6.beam columns

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6.beam columns

  1. 1. T.chhay VI. Fñwm-ssr Beam-Columns 6>1> esckþIepþIm Introduction enAeBlEdlGgát;eRKOgbgÁúMCaeRcInRtUv)anKitCassrrgkMlaMgtamGkS½ b¤CaFñwmEdlrgEtkM laMgBt; (flexural loading) Fñwm nigssrCaeRcInrgnUvkMlaMgTaMgBIrKw kMlaMgBt; nigkMlaMgtamGkS½. vaCakarBitCaBiesssMrab;eRKOgbgÁúMsþaTicminkMNt;. sUmbIEtTMr roller rbs;FñwmsamBaØGacpþl;nUvkM laMgkkitEdlGacTb;Fñwmclt½tambeNþay enAeBkEdlbnÞúkGnuvtþEkgnwgGkS½beNþayrbs;Fñwm. b:uEnþ kñúgkrNIBiessenH CaTUeTAT§iBlrg ¬TIBIr¦mantMéltUc ehIyGacecal)an. ssrCaeRcInRtUv)anCa Ggát;rgkMlaMgsgát;suT§CamYynwgkMrwtlMeGogEdlGacecal)an. RbsinebIssrCaGgát;sMrab;eRKOgbgÁúM mYyCan; ehIyTMrrbs;vaTaMgBIrRtUv)anKitCaTMr pinned FñwmnwgrgEt bending EdlCalT§plBIbnÞúkcM Nakp©itEdleRKaHfñak;tictYc. b:uEnþ sMrab;Ggát;eRKOgbgÁúMCaeRcIn T§iBlTaMgBIrnwgmantMélFM EdlGgát;TaMgenaHRtUv)aneKehA fa beam-columns. BicarNa rigid frame enAkñúgrUbTI 6>1. sMrab;lkçxNÐbnÞúkEdleGay Ggát;edk AB minRtwmEtRTbnÞúkbBaÄrBRgayesμIeT EfmTaMgCYyGgát;bBaÄredIm,ITb;nwgbnÞúkxagcMcMnuc P . Ggát; CD CakrNIEdleRKaHfñak;Cag eRBaHvaTb;;nwgbnÞúk P1 + P2 edayminmanCMnYyBIGgát;bBaÄrNa eT. mUlehtuKWfa x-bracing EdlbgðajedayExSdac; karBar sidesway enACan;xageRkam. sMrab;kar bgðajTisedArbs; P2 Ggát; ED nwgrgkMlaMgTaj ehIyGgát; CF nwgFUr RbsinebI bracing element RtUv)anKNnaedIm,ITb;EtkMlaMgTaj. b:uEnþsMrab;krNIenH Ggát; CD RtUvbBa¢ÚnbnÞúk P1 + P2 BI C eTA D. Ggát;bBaÄrrbs;eRKagenHk¾RtUv)anKitCa beam-columns. enACan;xagelI Ggát; AC nig BD nigekageRkamT§iBlrbs; P1 . elIsBIenH enARtg; A nig B m:Um:g;Bt;RtUv)anbBa¢ÚnBIGgát;edktamry³ 188 Fñwm -ssr
  2. 2. T.chhay tMNrwg. karbBa¢Únm:Um:g;enHk¾ekIteLIgenARtg; C nig D ehIyvaBitsMrab;RKb; rigid frame eTaHbI m:Um:g;TaMgenHtUcCagm:Um:g;Edl)anBIbnÞúkxagk¾eday. ssrCaeRcInenAkñúg rigid frames Ca beam- columns ehIyT§iBlrbs;m:Um:g;Bt;minRtUv)anecal. b:uEnþ ssrrbs;GaKarmYyCan;EdlenAdac;BIeK GacRtUv)anKitCaGgát;rgkMlaMgsgát;cMGkS½. eBlxøH]TahrN_epSgeTotrbs; beam-columns GacCYbenAkñúg roof trusses. eTaHbICaFmμta top chord RtUv)anKitCaGgát;rgkMlaMgsgát;tamGkS½k¾eday RbsinebI purlins RtUv)andak;enAcenøaH tMN kMlaMgRbtikmμrbs;vanwgbegáItCa bending Edldac;xatRtUv)anKitkñúgkarKNna. krNIenHnwg RtUv)anerobrab;enAkñúgCMBUkenH. 6>2> smIkarGnþrkmμ Interaction Formulas vismPaBrbs;smIkar @># GacRtUv)ansresrkñúgTMrg;xageRkam³ ∑ γ i Qi ≤ 1.0 ¬^>!¦ φRn b¤ ∑resistance ≤ 1.0 load effects RbsinebIman resistance eRcInRbePTBak;Bn§½ smIkar ^>! GacRtUv)ansresrkñúgTMrg;eKalrbs; interaction formulas. dUcEdl)anerobrab;enAkñúgCMBUk 5 Rtg;Epñkm:Um:g;Bt;BIrTis plbUkénpleFob load-to-resistance RtUv)ankMNt;RtwmmYyÉktþa. ]TahrN_ RbsinebIeKGnuvtþTaMgm:Um:g;Bt; nigkMlaMg tamGkS½ interaction formulas GacsresrCa Pu + Mu φc Pn φb M n ≤ 1 .0 ¬^>@¦ Edl Pu = bnÞúksgát;tamGkS½emKuN φc Pn = compressive design strength Mu = m:Um:g;Bt;emKuN φb M n = design moment sMrab;m:Um:g;Bt;BIrTis vanwgmanpleFobm:Um:g;Bt;Bt;BIr ⎛ M ux M uy ⎞ Pu +⎜ + φc Pn ⎜ φb M nx φb M ny ⎟ ≤ 1.0 ⎟ ¬^>#¦ ⎝ ⎠ Edl x nig y sMedAelIkarBt;eFobGkS½ x nigGkS½ y . 189 Fñwm -ssr
  3. 3. T.chhay smIkar ^># CasmIkareKalrbs; AISC sMrab;Ggát;rgkarBt; nigrgkMlaMgtamGkS½. eKeGay smIkarBIrenAkñúg Specification: mYysMrab;bnÞúkcMGkS½EdlmantMéltUc nigmYyeTotsMrab;bnÞúkcMGkS½ EdlmantMélFM. RbsinebIbnÞúktamGkS½mantMéltUc tYbnÞúktamGkS½RtUv)ankat;bnßy. sMrab;bnÞúktam GkS½EdlmantMélFM tYkMlaMgBt;RtUv)ankat;bnßybnþic. tMrUvkarrbs; AISC RtUv)aneGayenAkñúg Chapter H, “Members Under Combined Forces and Torsion,” ehIyRtUv)ansegçbdUcxageRkam³ sMrab; φPu ≥ 0.2 P c n Pu 8 ⎛ M ux M uy ⎞ + ⎜ + ⎟ ≤ 1.0 (AISC Equation H1-1a) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ sMrab;Pu φc Pn < 0 .2 Pu ⎛ M ux M uy ⎞ +⎜ + ⎟ ≤ 1.0 (AISC Equation H1-1b) 2φc Pn ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ ]TahrN_6>1 bgðajBIkarGnuvtþn_smIkarTaMgenH. ]TahrN_6>1³ Fñwm-ssrEdlbgðajenAkñúg rUbTI6>@ manTMr pinned enAcugsgçag ehIyrgnUvbnÞúkem KuNdUcbgðaj. karBt;KWeFobnwgGkS½xøaMg. kMNt;faetIGgát;enHbMeBjsmIkarGnþrkmμrbs; AISC Specification b¤eT. dMeNaHRsay³ dUcEdl)anbkRsayenAkñúgEpñk 6>3 m:Um:g;EdlGnuvtþenAkñúg AISC Equations H1-1a nig b eBlxøHnwgRtUv)anbegáInedaym:Um:g;bEnßm (moment amplification). eKalbMNgén]TahrN_ enHKWbgðajBIrebobeRbIsmIkarGnþrkmμ. 190 Fñwm -ssr
  4. 4. T.chhay BI ersIusþg;KNnakMlaMgsgát;tamGkS½ (axial compression design column load table strength) rbs; W 8× 58 CamYynwg F y = 50ksi nigRbEvgRbsiT§PaB K y L = 1.0 × 17 = 17 ft KW φc Pn = 365kips edaysarkarBt;eFobGkS½xøaMg m:Um:g;KNna (design moment) φb M n sMrab; Cb = 1.0 GacTTYl)an BI beam design chart in Part 4 of the Manual. sMrab; unbraced length Lb = 17 ft / φb M n = 202 ft − kips sMrab;lkçxNÐbnÞúk niglkçxNÐcugsMrab;bBaðaenH Cb = 1.32 ¬emIlrUbTI 5>15 c¦. sMrab; Cb = 1.32 / φb M n = 1.32(202) = 267 ft − kips b:uEnþm:Um:g;enHFMCag φb M p = 224 ft − kips ¬EdlTTYl)andUcKñaBI beam design charts ¦/ dUcenH design moment RtUv)ankMNt;Rtwm φb M p . dUcenH φb M n = 224 ft − kips m:Um:g;Bt;GtibrmaenAkNþalElVgKW 22(17 ) Mu = = 93.5 ft − kips 4 kMNt;faetIsmIkarGnþrkmμmYyNalub Pu = 200 φc Pn 365 = 0.547 > 0.2 dUcenHeRbI AISC Eq.H1-1a. Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.5479 + 8 ⎛ 93.5 + 0 ⎞ = 0.919 ≤ 1.0 + ⎜ + ⎜ ⎟ (OK) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 224 ⎠ cMeLIy³ Ggát;enHbMeBj AISC Specification. 6>3> m:Um:g;bEnßm Moment Amplification viFIBImunsMrab;karKNnaGgát;rgkarBt; nigkMlaMgtamGkS½GaceRbI)ansMrab;EtkMlaMgtamGkS½ mantMélminFMeBk. vtþmanrbs;bnÞúktamGkS½ ¬elIkElgenAeBlvamantMéltUc¦ begáItm:Um:g;TIBIr EdlRtUv)anKitbBa©ÚlkñúgkarKNna. rUb TI 6>3 bgðajBIFñwm-ssrCamYybnÞúktamGkS½ nigbnÞúkTTwg GkS½BRgayesμI. Rtg;cMnuc O NamYyEdlmanmanm:Um:g;Bt;EdlbegáIteLIgedaybnÞúkBRgayesμInwg 191 Fñwm -ssr
