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LocalandLateraltorsionalbucklingReferedcode:BS8118MaterialMaterialofthemullion:Alumniumalloy6063-T6Limitingstress:Po=160N/mm2ε=(250/P0)0.5=(250/160)0.5=1.25SectionpropertiesA=3556.01mm2Ix=4286132.85mm4Zx=54367.28mm3dx-x=31.9mmSx=A×dx-x=113436.72mm3Iy=21652709.00mm4Zy=127988.73mm3dy-y=63.7mmSy=A×d=226517.84mm3LocalBucklingCheckingElement-1Elementclassification:outstandelement,ref:BS8118,table4.3β0=7ε=8.75,β1=6ε=7.5AboutX-Xaxis:Elementunderstressgradientb=46.1mm,t=4.0mm,b/t=11.525yc=68.2mm,yo=22.1mmyo/yc=0.32,g=0.7+0.3yo/yc=0.80β=g(b/t)=9.22∵ββ0,∴theelementisslenderforX-Xaxis.AboutY-Yaxis:Elementunderuniformcompresionb=46.1mm,t=4.0mm,b/t=11.525β=b/t=11.525∵ββ0,∴theelementisslenderforY-Yaxis.Element-2Elementclassification:internalelement,ref:BS8118,table4.3β0=22ε=27.5,β1=18ε=22.5AboutX-Xaxis:Elementunderuniformcompresionb=107.6mm,t=3.5mm,b/t=30.74β=b/t=30.74∵ββ0,∴theelementisslenderforX-Xaxis.AboutY-Yaxis:Elementunderstressgradientb=107.6mm,t=3.5mm,b/t=30.74yc=109.6mm,yo=2mmyo/yc=0.018,g=0.7+0.3yo/yc=0.71β=g(b/t)=21.69∵β≤β1,∴theelementisfullcompactforY-Yaxis.ThesectionisslenderaboutaxisX-XInwhich,ref:BS8118,tableK.1Forelement1:X=β/ε=7.376Outstands,curveA,KL1=11/7.376-28/7.3762=0.80Forelement2:X=β/ε=30.74/1.25=24.59Internal,curveC,KL2=32/24.59-220/24.592=0.94KL=min(KL1,KL2)=0.80Zex=KL×Zx=0.8×54367.28=43493.82mm3MRs,x=PoZex/γm=160×43493.82/1.2=5799176N·mmThesectionisslenderaboutaxisY-YInwhich,ref:BS8118,tableK.1Forelement1:X=β/ε=11.525/1.25=9.22Outstands,curveB,KL1=10/9.22-24/9.222=0.80Forelement2:X=β/ε=21.69/1.25=17.35KL2=1KL=min(KL1,KL2)=0.80Zey=KL×Zy=0.8×127988.73=102390.98mm3MRs,y=PoZey/γm=160×102390.98/1.2=13652130.67N·mmLateralTorsionalBucklingEffectivelengthforlateraltorsionalbuckling:L=1600mmInwhich,c=0.1,λ1=0.6AboutX-XaxisP1=γmMRs,x/Sx=1.2×5799176/113436.72=61.35N/mm2RadiiaboutYaxis:ry=78.03mmλ=L/ry=1600/78.03=20.50λ'=λ×(P1/E)0.5/π=20.52×(61.35/70000)0.5/3.14159=0.19φ={1+c/λ'+(1-c×λ1)/λ'2}/2=(1+(0.1/0.19)+(1-0.1×0.6)/0.192)/2=13.78N=φ{1-(1-1/(λ12×φ2)0.5)}=13.78×(1-(1-1/(0.192×13.7832))0.5)=1.04＞1,N=1Ps=NP1=1×61.35=61.35N/mm2MRx,x=PsSx/γm=61.35×113436.72/1.2=5799452.31N·mmAboutY-YaxisP1=γmMRs,y/Sy=1.2×13652130.67/226517.84=72.32N/mm2RadiiaboutXaxis:rx=34.72mmλ=L/rx=1600/34.72=46.08λ'=λ×(P1/E)0.5/π=46.08×(72.32/70000)0.5/3.14159=0.47φ={1+c/λ'+(1-c×λ1)/λ'2}/2=(1+(0.1/0.47)+(1-0.1×0.6)/0.472)/2=2.73N=φ{1-(1-1/(λ12×φ2)0.5)}=2.73×(1-(1-1/(0.472×2.732))0.5)=1.02＞1,N=1Ps=NP1=1×72.32=72.32N/mm2MRx,y=PsSy/γm=72.32×226517.84/1.2=13651475.16N·mmMRmin,x=min(MRs,x;MRx,x)=5799176N·mmMRmin,y=min(MRs,y;MRx,y)=13651475.16N·mmCompare&ConclusionMx/1.2/MRmin,x+My/1.4/MRmin,y=0/1.2/5799176+1030000/1.4/13651475.16=0.05﹤1Pass!