DNV-RP-C203: Fatigue Strength Analysis of Offshore … · recommended practice rp-c203 fatigue strength analysis of offshore steel structures october 2001 det norske veritas

RECOMMENDED PRACTICE

RP-C203

FATIGUE STRENGTH ANALYSISOF

OFFSHORE STEEL STRUCTURES

OCTOBER 2001

DET NORSKE VERITAS

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��DET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, prop-erty and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification andconsultancy services relating to quality of ships, offshore units and installations, and onshore industries world-wide, andcarries out research in relation to these functions.

DNV Offshore publications consist of a three level hierarchy of documents:

�� Provide principles and procedures of DNV classification, certification, verification and con-sultancy services.

��Provide technical provisions and acceptance criteria for general use by the offshore industry as well as thetechnical basis for DNV offshore services.

��Provide proven technology and sound engineering practice as well as guidance for the higher levelOffshore Service Specifications and Offshore Standards.

DNV Offshore publications are offered within the following areas:

A) Quality and Safety Methodology

B) Materials Technology

C) Structures

D) Systems

E) Special Facilities

F) Pipelines and Risers

G) Asset Operation

��This Recommended Practice is developed in close co-operation with the offshore industry, research institutes and universities.All contributions are highly appreciated.

��Following main changes are made:

In the calculation of SCFs for butt welds and cruciform joints the misalignment may be reuduced with a value δ0 which areinherent in the S-N data. See Section 2.6,2.8.7 and 2.12.

Calculation of reduced hot spot stress when weld profiling is performed, equation (4.2.3).

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'� � $" !(�$% �� )1.1 General .................................................................. 41.2 Validity of standard ............................................... 41.3 Methods for fatigue analysis.................................. 41.4 Guidance to when a detailed fatigue analysis can be

omitted .................................................................... 41.5 Symbols ................................................................. 4�� #$%*(�� #+,-%-�.#-�!�� #$%*(��-$-�� /2.1 Introduction ........................................................... 62.2 Stresses to be considered ....................................... 62.3 S-N curves ............................................................. 72.4 Mean stress influence for non welded structures. 122.5 Effect of fabrication tolerances............................ 122.6 Stress concentration factors for plated structures 132.7 Stress concentration factors for ship details ........ 152.8 Stress concentration factors for tubular joints and

members ................................................................ 152.9 Stress concentration factors for joints with square

sections.................................................................. 22

2.10 Fillet and partial penetration welds ......................222.11 Bolts .....................................................................242.12 Pipelines...............................................................242.13 Calculation of hot spot stress by finite element

analysis ..................................................................252.14 Simplified fatigue analysis...................................28�� #$%*(��# #+,-%-�&#-�!� �0"#�$("��1# %�-��3.1 Introduction..........................................................32)� ��2" 3�� $� 0��#$%*(��%0��&,��#&"%�#$% ��4.1 General.................................................................334.2 Weld profiling by machining and grinding ..........334.3 Grinding ...............................................................334.4 TIG dressing.........................................................344.5 Hammer peening..................................................344� �5$� !�!�0#$%*(��+%0� ��4/� � ��"$# $%�-�% ��#$%*(��%0��"�!%�%$ ��/6.1 General.................................................................366� ��0�"� ��-��6

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'�'� �� "#+This Recommended Practice presents recommendations inrelation to fatigue analyses based on fatigue tests and fracturemechanics. Conditions for the validity of the RecommendedPractice are given in section 1.2 below.

The aim of fatigue design is to ensure that the structure hasan adequate fatigue life. Calculated fatigue lives also formthe basis for efficient inspection programmes duringfabrication and the operational life of the structure.

To ensure that the structure will fulfil its intended function, afatigue assessment, supported where appropriate by adetailed fatigue analysis, should be carried out for eachindividual member, which is subjected to fatigue loading.See also section 1.4. It should be noted that any element ormember of the structure, every welded joint and attachmentor other form of stress concentration, is potentially a sourceof fatigue cracking and should be individually considered.

'�� #+%!%$,� 0�-$# !#"!This Recommended Practice is valid for steel materials in airwith yield strength less than 700 MPa. For steel materials inseawater with cathodic protection or steel with free corrosionthe Recommended Practice is valid up to 500 MPa.

This Recommended Practice is also valid for bolts in airenvironment or with protection corresponding to thatcondition of grades up to 10.9, ASTM A490 or equivalent.

This RP may be used for stainless steel.

'�� $1 !-�0 "�0#$%*(��# #+,-%-The fatigue analysis should be based on S-N data,determined by fatigue testing of the considered weldeddetail, and the linear damage hypothesis. When appropriate,the fatigue analysis may alternatively be based on fracturemechanics. If the fatigue life estimate based on fatigue testsis short for a component where a failure may lead to severeconsequences, a more accurate investigation considering alarger portion of the structure, or a fracture mechanicsanalysis, should be performed. For calculations based onfracture mechanics, it should be documented that there is asufficient time interval between time of crack detectionduring in-service inspection and the time of unstable fracture.

All significant stress ranges, which contribute to fatiguedamage in the structure, should be considered. The long termdistribution of stress ranges may be found by deterministic orspectral analysis, see also ref. /1/. Dynamic effects shall beduly accounted for when establishing the stress history. Afatigue analysis may be based on an expected stress history,which can be defined as expected number of cycles at eachstress range level during the predicted life span. A practicalapplication of this is to establish a long term stress rangehistory that is on the safe side. The part of the stress rangehistory contributing most significantly to the fatigue damageshould be most carefully evaluated. See also Appendix 4,Commentary, for some guidance.

It should be noted that the shape parameter h in the Weibulldistribution has a significant impact on calculated fatiguedamage. For effect of the shape parameter on fatigue damagesee also design charts in Figure 2.14-1 and Figure 2.14-2.Thus, when the fatigue damage is calculated based on closedform solutions with an assumption of a Weibull long termstress range distribution, a shape parameter to the safe sideshould be used.

'�)� �(%!# ��$ �<1� �#�!�$#%+�!�0#$%*(��# #+,-%-�# �&�� %$$�!A detailed fatigue analysis can be omitted if the largest localstress range for actual details defined in eq. (2.2.1) is lessthan the fatigue limit at 107 cycles in Table 2.3-1 for air andTable 2.3-2 for seawater with cathodic protection. ForDesign Fatigue Factors larger than 1 the allowable fatiguelimit should also here be reduced by a factor (DFF) -0.33. Fordefinition of DFF see OS-C101 ref. /28/.

Requirements to detailed fatigue analysis may also beassessed based on the fatigue assessment charts in Figure2.14-1 and Figure 2.14-2.

'�4� �,�& +-C material parameter

D accumulated fatigue damage, diameter of chord

DFF Design Fatigue Factor

Dj cylinder diameter at junction

E Young’s modulus

F fatigue life

I moment of inertia of tubulars

Kmax, Kmin maximum and minimum stress intensity factorsrespectively

Kw stress concentration factor due to weld geometry

∆K Kmax - Kmin

L length of chord, length of thickness transition

N number of cycles to failure

Ni number of cycles to failure at constant stress range∆σi

NSd axial force in tubular

R outer radius of considered chord, reduction factor onfatigue life

SCF stress concentration factor

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SCFAS Stress concentration factor at the saddle for axialload

SCFAC Stress concentration factor at the crown for axialload

SCFMIP Stress concentration factor for in plane moment

SCFMOP Stress concentration factor for out of plane moment

T Thickness of chord

Te Equivalent thickness of chord

Td Design life in seconds

Q Probability for exceedance of the stress range ∆σa Crack depth

ai Half crack depth for internal cracks

� Intercept of the design S-N curve with the log N axis

e-α Exp(-α)

g Gap = a/D; factor depending on the geometry of themember and the crack.

h Weibull shape parameter, weld size

k number of stress blocks, exponent on thickness

l segment lengths of the tubular

m negative inverse slope of the S-N curve; crackgrowth parameter

ni number of stress cycles in stress block i

no is the number of cycles over the time period forwhich the stress range level ∆σo is defined.

tref reference thickness

t plate thickness, thickness of brace member

tc cone thickness

tp plate thickness

q Weibull scale parameter

Γ gamma function

η usage factor

α the slope angle of the cone; α = L/D

β d/D

δ eccentricity

δ0 eccentricity inherent in the S-N curve

γ R/T

νo average zero-crossing frequency

ν Poisson’s ratio

σnominal nominal stress

σhot spot hot spot stress or geometric stress

σx Maximum nominal stresses due to axial force

σmy and σmz maximum nominal stresses due to bending about they-axis and the z-axis

∆σ stress range

∆σo

stress range exceeded once out of n0 cycles

τ t/T

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��'� � $" !(�$% The fatigue life may be calculated based on the S-N fatigueapproach under the assumption of linear cumulative damage(Palmgren-Miner rule).

