Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference Stavanger, Norway, June 17-22, 2001 Copyright 2001 by Tile International Society of Offshore and Polar Engineers 1SBN 1-880653-51-6 (Set); ISBN 1-880653-53-2 (Vol. 11); ISSN 1098-6189(Set)

Burst and Gross Plastic Deformation Limit State Equations for Pipes: Part 2 - - Application

Finn Kirkemo and Harald Holden SeaFlex a.s

Asker, Norway

ABSTRACT

Design of pipes in the offshore industry implies use of design equations with appropriate safety factors to predict the resistance against failure modes such as burst and excessive plastic deformation. Analytical based equations for prediction of pipe burst and yielding deformation mode of failure is compared with finite element analysis and tests in this paper. Review and comparison are made of burst and excessive yielding design limitations in various design codes. The comparison can provide knowledge to engineers about design possibilities based more upon the properties of the materials than has been done in the past. This can in future result in wall thickness and cost savings.

KEYWORDS: Pipe, failure, burst, yielding, tests, FEA, codes

INTRODUCTION

From the standpoint of the pipe designer it is important to have design equations against structural failure which gives consistent factors of safety against burst from gross over-pressure or against gross plastic deformation from extreme combined load conditions. In choosing design equations for design codes, consideration must be given to simplicity, availability of material data and accuracy. If, due to unavailable variations in materials, the accuracy cannot be high, it must be known what the accuracy is so that adequate safety factors can be applied.

The traditional hoop design and yon Mises based component stress formulations in many design codes may be conservative compared to test and elastic plastic finite element results. There is thus a motivation to develop more rational design equations for burst and plastic deformation modes of failure.

The purpose of this article is to compare candidate straight pipe design equations, see Kirkemo (2001), to be used for design against burst and gross (excessive) plastic deformation with tests and finite element analysis. In light of these comparisons, design criteria from various design codes are compared for these failure modes. This information can be used for future design codes and standards.

ULTIMATE LOAD CAPACITY CONSIDERATIONS

Introduction

Pipe design codes allows for use of" calculations or experimental testing to be used to determine plastic or ultimate load capacities. Calculations may be analytical based on formula (elastic or limit load) or finite element analysis. Two different types of finite element analysis (FEA) are normally used to ensure adequate safety margin against burst and gross plastic deformation, i.e.,

1. Linear elastic analysis - stress categorisation route.

2. Elastic-plastic analysis - limit analysis and plastic analysis.

Both methods and experimental testing are briefly discussed below.

Linear elastic analysis

Linear elastic analysis with stress categorisation implies categorisation of stresses in primary and secondary stresses along lines the analysed component. The primary stress limits, either general primary membrane and local primary bending, are provided to prevent excessive plastic deformation and provide a factor of safety on the ductile burst pressure (ductile rupture) or plastic instability (collapse). The primary-plus-secondary stress range is limited to ensure shakedown of the component.

Elastic analysis with equivalent linearised stresses introduces some problems like:

1. Selection of stress components to be linearised. In the elastic analysis, there is a requirement to obtain membrane and bending components of primary stress and the calculated stresses must be categorised. This does not present a problem in cases where the analysis utilised thin shells. However, the use of stress classification to demonstrate structural integrity tbr heavy-wall pressure containing components, especially around structural discontinuities, may produce non-conservative results and is not recommended. The reason for the non-conservatism is related to the fact that the non-linear stress distributions associated with heavy wall sections are not accurately represented by the implicit linear stress distribution utilised in the stress categorisation and classification procedure.

85

2. Selection of the stress classification line. This should be a line through the weakest (expect to yield) part of the component wall. For straight pipes, this is easy, however, close to discontinuities, some warping and shear is expected and the concept of averaged membrane and linearised bending stress is tenuous. In 3-D analysis, it is difficult to find a consistent stress classification plane, which again could cause problems near fillets and gross structural discontinuities.

3. How to include preload in capacity evaluations? The categorisation problem can be interpreted as the need to isolate the primary stresses and secondary stresses. However, it is only necessary to identity the stresses causes gross plastic deformation, e.g. primary stresses. For preloaded components like threaded connectors and flanges, this may be a challenge.

4. Plastic moment capacity. Linear elastic analysis with linearised stresses may be used to estimate limit load envelopes for pipes subjected pressure and axial forces. However, bending moment induced limit loads envelopes (plastic hinges) alone or in combination with pressure and axial three cannot be accurately predicted by elastic analysis.

