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{"sheet":"CAP2","index":1,"n_rows":46,"n_cols":43,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
[null,"Purpose of calculation: ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Table of compatible units"]
[null,null,"Calculate stress in a pressure vessel ellipseoidal head.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Length","Time","Mass","Velocity","Acceleration","Force","LDForce","Work","Energy","Power","Density","Stress"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fundamental","m","s","kg","m/s","m/s²","kg.m/s²","kg/s²","kg.m/s².m","kg.m/s².m","kg.m²/s³","kg/m³","kg/m.s²"]
[null,"Calculation Reference",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SI","m","s","kg","m/s","m/s²","N","N/m","J","J","W","kg/m³","N/m²"]
[null,null,"http://school.mech.uwa.edu.au/~swright/DANotes/pressVessels/shells/shells.html",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SI (mm)","mm","s","t","mm/s","mm/s²","N","N/mm","mJ","mJ","mW","t/mm³","MPa"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"US Unit (ft)","ft","s","slug","ft/s","ft/s²","lbf","lbf.ft","ft.lb","ft.lb","ft.lb/s","slug/ft³","lbf/ft²"]
[null,"Calculation Validation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"US Unit (in)","in","s","lbf.s²/in","in/s","in/s²","lbf","lbf.in","in.lbf","in.lbf","in.lbf/s","lbf.s²/in⁴","psi"]
[null,null,"Formulas checked with XLC addin."]
[]
[null,"Calculation Units",null,null,null,3]
[]
[null,null,"depth of head"]
[null,null,null,"b =",13908,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"b =",{"$f":"$E$13","v":13908},{"$f":"$E$13","v":13908},13908,13908,13908,13908,13908,13908,13908,13908,13908,13908,13908]
[null,null,"Cylinder radius"]
[null,null,null,"a =",{"$f":"75400/2","v":37700},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a =",{"$f":"$E$15","v":37700},{"$f":"$E$15","v":37700},37700,37700,37700,37700,37700,37700,37700,37700,37700,37700,37700]
[null,null,"thickness"]
[null,null,null,"t =",46.5,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"t =",{"$f":"$E$17","v":46.5},{"$f":"$E$17","v":46.5},46.5,46.5,46.5,46.5,46.5,46.5,46.5,46.5,46.5,46.5,46.5]
[null,null,"internal pressure"]
[null,null,null,"P =",1.7270000000000001E-2,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P =",{"$f":"$E$19","v":1.7270000000000001E-2},{"$f":"$E$19","v":1.7270000000000001E-2},1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2,1.7270000000000001E-2]
[null,null,"position from cylinder axis"]
[null,null,null,"r =",{"$f":"E15-4524","v":33176},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"r =",0,{"$f":"AE21+$E$15/10","v":3770},{"$f":"AF21+$E$15/10","v":7540},11310,15080,18850,22620,26390,30160,{"$f":"AM21+$E$15/20","v":32045},{"$f":"AN21+$E$15/20","v":33930},35815,37700]
[]
[null,null,null,"ε =",{"$f":"SQRT(1-(OVD(E13)/UND(E15))^2)","v":0.92946414229245145},null,null,{"$f":"EQS(E23,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 41; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$23_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ε =",{"$f":"SQRT(1-(OVD(AE13)/UND(AE15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AF13)/UND(AF15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AG13)/UND(AG15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AH13)/UND(AH15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AI13)/UND(AI15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AJ13)/UND(AJ15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AK13)/UND(AK15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AL13)/UND(AL15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AM13)/UND(AM15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AN13)/UND(AN15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AO13)/UND(AO15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AP13)/UND(AP15))^2)","v":0.92946414229245145},{"$f":"SQRT(1-(OVD(AQ13)/UND(AQ15))^2)","v":0.92946414229245145}]
[]
[null,null,null,"u=",{"$f":"SQRT(1-E23^2*(OVD(E21)/UND(E15))^2)","v":0.57531996185106993},null,null,{"$f":"EQS(E25,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 42; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$25_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"u=",{"$f":"SQRT(1-AE23^2*(OVD(AE21)/UND(AE15))^2)","v":1},{"$f":"SQRT(1-AF23^2*(OVD(AF21)/UND(AF15))^2)","v":0.99567111240706663},{"$f":"SQRT(1-AG23^2*(OVD(AG21)/UND(AG15))^2)","v":0.98257002616999378},{"$f":"SQRT(1-AH23^2*(OVD(AH21)/UND(AH15))^2)","v":0.96033779303812161},{"$f":"SQRT(1-AI23^2*(OVD(AI21)/UND(AI15))^2)","v":0.92831860118754983},{"$f":"SQRT(1-AJ23^2*(OVD(AJ21)/UND(AJ15))^2)","v":0.8854513549869012},{"$f":"SQRT(1-AK23^2*(OVD(AK21)/UND(AK15))^2)","v":0.83005705041841593},{"$f":"SQRT(1-AL23^2*(OVD(AL21)/UND(AL15))^2)","v":0.75939926258481005},{"$f":"SQRT(1-AM23^2*(OVD(AM21)/UND(AM15))^2)","v":0.66865663927253172},{"$f":"SQRT(1-AN23^2*(OVD(AN21)/UND(AN15))^2)","v":0.61304947183659075},{"$f":"SQRT(1-AO23^2*(OVD(AO21)/UND(AO15))^2)","v":0.54793986041898024},{"$f":"SQRT(1-AP23^2*(OVD(AP21)/UND(AP15))^2)","v":0.46939003866058254},{"$f":"SQRT(1-AQ23^2*(OVD(AQ21)/UND(AQ15))^2)","v":0.36891246684350143}]
[]
[null,null,"meridional radius of curvature"]
[null,null,null,"rφ =",{"$f":"(OVD(E15^2)/UND(E13))*E25^3","v":19460.157341311904},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,{"$f":"EQS(E28,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 43; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$28_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rφ =",{"$f":"(OVD(AE15^2)/UND(AE13))*AE25^3","v":102192.26344549899},{"$f":"(OVD(AF15^2)/UND(AF13))*AF25^3","v":100870.8637162478},{"$f":"(OVD(AG15^2)/UND(AG13))*AG25^3","v":96941.236126253134},{"$f":"(OVD(AH15^2)/UND(AH13))*AH25^3","v":90508.648418268611},{"$f":"(OVD(AI15^2)/UND(AI13))*AI25^3","v":81754.031222139412},{"$f":"(OVD(AJ15^2)/UND(AJ13))*AJ25^3","v":70943.422964036043},{"$f":"(OVD(AK15^2)/UND(AK13))*AK25^3","v":58444.257658136616},{"$f":"(OVD(AL15^2)/UND(AL13))*AL25^3","v":44753.657268790623},{"$f":"(OVD(AM15^2)/UND(AM13))*AM25^3","v":30551.145741604902},{"$f":"(OVD(AN15^2)/UND(AN13))*AN25^3","v":23545.319403100213},{"$f":"(OVD(AO15^2)/UND(AO13))*AO25^3","v":16811.896306715826},{"$f":"(OVD(AP15^2)/UND(AP13))*AP25^3","v":10568.652656292257},{"$f":"(OVD(AQ15^2)/UND(AQ13))*AQ25^3","v":5130.8345888594213}]
[null,null,null,null,4524]
[null,null,"latitudinal radius of curvature (hoop)"]
