Section 6 - Stress Analysis in FFS Assessment
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Transcript of Section 6 - Stress Analysis in FFS Assessment
Fitness-for-Service (FFS) Assessment based on API RP579
Section 6 - Stress Analysis in FFS Assessment
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Stress Analysis for FFS Assessment
Stress Analysis for FFS Assessment
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IntroductionIntroduction
Essential in a FFS assessment to know the Essential in a FFS assessment to know the actual stresses applied to any damage:actual stresses applied to any damage:
•• What loads are applied?What loads are applied?•• Manufacturing residual or direct stress?Manufacturing residual or direct stress?•• Operation loads lower than design?Operation loads lower than design?•• Linear elastic or elastic plastic?Linear elastic or elastic plastic?•• Stress increase at local discontinuity?Stress increase at local discontinuity?•• Determining stresses and strain ?Determining stresses and strain ?•• InIn--situ measurement ?situ measurement ?
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Session agendaSession agenda
•• DefinitionsDefinitions•• StressStress--strain response of materialsstrain response of materials•• Stresses in pressure equipmentStresses in pressure equipment•• Stresses in ASME PV and piping Stresses in ASME PV and piping
standardsstandards•• Residual stressesResidual stresses•• Finite element analysisFinite element analysis•• Strain measurementStrain measurement•• Stresses for a FFS assessmentStresses for a FFS assessment
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Definition of stressDefinition of stress
Stress: Internal force exerted by either of Stress: Internal force exerted by either of two adjacent parts upon the other across two adjacent parts upon the other across an imagined plane of separation.an imagined plane of separation.
The bar, subjected to tension, has been cut perpendicular to theThe bar, subjected to tension, has been cut perpendicular to the axis axis into two free bodies to show the normal stress, into two free bodies to show the normal stress, σσxx, This multiplied by , This multiplied by the area (A) on which it acts must be in equilibrium with the apthe area (A) on which it acts must be in equilibrium with the applied plied force (F) hence:force (F) hence:
σσxx
FF FF
σσx x A = FA = F σσxx = F / A= F / A
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Definition stress termsDefinition stress terms•• Shear stress: when Shear stress: when
the force is parallel the force is parallel to the planeto the plane
•• Normal stress: when Normal stress: when the force is normal the force is normal to the planeto the plane
•• Compressive stress: Compressive stress: when the normal when the normal stress is directed stress is directed toward the planetoward the plane
•• Tensile stress: when Tensile stress: when the normal stress is the normal stress is acting away from acting away from the planethe plane
FF
FF
FF FF9090oo
FF FF9090oo
FF FF9090oo
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Definition stress termsDefinition stress terms
•• Bending Bending stress: when a stress: when a bending bending moment acts moment acts normal to the normal to the planeplane
•• Torsion stress: Torsion stress: when a torque when a torque acts parallel acts parallel to the plane to the plane
Point load on a beamPoint load on a beam
Through beam bending stressThrough beam bending stressTensileTensile
CompressiveCompressive
Solid cylinder with applied torqueSolid cylinder with applied torque
Through cylinder torsion stressThrough cylinder torsion stress
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Definition principal stressesDefinition principal stresses
•• At a point in a stressed body there pass At a point in a stressed body there pass 3 mutually perpendicular planes, the 3 mutually perpendicular planes, the stress on the planes are purely normal, stress on the planes are purely normal, tension or compression. These are tension or compression. These are termed the principal planes for that termed the principal planes for that point. The stresses on the planes are point. The stresses on the planes are principal stresses of which:principal stresses of which:–– One is the maximum stress at the point (σOne is the maximum stress at the point (σ11))–– One is the medium stress at the point (σOne is the medium stress at the point (σ22))–– One is the minimum stress at the point (σOne is the minimum stress at the point (σ33))
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Definition principal stressesDefinition principal stresses
θθ θθ
σσyy
σσyy
σσxxσσxx
ττxyxy
ττxyxy
ττyxyx
ττyxyxΤΤs s = 0= 0
σσ1 1 or σor σ22
Element subjected to general two Element subjected to general two dimensional stress systemdimensional stress system
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Definition strainDefinition strain
•• Strain: Any forced change in the Strain: Any forced change in the dimensions of a body. A stretch is a dimensions of a body. A stretch is a tensile strain; a shortening is a tensile strain; a shortening is a compressive strain; and an angular compressive strain; and an angular distortion is a shear strain.distortion is a shear strain.
