1. NPIC
Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat
Structural Steel Design Based on Allowable Stress
B >1> esckþIepþIm Introduction
PaBxusKñacMbgrvag allowable stress design nig loads and resistance factor design
KWemKuNsuvtßiPaB. * enAkñúg LRFD eKGnuvtþemKuNbnÞúkeTAelIbnÞúk nigemKuNersIusþg;eTAelIersIusþg;.
elIsBIenH tMélrbs;emKuNbnÞúkGaRs½ynwgRbePTrbs;bnÞúk nigkarbnSMbnÞúk. enAkñúg allowable
stress design (ASD) eKeRbIEtemKuNsuvtßiPaBmYyKt; ehIyvaRtUv)anGnuvtþeTAelIkugRtaMgEdl
manenAkñúgsßanPaBkMNt;. sßanPaBkMNt;rbs; ASD KWRsedogKñasMrab; LEFD KW yielding, fraturee
nig buckling. eKalkarN_rbs;allozable stress analysis and design KWmandUcteTA³
kugRtaMgenAkñúgsßanPaBkMNt;RtUv)anEckCamYynwgemKuNsuvtßiPaBedIm,ITTYl)ankugRtaMgGnuBaØat
ehIykugRtaMgGb,brmaEdlekIteLIgeday service load dac;xatminRtUvFMCagkugRtaMgGnuBaØatenH
eT. ]TahrN_ sMrab;kMlaMgTajtamG½kS
P
ft = ≤ Ft (B.1)
A
Edl kugRtaMgTajKNna
ft =
P = bnÞúkTajtamG½kSeFVIkar
Ft = kugRtaMgTajGnuBaØt
kugRtaMgTajGnuBaØtGacCaplEckrvag yield stress CamYynwgemKuNsuvtßiPaB b¤CaplEckrvag
ultimate tensile stress CamYynwgemKuNsuvtßiPaBepSgeTot. eyIgnwgerobrab;BIGgát;rgkarTajlMGit
enAkñúgEpñk B>2.
eKeRbI ASD sMrab;eRKOgbgÁúMEdkmuneBlEdlmankarENnaMBI LRFD Specification enAkñúgqñaM
1989. kare)aHBum<elIkcugeRkayrbs; ASD Specifcation (AISC, 1989b) ehIynig Manual of
steel Construction (AISC, 1989a) RtUv)anpSBVpSayenAkñúgqñaM 1989. karerobcMÉksarrbs;Éksar
TaMgBIrxagelImanlkçN³RsedogKñanwgkarerobcMÉksarrbs; LRFD Edr. eKEbgEck Specification
CaCMBUk ¬]TahrN_ “Chapter D, Tension members”¦ ehIy Manual RtUv)anEbgEckCaEpñk ¬dUcCa
“Part 2, Beam and Girder Design”¦. enAkñúg Specification mankarENnaM eday Commentary.
*
snμt;faeyIgsÁal; nigyl;BI AISC LRFD Specification nig Manual
473 Appendix B

2. T.Chhay
nimitþsBaØaenAkñúgsmIkar B.1 manlkçN³RsedogKñaeTAnwgkareRbIR)as;enAkñúg Specification.
eKeRbIGkSr f sMrab;kugRtaMgEdlKNnaCak;Esþg nigeKeRbIGkSr F sMrab;kugRtaMgGnuBaØat. snÞsSn_
R)ab;BIRbePTkugRtaMg.
edaysar]bsm<½n§enHRKan;EtCaesckþIENnaM dUcenHeyIgminRtUvkareRbIelxEpñkrbs; AISC
Specification b¤elxsmIkareT. smIkarenAkñúg]bsm<½n§enHykecjBI Specification EtelxsmIkar
RtUv)andak;eTAedayxøÜneyIg. elIsBIenH enAeBlEdleyIgeRbIBakü Specification b¤ Manual enA
kñúg]bsm<½n§enH )ann½faeyIgeRbI allowable stress elIkElgEtmankarENnaM.
Ggát;CaeRcInénkarKNnaeRKOgbgÁúMEdkKWRsedogKñasMrab; ASD nig LRFD. ]TahrN_ net
area sMrab;Ggát;rgkarTajKWdUcKña rYmbBa©ÚlTaMg s 2 / 4 g sMrab; staggered holed ¬kartMerobrn§qøas;¦
nigemKuN U sMrab; shear leg ¬eTaHbICa ASD Specification eRbItMélmFümrbs; U nigdak;smIkar
sMrab; U enAkñúg Commentary k¾eday k¾eKeRbIGVIEdlmanenAkñúg LRFD Specification Edr¦.
niymn½yrbs; compact member, noncompact member neg slender member KWdUcKña b:uEnþ LRFD
Specication cugeRkaymankarEklMGeRcIn. CaTUeTA enAeBlmanPaBminRtUvKñarvag ASD nig LRFD
provision eKKYredaHRsayedayQrelI LRFD Specification eRBaHvaTan;sm½ykal.
eTaHCavaminmanemKuNbnÞúkenAkñúg allowable stress design k¾eday eKenAEtGacKit
bnÞúksMxanepSg²enAkñúgkarbnSMbnÞúkEdr. ]TahrN_ CaTUeTAeKeRbIbnSMbnÞúksMrab;eRKOgbgÁúMdMbUldUc
teTA³ D + S / D + W / D + (S / 2) + W nig D + S + (W / 3) . elIsBIenH Specification GnuBaØat
eGay allowable stress ekIneLIgmYyPaKbIenAeBleKrab;bBa©ÚlbnÞúkxül; nigbnÞúkrBa¢ÜydI. Building
code CaeRcInk¾mankarpþl;EbbenHEdr.
ASD Manual k¾mantarag nigdüaRkamCaeRcInRsedogKñanwg LRFD Manual Edr. eyIgnwg
elIkykEttarag b¤düaRkamNaEdlsMxan;mkbkRsayenAkñúgkarENnaMd¾segçbenH.
B >2> Ggát;rgkarTaj Tension members
BIsmIkar B.1 kugRtaMgTajtamG½kSEdlKNnaKW ft = P / A . Allowable stress KWQrelI
sßanPaBkMNt; yielding nig fracture EdleRKaHfñak;CageK. sMrab; yielding rbs; gross section kug
RtaMgGnuvtþn_KW
474 Appendix B