[null,null,null,"rθ =",{"$f":"(OVD(E15^2)/UND(E13))*E25","v":58793.249106938965},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,{"$f":"EQS(E31,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 44; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$31_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rθ =",{"$f":"(OVD(AE15^2)/UND(AE13))*AE25","v":102192.26344549899},{"$f":"(OVD(AF15^2)/UND(AF13))*AF25","v":101749.88462417599},{"$f":"(OVD(AG15^2)/UND(AG13))*AG25","v":100411.05496801484},{"$f":"(OVD(AH15^2)/UND(AH13))*AH25","v":98139.092742820809},{"$f":"(OVD(AI15^2)/UND(AI13))*AI25","v":94866.979053915202},{"$f":"(OVD(AJ15^2)/UND(AJ13))*AJ25","v":90486.278136995446},{"$f":"(OVD(AK15^2)/UND(AK13))*AK25","v":84825.408771152594},{"$f":"(OVD(AL15^2)/UND(AL13))*AL25","v":77604.72950238458},{"$f":"(OVD(AM15^2)/UND(AM13))*AM25","v":68331.535435120546},{"$f":"(OVD(AN15^2)/UND(AN13))*AN25","v":62648.913131048896},{"$f":"(OVD(AO15^2)/UND(AO13))*AO25","v":55995.214568226373},{"$f":"(OVD(AP15^2)/UND(AP13))*AP25","v":47968.030489495206},{"$f":"(OVD(AQ15^2)/UND(AQ13))*AQ25","v":37700.000000000007}]
[null,null,null,null,67860]
[null,null,"meridional stress"]
[null,null,null,"σφ =",{"$f":"(OVD(E19*E15^2)/UND(2*E13*E17))*E25","v":10.91784314061114},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E34,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 45; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$34_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σφ =",{"$f":"(OVD(AE19*AE15^2)/UND(2*AE13*AE17))*AE25","v":18.976993437674921},{"$f":"(OVD(AF19*AF15^2)/UND(2*AF13*AF17))*AF25","v":18.89484416623139},{"$f":"(OVD(AG19*AG15^2)/UND(2*AG13*AG17))*AG25","v":18.646224938684046},{"$f":"(OVD(AH19*AH15^2)/UND(2*AH13*AH17))*AH25","v":18.22432399643565},{"$f":"(OVD(AI19*AI15^2)/UND(2*AI13*AI17))*AI25","v":17.616696002807696},{"$f":"(OVD(AJ19*AJ15^2)/UND(2*AJ13*AJ17))*AJ25","v":16.80320455296679},{"$f":"(OVD(AK19*AK15^2)/UND(2*AK13*AK17))*AK25","v":15.751987198686081},{"$f":"(OVD(AL19*AL15^2)/UND(2*AL13*AL17))*AL25","v":14.411114822647114},{"$f":"(OVD(AM19*AM15^2)/UND(2*AM13*AM17))*AM25","v":12.689092655532601},{"$f":"(OVD(AN19*AN15^2)/UND(2*AN13*AN17))*AN25","v":11.633835804013058},{"$f":"(OVD(AO19*AO15^2)/UND(2*AO13*AO17))*AO25","v":10.398251135411501},{"$f":"(OVD(AP19*AP15^2)/UND(2*AP13*AP17))*AP25","v":8.9076116833718526},{"$f":"(OVD(AQ19*AQ15^2)/UND(2*AQ13*AQ17))*AQ25","v":7.0008494623655935}]
[]
[null,null,"latitudinal stress (notethis may be compressive)"]
[null,null,null,"σθ =",{"$f":"E34*(2-1/E25^2)","v":-11.149425823383257},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E37,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 92; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$41_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σθ =",{"$f":"AE34*(2-1/AE25^2)","v":18.976993437674921},18.730188462272277,17.978820383044678,16.687899665306929,14.791063893910382,12.174409108648971,8.641698330794588,3.8327486533297956,-3.002589399137384,-7.6874051182013954,-13.836848592106062,-22.61382683599664,-37.438670114695348]
[null,null,"Principle stresses"]
[null,null,null,"σ1 =",{"$f":"MAX(E34,E37,0)","v":10.91784314061114},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E39,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 1; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$39_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ1 =",{"$f":"MAX(AE34,AE37,0)","v":18.976993437674921},{"$f":"MAX(AF34,AF37,0)","v":18.89484416623139},{"$f":"MAX(AG34,AG37,0)","v":18.646224938684046},{"$f":"MAX(AH34,AH37,0)","v":18.22432399643565},{"$f":"MAX(AI34,AI37,0)","v":17.616696002807696},{"$f":"MAX(AJ34,AJ37,0)","v":16.80320455296679},{"$f":"MAX(AK34,AK37,0)","v":15.751987198686081},{"$f":"MAX(AL34,AL37,0)","v":14.411114822647114},{"$f":"MAX(AM34,AM37,0)","v":12.689092655532601},{"$f":"MAX(AN34,AN37,0)","v":11.633835804013058},{"$f":"MAX(AO34,AO37,0)","v":10.398251135411501},{"$f":"MAX(AP34,AP37,0)","v":8.9076116833718526},{"$f":"MAX(AQ34,AQ37,0)","v":7.0008494623655935}]
