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43220064PROCESSEQUIPMENT&PIPINGVol143No12Apr12006()(,610041):():;;;:TH049:A:100923281(2006)0220011205AnalysisofStressesinPressurizedLongCylinder(Piping)StiffenedbyStiffenersHongDingchu(ChinaChengdaEngineeringCo.Chengdu,610041)AbstractByusingtheanalysissolutionofdifferentialequationsbasedonthinshelltheory,thestressesinpressurizedlongcylinderorpipingstiffenedwithstiffenerswereanalyzed.Keywordsstiffener,longcylinder,analysissolution,stress:2005211211:(1938),,,[1],,,,,11,111(1)/;(2),1;(3),10;(4)112,,22N+1,N+1,N,,QM,,QM;w;222112,2NQM,2N,4N,2N4N,4NQ1M1Q2M2Q2NM2N,Rmc[2]wcp=1-vER2icPi-R2ocPoR2oc-R2icRmc+1+vER2icR2oc(pi-po)(R2oc-R2ic)R2mc2VER2ic(pi-p0)R2ocR2icRmccp=0Rmcwcp=1-vER2irPi-R2orPoR2or-R2irRmc+1+vER2irR2or(pi-po)(R2or-R2ir)R2mc-vER2ir(pi-po)Rmcrp=0Rmc(pi-po)Rmc/2,Rmr(),,[3,4][4,ARTLCLE422]1Q1M1wycl=(B111/23cDc)Q1+(B112/22cDc)M1ycl=(B112/22cDc)Q1+(B122/2cDc)M1(l,s,r)H3=(B11/2D),H2=(B12/22D),H1=(B22/2D),K3=(G11/23D),K2=(G12/22D),K1=(G22/2D),wycl=H13Q1+H12M1ycl=H12Q1+H11M12Q1M1Q2M2wzr2=-(Br11/23rDr)Q1+(Br12/22rDr)M1-(Gr11/23rDr)+(Gr12/22rDr)M2zr2=(Br12/22rDr)Q1-(Br22/2rDr)M1+(Gr12/22rDr)Q2-(Gr22/2rDr)M2,2120062wzr2=-Hr3Q1+Hr2M1-Kr3Q2+Kr2M2zr2=Hr2Q1-Hr1M1+Kr2Q2-Kr1M221212,,,(H13+Hr3)Q1+(H12+Hr2)M1+Kr3Q2-Kr2M1=wrp-wcp(1)(H12+Hr2)Q1+(H11+Hr1)M1-Kr2Q2+Kr1M2=0(2)23Kr3Q1-Kr2M1-(Hs3+Hr3)Q2+(Hs2+Hr2)M2+Ks3Q3+Ks2M3=wrp-wcp(3)Kr2Q1-Kr1M1-(Hs2+Hr2)Q2-(Hs1+Hr1)M2-Ks2Q3-Ks1M3=0(4)3445NN+1(),2N2N+1Kr3Q2N-1-Kr2M2N-1+(H13+Hr3)Q2N+(H12+Hr2)M2N=wrp-wcp(2N-1)Kr2Q2N-1-Kr1M2N-1-(H12+Hr2)Q2N-(H11+Hr1)M2N=0(2N),J13=(H13+Hr3),J12=(H12+Hr2),J11=(H11+Hr1),Js3=(Hs3+Hr3),Js2=(Hs2+Hr2),Js1=(Hs1+Hr1),wp=wrp-wcp,2N,2NJ13J12Kr3-Kr2J12J11-Kr2Kr1Kr3-Kr2Js3-Js2Ks3Ks2Kr2-Kr1-Js2-Js1-Ks2-Ks1Ks3Ks2Js2Jr2Kr3-Kr2Ks2Ks1Js2Jr1-Kr2Kr1wKr2-Kr1-Js2-Js1-Ks2-Ks1Ks3Ks2Js3Js2Kr3-Kr2Ks2Ks1Js2Js1-Kr2-Kr1Kr3-Kr2Jl3Jl2Kr2-Kr1-Jl2-Jl1Q1M1Q2M2Q3M3M2N-2Q2N-1M2N-1Q2NM2N=wp0wp0wp00wp0wp0,2N:2,Ll=1000mm,Ls=60.5mm,Lr=4.5mm,Ric=650mm,Roc=654.5mm,Ror=700mm,pi=1.3MPa,po=0,100,316,v=0.3,E=191000MPa,14,28Q28M,,11(1),Q,Q2,QM,M2,Q,Q14M1415,Q15M1515,,QM31431(),15,1Q/NM/(Nmm)Q1-15.969458M1266.083773Q2-17