3. NPIC
P
ft = (B.2)
Ag
Edl Ag Ca gross cross-sectional area. The factor of safety sMrab;sßanPaBkMNt;enHKW 5 / 3
ehIykugRtaMgGnuBaØatKW
Fy Fy
Ft = = = 0.6 Fy (B.3)
F .S . 5/3
sMrab; fracture rbs; net section
P
ft = (B.4)
Ae
Edl Ae Ca effective net area. emKuNsuvtßiPaBKW 2.0 EdllT§plrbs;kugRtaMgGnuBaØatKW
Fu F
Ft = = u = 0.5 Fu (B.5)
F .S 2
]TahrN_ B>1³ RtYtBinitükugRtaMgenAkñúgGgát;rgkarTajEdlbgðajenAkñúgrUbTI B>1 EdlekItBIbnÞúk
eFIVkar 50kips . eKeRbIEdkRbePT A36 nigb‘ULúgGgát;p©it 7 8 in. .
dMeNaHRsay³ BIsmIkar B.2 nig B.3 kugRtaMgGnuvtþn_enAelI gross section KW
P 50
ft = = = 20.2ksi
Ag 2.48
ehIykugRtaMgGnuBaØatKW
Ft = 0.5Fy = 0.60(36) = 21.6ksi > 20.2ksi (OK)
kugRtaMgenAelI net area KW
An = Ag − (thickness × hole diameter )
3⎛ 7 1⎞
= 2.48 − ⎜ + ⎟ = 2.105in.2
8⎝ 8 8⎠
RbsinebIeyIgeRbItMélmFüm U enaH effective net area KW
475 Appendix B

4. T.Chhay
Ae = UAn = 0.85 An = 0.85(2.105) = 1.789in.2
sMrab;smIkar B.4 nig B.5
P 50
ft = = = 27.9ksi
Ae 1.789
Ft = 0.50 Fu = 0.50(58) = 29ksi > 27.9ksi (OK)
cemøIy³ Ggát;KWmanlkçN³RKb;RKan;.
B>3> Ggát;rgkarsgát; Compression members
kugRtaMgenAkñúgGgát;Edlrgkarsgát;tamG½kSKW
P
fa =
Ag
kugRtaMgGnuBaØat EdlsMKal;eday Fa RtUv)anTTYledayEck critical buckling load CamYy
nwgemKuNsuvtßiPaB. emKuNsuvtßiPaBsMrab;ssreGLasÞic (slender column) mantMélefr ehIyem
KuNsMrab;ssr inelastic mantMélERbRbYl. enAkñúg ASD ersIusþg;rgkarsgát;RtUv)ansresrCa
GnuKmn_én slenderness ratio KL / r b:uEnþenAkñúg LRFD ersIusþg;CaGnuKmn_eTAnwg λc =
(KL / rπ ) Fy / E . enAkñúgtMbn;eGLasÞic kugRtaMgeRKaHfñak;KWplEckrvag Euler buckling load
nwgRkLaépÞ b¤
Pcr π EAg
2
π 2E
Fcr = = ÷ Ag =
Ag ( )
KL / r 2 (KL / r )2
(B.6)
sMrab;tMbn; elastic EdnsmamaRtRtUv)ansnμt;esμInwg Fy / 2 eKnwgeRbIsmIkarEdl)anBIkarBiesaFdUc
xageRkamCMnYseGay tangent modulus formula³
⎡ (KL / r )2 ⎤
Fcr = Fy ⎢1 − 2 ⎥
(B.7)
⎢
⎣ 2Cc ⎥ ⎦
Edl Cc tMélrbs; KL / r EdlRtUvKñanwgkugRtaMg Fy / 2 . smIkar B.7 bgðajBIExS)a:ra:bUlEdlb:H
nwgExSekag Euler enARtg; KL / r = Cc ehIyb:HeTAnwgbnÞat;edkenARtg; KL / r = 0 . eyIgGacrk
smIkarsMrab; Cc edayEpñkxagsþaMrbs;smIkar B.6 esμInwg Fy / 2 ³
Fy π 2E π 2E
= =
2 (KL / r )2 2
Cc
2π 2 E
eyIgTTYl)an Cc =
Fy
(B.8)
476 Appendix B

