Hoop stressThickness Calculations- Hoops StressIIf Working Pressure is UsedThe Nominal Thickness of steel pipe is calculated as given below, Plus the permitted manufacturing tolerence for reduction in Thickness.Pipe Diametert = p DDia17502 a f e + pInside Ling15t = Thickness of the Pipe in mmTk12p = internal pressure Kgf/ cm26.45Kgf/ cm2OD1804D = OD of the pipe in mm1804mmMean Dia1792a = design factor ( 0.6 if p is the working pressure and 0.9 if p is the test pressure inclusive of surge pressure ).0.6Shell ID1780f = Minimum yield stress of the steel Kgf/ cm22500Kgf/ cm2e = Weld efficiency of the joint ( 0.9 for shop welding and 0.8 for field welding ).0.8Thickness required4.84mmIIIf hydraulic test Pressure is Usedt = P D2 a f e + PP = Hydraulic test pressuret = Thickness of the Pipe proposed in mm12D = OD of the pipe in mm1804mma = design factor ( 0.6 if p is the working pressure and 0.9 if p is the test pressure inclusive of surge pressure ).0.9f = Minimum yield stress of the steel Kgf/ cm22500Kgf/ cm2e = Weld efficiency of the joint ( 0.9 for shop welding and 0.8 for field welding ).0.8S = 60% of Yield stressP = 2 STDHydraulic Test pressure19.96Kgf/ cm2Thickness of pipe required for this hydraulic test pressure9.94mm12 mm satisfies this criteria

DeflectionThickness Calculations- DeflectionThe deflection is given by Spangler,s Theory ( AWWA Manual M11)a)x = D1 KW r3EI + 0.06 E' r3x = Deflection CmCmW = Load per unit length of pipe due to soil overburden Kgf/ cm232.26Kgf/ cm2r = Pipe radius cm89.6CmE = Modulus of elasticity of steel Kgf/ cm22100000Kgf/ cm2I = Transverse Moment of Inertia per unit length of pipe wall Cm30.1440Cm3E' = Modulus of soil reaction Kgf/ cm240Kgf/ cm2x =1.144CmD1=1 for lined and gunited pipeb)W = s D H100D = Mean diameter of pipe mtr1.792MtrH= Heigth of backfill above pipe top Mtr1Mtrs = Specific weigth of backfill material Kgf/ cm21800Kgf/ cm3The division by 100 is to convert the load per mtr length to load per cm length.W =32.26Kgf/ cm2Delection should be less than 2% of the Mean diameter2% of the mean dia3.584cmDeflection is less than 2% of mean dia, Hence Safe.

BucklingThickness Calculations- BucklingThe allowable buckling pressure is given by ( AWWA Manual M11)a)qa = 1 32 RwB' E' EIFS D 3qa = Allowable buckling pressure Kgf/ cm2Kgf/ cm2FS = design factor ( 2 as per 4th edition of AWWA manual M11)2Rw = water buoyancy factor given by 1-.33 (Hw / H)1Hw = heigth of water surface above top of pipe cm0CmAssuming water loggingH = Heigth of backfill above top of pipe cm100CmE' =Modulus of soil reaction Kgf/ cm240E = Modulus of elasticity of steel Kgf/ cm22100000Kgf/ cm2I = Transverse Moment of Inertia per unit length of pipe wall Cm30.144Cm3D = Diameter180.400CmCalculations are done for 1 Mtr overburden of soil with no waterlogging in the trench, that is Hw =0 as Hw is 0, Rw = 1. The value of B' is calcualted based on H value in Ft, as follows.qa =1.974Kgf/ cm2b)B' = 11+ 4 e ( -0.065 H)B' = empirical constant given byH is in ft3.28Fte is mathematical constant2.732B' =0.236c)The requirement of safety from buckling is verified by the following Equationw Hw + Rw W + Pv qaw = Specific Wt of water Kgf/ cm30.001W = Load per cm length due to soil overburden Kgf/ cm232.47Kgf/ cm2Pv = Internal vacuum Pressure Kgf/ cm21Hw =0Actual buckling Pressure =1.180Kgf/sq cmW = s D H100s= Specific weigth of backfill material Kgf/ cm21800Kgf/ cm2D= dia in Mtr1.804H= Heigth of backfill Mtr1W =32.47Kg/ Cm2Actual Buckling pressure is Less than Allowable Pressure , Hence Safe.

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Collapse PressureThickness Calculations- Collapse PressureFor truly circular pipe, The critical copplase pressure is given by Following ( AWWA Manula M11)Pc = 2 E t( 1 - 2 ) DPc= Critical collapse pressureKgf/ cm2E= Youngs Modulus of steelKgf/ cm2 = Poissons Ratio.t= Thickness of wall in mm12mmD is diameter in mm1780mmD/t raio148.3less than 165For steel pipe in FPS units the formula reduces to.Pc = 66 x 10^ 6 tDPc =is in PSIAWWA recommends more conservative formulaPc = 50.2 x 10^ 6 t 3DWhere Pc is in PSIPc15.38PSIPc1.082Kgf/ cm2Critical pressure is more than1kg/sq cm ie atmospheric pressure . Hence OK.

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