  5. 5. T.chhay m:Um:g;bEnßm Py EdlbegáIteLIgedaybnÞúktamGkS½eFVIGMeBIcMNakp©itBIGkS½beNþayrbs;Ggát;. m:Um:g; TIBIrenaHmantMélkan;EtFMenAkEnøgNaEdlmanPaBdabkan;EtFM. kñúgkrNIenH Rtg;kMBs;Bak;kNþal m:Um:g;srubesμInwg wL2 / 8 + Pδ . vaCakarBitEdl m:Um:g;bEnßmbegáItPaBdabbEnßmBIelIPaBdab Edl)anBIbnÞúkTTwgGkS½. edaysareKminGacrkPaBdabsrubedaypÞal; ¬bBaðaenHCa nonlinear¦ ehIyedaysarEteKminsÁal;PaBdab eKk¾minGacKNnam:Um:g;)anEdr. viFIviPaKeRKOgbgÁúMFmμta (ordinary structural analysis methode) Edlminykragpøas;TImk KitRtUv)aneKKitCa viFIdWeRkTImYy (first-order method). eKeRbI Iterative numerical technique ¬EdleKehAfa viFIdWeRkTIBIr (second-order method)¦ edIm,IrkPaBdab nigm:Um:g;TIBIr b:uEnþviFIenHmin GaceRbIsMrab;karKNnaedayéd EdlvaRtUv)aneRbICaTUeTACamYynwgkmμviFIkMuBüÚT½r. Design codes nig specifications bc©úb,nñPaKeRcIn rYmbBa©ÚlTaMg AIsc Specification GnuBaØatkareRbIR)as; second- order analysis b¤ moment amplification method. viFIenHtMrUvkarKNnam:Um:g;Bt;GtibrmaEdl)anBI lT§plBI flexural loading ¬bnÞúkTTwgGkS½ b¤m:Um:g;cugGgát;¦ eday first-order analysis bnÞab;mk KuNnwgemKuNm:Um:g;bEnßm (moment amplification factor) edIm,IKitm:Um:g;TIBIr. rUbTI 6>4 bgðajGgát;TMrsamBaØCamYynwgbnÞúkcMGkS½ nigPaBminRtg;dMbUg (initial out-of- straightness). PaBdabdMbUg (initial crookedness) enHGacsMEdgeday³ πx yo = e sin L Edl e CabMlas;TIGtibrmadMbUg EdlekIteLIgenAkNþalElVg. 192 Fñwm -ssr
  6. 6. T.chhay sMrab;RbBn§½kUGredaendUcEdl)anbgðaj eKGacsresrTMnak;TMngExSkMeNag-m:Um:g; (moment- curvature relationship) dUcxageRkam³ d2y M =− 2 EI dx m:Um:g;Bt; M ekIteLIgedaysarcMNakp©iténkMlaMgtamGkS½ Pu eFobGkS½rbs;Ggát;. cMNak p©itenHpSMeLIgeday initial crookedness yo bUknwgPaBdabbEnßm y EdlekItBIkarBt;. enARtg;TI taMgNamYy m:Um:g;KW M = Pu ( yo + y ) edayCMnYssmIkarenHeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an d2y P ⎛ πx ⎞ = − u ⎜ e sin + y ⎟ dx 2 EI ⎝ L ⎠ 2 d y Pu Pe πx + y = − u sin dx 2 EI EI L EdlCa ordinary, nonhomogenous differential equation. edaysarvaCasmIkardWeRkTIBIr dUcenHvamanlkçxNÐRBMEdnBIr. sMrab;lkçxNÐTMrEdlbgðaj lkçxNÐRBMEdnKW enARtg; x = 0 / y = 0 nigenARtg; x = L / y = 0 enHmann½yfa PaBdabesμIsUnüenAcugsgçag. GnuKmn_EdlbMeBjTaMgsmIkarDIepr:g;Esül niglkçxNÐRBMEdnKW πx y = B sin L Edl B CatMélefr. CMnYsvaeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an π2 πx P πx Pe πx − B sin + u B sin = − u sin 2 L EI L EI L L 193 Fñwm -ssr
  7. 7. T.chhay eKTTYl)antMélefr Pe − u EI = −e e B= = Pu π 2 π EI Pe − 1 2 − 1− Pu EI L2 Pu L2 Edl Pe = π 2 EI = Euler buckling load 2 L dUcenH y = B sin πLx = ⎡ (P / P ) − 1⎤ sin πLx ⎢ e ⎥ ⎣ e u ⎦ M = Pu ( yo + y ) ⎧ ⎪ πx ⎡ e ⎤ πx ⎫⎪ = Pu ⎨e sin + ⎢ ⎥ sin ⎬ ⎪ ⎩ L ⎣ (Pe / Pu ) − 1⎦ L⎪ ⎭ m:Um:g;GtibrmaekItenARtg; x = L / 2 ³ ⎡ e ⎤ M max = Pu ⎢e + ⎥ ⎣ (Pe / Pu ) − 1⎦ ⎡ (P / P ) − 1 + 1 ⎤ = Pu e ⎢ e u ⎥ ⎣ (Pe / Pu ) − 1 ⎦ ⎡ 1 ⎤ = Mo ⎢ ⎥ ⎣1 − (Pu / Pe )⎦ Edl M o minEmnCam:Um:g;bEnßmGtibrma (unampliflied maximum moment). kñúgkrNIenH vaTTYl)anBI initial crookedness b:uEnþCaTUeTAvaGacCalTßplénbnÞúkTTwgGkS½ b¤m:Um:g;cug. dUcenHem KuNm:Um:g;bEnßm (moment amplification factor) KW 1 1 − (Pu / Pe ) ¬^>$¦ dUcEdl)anerobrab;mkehIy TMrg;emKuNm:Um:g;bEnßmrbs; AISC GacxusEbøkBIsmIkar ^>$ bnþic. ]TahrN_6>2³ eRbIsmIkar ^>$ edIm,IKNnaemKuNm:Um:g;bEnßmsMrab;Fñwm-ssrén]TahrN_ 6>1. dMeNaHRsay³ edaysar Euler load Pe CaEpñkrbs;emKuNm:Um:g;bEnßm eKRtUvKNnavasMrab;GkS½én karBt; EdlkñúgkrNIenHKWGkS½ x . eKGacsresr Euler load Pe edayeRbI effective length nig slenderness ratio dUcxageRkam³ 194 Fñwm -ssr
  8. 8. T.chhay π 2 EAg Pe = (KL / r )2 ¬emIlCMBUk 4 smIkar $>^ a¦. sMrab;GkS½énkarBt; KL K x L 1.0(17 )(12 ) = = = 55.89 r rx 3.65 π 2 EAg π 2 (29000)(17.1) Pe = = = 1567kips (KL / r )2 (55.89)2 BIsmIkar ^>$ 1 1 = = 1.15 1 − (Pu / Pe ) 1 − (200 / 1567 ) EdlbgðajkarekIneLIg 15% BIelIm:Um:g;Bt;. m:Um:g;bEnßmKW 1.15 × M u = 1.15(93.5) = 107.5 ft − kips cMeLIy³ emKuNm:Um:g;bEnßm 1.15 6>4> Web Local Buckling in Beam-Columns karkMNt;rbs; design moment tMrUveGayRtYtBinitümuxkat;sMrab; compactness . enAeBl EdlKμanbnÞúktamGkS½ RTnugrbs;RKb;rUbragEdlmanenAkñúgtaragsuT§Et compact. RbsinebImanvtþ manbnÞúktamGkS½ RTnugTaMgenaHGacnwgmin compact. enAeBlEdleyIgeGay λ = h / t w / RbsinebI λ ≤ λ p rUbragKW compact. RbsinebI λ p < λ ≤ λr rUbragKW noncompact. RbsinebI λ > λr rUbragKW slender. ASIC B5 enAkñúg Table B5.1 erobrab;nUvkarkMNt;xageRkam³ sMrab; φ PP ≤ 0.125 / λ p = 640 ⎛1 − 2φ.75Pu ⎞ ¬xñat US¦ u F ⎜ ⎜ P ⎟ ⎟ b y y⎝ b y ⎠ 1680 ⎛ 2.75 Pu ⎞ λp = ⎜1 − Fy ⎜ φb Py ⎟ ⎟ ¬xñat ¦ IS ⎝ ⎠ 191 ⎛ ⎞ sMrab; φ PP u > 0.125 λ p / = ⎜ 2.33 − Pu ⎟ ≥ 253 Fy ⎜ φb Py ⎟ Fy ¬xñat US¦ b y ⎝ ⎠ 500 ⎛ ⎞ λp = ⎜ 2.33 − Pu ⎟ ≥ 665 Fy ⎜ φb Py ⎟ Fy ¬xñat IS¦ ⎝ ⎠ 195 Fñwm -ssr
  9. 9. T.chhay sMrab;tMélepSg²rbs; φ PP / λr = 970 ⎛1 − 0.74 φ PP ⎞ ¬xñat US¦ u F ⎜ ⎜ u ⎟ ⎟ b y y ⎝ b y ⎠ 2550 ⎛ ⎞ λr = Fy ⎜ ⎜1 − 0.74 Pu φb Py ⎟ ⎟ ¬xñat IS¦ ⎝ ⎠ Edl Py = Ag Fy / bnÞúktamGkS½caM)ac;edIm,IeTAdl;sßanPaBkMNt; yielding. edaysar Pu CaGBaØti eKminGacRtYtBinitü compactness rbs;RTnug nigminGacerobcMCata ragTukCamun)aneT. b:uEnþ rolled shape xøHbMeBjnUvkrNId¾GaRkk;bMput 665 / Fy Edlmann½yfarUb ragenaHmanRTnug compact edayminTak;TgnwgbnÞúktamGkS½. rUbragEdlmanenAkñúg column load table in Part 3 of the Manual EdlminbMeBjlkçxNÐRtUv)ankMNt;bgðaj enaHeKRtUvRtYtBinitü compactness rbs;RTnugrbs;va. rUbragEdlmansøabmin compact k¾RtUv)ankMNt;bgðaj dUcenHRKb; rUbragTaMgGs;Edlmin)anbgðaj enaHmann½yfarUbragTaMgenaHKW compact. ]TahrN_6>3³ Edk A36 EdlmanrUbrag W12 × 65 RtUv)andak;eGayrgm:Um:g;Bt; nigbnÞúktamGkS½em KuN 300kips . RtYtBinitü compactness rbs;RTnug. dMeNaHRsay³ rUbragenHKW compact sMrab;RKb;tMélbnÞúktamGkS½ BIeRBaHminmankarkMNt;cMNaMNa mYyenAkñúg column load table. b:uEnþ edIm,Ibgðaj eyIgRtYtBinitü width-thickness ratio rbs;RTnug Pu Pu 300 = = = 0.4848 > 0.125 ( ) φb Py φb Ag Fy 0.9(19.1)(36) ⎛ ⎞ dUcenH λp = ⎜ 2.33 − Pu ⎟ = 191 (2.33 − 0.4848) = 58.74 191 ⎜ Fy φb Py ⎟ 36 ⎝ ⎠ 253 253 = = 42.17 < 58.74 Fy 36 dUcenH λ p = 58.74 BI dimensions and properties tables/ h λ= = 24.9 < 58.74 tw dUcenH RTnugKW compact. cMNaMfa sMrab;RKb;tMélrbs; Fy enaH th nwgmantMéltUcCag w 253 / F y EdlCatMélEdltUcbMputrbs; λ p dUcenHRTnugrbs; W 12 × 65 nwgenAEtCa compact. 196 Fñwm -ssr
  10. 10. T.chhay 6>5> eRKagBRgwg nigeRKagGt;BRgwg Braced versus Unbraced Frame AISC Specification erobrab;BI moment amplification in Chapter C, Frames and other Structures”. eKmanemKuNbEnßmBIrEdleRbIenAkñúg LRFD: mYyedIm,IKitBIm:Um:g;bEnßmEdlCalT§plBI PaBdabrbs;Ggát; nigmYyeTotsMrab;KitBIT§iBl sway enAeBlEdlGgát;CaEpñkrbs; unbraced frame. viFIenHmanlkçN³RsedogKñaeTAnwgviFIEdleRbIenAkñúg ACI Building Code sMrab;ebtugBRgwg edayEdk (ACI, 1995). rUbTI 6>5 nwgbgðajBIGgát;TaMgBIr. enAkñúg rUbTI 6>5 a Ggát;RtUv)anTb;Rb qaMgnwg sidesway ehIym:Um:g;TIBIrGtibrmaKW Pδ EdlRtUvbEnßmeTAelIm:Um:g;GtibrmaenAkñúgGgát;enaH. RbsinebIeRKagminRtUv)anBRgwg vanwgelceLIgnUvm:Um:g;TIBIr EdlbgðajenAkñúg rUbTI 6>5 b EdlbegáIt eday sidesway. m:Um:g;TIBIrenHmantMélGtibrma PΔ EdlbgðajBIkarbEnßménm:Um:g;cug. edIm,IKItBIT§iBlTaMgBIrenH emKuNm:Um:g;bEnßm B1 nig B2 RtUv)aneRbIsMrab;m:Um:g;BIrRbePT. m:Um:g;bEnßmEdleRbIsMrab;KNnaRtUv)anKNnaBIbnÞúkemKuN nigm:Um:g;emKuNdUcxageRkam³ M u = B1M nt + B2 M lt (AISC Equation C1-1) Edl M nt = m:Um:g;GtibrmaEdlsnμt;faminman sidesway ekIteLIg eTaHbICaeRKagBRgwgb¤minBRgwg k¾eday ¬ nt mann½yfa no translation¦ M lt = m:Um:g;GtibrmaEdlekIteLIgeday sidesway ekIteLIg ¬ lt mann½yfa lateral translation¦. m:Um:g;enHGacekItBI lateral load b¤edaysar unbalanced gravity loads . bnÞúkTMnajGacbegáIt sidesway RbsinebIeRKagGt;sIuemRTI b¤k¾bnÞúkTMnaj enaHRtUv)andak;edayminmanlkçN³sIuemRTI. M lt nwgmantMélesμIsUnüRbsinebIeRKag RtUv)anBRgwg. 197 Fñwm -ssr