When the long-term stress range distribution is expressed bya stress histogram, consisting of a convenient number ofconstant amplitude stress range blocks ∆σi each with anumber of stress repetitions ni the fatigue criterion reads:

( ) ησ ≤∑ ∆⋅=∑===

PN

LLL

N

LL

L ��

��

11

1 =��'�'>

where

� = accumulated fatigue damage

� = intercept of the design S-N curve with the log N axis

� = negative inverse slope of the S-N curve

� = number of stress blocks

�i = number of stress cycles in stress block �

�i = number of cycles to failure at constant stress range∆σi

η = usage factor

= 1 / Design Fatigue Factor from OS-C101 Section 6Fatigue Limit States.

Applying a histogram to express the stress distribution, thenumber of stress blocks, �, should be large enough to ensurereasonable numerical accuracy, and should not be less than20. Due consideration should be given to selection ofintegration method as the position of the integration pointsmay have a significant influence on the calculated fatigue lifedependent on integration method.

See also section 2.14 for calculation of fatigue damage usingthe simplified method.

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The procedure for the fatigue analysis is based on theassumption that it is only necessary to consider the ranges ofcyclic principal stresses in determining the fatigue endurance(i. e. mean stresses are neglected for fatigue assessment ofwelded connections).

When the potential fatigue crack is located in the parentmaterial at the weld toe, the relevant hot spot stress is therange of maximum principal stress adjacent to the potentialcrack location with stress concentrations being taken intoaccount.

For joints other than tubular joints, the joint classificationand corresponding S-N curves takes into account the localstress concentrations created by the joints themselves and bythe weld profile. The design stress can therefore be regardedas the nominal stress, adjacent to the weld underconsideration. However, if the joint is situated in a region ofstress concentration resulting from the gross shape of thestructure, this must be taken into account in calculating thenominal stress. As an example, for the weld shown in Figure2.2-1a), the relevant local stress for fatigue design would bethe tensile stress, σ. For the weld shown in Figure 2.2-1b),the stress concentration factor for the global geometry mustin addition be accounted for, giving the relevant local stressequal to SCF·σnominal, where SCF is�the stress concentrationfactor due to the hole.

nominallocal SCF= =��'>

σlocal shall be used together with the relevant S-N curves Dthrough G, dependent on joint classification.

The maximum principal stress range within 45° of thenormal to the weld toe should be used for the analysis.

For detailed finite element analysis of welded connectionsother than tubular joints it may also be convenient to use thealternative hot spot stress for fatigue life assessment, seesection 2.13.3 for further guidance.

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For a tubular joint, i. e. brace to chord connection, t he stressto be used for design purpose is the range of idealised hotspot stress defined by: the greatest value of the extrapolationof the maximum principal stress distribution immediatelyoutside the region effected by the geometry of the weld. Thehot spot stress to be used in combination with the T-curve iscalculated as

nominalstressspothot SCF= =��>

Where

SCF = stress concentration factor as given in section 2.8.

Where support plating below bearings are designed withfillet welded connection, it should be verified that fatiguecracking of the weld will not occur. Even though the jointmay be required to carry wholly compressive stresses and theplate surfaces may be machined to fit, for fatigue purposes,the total stress fluctuation should be considered to betransmitted through the welds.

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If it is assumed that compressive loading is transferredthrough contact, it should be verified that contact will not belost during the welding. The actual installation conditionincluding maximum construction tolerances should beaccounted for.

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The relevant stress range for potential cracks in the weldthroat of load-carrying fillet-welded joints and partialpenetration welded joints may be found as:

2//

22w 0.2++= ⊥⊥

=��>

σ ττ

Throatsection

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The total stress fluctuation (i.e. maximum compressionand maximum tension) should be considered to betransmitted through the welds for fatigue assessments.

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For practical fatigue design, welded joints are divided intoseveral classes, each with a corresponding design S-Ncurve. All tubular joints are assumed to be class T. Othertypes of joint, including tube to plate, may fall in one ofthe 14 classes specified in Table 2.3-1, Table 2.3-2 andTable 2.3-3, depending upon:

• The geometrical arrangement of the detail;

• The direction of the fluctuating stress relative to thedetail;

• The method of fabrication and inspection of the detail.

Each construction detail at which fatigue cracks maypotentially develop should, where possible, be placed in itsrelevant joint class in accordance with criteria given inAppendix 1. It should be noted that, in any welded joint,there are several locations at which fatigue cracks maydevelop, e. g. at the weld toe in each of the parts joined, atthe weld ends, and in the weld itself. Each location shouldbe classified separately.

Label1

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The fatigue design is based on use of S-N curves, whichare obtained from fatigue tests. The design S-N curveswhich follows are based on the mean-minus-two-standard-deviation curves for relevant experimental data. The S-Ncurves are thus associated with a 97.6% probability ofsurvival.

The basic design S-N curve is given as

logmalogNlog ∆−= =��'>

N = predicted number of cycles to failure for stressrange ∆σ

∆σ = stress range

m = negative inverse slope of S-N curve

log� = intercept of log �-axis by S-N curve

s2alogalog −= =��>

where

a = constant relating to mean S-N curve

s = standard deviation of log N.

The fatigue strength of welded joints is to some extentdependent on plate thickness. This effect is due to the localgeometry of the weld toe in relation to thickness of theadjoining plates. See also effect of profiling on thicknesseffect in Section 4.2. It is also dependent on the stressgradient over the thickness. The thickness effect isaccounted for by a modification on stress such that thedesign S-N curve for thickness larger than the referencethickness reads, see also Appendix 4, Commentary:

−=

k

reft

tlogmalogNlog

=��>

where

m = negative inverse slope of the S - N curve

log� = intercept of log N axis

tref = reference thickness equal 25 mm for weldedconnections other than tubular joints. For tubularjoints the reference thickness is 32 mm. For boltstref = 25 mm.

t = thickness through which a crack will most likelygrow. t= tref is used for thickness less than tref.

k = thickness exponent on fatigue strength as given inTable 2.3-1, Table 2.3-2 and Table 2.3-3.

k = 0.10 for tubular butt welds made from one side.

k = 0.40 for threaded bolts subjected to stressvariation in the axial direction.

In general the thickness exponent is included in the designequation to account for a situation that the actual size ofthe structural component considered is different ingeometry from that the S-N data are based on. Thethickness exponent is considered to account for differentsize of plate through which a crack will most likely grow.To some extent it also accounts for size of weld andattachment. However, it does not account for weld lengthor length of component different from that tested such as e.g. design of mooring systems with a significant largernumber of chain links in the actual mooring line than whatthe test data are based on. Then the size effect should becarefully considered using probabilistic theory to achieve areliable design, see Appendix 4, Commentary.

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S-N curves for air environment are given in Table 2.3-1and Figure 2.3-1. The T curve is shown in Figure 2.3-3.

�#&+��'��("3�-�% �#%"�� 1logD

��≤��

2log�

��>��!��

"��#��

$%

&��' �� (��

��

B1 12.913 16.856 93.57 0

B2 12.739 16.566 81.87 0

C 12.592 16.320 73.10 0.15

C1 12.449 16.081 65.50 0.15

C2 12.301 15.835 58.48 0.15

D 12.164 15.606 52.63 0.20 1.00

E 12.010 15.350 46.78 0.20 1.13

F 11.855 15.091 41.52 0.25 1.27

F1 11.699 14.832 36.84 0.25 1.43

F3 11.546 14.576 32.75 0.25 1.61

G 11.398 14.330 29.24 0.25 1.80

W1 11.261 14.101 26.32 0.25 2.00

W2 11.107 13.845 23.39 0.25 2.25

W3 10.970 13.617 21.05 0.25 2.50

T 12.164 15.606 52.63 0.25 for SCF ≤ 10.00.30 for SCF >10.0

1.00

*) see also section 1.4

10

100

1000

1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

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S-N curves for seawater environment with cathodicprotection are given in Table 2.3-2 and Figure 2.3-2. The Tcurve is shown in Figure 2.3-3.

�#&+��("3�-�% �-�#<#$�"�<%$1��#$1 !%��2" $��$% ��

1log �

��≤��

2log�

��>��!��

"��#��

$%

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��

B1 12.513 16.856 93.57 0B2 12.339 16.566 81.87 0

C 12.192 16.320 73.10 0.15

C1 12.049 16.081 65.50 0.15

C2 11.901 15.835 58.48 0.15

D 11.764 15.606 52.63 0.20 1.00

E 11.610 15.350 46.78 0.20 1.13

F 11.455 15.091 41.52 0.25 1.27

F1 11.299 14.832 36.84 0.25 1.43

F3 11.146 14.576 32.75 0.25 1.61

G 10.998 14.330 29.24 0.25 1.80

W1 10.861 14.101 26.32 0.25 2.00

W2 10.707 13.845 23.39 0.25 2.25

W3 10.570 13.617 21.05 0.25 2.50

T 11.764 15.606 52.63 0.25 for SCF ≤ 10.00.30 for SCF >10.0

1.00

*) see also 1.4

10

100

1000

1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08


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S-N curves for tubular joints in air environment and inseawater with cathodic protection are given in Table 2.3-1,Table 2.3-2 and Figure 2.3-3.

