9.composite construction

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9.composite construction

  1. 1. T.chhay IX. eRKOgbgÁúMsmas Composite Construction 9>1> esckþIepþIm Introduction eRKOgbgÁúMsmasCaeRKOgbgÁúMsMNg;EdlGgát;rbs;vapÁúMeLIgedaysMPar³BIrRbePTKW EdkeRKag nigebtugGarem:. niyayeGayxøIGgát;eRKOgbgÁúMsmaspSMeLIgedaysMPar³BIr b¤eRcInRbePT. eRKOgbgÁúM smasRtUv)anerobrab;enAkñúg AISC Chapter I, “Composite Members.”. Fñwmsmas (composite beam) GacmaneRcInTMrg;. FñwmsmasBIdMbUgRtUv)ancak;bgáb;kñúgeb tug dUcbgðajenAkñúgrUbTI 9>1 a. vaCaCMerIsmYyenAeBlEdleKRtUvkarkarBareRKOgbgÁúMEdkBIePøIg (fireproofing) ehIymUlehtumYyeTotKWeKGacKitBIkarcUlrYmrbs;ersIusþg;ebtugeTAkúñgersIusþg;rbs; Fñwm. naeBlbc©úb,nñenH eKmanviFIkarBarePøIgEdlmanlkçN³esdækic© nigTMgn;Rsal dUcenHeKkMrcak; bgáb;eRKOgbgÁúMEdkkñúgebtugeToteT. eKGacTTYl)an composite behavior edayP¢ab;FñwmEdkeTAnwg kMralebtugEdlvaRTEdleFVIeGayEpñkTaMgBIreFVIkarCamYyKña. enAkñúgRbBn§½kMral b¤RbBn§½dMbUl Epñk rbs;kMralxNÐeFVIGMeBICamYynwgFñwmEdkedIm,IbegáItCaFñwmsmasEdlman rolled steel shape EdlenABI elIsøabxagelICasøabebtug ¬rUbTI 9>1 b¦. kareFVIkarrYmKñaenHGacRbRBwtþeTA)anRbsinebIeKkarBarkarrGiltamTisedk (horizontal slippage) rvageRKOgbgÁúMTaMgBIr. eKGaceFVIdUcenH)an RbsinebIkMlaMgkat;tamTisedkenARtg;épÞb:H RtUv)ankarBaredayeRKOgsMrab;P¢ab;EdleKeGayeQμaHfa shear connectors. eKOgsMrab;P¢ab;enHGac Ca headed studs, spiral reinforcing steel b¤CaEdkrag channel shape tUc²RbEvgxøIRtUv)anpSar P¢ab;eTAnwgsøabxagelIrbs;EdkFñwmeTAtamKMlatkMNt; edIm,Ipþl;nUvkarpSarP¢ab;CalkçN³emkanictamry³TMBk;enAkñúgebtugEdlrwgmaM ¬rUbTI 9>1 c¦. Stud CaRbePT shear connector EdleKniymeRbICageK eKGaceRbIvaelIsBImYyedImenARtg;TItaMgEtmYy RbsinebIsøabFñwmmanTMhMTUlayRKb;RKan; ¬vaGaRs½ynwgKMlatGnuBaØatEdlmanniyayenAkñúgEpñkTI 9>4¦. mUlehtumYyénPaBeBjniymrbs; shear stud KWPaBgayRsYlkñúgkartMeLIgrbs;va. eKRtUvkarcMnYn shear connector RKb;RKan;edIm,IeFVIeGayFñwmeTACaFñwmsmaseBjelj (fully composite beam). cMnYn shear conncter EdlticCagtMrUvkarnwgeFVIeGayekItmanPaBrGilxøHrvag eRKOgbgÁúMEdk nigebtug/ FñwmEbbenHeKeGayeQμaHfa FñwmsmasedayEpñk (partially composite). 356 eRKOgbgÁúMsmas
  2. 2. T.chhay Partially composite beam ¬EdlCak;EsþgmanT§iBlCag fully composite beam¦ RtUv)anbkRsay enAkñúgEpñkTI 9>7. eRKOgbgÁúMsmasenAkñúgGKarPaKeRcInRtUv)anbegáIteLIgedaykMralEdk (stell deck) EdleFVICa Bum<sMRab;ebtugkMral ehIyRtUv)anminRtUv)anykecjeRkayeBlebtugrwgmaM. kMralEdkk¾cUlrYmenA kñúgersIusþg;rbs;kMral EteyIgmin)anBicarNaBIkarKNnakMralEdkenATIenHeT. eKGaceRbIkMralEdk pñt;EdlrnUtmanTisEkg b¤RsbnwgTisrbs;Fñwm. enAkñúgRbBn§½kMralFmμta rnUtEtgEtEkgeTAnwgFñwmkM ral ehIyRsbeTAnwgrtEdlRTva. eKpSar Shear stud P¢ab;eTAnwgFñwmEdktamcenøaHrnUt dUcenHKMlat rbs; stud tambeNþayFñwmRtUv)ankMNt;edaycMnYnpñt;rbs;rnUt. rUbTI 9>2 bgðajBIkMralxNÐEdl begáIteLIgedaykMralEdkEdlrnUtEkgeTAnwgFñwm. s<an highway PaKeRcInEdleRbIFñwmEdkCaFñwmsmas ehIyCaerOy²FñwmsmasCaCMerIsEdl manlkçN³esdækic©sMrab;sMNg;GaKar. eTaHbICaeKGaceRbI rolled steel beam EdlmanrUbragtUcCag 357 eRKOgbgÁúMsmas
  3. 3. T.chhay manTMgn;RsalCagenAkñúgeRKOgbgÁúMsmask¾eday k¾ GtßRbeyaCn_rbs;vaRtUv)ankat;bnßyedaysar tMélbEnßmén shear connector. eTaHbICay:agdUcenHk¾eday k¾GtßRbeyaCn_epSgeTotrbs;vaGaceFVI eGayeRKOgbgÁúMsmasmankarTak;TajEdr. eKGaceRbI FñwmEdlrak;Cag ehIyPaBdabrbs;vanwgtUc CageRKOgbgÁúMFmμta (conventional noncomposite construction). kugRtaMgeGLasÞicenAkñúgFñwmsmas Elastic Stresses in Compostie Beams eTaHbICa design strength rbs;FñwmsmasCaTUeTAQrelIlkçxNÐenAkar)ak;k¾eday k¾karyl; dwgBIkareFVIkarCamYynwgbnÞúkeFVIkar (service load) mansar³sMxan;sMrab;mUlehtuCaeRcIn. eKEtgEteFVI karGegátPaBdabrbs;eRKOgbgÁúMeRkamGMeBIrbs; service load ehIyenAkñúgkrNIxøH design strength KW QrelIsßanPaBkMNt;én yield dMbUg. eKGacKNnakugRtaMgrgkarBt; (flexural stress) nigkugRtaMgrgkarkat; (shearing stress) enA kñúgFñwmrbs; homogeneous material BIrUbmnþ fb = Mc I nig f v = VQ It b:uEnþ edaysarFñwmsmasminEMmnCa homogeneous material dUcenHrUbmnþTaMgenHKμann½y. edIm,IGaceRbIrUbmnþTaMgenH)an eKRtUvbMElgmuxkat;rbs;ebtugeGayeTACamuxkat;Edk. viFisaRsþenH tMrUveGay strain rbs;EdkEdl)anRbDiteLIgBIebtugmantMéldUcKñanwg strain rbs;EdkBitR)akd. rUbTI 9>3 bgðajBIkMNat;rbs;FñwmsmasCamYynwgdüaRkam stress nig strain. RbsinebIkMralxNÐ RtUv)anP¢ab;y:agl¥eTAnwg rolled steel shape enaH strain RtUvEtmanragdUcGVIEdl)anbgðaj EdlRsb eTAnwg small displacement theory Edl)anniyayfa muxkat;EdlmanlkçN³erobesμImuneBlrgkar Bt;enAEtrkSalkçN³erobesμIeRkayeBlrgkarBt;. b:uEnþ karBRgaykugRtaMgCalkçN³smamaRt (linear stress distribution) Edl)anbgðajmann½yEtcMeBaHFñwmTaMgLayNaEdlRtUv)ansnμt;faCa 358 eRKOgbgÁúMsmas
  4. 4. T.chhay homogeneous material . dMbUg eKRtUvtMrUveGay strain enAkñúgebtugRtg;RKb;cMnucTaMgGs;esμInwg strain enAkñúgEdkCMnYsenARKb;cMnucenaH εc = εs b¤ Ec = Es f f c s nig E f s = s f c = nf c Ec ¬(>!¦ Edl m:UDuleGLasÞicrbs;ebtug Ec = n = s = pleFobm:UDul E Ec AISC I2.2 eGaym:UDuleGLasÞicebs;ebtug * Ec = w1.5 f 'c (US) c c ( Ec = w1.5 1.3 ⋅10 − 3 ) f 'c (SI) Edl wc = TMgn;maDrbs;ebtug f 'c = ersIusþg;rgkarsgát;rbs;ebtugenA @*éf¶ TMgn; normal-weight concrete mantMélRbEhl 145lb / ft 3 = 2320kg / m3 eKGacbkRsaysmIkar (>! dUcxageRkam³ eKRtUvkarebtug n in.2 edIm,ITb;Tl;nwgkMlaMgdUcKña EdlEdk 1in.2 GacTb;)an. edIm,IkMNt;RkLaépÞrbs;EdkEdlnwgTb;Tl;nwgkMlaMgdUcKñaEdlebtugGac eFVI)an eKRtUvEckRkLaépÞebtugeday n . mann½yfaCMnYs Ac eday Ac / n . lT§plEdlTTYl)an CaRkLaépÞbMElg (transformed area). * The ACI Building Code (ACI, 1995) eGaytMélrbs; E c = w1.5 (33) f ' c c KitCa psi b¤ Ec = w1.5 (0.043) c f 'c KitCa N / mm 2 359 eRKOgbgÁúMsmas
  5. 5. T.chhay BicarNamuxkat;smasEdlbgðajenAkñúgrUbTI 9>4 a ¬karkMNt;TTwgsøabRbsiT§PaB b enA eBlEdlFñwmCaEpñkrbs;RbBn§½kMralnwgENnaMenAxagmux¦. edIm,IbMElgRkLaépÞebtug Ac eGayeTACa RkLaépÞEdk eyIgRtUvEckvanwg n . viFId¾gayRsYlKWeKRtUvEckTTwgeday n ehIyrkSakMras;eGayenA dEdl. kareFVIdUcenHeKTTYl)an homogeneous steel section dUcbgðajkñúgrUbTI 9>4b. edIm,IKNna kugRtaMg eyIgRtUvrkTItaMgG½kSNWtrbs;rUbragsmas ehIyKNnam:Um:g;niclPaBEdlRtUvKña. bnÞab;mk eyIgGacKNna bending stresses CamYynwg flexural formula. enAEpñkxagelIbMputrbs;srésEdk Myt f st = I tr enAEpñkxageRkambMputrbs;Edk Myb f sb = I tr Edl M= m:Um:g;Bt;Gnuvtþn_ I st = m:Um:g;niclPaBeFobG½kSNWt ¬dUcKñanwgG½kSTIRbCMuTMgn;rbs; homogeneous section¦ yt = cMgayBIG½kSNWteTAEpñkxagelIbMputrbs;Edk yb = cMgayBIG½kSNWteTAEpñkxageRkambMputrbs;Edk eKGackMNt;kugRtaMgenAkñúgebtugtamviFIdUcKña b:uEnþedaysarsMPar³EdleyIgKitCaEdk enaHlT§pl tUvEcknwg n ¬emIlsmIkar (>!¦ dUcenHeK)an tMélGtibrmarbs; f c = nI yM tr Edl y CacMgayBIG½kSNWteTATItaMgx<s;bMputrbs;ebtug. dMeNIrkarKNnaenHmann½ysMrab;Etm:Um:g;Bt;viC¢man EdlkMlaMgsgát;enAxagelIeRBaHeKmin KitersIusþg;rgkarTajrbs;ebtug. 360 eRKOgbgÁúMsmas
  6. 6. T.chhay ]TahrN_ 9>1³ FñwmsmasmYypSMeLIgedayEdk A36 manrag W16 × 36 CamYynwgkMralebtugkMras; 5in. nigTTwg 87in. enABIxagelIFñwm. ersIusþg;rbs;ebtugKW f 'c = 4000 psi . kMNt;kugRtaMgGtibrma enAkñúgEdk nigebtugEdlekItBIm:Um:g;Bt;viC¢man 160 ft − klips . dMeNaHRsay³ Ec = w1.5 c f 'c = 1451.5 4 = 3495ksi n= E s 29000 Ec = 3495 = 8 .3 yk n = 8 edaysarEtm:UDuleGLasÞicrbs;ebtugCatMélRbhak;RbEhl dUcenHeyIgGacyktMél n CatMélKt; ehIyvanwgpþl;nUvPaBsuRkitRKb;RKan;. dUcenH b 87 = = 10.88in. n 8 rUbTI 9>5 bgðajBI transformed section. eKGackMNt;TItaMgrbs;G½kSNWtedayGnuvtþeKalkarN_m:Um:g;CamYynwgG½kSrbs;m:Um:g;enAEpñk xagelIbMputrbs;kMral. karKNnaRtUv)ansegçbenAkñúgtarag 9>1 ehIycMgayBITItaMgx<s;bMputrbs;kM raleTATIRbCMuTMgn;KW ∑ Ay 273.1 y= = = 4.202in. ∑ A 65.00 edayGnuvtþRTwsþIbTG½kSRsb nigedayerobCataragénkarKNnaenAkñúgtarag 9>2 eyIgTTYl)anm:Um:g; niclPaBrbs; transformed section KW I tr = 1526in.4 kugRtaMgenATItaMgx<s;bMputrbs;EdkKW yt = y − t = 4.202 − 5.00 = −0.7980in. Edl t CakMras;rbs;kMral 361 eRKOgbgÁúMsmas
  7. 7. T.chhay Myt (160 × 12 )(0.7980 ) f st = Ltr = 1526 = 1.00ksi ¬rgkarTaj¦ tarag 9>1 eRKOgbgÁúM A y Ay ebtug 54.40 2.50 136.0 W 16 × 36 10.6 12.93 137.1 65.00 273.1 tarag 9>21 eRKOgbgÁúM A y I d I + Ad 2 ebtug 54.40 2.50 113.3 1.702 270.9 10.6 12.93 448 8.728 1255 W 16 × 36 1525.9 ¬TItaMgx<s;bMputrbs;EdksßitenABIxageRkamG½kSNWt dUcenH f st CakugRtaMTaj¦ kugRtaMgenATItaMgeRkambMputrbs;Edk³ yb = t + d − y = 5 + 15.86 − 4.202 = 16.66in. Myb (160 × 12 )(16.66 ) f sb = I tr = 1526 = 21.0ksi ¬rgkarTaj¦ kugRtaMgenATItaMgx<s;bMputrbs;rbs;ebtugKW M y (160 × 12)(4.202) fc = = = 0.661ksi nI tr 8 × 1526 RbsinebIeKsnμt;ebtugminmanersIusþg;Tb;karTaj enaHebtuEdlsßitenABIeRkamG½kSNWtminRtUv)anyk mkKiteT. enaHragFrNImaRtrbs; transformed section xusBIragFrNImaRtedImEdl)ansnμt;. edIm,I TTYl)anlT§plsuRkit eKRtUveFVIkarKNnaTItaMgG½kSNWteLIgvijedayQrelIragFrNImaRtfμIenH. eyagtamrUbTI 9>6 nigtarag 9>3 eyIgGacKNnaTItaMgfμIrbs;G½kSNWtdUcxageRkam³ 2 ∑ Ay 5.44 y + 137.1 y= = ∑A 10.88 y + 10.6 ( ) 2 y 10.88 y + 10.6 = 5.44 y + 137.1 5.44 y + 10.6 y − 137.1 = 0 362 eRKOgbgÁúMsmas