[null,null,null,"σ3 =",{"$f":"MIN(E34,E37,0)","v":-11.149425823383257},"MPa",null,{"$f":"EQS(E40,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 2; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$40_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ3 =",{"$f":"MIN(AE34,AE37,0)","v":0},{"$f":"MIN(AF34,AF37,0)","v":0},{"$f":"MIN(AG34,AG37,0)","v":0},{"$f":"MIN(AH34,AH37,0)","v":0},{"$f":"MIN(AI34,AI37,0)","v":0},{"$f":"MIN(AJ34,AJ37,0)","v":0},{"$f":"MIN(AK34,AK37,0)","v":0},{"$f":"MIN(AL34,AL37,0)","v":0},{"$f":"MIN(AM34,AM37,0)","v":-3.002589399137384},{"$f":"MIN(AN34,AN37,0)","v":-7.6874051182013954},{"$f":"MIN(AO34,AO37,0)","v":-13.836848592106062},{"$f":"MIN(AP34,AP37,0)","v":-22.61382683599664},{"$f":"MIN(AQ34,AQ37,0)","v":-37.438670114695348}]
[null,null,"Stress Intensity (twice maximum shear - Tresca failure Criterion)"]
[null,null,null,"σe =",{"$f":"ABS(E39-E40)","v":22.067268963994398},"MPa",null,{"$f":"EQS(E42,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 3; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$41_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σe =",{"$f":"ABS(AE39-AE40)","v":18.976993437674921},{"$f":"ABS(AF39-AF40)","v":18.89484416623139},{"$f":"ABS(AG39-AG40)","v":18.646224938684046},{"$f":"ABS(AH39-AH40)","v":18.22432399643565},{"$f":"ABS(AI39-AI40)","v":17.616696002807696},{"$f":"ABS(AJ39-AJ40)","v":16.80320455296679},{"$f":"ABS(AK39-AK40)","v":15.751987198686081},{"$f":"ABS(AL39-AL40)","v":14.411114822647114},{"$f":"ABS(AM39-AM40)","v":15.691682054669986},{"$f":"ABS(AN39-AN40)","v":19.321240922214454},{"$f":"ABS(AO39-AO40)","v":24.235099727517564},{"$f":"ABS(AP39-AP40)","v":31.521438519368495},{"$f":"ABS(AQ39-AQ40)","v":44.439519577060942}]
[]
[]
[]
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{"sheet":"Head","index":2,"n_rows":46,"n_cols":43,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
[null,"Purpose of calculation: ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Table of compatible units"]
[null,null,"Calculate stress in a pressure vessel ellipseoidal head.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Length","Time","Mass","Velocity","Acceleration","Force","LDForce","Work","Energy","Power","Density","Stress"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fundamental","m","s","kg","m/s","m/s²","kg.m/s²","kg/s²","kg.m/s².m","kg.m/s².m","kg.m²/s³","kg/m³","kg/m.s²"]
[null,"Calculation Reference",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SI","m","s","kg","m/s","m/s²","N","N/m","J","J","W","kg/m³","N/m²"]
[null,null,"http://school.mech.uwa.edu.au/~swright/DANotes/pressVessels/shells/shells.html",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SI (mm)","mm","s","t","mm/s","mm/s²","N","N/mm","mJ","mJ","mW","t/mm³","MPa"]
[null,null,"D:\\SCAN\\1335-1-2106-1-2-20171103.pdf",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"US Unit (ft)","ft","s","slug","ft/s","ft/s²","lbf","lbf.ft","ft.lb","ft.lb","ft.lb/s","slug/ft³","lbf/ft²"]
[null,"Calculation Validation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"US Unit (in)","in","s","lbf.s²/in","in/s","in/s²","lbf","lbf.in","in.lbf","in.lbf","in.lbf/s","lbf.s²/in⁴","psi"]
[null,null,"Formulas checked with XLC addin."]