1

10

100

1000

1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09


6WUHVV�UDQJH��03D� Seawater with

cathodic protection

In air

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��4� ��("3�-�0 "��#-$� !�-

It is recommended to use the C curve for cast nodes. Basedon tests a more optimistic curve might be used. However,the C curve is recommended used in order to allow forweld repairs after possible defects after casting andpossible fatigue cracks after some service life.

For cast nodes a reference thickness tref = 38 mm may beused provided that any possible repair welds have beenground to a smooth surface.

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For forged nodes the B1 curve may be used for nodesdesigned with a Design Fatigue Factor equal to 10. Fordesigns with DFF less than 10 it is recommended to usethe C-curve to allow for weld repair if fatigue cracksshould occur during service life.

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S-N curves for free corrosion, i.e. without protection, aregiven in Table 2.3-3.

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– For Duplex and for Super Duplex steel one mayuse the same classification as for C-Mn steels.

– For austenitic steel one may downgrade the jointby one S-N class.

–

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�� Dlog

"��

&��' ��

B1 12.436 0

B2 12.262 0

C 12.115 0.15

C1 11.972 0.15

C2 11.824 0.15

D 11.687 0.20

E 11.533 0.20

F 11.378 0.25

F1 11.222 0.25

F3 11.068 0.25

G 10.921 0.25

W1 10.784 0.25

W2 10.630 0.25

W3 10.493 0.25

T 11.687 0.25 for SCF ≤ 10.00.30 for SCF >10.0

��)� ��# �-$"�--�% 0+(� ��0 "� �<�+!�!-$"(�$("�-For fatigue analysis of regions in the base material notsignificantly effected by residual stresses due to welding,the stress range may be reduced dependent on whethermean cycling stress is tension or compression.

This reduction may e.g. be carried out for cut-outs in thebase material. The calculated stress range obtained may bemultiplied by the reduction factor fm as obtained fromFigure 2.5-1 before entering the S-N curve.

��4� �00��$� 0�0#&"%�#$% �$ +�"# ��-Normally larger fabrication tolerances are allowed in realstructures than that accounted for in the test specimensused to derive S-N data, ref. DNV ��)*��+�"�(��&��#��. Therefore, additionalstresses resulting from normal fabrication tolerancesshould be included in the fatigue design. Special attentionshould be given to the fabrication tolerances for simplebutt welds in plates and tubulars as these give the mostsignificant increase in additional stress. Stressconcentration factors for butt welds are given in section2.6 and at tubular circumferential welds in section 2.8.

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A stress concentration factor may be defined as the ratio ofhot spot stress range over nominal stress range.

The eccentricity between welded plates may be accountedfor in the calculation of stress concentration factor. Thefollowing formula applies for a butt weld in an unstiffenedplate or for a pipe butt weld with a large radius:

t

)(31SCF 0m δ−

+==��/�'>

where δm is eccentricity (misalignment) and t is platethickness, see Figure 2.8-4. δ0 = 0.1t is misalignmentinherent in the S-N data for for butt welds.

The stress concentration for the weld between plates withdifferent thickness in a stiffened platefield may be derivedfrom the following formula:

( )

+

−++=

5.1

5.10m

1

61SCF

W

7W

Wδδδ =��/��>

where

δm = maximum misalignment

δt = ½ ( )W7 − eccentricity due to change in thickness

δ0 = 0.1t is misalignment inherent in the S-N data forbutt welds

T = thickness of thicker plate

t = thickness of thinner plate

See also Figure 2.8-3.

��

The stress concentration factor for cruciform joint may bederived from following formula:

+++

−+=

4

34

3

33

2

32

1

31

1

02

l

)(61SCF

O

W

O

W

O

W

O

W

W δδ ��

Where

δ = (δm + δW) is the total eccentricity.

δ0 = 0.15t is misalignment inherent in the S-N data forcruciform joints

t = thickness of the considered plate

The other symbols are defined in Figure 2.6-1.

l3

l4

l2 l1

t2 t1

t3

t4

δ

��

��

Stress concentration factors for rounded rectangular holesare given in Figure 2.6-2.

Where there is one stress raiser close to another detailbeing evaluated with respect to fatigue, the interaction ofstress between these should be considered. An example ofthis is a welded connection in a vicinity of a hole. Then theincrease in stress at the considered detail due to the holecan be evaluated from Figure 2.6-3.

Some guidelines on effect of interaction of different holescan be found in Peterson's “Stress Concentration Factors”,/15/).

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��

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

2.80

3.00

1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00

5HODWLYH�GLVWDQFH�IURP�FHQWUH�RI�KROH�[�U

5HODWLYH�VWUHVV

r

Stress direction

x/r

Line for calculation of stress

Line for calculationof stress

r

x

��&��

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Stress concentration factors for holes with reinforcementare given in Appendix 3.

At welds on reinforced rings fatigue cracking may occur atseveral locations depending on geometry of ring and weldsize:

• Fatigue cracking transverse to the weld toe in theregion with a large stress concentration giving largestress parallel to the weld.

• Fatigue cracking normal to the weld toe.• Fatigue cracking from the weld root.

All these potential regions for fatigue cracking should beinvestigated. For stresses to be used together with thedifferent S-N curves see section 2.2.

Potential fatigue cracking transverse to the weld toe

For stresses parallel with the weld the local stress to beused together with the C curve is obtained with SCF fromAppendix 3 (σt in Figure 2.6-4 c).

Potential fatigue cracking parallell wih the weld toe

For stresses normal to the weld the resulting hot spot stressto be used together with the D curve is obtained with SCFfrom Appendix 3 (σn Figure 2.6-4 a and b).

Potential fatigue cracking from the weld root

At some locations of the welds there are stress in the platetransverse to the fillet weld, σn, and stress in the plateparallel with the weld σt, see Figure 2.6-4 b. Then the filletweld is designed for a combined stress obtained as

22 2.02 WQZ �� σσσ ∆+∆=∆ ��

where

t = plate thickness

a = throat thickness for a double sided fillet weld.

This equation can be outlined from equation (2.2.3) andthe resulting stress range is to be used together with theW3 curve. The basic stress in the plate as shown in Figure2.6-4 is derived from Appendix 3. Also fatigue crackingfrom the weld root should be analysed for the stresscondition in Figure 2.6-4 a using equation (2.6.4) (withσt=0).(σn and σt include SCFs from Appendix 3)

σQ

σQ

σW

D� E�

σW

F�

��&�� (��

��)� �� *�� Stress concentration factors for ship details may be foundin “Fatigue Assessment of Ship Structures” (CN 30.7), ref./1/. S-N curve C from this RP may be used if theprocedure of CN 30.7 is used to determine the hot spot andKw stress. S-N curve D from this RP may be used if theprocedure of CN 30.7 is used to determine the local stress(Excluding the stress concentration factor due to the weldgeometry, Kw, from the analysis, as this factor is accountedfor in the D-curve).

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Stress concentration factors for simple tubular joints aregiven in Appendix 2 of this RP.

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The stresses are calculated at the crown and the saddlepoints, see Figure 2.8-1. Then the hot spot stress at thesepoints is derived by summation of the single stresscomponents from axial, in-plane and out of plane action.The hot spot stress may be higher for the intermediatepoints between the saddle and the crown. The hot spotstress at these points is derived by a linear interpolation ofthe stress due to the axial action at the crown and saddleand a sinusoidal variation of the bending stress resultingfrom in-plane and out of plane bending. Thus the hot spotstress should be evaluated at 8 spots around thecircumference of the intersection, ref. Figure 2.8-2.

mzMOPmyMIPxASAC8

mxMOPxAS7

mzMOPmyMIPxASAC6

myMIPxAC5

mzMOPmyMIPxASAC4

mxMOPxAS3

mzMOPmyMIPxASAC2

myMIPxAC1

SCF22

1SCF2

2

1)SCF(SCF

2

1

SCFSCF

SCF22

1SCF2

2

1)SCF(SCF

2

1

SCFSCF

SCF22

1SCF2

2

1)SCF(SCF

2

1

SCFSCF

SCF22

1SCF2

2

1)SCF(SCF

2

1

SCFSCF

−−+=

−=

−++=

+=

+++=

+=

+−+=

−= ��+��

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Here σx, σmy and σmz are the maximum nominal stressesdue to axial load and bending in-plane and out-of-planerespectively. SCFAS is the stress concentration factor at thesaddle for axial load and the SCFAC is the stress

concentration factor at the crown. SCFMIP is the stressconcentration factor for in plane moment and SCFMOP isthe stress concentration factor for out of plane moment.

Braced

Crown Toe

D

g

Saddle

Crown Heel

Chord

t

TΘ

NM OP

IPM

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Axial load

z

x y1 2

3456

78

In-plane Out-of-planebending moment bending moment

N MIP MOP

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Influence functions may be used as an alternative to theprocedure given here to calculate hot spot stress. See e.g.“Combined Hot-Spot Stress Procedures for TubularJoints”, ref. /23/ and “Development of SCF Formulae andGeneralised Influence Functions for use in FatigueAnalysis” ref. /2/.