•• Strain is generally used to denote unit Strain is generally used to denote unit strain (ε)strain (ε)
ε = ε = Change in length (δ)Change in length (δ)Original length (L)Original length (L)
•• As with stress there are principal As with stress there are principal strainsstrains
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Geometric stress concentrationsGeometric stress concentrations•• Stress concentration: Stress concentration:
Discontinuities of form may Discontinuities of form may produce high localised stressproduce high localised stress
•• Stress concentration factors Stress concentration factors (SCF) have been developed (SCF) have been developed to predict the stress at the to predict the stress at the discontinuitydiscontinuity
Plate with a hole showing stress trajectoriesPlate with a hole showing stress trajectories ( )tdw=AAF
=σ
σσ
=K
0
0nom
nom
maxt
-
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SCF exampleSCF example•• Determine the maximum stress Determine the maximum stress
at a sphere/nozzle junction for at a sphere/nozzle junction for a flush nozzle at the start and a flush nozzle at the start and end of end of life.end of end of life.
•• Nozzle OD = 170mmNozzle OD = 170mm•• Nozzle thickness = 7.2mmNozzle thickness = 7.2mm•• Sphere OD = 2500mmSphere OD = 2500mm•• Sphere thickness = 57.15mmSphere thickness = 57.15mm•• Pressure = 40barPressure = 40bar•• Future corrosion allowance = Future corrosion allowance =
2mm2mm
•• σσmaxmax = s.c.f x (PR/(2T’))= s.c.f x (PR/(2T’))Maximum stress in sphere for internal pressure (flush nozzle)Maximum stress in sphere for internal pressure (flush nozzle)
Where,Where,
P = pressure (MPa)P = pressure (MPa)R = mean radius of spherical shell (mm)R = mean radius of spherical shell (mm)r = mean radius of nozzle (mm)r = mean radius of nozzle (mm)t = wall thickness of nozzle (mm)t = wall thickness of nozzle (mm)T’ = wall thickness of spherical shell (mm)T’ = wall thickness of spherical shell (mm)
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Stress strain material responseStress strain material response
•• For most metallic For most metallic materials at 0.002 materials at 0.002 strain (or a defined strain (or a defined yielding point) the yielding point) the material is no longer material is no longer fully elastic and fully elastic and starts to plastically starts to plastically deform, which is deform, which is none recoverablenone recoverable
•• While in the elastic While in the elastic region stress and region stress and strain are strain are proportional proportional ((Hooke’sHooke’s law)law)
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Stress strain material responseStress strain material response•• The rate of change of The rate of change of
stress with respect to stress with respect to strain in the elastic strain in the elastic region is termed the region is termed the modulus of elasticity modulus of elasticity (or Young’s modulus) (or Young’s modulus) and is denoted as Eand is denoted as E
•• Most engineering Most engineering design codes and design codes and standards aim to limit standards aim to limit the normal stress in a the normal stress in a component to below component to below yield levels.yield levels.
Ultimate tensile strength (UTS)Ultimate tensile strength (UTS)
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Yielding criteriaYielding criteria•• Real structures have Real structures have
complex stress complex stress systems.systems.
