NPIC


              Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat
                         Structural Steel D...
T.Chhay


        nimitþsBaØaenAkñúgsmIkar B.1 manlkçN³RsedogKñaeTAnwgkareRbIR)as;enAkñúg Specification.
eKeRbIGkSr f sMra...
NPIC


               P
        ft =                                                               (B.2)
               Ag...
T.Chhay


        Ae = UAn = 0.85 An = 0.85(2.105) = 1.789in.2
sMrab;smIkar B.4 nig B.5
             P     50
        ft =...
NPIC


munnwgkarGnuvtþemKuNsuvtßiPaB ersIusþg;ssrelItMbn;     slanderness   eBj RtUv)anbgðajedayRkaPic
enAkñúgrUbTI B>2.

...
T.Chhay


]TahrN_ B>2³ kMNt;bnÞúkeFVIkarGnuBaØat P sMrab;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI B>3.




dMeNaHRsay³ RtYtBini...
NPIC


                   ⎡ (KL / r )2 ⎤           ⎡ (96.77 )2 ⎤
                Fy ⎢1 −         ⎥        36 ⎢1 −      2⎥
...
T.Chhay


CaBIrKW³ FñwmEdlmanTMrxag (laterally supported beam) nigFñwmEdlminmanTMrxag (laterally
unsupported beam). Rbsine...
NPIC


                ⎛              bf         ⎞
        Fb = Fy ⎜ 0.79 − 0.002         Fy ⎟
                ⎜          ...
T.Chhay


                  π 2E
       f nu =
                (Lb / ry )2
                                               ...
NPIC


        edIm,ITTYl)ansmIkar AISC sMrab;kugRtaMgBt;GnuBaØatEdlQrelI lateral-torsional
buckling, eKRtUveFVIkarEktMrUv...
T.Chhay


       yktMélFMCageKkñúgcMeNam
                170000Cb
        Fb =                   ≤ 0.60 Fy      (US)     (...
NPIC


           20000              20000
                     =                     = 336.0in = 28 ft
         (      )
...
T.Chhay


                      ⎡ 2 Fy (Lb / rT )2 ⎤
                 Fb = ⎢ −                ⎥ Fy ≤ 0.60 Fy
             ...
NPIC


B>5>   Beam-Columns

       eKviPaKGgát;eRKOgbgÁúMEdlrgTaMgkugRtaMgBt; nigkugRtaMgtamG½kSCamYynwgsmIkarGnþrGMeBI
ed...
T.Chhay


               f a f bx f by
                  +    +     ≤ 1 .0                                                ...
NPIC


dMeNaHRsay³ kugRtaMgrgkarsgát;tamG½kS
                 P   100
        fa =       =     = 6.944ksi
                ...
T.Chhay


         102000Cb   102000(1.0 )
                  =              = 53.2
            Fy          36
         510...
NPIC


                  12π 2 E      12π 2 (29000)
ehIy    F 'ex =                  =              = 87.21ksi
           ...
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Appendix b structural steel design based on allowable stress

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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