  8. 8. T.chhay y = 4.140in. m:Um:g;niclPaBrbs;RkLaépÞsmasEdleFVIeLIgvijenHKW I tr = 1 (10.88)(4.140)3 + 448 + 10.6(12.93 − 4.140)2 = 1524in.4 3 tarag 9>3 eRKOgbgÁúM A y Ay ebtug 10.88 y y/2 5.44 y 2 W 16 × 36 10.6 12.93 137.1 ehIykugRtaMgKW f st = (160 × 12)(5 − 4.140) = 1.08ksi ¬rgkarTaj¦ 1524 f sb = (160 ×12)(5 + 15.86 − 4.140) = 21.1ksi ¬rgkarTaj¦ 1524 fc = (160 × 12)(4.140) = 0.652ksi 8(1524) PaBxusKñarvagkarviPaKTaMgBIrGacecal)an ehIykarKNnaTItaMgG½kSNWteLIgvijminmanRbeyaCn_eT. cMeLIy³ kugRtaMgGtibrmaenAkñúgEdkKW kugRtaMgrgkarTaj 21.1ksi ehIykugRtaMgGtibrmaenAkñúgeb tugKW kugRtaMgrgkarsgát; 0.652ksi . ersIusþg;Tb;nwgkarBt; Flexural strength enAkñugkrNICaeRcIn eKnwgTTYl)an nomial flecural strength enAeBlEdlmuxkat;Edk aMgmUl yield ehIyebtugEbkedaysarkMlaMgsgát;. karEbgEckkugRtaMgEdlRtUvKñaenAelImuxkat;smasRtUv aneKehAfa karEbgEcgkugRtaMg)aøsÞic (plastic stress distribution). AISC Specification eGaynUv design strength sMrab;m:Um:g;Bt;viC¢manCa φb M n EdlRtUv)ankMNt;dUcxageRkam³ 363 eRKOgbgÁúMsmas
  9. 9. T.chhay !> sMrab;rUbragEdlman compact web ( h / t w ≤ 640 / Fy sMrab; US b¤ h / t w ≤ 1680 / Fy sMrab; SI) emKuNersIusþg; φb = 0.85 ehIy M n RtUv)anTTYlBI plastic stress distribution. @> sMrab;rUbragEdlman noncompact web ( h / t w > 640 / Fy sMrab; US b¤ h / t w > 1680 / Fy sMrab; SI) φ b= 0.9 ehIy M n RtUv)anTTYlBI elastic stress distribution Edl RtUvKñanwg yilding dMbUgrbs;Edk. rUbragTaMgGs;EdlmanenAkñúgtaragrbs; Manual Ca compact web dUcenHeKRtUveRbIlkçxNÐ TImYysMrab;karedaHRsayFñwmsmas elIkElgEt built-up steel shapes. enAkñúgCMBUkenHeyIgniyay Et compact shape b:ueNÑaH. enAeBlEdlFñwmsmaseTAdl;sßanPaBkMNt;)aøsc eKEbgEckkugRtaMgtamviFImYykñúgcMeNam Þi viFIbIEdlbgðajenAkñúgrUbTI 9>7. kugRtaMgebtugRtUv)anbgðajCakugRtaMgsgát;BRgayesμI 0.85 f 'c EdlbnøayBITItaMgx<s;bMputrbs;kMraleTACMerAEdlGactUcCag b¤esμInwgkMras;kMralsrub. karEbgEck enHKW Whitney equivalent stress distribution EdlkugRtaMgpÁÜbRtUvKñanwgkugRtaMgpÁÜbrbs;karEbgEck kugRtaMgBitR)akd (ACI, 1995). rUbTI 9>7 a bgðajBIkarEbgEckEdlRtUvKñanwg full tensil yielding rbs;Edk nigkugRtaMgsgát;edayEpñkrbs;ebtug CamYynwgG½kSNWt)aøsÞic (PNA) enAkñúgkMralxNÐ. edayersIusþg;Tajrbs;ebtugmantMéltUc ehIyvamintUv)aneKKitkñúgkarKNnaeTenaH KμankugRtaMgNa RtUv)anbgðajenAkEnøgEdlkugRtaMgTajmanGMeBIelI ebtug. lkçxNÐenHeKeRbICaTUeTAenAeBlEdlva man shear connectors RKb;RKan;edIm,ITb;Tl;nwgkarrGil KWedIm,IFananUvkareFVIkarCaeRKOgbgÁúMsmas. kñúgrUbTI 9>7 b bøúkkugRtaMgebtugRtUv)anbnøayeBj kMras;rbs;kMral ehIy PNA sßitenAkñúgsøabrbs; FñwmEdk. dUcenHEpñkrbs;søabnwgrgkugRtaMgsgát; edIm,IbegáInkMlaMgsgát;enAkñúgkMralxNÐ. rUbTI 9>7 c bgðajBIlT§PaBTIbI Edl PNAsßitenAkñúgRTnug. cMNaMfa sMrab;krNITaMgbIenH eKmincaM)ac;bnøaybøúk kugRtaMgebtugeBjkMras;kMraleT. kñúgkrNInImYy²EdlbgðajenAkñúgrUbTI 9>7 eyIgGacrk nominal moment capacity eday KNnam:Um:g; couple EdlekIteLIgedaykMlaMgTajpÁÜb nigkMlaMgsgát;pÁÜb. eyIgGacTTYlva)aneday eFVIplbUkm:Um:g;rbs;kMlaMgpÁÜbeFobnwgcMnucgayRsYlNamYy. edaysarkartP¢ab;rbs;FñwmEdkeTAnwg kMralebtug vaminmanbBaðCamYynwg lateral torsional buckling enAeBlEdlebtugrwgmaM ehIyeK TTYl)an composite action. 364 eRKOgbgÁúMsmas
  10. 10. T.chhay edIm,IkMNt;faetIeKRtUvykkrNINamkeRbI eKRtUvKNnakMlaMgsgát;pÁÜbNaEdltUcCageKkñúgcM eNam !> As Fy @> 0.85 f 'c Ac #> ∑ Qn Edl As = RkLaépÞmuxkat;rbs;EdkFñwm Ac = RkLaépÞrbs;ebtug = tb ¬emIlrUbTI 9>7¦ 365 eRKOgbgÁúMsmas
  11. 11. T.chhay ersIiusþg;kMlaMgkat;srubrbs; shear connector ∑ Qn = lT§PaBnImYy²bgðajBIkMlaMgkat;tamTisedkenARtg;épÞb:HrvagEdk nigebtug. enAeBlEdllT§PaBTI mYylub eKeRbIEdkTaMgmUl ehIyeKGnuvtþkarEbgEcgkugRtaMgrbs;rUbTI 9>7 a. lT§PaBTIBIrRtUvKñanwg ebtugEdllub ehIy PNA sßitenAkñúgEdk ¬rUbTI 9>7 b b¤ c¦. krNITIbIlubEtenAeBlEdleKeRbI shear connector ticCagtMrUvkarsMrab; full composite behavior EdleFVIeGayekItman partial composite behavior. eTaHbICa partial composite action GacekItmanCamYynwgkMralxNÐtan; b¤kM ralxNÐEdlekItBI steel deck k¾eday k¾vaRtUv)anykmkniyayenAkñúgEpñkTI 9>7/ “Composite Beams with Formed Steel Deck”. ]TahrN_ 9>2³ KNna design strength rbs;Fñwmsmasrbs;]TahrN_ 9>1. snμt;faeKman shear connector RKb;RKan;sMrab; full composite behavior. dMeNaHRsay³ kMNt;kMlaMgsgát; C enAkñúgebtug ¬kMlaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦. edaysarvaCa full composite action kMlaMgEdlmantMéltUcCagKW As Fy nig 0.85 f 'c Ac ³ As Fy = 10.6(36 ) = 381.6kips 0.85 f 'c Ac = 0.85(4)(5 × 87 ) = 1479kips kMlaMgsgát;enAkñúgEdklub C = 381.6kips . enHmann½yfaeKminRtUvkarkMras;TaMgmUlrbs;ebtugedIm,IbegáItkMlaMgsgát;EdlRtUvkareT. eKTTYl)an karEbgEckkugRtaMgenAkñúgrUbTI 9>8. eKk¾GacKNnakMlaMgsgát;rYmdUcxageRkam C = 0.85 f 'c ab 366 eRKOgbgÁúMsmas
  12. 12. T.chhay enaHeyIg)an a = 0.85Cf ' b = 0.85(4.)(687) = 1.290in. 381 c kMlaMg C nwgsßitenAelITIRbCMuTMgn;rbs;RkLaépÞrgkarsgát;enAkMBs; a / 2 BITItaMgx<s;bMput rbs;kMralxNÐ. kMlaMgTajpÁÜb T ¬esμInwg C ¦ nwgsßitenATIRbCMuTMgn;rbs;RkLaépÞEdk. ékXñas; rbs; couple RtUv)anbegáIteLIgeday C nig T KW d a 15.86 1.290 y= +t − = +5− = 12.28in. 2 2 2 2 Nominal strength KWm:Um:g; couple b¤ M n = Cy = Ty = 381.6(12.28) = 4686in.kips = 390.5 ft − kips ehIy design strength KW φb M n = 0.85(390.5) = 332 ft − kips cMeLIy³ design strength = 332 ft − kips enAeBlEdlvaman full composite behavior ]TahrN_ 9>2 CaKMrUsMrab;lkçxNÐenH. karvi PaKsMrab;krNI PNA EdlmanTItaMgsßitenAkñúgmuxkat;EdknwgRtUv)anrk enAeBlEdleKdwgfavaCa partial composite action. 9>2> karsagsg;edaymankarTb; nigedayminmankarTb; Shored Versus Unshored Construction Tal;EtebtugrwgmaM nwgvaTTYl)annUv design strength rbs;va ¬y:agtic 75% énersIusþg; sgát;enA 28 éf¶ f 'c ¦ enaHmanminmankareFVIkarCasmas (composite behavior) eT ehIyTMgn;rbs;kM raldac;xatRtUv)anRTedaymeFüa)ayepSg². enAeBlEdlebtugrwgmaM vaGaceFVIkarCaeRKOgbgÁúM smas ehIykMlaMgGnuvtþn_bnþbnÞab;RtUv)anTb;Tl;edayFñwmsmas. RbsinebIFñwmEdkRtUv)anRTeday CnÞl;RKb;RKan;tambeNþayRbEvgrbs;vamunnwgebtugRtUv)ancak; TMgn;rbs;ebtugRss;nwgRtUvRTeday CnÞl;beNþaHGasnñeRcInCagedayEdkFñwm. enAeBlEdlebtugrwgmaM CnÞl;beNþaHGasnñRtUv)anruHerI ecj ehIyTMgn;rbs;kMralxNÐk¾dUcCabnÞúkbEnßmnwgRtUvRTedayFñwmsmas. b:uEnþRbsinebIeKmineRbI CnÞl; rolled steel shape minRtwmEtRTTMgn;pÞal;rbs;vab:ueNÑaHeT b:uEnþvaRtUvRTTMgn;rbs;kMralxNÐ nigBum<kñúgeBlebtugeFVIkarrwgmaM. enAeBlEdleKTTYl)an composite behavior bnÞúkbEnßm TaMg 367 eRKOgbgÁúMsmas
  13. 13. T.chhay bnÞúkefr nigbnÞúkGefrnwgRtUvRTedayFñwmsmas. eyIgnwgBicarNalkçxNÐxusKñaedaylMGitdUcxag eRkam. KμanCnÞl;³ muneBlebtugrwgmaM Unshored: Before Concrete cures AISC I3.4 TamTarfa enAeBlEdleKmineRbICnÞl; EdkFñwmEtÉgdac;xatRtUvEtmanersIusþg; RKb;edIm,I Tb;Tl;nwgbnÞúkGnuvtþn_TaMgGs;munnwgebtugTTYl)an 75% énersIusþg;rbs;va. ersIusþg;Tb; karBt; (flexural strength) RtUv)anKNnaedayviFIFmμta edayQrelI Charpter F of the Specifica- tion ¬CMBUk 5 enAkñúgesovePAenH¦. edayGaRs½yeTAelIkarKNnarbs;va Bum<sMrab;kMralebtugGac pþl; b¤minGacpþl; lateral support sMrab;EdkFñwm. RbsinebIvaminpþl;Ca lateral support sMrab;EdkFñwm eT eKRtUvyk unbraced length Lb mkKit ehIy lateral-torsional buckling GaclubelI flexural strength. RbsinebIeKmineRbICnÞl;beNþaHGasnñeT EdkFñwmk¾GacRtUv)aneRbIedIm,ITb;Tl;nwgbnÞúksag sg;bnÞab;bnSMEdr. edIm,IkarBarbnÞúkTaMgenH eKRtUvbEnßmbnÞúk 20lb / ft 2 = 1kN / m 2 (Hansell et al., 1978). KμanCnÞl;³ eRkayeBlebtugrwgmaM Unshored: After Concrete cures eRkayeBleKTTYl)an composite behavior RKb;bnÞúkEdlGnuvtþCabnþbnÞab;TaMgGs;RtUv)an RTedayFñwmsmas. b:uEnþ enAeBldac; RKb;bnÞúkTaMgGs;RtUv)anRTeday couple xagkñúg EdlRtUvKñanwg karEbgEckkugRtaMgenAeBldac;. dUcenHmuxkat;smasRtUvEtmanersIusþg;RKb;RKan;edIm,IRTbnÞúkTaMgenH EdlrYmbBa©ÚlTaMgbnÞúkEdlGnuvtþeTAelIFñwmEdkmunnwgebtugrwgmaM. karsagsg;edayTl; Shored Construction kñúgkarsagsg;edayeRbICnÞl; eKBicarNaEtFñwmsmas edaysareKminRtUvkareGayEdkFñwmRT GVIepSgBIbnÞúkpÞal;rbs;vaeT. ersIusþg;kMlaMgkat; Shear Strength AISC I3.6 tMrUveGaykMlaMgkat;TaMgs;RtUvTb;Tl;edayRTnugrbs;EdkFñwm Edlpþl;eGayenA kñúg Chapter F of the Specification. ]TahrN_ 9>3³ Edk W12 × 50 eFVIkarrYmKñaCamYynwgkMralxNÐebtugkMras; 4in. . TTwgkMralxNÐ RbsiT§PaBKW 72in. . eKmineRbICnÞl; m:Um:g;Bt;EdlGnuvtþmkelIvamandUcteTA³ )anmkBITMgn;Fñwm 368 eRKOgbgÁúMsmas
  14. 14. T.chhay M beam = 13 ft − kips )anmkBITMgn;kMralxNÐ M slab = 77 ft − kips nigBIbnÞúkGefr M L = 38 ft − kips . ¬enAkñúg]TahrN_enH eKminKitbnÞúksagsg;bEnßmeT¦. EdkEdleRbIKW A36 ehIy f 'c = 4000 psi . kMNt;faetI flexural rbs;FñwmenHRKb;RKan;b¤Gt;. snμt;favaCa full composite action ehIyBum<pþl;Ca lateral suppoet dl;muxkat;EdkmuneBlebtugrwgmaM. dMeNaHRsay³ muneBlebtugrwgmaM vamanEtbnÞúkGefrb:ueNÑaH ¬minmanbnÞúksagsg;enAkñúg]TahrN_ enHeT¦. dUcenHbnSMbnÞúk A4-1 lub ehIym:Um:g;emKuNKW M u = 1.4(M D ) = 1.4(13 + 77 ) = 126 ft − kips BI beam design chart enAkñúg Part 4 of the Manual sMrab;Edk A36 φb M n = 195 ft − kips > 126 ft − kips (OK) eRkayeBlebtugrwgmaM FñwmsmasRtUvTb;Tl;nUvm:Um:g;emKuN M u = 1.2M D + 1.6M L = 1.2(13 + 77 ) + 1.6(38) = 168.8 ft − kips kMlaMgsgát; C CatMéltUcCageKén As F y = 14.7(36 ) = 529.2kips b¤ 0.85 f 'c Ac = 0.85(4)(4 × 72) = 979.2kips PNA KWsßitenAkñúgebtug ehIy C = 529.2kips . BIrUbTI 9>8 kMBs;rbs;bøúgkugRtaMgsgát;KW C 529.2 a= = = 2.162in. 0.85 f 'c b 0.85(4)(72) édXñas;m:Um:g;KW d a 12.19 2.162 y= +t − = +4− = 9.014in. 2 2 2 2 design moment KW φb M n = φb C y = 0.85(529.2 )(9.014 ) = 4055in.kips = 338 ft − kips > 168.8 ft − kips (OK) cemøIy³ FñwmmanersIusþg;Bt; (flexural strength) RKb;RKan; . Cak;Esþg karsagsg;edayeRBICnÞl;manRbsiT§PaBCagkarsagsg;EdlmineRbICnÞl; edaysar KmineRbImuxkat;EdkedIm,IRTGVIepSgeRkABIbnÞúkxøÜnva. kñúgsßanPaBxøH kareRbIR)as;CnÞl;GaceGayeKRbI R)as;muxkat;FñwmEdktUcCag. b:uEnþ eRKOgbgÁúMsmasCaeRcInminmaneRbICnÞl;eT edaysartMélbEnßm rbs;CnÞl; CaBiesséføBlkmμ cMNayGs;ticCagkarsnSMsMécelITMgn;Edk. 369 eRKOgbgÁúMsmas