  11. 11. T.chhay B1 = emKuNm:Um:g;bEnßmsMrab;m:Um:g;EdlekIteLIgenAkñúgGgát;EdlRtUv)anBRgwgTb;nwg sidesway. B2 = emKuNm:Um:g;bEnßmsMrab;m:Um:g;Edl)anBI sidesway. eyIgnwgerobrab;BIkarkMNt;emKuNTaMgBIr B1 nig B2 enAkñúgEpñkxageRkam. 6>6> Ggát;enAkñúgeRKagEdlBRgwg Members in Braced Frames emKuNm:Um:g;bEnßmEdleGayedaysmIkar ^>$ RtUv)anbMEbksMrab;Ggát;EdlBRgwgRbqaMgnwg sidesway. rUbTI 6>6 bgðajBIGgát;RbePTenHEdlrgm:Um:g;enAxagcugesμIKñaEdlbegáIt single- curvature bending ¬kMeNagEdlbegáItkarTaj nigkarsgát;enAEtEpñkmçagrbs;Ggát;¦. m:Um:g;bEnßm GtibrmaekItenARtg;Bak;kNþalkMBs; EdlPaBdabmantMélFMbMput. dUcenHm:Um:g;TIBIrGtibrma nigm:U m:g;emGtibrmaRtUv)anbUkbBa©ÚlKña. eTaHRbsinebIm:Um:g;enAxagcugminesIμKñak¾eday RbsinebIm:Um:g;mYy vilRsbTisRTnicnaLika nigmYyeTotvilRcasRTnicnaLika vanwgbegáIt single-curvature bending ehIym:Um:g;emGtibrma nigm:Um:g;TIBIrGtibrmanwgekIteLIgenAEk,Kña. vanwgminEmnCakrNIeT enAeBlEdlm:Um:g;enAcugEdlGnuvtþbegáIt reverse-curvature bending dUcbgðajenAkñúg rUbTI 6>7 . enAeBlenH m:Um:g;emGtibrmaKWenAcugmçag ehIym:Um:g;TIBIrGtibrmaekIt eLIgenAcenøaHcugTaMgBIr. m:Um:g;bEnßmGacFMCag b¤tUcCagm:Um:g;cugGaRs½ynwgbnÞúktamGkS½. dUcenHm:Um:g;GtibrmaenAkñúg beam-column GaRs½ynwgkarEbgEckm:Um:g;Bt;enAkñúgGgát;. kar EbgEckenHRtUv)anKitedayemKuN Cm EdlGnuvtþenAkñúgemKuNm:Um:g;bEnßm B1 . emKuNm:Um:g;bEnßm EdleGayedaysmIkar ^>$ RtUv)anbMEbksMrab;krNIGaRkk;bMput dUcenH Cm nwgminRtUvFMCag 1.0 . TMrg;cugeRkayrbs;emKuNm:Um:g;bEnßmKW³ 198 Fñwm -ssr
  12. 12. T.chhay Cm B1 = ≥1 (AISC Equation C1-2) 1 − (Pu / Pe1 ) Ag F y π 2 EAg Edl Pe1 = = λc 2 (KL / r )2 enAeBlKNna Pe1 eRbI KL / r sMrab;GkS½énkarBt; ehIyemKuNRbEvgRbsiT§PaB K ≤ 1.0 ¬EdlRtUv KñanwglkçxNÐEdlBRgwg¦. karKNnaemKuN Cm emKuN Cm GnuvtþEtelIlkçxNÐEdlBRgwgEtb:ueNÑaH. eKmanGgát;BIrRbePT EdlmYyman bnÞúkTTwgGkS½GnuvtþenAcenøaHcug nigmYyeTotminmanbnÞúkTTwgGkS½. rUbTI 6>8 b nig c bgðajBIkrNITaMgBIrxagelIenH ¬Ggát; AB Ca beam-column EdlRtUvKit¦. !> RbsinebIminmanbnÞúkTTwgGkS½eFVIGMeBIenAelIGgát; ⎛M ⎞ C m = 0.6 − 0.4⎜ 1 ⎟ ⎜M ⎟ (AISC Equation C1-3) ⎝ 2⎠ 199 Fñwm -ssr
  13. 13. T.chhay M1 / M 2CapleFobénm:Um:g;Bt;enAcugrbs;Ggát;. M1 CatMéldac;xaténm:Um:g;cugEdltUcCag eK ehIy M 2 CatMélFMCag enaHpleFobnwgviC¢mansMrab;Ggát;EdlekagkñúgTMrg; reversecurvature nigGviC¢mansMrab; single-curvature bending ¬rUbTI 6>9 ¦. Reverse curvature ¬pleFobviC¢man¦ ekIteLIgenAeBlEdl M1 nig M 2 vilRsbRTnicnaLikaTaMgBIr b¤RcasRTnicnaLikaTaMgBIr. @> sMrab;Ggát;rgbnÞúkTTwgGkS½ eKGacyk Cm = 0.85 RbsinebIcugrbs;vaRtUv)anTb;RbqaMg nwgkarvil nigesμInwg 1.0 RbsinebIcugrbs;vaminRtUv)anTb;nwgkarvil ¬pinned¦. CaTUeTAkarTb;cug (end restraint) ekItBIPaBrwgRkaj (stiffness) rbs;Ggát;EdlP¢ab;eTAnwg beam-column. lkçxNÐTMr pinned CalkçxNÐmYyEdlRtUv)aneRbIsMrab;TajrkemKuNm:Um:g;bEnßm dUcenHvaminmankarkat;bnßytM élemKuNm:Um:g;bEnßmsMrab;krNIenHeT EdlvaRtUvKñanwg Cm = 1.0 . eTaHbICalkçxNÐcugBitR)akdsßit enAcenøaHkarbgáb;eBj (fully fixity) nigknøas;Kμankkit (frictionless pin) k¾eday eKGaceRbItMélNa mYyk¾)anEdr eRBaHvanwgpþl;lT§plCaTIeBjcitþ. 200 Fñwm -ssr
  14. 14. T.chhay viFIsaRsþEdl)aneFVIeGayRbesIreLIgsMrab;Ggát;rgbnÞúkxagTTwgGkS½ ¬krNITIBIr¦ RtUv)anpþl; eGayenAkñúg section C1 of the commentary to the Specification. emKuNkat;bnßyKW P Cm = 1 +ψ u Pe1 sMrab;Ggát;TMrsamBaØ π 2δ o EI ψ= −1 M o L2 Edl δ o CaPaBdabGtibrmaEdlekItBIbnÞúkxagTTwgGkS½ ehIy M o Cam:Um:g;GtibrmaenA cenøaHTMrEdl)anBIbnÞúkxagTTwgGkS½. emKuN ψ RtUv)anKNnaBIsßanPaBFmμtaCaeRcInehIyRtUv)an pþl;eGayenAkñúg commentary Table C-C1.1. ]TahrN_6>4³ Ggát;EdlbgðajenAkñúg rUbTI 6>10 CaEpñkrbs; braced frame. bnÞúk nigm:Um:g;RtUv)an KNnaCamYybnÞúkemKuN ehIykarBt;KWwFobnwgGkS½xøaMg. RbsinebIeKeRbI A572 Grade 50 etIGgát; enHRKb;RKan;b¤eT? KL = KL y = 14 ft . dMeNaHRsay³ kMNt;faetIRtUveRbIrUbmnþGnþrkmμmYyNa KL K y L 14(12) maximum = = = 55.63 r ry 3.02 BI AISC Table 3-50, φc Fcr = 33.89ksi dUcenH φc Pn = Ag (φc Fcr ) = 19.1(33.89 ) = 647.4kips Pu 420 = = 0.6487 > 0.2 φc Pn 647.4 201 Fñwm -ssr
  15. 15. T.chhay dUcenHeRbI AISC Equation H1-1a. enAkñúgbøg;énkarBt; KL K x L 14(12 ) = = = 31.82 r rx 5.28 Ag F y π 2 EAg π 2 (29000 )(19.1) Pe1 = = = = 5399kips λc 2 (K x L / rx )2 (31.82)2 ⎛M ⎞ ⎛ 70 ⎞ C m = 0.6 − 0.4⎜ 1 ⎟ = 0.6 − 0.4⎜ − ⎟ = 0.9415 ⎜M ⎟ ⎝ 2⎠ ⎝ 82 ⎠ Cm 0.9415 B1 = = = 1.021 1 − (Pu / Pe1 ) 1 − (420 / 5399 ) BI Beam design charts,CamYynwg Cb = 1.0 nig Lb = 14 ft. moment strength KW φb M n = 347 ft − kips sMrab;tMél Cb BitR)akd edayeyagtamdüaRkam:Um:g;enAkñúg rUbTI 6>10³ 12.5M max 1.25(82 ) Cb = = = 1.06 2.5M max + 3M A + 4 M B + 3M C 2.5(82 ) + 3(73) + 4(76 ) + 3(79 ) dUcenH φb M n = Cb (347) = 1.06(347) = 368 ft − kips b:uEnþ φb M p = 358 ft − kips ¬BItarag¦ < 368 ft − kips dUcenHeRbI φb M n = 358 ft − kips m:Um:g;emKuNKW M nt = 85 ft − kips M lt = 0 BI AISC Equation C1-1, M u = B1M nt + B2 M lt = 1.021(82) + 0 = 83.72 ft − kips = M ux BI AISC Equation H1-1a, Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.6487 + 8 ⎛ 83.72 ⎞ = 0.857 < 1.0 + ⎜ + ⎜ ⎟ (OK) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 358 ⎠ cMeLIy³ Ggát;enHKWRKb;RKan;. ]TahrN_ 6>5³ Fñwm-ssredkEdlbgðajenAkñúgrUbTI 6>11 rgnUv service live loads dUcEdlbgðaj kñúgrUb. Ggát;enHRtUv)anBRgwgxagenAxagcugrbs;vaTaMgBIr ehIykarBt;KWeFobnwgGkS½ x . RtYtBinitü faetIGgát;enHRKb;RKan;tam AISC Specification. 202 Fñwm -ssr