These problems discussed above may introduce large uncertainties in predicting capacities. Elastic-plastic analyses and experimental testing may be used to overcome some of the problems in the elastic approach.

E las t i c -p las t i c ana lys i s and exper imenta l tes t ing

Elastic-plastic analysis computes the structural behaviour under given loads considering the strain hardening characteristics of the material, permanent deformations and stress redistribution occurring in the structure. There are two types of elastic-plastic analysis methods: limit analysis and plastic analysis. Limit analysis is based on elastic- perfectly plastic material model and small deformation theory. Plastic analysis is based on the actual non-linear stress-strain relationship of the component, including non-linear geometry effects. Application of elastic-plastic analysis, prescribed displacements or strains due to temperature fields need not to be considered. Their inclusion will not change the limit or plastic load provided the material has sufficient ductility.

However, using elastic-plastic analysis or considering experimental tests, one is confronted with the problem of defining a realistic measure of limit, ultimate or plastic loads. There are various estimation methods as described below.

1. The tangent-intersection load is the load at the intersection of two tangents, drawn to the elastic and plastic parts of the load- deflection curves, Figure 1. The load obtained by this method is sensitive to the localisation of the tangent-point in the plastic range.

2. The x% total strain load is defined as the load with a total strain of x%, where x is given in Table 1. Methods based upon an absolute maximum strain value not only will depend on the material assumed, but more significantly on the geometry.

3. The twice-elastic slope load is deft.ned to be the value at the intercept of a line drawn from the origin of a load-detbrmation curve at a slope of twice the slope of the elastic portion of the curve (see Figure 1). This method is sensitive to the initial slope and may give unexpected results for preloaded connectors.

4. Plastic-instability load, which is the plastic (collapse) load and is defined by a zero slope or the maximum load on the load- deflection curve. May be hard to find as it may require large deformations.

Figure 1 illustrates the four approaches above. ASME and prEN piping and pressure vessel code methods tbr determinations of limit and plastic loads are given in Table 1. Von Mises yield condition should be applied as it fits better to experimental tests. However, ASME and prEN base the limit and plastic analysis on the Tresca (maximum shear) yield condition which is conservative compared to von Mises. Tresca is simpler tbr hand calculations than yon Mises. This may be the reason for applying this in piping and pressure vessel codes.

120 - i : /P last ic, tangent Interse~lon, 97 MPa Plas~c

~oo- / _ ' . . . . . . . 2 . . . . . . .

~~, , , i '~" P,a=,o, 2 ',. =~,, ~' SO ~ elastic slope, 97 MPa

Plastic, 5 % strain 98.3 MPa

'Q 60 - /~ 92MPa

: Limit, 82 MPa

40-

20,

0 ' , 1 , f ~ , 0% 1% 2% 3% 4% 5% 6% 7%

Hoop strain

Figure 1: Capacity determination procedure

Table I : Code methods and criteria for determination of capacity

Code Method Criteria ~ ASME VIII Div.2 ASME VIII Div.2 ASME VIII Div.2 ASME VIII Div.3

ASME VIII Div.3 prEN 13445-3 Annex B

Limit Plastic Tests Limit

Test Limit

Twice-elastic slope Twice-elastic slope Twice-elastic slope The higher of the following: 1. the load which causes 5 %

strain 2. the load which causes

yielding through the thickness The load which causes 2 % strain The tangent intersection load with one tangent through the origin, the other through a point where the maximum principal strain does not exceed + 5 %

i) It should be noted that application of no more than two cycles of the maximum operating load (code dependent), alter any pressure testing, shall result in shakedown to elastic conditions, except in small areas associated with local stress (strain) concentrations. These small areas shall exhibit a stable hysteresis loop with no indication of progressive distortion (ratcheting). A simple conservative approach is to ensure that the maximum operating stress range in a pipe cross section is within the elastic range, i,e. 2 times the yield strength.

Based on the above it is a lack of consistency in defining ultimate or plastic capacity in different codes and research institutes. This has major effects especially for bending moment loading. However, pressure failure or burst is more easily defined by testing, as leakage is a unique failure criterion.

Mater ia l duct i l i ty and toughness

Plastic (ultimate) and limit load based design require that the materials in pipes, welds and connectors exhibit sufficient toughness

86

and ductility to ensure that the pipe cross section can attain the required plastically deformed state without premature failure. The welds and connectors are often made stronger to avoid large deformations in these locations. This is the common practice for most material applied in offshore pipes, risers and pipelines. For burst this imply that through the thickness yielding occur before final rupture or failure and for bending moment that a plastic hinge can be tormed before final failure occur .