  15. 15. T.chhay 9>3> TTwgsøabRbsiT§PaB Effect Flange Width Epñkrbs;kMralxNÐEdleFVIkarCaeRKOgbgÁúMsmasCamYynwgEdkFñwmCaGnuKmn_eTAnwgktþaCaeRcIn EdlrYmmanRbEvgElVg nigKMlatFñwm. AISC I3.1 tMrUveGayTTwgRbsiT§PaBrbs;kMralxNÐenAelIEpñk nImYy²rbs;G½kSFñwmKWtMélEdltUcCageKkñúgcMeNam³ !> mYyPaKR)aMbIénRbEvgElVg. @> mYyPaKBIrénKMlatFñwmEdlKitBIG½kSeTAG½kS. #> cMgayBIG½kSFñwmeTARCUgEKmrbs;kMral. lkçxNÐTIbIRtUv)anGnuvtþcMeBaHEtFñwmxagb:ueNaÑaH dUcenHsMrab;Fñwmxagkñúg TTwgRbsiT§PaBTaMgmUlRtUv mantMéltUcCageKénmYyPaKbYnénRbEvgElVg b¤KMlatrbs;FñwmEdlKitBIG½kSeTAG½kS ¬edaysnμt;fa FñwmmanKMlatesμI¦. ]TahrN_ 9>4³ RbB½n§kMralEdlpSMeLIgedayEdkFñwm W 12 × 44 EdlmanKMlatBIKña 9 ft nigRTnUvkM ralebtugGarem:kMras; 4.5in. . RbEvgElVgKW 30 ft . edaybEnßmBIelITMgn;rbs;kMral eKmanbnÞúk CBa¢aMgxNÐ 20 psf nigbnÞúkGefr 125 psf . EdkCaRbePT A36 ehIyersIusþg;rbs;ebtugKW f 'c = 4000 psi . cUreFVIkarGegátFñwmxagkñúgedayeKarBtam AISC Specificastion RbsinebIeKmineRbI CnÞl;beNþaHGasnñ. snμt; full lateral support kñúgGMLúgeBlsagsg; ehIybnÞúksagsg;bEnßmKW 20 psf . eKpþl;nUv shear connector RKb;RKan;sMrab; full composite action. dMeNaHRsay³ bnÞúkEdlGnuvtþmuneBlebtugrwgmaMrYmmanTMgn;rbs;kMralxNÐ (4.5 / 12)(150) = 56.25 psf .¬eTaHbICa normal-weight concrete manTMgn; 145 psf / EtebtugGarem: RtUv)ansnμt;famanTMgn; 150 psf ¦. sMrab;FñwmEdlmanKMlat 9 ft bnÞúkGefrKW 56.25 × 9t = 506lb / ft + TMgn;Fñwm = 44lb / ftt 550lb / ft bnÞúksagsg;KW 20(9) = 180lb / ft EdlRtUv)anKitCabnÞúkGefr. bnÞúk nigm:Um:g;emKuNKW wu = 1.2wD + 1.6wL = 1.2(550) + 1.6(180) = 948lb / ft M u = (0.948)(30)2 = 106.6 ft − kips 1 8 370 eRKOgbgÁúMsmas
  16. 16. T.chhay BI load Factor Design Selection Table φb M n = φb M p = 258 ft − kips > 106.6 ft − kips (OK) eRkayeBlebtugrwgmaM bnÞúksagsg;minmaneFVIGMeBIeToteT EtbnÞúlCBa¢aMgxNÐeFVIGMeBIvijmþg ehIyva RtUv)anKitCabnÞúkefr ¬emIl)TahrN_ 5>13¦³ w part = 20(9 ) = 180lb / ft wD = 506 + 44 + 180 = 730lb / ft bnÞúkGefrCa wL = 125(9 ) = 1125lb / ft bnÞúkGefr nigm:Um:g;GefrKW wu = 1.2wD + 1.6wL = 1.2(730) + 1.6(1125) = 2676lb / ft M u = (2.676)(30)2 = 301 ft − kips 1 8 TTwgRbsiT§PaBCatMélEdltUcCageKkñúgcMeNam span 30(12 ) = = 90in. 4 4 KMlatFñwm = 9(12) = 108in. edaysareRKOgbgÁúMEdlRtUvKNnaCaFñwmxagkñúg lkçxNÐTIbIminGacGnuvtþ)an. yk b = 90in. CaTTwg søabRbsiT§PaB. enaH tamkarbgðajenAkñúgrUbTI 9>9 kMlaMgsgát;RtUvEtCatMélEdltUcCageKkñúg cMeNam As F y = 13(36 ) = 468kips b¤ 0.85 f 'c Ac = 0.85(4)(4.5)(90) = 1377kips yk C = 468kips . BIrUbTI 9>9 C 468 a= = = 1.529in. 0.85 f 'c b 0.85(4)(90) d a 1.529 y = + t − = 10.33 + 4.5 − = 14.07in. 2 2 2 φb M n = φb Cy = 0.85(468)(14.07 ) = 5595in. − kips = 466 ft − kips > 301 ft − kips (OK) RtYtBinitükMlaMgkat; w L 2.676(30 ) Vu = u = = 40.1kips 2 2 BItaragbnÞúkBRgayesμIemKuN (facored uniform load tables) 371 eRKOgbgÁúMsmas
  17. 17. T.chhay φvVn = 141kips > 40.1kips cemøIy³ FñwmBitCaeKarBtam AISC Specification. 9>4> Shear Connectors dUcEdleyIg)aneXIjrYcmkehIy kMlaMgkat;tamTisedkEdlekIteLIgcenøaHebtug nigEdkesμI nwgkMlaMgsgát;enAkñúgebtug C . eyIgsMKal;kMlaMgkat;tamTisedkenHeday Vh . dUcenH Vh CatMél EdltUcCageKkúñgcMeNam As Fy / 0.85 f 'c Ac b¤ ∑ Qn . RbsinebI As Fy b¤ 0.85 f 'c Ac lub vanwg man full composite action ehIyeKRtUvkarcMnYn shear connectors cenøaHm:Um:g;sUnü nigm:Um:g;Gtibrma KW V N1 = h Qn ¬(>@¦ Edl Qn Ca nominal shear strength rbs; connector mYy². Connectors cMnYn N1 KYrRtUv)andak; edaymanKMlatesμI²KñaelIRbEvgEdlvatMrUv. AISC Specification eGaysmIkarsMrab;ersIusþg;TaMg stud connector nig channel shear connector. dUcEdl)anbgðajBIdMbUg stud connector CaRbePT EdleKniymeRbICageK ehIyeyIgBicarNaEtRbePTenH. sMrab; stud shear connector mYy Qn = 0.5 Asc f 'c Ec ≤ Asc Fu (AISC Equation I5-1) Edl Asc = RkLaépÞmuxkat;rbs; stud f 'c = ersIusþg;rgkarsgát;enA 28 éf¶ Ec = m:UDuleGLasÞicrbs;ebtug Fu = ersIusþg;rgkarTajrbs; stud sMrab; stud EdleRbICa shear connector enAkñúgFñwmsmas ersIusþg;rgkarTaj Fu KW 60ksi . tMél EdleGayeday AISC Equation I5-1 KWQrelIkarBiesaFn_ (Ollgaard, Stutter, and Fisher, 1971). 372 eRKOgbgÁúMsmas
  18. 18. T.chhay eKmineRbIemKuNersIusþg;sMrab; Qn eT flexural resistance factor φb )anKitsMrab;RKb;ersIusþg;Edl manPaBminRbRktI. smIkar (>@ eGaycMnYn shear connector EdlRtUvkarenAcenøaHcMnucm:Um:g;sUnü nigcMnucm:Um:g; Gtibrma. dUcenH sMrab;FñwmTMrsamBaØEdlRTbnÞb;BRgayesμI eKRtUvkar connector cMnYn 2N1 ehIy BYkvamanKMlatesμI²Kña. enAeBlmanbnÞúkcMcMnuc AISC I5-6 TamTareGaydak; connector cMnYn N1 enA cenøaHbnÞúkcMcMnuc nigcMnucm:Um:g;sUnüEdlenAEk,redIm,IbegáItm:Um:g;EdlTamTarenARtg;bnÞúk. EpñkenH RtUv)aneKsMKal;eday N 2 ehIytMrUvkarenHRtUv)anbgðajenAkñúgrUbTI 9>10. cMNaMfacMnYn shear connector srubminTTYlT§iBlBItMrUvkarenHeT. tMrUvkarepSg²sMrab; Headed Struds (AISC I5) Miscellaneous Requirements for Headed Studs (AISC I5) Ggát;p©itGtibrma = 2.5 × kMras;rbs;EdkFñwm RbEvgGb,brma = 4 × Ggát;p©it stud KMlattambeNþayGb,brma ¬BIG½kSeTAG½kS¦ = 6 × Ggát;p©it stud KMlattambeNþayGtibrma ¬BIG½kSeTAG½kS¦ = 8 × kMras;kMralxNÐ KMlattamTTwgGb,brma ¬BIG½kSeTAG½kS¦ = 4 × Ggát;p©it stud lateral cover Gb,brma = 1in. = 25mm ¬minmankarkMNt;sMrab; vertical cover Gb,brma¦ AWS Structural Code (AWS 1996) rayCabBa¢InUvGgát;p©it stud sþg;darCa 1/ 2 / 5 / 8 / 3 / 4 / 7 / 8 / nig 1in. . edaypÁÚrpÁgGgát;p©itenHCamYynwgRbEvgGb,brmaEdltMrUveday AISC eyIg 373 eRKOgbgÁúMsmas
  19. 19. T.chhay TTYl)anTMhM stud FmμtaKW 1/ 2 × 2 / 5 / 8 × 2 12 / 3 / 4 × 3 / 7 / 8 × 3 12 nig 1× 4 ¬b:uEnþ eKk¾GaceRbI stud EdlEvgCagenHEdr¦. ]TahrN_ 9>5³ KNna shear connectors sMrab;RbB½n§kMralenAkñúg]TahrN_ 9>4. dMeNaHRsay³ segçbTinñn½yEdl)anTTYlBI]TahrN_ 9>4³ W 21× 44 / Edk A36 f 'c = 4000 psi kMras;kMralxNÐ t = 4.5in. RbEvgElVg = 30 ft BI]TahrN_ 9>4 kMlaMgkat;tamTisedk Vh EdlRtUvKñanwg full composite action KW Vh = C = 468kips sakl,g stud 1/ 2 × 2 . Ggát;GnuBaØatGtibrmaKW 2.5t f = 2.5(0.450 ) = 1.125in. > 0.5in. (OK) RkLaépÞmuxkat;rbs; shear connector mYyKW π (0.5)2 Asc = = 0.1963in.2 4 RbsinebIeyIgsnμt;ebtugCaebtugTMgn;Fmμta (normal-weight concrete) m:UDuleGLasÞicrbs;ebtugKW Ec = w1.5 f 'c = (145)1.5 4 = 3492ksi c BI AISC Equation I5-1 ersIusþg;rgkMlaMgkat;rbs; connector mYyKW Qn = 0.5 Asc f 'c Ec ≤ Asc Fu = 0.5(0.1963) 4(3492 ) = 11.60kips Asc Fu = 0.1963(60) = 11.78kips > 11.60kips yk Qn = 11.60kips ehIy KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in. KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in. KMlattambeNþayGtibrmaKW 8d = 8(4.5) = 36in. cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalFñwmKW V 468 N1 = h = = 40.3 Qn 11.60 374 eRKOgbgÁúMsmas
  20. 20. T.chhay ykcMnYnGb,brma 41 sMrab;Bak;kNþalFñwm b¤cMnYnsrub 82 . RbsinebIenARtg;muxkat;nImYy²eKeRbI stud cMnYnmYy KMlatEdlcaM)ac;KW 30(12) s= 82 = 4.4in. yk s = 4in. sMrab;muxkat;mYyeRbI stud BIrRKab; 30(12) s= 82 / 2 = 8.8in. yk s = 8.5in. kartMerob stud mYyNak¾manlkçN³RKb;RKan; ehIyKMlatmYyNak¾sßitenAcenøaHEdnkMNt;TabbMput nigEdnkMNt;x<s;bMput. kartMerob stud RtUv)anbgðajenAkñúgrUbTI 9>11. eTaHbICakartMerobenHRtUvkar shear connector eRcInCagtMrUvkark¾eday EteKgayRsYlkñúgkarTTYl)anKMlattamtMrUvkar. cemøIy³ eRbI stud cMnYn 86 edImEdlmanTMhM 1/ 2in.× 2in. tMerobdUcbgðajkñúgrUbTI 9>11. 9>5> karKNnamuxkat; Design CMhandMbUgkñúgkarKNnamuxkat;rbs;RbB½n§kMralxNÐKWCakareRCIserIskMras;rbs;kMralxNÐ eTaHbIvaCakMraltan; b¤kMralrnUt ¬Edl)anBI steel deck¦ k¾eday. kMras;CaGnuKmn_eTAnwgKMlatFñwm nigbnSMCaeRcInénkMras;kMral nigKMlatFñwmEdlRtUvkarkarGegát dUcenHeKnwgGacrk)annUvRbB½n§kMral EdlmanlkçN³esdækic©bMput. karKNnakMralxNÐminRtUv)anelIkykmkniyayenAkñúgesovePAenH eT b:uEnþeyIgsnμt;faeyIgsÁal;kMras;kMralxNÐ nigKMlatFñwm. edaykareFVIsnμt;EbbenH eyIgGacGnuvtþ nUvCMhanxageRkamedIm,IbMeBjnUvkarKNnaRbB½n§kMralxNÐEdlKμanCnÞl;. !> kMNt;m:Um:g;emKuNEdleFVIGMeBImun nigeRkayebtugrwgmaM @> eRCIserIsmuxkat;EdkFñwmsakl,g #> KNna design strength rbs;EdkFñwm nwgeRbobeFobvaCamYynwgm:Um:g;emKuNEdleFVIGMeBI muneBlebtugrwgmaM. eKRtUvyk unbraced length mkKit RbsinebIBum<min)anpþl;Ca lateral 375 eRKOgbgÁúMsmas
