Sheet1Input Data:Diameter=4160mmInside Lining=15mmThickness of Plate=21mmOuter Diameter=4232mmMean Diameter=4211mmShell ID=4190mmHeight of Backfill=1m

IHoop Stress:

(a)If Working Pressure is UsedThe Nominal Thickness of steel pipe is calculated as givenbelow, plus the permitted manufacturing tolerance for reduction in Thickness.Internal Pressurep=10.50Kgf/cm2OD of the PipeD=4232mmDesign factora=0.60(0.6 if p is the working pressure and 0.9 if p is the test pressureinclusive of surge pressure)Minimum yield stress of the steelf=2500Kgf/cm2Weld efficiency of the jointe=0.80(0.9 for shop welding and 0.8 for field welding)Thickness requiredt=pD2afe + p

t=18.43mm

(b)If Hydraulic Test Pressure is UsedThickness of the Pipe proposedt=21mmOD of the pipeD=4232mmDesign factora=0.90(0.6 if p is the working pressure and 0.9 if p is the test pressureinclusive of surge pressure)Minimum yield stress of the steelf=2500Kgf/cm2Weld efficiency of the jointe=0.80(0.9 for shop welding and 0.8 for field welding)60% of Yield stressS=1500Kgf/cm2Hydraulic test pressureP=2StD=14.89Kgf/cm2Thickness of pipe required for this hydraulic test pressuret=PD2afe + P

t=17.43mm

IIDeflection:The deflection is given by Spangler's Theory (AWWA Manual M11)Mean diameter of pipeD=4.211mHeight of backfill above pipe topH=1mSpecific weight of backfill materialrs=1800Kgf/cm3Load per unit length of pipe due tosoil overburdenW=rsDH100=75.80Kgf/cm2Pipe radiusr=210.55cmModulus of elasticity of steelE=2100000Kgf/cm2Transverse Moment of Inertia perunit length of pipe wallI=0.772Cm3Modulus of soil reactionE'=40Kgf/cm2Lined and gunited pipeD1=1Bedding ConstantK=0.10Deflectionx=D1 KWr3 EI + 0.06 E' r3

x=2.945CmDeflection should be less than 2% of the Mean Diameter2% of the Mean Dia=0.08422m

=8.422CmDeflection is less than 2% of the mean dia, Hence Safe.

IIIBuckling:(a)Allowable Buckling PressureThe allowable buckling pressure is given by AWWA Manual M11Design factorFS=2Height of water surface above top of pipeHw=0CmHeight of backfill above top of pipeH=100Cm=3.28ftWater buoyancy factorRw=1-0.33(Hw/H)=1Modulus of soil reactionE'=40Kgf/cm2Modulus of elasticity of steelE=2100000Kgf/cm2Transverse Moment of Inertia per unit length of pipe wallI=0.772Cm3Outer DiameterD=423.2CmMathematical Constante=2.73Empirical constant given byB'=11+4 e(-0.065H)=0.236Allowable Buckling Pressureqa= 1 32 Rw B' E' EI0.50FS D3

Allowable Buckling Pressure=1.272Kgf/cm2

(b)Actual Buckling PressureThe requirement of safety from buckling is verified by the following equation=rw Hw + Rw W + Pv DSpecific weight of waterrw=0.001Kgf/cm3Specific weight of backfill materialrs=1800Kgf/cm2Outer DiameterD=4.232m=423.2cmHeight of BackfillH=1mLoad per cm length due to soil overburdenW=rsDH100=76.176Kgf/cm2Internal vacuum pressurePv=1Kgf/cm2

Actual Buckling Pressure=1.180Kgf/cm2Actual Buckling Pressure is less than Allowable Buckling Pressure, Hence Safe.

IVCollapse Pressure:Youngs Modulus of steelE=2100000Kgf/cm2Poissons RatiovThickness of wallt=21mmMean DiameterD=4211mmFor truly circular pipe, The critical collapse pressure is given by AWWA Manual M11.Pc= 2 E t3(1-v2) DFor steel pipe in FPS units the formula reduces toPc=66 x 10^6t 3DAWWA recommends more conservative formulaPc=50.2 x 10^6 t 3 D=6.23PSI=0.438Kgf/cm2=0.562Kgf/cm2=5.62m

Critical pressure is less than 1 kg/sq cm i.e. atmospheric pressure, protection is required to limit negative pressure to less than 5.62 m.

Sheet2

Sheet3