For high strength materials with modest strain hardening, the plastic load is reached quite soon after the limit load. The use of limit loads is appropriate for a pipe undergoing cyclic loading. However, for one- time accidental loading, it may be reasonable to use plastic loads. Through thickness limit load and first yield load can be applied for slender cross sections and/or brittle materials with limited ductility and toughness in addition tot materials susceptible to H2S.

When establishing pipe capacity equations, it is important to consider the Bauschinger effect and hysteresis, the assumption of yield in compression in general, or the validation of the strain hardening models. It is also important to be aware of the fundamental assumptions in the engineering yield strength, ultimate strength and failure strain. For example, these parameters are measured from uniaxial tensile tests normally in the longitudinal direction and used as a reference to develop multiaxial criteria.

The question of high yield to ultimate strength ratios (YRs) has been raised. The YR is indicative of the strain hardening capacity of a structural member. The yield ratio limits have been introduced to bound the applicability of codes to ensure safe practice and not based on a rigorously quantified evaluation of the factors influencing the structural performance of high strength steel components. Bending and pressure tests of pipes indicate that high strength steel with yield to ultimate strength ratios as high as 0.92-0.95 can be applied. Modem steels display excellent levels of ductility and impact toughness, despite their higher YR values.

Sufficient ductility and toughness in to apply limit or plastic design are normally ensured by the following requirements to:

1. minimum elongation in a tensile or bend (for welds) test, e.g. As< 14%;

2. minimum Charpy impact energy absorption at minimum temperature, 40 J average/30 J individual sometimes supplemented by fracture toughness testing;

3. maximum yield to ultimate tensile strength ratio (max. 0.93);

4. maximum defects sizes which may impair the ultimate capacity (or fatigue quality), e.g. NDT extent and detection limits.

CANDIDATE PRESSURE DESIGN EQUATIONS

For the prediction of burst pressure of pipes in the presence of net internal pressure only, several formulae have been proposed and used tbr the design of offshore risers and pipelines. Limit pressure for thin wall pipe, i.e. neglecting radial stress and applying outside diameter as pressure diameter, with capped ends are given by

2.t Phor = cry. D Tresca yield criterion (1)

2 2.t PhDM = ~ j----~ " CrY" D Mises yield criterion (2)

where D is the outside diameter, t is the wall thickness and cry is the

engineering yield strength. The hoop stress based on the outside diameter, Eq. (I) is often named Barlow formulae and is used in

ASME B31.8 and B31.4. It is valid for thin walled pipes, i.e. pipes with D/t in the range of 40-50. Eq. (2) is based on the assumption that the axial stress is one-half of the hoop stress. This is the usual (but not universal) case for piping.

The elastic, limit and plastic (1% total strain) pressure for von Mises yield condition and closed pipe ends is give by the following equations, Kirkemo (2001):

1 D z - (D- 2t) 2 (3) Py,c = ~cry"

D 2

2 2t Po,c = '~cr Y D - t (4)

2 cry + or, 2t Pp.c = ~ 2.075 D- t (5)

where cr.v is the ultimate tensile engineering strength. The Tresca limit

pressure tbr closed end pipes is the von Mises limit pressure, Eq. (4),

multiplied by 2/,qt3 and becomes

2t (6) Po,c = cry D - t

Eq. (6) is applied in ISO 13623 (2000) for offshore steel pipelines. An analytical solution for ductile rupture pressure is given by Stewart et al. (1994) as

""': +t J where N is a hardening index = 0. I for 1555 (XI0). N may be taken as the strain at ultimate tensile strength.

Thick walled pipe exposed to cyclic design pressure may require special consideration to avoid cyclic plastic strain at pipe inside diameter. E.g. for the limit pressure equation, Eq. (4) and an allowable stress equal to 0.6cry, initial yielding of the pipe with design pressure

will occur when D/t < 4.5.

NON-LINEAR FINITE ELEMENT ANALYSIS

Non-linear finite element analyses have been carried out by means of the non-linear FEM code MSC.MARC 2000. Axisymmetric finite element models have been prepared to simulate the performance of a pipe subjected to internal pressure and effective axial force.