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The root area of single-sided welded tubular joints may bemore critical with respect to fatigue cracks than the outsideregion connecting the brace to the chord. In such cases, itis recommended that stubs are provided for tubular jointswhere high fatigue strength is required, such that weldingfrom the backside can be performed.

Failure from the root has been observed at the saddleposition of tubular joints where the brace diameter is equalthe chord diameter, both in laboratory tests and in service.It is likely that fatigue cracking from the root might occurfor rather low stress concentrations. Thus, special attentionshould be given to joints other than simple joints, such asring-stiffened joints and joints where weld profiling orgrinding on the surface is required to achieve sufficientfatigue life. It should be remembered that surfaceimprovement does not increase the fatigue life at the root.

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Based on experience it is not likely that fatigue crackingfrom the inside will occur earlier than from the outside forsimple T and Y joints and K type tubular joints. The sameconsideration may be made for X-joints with diameterratio β �� joints with β > 0.90 it is recommended that a fatigueassessment of the root area is performed. Some guidanceon such an assessment can be found in Appendix 4,Commentary.

Due to limited accessibility for in service inspection ahigher design fatigue factor should be used for the weldroot than for the outside weld toe hot spot. Reference isalso made to Appendix 4, Commentary

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Equations for joints for ring stiffened joints are given in“Stress Concentration Factors for Ring-Stiffened TubularJoints”, ref. /3/. The following points should be notedregarding the equations:

• The derived SCF ratios for the brace/chordintersection and the SCF's for the ring edge are meanvalues, although the degree of scatter and proposeddesign factors are given.

• Short chord effects shall be taken into account whererelevant.

• For joints with diameter ratio β ≥ 0.8, the effect ofstiffening is uncertain. It may even increase the SCF.

• The maximum of the saddle and crown stressconcentration factor values should be applied aroundthe whole brace/chord intersection.

The following points can be made about the use of ringstiffeners in general:

• Thin shell FE analysis should be avoided forcalculating the SCF if the maximum stress is expectedto be near the brace-ring crossing point in the fatigueanalysis.

• Ring stiffeners have a marked effect on thecircumferential stress in the chord, but have little orno effect on the longitudinal stress.

• Ring stiffeners outside the brace footprint have littleeffect on the SCF, but may be of help for the staticstrength.

• Failures in the ring inner edge or brace ring interfaceoccur internally, and will probably only be detectedafter through thickness cracking, at which the majorityof the fatigue life will have been expired. These areasshould therefore be considered as non-inspectableunless more sophisticated inspection methods areused.

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Grouted joints have either the chord completely filled withgrout (single skin grouted joints) or the annulus betweenthe chord and an inner member filled with grout (doubleskin grouted joints). The SCF of a grouted joint dependson load history. The SCF is less if the bond between thechord and the grout is unbroken. For model testing ofgrouted joints the bond should be broken prior to SCFmeasurements. Due to the grout the tensile andcompressive SCF may be different.

To achieve a fatigue design that is to the safe side it isrecommended to use SCF’s derived from tests where thebounds are broken and where the joint is subjected to atension loading. The bounds can be broken by a significantloading in tension. This load level may be determinedduring the testing by an evaluation of the forcedisplacement relationship. (When incrementing theloading into a non-linear behaviour).

The grouted joints shall be treated as simple joints, exceptthat the chord thickness in the γ term for saddle SCFcalculation for brace and chord shall be substituted with anequivalent chord wall thickness given by

134T)/144(5DTe += ��+��

where D and T are chord diameter and thicknessrespectively.

Joints with high β or low γ ratios have little effect ofgrouting. The benefits of grouting should be neglected forjoints with β > 0.9 or γ ≤ 12.0 unless documentedotherwise.

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It is recommended that finite element analysis should beused to determine the magnitude and location of themaximum stress range in castings sensitive to fatigue. Thefinite element model should use volume elements at thecritical areas and properly model the shape of the joint.Consideration should be given to the inside of the castings.The brace to casting circumferential butt weld (which isdesigned to an appropriate S-N curve for suchconnections) may be the most critical location for fatigue.

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Due to less severe S-N curve for the outside than theinside, it is strongly recommended that tubular butt weldconnections are designed such that any thicknesstransitions are placed on the outside (see Figure 2.8-3). Forthis geometry, the SCF for the transition applies to theoutside. On the inside it is then conservative to use SCF =1.0. Thickness transitions are normally to be fabricatedwith slope 1:4.

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Outside

Inside

Neutralaxis

14

nominal

δσ

L

Tt

t

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Stress concentrations at tubular butt weld connections aredue to eccentricities resulting from different sources.These may be classified as concentricity (difference intubular diameters), differences in thickness of joinedtubulars, out of roundness and centre eccentricity, seeFigure 2.8-5 and Figure 2.8-6. The resulting eccentricitymay be conservatively evaluated by a direct summation ofthe contribution from the different sources. Theeccentricity due to out of roundness normally gives thelargest contribution to the resulting eccentricity δ.

It is conservative to use the formula for plate eccentricitiesfor calculation of SCF at tubular butt welds. The effect ofthe diameter in relation to thickness may be included byuse of the following formula, provided that T/t ≤ 2:

-5.2

0t e

t

T1

1

t

)6(1SCF

+

−++= δδP

��+��

where

2.5

t

T1

1

tD

1.82L

+

⋅=

δ0 = 0.1t is misalignment inherent in the S-N data.

This formula also takes into account the length over whichthe eccentricity is distributed: L, ref. Figure 2.8-4 andFigure 2.8-3. The stress concentration is reduced as L isincreased and/or D is reduced. It is noted that for small Land large D the last formula provides stress concentrationfactors that are close to but lower that of the simplerformula for plates.

t

D

L

δm

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The transition of the weld to base material on the outsideof the tubular can normally be classified corresponding toS-N curve E. If welding is performed in a horizontalposition it can be classified as D.

In tubulars, the root side of welds made from one side isnormally classified as F3. This requires goodworkmanship during construction, in order to ensure fullpenetration welds, and that work is checked by non-destructive examination. It may be difficult to document afull penetration weld in most cases due to limitations in thenon-destructive examination technique to detect defects inthe root area. The F3 curve can be considered to accountfor some lack of penetration, but it should be noted that amajor part of the fatigue life is associated with the initialcrack growth while the defects are small. This may beevaluated by fracture mechanics such as described inBS 7910 “Guidance on Methods for Assessing theAcceptability of Flaws in Fusion Welded Structures”, ref/7/. Therefore, if a fabrication method is used where lackof penetration is to be expected, the design S-N curvesshould be adjusted to account for this by use of fracturemechanics.

For global bending moments over the tubular section it isthe nominal stress derived at the neutral axis of Figure2.8-3 that should be used together with an SCF fromequation (2.8.3) for calculation of hot spot stress.

A A

Section A-Aa) Concentricity

t

t

δm

A A

b) Thickness Section A-A

T

t

δ = ½ (T-t)t

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A

Section A-Ac) Out of roundness

A

t

t

δm

δm

δm

A A

Section A-Ad) Center eccentricity

δ

t

t

mmδ

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The stress concentration at a ring stiffener can becalculated as

rA

rt1.56t1

shell theof inside for the0.54

1SCF

shell theof outside for the0.54

1SCF

+=

−=

+= ��+��

where

Ar = area of ring stiffener without effective shell.

r = radius of shell measured from centre to mean shellthickness

t = thickness of shell plating.

It can thus be noted that it is more efficient to place ringstiffeners on the inside of shell, as compared with theoutside. In addition, if the shell comprises longitudinalstiffeners that are ended, it is recommended to end thelongitudinal stiffeners against ring stiffeners for the inside.The corresponding combination on the outside gives aconsiderably larger stress concentration.

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The SCF = 1.0 if continuous longitudinal stiffeners areused.

In the case of a bulkhead instead of a ring, Ar is taken

as( )1

tr b

−, where tb is the thickness of the bulkhead.

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The stress concentration at each side of unstiffenedtubular-cone junctions outside can be estimated by thefollowing equations (the SCF shall be used together withthe stress in the tubular at the junction for both the tubularand the cone side of the weld):

tant

)t(tDt0.61SCF

2

cj ++=

��+�'�

tant

)t(tDt0.61SCF

2c

cj ++=

��+��

where

Dj = cylinder diameter at junction (Ds, DL)t = tubular member wall thickness (ts, tL)tc = cone thickness

α = the slope angle of the cone (see Figure 2.8-8)

The stress concentration at a junction with ring stiffenercan be calculated as

r

j

r

j

r

j

r

j

r

j

A

tD1.10t1

andjunction,diameterlargerinsidetheat

1tan

A

t0.91D0.541SCF

junctiondiameterlargeroutsidetheat

1tan

A

t0.91D0.541SCF

junctiondiametersmallerinsidetheat

1tan

A

t0.91D0.541SCF

junctiondiametersmalleroutsidetheat

1tan

A

t0.91D0.541SCF

+=

−−=

−+=

+−=

++=

��+�)�

where

Ar = area of ring stiffener without effective shell.