  21. 21. T.chhay support RKb;RKan;. RbsinebImuxkat;EdkFñwmenHminRKb;RKan; eKRtUvsakl,gmuxkat; FMCagenH. $> KNna design strength rbs;muxkat;smas nigeRbobeFobvaeTAnwgm:Um:g;emKuNsrub. Rb sinebImuxkat;smasminRKb;RKan; eRCIserIsmuxkat;EdkFñwmepSgeTotsMrab;sakl,g. %> RtYtBinitüersIusþg;rgkMlaMgkat; (shear strength) rbs;EdkFñwm. ^> KNna shear connectors³ a. KNna Vh / kMlaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk. b. EckkMlaMgenHeday Qn ¬ersIusþg;rgkMlaMgkat;rbs; connector eTal¦ edIm,I TTYl)ancMnYn chear connector srubEdlRtUvkar. cMnYn connector enHnwgpþl;nUv full composite action. RbsinebIeKcg;)an partial composite behavior eKGac kat;bnßycMnYn connectors enH ¬manbkRsayenAkñúgEpñkTI 9>7¦ &> RtYtBinitüPaBdab ¬RtUv)anbkRsayenAkñúgEpñkTI 9>6¦ kargard¾sMxan;enAkñúgdMeNIrkar trial-and-orror Edl)anerobrab;xagelIenHKWkareRCIserIsmux kat;EdkFñwmsakl,g. rUbmnþEdlnwgeGaynUvRkLaépÞcaM)ac; ¬b¤Gacniyaymü:ageTotKWTMgn;EdlRtUv karelIRbEvgÉktþa¦ GacekIteLIg)an RbsinebIeKsnμt;kMBs;Fñwm. edaysnμt;vaeFVIkarCaeRKOgbgÁúM smasTaMgRsug (full composite action) ehIy PNA sßitenAkñúgkMralxNÐ ¬Edlmann½yfa EdkFñwm lub ehIyvaCakrNIEdleKeRcInCYbRbTHCageK¦ eyIgGacsresr design strength ¬edayeyageTA elIrUbTI 9>12¦ Ca ( φb M n = φb (Ty ) = φb As Fy y ) edaydak;eGay design strength esμInwgm:Um:g;emKuN ehIyedaHRsayrk As eyIgTTYl)an 376 eRKOgbgÁúMsmas
  22. 22. T.chhay φb As Fy y = M u nig As = Mu φb F y y b¤ As = Mu φb Fy (d / 2 + t − a / 2) ¬(>#¦ eKk¾GacsresrsmIkar (># vaCaTMgn;CagkarsresrCaRkLaépÞ. edaysarRbEvg 1 ft manmaD As / 144 ft 3 ehIyEdkeRKOgbgÁúMmanTMgn;maD 490lb / ft 3 w = s (490 ) = 3.4 As lb / ft ¬sMrab; As KitCa in.2 ¦ A 144 BIsmIkar (># dUcenHTMgn;Edl)a:n;sμankñúgmYy ft KW w= 3.4 M u φ F (d / 2 + t − a / 2) lb / ft ¬(>$¦ b y Edl M u KitCa in. − kips / Fy KitCa ksi / ehIy d / t nig a KitCa in. . eKGaceRbIsmIkar (># b¤ (>$ edIm,IeRCiserIsmuxkat;sakl,g. smIkarTaMgBIrTamTarnUvkMBs;Edlsnμt; nigkar)a:n;sμan a / 2 . dUcenH CaTUeTAbøúkkugRtaMgmankMBs;tUcNas; kMritlMeGogkñúgkarKNna a / 2 nwgmanT§iBltictYcelI tMélEdl)anKNna As . eKsnμt; a / 2 = 1.0 . RbsinebIeKeRbIsmIkar (>$ ehIyeKsnμt; nominal depth d enaHeKGaceFVIkareRCIserIsrUbrag sakl,g)any:aggayRsYl. kareRbIsmIkarenHk¾pþl;nUvkarKNnaTMgn;FñwmedaypÞal;. ]TahrN_ 9>6³ RbEvgElVgrbs;RbB½n§kMralKW 30 ft ehIyKMlatFñwmKW 10 ft edayKitBIG½kSeTAG½kS. eRCIserIs rolled steel shape nig shear connector EdlcaM)ac;edIm,ITTYl)ankareFVIkarCaeRKOgsmas TaMgRsugCamYynwgkMralxNÐebtugGarem:kMras; 3.5in. . bnÞúkbEnßmEdlmanGMeBIelIkMralxNÐrYmman bnÞúkCBa¢aMgxNÐ 10 psf nigbnÞúkGefr 55 psf . ersIusþg;ebtugKW f 'c = 4000 psi nigEdkEdleRbICa RbePT A36 . snμt;faFñwmman full lateral support kñúgGMLúgeBlsagsg; ehIymanbnÞúksagsg; 20 psf . dMeNaHRsay³ bnÞúkEdlRtUvRTmuneBlebtugrwgmaMKW kMralxNг (3.5 /12)(150) = 43.75 psf TMgn;kñúg 1 ft : 43.75(10) = 437.5lb / ft bnÞúksagsg;³ 20(10) = 200lb / ft ¬TMgn;FñwmnwgRtUvKitenAeBleRkay¦ 377 eRKOgbgÁúMsmas
  23. 23. T.chhay bnÞúkEdlRtUvRTeRkayeBlebtugrwgmaMKW w part = 10(10 ) = 100lb / ft wD = wslab + w part = 437.5 + 100 = 537.5lb / ft wL = 55(10 ) = 550lb / ft wu = 1.2wD + 1.6 wL = 1.2(0.5375) + 1.6(0.550) = 1.525kips / ft M u = (1.525)(30)2 = 171.6 ft − kips 1 8 sakl,gkMBs; d = 16in. . BIsmIkar (>$ TMgn;FñwmEdl)anKNnaKW 3.4M u 3.4(171.6 × 12) w= = = 21.8lb / ft φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 3.5 − 1) sakl,g W 16 × 26 . RtYtBinitüFñwmEdkedayminmanCnÞl;sMrab;bnÞúkEdlGnuvtþmuneBlebtugrwgmaM ¬TMgn;rbs;kMralxNÐ TMgn;rbs;Fñwm nigbnÞúksagsg;¦ wu = 1.2(0.4375 + 0.026) + 1.6(0.200 ) = 0.8762kips / ft M u = (0.8762 )(30 )2 = 98.6 ft − kips 1 8 BI Load Factor Design Selection Table φb M n = φb M p = 119 ft − kips > 98.6 ft − kips (OK) eRkayeBlebtugrwgmaM nigeRkayeBlEdleKTTYl)an composite behavior wD = wslab + w part + wbeam = 0.4375 + 0.100 + 0.016 = 0.5535kips / ft wu = 1.2wD + 1.6 wL = 1.2(0.5535) + 1.6(0.550) = 1.544kips / ft M u = (1.544)(30)2 = 174 ft − kips 1 8 muneBlKNna design strength rbs;muxkat;smas dMbUgeyIgRtUvkMNt;TTwgsøabRbsiT§PaB. sMrab; Fñwmxagkñúg TTwgRbsiT§PaBCatMéltUcCageKkñúgcMeNam span 30(12) 4 = 4 = 90in. b¤ KMlatFñwm = 10(12) = 120in. yk b = 90in. . sMrab; full composite behavior kMlaMgsgát;enAkñúgebtugenA ultimate ¬esμInwgkMlaMg kat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦ CatMélEdltUcCageKkñúgcMeNam As F y = 7.68(36 ) = 276.5kips b¤ 0.85 f 'c Ac = 0.85(4)(90)(3.5) = 1071kips 378 eRKOgbgÁúMsmas
  24. 24. T.chhay yk C = Vh = 276.5kips . kMBs;bøúkkugRtaMgsgát;enAkñúgkMralxNÐKw C 276.5 a= = = 0.9036in. 0.85 f 'c b 0.85(4)(90) ehIyédXñas;rbs; internal resisting couple KW d a 15.69 0.9036 y= +t − = + 3.5 − = 10.89in. 2 2 2 2 design flexural strength KW φb M n = φb (Cy ) = 0.85(276.5)(10.89) = 2550in.kips = 213 ft − kips > 174 ft − kips (OK) RtYtBinitükMlaMgkat; w L 1544(30 ) Vu = u = = 23.2kips 2 2 BI factored uniform load tables φvVn = 76.3kips > 23.2kips (OK) cemøIy³ eRbI W 16 × 26 eKRtUvkarm:UDuleGLasÞicrbs;ebtugedIm,IKNna shear connector. BI]TahrN_ 9>5/ Ec = 3492ksi sMrab;ebtugFmμtaCamYynwg f 'c = 4000 psi . sakl,g stud 1 / 2 × 2in. ¬ Asc = 0.1963in.2 ¦ Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in. > 0.5in. (OK) BI AISC Equation I5-1/ ersIusþg;rgkMlaMgkat;rbs; connector mYyKW Qn = 0.5 Asc f 'c Ec ≤ Asc Fu = 0.5(0.1963) 4(3492 ) = 11.60kips Asc Fu = 0.1963(60) = 11.78kips > 11.60kips dUcenHyk Qn = 11.60kips cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalElVgKW V N1 = h = 276.5 Qn 11.60 = 23.8 eRbI 24 sMrab;Bak;kNþalFñwm b¤Casrub 48 nig KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in. KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in. KMlattambeNþayGtibrmaKW 8t = 8(3.5) = 28in. 379 eRKOgbgÁúMsmas
  25. 25. T.chhay RbsinebIeKeRbI stud mYysMrab;muxkat;nImYy² KMlatRbhak;RbEhlKW 30(12 ) s= = 7.5in. 48 KMlatenHsßitenAcenøaHEdnx<s;bMput nigEdnTabbMput dUcenHvabMeBjlkçxNÐ. cemøIy³ ykkarKNnaEdlbgðajenAkñúgrUbTI 9>13. 9>6> PaBdab Deflections edaysarm:Um:g;niclPaBrbs;muxkat;bMElg (transformed section) FM dUcenHPaBdabrbs; FñwmsmasnwgtUcCagFñwmFmμta. b:uEnþ eKGacTTYl)anm:Um:g;niclPaBFMenHEteRkayeBlebtugrwgmaMEt b:ueNÑaH. PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaMRtUv)anKNnaCamYynwgm:Um:g; niclPaBrbs;FñwmEdk. PaBdabbEnßmnwgekIteLIgenAeBlEdlFñwmrgnUvbnÞúkefrdUcCa TMgn;rbs;CBa¢aMg xNÐ enAeRkayeBlebtugrwgmaM. tMbn;m:Um:g;viC¢man ebtugnwgrgkMlaMgsgát;Cab;rhUt ehIyrgnUv)atuPUt EdleKsÁal;faCa creep. Creep CakMhUcRTg;RTayEdlekIteLIgeRkamGMeBIrbs;bnÞúksgát;. eRkay eBlekItmankMhUcRTg;RTaydMbUg kMhUcRTg;RTaybEnßmnwgekItmaneLIgedayGRtayWtelIry³eBld¾ Evg. T§iBlenAelIFñwmsmasKWkarekIneLIgnUvkMeNag EdlbNþaleGayPaBdabtambBaÄrekIneLIg Edr. eKGackMNt;EtPaBdabry³eBlyUr (long-term deflection) edayeRbIbec©keTsEdleKniym eRbI. bec©keTsenHKWeRbImuxkat;ebtugEdl)ankat;bnßyenAkñúgmuxkat;bMElg dUcenHeKnwgTTYl)an m:Um:g;niclPaBtUcCagmun ehIyeKnwgTTYl)anPaBdabFMCagmun. muxkat;Edl)ankat;bnßyRtUv)an KNnaedayeRbI 2n b¤ 3n CMnYseGaypleFobm:UDulCak;Esþg n . enAkñúgesovePAenH eyIgeRbI 2n . PaBdabEdlekIneLIgeday creep minRtUv)anENnaMeday AISC Specification eT. sMrab;karsagsg;edayKμanCnÞl; eKmanm:Um:g;niclPaBbIxusKñasMrab;KNna long-term deflection. 380 eRKOgbgÁúMsmas
  26. 26. T.chhay !> eRbI I s / m:Um:g;niclPaBrbs; rolled steel shape sMrab;PaBdabEdlekIteLIgedaysarbnÞúk Gnuvtþn_muneBlebtugrwgmaM. @> eRbI I tr / m:Um:g;niclPaBrbs; transfored section EdlKNnaCamYynwg b / n sMrab;PaBdab EdlekIteLIgedaybnÞúkGefr nigsMrab;PaBdabdMbUg (initial deflection) EdlekIteday bnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaM. #> eRbI I tr EdlKNnaCamYynwg b / 2n sMrab; long-term deflection EdlekIteLIgedaysar bnÞúkGefrEdlGnuvtþeRkayeBlebtugrwgmaM. ]TaheN_ 9>7³ KNnaPaBdabPøam² (immediate deflection) nig long-term deflection sMrab;Fñwm enAkñúg]TahrN_ 9>4. dMeNaHRsay³ segçbTinñn½yBI]TahrN_ 9>4³ W 21× 44 / Edk A36 kMras;kMralxNÐ t = 4.5in. ehIyTTwgRbsiT§PaBKW b = 90in. f 'c = 4000 psi bnÞúkGefrEdlGnuvtþmuneBlebtugrwgmaMKW wD = 550lb / ft ¬kMralxNÐbUknwgFñwm¦ bnÞúksagsg;KW wconst = 180lb / ft bnÞúkGefrKW wL = 125(9) = 1125lb / ft bnÞúkCBa¢aMgxNÐKW w part = 20(9) = 180lb / ft PaBdabPøam²³ sMrab;FñwmbUknwgkMralxNÐ w = 550lb / ft 5wL4 5(0.55 / 12 )(30 × 12 )4 Δ1 = = = 0.41in. 384 EI s 384(29000)(843) sMrab;bnÞúksagsg; w = 180lb / ft 5wL4 5(0.18 / 12 )(30 × 12 )4 Δ2 = = = 0.1342in. 384 EI s 384(29000 )(843) PaBdabPøam²srubKW Δ1 + Δ 2 = 0.41 + 0.1342 = 0.544in. 381 eRKOgbgÁúMsmas
  27. 27. T.chhay sMrab;PaBdabEdlenAsl; eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElgBIrKW I tr CamYynwgTTwg kMralxNÐbMElg b / n nig I tr CamYynwgTTwgkMralxNÐbMElg b / 2n . sMrab;ebtugTMgn;FmμtaEdl man f 'c = 4000 psi / Ec = 3492ksi nigpleFobm:UDulKW E n= s = Ec 29000 3492 = 8 .3 yk n = 8 sMrab;PaBdabrbs;muxkat;smasEdlminTak;Tgnwg creep TTwgRbsiT§PaBKW b 90 = = 11.25in. n 8 rUbTI 9>14 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnasMrab;TItaMgG½kSNWt nigm:Um:g;niclPaBRtUv)an segçbenAkñúgtarag 9>4. PaBdabdMbUgEdlbNþalBITMgn;CBa¢aMgxNÐKW 5w part L4 5(0.180 / 12)(30 × 12 )4 Δ3 = = = 0.0441in. 384 EI tr 384(29000)(2566) PaBdabEdlbNþalBIbnÞúkGefrKW 5wL L4 5(1.125 / 12 )(30 × 12 )4 Δ4 = = = 0.2755in. 384 EI tr 384(29000 )(2566 ) tarag 9>4 eRKOgbgÁúM A y Ay I d I + Ad 2 ebtug 50.62 2.25 113.9 85.43 2.571 420 W 12 × 44 13.00 14.83 192.8 843 10.01 2146 63.62 306.7 2566in.4 ∑ Ay 306.7 y= = = 4.821 ∑ A 63.62 382 eRKOgbgÁúMsmas