Two types of inelastic FE analysis methods have been used to evaluate the analytical based limit load and plastic load equations, i.e. limit analysis and plastic analysis, respectively. Limit analysis is based on the yon Mises yield criterion, a linear elastic ideal-plastic material model, associated flow and small deformation theory. Plastic analysis is based on yon Mises yield criterion and "true" non-linear stress-strain relationship of the pipe material stress and updated Lagrange formulation (non-linear geometry). Material data are for API 5L X80 or equivalent ISO 3183-3 L555 with yield strength equal to 555 MPa, tensile strength equal to 625 MPa, Ramberg - Osgood strain hardening exponent n=31.4, see Appendix A in Kirkemo (2001). L555 (X80) has minimum elongation at failure equal to 18 % and maximum yield to tensile ratio equal to 0.92.

87

8-node axisymmetric elements with reduced integration have been applied in the 2D analysis, (element type 51 with reduced integration) with 8 elements through thickness. The MARC Newton-Raphson procedure has been applied tbr the evaluation of the response. In load cases of combined pressure and effective tension, effective tension was applied first. Then the internal pressure was applied and increased until failure.

For combined pressure and effective tension, the limit and plastic pressure are given by the tbllowing equations, Kirkemo (2001),

. I I - (T~ / 2 (9) P"=P'x tTp)

where the limit and plastic (2% total strain) axial tension capacities are

T o = cry. A c (10)

Tp =(O.6+O.4.--I.crv .A ~ (11) c ry )

The pipe cross section area A c is A~ = (x/4). (D 2 -d2) .

Table 2: Limit and plastic FEA results normalised with respect to limit and plastic capacity equations.

Normalised capacities; FEA/Analytical

Plastic Load case D/t Limit I Twice 1% 2% 5%

Tangent I slope strain strain strain 5 1.00 1.00 0.95 0.98 1.01 1.04

Axial tension 15 1.00 0.99 0.95 0.98 1.01 1.05 only

40 1.00 0.99 0.95 0.98 1.01 1.05

5 1.02 1.05 1.00 1.04 1.06 1.08 Pressure, 15 1.00 1.03 0.97 1.00 1.03 1.05 open pipe

40 1.00 1.02 0.97 1.00 1.02 1.04

Pressure, 5 1.02 1.07 1.00 1.05 1.07 1.08 cappedpipe 15 1.00 1.03 0.98 1.01 1.03 1.05

T e = 0 40 1.00 1.01 0.94 1.01 1.03 1.04 Pressure and 5 1.02 1.07 1.03 1.07 1.09 1.11

tension, l 5 1.01 1.05 0.98 1.03 1.05 1.07 capped pipe Te = 0.25T 0 40 1.00 1.03 0.98 1.02 1.04 1.07

Pressure and 5 1.04 1.13 1.04 1.11 1.14 1.15 tension, 15 1.00 1.06 1.08 1.05 1.09 1.10

capped pipe Te = 0.5T 0 40 1.00 1.06 0.98 1.04 1.07 1.11

Normalised FEA results wrt. to limit and plastic capacities are given in Table 2, i.e. Eq. (4) and Eq. (5) tbr capped pipes with pressure and Eq. (10) and Eq. (11) tbr open and capped pipes with effective tension. The procedure used to determine the FEA capacities are illustrated in Figure 1. The limit load capacities determined by the FEA is the maximum load which occurred at small hoop strains at the pipe inside diameter (typically less than 0.5%).

The analytical limit load fits very well to the plastic FEA results, with a slight conservatism for low D/t ratios as expected, see Kirkemo (2001). For axial tension only, the plastic load fits well with the 2 % strain value as expected. For pressure only, the FEA 1% plastic load compares well with the analytical solutions, which is expected as this is based on 1% strain. For combined loading, the FEA x% methods gives capacities slightly in excess of the analytical plastic capacities.

For plastic analysis, the twice slope method predict conservative values of the plastic capacity compared to the analytical predictions. The tangent method and 2% hoop strain at pipe inside diameter gave approximately the same capacities.

Table 3: Pressure/effective axial tension tests, Pasley et al. (1998).

Grade O'y/O'~ TPo D/t API 5CT

14.49 L80 0.92 0.51

17.95 L80 0.92 0.92

18.65 I.,80 0.92 1.01 26.72 K55 0.63 1.06

18.12 Q125 0.91 1.01

Pressure capacity, Limit, Eq. (8) Plastic, Eq. (9)

p,,Jpo, c pt~/p~,c 1.13 1.11

1.71 1.39

2.11 1.70

1.77

Burst tests of capped pipes with high effective axial tension have been reported by Pasley et.al. (1998), see Table 3. For these tests, the analytical models are on the conservative side, especially for high effective tension. Pasley et.al. (1998) also reported that the burst pressure depend little on the load path tbr application of pressure and effective tension.