5. NPIC
munnwgkarGnuvtþemKuNsuvtßiPaB ersIusþg;ssrelItMbn; slanderness eBj RtUv)anbgðajedayRkaPic
enAkñúgrUbTI B>2.
edIm,ITTYlnUvkugRtaMgsgát;GnuBaØat eyIgEcksmIkar B.6 nig B.7 CamYynwgemKuNsuvtßiPaB.
emKuNsuvtßiPaBsMrab;ssreGLasÞicKW 23 /12 . sMrab;ssr inelastic eKeRbIemKuNEdlERbRbYldUc
xageRkam³
5 3(KL / r ) (KL / r )3
F .S . = + − 3
3 8Cc 8Cc
smIkarenHmantMél 5 / 3 enAeBl KL / r = 0 ¬dUcKñasMrab; yielding rbs;Ggát;rgkarTaj¦ ehIy
tMél 23 /12 enAeBl KL / r = Cc ¬RbEhl 15% eRcInCag 5 / 3 ¦. edayEcksmIkarersIusþg;CamYy
emKuNsuvtßiPaBEdlsmRsb eyIgTTYl)ankugRtaMgGnuBaØatdUcxageRkam³
sMrab; KL / r < Cc
⎡ (KL / r )2 ⎤
Fy ⎢1 − 2 ⎥
⎢
⎣ 2Cc ⎥ ⎦
Fa = (B.9)
5 3(KL / r ) (KL / r )3
+ − 3
3 8Cc 8Cc
sMrab; KL / r > Cc
π 2E 23 12π 2 E
Fa = ÷ = (B.10)
(KL / r )2 12 23(KL / r )2
sMrab;Ggát;Edlmanmuxkat; slender eKRtUveFVIkarkat;bnßykugRtaMgGnuBaØatedIm,IKitBIlT§PaBEdlGac
ekItman local buckling. eKTTYlemKuNkat;bnßyenHBI appendix EdlmanenAkñúg Specification.
477 Appendix B

6. T.Chhay
]TahrN_ B>2³ kMNt;bnÞúkeFVIkarGnuBaØat P sMrab;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI B>3.
dMeNaHRsay³ RtYtBinitüemIlfaetIGgát;CaGgát;Edlmanmuxkat; slenderb¤Gt;. pleFobTTwgelI
kMras;sMrab;Ggát;rgkarsgát;EdleGayenAkñúg ASD Specification manlkçN³dUcKñaenAkñúg LRFD
Specification:
bf
2t f
= 6 .4 ¬BI properties table EdlmanenAkñúg Manual¦
95 95
= = 15.8 > 6.4 (OK)
Fy 36
h
= 25.3
tw
253 253
= = 42.2 > 25.3 (OK)
Fy 36
kugRtaMgKW f a = P / Ag dUcenHbnÞúkEdlRtUvKñaKW P = f a Ag ehIybnÞúksgát;GnuBaØtKW Fa Ag . BI
smIkar B.8
2π 2 E 2π 2 (29000)
Cc = = = 126.1
Fy 36
pleFob slenderness GtibrmaKW
KL KL KL 1.0(20)(12)
= = = = 96.77
r rmin ry 2.48
lT§plEdlTTYl)antUcCag Cc dUcenHeKGacrk Fa BIsmIkar B.9:
478 Appendix B

7. NPIC
⎡ (KL / r )2 ⎤ ⎡ (96.77 )2 ⎤
Fy ⎢1 − ⎥ 36 ⎢1 − 2⎥
⎢ 2(126.1) ⎥
2
⎢
⎣ 2Cc ⎥ ⎦ ⎣ ⎦
Fa = = = 13.38ksi
5 3(KL / r ) (KL / r ) 3
5 3(96.77 ) (96.77 )3
+ − + −
3 8Cc 8Cc 3 3 8(126.1) 8(126.1)3
cemøIy³ P = F Aa g = 13.38(21.8) = 292kips
Design Aids
ASD manual man column design aids EdlmanTMrg;RsedogKñaenAkñúg LRFD Manual.
kñúgcMeNam aids TaMgenHPaKeRcInCataragsMrab;bnÞúktamG½kSGnuBaØat. enAeBleKbBa©ÚlRbEvgRbsiT§-
PaB KL niglT§PaBRTbnÞúkeFVIkarEdlTamTareTAkñúgtarag eKGacrk)annUvmuxkat;EdlmanlT§PaB
RKb;RKan;)any:agelOn. dUcKñanwg LRFD column load table Edr eKKYeRbIRbEvgRbsiT§PaB K y L
eFobnwgkaMniclPaBGb,brma ry . müa:geToteKGacbBa©Úl K x L / (rx / ry ) .
enAeBlEdleKrkemKuNRbEvgRbsiT§PaB K BI Jackson-Mooreland alignment chart eK
GacGnuvtþemKuNkat;bnßy stiffness RbsinebIssrCa inelastic enAeBl)ak; (KL / r < Cc ) . Manual
k¾pþl;taragsMrab;karcg;)anenHEdr.
B >4> Fñwm Beams
kugRtaMgBt;GtibrmaenAkñúg homogeneous beam EdlminmankugRtaMgeRkABIEdnsmamaRt
RtUv)aneGayeday flexural formula³
Mc M M
fb = = =
I I /c S
Edl M= m:Um:g;Bt;GtibrmaenAkñúgFñwm
c = cMgayBIG½kSNWteTAsésreRkAeKbMput
I = m:Um:g;niclPaBeFobG½kSBt;
S = m:UDulmuxkat;eGLasÞic
karBN’nakñúgEpñkenHRtUv)ankMNt;Rtwm hot-rolled I nig H-shaeped cross section EdlrgkarBt;
eFobG½kSEkgeTAnwgRTnug ¬G½kS x ¦.
kugRtaMgBt;GnuBaØatRtUv)ansMKal;eday Fb nigQrelIsßanPaBkMNt;dUcteTA³ yilding, local
buckling b¤ lateral-torional buckling. enAkñúg ASD eKnwgmanPaBgayRsYlRbsinebI eKbMEbkFñwm
479 Appendix B