  28. 28. T.chhay PaBdabry³eBlyUrEdlbNþalBI creep. eRbITTwgkMralxNÐbMElg b 90 = = 5.625in. 2n 2(8) muxkat;bMElgRtUv)anbgðajenAkñúgrUbTI 9>15. karKNnaTIRbCMuTMgn;nwg m:Um:g;niclPaBRtUv)ansegçb enAkñúgtarag 9>5. edayehAm:Um:g;niclPaBenHCa I 'tr eyIgGacKNnaPaBdabry³eBlyUrEdlekIt eLIgeday creep KW 5w part L45(0.180 / 12)(30 × 12)4 Δ5 = = = 0.0504in. 384 EI 'tr 384(29000)(2245) tarag 9>5 eRKOgbgÁúM A y Ay I d I + Ad 2 ebtug 25.31 2.25 56.95 42.71 4.269 504 W 12 × 44 13.00 14.83 192.8 843 8.311 1741 38.31 249.8 2245in.4 ∑ Ay 249.8 y= = = 6.519 ∑ A 38.31 cemøIy³ xageRkamenHCakarsegçbrbs;PaBdab PaBdabPøam²munTTYl)an composite behavior Δ1 + Δ 2 = 0.4100 + 0.1342 = 0.544in. PaBdabry³eBlxøICamYynwgCBa¢aMgxNÐedayKμanbnÞúkGefr Δ1 + Δ 3 = 0.4100 + 0.0441 = 0.454in. 383 eRKOgbgÁúMsmas
  29. 29. T.chhay PaBdabry³eBlxøIedaybEnßmbnÞúkGefr Δ1 + Δ 3 + Δ 4 = 0.4100 + 0.0441 + 0.2755 = 0.730in. PaBdabry³eBlEvgedayKμanbnÞúkGefr Δ1 + Δ 5 = 0.4100 + 0.0504 = 0.460in. PaBdabry³eBlEvgedaymanbnÞúkGefr Δ1 + Δ 4 + Δ 5 = 0.4100 + 0.2755 + 0.0504 = 0.736in. edaysarbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMmantMéltUc PaBdabEdl)anBI creep mantMéltUcenAkñúg]TahrN_enH. 9>7> FñwmsmasCamYynwgkMralBum<Edk Composite Beams with Formed Steel Deck kMralxNÐenAkñúgsMNg;eRKagEdkRtUv)anpÁúMeLIgkñúgTMrg;kMralEdkrnUt (ribbed steel deck) EdlRtUv)anTukenAnwgkEnøgedIm,IeGayvakøayeTACaEpñkrbs;eRKOgbgÁúM. eTaHbICamankrNIelIkElgk¾ eday k¾rnUtrbs;bnÞHEdkRtUv)andak;eGayEkgnwgFñwmkMral ehIyRsbeTAnwgrtEdlRTFñwmenaH. rUbTI 9>16 bgðajBIrnUtEdlmanTisEkgnwgFñwm. eKtMeLIg shear stud enAelIFñwmsmasEdlmankMralrnUt tamviFIdUcKñanwgkartMeLIg shear srud enAelIFñwmsmasEdlKμankMralrnUt. eKcat;TukfakarP¢ab;Kña rvag deck eTAnwgFñwmEdkpþl;nUvTMrxag (lateral support) sMrab;FñwmEdkmuneBlebtugrwgmaM. kar KNna nigkarviPaKFñwmsmasCamYynwg formed steel deck mansar³sMxan;dUcKñanwgkrNIFñwmsmas CamYynwgkMralEdlmankMralesμIEdr EtxageRkamCakrNIelIkElgmYycMnYn³ !> eKminKitebtugenAkñúgrnUt ¬EdlenABIeRkamEpñkxagelIrbs; deck¦ enAeBlrnUtTaMgenaH EkgnwgFñwm (AISC I3.5b). enAeBlrnUtRsbnwgFñwm ebtugenAkñúgrnUtenaHRtUv)anKitbBa©Úl eTAkñúgkarkMNt;lkçN³muxkat; ehIyRtUv)anbBa©ÚleTAkñúgkarKNna Ac . @> lT§PaBrbs; shear connector GacRtUv)ankat;bnßy #> CaTUeTA eKminGacTTYl)an full composite behavior eT. mUlehtuKWfa KMlatrbs; shear connector RtUv)ankMNt;edayKMlatrbs;rnUt ehIyeKminGaceRbIRKb;cMnYn connector Edl RtUvkar. eTaHbICaeKGaceRbI partial composite design edayKμan formed steel deck k¾ eday k¾vaRtUv)anelIkykmkniyayenATIenH BIeRBaHPaKeRcInvaRtUvkar formed steel deck. tamBitvaminEmnCaKuNvibtþieT EtvaCaCMerIsxagEpñkesdækic©. 384 eRKOgbgÁúMsmas
  30. 30. T.chhay FñwmsmasPaKeRcInCamYynwg formed steel deck CakMralFñwmEdlmanrnUtEkgnwgFñwm ehIy eyIgnwgniyayEtkñúgkrNIenH. tMrUvkarcaM)ac;EdlGnuvtþenAeBlrnUtmanTisRsbeTAnwgFñwmRtUv)an bgðajenAkñúg AISC I3.5 c. lT§PaBEdlkat;bnßyrbs; shear connectors Reduced Capacity of Shear connector edayBwgEp¥kelIkarBiesaF AISC I3.5b tMrUveGayKuN shear strength rbs; shear connector Qn eTAnwgemKuNkat;bnßyenAeBlEdlrnUtEkgeTAnwgFñwm³ 0.85 ⎛ wr ⎞ ⎡⎛ H s ⎞ ⎤ ⎜ ⎜h ⎟ ⎢⎜ ⎟ ⎜h ⎟ − 1.0⎥ ≤ 1.0 ⎟ (AISC Equation I3-1) Nr ⎝ r ⎠ ⎣⎝ r ⎠ ⎦ Edl Nr = cMnYn stud kñúgmYyrnUtRtg;kEnøgEdlkat;KñaCamYynwgFñwm ¬EdlkMNt;RtwmbIenAkñúgkar KNna¦ wr = TTwgmFümrbs;rnUt hr = kMBs;rbs;rnUt H s = RbEvgrbs; stud EdlkñúgkarKNnavaminRtUvFMCag (hr + 3) . TMhMTaMgenHRtUv)anbgðajenAkñúgrUbTI 9>17. 385 eRKOgbgÁúMsmas
  31. 31. T.chhay Partial Composite Action kareFVIkarCaeRKOgbgÁúMsmasedayEpñk (partial composite action) ekItmaneLIgenAeBlEdl vaminman shear connector RKb;RKan;edIm,IkarBarPaBrGilrvagebtug nigEdkFñwm. TaMgebtug nigEdk minGaceFVIkardl; strength rbs;vaeBjeljeT ehIykMlaMgsgát;RtUv)ankMNt;RtwmkMlaMgGtibrma ¬EdlCaersIusþg;rbs; shear connector ∑ Qn ¦ EdlGacbBa¢ÚnkMlaMgkat;tamépÞb:HrvagEdk nigebtug. rMlwkfa C CatMélEdltUcCageKkñúgcMeNam As Fy / 0.85 f 'c Ac nig ∑ Qn . CamYynwg partial composite action CaTUeTAG½kSNWt)aøsÞic (PNA) sßitenAñúgmuxkat;Edk. TI taMgenHnwgeFVIeGaykarviPaKersIusþg;mankarBi)akCagTItaMgrbs; PNA EdlsßitenAkñúgkMralxNÐbnþic EteKalkarN_cMbgKWdUcKña. enAeBlEdleKeFVI elastic analysis k¾dUcCaenAeBlEdleKKNnaPaBdab eKRtUveFVIkar KNna m:Um:g;niclPaBrbs; partially composite section. eKGaceRbIExSekag parabolic transition BI I s ¬sMrab;EtEdkFñwm¦ eTA I tr ¬sMrab; fully composite section¦ )an (Hansell et al., 1978). xageRkam CasmIkarEdlnwgpþl;nUvlT§plRbhak;RbEhlsMrab;m:Um:g;niclPaBRbsiT§PaBEdlbgðajeday Commentary to the AISC Specification³ I eff = I s + ∑ Qn / C f (I tr − I s ) (AISC Equation C-I3-6) Edl C f CakMlaMgsgát;enAkñúgebtugsMrab; fully composite condition ¬tMélEdltUcCageKkñúg cMeNam As Fy nig 0.85 f 'c Ac ¦. edaysarEt ∑ Qn CakMlaMgsgát;Cak;EsþgsMrab;krNI partially composite enaHpleFob ∑ Qn / C f CacMENkrbs; compositeness Edlman. RbsinebIpleFobenH tUcCag 0.25 enaHeKminKYreRbI AISC Equation C-I3-6 (Hansell et al., 1978). eKminGacTTYl)anersIusþg;EdkeBjenAkñúg partially composite beam eT dUcenHvaTamTar nUvmuxkat;EdkFñwmFMCag muxkat;EdkFñwmsMrab; fully composite behavior. b:uEnþ vaRtUvkar shear connector ticCag ehIytMélrbs;EdkFñwm nig shear connectors ¬EdlrYbbBa©ÚlTaMgtMéltMeLIg¦ RtUv)anKitcUleTAkñúgkarviPaKEpñkesdækic©. enARKb;eBlEdl fully composite beam manlT§PaB Tb;Tl;FM ¬EdleKEtgEtCYbRbTHkrNIEbbenH¦ eKGaceFVIkarkat;bnßycMnYn shear connector Edl eFVIeGayFñwmkøayCa partially composite beam. 386 eRKOgbgÁúMsmas
  32. 32. T.chhay tMrUvkarepSg² Miscellaneous Requirements xageRkamCatMrUvkarEdl)anBI AISC Section I3.5 a nig b. GVIEdlnwgerobrab;xageRkamCa tMrUvkarbEnßmBIelIGVIEdl)anerobrab;BIcxagedIm³ - kMBs;rnUtGtibrma hr = 3in. = 75mm - TTwgmFümGb,brmarbs;rnUt wr = 2in. = 50mm b:uEnþtMélrbs; wr EdleRbIenAkñúgkar KNnaminKYrFMCag clear width rbs;EpñkxagelIbMputrbs; deck eT. - kMras;kMralGb,brmaenABIelIEpñkx<s;bMputrbs; deck = 2in. = 50mm . - Ggát;p©it stud Gtibrma = 3 / 4in. . karTamTarsMrab; formed steel deck enHCakarbEnßmBI elIGgát;p©itGtibrma 2.5t f . - kMBs;Gb,brmarbs; stud BIelIEpñkx<s;bMputKW 1 1 2 in. - KMlattambeNþayGtibrmarbs; shear stud = 36in. = 915mm - eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlatmineGayFMCag 18in = 460mm eday stud b¤ eday spot weld. kareFVIEbbenHedIm,IkarBar uplift. TMgn; deck nigTMgn;kMral Slab and Deck Weight edIm,IsMrYldl;karKNnaTMgn;kMral eyIgeRbIkMras;rbs;kMralTaMgmUledayvas;BI)atrbs; deck eTAépÞxagelIrbs;kMralxNÐ. eTaHbICaviFIenH)a:n;sμanmaDebtugelIsk¾eday EtvamansuvtßiPaB. sMrab; TMgn;maDebtugGarem: eyIgeRbITMgn;ebtugmaDsuT§bUkbEnßm 5 pcf = 80kg / m3 . CaTUeTA edaysarkM ralxNÐenAelI formed steel deck CaebtugEdlBRgwgedayEdktic ¬eBlxøHeRbI welded wire mesh CMnYseGaykareRbI reinforcing bar¦ karbEnßm 5 pcf = 80kg / m3 sMrab;EdkBRgwgGacmantMélFM b:uEnþ deck manTMgn;cenøaHBI 2 psf = 9.6kg / m 2 eTA 3 psf = 14.5kg / m 2 . eKGaceRbIvFImü:ageTot edayKitplbUkrvagkMras;kMralEdlenABIelI deck Edlx<s;CageK CamYynwgBak;kNþalkMBs;rbs;rnUtCakMras;ebtugkñúgkarKNnaTMgn;rbs;kMral. kñúgkarGnuvtþ CaTUeTA eKGacrkplbUkrvagTMgn;kMral nig deck enAkñúgtaragEdlpþl;eGayedayeragcRkplit deck. ]TahrN_ 9>8³ kMralxNÐRTedayFñwmEdleRbI formed steel deck EdlbgðajenAkñúgrUbTI 9>18 Ca mYynwgkMralebtugGarem:EdlkMras;srubKW 4.75in. . rnUt deck EkgnwgFñwm. RbEvgElVgKW 30 ft 387 eRKOgbgÁúMsmas
  33. 33. T.chhay ehIyFñwmmanKMlatBIKña 10 ft edayKitBIG½kSeTAG½kS. EdkeRKOgbgÁúMCaRbePTEdk A36 ehIyersIusþg; rbs;ebtugKW f 'c = 3000 psi . TMgn;rbs;kMral nig deck KW 50 psf . TMgn;GefrKW 40 psf nigTMgn; CBa¢aMgKW 10 psf . kñúgkarsagsg;enH eKminmaneRbICnÞl;beNþaHGasnñeT ehIyTMgn;sagsg;KW 20 psf . !> eRCIserIs W shape @> KNna shear connector #> RtYtBinitüPaBdab. PaBdabry³eBlyUrsrubGnuBaØatGtibrmaKW 1/ 240 énRbEvgElVg. dMeNaHRsay³ !> KNnaFñwm eRCIserIsrUbragsakl,gedayQrelI full composite behavior kMralxNг 50(10) = 500lb / ft CBa¢aMgxNг 10(10) = 100lb / ft bnÞúkGefr³ 40(10) = 400lb / ft wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.1) + 1.6(0.4) = 1.360kips / ft M u = (1.36)(30)2 = 153 ft − kips 1 8 edaysnμt;fa d = 16in. / a / 2 = 1in. nigsnμt;TMgn;rbs;FñwmBIsmIkar (>$³ 3.4M u 3.4(153 × 12) w= = = 17.4lb / ft φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 4.75 − 1) sakl,g W 16 × 26 . RtYtBinitüersIusþg;rgkarBt;muneBlebtugrwgmaM bnÞúksagsg;³ 20(10) = 200lb / ft wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.026) + 1.6(0.4) = 0.9512kips / ft M u = (0.9512)(30)2 = 107 ft − kips 1 8 W 16 × 26 Ca compact section sMrab; A36 nigedaysar steel deck nwgpþl; lateral support RKb;RKan; dUcenH nominal strength M n esμInwgersIusþg;m:Um:g;)aøsÞic M p . BI Load Factor Design Selection Table 388 eRKOgbgÁúMsmas
  34. 34. T.chhay φb M p = 119 ft − kips > 107 ft − kips (OK) eRkayeBlebtugrwgmaM bnÞúkemKuNsrubEdlRtUvRTedayFñwmsmas EdlRtUv)anEksMrYledaysarTMgn; rbs;EdkFñwmKW wu = 1.2(0.5 + 0.026 + 0.1) + 1.6(0.4) = 1.391kips / ft ehIym:Um:g;emKuNKW Mu = 1 (1.391)(30)2 = 156 ft − kips 8 TTwgkMralxNÐRbsiT§PaBrbs;muxkat;smasRtUvEtmantMéltUcCageKkñúgcMeNam span 30(12) 4 = 4 = 90in. b¤ KMlatFñwm = 10(12) = 120in. yk b = 90in. . sMrab; fully composite action kMlaMgsgát; C enAkñúgebtugKWCatMéltUcCageKkñúg cMeNam As Fy = 7.68(36 ) = 276.5kips b¤ 0.85 f 'c Ac = 0.85(3)[90(4.75 − 1.5)] = 745.9kips EdleKKitEtebtugenAelIEpñkx<s;bMputrbs; deck ¬dUcbgðajenAkñúgrUbTI 9>19¦ b:ueNÑaHsMrab;smIkarTI BIrxagelI. CamYynwg C = 276.5kips kMBs;rbs;karBRgaykugRtaMgsgát;enAkñúgebtugKW C 276.5 a= = = 1.205in. 0.85 f 'c b 0.85(3)(90) édXñas;m:Um:g;rbs; internal resisting couple KW d a 15.69 1.209 y= +t − = + 4.75 − = 11.99in. 2 2 2 2 ehIy design strength KW 0.85(276.5)(11.99) φb M n = = 235 ft − kips > 156 ft − kips (OK) 12 RtYtBinitükMlaMgkat; 389 eRKOgbgÁúMsmas