BURST TEST DATA

Closed end burst tests conducted of umbilical super duplex pipe; steel casing, tubing and line pipe are compared with some candidate analytical burst prediction models in Table 4 and Table 5. The calculations are based on actual maximum diameter, minimum wall thickness and strength. The tests cover a wide range of sizes and strengths, i.e. D/t ratio range 6-36, yield strength range 303-1004 MPa, ultimate tensile strength range 502-1173 MPa and yield strength to ultimate strength ratio range 0.60-0.97.

Table 4: Comparison of burst e~ ~uations with all tests, 111 tests.

Mean CoV Burst pressure equation (Test/Predicted) (SD/Mean)

1.232 12.56% Elastic, closed, Eq. (3) Limit load, closed, Eq. (4) Plastic, closed, Eq. (5) Rupture, closed, Eq. (7) Hoop, Barlow, Eq. (I) Hoop, Din, Eq. (6)

Table 5: Comparison of burst equations with

1.065 10.09% 1.002 1.010

4.79% 4.12%

1.323 10.93% 1.230 10.09%

o~,/or, > 0.75,86 tests.

Mean CoV Burst pressure equation (Test/Predicted) (SD/Mean)

1.177 8.03 % Elastic, closed, Eq. (3) Limit load, closed, Eq. (4) Plastic, closed, Eq. (5) Rupture, closed, Eq. (7) Hoop, Barlow, Eq. (1) Hoop, D m, Eq. (6)

1.027 0.996 1.018 1.269 1.186

5.68 % 4.50 % 3.94 % 6.32% 5.68 %

88

A design equation should predict real failures relative accurate, i.e. mean value or bias close to 1.0 and low Coefficient of Variation (CoV = Standard deviation (SD)/Mean value) without significant dependence On:

1. the ratio of the ultimate tensile strength to the yield strength, and

2. the diameter to wall thickness ratio.

In addition should they be easy to manipulate when perfbrming design calculations and use available material data.

The smallest values of CoV are indicative of the equations, which provide best fits to data. The plastic pressure equation, Eq. (5) may be selected to represent the burst pressure in design codes. The equation predicts the burst pressure within 1% with respect to the mean value and with a CoV of 4 %. It is a very good predictor of burst pressure. Eq.(5) has been proposed to represent the burst pressure formulation in ISO 13628-7 (2001). It should be noted that the rupture equation, Eq. (7) provides a slightly better fit of the data than Eq. (5), however it may be difficult to apply as the hardening index N is not available from standard material testing and no requirements to it is given in standards like ISO 3183, ISO 11960, ISO 11961, API 5L or API 5CT.

1.15

~ 1.10

,~ ~.05

g 1.oo

u

0 .95

o.

0 .90 c

--~ 0.85

111 tests [Mean = 1 .002

. . . . . . . . . . . . . . . . . . *- . . . . . . . . . -~COV = 4 ,79 %

. . :';" . ." - -7 - - -

:-4 " t * t , , , * , . . . ; ; . . . . . .

. . . . . . . . . . - . - .~t - * . . . . . . . . . . . . . . . . . . . . . . . ** g .

- - - . . . . . . iv - . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . .

0.80

0 5 10 15 20 25 30 35

D/ t ratio

40

Figure 2: Comparison of test data with plastic capped model

-. 1 .10 .

1 .15 , 111 tests IMean = 1 .002

. - - *- . . . . . . . . . . . . . . . . . . . . . . . . [C0V = 4 .79 %

; ":" . 1.05 . . . . . . . . . . . . . . . . . . . . % . . . . . ~ '* - --.~- - - ~ . . . . . .

,=

==

.E =

' i ;; ', lOO ; ' i f "" "" ::

: *. ...~( $ 0.95 . . . . . . . . . . . . . % . . . . . . -* . . . . . . . .

0 .90 . . . . . . . . . . . . . . . . . . . . . . . . . . - * - - - *- - r . . . . . .

0 .85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 .80

0 .60 0 .65 0 .70 0 .75 030 0 ,85 0 .90 0 .95 1 ,00

Yield to ultimate tensile stress ratio, Y IU

Figure 3: Comparison of test data with plastic capped model.

Comparisons between proposed model and full scale test data i., shown in Figure 2 and Figure 3, where the ratio of actual to calculate( burst pressures are plotted against the diameter to thickness ratio an( yield to ultimate tensile strength, respectively. No significan, dependence on the burst predictions is observed wrt. D/t ratio and yiek to ultimate strength ratio.