8. T.Chhay
CaBIrKW³ FñwmEdlmanTMrxag (laterally supported beam) nigFñwmEdlminmanTMrxag (laterally
unsupported beam). RbsinebIFñwmman lateral support RKb;RKan; kugRtaMgGnuBaØatnwgQrelI
yielding kñúgkrNImuxkat; compact ehIyvanwgQrelI local buckling kñúgkrNImuxkat; uncompact.
kugRtaMgBt;GnuBaØatsMrab; laterally unsupported beams nwgQrelI lateral-torsional buckling.
Lateral support
eKKitfaFñwmEdlman man lateral support RKb;RKan;edIm,IkarBar
unbraced length Lb lateral-
torsional buckling enAeBlEdl Lb ≤ Lc Edl Lc CatMéltUcCageKkñúgcMeNam
76b f 20000
Lc = ≤
Fy ( )
d / A f Fy
(US) (B.12)
200b f 137900
Lc = ≤
Fy (d / A f Fy ) (IS)
eyIgeRbIlkçxNÐenHedIm,IkMNt;cMNat;fñak;rbs;FñwmfaCa laterally supported b¤ laterally
unsupported.
Laterally Supported Beams
RbsinebI laterally supported beam GacrgkugRtaMgdl;cMnuc yield edayKμan local buckling enaHem
KuNsuvtßiPaBKW 5 / 3 ehIykugRtaMgGnuBaØatKW
Fy Fy
Fb = = = 0.60 Fy
F .S . 5/3
lkçxNÐenHRtUvnwgrUbragEdlmanpleFobTTwgelIkMras;sßitenAEdnkMNt;x<s;bMputsMrab; noncompact-
ness Edl b f / 2t f = 95 / Fy (US) b¤ b f / 2t f = 250 / Fy (IS). ¬EdnkMNt;enHxusKñaBIEdn
kMNt;rbs; LRFD b:uEnþeKeRbIvaenATIenH edaysarvaminTak;TgenAkñúgsmIkar AISC sMrab; ASD¦.
RbsinebImuxkat;enH compact eKGacTTYllkçxNÐ)aøsÞiceBjedayKμan local buckling ehIyeK
GnuBaØateGaybEnßm 10% sMrab;kugRtaMgGnuBaØat. dUcenHkñúgkrNIenH kugRtaMgGnuBaØatKW
(
Fb = 1.10 0.60 Fy = 0.66 Fy )
sMrab; noncompact shape, AISC eRbI linear transition cenøaH 0.6Fy nig 0.66Fy edayQrelItMél
b f / 2t f . RKb; hot-rolled I- and H-shapes TaMgGs;enAkñúg Manual man compact web. kugRtaMg
GnuBaØatsMrab;krNIenHeGayenAkúñsmIkarxageRkam³
480 Appendix B

9. NPIC
⎛ bf ⎞
Fb = Fy ⎜ 0.79 − 0.002 Fy ⎟
⎜ 2t f ⎟
⎝ ⎠
rUbTI B >4 bgðajBITMnak;TMngrvagpleFoTTwgelIkMras;CamYynwgkugRtaMgGnuBaØatsMrab; laterally
supported beams. eKedaHRsay slender shape enAkñúg appendix EdlmanenAkñúg Specification
b:uEnþvaminman hot-rolled I- and H-shapes enAkñúg Manual Ca slender eT.
kugRtaMgsMrab; laterally supported beam mandUcxageRkam³
RbsinebIrUbragCa compact
Fb = 0.66 Fy (B.13)
RbsinebIrUbragCa noncompact
⎛ bf ⎞
Fb = Fy ⎜ 0.79 − 0.002 Fy ⎟ (B.14)
⎜ 2t f ⎟
⎝ ⎠
Laterally Unsupported Beams
ersIusþg;rbs; lateral unsupported beam KWQrelIsßanPaBkMNt;rbs; lateral-torsional
buckling. enAkñúg ASD, sßanPaBenHmanBIry:agKW³ uniform warping nig nonuniform warping.
Uniform warping KWmanlkçN³eGLasÞic ehIysßanPaBkMNt;KW
0.65E
fu = (B.15)
Lb d / A f
Edl d= kMBs;srubrbs;Fñwm
A f = RkLaépÞrbs;søabrgkarsgát;
cMENk nonuniform warping GacCa inelastic b¤k¾eGLasÞic. sMrab;eGLasÞic warping, failure
stress KW
481 Appendix B

