1999 omae99 pipe-5037 bai - bending moment capacity of pipes

7/23/2019 1999 OMAE99 PIPE-5037 Bai - Bending Moment Capacity of Pipes

1/13

Offshore Mechanical and Arctic Engineering, July 11-16, 1999

BENDING MOMENT CAPACITY OF PIPES

Snrren Hauch and Yong BaiJP Kenny A/S, *) Stavanger University CollegeStavanger, Norway

ABSTRQCTIn most modem pipeline design, the required minimum wallthickness is determined based on the maximum allowable hoopstressunder design pressure.This has shown an efficient way tocome up with an initial wall thickness design under theassumption hat pressure will be the governing load. A pipelinemay though be subjected o additional loads due to installation,seabed contours and high-pressure/high-temperatureoperatingconditions for which the bending moment capacity often will bethe limiting parameter. If in-place analyses predict that themaximum allowable moment to a pipeline will be exceeded, twill be necessary o either increase he wall thickness or, as morenormal, to perform seabed ntervention to reduce the bending ofthe pipe.In this paper the bending moment capacity for metallic pipes hasbeen investigated with the intention to optimise the costeffectiveness in the seabed intervention design withoutcompromising the safety to the pipe. Ihe focus has been on howto account or the interaction betweenpressure, ongitudinal forceand bending in the bending moment capacity calculations. Thestudy is basedon an analytical approachand the solution has beencomparedagainst results obtained rom finite element analyses.

NOMENCLATUREADEFFIfoMMCPPCPePerPiPtPPPYrSMTSSMYS

AreaAverage diameterYoungs modulusTrue longitudinal forceLimit true longitudinal forceInitial out-of-roundnessMomentMoment capacityPressureCharacteristic collapsepressureExternal pressureElastic buckling pressureInternal pressureLimit pressurePlastic bucklingpressureYieldpressureAveragepipe radiusSpecifiedMinimum Tensile StrengthSpecifiedMinimum Yield Strength

Proceedings of OMAE99, 18th

International Conference

On Offshore Mechanics and Arctic Engineering

July 1116, 1999, St. Johns, Newfoundland, Canada

OMAE99/PIPE-5037


2/13


INTRODUCTIONThe European design of risers and offshore pipelines are todaymainly basedon a Limit State design. In a limit state design, allforeseeable ailure scenarios are considered and the system isdesignedagainst he failure mode hat provides the lowest strengthcapacity. A pipe must sustain installation loads and operationalloads. In addition external loads such as those nduced by waves,current, uneven seabed , rawl-board impact, pullover, expansiondue to temperature hangesetc need to be considered.Experiencehas shown that the main load effect on o ffshore pipes is bendingcombined with longitudinal force while subjected to externalhydrostatic pressureduring installation and nternal pressurewhilein operation. A pipe subjected o increasedbending may fail dueto local buckling/collapse or fracture, but it is the localbuckling/collapse Limit State that commonly dictates the design.The local buckling and collapse strength of metallic pipes hasbeen the main subject for many stud ies in offshore and civilengineering and this paper should be seen as a supplement o theongoing debate. See Murphey & Langner (1985), Winter et al(1985), Ellinas (1986), Winter et al (1988), Mohareb et al (1994),Bai et al (1993, 1997) etc.BENDING MOMENT CAPACITYThe pipe cross sectional bending moment s directly proportionalto the pipe curvature, see Figure 1. The example illustrates aninitial straight pipe with low D /t (~60) subjected o a load scenariowhere pressureand longitudinal force are kept constant while anincreasing curvature s applied.