  35. 35. T.chhay w L 1.391(30 ) Vu = u = = 20.9kips 2 2 BI factored uniform load tables φvVn = 76.3kips > 20.9kips (OK) cemøIy³ !> eRbI W 16 × 26 @> Shear connectors edaysarFñwmenHmanersIusþg;m:Um:g;FMKYrsm eKGaceGayvaeFVIkarCa patial composite behavior. dMbUg eyIgRtUvrkcMnYn shear connector caM)ac;sMrab; full composite behavior nwgbnÞab;mkkat;bnßycMnYn conntector. sMrab; fully composite beam/ C = Vh = 276.5kips . sakl,g stud 3 4 × 3in. ¬ Asc = 0.4418in 2 ¦mYyenARtg;muxkat;mYy³ Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in. b¤ 3 in. lub 4 Ggát;p©itCak;Esþg = 3 in. (OK) 4 KNnaemKuNkat;bnßyersIusþg;rbs; stud Nr = 1 kMBs;rbs; stud BIelIEpñkx<s;bMputrbs; deck = 3 − 1.5 = 1.5in. = tMélGnuBaØat (OK) BI AISC Equation I3-1, emKuNkat;bnßy = 0.N ⎛ wr ⎞⎡⎛ H s ⎞ − 1.0⎤ ≤ 1.0 85 ⎜ ⎜ h ⎟ ⎢⎜ h ⎟ ⎟ ⎜ ⎟ ⎥ r ⎝ r ⎠ ⎣⎝ r ⎠ ⎦ 0.85 ⎛ 2.25 ⎞⎛ 3 ⎞ = ⎜ ⎟⎜ − 1.0 ⎟ = 1.275 > 1.0 1.0 ⎝ 1.5 ⎠⎝ 1.5 ⎠ eKminRtUvkarkat;bnßyersIusþg; stud eT. sMrab; f 'c = 3000 psi m:UDuleGLasÞicrbs;ebtugKW Ec = w1.5 f 'c = 1451.5 3 = 3024ksi c BI AISC Equation I5-1, ersIusþg;rgkMlaMgkat;rbs; connector mYyKW Qn = 0.5 Asc f 'c Ec ≤ Asc Fu = 0.5(0.4418) 3(3024) = 21.04kips Asc Fu = 0.4418(60) = 26.51kips > 21.04kips dUcenHyk Qn = 21.04kips 390 eRKOgbgÁúMsmas
  36. 36. T.chhay cMnYnrbs; stud EdlRtUvkarenAcenøaHcugrbs;Fñwm nigkNþalElVgKW V 276.5 N1 = h = = 13.1 Qn 21.04 yk 14 sMrab;Bak;kNþalFñwm dUcenHsrub 28 . CamYy stud mYysMrab;rnUtmYy KMlatKW 6in. ehIycMnYnGtibrmaENnaMKW 30(12) = 60 > 28 EdlTamTar 6 ebIeKeRbI stud mYysMrab;ral;BIrrnUt dUcenHeKRtUvkarva 30 edIm EdlenAEtCacMnYneRcIn. Rbsin ebIeKeRbI stud mYysMrab;ral;bIrnUt enaHKMlatnwgkøayCa 3(6) = 18in. ehIycMnYnrbs; stud nwg 30(12) / 18 = 20 EdlvatUcCagtMrUvkarsMrab; full composite action. b:uEnþ vaman flexural strength FM dUcenH partial composite action GacnwgRKb;RKan;. sakl,g stud 20 edIm sMrab;FñwmmYy dUcenH N1 Edlpþl;eGay = 20 / 2 = 10 ∑ Qn = 10(21.04) = 210.4kips < 276.5kips dUcenH C = Vh = 210.4kips edaysar C tUcCag As Fy dUcenHEpñkxøHrbs;muxkat;EdkFñwmRtUvrgkMlaMgsgát; ehIyG½kSNWt)aøsÞic KWsßitenAkñúgmuxkat;Edk. edIm,IviPaKkrNIenH dMbUgeyIgRtUvkMNt;faetI PNA sßitenAelIsøabxagelI b¤sßitenAelIRTnug. RbsinebI PNA sßitenA)atrbs;søabxagelI enaHtYsøabTaMgmUlnwgrgkMlaMgsgát; ehIykMlaMgsgát;pÁÜb EdlbgðajenAkñúgrUbTI 9>20 KW Pyf = b f t f F y = 5.5(0.345)(36 ) = 68.31kips 391 eRKOgbgÁúMsmas
  37. 37. T.chhay kMlaMgsuT§EdlRtUvepÞrenARtg;épÞb:HrvagEdk nigebtugKW ( ) T − C s = T − Pyf = As Fy − Pyf − Pyf = 276.5 − 2(68.31) = 139.9kips EdlvatUcCagkMlaMgTajsuT§Cak;Esþg 210.4kips dUcenHsøabxagelIminRtUvkarrgkMlaMgsgát;eBj kMras;søabrbs;vaeT. enHmann½yfa PNA sßitenAkñúgsøab. BIrUbTI 9>21 kMlaMgkat;tamTisedkEdl RtUvepÞrKW ( ) T − C s = As Fy − b f t ' Fy − b f t ' Fy = Vh 276.5 − 2[5.5t ' (36)] = 210.4 edayKNnarkkMBs;énkMlaMgsgát;enAkñúgsøab eyIgTTYl)an t ' = 0.1669in. kMlaMgTajpÁÜbnwgeFVIGMeBIenAelITIRbCMuTMgn;rbs;RkLaépÞBIeRkam PNA. muneBleyIgKNna moment strength eKRtUvkMNt;TItaMgTIRbCMuTMgn;sin. karKNnacMgayBITItaMgx<s;bMputrbs;EdkFñwm y RtUv)an segçbenAkñúgtarag 9>6. tarag 9>6 eRKOgbgÁúM A y Ay W 16 × 36 7.68 15.69 / 2 = 7845 60.25 søab − 0.1669(5.50 ) = − 0.918 0.1669 / 2 = 0.0834 − 0.08 srub 6.762 60.17 ∑ Ay 60.17 y= = = 8.898in. ∑ A 6.762 392 eRKOgbgÁúMsmas
  38. 38. T.chhay kMBs;rbs;bøúkkugRtaMgsgát;enAkñúgebtugKW C 210.4 a= = = 0.9168in. 0.85 f 'c b 0.85(3)(90) édXñas;sMrab;kMlaMgsgát;rbs;ebtugKW a 0.9168 y+t − = 8.819 + 4.75 − = 13.11in. 2 2 édXñas;m:Um:g;sMrab;kMlaMgsgát;enAkñúgEdkKW t' 0.1669 y− = 8.819 − = 8.736in. 2 2 Kitm:Um:g;eFobkMlaMgTaj nigedayeyagtamrUbTI 9>20 eyIgTTYl)an nominal strength³ M n = C (13.11) + C s (8.736) = 210.4(13.11) + 0.1669(5.50)(36 )(8.736 ) = 3047in. − kips = 253.9 ft − kips Design strength KW φb M n = 0.85(253.9) = 216 ft − kips > 156 ft − kips (OK) eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlat 18in. dUcenHeKminRtUvkar spot weld edIm,IkarBar uplift eT. cemøIy³ @> eRbI shear connector dUcbgðajenAkñúgrUbTI 922. #> PaBdab muneBlebtugrwgmaM wD = wslab + wbeam = 0.500 + 0.026 = 0.526kips / ft 5wD L4 5(0.526 / 12)(30 × 12 )4 Δ1 = = = 1.098in. 384 EI s 384(29000 )(301) PaBdabEdlbNþalmkBIbnÞúksagsg;KW 5wconst L4 5(0.200 / 12)(30 × 12 )4 Δ2 = = = 0.418in. 384 EI s 384(29000 )(301) 393 eRKOgbgÁúMsmas
  39. 39. T.chhay PaBdabsrubmuneBlebtugrwgmaMKW Δ1 + Δ 2 = 1.098 + 0.418 = 1.52in. sMrab;PaBdabEdlekItmaneRkayeBlebtugrwgmaM eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElg BIrKW I tr CamYynwgTTwgkMralbMElg b / n nig I tr CamYy nwgTTWgkMlagbMElg b / 2n . pleFobm:UDulKW E n= s = Ec 29000 3024 = 9 .6 yk n = 10 sMrab;PaBdabrbs;muxkat;smasEdlBak;B½n§nwg creep TTwgRbsiT§PaBKW b 90 = = 9in. n 10 rUbTI 9>23 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnaTItaMgG½kSNWt nigm:Um:g;niclPaB RtUv)anbgðajenAkñúgtarag 9>7. tarag 9>7 eRKOgbgÁúM A y Ay I d I + Ad 2 ebtug 29.25 1.625 47.53 25.75 2.282 178 W 16 × 26 7.68 12.60 96.77 301 8.693 881 srub 36.93 144.30 1059in.4 ∑ Ay 144.3 y= = = 3.907in. ∑ A 36.93 edaysareKeRbI partial composite action dUcenHeKRtUvkareRbIm:Um:g;niclPaBbMElgEdlkat; bnßy. BI AISC Equation C-I3-6 m:Um:g;niclPaBRbsiT§PaBKW I eff = I s + ∑ Qn / C f (I tr − I s ) = 301 + 210.4 / 276.5 (1059 − 301) = 962.2in.4 PaBdabEdlekIteLIgedaysarbnÞúkGefrKW 5wL L4 5(0.400 / 12)(30 × 12)4 Δ3 = = = 0.2613in. 384 EI eff 384(29000)(962.2 ) PaBdabEdlbNþalmkBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKYrQrelIm:Um:g;niclPaBbM ElgEdlTTYlCamYynwg 2n RbesIrCagCamYynwg n . dUcenH eRbITTwgkMralbMElg 394 eRKOgbgÁúMsmas
  40. 40. T.chhay b 90 = = 4.5in. 2n 2(10) BIrUbTI 9>24 nig tarag 9>8 m:Um:g;niclPaBbMElgKW I 'tr = 920.4in.4 tarag 9>8 eRKOgbgÁúM A y Ay I d I + Ad 2 ebtug 14.62 1.625 23.76 12.87 3.780 221.8 W 16 × 26 7.68 12.60 96.77 301 7.195 698.6 srub 22.30 120.53 920.4in.4 ∑ Ay 120.5 y= = = 5.405in. ∑ A 22.30 m:Um:g;niclPaBRbsiT§PaBEdleyIgnwgehAfa I 'eff KW I 'tr = I s + ∑ Qn / C f (I 'tr − I s ) = 301 + 210.4 / 276.5 (920.4 − 301) = 841.3in.4 PaBdabry³eBlyUrEdlbNþalBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKW 5(0.100 / 12)(30 × 12)4 Δ4 = = 0.0747in. 384(29000)(841.3) PaBdabsrubKW Δ1 + Δ 3 + Δ 4 = 1.098 + 0.2613 + 0.0747 = 1.43in. 30(12) nig L 240 = 240 = 1.50in. > 1.43in. (OK) cemøIy³ #> PaBdabGacTTYlyk)an. 395 eRKOgbgÁúMsmas
  41. 41. T.chhay 9>8> taragsMrab;karviPaK nigkarKNnaFñwmsmas Tables for Composite Beam Analysis and Design enAeBlG½kSNWt)aøsÞicsßitenAkñúgmuxkat;Edk karKNna flexural strength Gacnwgmankar lM)ak. eK)anbegáItrUbmnþedIm,IsMrYldl;karKNnaenH (Hansell et al., 1978) b:uEnþtaragEdlbgðaj enAkñúg Part 5 of the manual manPaBgayRsYlCag. eKmantaragBIrKW³ design strengths rbs;bnSM énrUbragepSg²CamYynwgkMralsMrab; Fy = 36ksi ≈ 250MPa nigsMrab; Fy = 50ksi ≈ 350MPa nig taragénm:Um:g;niclPaB “lower bound” sMrab;bnSMdUcKña. Design strength table EdlmaneQμaHfa “Composite Beam Selection Table,” GaceRbI)an sMrab;EtrUbragEdlman compact web nigersIusþg; shear connector srub ∑ Qn ≥ 0.25 As Fy ¬Edn kMNt;EdlENnaMTabCageKsMrab; partially composite beams¦ eKeGayersIusþg;KNna (design strength) φM n sMrab;TItaMgrbs; PNA 7 EnøgdUcbgðajenA kñúgrUbTI 9>25³ Epñkx<s;bMputrbs;søabxagelI/ EpñkTabbMputrbs;søabxagelI/ bITItaMgEdlmanKMlat esμI²KñaEdlsßitenAkñúgsøabxagelI/ nigBIrTItaMgenAkñúgRTnug*. TItaMg PNA TabCageK ¬nIv:U &¦ RtUvnwg EdkkMNt;EdlENnaMTabCageK ∑ Qn = 0.25 As Fy . PNA TItaMg ^ RtUvnwg ∑ Qn EdlsßitenAcenøaH TItaMg & nigTItaMg %. edIm,IeRbItaragsMrab;viPaKFñwmsmas dMbUgrkEpñkrbs;taragEdlRtUvnwgrUbragEdk ehIyGnuvtþ dUcxageRkam³ * nimtþsBaØa φM RtUv)aneKeRbIenAkñúgtaragsMrab; design strength of composite shapes, nig φ M RtUv)aneRbIsMrab; design i n b p strength of steel shape alone. emKuNRtUv)ansMKal;edayviFIBIrepSgKñaBIeRBaHvamantMélBIrepSgKña. 396 eRKOgbgÁúMsmas
  42. 42. T.chhay !> eRCIserIs ∑ Qn . enHCakarkMNt;rbs; Manual sMrab;kMlaMgsgát; C EdlCatMéltUcCag eKén As Fy / 0.85 f 'c Ac nigersIusþg;rbs; shear connector srub ¬EdleyIgehAfa ∑ Qn ¦. @> eRCIserIs Y 2 cMgayBITItaMgx<s;bMputrbs;EdkFñwmeTAkMlaMgsgát;pÁÜbenAkñúgebtugEdl KNnaCa a Y2 = t − 2 TMhMenHRtUv)anbgðajenAkñúgrUbTI 9>26. #> Gan φM n RbsinebIcaM)ac;eKRtUveFVI interpolation sMrab;karKNna eKGacbBa©Úl φM n EdlTamTareTAkñúgtarag ehIyeKGacGaceRCIserIsEdk Fñwm nig ∑ Qn . eKGacRtUvkartMél Y 2 dUcenHeKRtUvsnμt;kMBs;rbs;karBRgaykugRtaMgsgát;rbs; ebtug ehIyeKGaceFVIkarKNnaeLIgvijeRkayeBlEktMrUv. Manual eGaynUvsmIkarsMrab;)a:n;sμan TMgn;Fñwm EtRbsinebIeKeRbItarag eKminRtUvkarsmIkarenaHeT. taragk¾eGaypgEdrnUvtMél φb M p EdlGacRtUvkarsMrab;RtYtBinitüFñwmEdlKμanCnÞl;kñúg GMLúgeBlebtugrwgmaM ehIy Y1 CacMgayBITItaMgx<s;bMputrbs;EdkFñwmeTA PNA. ]TahrN_ 9>9³ KNna design strength rbs;FñwmsmasenAkñúg]TahrN_ 9>1 nig 9>2 edayeRbI taragenAkñúg Part 5 of the Manual. dMeNaHRsay³ BI]TahrN_ 9>1 FñwmsmaspSMeLIgedayEdk W 16 × 36 CamYynwgkMralxNÐEdlman kMras; t = 5in. nigTTwgRbsiT§PaB b = 87in. . ersIusþg;sgát;enA @* éf¶rbs;ebtugKW f 'c = 4000 psi . kMlaMgsgát;enAkñúgebtugCatMéltUcCageKén As Fy = 10.6(36) = 381.6kips 397 eRKOgbgÁúMsmas