[]
[null,"Calculation Units",null,null,null,3]
[]
[null,null,"depth of head"]
[null,null,null,"b =",700,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"b =",{"$f":"$E$13","v":700},{"$f":"$E$13","v":700},700,700,700,700,700,700,700,700,700,700,700]
[null,null,"Cylinder radius"]
[null,null,null,"a =",1400,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a =",{"$f":"$E$15","v":1400},{"$f":"$E$15","v":1400},1400,1400,1400,1400,1400,1400,1400,1400,1400,1400,1400]
[null,null,"thickness"]
[null,null,null,"t =",3,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"t =",{"$f":"$E$17","v":3},{"$f":"$E$17","v":3},3,3,3,3,3,3,3,3,3,3,3]
[null,null,"internal pressure"]
[null,null,null,"P =",1.65,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P =",{"$f":"$E$19","v":1.65},{"$f":"$E$19","v":1.65},1.65,1.65,1.65,1.65,1.65,1.65,1.65,1.65,1.65,1.65,1.65]
[null,null,"position from cylinder axis"]
[null,null,null,"r =",1200,{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"r =",0,{"$f":"AE21+$E$15/10","v":140},{"$f":"AF21+$E$15/10","v":280},420,560,700,840,980,1120,{"$f":"AM21+$E$15/20","v":1190},{"$f":"AN21+$E$15/20","v":1260},1330,1400]
[]
[null,null,null,"ε =",{"$f":"SQRT(1-(OVD(E13)/UND(E15))^2)","v":0.8660254037844386},null,null,{"$f":"EQS(E23,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 41; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$23_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ε =",{"$f":"SQRT(1-(OVD(AE13)/UND(AE15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AF13)/UND(AF15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AG13)/UND(AG15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AH13)/UND(AH15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AI13)/UND(AI15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AJ13)/UND(AJ15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AK13)/UND(AK15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AL13)/UND(AL15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AM13)/UND(AM15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AN13)/UND(AN15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AO13)/UND(AO15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AP13)/UND(AP15))^2)","v":0.8660254037844386},{"$f":"SQRT(1-(OVD(AQ13)/UND(AQ15))^2)","v":0.8660254037844386}]
[]
[null,null,null,"u=",{"$f":"SQRT(1-E23^2*(OVD(E21)/UND(E15))^2)","v":0.6700593942604901},null,null,{"$f":"EQS(E25,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 42; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$25_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"u=",{"$f":"SQRT(1-AE23^2*(OVD(AE21)/UND(AE15))^2)","v":1},{"$f":"SQRT(1-AF23^2*(OVD(AF21)/UND(AF15))^2)","v":0.9962429422585638},{"$f":"SQRT(1-AG23^2*(OVD(AG21)/UND(AG15))^2)","v":0.98488578017961048},{"$f":"SQRT(1-AH23^2*(OVD(AH21)/UND(AH15))^2)","v":0.96566039579139828},{"$f":"SQRT(1-AI23^2*(OVD(AI21)/UND(AI15))^2)","v":0.93808315196468595},{"$f":"SQRT(1-AJ23^2*(OVD(AJ21)/UND(AJ15))^2)","v":0.90138781886599728},{"$f":"SQRT(1-AK23^2*(OVD(AK21)/UND(AK15))^2)","v":0.8544003745317531},{"$f":"SQRT(1-AL23^2*(OVD(AL21)/UND(AL15))^2)","v":0.79529868602934339},{"$f":"SQRT(1-AM23^2*(OVD(AM21)/UND(AM15))^2)","v":0.72111025509279791},{"$f":"SQRT(1-AN23^2*(OVD(AN21)/UND(AN15))^2)","v":0.67684931853404429},{"$f":"SQRT(1-AO23^2*(OVD(AO21)/UND(AO15))^2)","v":0.62649820430708347},{"$f":"SQRT(1-AP23^2*(OVD(AP21)/UND(AP15))^2)","v":0.5684408500451037},{"$f":"SQRT(1-AQ23^2*(OVD(AQ21)/UND(AQ15))^2)","v":0.50000000000000011}]
[]