•• A number of A number of different yielding different yielding criteria have been criteria have been developed, the two developed, the two most common are;most common are;TrescaTresca (maximum (maximum shear stress) or Vonshear stress) or Von--mises mises (shear strain (shear strain energy)energy)Yielding criteria envelope (2D) with Yielding criteria envelope (2D) with
actual test dataactual test data
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Stresses in pressure equipmentStresses in pressure equipment•• Stresses in pressure equipment are generally Stresses in pressure equipment are generally
produced from the following loads:produced from the following loads:–– Internal and external pressureInternal and external pressure–– Weight of equipment, including contents, live and Weight of equipment, including contents, live and
dead loadsdead loads–– Loads from attached equipment e.g. pipingLoads from attached equipment e.g. piping–– Attachment of internals (trays etc.), lugs, supports, Attachment of internals (trays etc.), lugs, supports,
skirts etc.skirts etc.–– Temperature gradients and differential thermal Temperature gradients and differential thermal
expansionexpansion–– Wind, snow, seismic reactionsWind, snow, seismic reactions–– Impact or shock loadingImpact or shock loading
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Pressure equipment stressesPressure equipment stresses
σσCC
σσLL
σσRR
•• Circumferential Circumferential stress (σstress (σCC), also ), also termed hooptermed hoop
•• Longitudinal stress Longitudinal stress (σ(σLL), also termed ), also termed axialaxial
•• Radial stress (σRadial stress (σRR), in ), in thin wall cylinders thin wall cylinders this value is small this value is small
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Pressure equipment stressesPressure equipment stresses•• For the internal pressure only case for the For the internal pressure only case for the
circumferential (hoop) stress, in thinned circumferential (hoop) stress, in thinned walled cylinders:walled cylinders:
•• The corresponding longitudinal (axial) stress The corresponding longitudinal (axial) stress is:is:
•• Which is also the equation for a spherical Which is also the equation for a spherical shell in both directionsshell in both directions
P = pressure P = pressure
D = Outside diameterD = Outside diameter
t = wall thicknesst = wall thicknesst2PD
=σh
t4PD
=σ l
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Pressure equipment designPressure equipment design
•• Pressure equipment is usually designed Pressure equipment is usually designed to construction standards requirements to construction standards requirements by either:by either:–– Design by rule (DBR): engineering formulas Design by rule (DBR): engineering formulas
to produce simple calculations to derive to produce simple calculations to derive sizes etc. utilising an allowable standardised sizes etc. utilising an allowable standardised design stress followed by strict adherence design stress followed by strict adherence to specific rules. Does not provide the to specific rules. Does not provide the designer with a value of the stress. designer with a value of the stress. This is the philosophy of many national pressure vessel design standards
–– Design by analysis (DBA): usually finite Design by analysis (DBA): usually finite element analysis and stress categorisationelement analysis and stress categorisation
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Pressure equipment DBAPressure equipment DBA•• Most of the design by analysis guidelines given Most of the design by analysis guidelines given
in the codes relates to design based on elastic in the codes relates to design based on elastic analysis (1960’s). analysis (1960’s).
•• The rules were developed to guard against The rules were developed to guard against elastic failure mechanisms. Thus guidelines elastic failure mechanisms. Thus guidelines guard against three specific failure modes:guard against three specific failure modes:–– gross plastic deformation, incremental plastic gross plastic deformation, incremental plastic
collapse (collapse (ratchettingratchetting) and fatigue.) and fatigue.•• In this approach the designer is required to In this approach the designer is required to
classify the stress into primary, secondary and classify the stress into primary, secondary and peak categories and apply allowable stress peak categories and apply allowable stress limits. limits.
•• See appendix B in API RP 579See appendix B in API RP 579
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ASME standardsASME standards
•• The most widely used standards in the The most widely used standards in the world.world.
•• ASME section VIII division 1 “Rules for ASME section VIII division 1 “Rules for the construction of pressure vessels”the construction of pressure vessels”
•• ASME section VIII division 2 ASME section VIII division 2 “Alternative rules for the construction of “Alternative rules for the construction of pressure vessels”pressure vessels”
•• ASME B31.3 “Process piping”ASME B31.3 “Process piping”
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Cylindrical shell formulae (ASME)Cylindrical shell formulae (ASME)•• S is the allowable stress for the S is the allowable stress for the
materialmaterial•• E is the weld joint efficiencyE is the weld joint efficiency•• P is the internal pressureP is the internal pressure•• RRcc is the internal radius adjusted for is the internal radius adjusted for
future corrosion future corrosion ectect..•• ttslsl is the extra material required for is the extra material required for
other loads (e.g. bending due to other loads (e.g. bending due to wind)wind)
•• ttminmin is the minimum required wall is the minimum required wall thicknessthickness
•• MWAP is the maximum allowable MWAP is the maximum allowable wall thicknesswall thickness
•• σσm m is the nominal membrane stressis the nominal membrane stress•• Formulae summarised in the Formulae summarised in the
appendix of API RP 579 for various appendix of API RP 579 for various pressure equipment and sectionspressure equipment and sections
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Allowable stress (ASME)Allowable stress (ASME)•• The maximum allowable stress value to be The maximum allowable stress value to be
used in any construction code is defined in the used in any construction code is defined in the pressure vessel standard. pressure vessel standard.
