1) This document discusses allowable stress design (ASD) based on the 1989 AISC specification for structural steel design. It compares ASD to load and resistance factor design (LRFD) and outlines the key differences between the two approaches. 2) Formulas and examples are provided for calculating allowable stresses in tension members based on yielding and fracture, as well as for calculating allowable stresses in compression members based on buckling strength. 3) The document notes that while the AISC Manual still references the older ASD approach, the specification has been updated to the LRFD method, and engineers should follow the specification over the manual.

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