If a ring stiffener is placed a distance δ away from theintersection lines, an additional stress concentration shouldbe included to account for this eccentricity:

tant

31SCF += ��+�+�

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Ds

DL

ts

tL

α

.

tC

Ds

D L

ts

t L

α

δtc

e

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This section applies to tubular sections welded together tolong strings and subjected to axial tension. Tethers andrisers of a TLP are examples of such structures.

The colinearity with small angle deviation betweenconsecutive fabricated tubular segments results inincreased stress due to a resulting global bending moment,see Figure 2.8-9. The eccentricity due to colinearity is afunction of axial tension in the tubular and is significantlyreduced as the axial force is increased by tension.Assuming that the moment M results from an eccentricityδN where pretension is accounted for in the analysis, thefollowing derivation of a stress concentration factor isperformed:

( ) SCFttD

N

−= ��+�/�

where the stress concentration factor is:

tD

41SCF N

−+=

δ ��+��$�

where δN is eccentricity as function of the axial force NSd

and D is outer diameter. The eccentricity for two elementsis indicated in Figure 2.8-10. With zero tension theeccentricity is δ. With an axial tension force NSd theeccentricity becomes:

kl

kltanhN δδ =

��+��

where

k =EI

NSd

� = segment lengths of the tubulars

NSd= axial force in tubulars

I = moment of inertia of tubulars

E = Young’s modulus.

The formula for reduction in eccentricity due to increasedaxial force can be deduced from differential equation forthe deflected shape of the model shown in Figure 2.8-10.Thus the non-linearity in terms of geometry is included inthe formula for the stress concentration factor.

Judgement should be used to evaluate the number ofelements to be considered, and whether deviation from astraight line is systematic or random, ref. Figure 2.8-9. Inthe first case, the errors must be added linearly, in thesecond case it may be added quadratically.

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��/� �� (��7� ��Stress concentration factors for T- and X- square to squarejoints may be found in “Proposed Revisions for FatigueDesign of Planar Welded Connections made of HollowStructural Sections”, ref. /27/.

Stress concentration factors for Y- and K square to squarejoints for d/Dw less or equal to 0.75 may be found from“Stress Concentrations in T/Y and K Square-to-Square andSquare-to- Round Tubular Joints”, ref. /8/, where d = depthand width of brace; Dw = depth and width of chord. Thesestress concentration factors may be used together with theD-curve.

The following stress concentration factors may be used ford/Dw = 1.0, in lieu of a more detailed analysis forcalculation of hot spot stress:

– Axial: 1.90– In-plane bending: 4.00– Out-of plane bending: 1.35These stress concentration factors should be used togetherwith the F-curve.

��$� �� * �� *�� (��Design should be performed such that fatigue crackingfrom the root is less likely than from the toe region. Thereason for this is that a fatigue crack at the toe can befound by in-service inspection while a fatigue crackstarting at the root can not be discovered before the crackhas grown through the weld. Thus the design of the weldgeometry should be performed such that the fatigue life forcracks starting at the root is longer than the fatigue life ofthe toe. Figure 2.10-2 can be used for evaluation ofrequired penetration. The lack of penetration, (2ai),obtained from this figure may be further reduced by afactor of 0.80 in order to obtain a recommended designvalue for avoidance of fatigue cracking from the root. Thenotation used is explained by Figure 2.10-1.

It should be added that it is difficult to detect internaldefects by NDE in fillet/partial penetration welds. Suchconnections should therefore not be used in structuralconnections of significant importance for the integrity.

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0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

�DL�WS

K�WS

tp = 50 mm

tp = 25 mm

tp = 12 mm

tp = 6mm

Weld toe failure

Weld root failure

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�� 9��A bolted joint connection subjected to dynamic loadingshould be designed with pretensioned bolts. Thepretension should be high enough to avoid slipping afterrelevant loss of pretension during service life. Connectionswhere the pretensioned bolts are subjected to dynamicaxial forces should be designed with respect to fatiguetaking into account the stress range in the bolts resultingfrom tension and compression range. The stress range inthe bolts may be assessed based on e.g. “Maskindeler 2”,ref. /23/, or “Systematic Calculation of High Duty BoltedJoints”, ref. /26/.

�� *��Welds in pipelines are normally made with a symmetricweld groove with welding from the outside only. Thetolerances are rather strict compared with other structuralelements with eccentricity less than 0.1*t or maximum 3mm. (t = wall thickness) The fabrication of pipelines alsoimplies a systematic and standardised NDE of the root areawhere defects are most critical. Provided that the sameacceptance criteria are used for pipelines with larger wallthickness as for that used as reference thickness (25 mm),a thickness exponent k = 0 may be used for hot spot at theroot and k = 0.15 for the weld toe. Provided that theserequirements are fulfilled, the detail at the root side may beclassified as F1 with SCF = 1.0, ref. Table 2.12-1. The F-curve and SCF = 1.0 may be used for welding ontemporary backing, ref. Table 2.12-1.

Reference is made to Table 2.12-1 for other tolerances andwelding from both sides.

For weld grooves that are not symmetrical in shape a stressconcentration due to maximum allowable eccentricityshould be included. This stress concentration factor can beassessed based on the following analytical expression

−+=

−0.50

t

Dexp

t

)-3(1SCF

δ ��

where:

δ0 = 0.1t is misalignment inherent in the S-N data.

This stress concentration factor can also be used forfatigue assessments of the weld toes, ref. also Table2.12-1.

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Description

Welding Geometry and hotspot

Tolerance requirement S-Ncurve

Thicknessexponent k

SCF

δ ≤ min(0.1t, 3 mm) F1 0.00 1.0Single side

Hot spotδ > min(0.1t, 3 mm) F3 0.00 1.0

δ ≤ min(0.1t, 2 mm) F 0.00 1.0Single side

on backing

Hot spotδ > min(0.1t, 2 mm) F1 0.00 1.0

Single side

Hot spot

)mm4,t15.0min(≤δ D 0.15 Eq.(2.12.1)

Double side

Hot spot

)mm4,t15.0min(≤δ D 0.15 Eq.(2.12.1)

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From detailed finite element analysis of structures it maybe difficult to evaluate what is “nominal stress” to be usedtogether with the S-N curves, as some of the local stressdue to a detail is accounted for in the S-N curve.

In many cases it may therefore be more convenient to usean alternative approach for calculation of fatigue damagewhen local stresses are obtained from finite elementanalysis.

It is realised that it is difficult to calculate the notch stressat a weld due to a significant scatter in local weldgeometry and different types of imperfections. This scatteris normally more efficiently accounted for by use of anappropriate S-N curve. In this respect it should also bementioned that the weld toe region has to be modelledwith a radius in order to obtain reliable results for thenotch stress.

If a corner detail with zero radius is modelled thecalculated stress will approach infinity as the element sizeis decreased to zero. The modelling of a relevant radiusrequires a very fine element mesh, increasing the size of

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the computer model. In addition, a proper radius to be usedfor the analysis will likely be a matter of discussion.

Hence, for design analysis a simplified numericalprocedure is used in order to reduce the demand for largefine mesh models for the calculation of SCF factors:

• The stress concentration or the notch factor due to theweld itself is included in the S-N curve to be used, theD-curve.

• The stress concentration due to the geometry effect ofthe actual detail is calculated by means of a fine meshmodel using shell elements (or solid elements),resulting in a geometric SCF factor.

This procedure is denoted the hot spot method.

It is important to have a continuous and not too steep,change in the density of the element mesh in the areaswhere the hot spot stresses are to be analysed.

The geometry of the elements should be evaluatedcarefully in order to avoid errors due to deformed elements(for example corner angles between 60° and 120° andlength/breadth ratio less than 5 are recommended).

The size of the model should be so large that the calculatedresults are not significantly affected by assumptions madefor boundary conditions and application of loads.

�� -�&��

The stress range at the hot spot of tubular joints should becombined with the T-curve.

Analysis based on thick shell elements may be used. Inthis case, the weld is not included in the model. The hotspot stress may be determined as for welded connections.

More reliable results are obtained by including the weld inthe model. This implies use of three-dimensional elements.Here the Gaussian points, where stresses are calculated,may be placed ��1.0 from the weld toe (r = radius ofconsidered tubular and t = thickness). The stress at thispoint may be used directly in the fatigue assessment.

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The stress range at the hot spot of welded connectionsshould be combined with S-N curve D. The C-curve maybe used if machining of the weld surface to the basematerial is performed. Then the machining has to beperformed such that the local stress concentration due tothe weld is removed.