•• For ASME VIII division 1 the listing of For ASME VIII division 1 the listing of materials and allowable stress values are given materials and allowable stress values are given in ASME section II, Part Din ASME section II, Part D
•• For the piping standard B31.3 the allowable For the piping standard B31.3 the allowable stresses are given in its Appendix Astresses are given in its Appendix A
•• The allowable stresses are given for various The allowable stresses are given for various temperaturestemperatures
•• The materials are grouped by general alloying The materials are grouped by general alloying contentcontent
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Extract ASME II, Part D, Table 1A Extract ASME II, Part D, Table 1A
ImportantImportant
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Allowable stress basis (ASME)Allowable stress basis (ASME)
•• ASME VIII division 1 pre 1999 the allowable ASME VIII division 1 pre 1999 the allowable room temperature stress was defined as:room temperature stress was defined as:•• Minimum of 2/3 yield or ¼ of UTSMinimum of 2/3 yield or ¼ of UTS
•• ASME VIII division 1 post 1999 the allowable ASME VIII division 1 post 1999 the allowable room temperature stress is defined as:room temperature stress is defined as:•• Minimum of 2/3 yield or UTS/3.5Minimum of 2/3 yield or UTS/3.5
•• ASME VIII division 2 the allowable room ASME VIII division 2 the allowable room temperature stress is defined as:temperature stress is defined as:•• Minimum of 2/3 yield or UTS/3Minimum of 2/3 yield or UTS/3
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ASME joint efficiencies (E)ASME joint efficiencies (E)
•• Table UWTable UW--12 in ASME VIII division 1, efficiencies based 12 in ASME VIII division 1, efficiencies based on:on:–– Joint type i.e. butt single or double sidedJoint type i.e. butt single or double sided–– Level of radiography i.e. 100%, spot or noneLevel of radiography i.e. 100%, spot or none
•• For example:For example:–– A double V seam weld with 100% radiography E=1.A double V seam weld with 100% radiography E=1.–– A double V seam weld with spot radiography E=0.85.A double V seam weld with spot radiography E=0.85.
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Extract table UW-12Extract table UW-12
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Example problemExample problemVessel has full radiography applied to all joints. Determine theVessel has full radiography applied to all joints. Determine theminimum require thickness for the shell. Material of constructiominimum require thickness for the shell. Material of construction n is A516 grade 65is A516 grade 65
Design pressureDesign pressure
Design temperatureDesign temperature
Corrosion allowanceCorrosion allowance
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Residual stresses causesResidual stresses causesMaterial ManufactureMaterial Manufacture–– castingcasting–– forgingforging–– rollingrolling–– heat treatmentsheat treatments–– quenchingquenching–– straighteningstraightening
FabricationFabrication–– cuttingcutting–– formingforming–– bendingbending–– jigging, fit upjigging, fit up–– weldingwelding–– claddingcladding–– PWHTPWHT–– case hardeningcase hardening–– machiningmachining–– peaningpeaning–– auto auto frettagefrettage
Service lifeService life–– proof loadproof load–– service loadservice load–– service temperatureservice temperature
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Rolling & cooling residual stresses Rolling & cooling residual stresses
AC
Heatingfurnace
slabs
4-High Primaryleveler
Cooling bed Trimming
Discrete plate product
Reverse Mill Process
Thermal cooling controlled
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Residual stresses due to weldingResidual stresses due to welding
•• Tensile residual stresses in weld metal Tensile residual stresses in weld metal are caused by the contraction of the are caused by the contraction of the weld metal from softening temperatureweld metal from softening temperature
•• The maximum residual stresses are The maximum residual stresses are usually approximately equal to the yield usually approximately equal to the yield strength strength if if there is restraint against there is restraint against contraction and the contraction strain is contraction and the contraction strain is greater than the yield straingreater than the yield strain
•• i.e. i.e. ifif αα(T(Tss--TT00) > ) > σσy y /E/E
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Typical residual stressesTypical residual stresses
Residual stresses in an Residual stresses in an ““as weldedas welded”” thick section Vthick section V--butt butt
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Standard residual stress profilesStandard residual stress profiles
•• BS 7910:1999 Amendment 1, BS 7910:1999 Amendment 1, October 2000, Annex QOctober 2000, Annex Q