Figure I: Examplesof bending moment ersus curvature relation.

onset of local buckling has occurred, the global deformation willcontinue, but more and more of the applied bending energy will beaccumulated n the local buckle which will continue until theLIMIT POINT is reached. At this point the maximum bendingresistanceof the pipe is reached and a geometrical collapse willoccur if the curvature is additional increased.Until the point ofSTART OF CATASTROPHICALLY CAPACITY REDUCTIONhas been reached, he geometric collapse will be slow and thechanges in cross sectional area negligible. After this point,material softening sets n and the pipe cross section will collapseuntil the upper and lower pipe wall is in contact. For pipessubjected to longitudinal force and/or pressure close to themaximum capacity, START OF CATASTROPHICALLYCAPACITY REDUCTION occurs immediately after the LIMITPOINT. The moment curvature relation for these oad conditionswill be closer to that presented y the dashed ine in Figure 1.The moment curvature relationship provides informationnecessary or design against ailure due to bending. Depending onthe function of the pipe, any of the above-described oints can beused as design limit. If the pipe is a part of a carrying structure,the elastic limit may be an obvious choice as he design imit. Forpipelines and risers where the global shape s less mportant, thiscriterion will though be overly conservative due to the significantresources n the elastic-plastic range. Higher design strength cantherefore be obtained by using design criteria based on thestress/strain evels reachedat the point of onset for local bucklingor at the limit point. For displacement-controlled onfigurations, tcan even be acceptab le o allow the deformation of the pipe tocontinue into the softening region (not in design). The rationale ofthis is the knowledge of the carrying capacity with highdeformations combined with a precise prediction of thedeformation pattern and ts amplitude.The limit bending moment for steel pipes is a function of manyparameters.The main parameters are given below in arbitrarysequence:

. Diameter over wall thickness atio. Material stress-strain elationship. Material imperfections. Welding (Longitudinal as well as circumferential). Initial out-of-roundness. Reduction in wall thicknessdue to e.g. corrosion. Cracks in pipe and/or welding)


3/13


FAILURE MODES PURE EXTERNALPRESSUREAs pointed out in the previous section the limit moment s highlydependenton the amount of longitudinal force and pressure oadsand for cases with high external pressure also initial out-of-roundness.To clarify the approachused n the developmentof theanalytical equations and to give a better understanding of theobtained results, characteristicsof the ultimate strength for pipessubjected o single loads and combined oads are discussed elow.

Theoretically, a circular pipe without imperfections shouldcontinue being circular when subjected to increasing uniformexternal pressure. Due to material and/or geometricalimperfections, there will though always be a flattening of the pipe,which with increased external pressure will end with a totalcollapse of the cross section. The change in out-of-roundness,causedby the external pressure, ntroduce circumferential bendingstresses, where the highest stresses occurs a t respective thetop/bottom and two sides of the flattened cross-section.For lowD/t ratios, material softening will occur at these points and thepoints will behave as a kind of hinge at collapse. The averagehoop stressat failure due to external pressurechangewith the D/tratio. For small D/t ratios, the failure is governed by yielding ofthe cross section, while it for larger D/t ratios is governed byelastic buckling. By elastic buckling is meant that the collapseoccurs before the averagehoop stressover the cross section hasreached he yield stress.At D/t ratios in-between, the failure is acombination of yielding and elastic buckling.

The cross sectional deformations just before failure o f pipessubjected o single loads are shown in Figure 2.

Pure bending Pure pressure Pure longitudinal force

Figure 2: Pipe cross sectional deformation of pipes subjected osingle loaakPURE BENDINGA pipe subjected o increasing pure bending will fail as a result ofincreasedovalisation of the cross section and reducedslope n thestress-strain curve. Up to a certain level of ovalisation, thedecrease in moment of inertia will be counterba lanced byincreasedpipe wall stressdue to strain hardening. When the losein moment of inertia can no more be compensatedor by the strainhardening, the moment capacity has been reached andcatastrophically cross sectional collapse will occur if additionalbending is applied. For low D/t, the failure will be initiated on thetensile side of the pipe due to stresses t the outer fibres exceedingthe limiting longitudinal stress.For D/t higher than approximately30-35, the hoop strength of the pipe will be so low compared othe tensile strength that the failure mode will be an inwardbuckling on the compress ive side of the pipe. The geometrical

