PE Pipe Technical Catalogue (PDF) - Pipelife Norge AS

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Pipelife Norge ASPE CATALOGUE-SUBMARINE APPLICATIONS, PIPELIFE NORGE AS, December 2002.A.3.5Bending stressesA PE-pipe can, due to its flexibility, be bent to a certain curvature. However, there is a minimumradius that can not be ”exceeded” if buckling should be avoided.During such bending it will occur stress and strains both in longitudinal and radial direction ofthe pipe.When the bending radius is too little, the pipe will buckle.Especially during sinking of a subwater pipeline it is necessary to ensure that the bending radiusis greater than the critical buckling radius.During installation the balance between forces; weight of the concrete block, forces from boats,buoyancy forces, forces from currents and waves or other man made forces defines theconfiguration and the maximum curvature.When a pipe is bent to a curvature with radius R in axial direction there will occur a strain, ε a , inthe pipe wall. This strain can be expressed :r Dε a = =A.3-29)R 2 ⋅ Rr = pipe radiusR = bending radiusD = pipe’s outside diameterThe case is shown in fig. A.3.5.1.ε arDRFig. A.3.5.1 PE-pipe under pure bendingTo bend a pipe to this radius, R, it must be subject to an external moment caused by the forcesmentioned earlier. The moment (M) can be expressed :E ⋅ IM = A.3-30)RE = modulus of elasticity (creep modulus)I = π4⋅ (D− d )64(moment of inertia)D = outside diameterd = inside diameterA.3-31)The maximum stress in the pipe wall can be estimated from Hook’s law (ref.A.3-14) :r Dσ a = E ⋅ ε a = E ⋅ = E ⋅A.3-32)R 2 ⋅ RSide 40 av 84
Pipelife Norge ASPE CATALOGUE-SUBMARINE APPLICATIONS, PIPELIFE NORGE AS, December 2002.The stress is a tension in the outer curve and a compression in the inner curve.The value of the stress will decrease by time due to relaxation in the PE material.RWe often introduce the ratio = a .DFormula A.3-29) and A.3-32) can be rewritten :εσaa1=2 ⋅ aE=2 ⋅ aA.3-33)A.3-34)Note that the stress and strain in longitudinal direction are independent of the pipe’s SDR class.Example 14Estimate the maximum bending stress in a Ø 1200 mm PE100 pipe bent to a radius 30 ⋅ Dduring sinking. Assume E-modulus = 700 Mpa.Solution :First we decide the radius of curvature : R = 30 ⋅ 1.2 m = 36 m1.2The stress is, for instance, calculated from formula A.3-32) : σ = 700 ⋅ MPa2 ⋅ 36a =11.71MPaIf we look back to table A.1.2, we can find the burst stress for short-term loads to be 15 Mpa.15The safety factor against rupture is F = = 1.311,7For practical purposes a bending radius of 30 ⋅ D can be considered to be minimum radius fora PE-pipe during sinking (SDR < 26).As we have seen the bending stresses can be significant.When a pipe is permanent installed in a curve over lifetime, these stresses can contribute toa reduction in allowable pressure.As a rule of thumb, in situations with combined loads e.g. pressure, temperature loads, waves etc.,we recommend :R min= 60 ⋅ DAs mentioned earlier the relaxation in the PE material will reduce the stresses due to bendingmore than the reduction in the burst stress for the material. Hence the factor of safety will increaseas time passes.A.3.5.1 Buckling of PE pipe during bendingWhen a pipe is bent continuously it will sooner or later buckle. Theoretically there are 2 possiblecases :−−Axial bucklingRadial bucklingSide 41 av 84
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PE Pipe Technical Catalogue (PDF) - Pipelife Norge AS

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