InstructionsHow to use this spreadsheetSome general notes:Hull is cylindrical with sperical endcapsSame material used throughoutOptionally stiffeners may be usedStiffeners are of T profile, internal, with flange on smaller diameterThere are no significant hull openings (stress at discontinuities not calculated)White columns are for data entry, green are calculated resultsEach row is for a separate design, so they may be comparedTo start a new design, copy a previous row to get a new instance of all the formulasSTEPS:1) Complete all white columns in the shell definition, frame definition and material definition sheetsIn the frame definition sheet, by "bulkhead" I do not mean necessarily a wall in your sub - I just meanone or more rings that are much heavier than the rest.2) Do not enter any data in the auxiliary functions sheet, it is purely a placeholder for spreadsheet formulas3) Check the failure depth for each of the 3 failure modes on the "predicted failure" sheet.The "predicted failure" column highlights the failure mode that will occur at the least depth.4) Check the "weight & volume" sheet to see if your design is within the boundaries you need.5) Vary the configuration attempting to balance the three failure modes. In a balanced design, none ofthe three modes should occur much earlier than the other two.

Shell DefinitionDesignD = Diameter to Midplane of Shell (in)t = Shell Plating Thickness (in)n = Num. of Circumferential Lobes for Failure CalculationCylinder Length (in)Length Overall1450.256120165.252450.255120165.253450.386120165.38

Frame DefinitionDesignNumber of Framesb = Thickness (in)L = Frame Separation (in)c = Frame Depth (in)d = Flange Thickness (in)Internal Diameter of Pressure Hull (in)e = Flange Width (in)Ls = Length Between Bulkheads (in)1240.254.9620.2540.250.590260.523.4020.2540.251903120.510.3620.2540.13145

Material DefinitionDesignMaterialE = Young's Modulusm = Poisson's Ratiosy = Yield StressWeight per in3 (lbs)1SAE950284460000.3500000.28352SAE950284460000.3500000.28353SAE950284460000.3500000.2835

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Auxiliary FunctionsDesignAuxiliary FunctionsA (in2)momentIDEI (in4)Df (in)qHBNbKQmext. shell radiusint. shell radiusWeight of Cyl. Section (lbs)Weight Per Endcap (lbs)Weight Per Frame (lbs)10.56250.51560.66930.196642.83332.6895-0.39530.10001.06831.57600.88751.39710.785422.625022.37501202.3660225.445921.458921.12501.03131.33850.393242.833312.6973-0.00550.10001.00000.73761.00002.09180.785422.625022.37501202.3660225.445942.917831.12501.03131.33850.393242.83334.59160.13710.14291.02321.32051.04111.90841.570822.687522.31251803.5491338.173242.9178

Predicted FailureDesign NumberShell Failure (psi)Frame Failure (psi)Predicted FailureYieldBuckleat frameat midbayGeneral InstabilityYieldInstabilityCrush Depth (ft)Failure Mode12,2195736282589941,223546general instability23494335573951,3281,633751shell buckle32,4757758001,1521,5281,7901,706shell yield

Weight & VolumeDesign NumberPressure Hull Weight (lbs)Pressure Hull Displacement (lbs)Gross Payload (lbs)12168.27148942.40436774.132921910.76468942.40437031.639732994.90908996.86806001.9590

LookupsLookup List for Failure Mode:123456shell buckleshell yieldshell yieldgeneral instabilityframe compressionframe instability

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ReferencesShell BucklePrinciples of Naval Architecture, p.209, equation 19 (Windenburg)Shell Yield at framePrinciples of Naval Architecture, p.210, equation 21a (von Sanden and Gunther equation "92")Shell Yield at midbayPrinciples of Naval Architecture, p.210, equation 21b (von Sanden and Gunther equation "92a")Frame YieldPrinciples of Naval Architecture, p.212, equation 27Frame InstabilityPrinciples of Naval Architecture, p.212, equation 31Note: We are assuming no eccentricities in hull round. For out-of-round situations equation #29 would be used in addition to the ones here.General InstabilityPrinciples of Naval Architecture, p.213, equation 33 (Bryant)

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