity d¾FMenaH)aneT.
φvVn = 141kips > 22.98kips (OK)
cMeLIy³ eRbI W 21× 44 .
5>11> rn§RbehagenAkñúgFñwm Holes in Beam
RbsinebIkartP¢ab;FñwmRtUv)aneFVIeLIgCamYyb‘ULúg søab b¤RTnugrbs;FñwmRtUv)anecaHRbehag
b¤xYg. elIsBIenH eBlxøHRTnugFñwmRtUv)anecaHrn§FM²edIm,Irt;eRKOgbrikçaepSg²dUcCa bMBugExSePøIg
GKÁisnI bMBugxül;CaedIm. eKcUlcitþecaHrn§enAelIRTnugFñwmRtg;kEnøgNaEdlmankMlaMgkat;TTwgtUc
ehIyrn§RbehagRtUv)anecaHenAelIsøabRtg;kEnøgNaEdlmanm:Um:g;tUc. b:uEnþeKminGaceFVIEbbenH)an
rhUteT dUcenHeKRtUvKitBIT§iBlrbs;rn§Rbehag.
sMrab;rn§RbehagtUc dUcsMrab;b‘ULúg T§iBlrbs;vanwgtUc CaBiesssMrab; flexure edaymUl
ehtuBIr. TI1KW karkat;bnßymuxkat;tUc. TI2KW muxkat;EdlenAEk,rmin)ankat;bnßy ehIykarpøas;
bþÚrmuxkat;énPaBminCab;tUcFMCag “weak link”.
dUcenH AISC B10 GnuBaØateGayecalnUvT§iBlrbslrn§RbehagenAeBlEdl
0.75 Fu A fn ≥ 0.9 Fy A fg (AISC Equation B10-1)
Edl A fg = gross flange are
A fn = net flange are
RbsinebIeKminCYbnUvlkçxNÐenHeT flexural properties RtUvEtQrelIRkLaépÞsøabrgkarTajRbsiT§
PaB
5 Fu
A fe = A fn (AISC Equation B10-3)
6 Fy
157 Fñwm

45. T.chhay
]TahrN_ 5>14³ KNna elastic section modulus EdlRtUv)ankat;bnßy S x sMrab;muxkat;Edl
bgðajenAkñúgrUbTI 5>32. eKeRbIEdk A36 nigRbehagsMrab;b‘ULúgGgát;p©it 1in. .
dMeNaHRsay³ A fg = b f t f = 7.635(0.81) = 6.184in 2
Ggát;p©itRbehagRbsiT§PaBKW
1 1
dh =1+ =1 in.
8 8
net flange area KW
A fn = A fg − ∑ d h t f = 6.184 − 2(1.125)(0.810 ) = 4.362in.2
BI AISC Equation B10-1
0.75 Fu A fn = 0.75(58)(4.362 ) = 189.7kips
nig 0.9Fy A fg = 0.9(36)(6.184) = 200.4kips
edaysar 0.75Fu A fn < 0.9Fy A fg eyIgRtUvEtKitrn§Rbehag. edayeRbI AISC Equation B10-3
eGayRkLaépÞsøabRbsiT§PaB
5 Fu 5 ⎛ 58 ⎞
A fg = A fn = ⎜ ⎟4.362 = 5.856in.2
6 Fy 6 ⎝ 36 ⎠
RkLaépÞsøabenHRtUvKñanwgkarkat;bnßyeday 6.184 − 5.856 = 0.328in.2 . GkS½NWteGLasÞicsßitenA
cMgay y BIkMBUlrbs;muxkat;
20.8(18.47 / 2 ) − 0.328(18.47 − 0.405)
y= = 9.094in.
20.8 − 0.328
m:Um:g;niclPaBEdlRtUv)ankat;bnßyKW
I x . = 1170 + 20.8(9.094 − 9.235)2 − 0.328(9.094 − 18.06)2 = 1144in.4
Sx sMrab;søabxagelIKW
158 Fñwm