  16. 16. T.chhay dMeNaHRsay³ bnÞúkemKuNKW Pu = 1.6(20) = 32.0kips ehIym:Um:g;GtibrmaKW M nt = (1.6 × 20)(10) + (1.2 × 0.035)(10)2 = 80.52 ft − kips 4 8 Ggát;enHRtUv)anBRgwgTb;nwgkarbMlas;TIxagcug dUcenH M lt = 0 . KNnaemKuNm:Um:g;bEnßm sMrab;Ggát;rgbnÞúkxagEdlRtUv)anBRgwgTb;nwg sidesway ehIy unrestrained end enaH Cm = 1.0 . tMélEdlsuRkitCagEdl)anBI AISC Commentary Table C-C1.1 KW P C m = 1 − 0 .2 u Pe1 sMrab;GkS½énkarBt; KL K x L 1.0(10 )(12 ) = = = 34.19 r rx 3.51 π 2 EAg π 2 (29000)(10.3) Pe1 = = = 2522kips (KL / r )2 (34.19)2 ⎛ 32.0 ⎞ C m = 1 − 0.2⎜ ⎟ = 0.9975 ⎝ 2522 ⎠ emKuNm:Um:g;bEnßm Cm 0.9975 B1 = = = 1.010 > 1.0 1 − (Pu / Pe1 ) 1 − (32.0 / 2522 ) sMrab;GkS½énkarBt; M u = B1M nt + B2 M lt = 1.010(80.52) + 0 = 81.33 ft − kips edIm,ITTYl design strengths dMbUgemIleTA column load tables in Part 3 of the Manual Edl eGay φc Pn = 262kips BI beam design charts in Part 4 of the Manual sMrab; Lb = 10 ft nig Cb = 1.0 203 Fñwm -ssr
  17. 17. T.chhay φb M n = 91.8 ft − kips edaysarTMgn;FñwmtUcNas;ebIeRbobeFobnwgbnÞúkGefrcMcMnuc enaH Cb = 1.32 BI rUbTI 5>13 c. φb M n = 1.32(91.8) = 121 ft − kips m:Um:g;enHFMCag φb M p = 93.6 ft − kips EdlTTYl)anBI beam design chart dUcKña dUcenH design strength RtUv)ankMNt;RtwmtMélenH. dUcenH φb M n = 93.6 ft − kips RtYtBinitürUbmnþGnþrkmμ³ Pu 32.0 = = 0.1221 < 0.2 φc Pn 262 dUcenHeRbI AISC Equation H1-1b³ Pu ⎛ M ux M uy ⎞ 0.1221 ⎛ 81.33 ⎞ +⎜ + ⎟= +⎜ + 0 ⎟ = 0.930 < 1.0 (OK) 2φc Pn ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 2 ⎝ 93.6 ⎠ cMeLIy³ W 8× 35 KWRKb;RKan; ]TahrN_ 6>6³ Ggát;EdlbgðajenAkñúg rUbTI6>12 eFVIBIEdk A242 EdlmanrUbrag W 12 × 65 ehIy RtUvRTnUvbnÞúksgát;tamGkS½emKuN 300kips . enAcugTMenrmçagCa pinned nigcugmçageTotrgnUvm:Um:g; emKuN 135 ft − kips eFobGkS½xøaMg nig 30 ft − kips eFobGkS½exSay. eRbII K x = K y = 1.0 cUreFVIkar GegátBIGgát;enH. dMeNaHRsay³ dMbUg kMNt; yield stress Fy . BI Table 1-2, Part 1 of the Manual, W 12 × 65 CarUbragRkumTIBIr. BI Table 1-1, Edk A242 manersIusþg;EtmYyKW Fy = 50ksi . 204 Fñwm -ssr
  18. 18. T.chhay bnÞab;mkeTot rk compressive strength. sMrab; KL = 1.0(15) = 15 ft axial compressive design strength BI column load table KW³ φc Pn = 626kips cMNaMfa taragbgðajfasøabrbs; W 12 × 65 KW noncompact sMrab; Fy = 50ksi . KNnam:Um:g;Bt;eFobGkS½xøaMg (strong axis bending moment). = 0.6 − 0.4(0) = 0.6 M1 C mx = 0.6 − 0.4 M2 K x L 15(12 ) = = 34.09 rx 5.28 π 2 EAg π 2 (29000 )(19.1) Pe1x = = = 4704kips (K x L / rx )2 (34.09)2 C mx 0 .6 B1x = = = 0.641 < 1.0 1 − (Pu / Pe1x ) 1 − (300 / 4704 ) dUcenH eRbI B1x = 1.0 M ux = B1x M ntx + B2 x M ltx = 1.0(135) + 0 = 135 ft − kips BI beam design charts CamYy Lb = 15 ft / φb M nx = 342 ft − kips sMrab; Cb = 1.0 ehIy φb M px = 357.8 ft − kips . BI rUbTI 5>15 g, Cb = 1.67 ehIy Cb × (φb M nx for Cb = 1.0) = 1.67(342) = 571 ft − kips lT§plenHFMCag φb M px dUcenHeRbI φb M nx = φb M px = 357.8 ft − kips KNna m:Um:g;Bt;eFobGkS½exSay (weak axis bending moment). = 0.6 − 0.4(0) = 0.6 M1 C my = 0.6 − 0.4 M2 K yL 15(12) = = 59.60 ry 3.02 π 2 EAg π 2 (29000)(19.1) Pe1 y = = = 1539kips (K y L / ry )2 (59.60)2 C mx 0.6 B1 y = = = 0.745 < 1.0 ( ) 1 − Pu / Pe1 y 1 − (300 / 1539 ) dUcenH eRbI B1y = 1.0 M uy = B1 y M nty + B2 y M lty = 1.0(30 ) + 0 = 30 ft − kips 205 Fñwm -ssr
  19. 19. T.chhay edaysarsøabrbs;rUbragenH noncompact enaHersIusþg;m:Um:g;Bt;eFobGkS½exSayRtUv)ankMNt;eday FLB. bf λ= = 9.9 2t f 65 65 λp = = = 9.192 Fy 50 141 141 λr = = = 22.29 F y − 10 50 − 10 edaysar λ p < λ < λr ⎛ λ − λp ⎞ ( Mn = M p − M p − Mr ⎜ ⎟ ⎜ λr − λ p ⎟ ) (AISC Equation A-F1-3) ⎝ ⎠ 50(44.1) M p = M py = Fy Z y = = 183.8 ft − kips 12 ( ) M r = M ry = F y − Fr S y = (50 − 10 )(29.1) = 1164in. − kips = 97.0 ft − kips edayCMnYscUleTAkñúgsmIkar AISC Equation A-F1-3 eyIgTTYl)an ⎛ 9.9 − 9.192 ⎞ M n = M ny = 183.8 − (183.8 − 97.0)⎜ ⎟ = 179.1 ft − kips ⎝ 22.29 − 9.192 ⎠ φb M ny = 0.90(179.1) = 161.2 ft − kips rUbmnþGnþrkmμeGay Pu 300 = = 0.4792 > 0.2 φc Pn 626 dUcenHeRbI AISC Equation H1-1a³ Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.4792 + 8 ⎛ 135 + 30 ⎞ = 0.980 < 1.0 (OK) + ⎜ + ⎜ ⎟ φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 357.8 161.2 ⎠ cMeLIy³ W12 × 65 RKb;RKan; 6>7> Ggát;enAkñúgeRKagEdlminBRgwg Members in Unbraced Frames Fñwm-ssrEdlcugrbs;vaGacrMkil)an m:Um:g;dMbUgGtibrmaEdl)anBI sidesway CaTUeTAeRcIn sßitenAelIEtcugmçag. dUcEdl)anbgðajenAkñúgrUbTI 6>5 m:Um:g;TIBIrGtibrmaEdl)anBI sidesway Etg EtsßitenAelIcugmçag. dUcenHsMrab;krNIenH m:Um:g;TImYy nigm:Um:g;TIBIrGtibrmaCaTUeTARtUv)anbUkbBa©Úl Kña ehIyminRtUvkaremKuN Cm eT ¬karBit Cm = 1.0 ¦. eTaHbICaenAeBlEdlmankarkat;bnßy k¾va 206 Fñwm -ssr
  20. 20. T.chhay mantMéltictYc nigGacecal)an. cUrBicarNaFñwm-ssrEdlbgðajenAkñúgrUbTI 6>13. m:Um:g;esμIKñaenA xagcug)anmkBI sidesway ¬BIbnÞúkedk¦. bnÞúktamGkS½ ¬EdlCaEpñkmYyénbnÞúkEdlmanGMeBIelIFñwm- ssrminbNþaleGayman sidesway¦RtUv)anKitbBa©ÚleTAkñúgm:Um:g;cugEdr. emKuNm:Um:g;bEnßmsMrab; sidesway moments B2 RtUv)aneGaysmIkarBIr. eKGaceRbIsmIkar NamYyk¾)anEdr GaRs½ynwgPaBgayRsYlsMrab;GñkKNna³ 1 B2 = (AISC Equation C1-4) 1 − ∑ Pu (Δ oh / ∑ HL ) b¤ B2 = 1 1 − (∑ Pu / ∑ Pe 2 ) (AISC Equation C1-5) Edl ∑ Pu = plbUkbnÞúkemKuNenAelIRKb;ssrenAelICan;EdlBicarNa Δ oh = drift (sidesway displacement) rbs;Can;EdlBIcarNa ∑ H = plbUkénbnÞúkedkTaMgGs;EdlbegáIt Δ oh L = kMBs;Can; ∑ Pe 2 = plbUkén Euler loads rbs;ssrTaMgGs;enAelICan;EdlBicarNa ¬enAeBlEdl KNna Pe2 eKRtUveRbI KL / r sMrab;GkS½énkarBt; ehIy K CatMélEdlRtUvKñanwg unbraced condition. 207 Fñwm -ssr
  21. 21. T.chhay plbUkén Pu nigplbUkén Pe2 GnuvtþeTARKb;ssrEdlsßitenAkñúgCan;EdlBicarNaCamYyKña. eKeRbIplEckrvagplbUkbnÞúkTaMgBIrsMrab;smIkarxagelIedaysar B2 GnuvtþsMrab; unbraced frames ehIyRbsinebI sidesway nwgekItman enaHssrTaMggs;enAkñúgCan;EdlBicarNanwg sway kñúgeBlCa mYyKña. enAkñúgkrNICaeRcIn eRKOgbgÁúMRtUv)anKNnaenAkñúgbøg; dUcenH ∑ Pu nig ∑ Pe2 KWsMrab;ssr enACan;rbs;eRKag ehIybnÞúkxag H CabnÞúkxagEdleFVIGMeBIenAelIeRKag nigBIelICan;EdlBicarNa. CamYynwg Δ oh EdlekIteLIgeday ∑ H pleFob Δ oh / ∑ H GacQrelIbnÞúkemKuN b¤bnÞúkKμanem KuN. TMrg;epSgeTotrbs; B2 RtUv)aneGayeday AISC Equation C1-5 manlkçN³RsedognwgsmI karsMrab; B1 elIkElgsMrab;plbUk. AISC Equations C1-4 nig C1-5 RtUv)anbMEbkedayviFIBIrepSgKña b:uEnþenAkñúgkrNICaeRcInva nwgpþl;nUvlT§pldUcKña (Yura, 1988). enAkñúgkrNICaeRcInEdltMél B2 TaMgBIrxusKñaxøaMg tYénbnÞúk cMGkS½rbs;rUbmnþGnþrkmμnwglub ehIylT§plcugeRkaynwgminxusKñaeRcIneT. dUcEdl)anerobrab;BI xagedIm kareRCIserIsKWsßitenAelIPaBgayRsYl vaGaRs½ynwgtYenAkñúgsmIkar. kñúgkrNIEdl M nt nig M lt eFVIGMeBIenAcMnucBIrepSgKñaenAelIGgát; dUcbgðajenAkñúgrUbTI 6>14/ AISC Equation C1-1 nwgpþl;nUvlT§plEdlsnSMsMéc. 208 Fñwm -ssr