Experiments have also been perlbrmed of pipe bend to 3-4 % strain or even buckled, bursts at the pressure as a straight pipe (an usually at location away from the plastically bent section), Langner (2000). I~ have therefore be concluded that displacement induced bending doe., not reduce the burst pressure. This is also predicted by theory ant observed in practice, Gresnight et al (1996). This means that the bursl pressure of a sufficient ductile and tough pipe is unaffected by the presence of external displacement controlled loads.

DESIGN FOR INTERNAL PRESSURE

Table 6 lists seven piping, riser and pipeline codes, and summarises allowable stress and wall thickness equations for pressure design. The equations in ASME B31.4 and API RP 1111 calculate the nominal wall thickness while the others calculate the minimum wall thickness where wall thickness under tolerance have to added. All codes add corrosion allowance to the calculated wall thickness.

Table 6: Code comparison - internal pressure design.

Code

ASME B31,3

ASME B 31.4

API 1111

prEN 13480

1SO 13623

ISO/CD 13628-7

DNV OS- F201 and OS-FI01

Allowable stress,f

f = min('Y ; or" / /1.5 3.0)

f=0.5 .o 'y

/--0.27

f= min(CrY; a~ ~, ~,1. 5 2.4)

f = 0.67. cry

/=o.33.(o-,+o-J

Min. wail thickness, tl

p.D t, = 2" (f .z -0.4. p)

p.D tin = -

2.f.z p-D

tin = ~ 2. f+p

p.D t,= 2. f . z -2 .p

p.D t I =

2. f+p p.D

tl = m 2. f+p

p.D tl= 4

~f~ f+P

The fbllowing should be noted:

1. ASME B31.3 and prEN 13480:1999 are piping codes.

2. DNV are for safety class is high, incidental pressure 10 % higher than design pressure and no increased confidence in material strength.

3. AMSE B31.4 and API RP 1111 calculate the minimum nominal wall thickness including fabrication tolerances compared to the others, which predicts the minimum wall thickness without fabrication tolerances.

Figure 4 compares the required minimum wall thickness tbr different design pressures tbr a seamless pipe with wall thickness undertolerance equal to 12.5 %, corrosion allowance equal to 1 mm and weld joint factor equal to t.0. The minimum required thicknesses for the pipe selected with allowances and manufactures minus tolerances tbr some design codes, see Table 6, are given by

89

,, =( , , +4 ( lOO ] =) 02)

For a given design pressure, the required wall thickness varies very much between piping design codes and riser and pipeline design codes as illustrated in Figure 4. The required wall thickness for the riser and pipeline codes are within + 5% for the considered pressure range with exception of ASME B31.4. ASME B31.4 which is based on the thin walled hoop equation require 10 to 30% extra wall thickness than the other riser and pipeline code. For a given design pressure, the required wall thickness may vary over 100 % between piping codes and riser/pipeline codes, depending on the pressure. Such a large variation in safety factors indicates the need for better understanding of pipe behaviour in the bursting mode.

2- t 1.8 ASME B N 13480 o 1. 4 / /

.............. t . . . . . . . . . . . . o . . / ~"" i " " 1111 , NVO,S - 0 , , 180 13628-7 0 10 20 30 40 50 60 70 I~0 90 100

Design pressure, MPa

Figure 4: Walt thickness as function of design pressure.

The design stress at room temperature is generally defined as the lower of one third (or 1/2.4) of the ultimate tensile strength or two- thirds of the yield strength in piping codes. The limit of one-third ultimate tensile strength does not permit full utilisation of quenched and tempered alloyed steels, where the yield strength is close to the ultimate tensile strength. This limit also provides some protection against brittle fracture. The design strength for riser and pipeline pipes is typically a fraction of the yield strength, e.g. two-thirds of the yield strength, typically implying a design margin of minimum 1.5 on the burst pressure. In this way, materials with high yield strength can be better utilised and still maintaining sufficient safety margin. However, it should be noted that the riser and pipeline materials typically have addition requirements to avoid premature brittle fracture. The minimum safety margin against burst in piping codes is somewhat unclear as the design stress is governed by from the factor of 3 on the ultimate tensile strength. Based on burst tests, the design stress is influenced by both the yield and ultimate tensile strength model, see Eq. (5) and not the ultimate tensile strength as govern for piping codes. A design margin of 3.0 on ultimate tensile strength does not directly imply a safety margin of 3.0 against burst pressure.