Several formulations have been proposed for estimating theexternal collapse pressure,but in this paper, only Timoshenkosand Haagsmasequations are described. Timoshenkos equation,which gives the pressureat which yielding in the extreme fibresbegins, will in general representa lower bound, while Haagsmasequation, using a fully plastic yielding conditions, will representan upper bound for the collapse pressure.The collapse pressureofpipes is very dependenton geometrical mperfections and here inspecial initial out-off-roundness. Both Timoshenkos andHaagsmas ollapse equation account or initial out-off-roundness.Timoshenkos equation giving the pressure causing yield at theouter pipe fibre:

P~-[P~+(l+l.5.y).P4PC+P,.P~,=0 (2)where:

PC = Characteristiccollapse pressure

PPfo = Initial out-of-roundness, D--Dmi,)/D(3)


4/13


Haagsmas equation giving the pressure at which fully plasticyielding over the wall thicknessoccurs can be expressed s:P:-Pd.PcZ-

cP;+Pe,-P~&q .Pc+Per.P:=o

1(5)

and represent the theoretical upper bound for the collapsepressure.For low D/t, the collapse pressurewill be closer to thecollapse pressure calculated by Haagsmas equation than thatcalculated by Timoshenkos equation, Haagsma and Schaap(1981).The use of Timoshenkos and Haagsmas eguation relatesspecifically to a pipe that has initially linear elastic materialpropertiesand where the elastic buckling pressure s derived fromclassical analysis. This would be appropria te or seamless ipes orfor pipes that has been subjected to an annealing process.However, for pipe fabricated using the UO or UOE method thereare significant non-linearities in the materia l properties in thehoop direction, due to residual strains and the Bauschingereffect.These effects may be accounted for by introducing a strengthreduction factor to the plastic buckling pressure erm given by Eq.(4). No effort has n this study been given to estimate he size ofthis reduction factor, but according to DNV 1996 the plasticbuckling pressureshall be reduced with 7.5% and 15% for pipesfabricatedby the UO and UOE process espectively.For Pure nternal pressure, he failure mode will be bursting of thecross-section.Due to the pressure, he pipe c ross section expandand the pipe wall thickness decrease.The decreasen pipe wallthickness s compensatedor by an increase n the hoop stress.Ata certain pressure, he material strain hardening can no longercompensate he pipe wall thinning and the maximum internalpressure has been reached. The bursting pressure can inaccordancewith API (1999) be given as:

where O.S(SMTS+SMYS) s the hoop stressat failure.PURE ENSIONFor pure tension, the failure of the pipe will be, as for bursting,results of pipe wall thinning. When the longitudinal tensile forceare increased, he pipe cross section will narrow down and thepipe wall thickness decrease.At a certain tensile force, the cross

maximum compress ive force will be close to the tensile failureforce.6 =SMTS.A (8)

COMBINEDLOALBFor pipes subjected to single loads, the failure is, as describedabove, dominated by either longitudinal or hoop stresses. or thecombination of pressure, ongitudinal force and bending the stresslevel at failure will be an interaction between longitudinal andhoop stresses. n accordance with among others DNV (1995)classification notes for buckling strength analysis of plates, thisinteraction can, neglecting the radial stress component and theshearstress omponents,be describedas:(9)

where q is the applied longitudinal s tress,ch the applied hoopstressand ou and ou the limit stress n their respective direction.The limit stress may differ depending on if the applied load iscompressiveor tensile. a is a correction factor depending on theratio between the limit stress in the longitudinal and hoopdirection respectively. Basedon Eq. (9), Eq. (5), Eq. (6), Eq. (12)and finite element analyses, the following definition for thecorrection factor have been suggested or external and internaloverpressure espectively:

a=0.25P"8a=0.25$ IFor pipes under combined pressureand ongitudinal force, Eq. (9)may be used to find the pipe strengthcapacity. Alternatives to Eq.(9) are Von Mises, Trescas,Hills and T&Hills yield condition.