  43. 43. T.chhay b¤ 0.85 f 'c Ac = 0.85(4 )(5 × 87 ) = 1487kips yk C = 381.6kips . kMBs;rbs;bøúkkugRtaMgsgát; C 381.6 a= = = 1.290in. 0.85 f 'c b 0.85(4)(87 ) cMgayBITItaMgx<s;bMputrbs;EdkeTAkMlaMgsgát; C KW a 1.290 Y2 = t − = 5− = 4.36in. 2 2 bBa©ÚleTAkñúgtaragCamYynwg ∑ Qn = 382kips nig Y 2 = 4.36 . edayeFVI interpolation eyIg TTYl)an φM n = 332 ft − kips edayepÞógpÞat;CamYynwglT§plenAkñúg]TahrN_ 9>2 eyIgeXIjfavamantMéldUcKña. karKNnatam rUbmnþ nigedayeRbItaragTTYl)anlT§plRsedogKña enAeBlEdl PNA sßitenAkñúgmuxkat;EdkFñwm. cemøIy³ Design strength = 332 ft − kips taragsMrab;m:Um:g;niclPaB lower bound EdlsMKal;eday I LB pþl;nUvkar)a:n;sμanm:Um:g;nicl PaBrbs;muxkat;bMElgmanlkçN³suvtßiPaBsMrab;FñwmdUcKñaEdlmanenAkñúg design strength table. karsnμt;d¾cMbgkñúgkareFVItaragenHKWfamanEtRkLaépÞebtugEdlTb;Tl;nwgm:Um:g;eTEdlmanRbsiT§PaB kñúgkarKNnam:Um:g;niclPaB. kMlaMgenAkñúgebtugKW C = ∑ Qn nig RkLaépÞénmuxkat;bMElgEdlRtUv KñaKW ∑ Qn ∑ Qn Ac = = stress in transformed area Fy edIm,ICakarsMrYlteTAeTotkñúgkarKNna eKecalm:Um:g;niclPaBrbs;ebtugeFobnwgG½kSTIRbCMuTMgn;. edIm,IbgðajBIviFIsaRsþenH eKnwgyktMélmYyenAkñúgtaragmkbMEbkenAkñúg]TahrN_ 9>10. ]TahrN_ 9>10³ karKNnapþl;nUvlT§plCa W 16 × 31 CamYynwg ∑ Q n = 241kips ¬TItaMg PNA 3¦ Y 2 = 4in. nig Fy = 36ksi . KNnam:Um:g;niclPaB lower bound. dMeNaHRsay³ RkLaépÞebtugEdlRtUv)aneRbIKW ∑ Qn 241 Ac = = = 6.694in.2 Fy 36 398 eRKOgbgÁúMsmas
  44. 44. T.chhay muxkat;bMElgEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>27 ehIykarKNnaRtUv)ansegçbenAkñúgtarag 9>9. kMNt;TItaMgTIRbCMuTMgn; Kitm:Um:g;eFobG½kSenA)atrbs;muxkat;Edk. tarag 9>9 eRKOgbgÁúM A y Ay I d I + Ad 2 ebtug 6.694 19.88 133.1 - 6.88 316.9 W 16 × 31 9.12 7.94 72.4 375 5.06 608.5 srub 15.81 205.5 925.4in.4 ∑ Ay 205.5 y= = = 13.00in. ∑ A 15.81 m:Um:g;niclPaBBItaragm:Um:g;niclPaB lower bound KW I LB = 925in.4 edayepÞógpÞat;CmYynwg lT§plEdl)anKNna. cemøIy³ I LB = 925in.4 ]TahrN_ 9>11³ eFVIkarKNna]TahrN_ 9>8 eLIgvijCamYynwgCMnYyrbs;taragenAkñúg Part 5 of the Manual . dMeNaHRsay³ !> KNnaFñwm BI]TahrN_ 9>8 M u = 153 ft − kips ¬edayminKitbBa©ÚlTMgn;Fñwm¦. edaysnμt;fa a = 2in. eyIgTTYl)an a 2 Y2 = t − = 4.75 − = 3.75in. 2 2 399 eRKOgbgÁúMsmas
  45. 45. T.chhay BI Composite Beam Selection Table, ral;karbnSMénEdkFñwm/ ∑ Qn nig Y 2 Edlpþl;nUv design strength FMCag 153 ft − kips KWCaFñwmsakl,gEdlGacTTYlyk)an. lT§PaBBIrnwgRtUv)an segçbenAkñúgtarag 9>10. tarag 9>10 φM n (ft-kips) rUbrag TItaMg PNA ∑ Qn (kips) ¬edayeFVI interpolation¦ W 16 × 26 7 69.1 160 W 14 × 22 3 159 159 Edk W 14 × 22 CarUbragEdlRsalCag b:uEnþedaysar ∑ Qn FMCag vanwgRtUvkar shear connector eRcInCag ¬GaceRcInCagBIrdg¦. sMrab;mUlehtuenH sakl,g W 16 × 26 . KNna Y 2 eLIgvij³ C ∑ Qn 69.1 a= = = = 0.3011in. 0.85 f 'c b 0.85 f 'c b 0.85(3)(90 ) a 0.3011 Y 2 = t − = 4.75 − = 4.60in. 2 2 ¬Edl b = 90in. KW)anmkBI]TarhN_ 9>8¦ φM n = 164.4 ft − kips BI]TahrN_ 9>8/ M u = 156 ft − kips CamYynwgkarKitbBa©ÚlTMgn;Fñwm . vanwgtUcCag design strength 164.4 ft − kips dUcenHkareRCIserIsenHGacTTYlyk)an. dUcKñaBI]TahrN_ 9>8 TaMg flexural strength kñúgeBlsagsg; nig shear strength KWRKb;RKan;sMrab; W 16 × 26 . cemøIy³ !> eRbI W 16 × 26 . @> Shear connector dMbUg sakl,g stud 3 / 4 × 3in. . cMnYnrbs; strud EdlRtUvkarKW ∑ Qn N1 = Qn = 69.1 21.04 = 3 .3 yk 4 sMrab;Bak;kNþalFñwm dUcenHsrubKW 8 edIm Stud 8 edImRtUvnwgKMlat 30(12) = 45in. 8 400 eRKOgbgÁúMsmas
  46. 46. T.chhay KMlatenHFMCagKMlatGnuBaØatGtibrma 36in. dUcenHeKRtUveRbI stud eRcInCagenH. RbsinebI eKdak; stud ral; 6 rnUtmþg KMlatnwgesμInwg 36 ehIycMnYn stud srubKW 30(12) = 10, N1 = 5 36 kMlaMgkat;EdlRtUvKñaEdlRtUvepÞrKW ∑ Qn = 5(21.04) = 105.2kips edIm,IgayRsYlkñúgkareRbItarag eyIgnwgyktMél ∑ Qn = 104kips enaH 104 a= = 0.4532in. 0.85(3)(90) 0.4532 Y 2 = 4.75 − = 4.523in. 2 BI Composit Beam Selection Table, design strength KW φM n = 182 ft − kips > 156 ft − kips (OK) cemøIy³ @> eRbI stud 3 / 4 × 3in. cMnYn 10 edIm edayKMlatesμI²Kña. edIm,IkarBar uplift eFVI spot weld ral;KMlat 18in. ¬sßitenAcenøaH stud¦. #> PaBdab BI]TahrN_ 9>8 PaBdabrbs;EdkFñwmmuneBlTTYl)an composite behavior KW Δ1 = 1.098in. ¬edayminKitbnÞúksagsg;¦ sMrab;PaBdabEdlekIteLIgeRkayeBlebtugrwgmaM eKGaceRbIm:Um:g;niclPaB lower bound Edl)anBItarag. eRbI W 16 × 26 CamYynwg ∑ Qn = 104kips ¬PNA TItaMg ^¦ nig Y 2 = 4.523in. I LB = 623in.4 vaminmankarEbgEckm:Um:g;niclPaBsMrab;karKNnaPaBdabbEnßmEdlekIteLIgedaysar creep. b:uEnþ m:Um:g;niclPaB lower bound mantMéltUcCagm:Um:g;niclPaBmuxkat;bMElgCak;Esþg ehIyT§iBlTaMgmUlKWnwgpþl;nUvPaBdabFMCagkar)a:n;sμan. RbsinebIbnÞúkefrry³eBlyUrtUc eKGaceRbIm:Um:g;niclPaB lower bound. w = wD + wL = 0.100 + 0.400 = 0.500kips / ft ehIyPaBdabEdlRtUvKñaKW 5wL4 5(0.500 / 12 )(30 × 12 )4 Δ2 = = = 0.5044in. 384 EI LB 384(29000 )(623) PaBdabsrubKW 401 eRKOgbgÁúMsmas
  47. 47. T.chhay Δ1 + Δ 2 = 1.098 + 0.5044 = 1.602in. PaBdabGnuBaØatGtibrmaKW L 30(12) = = 1.500in. < 1.602in. (N.G.) 240 240 kñúgkarKNna Rtg;cMnucenH eyIgmanCMerIsBIr³ ¬!¦ KNnaPaBdabEdlmanPaBsuRkitCageday eRbImuxkat;bMElg b¤¬@¦ eRCIserIskarbnSMrvagEdkFñwm nig shear connector CamYynwgm:Um:g;niclPaB lower bound. edaysareKalbMNgrbs;]TahrN_enHcg;bgðajBIkareRbItarag eyIgnwgeRCIserIsCM erIsTI @. KNnam:Um:g;niclPaB lower bound EdlRtUvkar. PaNdabEdlekItBIkMralxNÐ nigTMgn;Fñwm nwgminpøas;bþÚr dUcenHPaBdabGnuBaØatGtibrmaEdlekIteLIgedaysarbnÞúkEdlGnuvtþeRkayeBlebtug rwgmaMKW Δ 2 Gtibrma = 1.50 − Δ1 = 1.50 − 1.098 = 0.4020in. 5wL4 BI Δ 2 = 384EI LB I LB EdlRtUvkarKW 5wL4 5(0.500 / 12 )(30 × 12 )4 I LB ≥ = = 782in.4 384 EΔ 2 384(29000 )(0.4020 ) sMrab; W 16 × 26 CamYynwg PNA # nig Y 2 = 4.5in. / m:Um:g;niclPaB lower bound KW I LB = 804in.4 . BI Composite Design Selection Table, sMrab; PNA # kMlaMgkat;tamTisedkKW ∑ Qn = 208kips edIm,ITTYltMélRtwmRtUv Y 2 nig I LB dMbUgKNnaTItaMgrbs;kMlaMgsgát;enAkñúgebtug ∑ Qn 208 a= = = 0.9063in. 0.85 f 'c Ac 0.85(3)(90 ) a 0.9063 Y 2 = t − = 4.75 − = 4.30in. 2 2 BItaragm:Um:g;niclPaB lower bound edayeFVI interpolation I LB = 788in.4 > 782in.4 (OK) cMnYnrbs; shear connector EdlRtUvkarKW ∑ Qn N1 = Q = 208 21.04 = 9 .9 yk 10 sMrab;Bak;kNþalFñwm b¤srub 20 edIm n 402 eRKOgbgÁúMsmas
  48. 48. T.chhay edaysarKMlatrbs;rnUt deck, stud mYysMrab;ral;rnUt 3 sMrab;KMlat 18in. nwgpþl;nUv stud 20 edIm. cemøIy³ #> edIm,IbMeBjtMrUvkarPaBdab begáIncMnYn stud BI 10 eTA 20 dak;mYyenAkñúgral;rnUt 3 . ]TahrN_ 9>11 bgðajplRbeyaCn_rbs;tarag. CaBiess composite Beam Selection Table sMrYlkarKNna partially composite beam Edl PNA sßitenAkñúgmuxkat;EdkFñwm. 9>9> FñwmCab; Continuous Beams sMrab;FñwmTMrsmBaØ cMnucénm:Um:g;sUnüenARtg;TMr. cMnYn connector EdlRtUvkarenAcenøaHTMr nig cMnucEdlmanm:Um:g;GtibrmaKWcMnYnBak;kNþaléncMnYnsrubRtUvkar. sMrab;FñwmCab; cMnucrbt;k¾CacMnucén m:Um:g;sUnüEdr nigCaTUeTAeKRtUvkar connector 2N1 sMrab;ElVgnImYy². rUbTI 9>28 a bgðajBIRbePT FñwmCab; nigtMbn;EdlRtUvkar shear connector. enAtMbn;m:Um:g;GviC¢man kMralebtugnwgrgkMlaMgTaj dUcenHvanwgKμanRbsiT§PaB. enAkñúgtMbn;enH vanwgminman composite behavior EdleyIgRtUvBicarNa enaHeT. RbePT composite behavior EtmYyKt;EdlGacmanKWenAcenøaHFñwmEdk nigEdkBRgwgtam beNþayenAkñúgkMral. muxkat;FñwmsmasEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>28 b. RbsinebIeK eRbIKMnitenH eKRtUvpþl;nUvcMnYn shear connector RKb;RKan;edIm,ITTYlnUvdWeRkénPaBCab;rvagEdkFñwm nigEdkBRgwg. AISC Specification in Section I3.2 pþl;nUvCMerIsBIrsMrab;m:Um:g;GviC¢man. !> edayQrEtelIersIusþg;rbs;EdkFñwmb:ueNÑaH. @> edayrYmbBa©ÚlTaMgEdkBRgwgenAkñúgmuxkat;smasRtUvRbQmnwglkçxNÐxageRkam³ a. EdkFñwmRtUvEt compact nigman latereal support RKb;RKan; b. eKRtUvEtdak; shear connector enAtMbn;mUm:g;GviC¢man ¬cenøaHcMnucm:Um:g;sUnü : nigcMnucm:Um:g;GviC¢manGtibrma¦ c. EdkBRgwgenAkñúgTTwgRbsiT§PaBRtUvEtmanRbEvgbgáb;RKb;RKan; ¬TMBk;¦ ersIusþg;rbs;muxkat;smasKYrEtQrelIkarBRgaykugRtaMg)aøsÞicCamYynwg φb = 0.85 . 403 eRKOgbgÁúMsmas
  49. 49. T.chhay RbsinebIeKKit composite behavior AISC I5.2 tMrUveGayykkMlaMgkat;tamTisedkEdl RtUv)anepÞrrvagcMnucénm:Um:g;GviC¢manGtibrma nigcMnucm:Um:g;sUnümantMéltUcCageKkñúgcMeNam Ar Fyr nig ∑ Qn Edl Ar = RkLaépÞrbs;EdkBRgwgenAkñúgTTwgRbsiT§PaBrbs;kMral Fyr = yield stress rbs;EdkBRgwg ersIusþg;bEnßmEdlTTYlBIkarbBa©ÚlEdkBRgwgmantMélNas; b:uEnþeBlxøHeKeRbI cover plate enAkñúg tMbn;m:Um:g;GviC¢man. 9>10> ssrsmas Composite Columns ssrsmasRtUv)anEbgEckCaBIrTMrg;KW EdkbMBgTIbmUl b¤RCugEdlbMeBjedayebtug b¤ rolled steel shape dak;enAkñúgebtugCamYynwgEdkBRgwgbBaÄr nigEdkkgTTwgdUcenAkñúgssrebtug BRgwgedayEdk. rUbTI 9>29 bgðajBITMrg;TaMgBIrenH. 404 eRKOgbgÁúMsmas