The aim of the finite element analysis is not normally tocalculate directly the notch stress at a detail, but tocalculate the geometric stress distribution in the region atthe hot spot such that these stresses can be used as a basisfor derivation of stress concentration factors. Reference ismade to Figure 2.13-1 as an example showing the stressdistribution in front of an attachment (A-B) welded to a

plate with thickness �. The notch stress is due to thepresence of the attachment and the weld. The aim of thefinite element analysis is to calculate the stress at the weldtoe (hot spot) due to the presence of the attachment,denoted geometric stress, σ hot spot. The stress concentrationfactor due to this geometry effect is defined as,

inalnom

spothotSCF =��

Thus the main emphasis of the finite element analysis is tomake a model that will give stresses with sufficientaccuracy at a region outside that effected by the weld. Themodel should have a fine mesh for extrapolation ofstresses back to the weld toe in order to ensure asufficiently accurate calculation of SCF.

FEM stress concentration models are generally verysensitive to element type and mesh size. By decreasing theelement size the FEM stresses at discontinuities willapproach infinity. It is therefore necessary to set a lowerbound for element size and use an extrapolation procedureto the hot spot to have a uniform basis for comparison ofresults from different computer programs and users. Onthe other hand, in order to pick up the geometric stress, σg,increase properly, it is important that the stress referencepoints in t/2 and 3t/2 (see Figure 2.13-1) are not inside thesame element. This implies that element sizes of the orderof the plate thickness are to be used for the modelling. Ifsolid modelling is used, the element size in way of the hotspot may have to be reduced to half the plate thickness incase the overall geometry of the weld is included in themodel representation.

Element stresses are normally derived at the gaussianintegration points. Depending on element type it may benecessary to perform several extrapolations in order todetermine the stress at the location representing the weldtoe. In order to preserve the information of the direction ofprincipal stresses at the hot spot, component stresses are tobe used for the extrapolation. When shell elements areused for the modelling and the overall geometry of theweld is not included in the model, the extrapolation shallbe performed to the element intersection lines. If the(overall) weld geometry is included in the model (3Dmodel), the extrapolation is related to the weld toe asshown in Figure 2.13-1. If 8 node shell elements are usedthe hot spot is considered to be at the element intersectionline.

Two different definitions for hot spot stresses are used:

1. The stress is derived by extrapolating the stress to theweld toe (intersection line).

2. The stress at 0.5t from the considered hot spot

�� The stresses are first extrapolated from thegaussian integration points to the plate surface. A furtherextrapolation to the line A - B is then conducted. The finalextrapolation of component stresses is carried out as a

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linear extrapolation of surface stresses along line A - B at adistance t/2 and 3t/2 from either the weld toe, oralternatively the element intersection line (where t denotesthe plate thickness). Having determined the extrapolatedstress components at the hot spot, the principal stresses areto be calculated and used for the fatigue evaluation.

Some comments on element size are given in Appendix 4,Commentary.

It is recommended to perform a verification of theprocedure on a detail that is S-N classified and that issimilar in geometry and loading to that being analysed. Ifthe verification analysis comes out with a different SCF(SCF Verification) than that inherent in the S-N detail, ref.e.g. Table 2.3-1, a resulting stress concentration factor canbe calculated as

onVerificati

12.3TableNSAnalysis SCF

SCFSCFSCF −−⋅=

where

SCFS-N Table 2.3-1 = Stress concentration in the S-Ndetail as derived by the hot spotmethod, see Table 2.3-1.

SCFAnalysis = Stress concentration factor for theanalysed detail.

It should be noted that the hot spot concept can not be usedfor fatigue checks of cracks starting from the weld root offillet/partial penetration welds. The weld should bechecked separately considering the stresses in the welditself, ref. section 2.2.3.

��: The hot spot stress is derived directly from thefinite elements at a distance 0.5t from the weld toe using20 node solid elements or 0.5t from the intersection lineusing 8 node shell elements.

It is also here recommended to perform a verification ofthe procedure on a detail that is S-N classified and that issimilar in geometry and loading to that being analysed. Ifthe verification analysis comes out with a different SCF(SCF Verification) than that inherent in the S-N detail, ref.e.g. Table 2.3-1, a resulting stress concentration factor canbe calculated as shown in the example above.

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�� *�� 0��

�� ,��

The long term stress range distribution may be presentedas a two-parameter Weibull distribution

−=

h

qexp)Q( σ

��

where

Q = probability for exceedance of the stress range ∆σ

h = Weibull shape parameter

q = Weibull scale parameter is defined from the stressrange level, ∆σ0, as

1/h0

0

)n(ln q = ��

∆σ0 is the largest stress range out of n0 cycles..

When the long-term stress range distribution is definedapplying Weibull distributions for the different loadconditions, and a one-slope S-N curve is used, the fatiguedamage is given by

)h

m��q

a

TD md0 ≤+=

��

where

Td = design life in seconds

h = Weibull stress range shape distribution parameter

q = Weibull stress range scale distribution parameter

ν0 = average zero-crossing frequency

)h

m��+ = gamma function. Values of the gamma

function are listed in Table 2.14-1.

Use of one slope S-N curves leads to results on the safeside for calculated fatigue lives (with slope of curve atN < 106-107 cycles).

For other expressions for fatigue damage see Appendix 4 ,Commentary.

- &��"�� 2 ��Γ��:�;��

0.600.610.620,630,640,650,660,670,680,690,700,710,720,730,740.750.76

120.000104.40391.35080.35871.04863.11956.33150.49145.44241.05837.23433.88630.94228.34426.04424.00022.178

0.770.780.790.800.810.820.830.840.850.860.870.880.890.900.910.920.93

20.54819.08717.77216.58615.51414.54213.65812.85312.11811.44610.82910.263 9.741 9.261 8.816 8.405 8.024

0.940.950.960.970.980.991.001.011.021.031.041.051.061.071.081.091.10

7.671 7.342 7.035 6.750 6.483 6.234 6.000 5.781 5.575 5.382 5.200 5.029 4.868 4.715 4.571 4.435 4.306

��

Design charts for steel components in air and in seawaterwith cathodic protection are shown in Figure 2.14-1 andFigure 2.14-2 respectively. These charts have been derivedbased on the two slopes S-N curves given in this RP. Thecorresponding numerical values are given in Table 2.14-2and Table 2.14-3.

These design charts have been derived based on anassumption of an allowable fatigue damage η = 1.0 during108 cycles (20 years service life and an average waveperiod of 6.3 sec). For design with other allowable fatiguedamages, η, the allowable stress from the design chartsshould be reduced by factors derived from Table 2.14-2and Table 2.14-3 for conditions in air and in seawaterwith cathodic protection respectively.

The stresses derived here correspond to the referencethickness. For thickness larger than the referencethickness, an allowable extreme stress range during 108

cycles may be obtained as

N

=

t

t reftref0,t0,

��

where

k = thickness exponent, see section 2.3.1 and Table2.3-1

σ0,tref = allowable stress as derived from Table 2.14-2 -Table 2.14-5.

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C 1319.3 919.6 688.1 542.8 445.5 377.2 326.9 289.0

C1 1182.0 824.0 616.5 486.2 399.2 337.8 292.9 258.9

C2 1055.3 735.6 550.3 434.1 356.3 301.6 261.5 231.1

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W2 422.1 294.1 220.1 173.6 142.5 120.6 104.6 92.5

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C2 830.7 596.3 458.7 371.3 311.7 269.2 237.6 213.1

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F 589.8 423.4 325.8 263.6 221.4 191.1 168.6 151.3

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F3 465.3 334.0 257.0 208.0 174.6 150.9 133.1 119.3

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W2 332.3 238.4 183.5 148.5 124.7 107.7 95.0 85.3

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0.50 0.805 0.810 0.816 0.821 0.826 0.831 0.835 0.839

0.30 0.688 0.697 0.706 0.715 0.723 0.730 0.737 0.742

0.10 0.497 0.512 0.526 0.540 0.552 0.563 0.573 0.581

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0.30 0.713 0.729 0.743 0.753 0.762 0.769 0.773 0.778

0.10 0.535 0.558 0.577 0.592 0.604 0.613 0.619 0.623

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�� 4��Fracture mechanics may be used for fatigue analyses assupplement to S-N data.

Fracture mechanics is recommended for use in assessmentof acceptable defects, evaluation of acceptance criteria forfabrication and for planning in-service inspection.

The purpose of such analysis is to document, by means ofcalculations, that fatigue cracks, which might occur duringservice life, will not exceed the crack size correspondingto unstable fracture. The calculations should be performedsuch that the structural reliability by use of fracturemechanics will not be less than that achieved by use of S-N data. This can be achieved by performing the analysisaccording to the following procedure:

• Crack growth parameter C determined as mean plus 2standard deviation.

• A careful evaluation of initial defects that might bepresent in the structure when taking into account theactual NDE inspection method used to detect cracksduring fabrication.

• Use of geometry functions that are on the safe side.• Use of utilisation factors similar to those used when

the fatigue analysis is based on S-N data.

As crack initiation is not included in the fracturemechanics approach, shorter fatigue life is normallyderived from fracture mechanics than by S-N data.