46. T.chhay
I 1144
Sx = x = = 126in.3
y 9.094
Sx sMrab;søabxageRkamKW
Ix 1144
Sx = = = 122in.3
d−y 18.47 − 9.094
cMeLIy³ The reduced elastic section modulus sMrab;EpñkxagelIKW 126in.3 nigsMrab;EpñkxageRkamKW
122in.3 .
FñwmEdlmanrn§RbehagFMenAelIRTnug RtUvkarkarKNnaBiessEdlminmanerobrab;enAkñúgesov
ePAenHeT. Design of Steel and Composite Beam with Web Openings KWCakarENnaMd¾manRb
eyaCn_sMrab;RbFanbTenH (Darwin, 1990).
5>12> Open-Web Steel Joists
Open-web steel joists CaRbePT truss EdlplitrYcCaeRscdUcbgðajenAkñúgrUbTI 5>33.
Open-web steel joists xøHEdlmanTMhMtUc eRbIr)arEdkmUlCab;sMrab;eFVICaGgát;RTnug (web member)
ehIyvaRtUv)aneKehA bar joists. vaRtUv)aneKeRbIenAkñúgkMral nigRbBn§½dMbUlsMrab;eRKOgbgÁúMCaeRcIn.
sMrab;RbEvgElVgEdleGaydUcKña open-web steel joists manTMgn;RsalCag rolled shapes ehIyGvtþ
manrbs;RTnugtan;GnuBaØateGayeKrt;RbBn§½brikçay:agRsYl. GaRs½yeTAnwgRbEvgElVg open-web
steel joist manlkçN³esdækic©Cag rolled shapes eTaHbICavaKñaeKalkarN_ENnaMsMrab;karkMNt;vak¾
eday.
eKGacrk open-web steel joists CamYynwgkMBs;sþg;dar niglT§PaBRTbnÞúkBIeragcRkCaeRcIn.
Open-web steel joist xøHRtUv)anKNnaedIm,IeFVIkarCa floor b¤ roof joists ehIy open-web steel
joists xøHeTotRtUv)anKNnaedIm,IeFVIkarCa girder EdlRTRbtikmμEdlRbmUlpþúMBI joists. AISC
Specification min)anerobrab;BI open-web steel joists eT Etsßabn½mYyepSgeTotEdleKehAfa Steel
Joist Institute (SJI) manBiBN’naBIva. ral;kareRbIR)as; steel joists rYmTaMgkarKNna nigkarplit
RtUv)ane)aHBum<pSayenAkñúg Standard Specifications, Load Tables, nig Weight Table for Steel
Joists and Joist Girders (SJI, 1994).
159 Fñwm

47. T.chhay
eKGaceRCIserIs open-web steel joists CamYynwg the aid of the standard load tables (SJI,
1994) ehIytaragmYyenAkñúgcMeNamenaHRtUv)anbgðajenAkñúgrUbTI 5>34 . CamYynwgkarpSMKñarvag
ElVg nig joist eKnwgTTYl)antMélbnÞúkmYyKUr. elxxagelICa total service load capacity KitCa
pounds kñúgmYy foot ehIyelxenAxageRkamCa service live load kñúgmYy foot EdlnwgbegáItPaBdab
esμInwg 1/ 360 énRbEvgElVg. ¬eTaHbICabnÞúkenAkñúgtaragCa service load capacities k¾eday k¾eK
GaceRbItaragenHy:aggayRsYlCamYynwgviFI LRFD EdleyIgnwgbgðajenATIenH¦. elxdMbUgénelx
160 Fñwm