  22. 22. T.chhay rUbTI 6>14 bgðajbEnßmeTotBI superposition concept. rUbTI 6>14 a bgðajBI braced frame rgnUvTaMgbnÞúkTMnaj (gravity load) nigbnÞúkxag (lateral load). m:Um:g;enA M nt enAkñúgGgát; AB RtUv)anKNnaedayeRbIEt gravity load. edayPaBsIuemRTI eKminRtUvkar bracing edIm,IkarBar sidesway BIbnÞúkenH. m:Um:g;enHRtUv)anbEnßmCamYyCamYynwgemKuN B1 edIm,IkarBarT§iBl Pδ . M lt m:Um:g;EdlRtUvKñanwg sway ¬EdlbegáIteLIgedaybnÞúkedk H ¦ nwgRtUv)anbEnßmeday B2 edIm,I karBarnwgT§iBl PΔ . enAkñúg rUbTI 6>14 b unbraced frame RTEtbnÞúkbBaÄr. edaysarkardak;bnÞúkenHminsIuemRTI vanwgman sidesway bnþic. m:Um:g; M nt RtUv)anKNnaedayBicarNafaeRKagRtUv)anBRgwg ¬kñúgkrNI enH edaysarTMredkkkit nigkMlaMgRbtikmμRtUvKμaEdleKehAfa tMNTb;nimitþ (artificial joint restraint AJR). edIm,IKNnam:Um:g; sidesway eKRtUvykTMrkkitecj ehIyCMnYsedaykMlaMgEdlmantMélesμInwg artificial joint restraint b:uEnþmanTisedApÞúyKña. kñúgkrNIenH m:Um:g;TIBIr PΔ nwgmantMéltUcNas; ehIyeKGacecal M lt )an. RbsinebITaMgbnÞúkxag nigbnÞúkTMnaj minsIuemRTI eKGacbEnßmkMlaMg AJR eTAelIbnÞúkxagBit R)akd enAeBlEdl M lt RtUv)ankMNt;. ]TahrN_ 6>7³ Edk W 12 × 65 RbePT A572 grade 50 RbEvg 15 ft sMrab;eRbICassrenAkñúg unbraced frame. bnÞúkcMGkS½ nigm:Um:g;cugTTYl)anBI first-order analysis énbnÞúkTMnaj ¬bnÞúkefr nigbnÞúkGefr¦ RtUv)anbgðajenAkñúg rUbTI 6>15 a . eRKagmanlkçN³sIuemRTI ehIybnÞúkTMnajk¾ RtUv)andak;sIuemRTIEdr. rUbTI 6>15 b bgðajBIm:Um:g;énbnÞúkxül;Edl)anBI first-order analysis. m:U m:g;Bt;TaMgGs;KWeFobnwgGkS½xøaMg. emKuNRbEvgRbsiT§PaB K x = 1.2 sMrab;krNI sway nig K x = 1.0 sMrab;krNI nonsway ehIy K y = 1.0 . kMNt;faetIGgát;enHeKarBtam AISC Specification b¤eT? dMeNaHRsay³ karbnSMbnÞúkTaMgGs;EdleGayenAkñúg AISC A4.1 suT§EtmanbnÞúkGefr ehIyelIk ElgEtkarbnSMbnÞúkTImYyecj EdlkarbnSMbnÞúkTaMgGs;manbnÞúkxül; b¤bnÞúkGefr b¤TaMgBIr. Rbsin ebIRbePTbnÞúk ¬ E, Lr , S , nig R ¦ enAkñúg]TahrN_enHminRtUv)anbgðaj lkçxNÐénkarbnSMbnÞúk RtUv)ansegçbdUcxageRkam³ 1 .4 D (A4-1) 1 .2 D + 1 .6 L (A4-2) 209 Fñwm -ssr
  23. 23. T.chhay 1.2 D + (0.5 L or 0.8W ) (A4-3) 1.2 D + 1.3W + 0.5 L (A4-4) 1 .2 D + 0 .5 L (A4-5) 0.9 D ± 1.3W (A4-5) enAeBlEdlbnÞúkefrtUcCagbnÞúkGefrR)aMbIdg enaHbnSMbnÞúk (A4-1) GacminRtUvKit. bnSM bnÞúk (A4-4) nwgmantMélFMCag (A4-3) dUcenH (A4-3) Gacdkecj)an. bnSMbnÞúk (A4-5) k¾Gac ecal)anedaysarvanwgpþl;eRKaHfñak;tUcCag (A4-2). cugeRkay karbnSMbnÞúk (A4-6) nwgmineRKaH fñak;dUc (A4-4) ehIyk¾Gacdkecj)anBIkarBicarNa EdlenAsl;EtbnSMbnÞúkBIrEdlRtUveFVIkarGegátKW (A4-2)nig (A4-4) ³ 1.2 D + 1.6 L nig 1.2 D + 1.3W + 0.5 L rUbTI 6>16 bgðajBIbnÞúktamGkS½ nigm:Um:g;Bt;EdlKNnaecjBIbnSMbnÞúkTaMgBIrenH kMNt;GkS½eRKaHfñak;sMrab;ersIusþg;kMlaMgsgát;tamGkS½ K y L = 15 ft K x L 1.2(15) = = 10.29 ft < 15 ft rx / ry 1.75 dUcenHeRbI KL = 15 ft BI column load tables CamYynwg KL = 15 ft / φc Pn = 626kips sMrab;lkçxNÐbnÞúk (A4-2)/ Pu = 454kips / M nt = 104.8 ft − kips nig M lt = 0 ¬eday sarEtsIuemRTI vaminmanm:Um:g; sidesway¦. emKuNm:Um:g;Bt;KW 210 Fñwm -ssr
  24. 24. T.chhay ⎛M ⎞ ⎛ 90 ⎞ C m = 0.6 − 0.4⎜ 1 ⎟ = 0.6 − 0.4⎜ ⎜M ⎟ ⎟ = 0.2565 ⎝ 2⎠ ⎝ 104.8 ⎠ sMrab;GkS½énkarBt; KL K x L 1.0(15)(12 ) = = = 34.09 r rx 5.28 ¬krNIenHKμan sidesway dUcenHeKeRbI K x sMrab; braced condition¦. enaH π 2 EAg π 2 (29000)(19.1) Pe1 = = = 4704kips (KL / r )2 (34.09)2 emKuNm:Um:g;bEnßmsMrab;m:Um:g; nonsway KW Cm 0.2565 B1 = = = 0.284 < 1.0 1 − (Pu / Pe1 ) 1 − (454 / 4704 ) 211 Fñwm -ssr
  25. 25. T.chhay dUcenHeRbI B1 = 1.0 M u = B1M nt + B2 M lt = 1.0(104.8) + 0 = 104.8 ft − kips BI beam design charts CamYynwg Lb = 15 ft φb M n = 343 ft − kips ¬sMrab; Cb = 1.0 ¦ φb M p = 358 ft − kips rUbTI 6>17 bgðajBIdüaRkamm:Um:g;Bt;sMrab;m:Um:g;énbnÞúkTMnaj. ¬karKNna Cb KWQrelItMél dac;xat dUcsBaØaenAkñúgdüaRkamenHminmansar³sMxan;eT¦. dUcenH 12.5M max Cb = 2.5M max + 3M A + 4M B + 3M C 12.5 × (104.8) = = 2.24 2.5(104.8) + 3(41.3) + 4(74) + 3(56.1) sMrab; Cb = 2.24 φb M n = 2.24(343) > φb M p = 358 ft − kips dUcenHeRbI φb M n = 358 ft − kips kMNt;smIkarGnþrkmμEdlsmRsb Pu 454 = = 0.7252 > 0.2 φc Pn 626 eRbIsmIkar AISC Equation H1-1a. Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.7252 + 8 ⎛ 104.8 + 0 ⎞ = 0.985 < 1.0 + ⎜ + ⎜ ⎟ (OK) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 358 ⎠ sMrab;lkçxNÐbnÞúk (A4-4), Pu = 212kips / M nt = 47.6 ft − kips ehIy M lt = 171.6 ft − kips . sMrab; unbraced condition/ 212 Fñwm -ssr
  26. 26. T.chhay ⎛M ⎞ ⎛ 40.5 ⎞ C m = 0.6 − 0.4⎜ 1 ⎟ = 0.6 − 0.4⎜ ⎜M ⎟ ⎟ = 0.2597 ⎝ 2⎠ ⎝ 47.6 ⎠ Pe1 = 4704kips ¬ Pe1 minGaRs½ynwglkçxNÐbnÞúk¦ Cm 0.2597 B1 = = = 0.272 < 1.0 1 − (Pu / Pe1 ) 1 − (212 / 4704 ) dUcenH B1 = 1.0 eyIgminmanTinñy½nRKb;RKan;edIm,IKNnaemKuNm:Um:g;bEnßmeGay)ansuRkitsMrab; sway moment B2 BI AISC Equation C1-4 b¤ C1-5. RbsinebIeyIgsnμt;fapleFobrvagbnÞúktamGkS½ EdlGnuvtþmkelIGgát; nig Euler load capacity mantMéldUcKñasMrab;RKb;ssrenAkñúgCan; nigsMrab; ssrEdleyIgBicarNa enaHeyIgGacsresr Equation C1-5³ 1 1 B2 = ≈ 1 − (∑ Pu / ∑ Pe 2 ) 1 − (Pu / Pe 2 ) sMrab; Pe2 eRbI K x EdlRtUvnwg unbraced condition³ KL K x L 1.2(15)(12 ) = = = 40.91 r rx 5.28 π 2 EAg π 2 (29000)(19.1) Pe 2 = = = 3266kips (KL / r )2 (40.91)2 BI AISC Equation C1-5/ 1 1 B2 ≈ = = 1.069 1 − (Pu / Pe 2 ) 1 − (212 / 3266) m:Um:g;bEnßmsrubKW M u = B1M nt + B2 M lt = 1.0(47.6 ) + 1.069(171.6) = 231.0 ft − kips eTaHbICam:Um:g; M nt nig M lt mantMélxusKñak¾eday k¾BYkvaRtUv)anEbgEckdUcKña ehIy Cb nwgenAdEdl . enARKb;GRtaTaMgGs; BYkvamantMélFRKb;RKan;Edl φb M p = 358 ft − kips Ca design strength edayminKitBIm:Um:g;NamYyeLIy. Pu 212 = = 0.3387 > 0.2 φc Pn 626 dUcenHeRbI AISC Epuation H1-1a³ Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.3387 + 8 ⎛ 231.0 + 0 ⎞ = 0.912 < 1.0 + ⎜ + ⎜ ⎟ (OK) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 358 ⎠ cMeLIy³ Ggát;enHbMeBjtMrUvkarrbs; AISC Specification. 213 Fñwm -ssr