10. T.Chhay
π 2E
f nu =
(Lb / ry )2
(B.16)
sMrab; inelastic warping, eKeRbIsmIkarEdl)anmkBIkarBiesaFEdlmanlkçN³RsedogKñanwgsmIkar
sMrab;Ggát;rgkarsgát;
f nu
10 ⎡
= Fy ⎢1 −
(
Lb / ry )2 ⎤
⎥ (B.17)
9 ⎢
⎣ 2C 2 ⎥
⎦
Edl C= tMélGtibrmarbs; Lb sMrab; nonuniform warping Ca inelastic ¬RbsinebI Lb > C /
warping Ca elastic¦
E
= 3π
5Fy
Buckling stress EdleGayedaysmIkar B.15-B.17 RtUv)ankMNt;RtwmEdnx<s;bMputrbs; Fy . rUbTI
B.5 bgðajBI uniform warping stress CaGnuKmn_eTAnwg Lb nigrUbTI B.6 bgðajBI nonuniform
warping stress.
482 Appendix B

11. NPIC
edIm,ITTYl)ansmIkar AISC sMrab;kugRtaMgBt;GnuBaØatEdlQrelI lateral-torsional
buckling, eKRtUveFVIkarEktMrUveTAelIsmIkarEdl)anerobrab;BImundUcteTA³
!> eKRtUvEck failure stress TaMgGs;CamYynwgemKuNsuvtßiPaB 5 / 3
@> eKCMnYskaMniclPaB ry eday rT EdlCakaMniclPaBeFobG½kSexSaysMrab;cMENkrbs;mux
kat;Edlmansøabrgkarsgát; nigmYyPaKbIénEpñksgát;rbs;RTnug. tMélenHminCaxusKñaBI
ry EdlmanenAkñúgtaragrbs; ASD Manual eT.
#> RKb;smIkarTaMgGs;RtUv)ansresredaymanpleFob Lb / rT
$> emKuN Cb RtUv)anKitbBa©ÚlsMrab;bMErbMrYlrbs;m:Um:g;Bt;elI unbraced length ¬smIkar
warping KWQrelIm:Um:g;BRgayesμI¦
%> eTaHbICa lateral-torsional buckling strength RtUv)anbMEbkecjBIbgÁúM uniform nig
nonuniform warping k¾eday k¾ AISC eRbIbgÁúMNaEdlmantMélFMCag.
eKGacsegçbsmIkar AISC sMrab;kugRtaMgBt;GnuBaØatsMrab; laterally unsupported beam dUc
xageRkam³
sMrab; Lb < 102000Cb (US) Lb < 703300Cb (IS)
r F r F
T y T y
Fb = 0.60 Fy
sMrab; 102000Cb Lb
Fy
≤
rT
≤
510000Cb
Fy
yktMélEdlFMCageKkñúgcMeNam
⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy (US) (inelastic nonuniform warping) (B.18)
⎢ 3 1530000Cb ⎥
⎣ ⎦
⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy (IS)
⎢ 3 10550000Cb ⎥
⎣ ⎦
nig Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy (US) (uniform warping) (B.19)
82750Cb
Fb = ≤ 0.60 Fy (IS)
Lb d / A f
sMrab; Lb >
r
510000Cb
Fy
(US)
Lb
rT
>
3516500Cb
Fy
(IS)
T
483 Appendix B

12. T.Chhay
yktMélFMCageKkñúgcMeNam
170000Cb
Fb = ≤ 0.60 Fy (US) (elastic nonuniform warping) (B.20)
(Lb / rT )2
1172150Cb
Fb = ≤ 0.60 Fy (IS)
(Lb / rT )2
nig Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy (US) (uniform warping) (B.19)
82750Cb
Fb = ≤ 0.60 Fy (IS)
Lb d / A f
ASD Specification eGaynUvsmIkarsMrab; Cb EdlxusBI Cb EdleGayeday LRFD
Specification b:uEnþeKGaceRbImYyNak¾)an. cMNaMfa eTaHbICa flexural strength Edleyagtam
LRFD KWsmamaRtedaypÞal;eTAnwg Cb k¾eday k¾vaminEmnCakrNIsMrab; allowable stress Edl
eGayedaysmIkar B.18 - B.20 Edr. vamankarsμúKsμajxøHkñúgkarKNna allowable stress rbs;Fñwm.
Shear
kugRtaMgkMlaMgRtUv)anKNnaedayykbnÞúkkMlaMgkat;eFVIkarGtibrmaEcknwgRkLaépÞRTnug.
V V
fv = ≈
Aw t w d
kugRtaMgkMlaMgkat;KWQrelI shear yielding ehIyRtUv)anykesμInwgBIrPaKbIénkugRtaMgTaj
GnuBaØatelI gross section.
Fv =
2
3
2
( )
Ft = 0.60 Fy = 0.40 Fy
3
(B.21)
]TahrN_ B>3³ eKeRbI sMrab;FñwmTMrsamBaØEdlrgbnÞúkBRgayesμIehIyman lateral
W 16 × 100
bracing EtenAxagcugrbs;va. RbsinebIeKeRbIEdkRbePT A36 kMNt;m:Um:g;Bt;eFVIkarGtibrmaEdlFñwm
enHGacTb;)ansMrab;ElVgEdlmanRbEvg (a) 10 ft (b) 15 ft nig (c) 40 ft .
dMeNaHRsay³ dMbUg kMNt; Lc
BIsmIkar B.12
76b f 76(10.42 )
= = 132in = 11 ft
Fy 36
484 Appendix B