Experimental tests have been performed by e.g. Corona andKyriakides (1988). For combined pressureand longitudinal force,the failure mode will be very similar to the ones or single loads.In general, the ultimate strength nteraction between ongitudinalforce and bending may be expressed by the fully plasticinteraction curve for tubular cross-sections.However, if D/t ishigher than 35, local buckling may occur at the compressiveside,leading to a failure slightly inside the fully plastic interactioncurve, Chen and Sohal (1988). When tension is dominating, the


5/13


capacity. For bending combined with internal overpressure, hetwo failure modes work against each other and therebystrengthen the pipe. For high internal overpressure, he collapsewill always be initiated on the tensile side of the pipe due tostressesat the outer flbres exceeding the material limit tensilestress. On the compressive side of the pipe, the high internalpressure will tend to initiate an outward buckle, which willincrease the pipe diameter locally and thereby increase themoment of inertia and the bending moment capacity to the pipe.The moment capacity will therefore be expected o be higher forinternal overpressure compared with a corresponding externalpressure.ADDITIONAL FAILURE MODEIn addition to the failure modes described above, fracture is apossible failure mode for all the described load conditions. Inparticular for the combination of tension, high internal pressureand bending, it is important to check against fracture becauseofthe high stress evel a t the limit bending moment. The fracturecriteria are not included in this paper, but shall be addressedndesign.ANALYTICAL EXPRESSION FOR THE LIMIT MOMENTIn the following, the limit moment for pipes subjec ted tocombined oads s derived. To keep he complexity of the bendingmomentLimit Stateequationson a reasonableevel, the followingassumptions ave been made:

Geometrical perfect pipe except from initial out-off-roundnessElastic- perfectly plastic materialEntire cross section has reached he limit stressNo change n cross section geometrybefore the limit stressis reachedThe limit stresssurface can be described n accordance oEq. (9)

LIMITSTZESSSURFACEThe pipe wall stress ondition for the bending momentLimit Statecan be consideredas that of a material under biaxial loads. It isassumed hat the pipe wall limit stresssurfacecan be described naccordance o Eq. (13). The limit stresssurface s here, neglectingthe radial stress component and the shear stress components,described as a function of the longitudinal stress or, the hoop

a,, is now defined as he limit longitudinal compressive tress nthe pipe wall and thereby equal to 01as determinedabove with thenegative sign before he square oot. The limit tensile stressa;, isaccordingly equal to q with the positive sign in front of the squareroot.(15)

(16)THEBENDINGMOMENTThe bending moment capacity of a pipe with an elastic- perfectlyplastic m aterial behaviour can, assumed that the entire crosssection has reached he limit stress,be calculated as:

where Acompnd&.,, are respectively the cross sectional area ncompression and tension, v their mass centres distance to thepipe centre and o the stress evel, seeFigure 3.! Planof bending

Figure 3: Pipe cross section with stress distribution diagram(dashed line) and idealised stress diagram for plastified crosssection fill line).For a geometrical perfect circular pipe, the area n compression


6/13


where r is the averagepipe wall radius and vthe angle from thebending plan to the plastic neutral axis. The plastic neutral axis isdefined as the axis at which the longitudinal pipe wall stresseschange rom tensile to compressive, eeFigure 3.Inserting Eq. (18) to (21) in Eq. (17) gives the bending momentcapacity as:

M c(u,,.u,) -2tr * sin(y) + 2tr sin&)a,~~~ (22)Loc*r~ONOFFUUYPLAsTICNEUTRAL~STo ca lculate the angle to the fully plastic neutral axis from theplan of bending, it is necessary o s tart with looking at the truelongitudinal pipe wall force, which approximately can beexpressed s:

F = -%cwn,op + &so tens ( 23 >where the area n compression&O,,,ps calculated as:

Amp=2y,rt (24)and the area n tension &, as;

A,, = 2(x - y)r t ( 25 1Giving:

F=2rt~omp+(~-~)o,)Solving Eq. (26) for w gives:

(26)

( 27 1or

FINK EXPRESSION ORMOMENT CAPACITYSubstituting the expression for the plastic neutral axis, Eq. (28),into the equation for the momentcapacity, Eq. (22) gives:

1)whereMC = Bending momentcapacityMp = Plastic momentP = Pressureacting on the pipePI = Limit pressureF = True longitudinal force acting on the pipeFI = Limit longitudinal forceAPPLICXBLERANGEFORMOMENTCAPACITYEQUAITONTo avoid complex solutions when solving Eq. (31), theexpressionsunder the square root must be positive, which givesthe theoretical range or the pressure o:-~s~5~ (32)

where the limit load p1dependon the load condition and a on theratio between he limit force and the limit pressure.Since the wall thickness design s basedon the operating pressureto the pipeline, this range should not give any problems in thedesign.Given by the physical limitation that the angle to the plasticneutral axis must be between 0 and 180 degree, he equation isvalid for the following rangeof longitudinal force:

(33)where the limit loads Fi and pI dependson the load condition anda on the ratio between he limit force Fi and the limit pressurepi.For the design of pipelines, this range is normally not going togive any problems,but again, he range may be reduceddue to thequestion of fracture.


7/13


equilibrium into algebraic equations. In a few words, the finiteelement method can be defined as a Rayleigh-Ritz method inwhich the approximating field is interpolated n piece wise fashionfrom the degreeof freedom hat are nodal values of the field. Themodelled pipe section s subject o pressure, ongitudinal force andbending with the purpose o provoke structural failure of the pipe.The deformation pattern at failure will introduce both geometrica land material non-linearity. The non-linearity of thebuckling/collapse phenomenon makes finite element analysessuperior to analytical expressions for estimating the strengthcapacity.In order to get a reliable finite element prediction of thebuckling/collapse deformation behaviour the following factorsmust be taken nto account:

l A proper representationof the constitutive law of the pipemateriall A proper representationof the boundary conditionsl A proper application of the load sequencel The ability to address arge deformations, arge rotations, andfinite strainsl The ability to model/describeall relevant failure modes

The material definition included in the finite element mode l is ofhigh importance, since the m odel is subjected to deformationslong into the elasto-plas tic range. In the post buckling phase,strain levels between 10% and 20% is usual and the materialdefinition should therefore at least be governing up to this leve l. Inthe present analyses,a Ramberg-Osgood tress-strain elationshiphas been used. For this, two points on the stress-strain urve arerequired along with the material Youngs modules.The two pointscan be anywhere along the curve, and for the present model,specified minimum yield strength (SMYS) associa tedwith a strainof 0.5% and the specified minimum tensile strength (SMTS)corresponding to approximately 20% strain has been used. Thematerial yield limit has been defined as approximately 80% ofSMYS.The advantagen using SMYS and SMTS insteadof a stress-straincurve obtained rom a specific test s that the statistical uncertaintyin the material stress-strain elation is accounted or. It is therebyensured that the s tress-strain curve used in a finite elementanalysis in general will be more conservative than that from aspecific laboratory test.

thick shell theory when the shell thickness ncreasesand discreteKirchoff thin shell theory as he thicknessdecreases.For a further discussion and verification of the used inite elementmodel, see Bai et al (1993), Mohareb et al (1994), Bruschi et al(1995) and Hauch & Bai (1998).ANALYTICAL SOLUTION VERSUS FllvITE ELEMENTRESULTSIn the following, the above-presentedequations are comparedwith results obtained from finite element analyses. First are thecapacity equations for pipes subjected o single loads comparedwith finite element results for a D/t ra tio from 10 to 60. Secondlythe moment capacity equation for combined longitudinal force,pressureand bending are comparedagainst inite element esults.STRENGTHCAPACITYOF PIPES SUBJECTEDTOSINGLELOADSAs a verification o f the finite element mode l, the strengthcapacities or single loads obtained from finite element analysesare comparedagainst he verified analytical expressionsdescribedin the previous sections of this paper. The strength capacity hasbeen compared or a large range of diameter over wall thicknessto demonstrate he finite element models capability to catch theright failure mode independently of the D/t ratio. For all theanalyses, he averagediameter s 0.5088m, SMYS = 450 MPa andSMTS = 530 MPa. In Figure 4 the bending moment capacityfound from finite element analysis has been comparedagainst hebending moment capacity equation, Bq. (1) . In Figure 5 the limittensile longitudinal force Bq. (7), in Figure 6 the collapse pressureBq. (2, 5) and in Figure 7 the bursting pressure Bq. (6) arecompared against finite element results. The good agreementbetween the finite element results and analytical solutionspresented n figure 4-7 give good reasons o expect that the finiteelement mode l also will give reliable predictions for combinedloads.