48. T.chhay
sMKal;CakMBs;rbs; open-web steel joist EdlKitCa in. . taragk¾eGaypg EdrnUvTMgn;Rbhak;Rb
EhlEdlKitCa pound kñúgmYy foot énRbEvg.
eKGacrk open-web steel joists EdlRtUv)anKNnaedIm,ImannaTICa floor or roof joist ¬Edl
pÞúyBImannaTICa girder¦ Ca open-web steel joist (K-series, both standard and KCS), longspan
steel joists (LH-series), nig deep longspan steel joist (DLH-series). enAeBleyIgrMkilesrIeLIg
kan;Etx<s; eyIgnwgTTYl)anRbEvgElVg niglT§PaBRTbnÞúkkan;EtFM. Ca]TahrN_ 8K1 manRbEvg
ElVg 8 ft. niglT§PaBRTbnÞúk 550lb / ft. b:uEnþ 72DLH19 GacRTbnÞúk)an 497lb / ft. elIRbEvg 144 ft. .
edayelIkElg KCS joists, open-web steel joists TaMgGs;RtUv)anKNnaCa trusses EdlRT
edayTMrsamBaØ CamYynwgbnÞúkBRgayesμIenAelI top chord. kardak;bnÞúkenHeFVIeGay top chord rgnUv
bending k¾dUc axial compression dUcenH top chord RtUv)anKNnaCa beam-column ¬emIlCMBUk 6¦.
edIm,IFananUvesßrPaBrbs; top chord eKRtUvP¢ab; the floor or roof deck kñúgviFIEbbNaedIm,IeFVIeGay
man continuous lateral support.
TaMg top nig bottom chord members rbs; K-series joists RtUv)anplitedayEdkEdlman
yield stress 50ksi . lT§PaBRTbnÞúkrbs; K-series joists RtUv)anepÞógpÞat;edaykarBiesaFn_ ehIy
emKuNsuvtßiPaBGb,brmaRtUv)anbgðajeGayeXIjesμInwg 1.65 .
viFIsaRsþd¾samBaØsMrab;eRbIR)as; standard load tables CamYynwg LRFD RtUv)anENnaMeday
SJI (1994) ehIyRtUv)anbgðajenATIenH kñúgTMrg;EkERbbnþicbnþÜc. BicarNa TMnak;TMngeKal LRFD
smIkar @>#³
∑ γ i Qi ≤ φRn
vaRtUv)ansresrsMrab;bnÞúkBRgayesμIkñúgTMrg;Ca
wu ≤ φwn ¬%>&¦
Edl wu CabnÞúkBRgayesμIemKuN nig wn Ca nominal uniform load strength of the joist. Rbsin
ebIeyIgeRbIpleFobmFümén nominal strength elI allowable strength esμInwg 1.65 eyIgGac *
sresr nominal strength eday
wn = 1.65wsji
*
cMNaMfaemKuNsuvtßiPaBsMrab; K-series joists RtUv)ankMNt;edaykarBesaFn_EdleFVIelIgedayplitkr.
161 Fñwm

49. T.chhay
Edl wsji Ca allowable strength (allowable load) EdleGayenAkñúg standard load tables.
Design strength KW
( )
φwn = 0.9 1.65wsji = 1.485wsji ≈ 3 2 wsji
LÚveyIgGacsresrsmIkar %>& Ca
wu ≤ 3 2 wsji
sMrab;eKalbMNgénkarKNna eyIgGacsresrTMnak;TMngenHCa
required wsji = 2 3 wu
]TahrN_ 5>15³ eRbI load table EdleGayenAkñúg rUbTI 5>34 eRCIserIs open-web steel joist
sMrab;RbBn§½kMral nigbnÞúkxageRkam.
Joist spacing = 3 ft
Span length = 20 ft
bnÞúkKW³ kMralxNнkMras; 3in.
bnÞúkefrepSgeTot = 20 psf
bnÞúkGefr = 50 psf
dMeNaHRsay³ sMrab;bnÞúkefr
kMralxNн³ 50⎛⎝⎜ 12 ⎞⎟⎠ = 37.5 psf
3
bnÞúkefrepSgeTot = 20 psf
TMgn;rbs; joist = 3 psf ¬]bma¦
srub = 60.5 psf
wD = 60.5(3) = 181.5lb / ft
sMrab;bnÞúkGefr 50 psf
wL = 50(3) = 150lb / ft
bnÞúkemKuNKW
wu = 1.2 wD + 1.6 wL = 1.2(181.5) + 1.6(150 ) = 457.8lb' ft
bMElgbnÞúkenHeTACa required service load³
wu = (457.8) = 305lb / ft
2 2
required wsji =
3 3
162 Fñwm