In a case that the results from fracture mechanics analysescannot directly be compared with S-N data it might berecommended to perform a comparison for a detail whereS-N data are available, in order to verify the assumptionsmade for the fracture mechanics analyses.

The initial crack size to be used in the calculation shouldbe considered in each case, taking account of experiencedimperfection or defect sizes for various weldments,geometries, access and reliability of the inspection method.For surface cracks starting from transitions betweenweld/base material, a crack depth of 0.5 mm (e.g. due toundercuts and microcracks at bottom of the undercuts)may be assumed if other documented information aboutcrack depth is not available.

It is normally, assumed that compressive stresses do notcontribute to crack propagation. However, for weldedconnections containing residual stresses, the whole stressrange should be applied. Only stress components normal tothe propagation plane need to be considered.

The Paris’ equation may be used to predict the crackpropagation or the fatigue life:

( )m�CdN

da = ��

where

∆K = Kmax - Kmin

N = Number of cycles to failure

a = crack depth. It is here assumed that the crackdepth/length ratio is low (less than 1:5).

C, m = material parameters, see BS 7910, ref. /7/.

The stress intensity factor K may be expressed as:

agK = ��

where

σ = nominal stress in the member normal to the crack

g = factor depending on the geometry of the memberand the crack.

See BS 7910, ref. /7/, for further guidelines related tofatigue assessment based on fracture mechanics.

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�� ,�� It should be noted that improvement of the toe will notimprove the fatigue life if fatigue cracking from the root isthe most likely failure mode. The considerations made inthe following are for conditions where the root is notconsidered to be a critical initiation point. The effect fromdifferent improvement methods as given in the followingcan not be added.

�� 8��*��&0� �� By weld profiling in this section is understood profiling bymachining or grinding as profiling by welding only is notconsidered to be an efficient mean to improve fatiguelives.

In design calculations, the thickness effect may be reducedto an exponent 0.15 provided that the weld is profiled byeither machining or grinding to a radius of approximatelyhalf the plate thickness, (T/2 with stress direction as shownin Figure 4.3-1, B).

Where weld profiling is used, the fatigue life can beincreased by a factor of 2.

As an alternative to including a factor 2 to increase fatiguelife one may take account of a reduced local stressconcentration factor achieved by weld profiling. A reducedlocal stress due to weld profiling can be obtained asfollows.

When weld profiling is performed, a reduced hot spotstress can be calculated as

βσασσ %HQGLQJ0HPEUDQHUHGXFHG/RFDO += ��

where α and β are derived from equations (4.2.2) and(4.2.3) respectively.

5.025.0 )/()(tan17.047.0 $%ϕα += ��

5.025.0 )/()(tan13.060.0 $%ϕβ += ��

For description of geometric parameters see Figure 4.2-1.

The membrane part and the bending part of the stress haveto be separated from the local stress as

%HQGLQJ0HPEUDQH/RFDO σσσ += ��

where

σMembrane = Membrane stress

σBending = Bending stress

If a finite element analysis of the considered connectionhas been performed, the results from this can be useddirectly to derive membrane stress and bending stress.

For cruciform joints and heavy stiffened tubular joints itmay be assumed that the hot spot stress is mainly due tomembrane stress.

For simple tubular joints it may be assumed that the hotspot stress in the chord is due to bending only.

The reduced local stress in equation (4.2.1) is to be usedtogether with the same S-N curves as the detail isclassified for without weld profiling. (It is assumed thatR/T = 0.1 without weld profiling for a plate thickness T =25 mm).

(The fatigue life can not be increased by a factor of 2 at thesame time as the hot spot stress is reduced due to weldprofiling).

Weld ProfilingT

Rϕ

��8��*��

�� ,��

Where local grinding of the weld toes below any visibleundercuts is performed the fatigue life may be increasedby a factor of 2. In addition the thickness effect may bereduced to an exponent k = 0.20. Reference is made toFigure 4.3-1. Grinding a weld toe tangentially to the platesurface, as at A, will produce only little improvement infatigue strength. To be efficient, grinding should extendbelow the plate surface, as at B, in order to remove toedefects. Grinding is normally carried out by a rotary burr.The treatment should produce a smooth concave profile atthe weld toe with the depth of the depression penetratinginto the plate surface to at least 0.5 mm below the bottomof any visible undercut (see Figure 4.3-1). The grindingdepth should not exceed 2 mm or 10% of the platethickness, whichever is smaller.

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In general grinding has been used as an efficient methodfor reliable fatigue life improvement after fabrication.Grinding also improves the reliability of inspection afterfabrication and during service life. However, experienceindicates that it may be a good design practice to excludethis factor at the design stage. The designer is advised toimprove the details locally by other means, or to reducethe stress range through design and keep the possibility offatigue life improvement as a reserve to allow for possibleincrease in fatigue loading during the design andfabrication process, see also OS-C101 Design of SteelStructures, section 6.

It should also be noted that if grinding is required toachieve a specified fatigue life, the hot spot stress is ratherhigh. Due to grinding a larger fraction of the fatigue life isspent during the initiation of fatigue cracks, and the crackgrows faster after initiation. This implies use of shorterinspection intervals during service life in order to detectthe cracks before they become dangerous for the integrityof the structure.

Depth of grinding shouldbe 0.5mm below bottomof any visible undercut.BA

σ σ

T

��,��(��

�� -4,��The fatigue life may be improved by a factor 2 by TIGdressing.

Due to uncertainties regarding quality assurance of thewelding process, this method may not be recommended forgeneral use at the design stage.

��'� ? ��*��The fatigue life may be improved by a factor of 4 bymeans of hammer peening.

However, the following limitations apply:

• Hammer peening should only be used on memberswhere failure will be without substantialconsequences, ref. OS-C101 Design of SteelStructures, section 6.

• Hammer peening may only be used when minimumload of predominant load ranges is compressive orzero.

• Overload in compression must be avoided, becausethe residual stress set up by hammer peening will bedestroyed.

• Peening tip must be small enough to reach weld toe.

Due to uncertainties regarding quality assurance of theprocess, this method may not be recommendable forgeneral use at the design stage.

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'�� 61�� An extended fatigue life is considered to be acceptable andwithin normal design criteria if the calculated fatigue lifeis longer than the total design life times the Fatigue DesignFactor.

Otherwise an extended life may be based on results fromperformed inspections throughout the prior service life.Such an evaluation should be based on:

1) Calculated crack growth.– Crack growth characteristics; i. e. crack length/depth

as function of time/number of cycles (this depends ontype of joint, type of loading, and possibility forredistribution of stress).

2) Reliability of inspection method used.– Elapsed time from last inspection performed.

It is recommended to use Eddy Current or MagneticParticle Inspection for inspection of surface cracksstarting at hot spots.

For welded connections that are ground and inspected forfatigue cracks the following procedure may be used forcalculation of an elongated fatigue life. Provided thatgrinding below the surface to a depth of approximately 1.0mm is performed and that fatigue cracks are not found by adetailed Magnetic Particle inspection of the considered hotspot region at the weld toe, the fatigue damage at this hotspot may be considered to start again at zero. If a fatiguecrack is found, a further grinding should be performed toremove any indication of this crack. If more than 10% ofthe thickness is removed by grinding, the effect of this onincreased stress should be included when a new fatigue lifeis assessed. In some cases as much as 30% of the platethickness may be removed by grinding before a weldrepair is resorted to. This depends on type of joint, loadingcondition and accessibility for a repair.

It should be noted that fatigue cracks growing from theweld root of fillet welds can hardly be detected by NDT.Also, the fatigue life of such regions can not be improvedby grinding of the surface.

It should also be remembered that if renewal of one hotspot area is performed by local grinding, there are likelyother areas close to the considered hot spot region that arenot ground and that also experience a significant dynamicloading. The fatigue damage at this region is the same asearlier. However, also this fatigue damage may bereassessed taking into account:

• the correlation with a ground neighbour hot spotregion that has not cracked

• an updated reliability taking the reliability ofperformed in-service inspections into account asdiscussed above.

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�� ,�� Large uncertainties are normally associated with fatiguelife assessments. Reliability methods may be used toillustrate the effect of uncertainties on probability of afatigue failure. An example of this is shown in Figure6.1-1 based on mean expected uncertainties for a jacketdesign from ”Reliability of Calculated Fatigue Lives ofOffshore Structures”, ref. /17/.

The calculated probability of failure is sensitive toassumptions made for the analysis. However, calculatedreliability values in a relative sense. Using Figure 6.1-1 inthis way, it might be concluded that a design modificationto achieve a longer calculated fatigue life is an efficientmean to reduce probability of a fatigue failure, ref. Figure6.1-1.

The effect of scatter in S-N data may be illustrated byFigure 6.1-2 where the difference between calculated lifeis shown for mean S-N data and design S-N data (which isdetermined as mean minus 2 standard deviations).