BENDING MOMENT CAPACITY

Ductile sections and compact sections may be evaluated by plastic limit states without any effects of local buckling. The limit (Mo) and plastic (Mp) bending moment capacity of plastic pipe cross sections may be calculated by:

~

hinge mechanism forms over a short length of the beam. As the end support rigidity is reduced, the hinge mechanism forms over a longer length with the same rotation. As o~ .DIE .t increases, both the moment and rotational capacity decreases. The use of elastic and elastic plastic moment capacity, see Kirkemo (2001) implies a significant increase in the bias, i.e. minimum 27 %, and is not evaluated further. For L555 (X80) pipes with o-y = 555 MPa and E =

205 000 MPa, the development of full plastic or limit moment capacity is realised when D/t < 19. This capacity is linearly reduced to about 0.84 of the plastic or limit load capacity when D/t < 38.5.

1.4

1.2

"i . 1 .o

0.8 o

oE 0.6 E

,~ 0 .4 =

,.n 0.2

0.0

0 .00

i t , i i

i ~ i ~ ~ Mean = 1.036 I . . . . . . . . . . . . . . . . . , , , L - - -~- . . . . . . . . 00V=10.1% '!

I i $ I I I I ~' I i I I , i . I I

i t~r - - -T . . . . . . . . . I . . . . I . . . . . l I I I t I I i I t i I I I !

I I I I I I I I

I

: I I l

i I i

. . . . T . . . . . . . . . . i . . . . ' . . . . T - - - ~ . . . . ! . . . . . . . .

r I I

I

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Sect ion s lenderness, a lpha

Figure 6: Comparison of test data with bending plastic load model.

The plastic moment capacity is compared to the results from Foeken and Gresnight (1999) and Lotsberg and Johansen (1991) as they also reported both yield and ultimate tensile strength. The data is for pipes with D/t ratio from 16.7 to 45.7 and yield strength ranging from 326 MPa to 736 MPa and ultimate tensile strength from 527 MPa to 827 MPa. The results of the calculations are shown in Figure 6 and Table 7.

For cyclic bending moment loading, the maximum bending moment capacity should be limited to limit moment capacity of the pipe in code application, hence Eq. (16) should be applied.

Table 7: Bending moment capacities of pipes.

Prediction model

Limit load, Eq. (16)

Plastic load, Eq. (17)

Number of tests

54

Mean or bias (Test/Predicted)

CoV (SD/Mean)

1.146 0.108

8 1.036 0.101

lnternal pressure and effective axial tension will have the same effects as reducing the sectional slenderness, hence reduce pipe ovalisation and the risk for local buckling. The positive effect on the bending capacity due to these effects are not included in the equations above, which in these cases will be slightly conservative.

Geometry boundary conditions of the pipe affect the ultimate load. For a simply supported beam in bending, formation of a yield hinge and further the cross section ultimate load will mark the limit of the load-carrying capacity. If the beam is restrained axially, further loads can be carried by activation of membrane (axial) effects in the beam. Thus formation of a cross section ultimate load in bending is not necessary the ultimate limit of the load-carrying capacity; generally a piping system or riser/pipeline will only tail once sufficient number of plastic hinges are formed to make a kinematic mechanism.

When plastic methods are used tbr design, the pipes shall be thus be capable of forming plastic hinges with sufficient rotational capacity to enable the required redistribution of bending moments to develop. Strains in the outer fibre in the range of 2-4 % may be necessary for pure bending. It should be noted that necessary outer fibre bending strain to mobilise the plastic capacity above under pure bending is reduced for combined loading which normally are present.

DESIGN FOR COMBINED LOADING

Table 8 and Table 9 summarises how various codes address design against excessive yielding for the combination of net internal pressure, effective axial tension and bending moment. All codes apply nominal outside diameter and nominal wall thickness minus any corrosion allowance.

Table 8: Code comparison - combined loading design equations

Code

API RP 2RD

ISO 13679

ISO 13628-7

Equation

; ,r,>l ,, U

-P--~]2+'T-~ + M/dtT_

1.0 t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . o, :o125 0.5 ISO 13628-7 o,t /

~ 0.3"

12 . , , . . . . . 0,0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Effective axial tension, T/To

Figure 7: Comparison of bending and pressure loading, extreme.

1.0"

0.9"

0.8

0.7 1

0.6"

0 .5 '

0.4 '

0.3 '

0 .2

0 .1

0.0 0.0

D/ t=15 ISO 13679 M/Mo_O.05

--nk---- - , - ISO 13628-7

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internal pressure, P/I~

Figure 8: Comparison for pressure and effective axial force, extreme.