13. NPIC
20000 20000
= = 336.0in = 28 ft
( )
d / A f Fy 16.97
(36)
10.42(0.985)
eKyktMélEdltUcCageK dUcenH Lc = 11.0 ft
a) sMrab;ElVgEdlmanRbEvg 10 ft
Lb = 10 ft < Lc
dUcenHFñwmCa laterally supported beam.
eday W 16 ×100 Ca compact shape sMrab;Edk A36 / kugRtaMgGnuBaØatEdl)anBIsmIkar
B.13 KW
Fb = 0.66 Fy = 0.66(36) = 23.76ksi
kugRtaMgBt;GtibrmasMrab;m:Um:g; M EdleGayedaysmIkar B.11 KW f b = M / S dUcenHm:Um:g;
GtibrmaEdlekIteLIgenAeBlkugRtaMg f a esμInwgkugRtaMgGnuBaØat Fb
M = Fb S = 23.76(175) = 4158in. − kips = 346 ft − kips
cemøIy³ a) m:Um:g;Gtibrma = 346 ft − kips
b) sMrab;ElVgEdlmanRbEvg 15 ft
Lb = 15 ft > Lc = 11.0 ft
dUcenHFñwmCa laterally unsupported beam.
rT = 2.81in. ¬tMélenHRtUv)aneGayenAkñúg properties table enAkñúg ASD Manual¦
Lb 15(12 )
= = 64.06
rT 2.81
sMrab;FñwmTMrsamBaØrgbnÞúgBRgayesμIEdlman lateral bracing enAxagcug/ Cb = 1.14 ¬Edl
KNnaCamYynwg LRFD Specification equation b:uEnþeKk¾GaceRbIvaCamYynwg ASD equation
pgEdr¦. kMNt;EdnkMNt;sMrab; Lb / rT
102000Cb 102000(1.14)
= = 56.8
Fy 36
510000Cb 510000(1.14)
= = 127
Fy 36
edaysar 56.8 < Lb / rT < 127 eKeRbIsmIkar B.18 nig B.19
485 Appendix B

14. T.Chhay
⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy
⎢ 3 1530000Cb ⎥
⎣ ⎦
⎡2 36(64.06) 2 ⎤
=⎢ − ⎥36 = 20.95ksi
⎢ 3 1530000(1.14) ⎥
⎣ ⎦
b¤ Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy
12000(1.14)
= = 45.97ksi
(15 × 12)(16.97 ) / (10.42 × 0.985)
lT§plxagelImantMélFMCag 0.60Fy = 0.60(36) = 21.6ksi . dUcenHyk
Fb = 0.60 Fy = 21.6ksi
m:Um:g;Bt;GtibrmaKW
M = Fb S = 21.6(175) = 3780in.kips = 315 ft − kips
cemøIy³ b) m:Um:g;Gtibrma = 315 ft − kips
c) sMrab;ElVgEdlmanRbEvg 40 ft
Lb 40(12) 510000Cb
= = 170.8 > = 127
rT 2.81 Fy
eRbIsmIkar B.19 nig B.20:
170000Cb 170000(1.14)
Fb = = = 6.643ksi < 0.6 Fy
(Lb / rT )2 (170.8)2
12000(1.14)
b¤ Fb =
12000Cb
Lb d / A f
=
(40 ×12)(16.97 ) / (10.42 × 0.985)
= 17.24ksi < 0.60 Fy
yk Fb = 17.24ksi . m:Um:g;GtibramKW
M = Fb S = 17.24(175) = 3017in. − kips = 251 ft − kips
cemøIy³ c) m:Um:g;Gtibrma = 251 ft − kips .
Design Aids
Design aidssMrab;FñwmPaKeRcInEdlmanenAkñúg LRFD Manual k¾manenAkñúg ASD Manual Edr.
varYmmanTaMg design chart EdleGay allowable bending moment CaGnuKmn_én unbraced length
sMrab;rUbragEdleKeRbIsMrab;FñwmCaTUeTA. ExSekagTaMgenHQrelI Cb = 1.0 b:uEnþeKminGaceRbIvaeday
pÞal;sMrab;tMélepSgeTotrbs; Cb eT edaysar allowable stress Fb minsmamaRtedaypÞal;eTAnwg Cb .
486 Appendix B