  27. 27. T.chhay 6>8 KNnamuxkat;Fñwm-ssr Design of Beam-Column edaysarenAkñúgrUbmnþGnþrkmμmanGBaØtiCaeRcIn enaHkarKNnamuxkat;Fñwm-ssrCadMeNIrkar KNnaEdlRtUvkarCacaM)ac;nUv trial-and-error process. sMrab;kareRCIserIscugeRkay KWeKeRCIserIs rUbragNakan;EtEk,r kan;Etl¥. muxkat;sakl,gRtUv)aneRCIserIs nigRtUv)anepÞógpÞat;eLIgvijeday eRbIrUbmnþGnþrkmμ. dMeNIrkard¾manRbsiT§PaBbMputkñúgkareRCIserIsmuxkat;sakl,gRtUv)anbegáIteLIg CadMbUgsMrab; allowable stress design (Burgett, 1973), ehIyRtUv)anTTYl ykmkeRbIsMrab; LRFD Edlmanerobrab;enAkñúg part 3 of the Manual, “Column Design”. lkçN³sMxan;sMrab;viFIenHKWCa karbMElgBIm:Um:g;Bt;eTACabnÞúktamGkS½smmUl. bnÞúkEdl)anBIkarbMElgRtUv)anyk eTAbEnßmelI bnÞúkCak;Esþg ehIyrUbragEdlRtUvRTbnÞúksrubRtUv)aneRCIserIsBI column load tables. bnÞab;mk eK RtUvBinitürUbragsakl,genHCamYy Equation H1-1a b¤ H1-1b. bnÞúktamGkS½RbsiT§PaBsrubRtUv)an eGayeday Pu eq = Pu + M ux m + M uy mu Edl Pu = bnÞújktamGkS½emKuNCak;Esþg M ux = m:Um:g;emKuNeFobGkS½ x M uy = m:Um:g;emKuNeFobGkS½ y m = tMélefrEdlmanenAkúñgtarag n = tMélefrEdlmanenAkúñgtarag eKalkarN_énkarviFIenHGacRtUv)anRtYtBinitüedaysresrsmIkar ^># eLIgvijdUcxageRkam. dMbUgKuNGgÁTaMgBIreday φc Pn ³ φ PM φc Pn M uy Pu + c n ux + ≤ φc Pn φb M nx φb M ny b¤ Pu + (M ux × a constant ) + (M uy × a constant ) ≤ φc Pn GgÁxagsþaMénvismIkarCa design strength rbs;Ggát;EdlBicarNa ehIyGgÁxageqVgGacCa bnÞúkemKuNxageRkAEdlRtUvTb;Tl;. tYnImYy²énGgÁxageqVgmanxñatkMlaMg dUcenHtMélefrCaGñkbM Elgm:Um:g;Bt; M ux nig M uy eTACakMub:Usg;bnÞúktamGkS½. tMélefrmFüm m RtUv)anKNnasMrab;RkumepSgKñarbs; W-shape ehIyRtUv)aneGayenAkñúg Table 3-2 in Part 3 of the Manual. tMél u RtUv)aneGayenAkñúg column load table sMrab;rUbrag 214 Fñwm -ssr
  28. 28. T.chhay nImYy²EdlmanenAkñúgtarag. edIm,IeRCIserIsrUbragsakl,gsMrab;Ggát;CamYynwgbnÞúktamGkS½ nigm:U m:g;Bt;eFobGkS½TaMgBIr eKRtUvGnuvtþdUcxageRkam. !> eRCIserIstMélsakl,g m edayQrelIRbEvgRbsiT§PaB KL . yk u = 2.0 @> KNnabnÞúksgát;tamGkS½RbsiT§PaB³ Pu eq = Pu + M ux m + M uy mu eRbIbnÞúkenHedIm,IeRCIserIsrUbragBI column load tables. #> eRbItMél u EdleGayenAkñúg column load tables nigtMélfμIrbs; m BI Table 3-2 edIm,I KNnatMélfμIrbs; Pu eq . eRCIserIsrUbragepSgeTot. $> eFVIeLIgvijrhUtdl;tMél Pu eq ElgERbRbYl. ]TahrN_ 6>8³ Ggát;eRKOgbgÁúMxøHenAkñúg braced frame RtUvRTbnÞúksgát;tamGkS½emKuN 150kips nig m:Um:g;cugemKuN 75 ft − kips eFobnwgGkS½xøaMg ehIy 30 ft − kips eFobnwgGkS½exSay. m:Um:g;TaMgBIr enHeFVIGMeBIenAelIcugmçag ÉcugmçageTotCaTMr pinned. RbEvgRbsiT§PaBeFobnwgGkS½nImYy²KW 15 ft . minmanbnÞúkxageFVIGMeBIelIGgát;enHeT, eRbIEdk A36 nigeRCIserIs W-shape EdlRsalCageK. dMeNaHRsay³ emKuNm:Um:g;bEnßm B1 Gacsnμt;esμInwg 1.0 edIm,IeFVIkareRCIserIsmuxkat;sakl,g. sMrab;GkS½nImYy² M ux = B1M ntx ≈ 1.0(75) = 75 ft − kips M uy = B1M nty ≈ 1.0(30 ) = 30 ft − kips BI Table 3-2, part 3 of the Manual, m = 1.75 edayeFVI interpolation eRbItMéledIm u = 2.0 Pu eq = Pu + M ux m + M uy mu = 150 + 75(1.75) + 30(1.75)(2.0 ) = 386kips cab;epþImCamYynwgrUbragtUcCageKenAkñúg column load tables, sakl,g W 8 × 67 ¬ φc Pn = 412kips / u = 2.03 ¦³ m = 2 .1 Pu eq = 150 + 75(2.1) + 30(2.1)(2.03) = 435kips tMélenHFMCag design strength= 412 ft − kips dUcenHeKRtUvsakl,gmuxkat;epSgeTot. sakl,g W 10 × 60 ¬ φc Pn = 416kips / u = 2.0 ¦³ 215 Fñwm -ssr
  29. 29. T.chhay m = 1.85 Pu eq = 150 + 75(1.85) + 30(1.85)(2.00 ) = 400kips < 416kips (OK) dUcenH W 10 × 60 CarUbragsakl,gEdlGaceRbIkar)an. RtYtBinitü W 12s nig W 14s . sakl,g W 12 × 58 ¬ φc Pn = 397kips / u = 2.41 ¦³ m = 1.55 Pu eq = 150 + 75(1.55) + 30(1.55)(2.41) = 378kips < 397 kips (OK) dUcenH W 12 × 58 CarUbragsakl,gEdlGaceRbIkar)an. W 14 EdlRsalCageKsMrab;eFVIkarCamYy nwgbnÞúkxageRkAKW W 14 × 61 EtvaF¶n;Cag W 12 × 58 . dUcenHeRbI W 12 × 58 CarUbragsakl,g³ Pu 150 = 0.3778 > 0.2 φc Pn 397 dUcenHeRbI AISC Equatiom H-1-1a KNnam:Um:g;Bt;eFobGkS½ x K x L 15(12 ) = = 34.09 rx 5.28 π 2 EAg π 2 (29000)(17.0) Pe1 = = = 4187kips (KL / r )2 (34.09)2 C m = 0.6 − 0.4(M 1 / M 2 ) = 0.6 − 0.4(0 / M 2 ) = 0.6 ¬sMrab;GkS½TaMgBIr¦ Cm 0 .6 B1 = = = 0.622 < 1.0 1 − (Pu / Pe1 ) 1 − (150 / 4187 ) dUcenHeRbI B1 = 1.0 M ux = B1M ntx = 1.0(75) = 75 ft − kips bnÞab;mk kMNt; design strength. BI beam designth curves, sMrab; Cb = 1 nig Lb = 15 ft / φb M n = 220 ft − kips . BIrUbTI 5>15g, Cb = 1.67 . sMrab; Cb = 1.67 design strength KW Cb × 220 = 1.67(220) = 367 ft − kips m:Um:g;enHFMCag φb M p = 233 ft − kips dUcenHeRbI φb M n = 233 ft − kips KNnam:Um:g;Bt;eFobGkS½ y K yL 15(12) = = 71.71 ry 2.51 216 Fñwm -ssr
  30. 30. T.chhay π 2 EAg π 2 (29000)(17.0) Pe1 = = = 946.2kips (KL / r )2 (71.71)2 Cm 0 .6 B1 = = = 0.713 < 1.0 1 − (Pu / Pe1 ) 1 − (150 / 946.2 ) dUcenHeRbI B1 = 1.0 M uy = B1M nty = 1.0(30 ) = 30 ft − kips W 12 × 58CarUbrag compact sMrab;RKb;tMélrbs; Pu dUcenH nomical strength KW M py ≤ 1.5M yy . Design strength KW φb M ny = φb M py = φb Z y F y = 0.90(32.5)(36) = 1053in. − kips = 87.75 ft − kips b:uEnþ Z y / S y = 32.5 / 21.4 = 1.52 > 1.5 Edlmann½yfa φb M ny KYrEtykesμInwg φb (1.5M yy ) = φb (1.5F y S y ) = 0.90(1.5)(36 )(21.4) = 1040in. − kips = 86.67 ft − kips BI AISC Equation H1-1a, Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.3778 + 8 ⎛ 75 + 30 ⎞ + ⎜ + ⎜ ⎟ φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 233 86.67 ⎠ = 0.972 < 1.0 (OK) cMeLIy³ eRbI W 12 × 58 . ebIeTaHbICaviFIEdleTIbnwgbgðajsMrab;eRCIserIsrUbragsakl,gqab;rkeXIjk¾eday k¾viFIEdl manlkçN³smBaØCagenHRtUv)anesñIeLIgeday Yura (1988). bnÞúktamGkS½EdlsmmUlEdlRtUv)an eRbIKW 2M x 7.5M y Pequiv = P + d + b ¬^>%¦ Edl P = bnÞúktamGkS½emKuN M x = m:Um:g;emKuNeFobGkS½ x M y = m:Um:g;emKuNeFobGkS½ y d = kMBs;Fñwm b = TTwgFñwm tYTaMgGs;enAkñúgsmIkar ^>@ RtUvEtmanxñatRtUvKña. 217 Fñwm -ssr
  31. 31. T.chhay ]TahrN_ 6>9³ eRbI Yura’s method edIm,IeRCIserIsrUbragsakl,g W 12 sMrab;Fñwm-ssrén]TahrN_ 6>8. dMeNaHRsay³ BIsmIkar 6>5 bnÞúktamGkS½smmUlKW 2M x 7.5M y 2(75 × 12) 7.5(30 × 12) Pequiv = P + + = 150 + + = 525kips d b 12 12 EdlTTwg b RtUv)ansnμt;esμInwg 12inches . BI column load tables, sakl,g W 12 × 72 ¬ φc Pn = 537kips ¦. CamYynwg Yura’s method eKTTYl)anrUbragsakl,gFMCag Manual method Etvaminy:agdUcenH rhUteT. enAeBlEdltYm:Um:g;Bt;lub ¬]TahrN_ Ggát;manlkçN³CaFñwmCagssr¦ Yura ENnaMfa bnÞúk tamGkS½RtUvbMElgeTACam:Um:g;Bt;smmUleFobGkS½GkS½ x . bnÞab;mkrUbragsakl,gRtUv)aneRCIserIs BI beam design charts in part 3 of the Manual. m:Um:g;smmUlKW³ d M equiv = M x + P 2 karKNnamuxkat;Fñwm-ssrEdlminBRgwg Design of Unbraced Beam-Column karKNnamuxkat;dMbUgrbs;Fñwm-ssrenAkñúg braced frame RtUv)anbgðajrYcehIy. emKuNm:U m:g;bEnßm B1 RtUv)ansnμt;esμI 1.0 edIm,IeRCIserIsmuxkat;sakl,g bnÞab;mk B1 RtUv)ankMNt;sMrab; rUbragenaH. sMrab;Fñwm-ssrRbQmnwg sidesway emKuNm:Um:g;bEnßm B2 EdlQrelIGBaØtiCaeRcIn EdlminsÁal;rhUtdl;ssrTaMgGs;enAkñúgeRKagRtUv)aneRCIserIs. RbsinebI AISC Equation C1-4 RtUv)aneRbIsMrab; B2 enaHeKminman sidesway deflection Δ oh sMrab;karKNnamuxkat;dMbUgeT. Rb sinebIeKeRbI AISC Equation C1-5 enaHeKGacminsÁal; ∑ Pe2 . viFIxageRkamRtUv)anesñIeLIgedIm,Irk B2 . viFITI1> snμt; B2 = 1.0 . bnÞab;BIeRCiserIsrUbragsakl,g KNna B2 BI AISC Equation C1-5 eday snμt;fa ∑ Pu / ∑ Pe2 KWdUcKñanwg Pu / Pe2 sMrab;Ggát;EdlBicarNa ¬dUcenAkñúg]TahrN_6>7¦. viFITI2> eRbIkarkMNt;dMbUg (predetermined limit) sMrab; drift index Δ oh / L EdlCapleeFob story drift elIkMBs;Can;. kareRbInUv drift index GnuBaØatGtibrmasMrab; serviceability 218 Fñwm -ssr