X = FE results- = Analytical


8/13

Offshore Mechanical and Arctic Engineering, July 11 16, 1999

X = FE results -- = Analytical

1.5-

l-


9/13


Figure 9: Limit bending moment ur$aceas a inction ofpressureand longitudinal force including cross sections or whichcomparisonbetweenanalytical solution and resultsporn finiteelementanalyseshas beenperformed.

= FE results

-1.51 I-0.4 -0.2 0 02 0.4 0.6 0.6 1 12Pressue I PfastiC Bucknrg PmssueFigure 10: Normalised bending momentcapacity as a unction ofpressure.No longitudinalforce is applied.

0.6 x x x

$0 xt ( X = FE resultss x -= Analytical

-0.6 , X,x 1-1 4.6 -0.6 -0.4 -0.2 0 0.2 0.4 0.6Longitudinal force I Longitudinal limit force 6Figure 12: Normalised bending moment apacity as a unction oflongitudinal force. Pressureequal to 0.8 timesHaagsma scollapsepressure Eq. (5).

t- x xx0.6 -.6 -h 0.6 -.6 - 0.4 -.4 -i!! 0.2-.2-: o- = FE resultsFE resultso-bl -0.2 -0.2 -

-0.40.4-0.6 -0.6 --0.6 - x xx

-0.4 -02 0 02 0.4 0.6 0.6 1 1.2 1.4Longitiinal force I Longitudinal Umit forceFigure 13: Normalised bending moment apacity as ajimction oflongitudinalforce. Pressureequal to 0.9 times heplastic bucklingpressure Eq. (4).USAGhZAFETYFACTORSThe local buckling check can be separated nto a check for loadcontrolled situations (bending moment) and one for displacement


10/13


The usage factor approach presented n this paper is based onshrinking the failure surface shown in Figures 8 and 9. Instead ofrepresenting he bending momentcapacity, he surface s scaled orepresent the maximum allowable bending moment associatedwith a given target safety level. The shape of the failure surfacegiven Eq. (31) is d ictated by four parameters; he plastic momentM,, the limit longitudinal force Fi, the limit pressurePi and thecorrection factor (shape parameter) a. To shrink the failuresurface usage factors are applied to the plastic moment,longitudinal limit force and the limit pressure respectively. Theusage actors are functions of modelling, geometrical and materialuncertainties and will therefore vary for the three capacityparameters. In general, the variation will be small and forsimplification purposes, he most conservative usage factor maybe applied to all capacity loads. The correction factor a is afunction of the longitudinal limit force and the limit pressureandno usage factor is applied to this parameter. The modellinguncertainty is highly connected o the use of the equation. In theSLJPEBB 1996) project, the use of the moment criteria is dividedinto four unlike scenarios; 1) pipelines resting on uneven seabed,2) pressure est condition, 3) continues stiff supportedpipe and 4)all o ther scenarios. To account for the variation in modellinguncertainty, a condition load factor 2 is applied to the plasticmoment and the limit longitudinal force. The pressure,which is afunction of internal pressureand waterdepth,will not be subjectedto the same model uncertainty and the condition load factor willbe close to one and can be neglected. Based on the abovediscussion, the maximum allowable bending moment may beexpressed s:

(34)where~AIkmnbk = Allowable bending momentY? = Condition load factor17R = Strengthusage actors

The usage/safety actor methodologyused n Eq. (34) ensures hatthe safety levels are uniformly maintained for all loadcombinations.

side of the pipe. The criteria given in this guideline may be usedto calculate the maximum allowable bending moment for agiven scenario. It shall be noted that the maximum allowablebending moment given in this guideline does not take fractureinto account and that fracture criteria therefore may reduce thebending capacity to the pipe. This particularly applies for high-tension/high-pressureoad conditions.