15. NPIC
B>5> Beam-Columns
eKviPaKGgát;eRKOgbgÁúMEdlrgTaMgkugRtaMgBt; nigkugRtaMgtamG½kSCamYynwgsmIkarGnþrGMeBI
edayKitpleFobkugRtaMgCak;EsþgelIkugRtaMgGnuBaØat. ASD Specification equation KW
f a f bx f by
+ + ≤ 1 .0
Fa Fbx Fby
Edl x nig y sMKal;karBt;tamG½kS. eKeRbIsmIkarBIrenAkñúg Specification³ EdlmYyKNnaCamYy
nwgkugRtaMgBt;EdlQrelIm:Um:g;Gtibrmadac;xatenAkñúgGgát; nigmYyeTotCamYykugRtaMgBt;EdlQrelI
m:Um:g;cugGtibrma. eKeRbI amplification factor EtmYy vaminmanemKuNdac;edayELkkñúgkarKit
sway nig nonsway components. Amplification factor enHmanTMrg;dUcxageRkam³
Cm
1− ( f a / F 'e )
Edl Cm RtUv)ankMNt;esμInwg³
sMrab;Ggát;RbQmnwg sidesway
C m = 0.85
sMrab;Ggát;EdlminRbQmnwg sidesway ehIynigminman transverse load
C m 0.6 − 0.4(M 1 / M 2 ) (B.22)
Edl M 1 nig M 2 Cam:Um:g;enAxagcugrbs;Ggát; ehIyEdltMéldac;xatrbs; M 1 tUcCag.
pleFob M 1 / M 2 viC¢manRbsinebIGgát;ekagDub ehIyvamantMélGviC¢mansMrab;kMeNageTal.
sMrab;Ggát;EdlTb;RbqaMgnwg sidesway ehIyman transverse load
C m = 0.85 RbsinebIcugRtUv)anTb;mineGayvil
C m = 1.0 RbsinebIcugminRtUv)anTb;
emKuN F 'e CaplEckrvag Euler buckling stress CamYynwgemKuNsuvtßiPaB 23 /12 ³
12π 2 E
F 'e = (B.23)
23(KLb / rb )2
GkSr b sMedAelIG½kSénkarBt;. RbsinebIeKBicarNakarBt;eFobnwgG½kS x enaH F 'e = F 'ex nig
KLb / rb = KL x / rx . dUcKñasMrab; F 'ey eRbI K y L / ry .
eKRtUvRtYtBinitüsmIkarGnþrGMeBIxageRkam³
RbsinebI f a / Fa ≤ 0.15 / eKminRtUvkar moment amplification ehIy
487 Appendix B

16. T.Chhay
f a f bx f by
+ + ≤ 1 .0 (B.24)
Fa Fbx Fby
RbsinebI f a / Fa > 0.15 / eKRtUvRtYtBinitüsmIkarTaMgBIrxageRkam³
fa C mx f bx C my f by
+ + ≤ 1 .0 (B.25)
Fa ⎛ fa ⎞ ⎛ fa ⎞
⎜1 −
⎜ F ' ⎟ Fbx ⎜1 −
⎟ ⎟F
⎝ ex ⎠ ⎜ F 'ey ⎟ by
⎝ ⎠
f by
nig fa f
+ bx +
0.6 Fa Fbx Fby
≤ 1 .0 (B.26)
smIkar B.25 CakarRtYtBinitüesßrPaB ehIyeKeRbIm:Um:g;Bt;GtibrmaedIm,IKNna f bx nig f by .
smIkar B.26 EdlmineRbI amplification factor CakarRtYtBinitükugRtaMg ehIyeKeRbIm:Um:g;cugGtibrma
edIm,IKNna f bx nig f by . cMNaMfa eKeRbI 0.60Fy CMnYseGay Fa enAkñúgsmIkar B.26 edaysar
sßanPaBkMNt;Ca yielding CaCag buckling. sMrab;mUlehtudUcKña eKGacBicarNaGgát;Ca laterally
supported member sMrab;karKNna Fbx enAkñúgsmIkar B.26 b:uEnþeKRtUvKitlkçxNÐ lateral bracing
Cak;EsþgenAeyIgeRbIsmIkar B.25 edIm,IRtYtBinitü.
eKalbMNgrbs;emKuN Cmx enAkñúgsmIkar B.25 KWedIm,IKitBI gradient m:Um:g;eFobG½kS x
rbs;Ggát;. enAkñúg laterally supported member eKeRbIemKuN Cb kñúgkarKNna Fbx k¾edIm,IKitBI
gradient Edr. dUcenH Specification yk Cb esμImYyenAeBlEdleKKit Fbx sMrab;eRbIenAkñúgsmIkar
B.25 sMrab;Ggát;EdlBRgwgRbqaMgnwgkarrMkiltMN (members braced againt joint translation).
]TahrN_ B>4³ Beam-column EdlbgðajenAkñúgrUbTI B.7 CaEpñkrbs; braced frame. karBt;KWeFob
nwgG½kS x ehIycugrbs;vaRtUvman lateral bracing . snμt;fa K x = K y = 1.0 cUrviPaKGgát;eday
eKarBtam AISC Specification.
488 Appendix B

17. NPIC
dMeNaHRsay³ kugRtaMgrgkarsgát;tamG½kS
P 100
fa = = = 6.944ksi
Ag 14.4
KNnakugRtaMgsgát;GnuBaØat
Slenderness ration GtibrmaKW
KyL 1.0(15)(12 )
= = 70.87
ry 2.54
BIsmIkar B.8
2π 2 E 2π 2 (29000 )
Cc = = = 126.1
Fy 36
edaysar KL / r ≤ Cc / kMNt;kugRtaMgsgát;GtibrmaCamYysmIkar B.9
⎡ (KL / r )2 ⎤ ⎡ (70.87 )2 ⎤
Fy ⎢1 − 2 ⎥
36⎢1 − 2⎥
⎢
⎣ 2Cc ⎥ ⎦ ⎢ 2(126.1) ⎥
⎣ ⎦
Fa = = = 16.34ksi
5 3(KL / r ) (KL / r )3 5 3(70.87 ) (70.87 )3
+ − + −
3 8Cc 8Cc3 3 8(126.1) 8(126.1)3
f a 6.944
= = 0.4250 > 0.15
Fa 16.34
dUcenHRtYtBinitüsmIkar B.25 nig B.26
M x 60(12 )
f bx = = = 13.19ksi
Sx 54.6
f bv = 0
KNnakugRtaMgBt;GnuBaØat
BIsmIkar B.12
76b f 76(10.00)
= = 126.7in. = 10.6 ft
Fy 36
20000 20000
= = 311.7in. = 26.0 ft
(d / A f Fy ) 9.98
(36)
0.560(10.00)
tMélEdltUcCaglub dUcenH Lc = 10.6 ft . RbEvgenHKWtUcCag unbraced length Lb = 15 ft
dUcenHGgát;enHRtUv)aneKKitCa laterally unsupported beam. edaysarGgát;enHRtUv)anTb;nwg
sidesway dUcenHyk Cb = 1.0
489 Appendix B