•• R6 Revision 4, September 2000, R6 Revision 4, September 2000, Chapter IV.4Chapter IV.4
•• API 579, January 2000, Appendix EAPI 579, January 2000, Appendix E
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Finite Element AnalysisFinite Element Analysis•• The finite element method was first introduced The finite element method was first introduced
in the 1950in the 1950’’s s •• It is a mathematical technique which models a It is a mathematical technique which models a
structure as thousands of small pieces structure as thousands of small pieces (elements)(elements)
•• For each element, calculations can be For each element, calculations can be performed simulating various loads to performed simulating various loads to determine the structure's response (e.g. determine the structure's response (e.g. deflection, strain, stress, etc.) deflection, strain, stress, etc.)
•• The technique requires large computational The technique requires large computational resources, thus it has become more accessible resources, thus it has become more accessible over the last twenty years.over the last twenty years.
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Finite Element AnalysisFinite Element Analysis•• FEA shows results for FEA shows results for
whole structurewhole structure•• Strain measurement only Strain measurement only
provides the material provides the material response at the surface response at the surface location of measurementlocation of measurement
•• FEA only as good as the FEA only as good as the analyst conducting the analyst conducting the assessment (validation)assessment (validation)
•• Hand calculations Hand calculations provide accurate results provide accurate results but are typically useful but are typically useful for only simple for only simple geometries.geometries.
•• See appendix B of API RP See appendix B of API RP 579 for the use of FEA in 579 for the use of FEA in a FFSa FFS
FEA results of a 2:1 elliptical head with FEA results of a 2:1 elliptical head with nozzles, under pressurenozzles, under pressure
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Strain measurementStrain measurement•• While there are While there are
several methods of several methods of measuring strain, the measuring strain, the most common is with most common is with a strain gaugea strain gauge
•• A stain gauges A stain gauges electrical resistance electrical resistance varies in proportion varies in proportion to the amount of to the amount of strainstrain
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Strain measurementStrain measurement•• Surface only stresses Surface only stresses
from the structure under from the structure under assessmentassessment
•• Limited number of Limited number of readingsreadings
•• Can become detachedCan become detached•• Requires good bonding Requires good bonding
between the gauge and between the gauge and structurestructure
•• FEA and strain gauge FEA and strain gauge combination excellent for combination excellent for accurate determination accurate determination of structure stressesof structure stresses
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Stresses required for FFSStresses required for FFS
•• Depending on the assessment type, two Depending on the assessment type, two components of stress may be required:components of stress may be required:–– Primary stresses are developed by loads to Primary stresses are developed by loads to
satisfy the laws of equilibrium of external satisfy the laws of equilibrium of external and internal forces and moments (e.g. and internal forces and moments (e.g. pressure)pressure)
–– Secondary stress distribution is developed Secondary stress distribution is developed by the constraint of adjacent parts or by by the constraint of adjacent parts or by selfself--constraint of a structure (e.g. thermal constraint of a structure (e.g. thermal expansion stresses)expansion stresses)
–– If it is uncertain whether a given stress is a If it is uncertain whether a given stress is a primary or secondary stress, it is more primary or secondary stress, it is more conservative to treat it as primaryconservative to treat it as primary
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Stresses required for FFSStresses required for FFS•• Stresses required for Stresses required for
assessment generally assessment generally based on a damage typebased on a damage type
•• Most complex is possibly Most complex is possibly for crackfor crack--like flaws like flaws –– The through wall stress The through wall stress
distribution is required distribution is required to be knownto be known
–– The distribution may be The distribution may be linear (made up of linear (made up of membrane and/or membrane and/or bending distributions) or bending distributions) or highly nonhighly non--linear based linear based on the component on the component geometry and loading geometry and loading conditions.conditions.