[null,null,"meridional radius of curvature"]
[null,null,null,"rφ =",{"$f":"(OVD(E15^2)/UND(E13))*E25^3","v":842.3603813560452},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,{"$f":"EQS(E28,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 43; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$28_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rφ =",{"$f":"(OVD(AE15^2)/UND(AE13))*AE25^3","v":2800},{"$f":"(OVD(AF15^2)/UND(AF13))*AF25^3","v":2768.559136536549},{"$f":"(OVD(AG15^2)/UND(AG13))*AG25^3","v":2674.9497789678221},{"$f":"(OVD(AH15^2)/UND(AH13))*AH25^3","v":2521.3392934113408},{"$f":"(OVD(AI15^2)/UND(AI13))*AI25^3","v":2311.4368864409867},{"$f":"(OVD(AJ15^2)/UND(AJ13))*AJ25^3","v":2050.6572879201435},{"$f":"(OVD(AK15^2)/UND(AK13))*AK25^3","v":1746.3943655429032},{"$f":"(OVD(AL15^2)/UND(AL13))*AL25^3","v":1408.4739729579676},{"$f":"(OVD(AM15^2)/UND(AM13))*AM25^3","v":1049.9365314151139},{"$f":"(OVD(AN15^2)/UND(AN13))*AN25^3","v":868.22846334954568},{"$f":"(OVD(AO15^2)/UND(AO13))*AO25^3","v":688.52152653348492},{"$f":"(OVD(AP15^2)/UND(AP13))*AP25^3","v":514.29685907830765},{"$f":"(OVD(AQ15^2)/UND(AQ13))*AQ25^3","v":350.00000000000023}]
[]
[null,null,"latitudinal radius of curvature (hoop)"]
[null,null,null,"rθ =",{"$f":"(OVD(E15^2)/UND(E13))*E25","v":1876.1663039293724},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"length\",$AE$2:$AP$2,0))","v":"mm"},null,{"$f":"EQS(E31,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 44; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$31_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rθ =",{"$f":"(OVD(AE15^2)/UND(AE13))*AE25","v":2800},{"$f":"(OVD(AF15^2)/UND(AF13))*AF25","v":2789.4802383239785},{"$f":"(OVD(AG15^2)/UND(AG13))*AG25","v":2757.6801845029095},{"$f":"(OVD(AH15^2)/UND(AH13))*AH25","v":2703.8491082159153},{"$f":"(OVD(AI15^2)/UND(AI13))*AI25","v":2626.6328255011208},{"$f":"(OVD(AJ15^2)/UND(AJ13))*AJ25","v":2523.8858928247923},{"$f":"(OVD(AK15^2)/UND(AK13))*AK25","v":2392.3210486889088},{"$f":"(OVD(AL15^2)/UND(AL13))*AL25","v":2226.8363208821615},{"$f":"(OVD(AM15^2)/UND(AM13))*AM25","v":2019.1087142598342},{"$f":"(OVD(AN15^2)/UND(AN13))*AN25","v":1895.1780918953241},{"$f":"(OVD(AO15^2)/UND(AO13))*AO25","v":1754.1949720598336},{"$f":"(OVD(AP15^2)/UND(AP13))*AP25","v":1591.6343801262904},{"$f":"(OVD(AQ15^2)/UND(AQ13))*AQ25","v":1400.0000000000002}]
[]
[null,null,"meridional stress"]
[null,null,null,"σφ =",{"$f":"(OVD(E19*E15^2)/UND(2*E13*E17))*E25","v":515.94573358057733},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E34,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 45; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$34_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σφ =",{"$f":"(OVD(AE19*AE15^2)/UND(2*AE13*AE17))*AE25","v":770},{"$f":"(OVD(AF19*AF15^2)/UND(2*AF13*AF17))*AF25","v":767.10706553909415},{"$f":"(OVD(AG19*AG15^2)/UND(2*AG13*AG17))*AG25","v":758.36205073830013},{"$f":"(OVD(AH19*AH15^2)/UND(2*AH13*AH17))*AH25","v":743.55850475937666},{"$f":"(OVD(AI19*AI15^2)/UND(2*AI13*AI17))*AI25","v":722.32402701280819},{"$f":"(OVD(AJ19*AJ15^2)/UND(2*AJ13*AJ17))*AJ25","v":694.06862052681788},{"$f":"(OVD(AK19*AK15^2)/UND(2*AK13*AK17))*AK25","v":657.88828838944994},{"$f":"(OVD(AL19*AL15^2)/UND(2*AL13*AL17))*AL25","v":612.37998824259444},{"$f":"(OVD(AM19*AM15^2)/UND(2*AM13*AM17))*AM25","v":555.25489642145442},{"$f":"(OVD(AN19*AN15^2)/UND(2*AN13*AN17))*AN25","v":521.17397527121409},{"$f":"(OVD(AO19*AO15^2)/UND(2*AO13*AO17))*AO25","v":482.4036173164543},{"$f":"(OVD(AP19*AP15^2)/UND(2*AP13*AP17))*AP25","v":437.69945453472985},{"$f":"(OVD(AQ19*AQ15^2)/UND(2*AQ13*AQ17))*AQ25","v":385.00000000000011}]