18. T.Chhay
102000Cb 102000(1.0 )
= = 53.2
Fy 36
510000Cb 510000(1.0)
= = 119
Fy 36
Lb 15(12 )
rT
=
2.74
= 65.69 ¬ rT RtUv)anerobCataragenAkñúg Manual¦
edaysar 53.2 < Lb / rT < 119 yktMélEdlKNnaCamYynwgsmIkar B.18 nig B.19 EdlFMCagEtmin
RtUvFMCagEdnkMNt;x<s;bMputén
0.60 Fy = 0.60(36) = 21.6ksi
BIsmIkar B.18
⎡ 2 Fy (Lb / rT )2 ⎤ ⎡ 2 36(65.69)2 ⎤
⎢ − ⎥ Fy = ⎢ − ⎥ = 20.34ksi
⎢ 3 1530000Cb ⎥
⎣ ⎦ ⎢ 3 1530000(1.0) ⎥
⎣ ⎦
BIsmIkar B.19
12000Cb 12000(1.0)
= = 37.4ksi
lb d / A f (15 × 12)(9.98) / (0.560 × 10.00)
tMélEdl)ansmIkarTaMgBIrxagelIFMCag 0.6Fy dUcenH
Fbx = 0.60 Fy = 21.6ksi
dMbUgRtYtBinitüsmIkar B.26. enAkñúgsmIkarenH GVIEdlRtUvRtYtBinitüKWlkçxNÐkugRtaMgenARtg;TMr
dUcenHeKRtUvKNnakugRtaMgBt;GnuBaØatrbs;Ggát;enH RbsinebIGgát;rgkarsgát;rbs;vaman full lateral
support. W 16 × 49 Ca compact sMrab;Edk A36 dUcenHeKGacykkugRtaMgGnuBaØat 0.66 Fy . eday
karBt;eFobnwgG½kS x dUcenHeKecaltYEdlTak;TgnwgkarBt;eFobG½kS y . dUcenHeK)an
fa f 6.944 13.19
+ bx = + = 0.877 < 1.0 (OK)
0.60 Fy Fbx 0.60(36 ) 0.66(36)
RtYtBinitüsmIkar B.25
BIsmIkar B.22
M1 ⎛ 35 ⎞
C m = 0 .6 − 0 .4 = 0.6 − 0.4⎜ − ⎟ = 0.8333
M2 ⎝ 60 ⎠
Slenderness ratio EdleRbIkñúgkarKNna F 'ex KW
KLb K x L 1.0(15)(12 )
= = = 41.38
rb rx 4.35
490 Appendix B

19. NPIC
12π 2 E 12π 2 (29000)
ehIy F 'ex = = = 87.21ksi
23(K x L / rx )2 23(41.38)2
fa C mx f bx 0.8333(13.19)
+ = 0.4250 + = 0.978 < 1.0 (OK)
Fa ⎛ fa ⎞ ⎛ 6.944 ⎞
⎜1 −
⎜ F ' ⎟ Fbx ⎟ ⎜1 − ⎟21.6
⎝ ex ⎠ ⎝ 87.21 ⎠
cemøIy³ W 10 × 49 RKb;RKan;
Design Aids
eRkABItarag nigdüaRkamsMrab;KNnassr nigFñwm principal Manual design aid sMrab; beam-
column CataragéntMélefrsMrab;eRbIkñúgkareRCIserIsmuxkat;dMbUg (Burgett, 1973). tMélefrTaMgenH
GaceGayGñkKNnabMElgm:Um:g;Bt;eGayeTACabnÞúktamG½kSsmmUlEdlGacpSMCamYynwgbnÞúkCak;
EsþgedIm,ITTYl)anbnÞúktamG½kSRbsiT§PaBsrub. bnÞab;mkeKGacbBa©ÚlbnÞúktamG½kSRbsiT§PaBenH
eTAkñúg Column allowable load table eKnwgTTYl)anmuxkat;sakl,gEdleKGacykvaeTAsikSa
epÞógpÞat;)an.
B >6> snñidæan Concluding Remarks
eTaHbICa ASD RtUv)anCMnYsy:agelOneday LRFD k¾eday k¾vaenAEtRtUv)anGnuBaØateGay
eRbIeday AISC dEdl ehIyeBlxøHk¾eKenAEteRbIvaEdr. sMrab;GñksikSaEdlmanbMNgcg;dwglMGitBI
ASD elIsBIGVIEdl)anerobrab;kñúg]bsm<½n§enHGacrk)anenAkñúg Design of Steel structure (Gaylord
and stallmeyer, 1992) EdlenAkñúgenaHk¾manerobrab;BI AISC Specification provision pgEdr.
491 Appendix B