l LOAD VER.WS ISPLACEMENTCONTROLLED ITUATIONS:The local buckling check can be separatednto a check for loadcontrolled situations (bending moment) and one fordisplacement controlled situations (strain level). Due to therelation between applied bending moment and maximum strainin a pipe, a higher allowable strength for a given target safetylevel can be achieved by using a strain-basedcriterion than thebending moment criterion. The bending moment criterion candue to this, conservatively be used for both load anddisplacement controlled situations. In this guideline only thebending momentcriterion is given.

l Locar. BUCKLINGANDACCUWLATED OUT-OF-ROUNDNESS:Increased out-of-roundness due to installation and cyclicoperating loads may aggravate local buckling and is to beconsidered. It is recommended hat out-of-roundness, due tothrough life loads, be simulated using finite element analysis.l M~MUMALLO WMLEBENDINGMOME~T:The allowable bending moment or local buckling under loadcontrolled situations can be expressed s:

iwhereMAlmk = Allowable bending moment4 = Plastic momentPI = Limit pressureP = Pressure cting on the pipeFl = Limit longitudinal forceF = Longitudinal force acting on the pipea = Correction factor1% = Condition load factor17R = Strengthusage actor


11/13


M -C(F=O,W) - 1.05-0.0015.~ .SMys.# .ttwhereSMYS = Specified Minimum Yield Strength nlongitudinal directionD = Average diametert = Wall thickness

l LIMIT LONGITUDINALFORCEFOR COMWKWIONAND TENSION:The limit longitudinal force may be estimatedas:4 =05(sMYs+SMTs)~AA =SMYS =SMTS =

Cross sectional area,which may becalculated as rtXDxt.Specified Minimum Yield Strength nlongitudinal directionSpecified Minimum Tensile Strength nlongitudinal directiona LIMIT PRESSURE OREXTERML O~RPRESSURECONDI~ON:The limit external pressure pL( s to be calculated basedon:

where 2E t3PC1 = - -01-v) DPP

2t 1)= qJdsMYsDfo = Initial out-of-roundness ), (D--D,,)/DSMYS = Specified Minimum Yield Strength n hoopdirectionE = Youngs ModuleII = Poissons atio

Guidance note:) ntit, is 0.925 for pipes fabricatedby the UO precess, .85 forpipes fabricated by the UOE processand 1 for seemless r) annealedpipes.Gut-of-roundnesscausedduring the construction phase s tobe included, but not flattening due to external water pressureor bending n as-laid position.

l LIMT PRESSURE OR NTERNAL OVERPRE~~URE ONDITION:

Guidancenotes:- Load Condition Factors may be combined e.g. LoadCondition Factor for pressure est of pipelines resting onuneven seabed,1.07x0.93 = 1 OO- Safety class s low for temporary phases.For the operatingphase,safety class is normal and high for area classified aszone 1 and zone 2 respectively.

CONCLUSIONSThe moment capacity equations n the existing codesare for someload conditions overly conservative and for others non-conservative. This paper presents a new set of design equationsthat are accurate and simple. The derived analytical equationshave been based on the mechanism of failure modes and havebeen extensively comparedwith finite element results. The use ofsafety factors has been simplified comparedwith existing codesand the target safety levels are in accordancewith DNV (1996),IS0 (1998) and API (1998). The applied safety factormethodology ensures that the target safety levels are uniformlymaintained for all load combinations. t is the hope of the authorsthat this paper will help engineers n their aim at designing saferand m ore cost-effective pipes.It is recommended hat the alpha correction factor and fabricationprocess eduction factor are nvestigated n more details.REFERENCESAPI (1998) Design, Construction, Operation and Maintenance ofOffshore Hydrocarbon Pipelines (Limit StateDesign).Bai, Y., Igland, R. and Moan, T. (1993) Tube Collapse underCombinedPressure,Tensionand Bending, International Journal ofOffshore and Polar Engineering,Vol. 3(2), pp. 121-129.


12/13


13/13

1999 omae99 pipe-5037 bai - bending moment capacity of pipes

Documents