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”.
163 Fñwm

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
164 Fñwm

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)
165 Fñwm

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
166 Fñwm

54. T.chhay
Edl Ru / BN Ca bearing pressure mFümrvagbnÞHnigebtug. sMrab;muxkat;ctuekaNEkg
EdlekageFobGkS½exSay (minor axis) enaH nominal moment strength M u esμInwg plastic
moment capacity M p . dUcbgðajenAkñúgrUbTI 5>39 plastic moment sMrab;muxkat;ctuekaNEkg
EdlmanTMhMTTwgmYyÉktþa nigkMras; t KW
⎛ t ⎞⎛ t ⎞ t2
M p = Fy ⎜1× ⎟⎜ ⎟ = Fy
⎝ 2 ⎠⎝ 2 ⎠ 4
edaysar φb M n RtUvEttUcCag M u
φb M n ≥ M u
t 2 Ru n 2
0 .9 F y ≥
4 2 BN
2 Ru n 2 2.222 Ru n 2
t≥
0.9 BNF y
b¤ t≥
BNF y
¬%>* / %>(¦
]TahrN_ 5>16³ KNna bearing plate edIm,IEbgEckRbtikmμrbs; W 21× 68 CamYynwgRbEvgElVg
15 ft. 10in. KitBIGkS½eTAGkS½rbs;TMr. Service load srub EdlKitbBa©ÚlTaMgTMgn;FñwmKW 9kips / ft
EdlmanbnÞúkefr nigbnÞúkGefresμIKña. FñwmRtUv)anRTenABIelICBa¢aMgebtugGarem:Edlman
f 'c = 3500 psi . TaMgbnÞHEdk nigFñwmCaEdk A36 .
dMeNaHRsay³ bnÞúkemKuNKW
wu = 1.2wD + 1.6wL = 1.2(4.5) + 1.6(4.5) = 12.6kips / ft.
ehIyRbtikmμKW
w L 12.6(15.83)
Ru = u = = 99.73kips
2 2
kMNt;RbEvgrbs; bearing N EdlcaM)ac;edIm,IkarBar web yielding. BI AISC Equation K1-3,
design strength sMrab;sßanPaBkMNt;enHKW
Rn = (2.5k + N )Fy t w
sMrab; φRn ≥ Ru /
1[2.5(1.438) + N ](36 )(0.430 ) ≥ 99.73
N ≥ 2.85in.
167 Fñwm

55. T.chhay
eRbI AISC Equation K1-5edIm,IkMNt;tMélrbs; N EdlcaM)ac;edIm,IkarBar web crippling. snμt;
N / d ≥ 0.2 nigsakl,gTMrg;TIBIrrbs;smIkar. sMrab; φRn ≥ Ru /
⎡ 1.5 ⎤
2⎢ ⎛ N ⎞⎛ t w ⎞ ⎥ Fy t f
φ 68t w 1 + ⎜ 4 − 0.2 ⎟⎜ ⎟ ≥ Ru
⎢ ⎝ d ⎠⎜ t f ⎟ ⎥
⎝ ⎠ tw
⎢
⎣ ⎥
⎦
⎡ ⎛ 4N ⎞⎛ 0.43 ⎞ ⎤ 36(0.685)
1.5
0.75(68)(0.43) ⎢1 + ⎜
2
− 0.2 ⎟⎜ ⎟ ⎥ ≥ 99.73
⎢ ⎝ 21.13
⎣ ⎠⎝ 0.685 ⎠ ⎥ ⎦
0.43
N ≥ 5.27in. (controls)
RtYtBinitükarsnμt;
N 5.268
= = 0.25 > 0.2 (OK)
d 21.13
sakl,g N = 6in. . kMNt;TMhM B BI bearing strength. karsnμt;EdlmansuvtßiPaBKWRkLaépÞeBj
TaMgGs;rbs;TMrRtUv)aneRbI.
φc (0.85) f 'c A1 ≥ Ru
0.6(0.85)(3.5)A1 ≥ 99.73
A1 ≥ 55.87in 2
tMélGb,brmarbs;TMhM B KW
A 55.87
B= 1 = = 9.31in.
N 6
TTwgsøabrbs; W 21× 68 KW 8.270in. EdleFVIeGaybnÞHEdkFMCagsøabbnþic EdleKcg;)an. sakl,g
B = 10in. .
kMNt;kMras;bnÞHEdkEdlcaM)ac;
B − 2k 10 − 2(1.438)
n= = = 3.562in.
2 2
BIsmIkar ¬%>(¦
2.222 Ru n 2 2.222(99.73)(3.562 )2
t= = = 1.14in.
BNF y 10(6 )(36 )
cMeLIy³ eRbI PL1 14 × 6 ×10 .
168 Fñwm