.028932M2263.403465Q3-14.088636M3158.408307Q4-15.701639M4154.807744Q5-15.355234M5149.272161Q6-15.225881M6149.571318Q7-15.343269M7153.363334Q8-15.297555M8153.464768Q9-15.302130M9153.425776Q10-15.309077M10153.409961Q11-15.304936M11153.287072Q12-15.306028M12153.284671Q13-15.306131M13153.293641Q14-15.305856M14153.294264Q15-15.305856M15153.294264Q16-15.306131M16153.293641Q17-15.306028M17153.284671Q18-15.304936M18153.287072Q19-15.309077M19153.409961Q20-15.302130M20153.425776Q21-15.297555M21153.464768Q22-15.343269M22153.363334Q23-15.225881M23149.571318Q24-15.355234M24149.272161Q25-15.701639M25154.807744Q26-14.088636M26158.408307Q27-17.028932M27263.403465Q28-15.969458M28266.0837732,QM212,,(N+1)(:)x[4]:N+11(x)=6M(x)/t2cN+12(x)=Ew(x)/Emc6vM(x)/t2ctN+1(x)=Q(x)/tcw(x)=(QcN/23cDc)F(cx)+(McN/22cDc)F12(cx)+(cN/c)F13(cx)+wcNF14(cx)M(x)=(QcN/x)F13(cx)+McNF14(cx)-22cDc[(cN/c)F11(cx)-wcNF12(cx)]Q(x)=QcNF14(cx)-2McNcF11(cx)-23cDc[(cN/c)F12(cx)-2wcNF13(cx)]wcN=H3QcN+H2McN+K3QcN+1+K2QcN+1cN=-H2QcN-H1McN-K2QcN+1-K1McN+1,,:1m=(p1-po)Rmc2tc2m=(p1-po)Rmctc,,,(),3/[4],v0.3,3/21334Rmt,,510Rmt,2[510Rmctc/(Lsc+Lr)]+2=2[510652125415/(6015+415)]+2=10131214,15,N14,tc=Roc-Ric=415mmRmc=Ric+015tc=652125mmLs=6015mmQ14=Q15=-151305856N4120062M14=Q15=1531294264Nmm/mm15,x=0x=30.25,x=60.5,15x=0x=30.25:1(0)=45142MPa1(30125)=º22157MPa2(0)=-7510513163MPa2(30125)=-71184º6177MPa(0)=-314MPa(30125)=414210-14MPa1m=94121MPa2m=188143MPa3,,t,mm;L,mm;Ro,mm;Ri,mm;Rm,mm;E,MPa;v;pi,MPa;po,MPa;M,Nmm/mm;Q,N/mm;w,mm;,rad;x,mm;1(),MPa;2,MPa;c,;r,;s,;l,;z,;y,;=[3(122)/R2mt2]i/4,1/mm;D=Et3/12(1-2),Nmm[4]:B11=(sinh2L-sin2L)/2(sinh2L-sin2L);B12=(cosh2L-cos2L)/2(sinh2L-sin2L);B22=(sinh2L+sin2L)/(sinh2L-sin2L);G11=-(coshLsinL-sinhLcosL)/(sinh2L-sin2L);G12=-2sinhLsinL/(sinh2L-sin2L);G22=-(coshLsinL+sinhLcosL)/(sinh2L-sin2L);F11(x)=(coshxsinx-sinhxcosx)/2;F12(x)=sinhxsinx;F13(x)=(coshxsinx+sinhxcosx)/2;F14(x)=coshxcosx11[M]1:,19542S1[M]1:,19643JB4732-95[S]4ASME22[S]12001HG/T2151421535-2005HG/T21514215352005,200611,HG21514215351995HG21514215351995HG21514215351995,:1121,31,600mm4109MnNiD51()()61400mm71812.5MPa4.0MPaHG/T2151421535-2005(/:21-62488580)51431()