  50. 50. T.chhay karviPaKssrsmasRtUv)aneFVIeLIgkñúgviFIdcKñasMrab;Ggát;rgkarsgát;eRKOgbgÁúMEdkFmμtaEdr U edayeRbIsmIkardUcKñaBI AISC Charpter E b:uEnþCamYynwgtMél Fy / E nig r EdlRtUv)anEkERbedIm,I TTYllT§plEdlTTYl)anBIkarBesaF nigkarKNnaRtUvKña. munBicarNasmIkar AISC sMrab;tMél TaMgenH eyIgRtUvRtYtBinitüBIeKalkarN_rbs;smIkarsin. RbsinebIeKFananUvsßanPaBlMnwg eKKitfa ersIusþg;rbs;Ggát;smasrgkarsgát;CaplbUkénersIsþg;tamG½kSrbs;EdkFñwm/ EdkBRgwg nigebtug. u vaRtUv)aneKehAfa squash load ehIyRtUv)aneGayeday Pn = As Fy + Ar Fyr + 0.85 f 'c Ac ¬(>%¦ Edl As = RkLaépÞmuxkat; rolled steel shape Ar = RkLaépÞmuxkat;srubrbs;EdkBRgwgbBaÄr Fyr = yield stress rbs;EdkBRgwg Ac = RkLaépÞmuxkat;rbs;ebtug srésEdkBRgwgCaeBlbc©úb,nñCaRbePT deformed EdlépÞrbs;vamansac;lanecjEdlCYy begáItPaBs¥itrvaEdk nigebtug)anl¥. RkLaépÞmuxkat; Ar EdlRtUv)aneRbIkñúgkarKNnaCa nominal area EdlKitfaRkLaépÞrbs;EdkrelagEdlmanTMgn;kñúgmYyÉktþaRbEvgdUcKñanwg deformed bar. tarag 9>11 bgðajBI nomial diameter nigRkLaépÞsMrab;TMhMEdksþg;darEdlkMNt;eday ASTM (1996) nig ACI (1995). edIm,ITTYl)ankugRtaMgsrub EckbnÞúkEdlTTYl)anBIsmIkar 9>5 edayRkLaépÞrbs;EdkFñwm³ Fyr Pn As = Fmy = Fy + Ar As A + 0.85 f 'c c As ¬(>^¦ tMélrbs; Fmy EdlTTYlBIsmIkar (>^ ¬enAeBlEdleRbICMnYseGaytMél Fy enAkñúgsmIkarGgát;rg karsgát;¦ eGaylT§pll¥sMrab;EdkbMBg;TIbmUl b¤RCugEdlbMeBjedayebtugEdlebtugsßitenAkñúg steel shape. ¬EdkBRgwgbBaÄrminRtUv)aneRbICamYynwgEdkbMBg;TIbmUl b¤RCug (concrete-filled pipe or tube) eT dUcenH Ar Gacniwg mantMélsUnüsMrab;ssrsmasRbePTenH¦. 405 eRKOgbgÁúMsmas
  51. 51. T.chhay tarag 9>11 elxEdk Ggát;Edk RkLaépÞmuxkat; in. mm in.2 mm2 3 0.375 9.50 0.11 71.00 4 0.500 12.70 0.20 129.00 5 0.625 15.87 0.31 200.00 6 0.750 19.05 0.44 283.87 7 0.875 22.23 0.60 387.10 8 1.000 25.40 0.79 509.70 9 1.128 28.65 1.00 645.16 10 1.270 32.26 1.27 819.35 11 1.410 35.81 1.56 1006.45 14 1.693 43.00 2.25 1451.61 18 2.257 57.33 4.00 2580.64 sMrab;eRKOgbgÁúMEdkEdkbgáb;kñúgebtug vaminmanEdkhMuB½T§vaeT ehIy structural stability Reseach Council (SSRC, 1979) ENnaMfaemKuNkat;bnßyersIusþg; ACI code (ACI, 1995) Edl mantMél 0.7 RtUv)anGnuvtþeTAelItYénEdkBRgwg nigebtugénsmIkar (>^ dUcxageRkam³ Fyr Fmy = Fy + 0.7 Ar A A + 0.7(0.85) f 'c c A ¬(>&¦ s s Fyr Ac = Fy + 0.7 Ar + 0.595 f 'c As As edIm,IkarBarT§iBl slenderness eKRtUvEktMrUvPaBrwgRkajkñúgkarBt;rbs;Ggát; EdlsmamaRt eTAnwgbrimaN EI / L . karEktMrUvenHRtUv)aneFVIeLIgedayEkERbtMélrbs; E dUcxageRkam³ A E m = E + constant × Ec c As ¬(>*¦ Edl E = m:UDuleGLasÞicrbs;EdkeRKOgbgÁúM Ec = m:UDuleGLasÞicrbs;ebtug eTaHbICaPaBrwgRkaj (stiffeness) smamaRteTAnwgm:Um:g;niclPaB pleFobRkLaépÞsMrab;ssrsmas pþl;lT§pll¥CagpleFobm:Um:g;niclPaB (SSRC, 1979). tMélefrenAkñúgsmIkar 9>8 KWesμInwg 0.4 sMrab;EdkTIbmUl b¤RCugEdlbMeBjedayebtugEdlbgðajBIPaBGnuBaØaténPaBrwgRkajrbs;ebtug 40% nig 0.2 sMrab;EdkeRKOgbgÁúMEdlbgáb;kñúgebtug (encased shape). 406 eRKOgbgÁúMsmas
  52. 52. T.chhay kaMniclPaBrbs;muxkat;smasKWFMCagkaMniclPaBrbs;muxkat;EdkeRKagbgÁúM nigrbs;ebtug. viFIEdlsuvtßiPaBKWRtUveRbIkaMniclPaBEdlmantMélFMénkaMniclPaBrbs;muxkat;EdkeRKOgbgÁúM b¤kaM niclPaBénmuxkat;ebtug EdleKGacykesμInwg 0.3 dgénvimaRtNamYyrbs;muxkat;enAkñúgbøg; buckling. edaykMNt;kaMniclPaBrbs;muxkat;smasCa rm enaHeKTTYl)an rm = r ≥ 0.3b Edl r= kaMniclPaBrbs;muxkat;EdkeRKOgbgÁúMenAkñúgbøg; buckling b = vimaRtrbs;muxkat;ebtuenAkñúgbøg; buckling tMrUvkarrbs; Specification sMrab;ssrsmasmansar³sMxan;dUcKñaeTAnwgGVIEdlerobrab;xagelI. eKeRbI AISC provisions Equation E2-1 nig E2-3 BI Chapter E of the specification edIm,IkMNt; design strength b:uEnþtMél rbs; Fy / E nig r RtUv)anEksMrYl. eKRtUvBwgEp¥kelIsmIkar (>^ nig (>& edIm,IeFVIkarEksMrYltMél TaMgenH. BI AISC Section I2.2, tMélEksMrYlrbs; Fy KW Fmy = Fy + c1 Fyr ( Ar / As ) + c2 f 'c ( Ac / As ) (AISC Equation I2-1) EdltMélefr c1 nig c2 RtUv)anKitsMrab;PaBxusKñarvag encased sectoon nig concrete-filled pipes and tubes: nig c2 = 0.85 sMrab; pipes and tubes c1 = 1.0 c1 = 0.7 nig c2 = 0.6 sMrab; encased shapes tMélEdlEksMrYl AISC E KWdUcKñaeTAnwgGVIEdleGayedaysmIkar (>* b¤ E m = E + c3 Ec ( Ac / As ) (AISC Equation I2-2) Edl sMrab; pipes and tubes c3 = 0.4 c4 = 0.2 sMrab; encased shapes AISC I2.2 kMNt;tMél rm eGayesμIeTAnwgGVIEdleGayedaysmIkar (>( rm = r ≥ 0.3b edIm,IeGayssrsmasmanlkçN³RKb;RKan; eKRtUvBinitüemIlnUvkarkMNt;xageRkamEdleGayeday AISC I2.1³ !> EdkeRKOgbgÁúMRtUvEtmany:agtic 4% énRkLaépÞmuxkat;srub b¤Ggát;rgkarsgát;eFVIkardUc ssrebtugGarem:CaCageFVIkardUcssrsmas. 407 eRKOgbgÁúMsmas
  53. 53. T.chhay @> Encased sections RtUvEteKarBtamlkçxNÐlMGitxageRkam³ a. eKRtUvEteRbITaMgEdlbBaÄr nigEdkkg. KMlatrbs;EdkkgminRtUvFMCagBIrPaKbI én vimaRttUcCageKrbs;ebtug. RkLaépÞmuxkat;rbs;Edkem nigEdkkgminRtUvtUcCag 0.007in.2 / in. b¤ 0.18mm 2 / mm énKMlatEdk. b. vaRtUvEtmankMras;ebtugkarBarEdky:agtic 1.5in. ≈ 38mm sMrab;Edkkg nigEdkbBaÄr. c. EdkbBaÄrEdlRTbnÞúk (load-carrying longitudinal reinforcement) RtUvEtCab;enA framed level. EdkbBaÄrsMrab;Tb;ebtugGacpþac;enARtg; framed level. #> ersIusþg;rbs;ebtug f 'c RtUvEtsßitenAcenøaH 3ksi ≈ 21MPa nig 8ksi ≈ 55MPa sMrab;eb tugTMgn;Fmμta ¬minmanlT§plBiesaFn_sMrab; f 'c FMCag 55MPa eT¦ nigy:agticbMput 4ksi ≈ 28MPa sMrab;ebtugTMgn;Rsal. $> kñúgkarKNna Yield stress rbs;EdkeRKOgbgÁúM nigEdkBRgwgbBaÄrminRtUvFMCag 55ksi ≈ 380 MPa eT. karkMNt;RtUv)anTTYlBIkarBicarNa local stability. enAeBlEdlEdk eRKOgbgÁúMhMuB½T§edayebtug vanwgminman local stability eT. ebtugnwgGachMuB½T§Edk)an RKb;RKan;ebIvaminmankarpÞúHépÞebtug (spall). RbsinebIeKsnμt;eGayebtugman spall enA eBlebtugman strain 0.0018 enaHkugRtaMgEdkRtUvKñaenAkñúgEdkKW Fmax = ε max E = 0.0018(29000) = 52.2ksi EdlRtUv)anKitCatMélkMNt;Rtwm 55ksi . %> edIm,IkarBar local buckling enAkñúg pipes b¤ tubes EdlbMeBjedayebtug kMras;rbs; pipes b¤ tubes minRtUvtUcCag t = b Fy / 3E sMrab;muxkat;ctuekaNEdlmanTTwgxageRkA b b¤ t = D Fy / 8E sMrab;muxkat;rgVg;EdlmanGgát;p©itxageRkA D ]TahrN_ 9>12³ Ggát;rgkarsgát;smasEdlman W 12 ×136 RtUv)andak;enAkñúgssrebtugEdlman TMhM 20 × 22in. dUcbgðajenAkñúgrUbTI 9>30. eKeRbIEdk #10 bYnedImCaEdkbBaÄr nigEdk #3 CaEdk kgEdlmanKMlat 13in. edayKitBIG½kSeTAG½kS. Edkman yield stress Fy = 50MPa ehIyeKeRbI EdkBRgwgRbePT Grade 60. ersIusþg;rbs;ebtugKW f 'c = 5ksi . KNna design strength sMrab;RbEvg RbsiT§PaB 16 ft sMrab;G½kSTaMgBIr. 408 eRKOgbgÁúMsmas
  54. 54. T.chhay cemøIy³ eKkMNt;tMélEksMrYl F nig E Edl)anBI AISC Equation I2-1 nig I2-2. tMélEdl my m RtUvkarsMrab;smIkarTaMgenHKW³ Fyr = 55ksi tMélEdlkMNt;eday AISC I2.1 Ar = 4(1.27 ) = 5.08in.2 Ac = net area rbs;ebtug = 20(22) − As − Ar = 440 − 39.9 − 5.08 = 395.0in.2 sMrab; f 'c = 5ksi Ec = w1.5 f 'c = (145)1.5 5 = 3904ksi c BI AISC Equation I2-1, yield stress EdlEksMrYlKW ⎛A ⎞ ⎛A ⎞ Fmy = Fy + c1 Fyr ⎜ r ⎟ + c2 f 'c ⎜ c ⎟ ⎜A ⎟ ⎜A ⎟ ⎝ s⎠ ⎝ s⎠ ⎛ 5.08 ⎞ ⎛ 395 ⎞ = 50 + 0.7(55)⎜ ⎟ + 0.6(5)⎜ ⎟ = 84.60ksi ⎝ 39.9 ⎠ ⎝ 39.9 ⎠ BI AISC Equation I2-2, m:UDuleGLasÞicEdlEksMrYlKW ⎛A ⎞ ⎟ = 29000 + 0.2(3904)⎛ 395 ⎞ E m = E + c3 E c ⎜ c ⎜A ⎟ ⎜ ⎟ = 36730ksi ⎝ s ⎠ ⎝ 39.9 ⎠ kaMniclPaBEdlRtUv)aneRbIenAkñúgsmIkarGgát;rgkarsgát;én AISC Cahpter E GacCa r sMrab;Edk eRKOgbgÁúM b¤ 0.3b edayykmYyNaEdlmantMélFMCag. enAkñúg]TahrN_enH buckling nwgekIteLIg eFobnwgG½kS y rbs;Ggát; dUcenH r sMrab;muxkat;KW ry = 3.16in . enAkñúgbøg; buckling 0.3b = 0.3(20 ) = 6in. ¬lub¦ dUcenH rm = 6in. . eKGacKNna design strength dUcKñasMrab;Ggát;rgkarsgát;FmμtaedayeRbI tMélEksMrYl Fmy / Em nig rm CMnYseGay Fy / E nig r 409 eRKOgbgÁúMsmas
  55. 55. T.chhay KL Fmy 16(12 ) 84.60 λc = = = 0.4888 < 1.5 rmπ Em 6π 36730 Fcr = (0.658)λc Fmy = (0.658)(0.4888 ) (84.60 ) = 76.55ksi 2 2 nominal strength KW Pn = As Fcr = 39.9(76.55) = 3054kips ehIy design strength KW φc Pn = 0.85(3054) = 2600kips cemøIy³ design compressive strength KW 2600kips taragsMrab;viPaK nigKNna Tables for Analysis and Design mantaragEdlsMrYly:agxøaMgdl;karviPaK nigkarKNnassrsmas. Part 5 of the Manual taragTaMgenHmanlkçN³RsedogKñanwg column strength table enAkñúg Part 3 of the Manual. eK eGay axial compressive design strength CaGnuKmn_eTAnwgRbEvgRbsiT§PaBsMrab; concrete-filled pipes and tubes nigsMrab; encased W-shapes. sMrab; encased column Edkem nigEdkkgEdlbM eBjtMrUvkar AISC RtUv)anrab;bBa©Úl. eKeGaytMél rmx / rmy sMrab;krNITaMgenaHEdl K x L ≠ K y L . ]TahrN_ 9>13³ Ggát;rgkarsgát;EdlmanRbEvg 18 ft RtUvRTnUvbnÞúkeFVIkar (service load) srub 1000kips EdlpSMeLIgedaycMENkesμIKñaénbnÞúkefr nigbnÞúkGefr. Ggát;enHmanTMr pinned enAcug TaMgsgçag CamYynwgTMrbEnßmenAkMBs;Bak;kNþaltamG½kSexSay. eRbItaragenAkñúg Part 5 of the Manual edIm,IeRCIserIsEdk W EdlmanrUbragkaerEdlbgáb;kñúgebtug (square encased W-shape) CamYynwgRkLaépÞebtugEdltUcCageKEdlGaceFVIeTA)an. eRbIEdk A36 Edksrés grade 60 nig f 'c = 3.5ksi . dMeNaHRsay³ bnÞúktamG½kSemKuNKW Pu = 1.2(500 ) + 1.6(500 ) = 1400kips tamkarGegátelItaragbgðajfa sMrab; f 'c = 3.5ksi nigtMélén rmx / rmy ERbRbYlBI 1.0 eTA 1.22 EdltMélPaKeRcInesμInwg 1.0 . edaysar 410 eRKOgbgÁúMsmas
  56. 56. T.chhay KxL = 2 > 1.22 KyL KxL nwglub. snμt;fa rmx / rmy = 1.0 rYcbBa©ÚleTAkñúgtaragCamYynwg KxL 18 KL = = = 18 ft rmx / rmy 1.0 taragxageRkambgðajBICMerIsEdlGaceFVI)an TMhMmuxkat;ebtug EdkeRKOgbgÁúM rmx / rmy φc Pn 18×18 W10×112 1.0 1450kips 20×20 W12×87 1.0 14250kips eTaHbICassr 20×20 RtUvkarEdkeRKOgbgÁúMtUcCagk¾eday EtlkçxNÐtMrUveGayykTMhMebtugGb,brma dUcenHeyIgeRCIserIs 18×18. cemøIy³ eRbIssrmukat; 18×18 CamYynwg W10×12 Edksrés #8 bYnedIm Edkkg #3 edayKMlat 12in.. KitBIG½kSeTAG½kS. 411 eRKOgbgÁúMsmas

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