[]
[null,null,"latitudinal stress (notethis may be compressive)"]
[null,null,null,"σθ =",{"$f":"E34*(2-1/E25^2)","v":-117.26039399558519},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E37,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 92; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$41_0\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σθ =",{"$f":"AE34*(2-1/AE25^2)","v":770},{"$f":"AF34*(2-1/AF25^2)","v":761.31028670630496},734.90755432371338,689.73523497786675,623.82529605651621,533.89893886678294,414.55974336869451,256.57027175381455,42.711915109342868,-95.276006393372938,-264.24656744722927,-479.18354210185095,-769.99999999999955]
[null,null,"Principle stresses"]
[null,null,null,"σ1 =",{"$f":"MAX(E34,E37,0)","v":515.94573358057733},{"$f":"INDEX($AE$3:$AP$7,$F$10,MATCH(\"Stress\",$AE$2:$AP$2,0))","v":"MPa"},null,{"$f":"EQS(E39,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 1; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$39_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ1 =",{"$f":"MAX(AE34,AE37,0)","v":770},{"$f":"MAX(AF34,AF37,0)","v":767.10706553909415},{"$f":"MAX(AG34,AG37,0)","v":758.36205073830013},{"$f":"MAX(AH34,AH37,0)","v":743.55850475937666},{"$f":"MAX(AI34,AI37,0)","v":722.32402701280819},{"$f":"MAX(AJ34,AJ37,0)","v":694.06862052681788},{"$f":"MAX(AK34,AK37,0)","v":657.88828838944994},{"$f":"MAX(AL34,AL37,0)","v":612.37998824259444},{"$f":"MAX(AM34,AM37,0)","v":555.25489642145442},{"$f":"MAX(AN34,AN37,0)","v":521.17397527121409},{"$f":"MAX(AO34,AO37,0)","v":482.4036173164543},{"$f":"MAX(AP34,AP37,0)","v":437.69945453472985},{"$f":"MAX(AQ34,AQ37,0)","v":385.00000000000011}]
[null,null,null,"σ3 =",{"$f":"MIN(E34,E37,0)","v":-117.26039399558519},"MPa",null,{"$f":"EQS(E40,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 2; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$40_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ3 =",{"$f":"MIN(AE34,AE37,0)","v":0},{"$f":"MIN(AF34,AF37,0)","v":0},{"$f":"MIN(AG34,AG37,0)","v":0},{"$f":"MIN(AH34,AH37,0)","v":0},{"$f":"MIN(AI34,AI37,0)","v":0},{"$f":"MIN(AJ34,AJ37,0)","v":0},{"$f":"MIN(AK34,AK37,0)","v":0},{"$f":"MIN(AL34,AL37,0)","v":0},{"$f":"MIN(AM34,AM37,0)","v":0},{"$f":"MIN(AN34,AN37,0)","v":-95.276006393372938},{"$f":"MIN(AO34,AO37,0)","v":-264.24656744722927},{"$f":"MIN(AP34,AP37,0)","v":-479.18354210185095},{"$f":"MIN(AQ34,AQ37,0)","v":-769.99999999999955}]
[null,null,"Stress Intensity (twice maximum shear - Tresca failure Criterion)"]
[null,null,null,"σe =",{"$f":"ABS(E39-E40)","v":633.20612757616254},"MPa",null,{"$f":"EQS(E42,\"Units= ; EqnPrefix=Eqn. ; EqnNo= 3; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$41_2\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σe =",{"$f":"ABS(AE39-AE40)","v":770},{"$f":"ABS(AF39-AF40)","v":767.10706553909415},{"$f":"ABS(AG39-AG40)","v":758.36205073830013},{"$f":"ABS(AH39-AH40)","v":743.55850475937666},{"$f":"ABS(AI39-AI40)","v":722.32402701280819},{"$f":"ABS(AJ39-AJ40)","v":694.06862052681788},{"$f":"ABS(AK39-AK40)","v":657.88828838944994},{"$f":"ABS(AL39-AL40)","v":612.37998824259444},{"$f":"ABS(AM39-AM40)","v":555.25489642145442},{"$f":"ABS(AN39-AN40)","v":616.44998166458709},{"$f":"ABS(AO39-AO40)","v":746.65018476368357},{"$f":"ABS(AP39-AP40)","v":916.88299663658086},{"$f":"ABS(AQ39-AQ40)","v":1154.9999999999995}]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"0.816*2470","v":2015.52}]