  32. 32. T.chhay requirement RsedogKñanwgkarkMNt;PaBdabrbs;Fñwm. eKENnaMeGayeRbI drift index cenøaHBI 1 / 500 eTA 1 / 200 . cMNaMfa Δ oh Ca drift EdlekItBI ∑ H dUcenHRbsinebI drift index QrenAelI service load enaHbnÞúkxag H RtUvEtCa service load Edr. ]TahrN_ 6>10³ rUbTI 6>18 bgðajBI single-story unbraced frame EdlrgnUvbÞúkefr bnÞúkGefrelI dMbUl nigxül;. rUbTI 6>18 a bgðajBI service gravity load nig rUbTI6>18 b bgðajBI service wind load ¬EdlrYmbBa©ÚlTaMg uplift b¤ suction enAelIdMbUl¦. eRbIEdk A572 grade 50 nigeRCIserIs rUbrag W 12 sMrab;ssr ¬Ggát;bBaÄr¦. KNnamuxkat;sMrab; drift index 1/ 400 edayQrelI service wind load. m:Um:g;Bt;eFobnwgGkS½xøaMg ehIyssrnImYy²BRgwgxagenAxagcug nigKl;. dMeNaHRsay³ eRKagenHCaeRKagsþaTicminkMNt;mYydWeRk. karviPaKrcnasm<n§½minkMNt;minRtUv)aneFVI enATIednHeT. lT§plénkarviPaKeRKagRtUv)anbgðajenAkñúgrUbTI 6>19edaysegçb. bnÞúktamGkS½ nig m:Um:g;cugRtUv)aneGaydac;edayELkBIKñasMrab;bnÞúkefr bnÞúkGefr bnÞúkxül;EdlmanGMeBIelIdMbUl nig bnÞúkxül;xag. bnÞúkbBaÄrTaMgGs;RtUv)andak;sIuemRTIKña ehIycUlrYmEtCamYynwgm:Um:g; M nt b:ueNÑaH. bnÞúkxagbegáItm:Um:g; M lt . bnSMbnÞúkEdlBak;Bn§½CamYynwgbnÞúkefr D / bnÞúkGefrelIdMbUl Lr nigbnÞúkxül; W KWdUcxageRkam³ A4-2: 1.2 D + 0.5 Lr Pu = 1.2(14) + 0.5(26) = 29.8kips M nt = 1.2(50) + 0.5(94) = 107 ft − kips M lt = 0 A4-3: 1.2 D + 1.6 Lr + 0.8W Pu = 1.2(14) + 1.6(26) + 08(− 9 + 1) = 52.0kips 219 Fñwm -ssr
  33. 33. T.chhay M nt = 1.2(50) + 1.6(94) + 0.8(− 32) = 184.8 ft − kips M lt = 0.8(20) = 16.0 ft − kips A4-4: 1.2 D + 0.5 Lr + 1.3W Pu = 1.2(14) + 0.5(26 ) + 1.3(26) = 19.4kips M nt = 1.2(50) + 0.5(94) + 1.3(− 32 ) = 65.4 ft − kips M lt = 1.3(20) = 26 ft − kips bnSMbnÞúk A4-3 pþl;nUvtMélFMCageK. sMrab;eKalbMNgénkareRCIserIsrUbragsakl,g snμt;fa B1 = 1.0 . tMélrbs; B2 Gac RtUv)anKNnaBI AISC Equation C1-4 nig design drift index³ 1 1 1 B2 = = = = 1.107 1 − ∑ Pu (Δ oh / ∑ HL ) 1 − (∑ Pu / ∑ H )(Δ oh / L ) 1 − [2(52.0 ) / 2.7](1 / 400) bnÞúkedkKμanemKuN ∑ H RtUv)aneRbIBIeRBaH drift index KWQrelI drift GtibrmaEdlbNþalmkBI service load. dUcenH M u = B1M nt + B2 M lt = 1.0(184.8) + 1.107(16) = 202.5 ft − kips edayminsÁal;TMhMrbs;Ggát; eKminGaceRbI alignment chart sMrab;emKuNRbEvgRbsiT§PaB)aneT. Table C-C2.1 enAkñúg Commentary to the Specification bgðajfakrNI (f) RtUvKñay:agxøaMgeTAnwg lkçxNÐcugsMrab;krNI sidesway én]TahrN_enH ehIyEdl K x = 2.0 . 220 Fñwm -ssr
  34. 34. T.chhay sMrab; braced condition, eKeRbI K x = 1.0 . edaysarEtGgát;TaMgGs;RtUv)anBRgwgTisedA mYyeTotEdr enaHeKyk K y = 1.0 . bnÞab;mk eKGaceRCIserIsmuxkat;sakl,gEdlmaneGayenAkñúg Part 3 of the Manual. BI Table 3-2 emKuNm:Um:g;Bt; m = 1.5 sMrab; W 12 CamYynwg KL = 15 ft . Pu eq = Pu + M ux m + M uy mu = 52.0 + 202.5(1.5) + 0 = 356kips sMrab; KL = K y L = 15 ft / W 12 × 53 man design strength φc Pn = 451kips . sMrab;GkS½ x K x L 2.0(15) = = 14.2 ft < 15 ft rx / ry 2.11 dUcenH KL = 15 ft lub sakl,g W 12 × 53 . sMrab; braced condtition K x L 1.0(15)(15) = = 34.42 rx 5.23 π 2 EAg π 2 (29000 )(15.6) Pe1x = = = 3769 (K x L / rx )2 (34.42)2 ⎛M ⎞ ⎛ 0 ⎞ C m = 0.6 − 0.4⎜ 1 ⎟ = 0.6 − 0.4⎜ ⎜M ⎟ ⎜ M ⎟ = 0 .6 ⎟ ⎝ 2⎠ ⎝ 2⎠ BI AISC Equation C1-2 Cm 0 .6 B1 = = = 0.608 < 1.0 1 − (Pu / Pe1 ) 1 − (52.0 / 3769 ) dUcenHeRbI B1 = 1.0 cMNaMfa B1 = 1.0 CatMélsnμt;dMbUg ehIyedaysarEt B2 minRtUv)anpøas;bþÚr enaHtMél M u = 202.5 ft − kips Edl)anKNnaBIdMbUgk¾minRtUv)anpøas;bþÚrEdr. BI beam design chart in Part 4 of the manual CamYynwg Lb = 15 ft design moment sMrab; W 12 × 53 CamYynwg Cb = 1.0 KW φb M n = 262 ft − kips sMrab;m:Um:g;Bt;EdlERbRbYlsmamaRtBIsUnüenAcugmçag eTAGtibrmaenAcugmçageTot tMélrbs; Cb = 1.67 ¬emIlrUbTI 5>15 g¦. dUcenHtMélEdlEktMrUvén design moment KW φb M n = 1.67(262) = 438 ft − kips b:uEnþ m:Um:g;enHFMCag plastic moment capasity φb M p = 292 ft − kips / EdleKGacek)anenA kñúg charts. dUcenH design strength RtUv)ankMNt;Rtwm φb M n = φb M p = 292 ft − kips 221 Fñwm -ssr
  35. 35. T.chhay kMNt;rUbmnþGnþrkmμEdlsmRsb Pu 52 = = 0.1153 < 0.2 φc Pn 451 dUcenHeRbI AISC Equation H1-1b: Pu ⎛ M ux M uy ⎞ 0.1153 ⎛ 202.5 ⎞ +⎜ + ⎟= +⎜ + 0 ⎟ = 0.751 < 1.0 (OK) 2φc Pn ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 2 ⎝ 292 ⎠ edaysarlT§plenHtUcCag 1.0 xøaMg dUcenHsakl,grUbragEdltUcCagenHBIrTMhM. sakl,g W 12 × 45 . sMrab; KL = K y L = 15 ft, φc Pn = 299kips . sMrab;GkS½ x K x L 2.0(15) = = 11.3 ft < 15 ft rx / ry 2.65 dUcenH KL = 15 ft lub sMrab; braced condtition K x L 1.0(15)(15) = = 34.95 rx 5.15 π 2 EAg π 2 (29000 )(13.2) Pe1x = = = 3093 (K x L / rx )2 (34.95)2 BI AISC Equation C1-2, Cm 0 .6 B1 = = = 0.610 < 1.0 1 − (Pu / Pe1 ) 1 − (52.0 / 3093) dUcenHeRbI B1 = 1.0 BI beam design charts CamYynwg Lb = 15 ft m:Um:g;KNnasMrab; W 12 × 45 CamYynwg Cb = 1.0 KW φb M n = 201 ft − kips sMrab; Cb = 1.67 φb M n = 1.67(201) = 336 ft − kips > φb M p = 242.5 ft − kips dUcenH design strength KW φb M n = φb M p = 242.5 ft − kips kMNt;rUbmnþGnþrkmμEdlsmRsb³ Pu 52.0 = = 0.1739 < 0.2 φc Pn 299 222 Fñwm -ssr
  36. 36. T.chhay dUcenHeRbI AISC Equation H1-1b: Pu ⎛ M ux M uy ⎞ 0.1739 ⎛ 202.5 ⎞ +⎜ + ⎟= +⎜ + 0 ⎟ = 0.922 < 1.0 (OK) ⎜ 2φc Pn ⎝ φb M nx φb M ny ⎟ 2 ⎝ 242.5 ⎠ ⎠ cMeLIy³ eRbI W 12 × 45 . enA]TahrN_6>10 karkMNt; drift index CaviFIkñúgkarKNna ehIyeKminmanviFINaedIm,I KNnaemKuNm:Um:g;bEnßm B2 . RbsinebIeKminR)ab; drift index tMélrbs; B2 GacRtUv)ankMNt;ecj BI AISC Equation C1-5 dUcxageRkam ¬edayeRbIlkçN³rbs; W 12 × 45 ¦³ K x L 2.0(15)(12) = = 69.90 rx 5.15 π 2 EAg π 2 (29000)(13.2) Pe2 x = = = 773.2kips (K x L / rx )2 (69.90)2 1 1 B2 = = = 1.072 1 − (∑ Pu / ∑ Pe 2 ) 1 − [2(52.0) / 2(773.2)] 6>9> Trusses With Top Chord Loads Between Joints RbssinebIGgát;rgkarsgát;rbs; truss RtUvRTbnÞúkEdlmanGMeBIenAcenøaHcugsgçagrbs;va enaH vanwgRtUvrgnUvm:Um:g;Bt; k¾dUcCabnÞúksgát;tamGkS½ dUcenHGgát;enHCa beam-colum. krNIenHGacekIt manenAelI top chord of the roof truss edayédrEngsßitenAcenøaHtMN. eKk¾RtUvKNna top chord of an open-web steel joist Ca beam-column Edr BIeRBaH open-web steel joist RtUvRTbnÞúkTMnajEdl BRgayesμIenAelI top chord rbs;va. edIm,IkarBarbnÞúkenH eKRtUveFVIm:UEdl truss CakarpSMeLIgeday man continuous chord member nig pin-connected web members. bnÞab;mkeKGacedaHRsayrk bnÞúktamGkS½ nigm:Um:g;Bt;edayeRbIkarviPaKeRKOgbgÁúMdUcCag stiffness method. eK)anesñIeLIgnUvviFI saRsþdUcxageRkam³ !> KitGgát;nImYy²rbs; top chord CaFñwmbgáb;cug. eRbIm:Um:g;bgáb;cugCam:Um:g;GtibrmaenAkñúg Ggát;. Cak;Esþg top chord CaGgát;Cab; CagCaesrIénGgát;tMNsnøak; dUcenHkarcat;TukenH manlkçN³suRkitCagkarEdlcat;TukGgát;nImYy²CaFñwmsmBaØ. @> bEnßmkMlaMgRbtikmμBIFñwmbgáb;cugenHeTAbnÞúkenARtg;tMNedIm,ITTYl)anbnÞúkelItMNsrub. 223 Fñwm -ssr