The ISO 13628-7 gives almost a constant safety factor for all load combinations of pressure, tension and bending. It should be noted that for almost pure pressure and tension, the ISO 13679 allows higher loads than the other codes. This means that ISO 13679 has a lower safety margin for this load combination than for bending dominated load combinations.

CONCLUSIONS

The recommended internal pressure design equation, Eq. (5), provides a uniform safety margin against burst failure with respect to D/t (D/t > 5) and yield to ultimate strength ratio (YR < 0.93). It requires only the knowledge of material ultimate tensile strength and yield strength.

The recommended combined loading equation, i.e. the ISO 13628-7 equation in Table 8, provides a uniform safety margin for combined pressure, effective axial force and bending moment. The equation can be expected to accurate predict the capacity of a pipe, provided the material is sufficient ductile. For single loads, it simplifies to equations, which fits very well with experimental data. The recommended equations appear to give an adequate compromise between simplicity and accuracy.

In addition to the explicit design margin used in the design equations, the effective safety margin also depends on implicit margins in the materials, ductility and toughness requirements, fabrication requirements, overpressure protection, quality control (NDT, dimension control), approximations inherent in the design approach,

corrosion protection, fail-sate design, maintenance and number of other factors. These effects are difficult to quantify but should be evaluated in combination with experience when safety factors are established.

REFERENCES

API RP 2RD (1998), Design of Risers fbr Floating Production Systems (FPSs) and Tension-Leg Platforms (TLPs).

API Spec 5L (2000), Specification for Line Pipe, 14 u~ Edition.

API RP 1111 (1999), Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines.

ASME B31.3 (1996), Process piping.

ASME B31.4 (1992), Liquid transportation systems for hydrocarbons.

ASME Boiler and Pressure Vessel Code (1998), Section VIII, Rules for construction of pressure vessels, Div.2 - Alternative rules.

ASME Boiler and Pressure Vessel Code (1999), Section VIII, Rules for construction of pressure vessels, Div.3 - Alternative rules for construction of high pressure vessels.

DNV OS-F 101 (2000), Submarine pipeline systems.

DNV Draft OS-F201 (2000), Dynamic risers.

prEN 13445-3 (1999), Unfired pressure vessels -Part 3: Design.

prEN 13480-3 (1999), Metallic industrial piping- Part 3: Design and calculations.

Foeken, R.J. and Gresnight, A.M. (1998), Buckling and collapse of UOE manufactured steel pipes, TNO-report 96-CON-R0500.

Gresnight, A.M., van Foeken, R.J. and Chen, S.L. (1996), Effect of local buckling on burst pressure, ISOPE.

ISO 3183-3:1999, Petroleum and natural gas industries - Steel pipe tot pipelines - Technical delivery conditions - Part 3: Pipes of requirement class C.

ISO 13623:2000, Petroleum and natural gas industries - Pipeline transportation systems for the petroleum and natural gas industries.

ISO/DIS 13628-7:2001, Petroleum and natural gas industries - Design and operation of subsea production systems - Part 7: Completion/workover riser systems.

ISO/DIS 13679:1999, Petroleum and natural gas industries - Testing procedures for casing and tubing connections

ISO 13819-2 (1995 and WD 1999), Petroleum and natural gas industries - offshore structures - Part 2: Fixed structures.

Kirkemo, F. (2001), Burst and gross plastic delormation limit state equations for pipes: Part 1 - Theory, ISOPE.

Langner, C. (2000), Burst test basis for the internal pressure design formulation in the revised API recommended practice 1111 for offshore pipelines, Deepwater Pipeline & Riser Technology Conference, Houston, Texas.

Lotsberg, I. and Johansen, A. (1991), High strength steel in toad carrying structures offshore, Phase 2. Part project 1. Significance of a high Re/Rm-ratio. Laboratory tests, Veritec report No. 91-3112.

Paslay, P.R., Cernocky, E.P. and Wink, R. (1998), Burst pressure prediction of thin-walled, ductile tubulars subjected to axial load, SSPE 48327.

Sherman, D.R. (1986), Inelastic flexural buckling of cylinders, Steel Structures, Recent Research Advances and Their Applications to Design, Ed. by M.N.Pavlovic, Elsevier Applied Science Publishers.

Stewart, G., Klever, F.J., and Ritchie, D. (1994), An analytical model to predict the burst capacity of pipelines, OMAE.

92

MAIN MENUPREVIOUS MENU---------------------------------Search CD-ROMSearch ResultsPrint