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Stresses required for crack-like flawsStresses required for crack-like flaws
•• The stress distribution normal to the crack face The stress distribution normal to the crack face should be determined for the primary, should be determined for the primary, secondary, and residual loading conditions secondary, and residual loading conditions based for an uncracked componentbased for an uncracked component
•• For linear stress distributions and less For linear stress distributions and less complicated noncomplicated non--linear stress distributions the linear stress distributions the membrane and bending components can be membrane and bending components can be found using the found using the linearisationlinearisation process.process.
•• For highly nonFor highly non--linear stress distributions API linear stress distributions API 579 appendix C gives a Fourth Order 579 appendix C gives a Fourth Order Polynomial Stress Distribution method for Polynomial Stress Distribution method for determining the membrane and bending determining the membrane and bending components.components.
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Stress linearisationStress linearisation•• Stress distribution Stress distribution
broken down into broken down into membrane, bending membrane, bending componentscomponents
•• Needed for both primary Needed for both primary and secondary stressesand secondary stresses
•• LinearisationLinearisation can be over can be over the cross section or just the cross section or just the flaw, depends on the flaw, depends on assessment typeassessment type
LinearisedLinearised membrane stress is:membrane stress is:σσmm = = σσ11 + σ+ σ22
22LinearizedLinearized bending stress is:bending stress is:σσbb = = σσ11 -- σσ22
22
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Stress linearisation exampleStress linearisation example
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30 35 40 45
Distance through section, mm
Perp
endi
cula
r str
ess
to fl
aw, M
Pa
Surface breaking flaw 10mm deep
310MPa at surface
100MPa at surface
Wall thickness of section 45mm
•• Linearise Linearise the stresses over the flaw the stresses over the flaw
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•• The fourth order polynomial stress distribution The fourth order polynomial stress distribution can be obtained by curvecan be obtained by curve--fitting the general fitting the general stress distribution. The general form of the stress distribution. The general form of the fourth order polynomial stress distribution is fourth order polynomial stress distribution is as follows:as follows:
•• The equivalent membrane and bending stress The equivalent membrane and bending stress distributions for the fourth order polynomial distributions for the fourth order polynomial stress distribution are:stress distribution are:
Fourth Order Polynomial Stress Distribution
Fourth Order Polynomial Stress Distribution
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Fourth Order Polynomial Stress Distribution
Fourth Order Polynomial Stress Distribution
Best fit 4th order polynomial equation y = 1394.3x4 + 625.24x3 - 2131.9x2 - 22.318x + 240
-400
-300
-200
-100
0
100
200
300
0 0.2 0.4 0.6 0.8 1
Stress, MPa
Dis
tanc
e th
roug
h w
all (
x/t)
Stress data Membrane Bending 4th Order polynominal
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Stresses in FFSStresses in FFS•• Most level 3 assessment methods in API RP Most level 3 assessment methods in API RP
579 allow the use of a detailed stress analysis 579 allow the use of a detailed stress analysis to determine the acceptability of the flawto determine the acceptability of the flaw
•• The stress analysis techniques discussed in The stress analysis techniques discussed in Appendix B of API RP 579 can be utilized Appendix B of API RP 579 can be utilized
•• FEA is typically usedFEA is typically used•• Handbook solutions may also be used if the Handbook solutions may also be used if the
solution is an exact match. solution is an exact match. •• The evaluation based on a linear stress The evaluation based on a linear stress
analysis and stress categorization, or a nonanalysis and stress categorization, or a non--linear stress with plastic collapse. linear stress with plastic collapse.
•• NonNon--linear stress analysis techniques are linear stress analysis techniques are recommended, if data is availablerecommended, if data is available