  37. 37. T.chhay #> viPaK truss CamYynwgbnÞúkRtg;tMNTaMgenH. bnÞúktamGkS½EdlCalT§plenAkñúg top chord member CabnÞúksgát;tamGkS½EdlRtUvykeTAeRbIkñúgkarKNna. viFIenHRtUv)anbgðajCalkçN³düaRkamenAkñúg rUbTI 6>20. müa:gvijeTot eKGacrkm:Um:g;Bt; nigRbtikmμrbs;Fñwmedaycat;Tuk top chord CaFñwmCab;EdlmanTMrenARtg;tMNnImYy². ]TahrN_ 6>11³ rUbTI 6>21 bgðajBI parallel-chord roof trussEdl top chord RTédrENgenA Rtg;tMN nigenARtg;cenøaHtMN. bnÞúkemKuNEdlbBa¢ÚnedayédrENgRtUv)anbgðaj. KNnamuxkat; top chord. eRbIEdk A36 nigeRCIserIs structural tee Edlkat;ecjBI W-shape. 224 Fñwm -ssr
  38. 38. T.chhay dMeNaHRsay³ m:Um:g;Bt; nigkMlaMgelItMNEdlbNþalmkBIbnÞúkEdlmanGMeBIenAcenøaHtMNRtUv)anrk edaycat;Tuk top chord nImYy²CaFñwmbgáb;cug. BI Part 4 of the Manual, “Beam and girder Design,”m:Um:g;bgáb;cugsMrab;Ggát; top chord nImYy²KW PL 2.4(10) M = M nt = = = 3.0 ft − kips 8 8 m:Um:g;cug nigkMlaMgRbtikmμTaMgenHRtUv)anbgðajenAkñúg rUbTI 6>22 a. enAeBlEdleKbEnßmkMlaMg RbtikmμeTAelIbnÞúkelItMN enaHeKTTYl)ankardak;bnÞúkdUcbgðajenAkñúgrUbTI 6>22 b. kMlaMgsgát; GtibrmatamGkS½nwgekItmanenAkñúgGgát; DE ¬nwgenAkñúgGgát;EdlenAEk,r EdlenAxagsþaMGkS½rbs; ElVg¦ nigGacRtUv)anrkedayBicarNalMnwgrbs;GgÁesrIrbs;Epñkrbs; truss EdlenAxageqVgmuxkat; a-a³ ∑ M I = (19.2 − 2.4 )(30 ) − 4.8(10 + 20 ) + FDE (4 ) = 0 FDE = −90kips¬rgkarsgát;¦ KNnamuxkat;sMrab;bnÞúktamGkS½ 90kips nigm:Um:g;Bt; 3.0 ft − kips 225 Fñwm -ssr
  39. 39. T.chhay Table 3-2 in Part 3 of the Manual min)anpþl;eGaysMrab; structural tee. eKGaceRbI Yura’s method (Yura, 1988) Edl)anbegáIteLIgsMrab;Ggát; I- nig H-shape. eKRtUvkarrUbragtUc BIeRBaH bnÞúktamGkS½tUc ehIym:Um:g;k¾tUcebIeFobnwgbnÞúktamGkS½. RbsinebIeKeRbI tee EdlmankMBs; 6in. 2M x 7.5M y 2(3)(12) Pequiv = P + + = 90 + + 0 = 102kips d b 6 BI column load table CamYynwg K x L = 10 ft nig K y L = 5 ft / sakl,g WT 6 ×17.5 ¬ φc Pn = 124kips ¦. m:Um:g;Bt;KWeFobnwgGkS½ x ehIyGgát;RtUv)anBRgwgRbqaMgnwg sidesway³ M nt = 3.0 ft − kips M lt = 0/ edaysarmankMlaMgxagmanGMeBIelIGgát; ehIycugRtUv)anTb;enaH Cm = 0.85 ¬Commentary approach minRtUv)aneRbIenATIenHeT¦. KNna B1 ³ KL K x L 10(12 ) = = = 68.18 r rx 1.76 π 2 EAg π 2 (29000)(5.17 ) Pe1 = = = 318.3kips (KL / r )2 (68.18)2 Cm 0.85 B1 = = = 1.185 1 − (P / Pe1 ) 1 − (90 / 318.3) 1 m:Um:g;bEnßmKW M u = B1M nt + B2 M lt = 1.185(3.0) + 0 = 3.555 ft − kips RbsinebImuxkat;RtUv)ancat;fñak;Ca slender enaH nominal moment strength rbs; structural tee nwgQrelI local buckling EtRbsinebImindUecñaHeT vanwgQrelI lateral-torsional buckling ¬emIl AISC Equation F1.2c nig Epñk 5>14 kñúgesovePAenH¦. sMrab;søab bf 6.560 λ= = = 6.308 2t f 2(0.520) 95 95 λr = = = 15.83 > λ Fy 36 sMrab;RTnug d 6.25 λ= = = 20.83 t w 0.300 127 127 λr = = = 21.17 > λ Fy 26 226 Fñwm -ssr
  40. 40. T.chhay edaysar λ < λr sMrab;TaMgsøab nigRTnug rUbragminEmnCa slender eT ehIy lateral-torsional buckling lub. BI AISC Equation F1-15/ π EI y GJ ⎛ 2⎞ M n = M cr = ⎜ B + 1+ B ⎟ (AISC Equation F1-15) Lb ⎝ ⎠ ≤ 1 .5 M ysMrab;eCIg b¤tYxøÜnrgkarTaj ≤ 1.0 M y sMrab;eCIg b¤tYxøÜnrgkarsgát; BI AISC Eqution F1-16, ⎡ 6.25 ⎤ 12.2 B = ±2.3(d / Lb ) I y / J = ±2.3⎢ ⎥ = ±1.378 ⎣ 5(12 ) ⎦ 0.369 ehIy nominal strength BI AISC Equation F1-15 KW` π 29000(12.2 )(11200)(0.369) ⎛ 2⎞ Mn = ⎜ ± 1.378 + 1 + (1.378) ⎟ 5(12) ⎝ ⎠ = 2002(± 1.378 + 1.703) = 6168in. − kips b¤ 650.5in. − kips tMélviC¢manrbs; B RtUvKñanwgkMlaMgTajenAkñúgtYxøÜnrbs; tee ehIysBaØaGviC¢manRtUv)aneRbIedIm,ITTYl ersIusþg;enAeBltYxøÜnrgkMlaMgsgát;. sMrab;kardak;bnÞúkenAkñúg]TahrN_enH m:Um:g;GtibrmaekItmanenA TaMgcugbgáb; nigkNþalElVg dUcenHersIusþg;RtUv)anRKb;RKgedaykMlaMgsgát;enAkñúgtYxøÜn ehIy M n = 650.5in. − kips = 54.12 ft − kips RbQmnwgtMélGtibrmaén 1.0(36)(3.23) 1.0 M y = 1.0 Fy S x = = 9.690 ft − kips < 54.21 ft − kips 12 dUcenHeRbI M n = 9.690 ft − kips φb M n = 0.90(9.690) = 8.721 ft − kips kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI Pu 90 = = 0.7258 > 0.2 φc Pn 124 dUcenHeRbI AISC Equation H1-1a: Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.7258 + 8 ⎛ 3.555 + 0 ⎞ + ⎜ + ⎜ ⎟ φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 8.721 ⎠ = 1.09 > 1.0 (N>G) 227 Fñwm -ssr
  41. 41. T.chhay enAkñúg]TahrN_enH m:Um:g;Bt;mantMéltUc ehIydUcKñasMrab; bending strength dUcenHehIyeFVIeGaytY m:Um:g;Bt;rbs;rUbmnþGnþrkmμmantMélFM. kñúgkareRCIserIsmuxkat;EdlsmRsb GñkKNnaRtUvdwgc,as; fa bending strength nig axial compressive strength mantMélFM. rUbragbnÞab;enAkñúg column load tables KW WT 6 × 20 CamYynwg axial compressive strength 133kips . tamkarGegátenAelI dimensions and peoperties tables bgðajfaeyIgkMBugbBa©ÚlRkumrUbragEdlmanGkS½ x CaGkS½ exSay. dUcenHkarBt;rbs;eyIgLÚvenHKWeFobnwgGkS½exSay ehIyvaKμansßanPaBkMNt; lateral- torsional buckling. elIsBIenH RbsinebIrUbrag slender enaH nominal strength nwgQrelI yielding ehIyesμInwg plastic moment capacity EdlRtUvnwgEdlx<s;bMputRtwm 1.5M y . dUcenHsakl,g WT 6 × 20 ¬ φc Pn = 133kips ¦. dMbUg KNna B1 ³ KL K x L 10(12 ) = = = 76.43 r rx 1.57 π 2 EAg π 2 (29000)(5.89 ) Pe1 = = = 288.6kips (KL / r )2 (76.43)2 Cm 0.85 B1 = = = 1.235 1 − (P / Pe1 ) 1 − (90 / 288.6 ) 1 m:Um:g;bEnßmKW M u = B1M nt = 1.235(3.0 ) = 3.705 ft − kips RtYtBinitü slenderness parameters. sMrab;søab bf 8.005 λ= = = 7.772 < λr = 15.83 2t f 2(0.515) sMrab;RTnug λ = td = 5..970 = 20.2 < λr = 21.17 0 295 w edaysarkarBt;eFobnwgGkS½exSay 5.30(36) M n = M p = Z x Fy = = 15.9 ft − kips 12 RbQmnwgtMélGtibrmaén 1.5(36)(2.95) 1.5M y = 1.5Fy S x = = 13.28 ft − kips 12 edaysarEt M p > 1.5M y φb M n = φb (1.5M y ) = 0.90(13.28) = 11.95 ft − kips kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI 228 Fñwm -ssr
  42. 42. T.chhay Pu 90 = = 0.6767 > 0.2 φc Pn 133 dUcenHeRbI AISC Equation H1-1a: Pu 8 ⎛ M ux M uy ⎞ ⎟ = 0.6767 + 8 ⎛ 3.705 + 0 ⎞ = 0.952 < 1.0 + ⎜ + ⎜ ⎟ (OK) φc Pn 9 ⎜ φb M nx φb M ny ⎝ ⎟ ⎠ 9 ⎝ 11.95 ⎠ cMeLIy³ eRbI WT 6 × 20 . 229 Fñwm -ssr

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