0.000000001

0.00000001

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

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0

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120

140

160

180

200

200 250 300 350 400

0D[LPXP�DOORZDEOH�VWUHVV�UDQJH�LQ�03D

&DOFXODWHG�IDWLJXH�OLIH�LQ�\HDUV

Design S-N data (mean minus 2 standard deviations)

Mean S-N data

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)�� /1/ Classification Note No 30.7 Fatigue

Assessment of Ship Structures. Det NorskeVeritas 1998.

/2/ Efthymiou, M.: Development of SCFFormulae and Generalised InfluenceFunctions for use in Fatigue Analysis. RecentDevelopments in Tubular Joint Technology,OTJ’88, October 1988, London.

/3/ Smedley, S. and Fischer, P.: StressConcentration Factors for Ring-StiffenedTubular Joints. : Proceedings of the FirstInternational Offshore and Polar EngineeringConference, Edinburgh, August 1991. pp.239-250. Publ by Int Soc of Offshore andPolar Engineers (ISOPE), P.O.Box 1107,Golden, CO, USA.

/4/ Lotsberg, I., Cramer, E., Holtsmark, G.,Løseth, R., Olaisen, K. and Valsgård, S.:Fatigue Assessment of Floating ProductionVessels. BOSS’97, July 1997.

/5/ Eurocode : Design of steel structures. Part 1-1:General rules and rules for buildings. February1993.

/6/ Guidance on Design, Construction andCertification. HSE. February 1995.

/7/ BS7910:1999. Guidance on Methods forAssessing the Acceptability of Flaws inFusion Welded Structures. BSI. Draft 1999.

/8/ Soh, A. K. and Soh, C. K.: StressConcentrations in T/Y and K Square-to-Squareand Square-to- Round Tubular Joints. Journal ofOffshore Mechanics and Arctic Engineering.August 1992, Vol. 114.

/9/ Gulati, K. C., Wang, W. J. and Kan, K. Y.: AnAnaltyical study of Stress ConcentrationEffects in Multibrace Joints under CombinedLoading. OTC paper no 4407, Houston, May1982.

/10/ Gurney,T.R.: Fatigue Design Rules for weldedSteel Joints, the Welding Institute ResearchBulletin. Volume 17, number 5, May 1976.

/11/ Gurney, T. R.: The Basis for the RevisedFatigue Design Rules in the Department ofEnergy Offshore Guidance Notes. Paper No55.

/12/ Berge, S.: Effect of Plate Thickness in FatigueDesign of Welded Structures. OTC Paper no4829. Houston, May 1984.

/13/ Buitrago, J. and Zettlemoyer, N.: Fatigue ofWelded Joints Peened Underwater. 1997OMAE, ASME 1997.

/14/ Stacey, A., Sharp, J. V. and Nichols, N. W.:Fatigue Performance of Single-sidedCircumferential and Closure Welds inOffshore Jacket Structures. 1997 OMAE,ASME 1997.

/15/ Pilkey, W. D.: Peterson’s Stress ConcentrationFactors. Second Edition. John Wiley & Sons.1997.

/16/ Haagensen, P. J., Drågen, A., Slind, T. andØrjasæter, O.: Prediction of the Improvementin Fatigue Life of welded Joints Due toGrinding, Tig Dressing, Weld Shape Controland Shot Peening. Steel in Marine Structures,edited by C. Noorhook and J. deBack ElsevierScience Publishers B.V., Amsterdam, 1987,pp. 689-698.

/17/ Lotsberg, I., Fines, S. and Foss, G.:”Reliability of Calculated Fatigue Lives ofOffshore Structures”, Fatigue 84, 2nd Int.Conf. on Fatigue and Fatigue Thresholds, 3-7September 1984. Birmingham.

/18/ Haagensen, P. J.,Slind, T. and Ørjasæter, O.:Scale Effects in Fatigue Design Data forWelded and Unwelded Components. Proc.Ninth Int. Conf. On Offshore Mechanics andArctic Engineering. Houston, February 1990.

/19/ Berge, S., Eide, O., Astrup, O. C., Palm, S.,Wästberg, S., Gunleiksrud, Å. and Lian,B.:Effect of Plate Thickness in Fatigue ofWelded Joints in Air ans in Sea Water. Steelin Marine Structures, edited by C. Noorhookand J. deBack Elsevier Science PublishersB.V., Amsterdam, 1987, pp. 799-810.

/20/ Razmjoo, G. R.: Design Guidance on Fatigueof Welded Stainless Steel Joints. OMAE1995.

/21/ Madsen, H. O., Krenk, S. and Lind, N. C.(1986) Methods of Structural Safety, Prentice-Hall, Inc., NJ.

/22/ Marshall, P. W.: API Provisions for SCF, S-N,and Size-Profile Effects. OTC Paper no 7155.Houston, May 1993.

/23/ Waløen, Å. Ø.: Maskindeler 2, Tapir, NTNU(In Norwegian).

/24/ Buitrago, J., Zettlemoyer, N. and Kahlish, J.L.: Combined Hot-Spot Stress Procedures for

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DET NORSKE VERITAS

Tubular Joints. OTC Paper No. 4775.Houston, May 1984.

/25/ Lotsberg, I.: Stress Concentration Factors atCircumferential Welds in Tubulars. Journal ofMarine Structures, January 1999.

/26/ VDI 2230 Part 1: Systematic Calculation ofHigh Duty Bolted Joints. Verein DeutscheIngenieure, August 1988.

/27/ Van Wingerde, A.M., Packer, J.A.,Wardenier, J., Dutta, D. and Marshall, P.:Proposed Revisions for Fatigue Design ofPlanar Welded Connections made of HollowStructural Sections. Paper 65 in "TubularStructures V," Ed. M.G. Coutie and G.Davies, 1993 E & FN spon.

/28/ DNV Offshore Standard. OS-C101 Design ofSteel Structures

/29/ Lotsberg, I., and Rove, H.: StressConcenteration Factors for Butt Welds inStiffened Plates.OMAE, ASME 2000.

/30/ IIW. Fatigue Design of Welded Joints andComponents. Recommendations of IIW JointWorking Group XIII-1539-96/XV-845-96.Edited by A. Hobbacher Abington Publishing,1996, The International Institute of Welding.

Recommended Practice – DNV-RP-C203Appendix 1October 2001

DET NORSKE VERITAS

39

APPENDIX 1 CLASSIFICATION OF STRUCTURAL DETAILSTable 1 Non-welded details

Notes on potential modes of failureIn plain steel, fatigue cracks will initiate at the surface, usually either at surface irregularities or at corners ofthe cross-section. In welded construction, fatigue failure will rarely occur in a region of plain material sincethe fatigue strength of the welded joints will usually be much lower. In steel with boltholes or other stressconcentrations arising from the shape of the member, failure will usually initiate at the stress concentration.The applied stress range shall include applicable stress concentration factors arising from the shape of themember.

Detailcategory Constructional details Description Requirement

B1 1.

2.

1. Rolled or extruded platesand flats

2. Rolled sections

1. to 2.:- Sharp edges, surface and

rolling flaws to beimproved by grinding.

- For members that canacquire stressconcentrations due to rustpitting etc. curve C isrequired.

B2 3. 3. Machine gas cut orsheared material with nodrag lines

3.- All visible signs of edge

discontinuities should beremoved.

- No repair by weld refill.- Re-entrant corners (slope

<1:4) or aperture shouldbe improved by grindingfor any visible defects.

- At apertures the designstress area should betaken as the net cross-section area.

C 4. 4. Manually gas cutmaterial or material withmachine gas cut edges withshallow and regulardraglines.

4.- Subsequently dressed to

remove all edgediscontinuities

- No repair by weld refill.- Re-entrant corners (slope

<1:4) or aperture shouldbe improved by grindingfor any visible defects.

- At apertures the designstress area should betaken as the net cross-section area.

Recommended Practice DNV-RP-C203Appendix 1

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40

Table 2 Bolted connectionsDetailcategory Constructional details Description Requirement

C1 1., 2. 1. Unsupported one-sided connections shallbe avoided or elseeffects of eccentricitiesshall be taken intoaccount whencalculating stresses.

2. Beam splices or boltedcover plates.

1. and 2.:- Stresses to be calculated

in the gross section.- Bolts subjected to

reversal forces in shearshall be designed as aslip resistant connectionand only the membersneed to be checked forfatigue.

3. 3. Bolts and threadedrods in tension.

F1 Cold rolled threads withno following heattreatment like hotgalvanising

W3 Cut threads

3.:- Tensile stresses to be

calculated using thetensile stress area of thebolt.

- For preloaded bolts, thestress-range in the boltdepends upon the levelof preload and thegeometry of theconnection, see e.g.“Maskindeler 2”, ref./23/.

Recommended Practices DNV-RP-C203 41Appendix 1October 2001

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Table 3 Continuous welds essentially parallel to the direction of applied stressNotes on potential modes of failure.With the excess weld material dressed flush, fatigue cracks would be expected to initiate at weld defectlocations. In the as welded condition, cracks may initiate at start-stop positions or, if these are not present, atweld surface ripples.

General comments

a) Backing strips

If backing strips are used in these joints, they must be continuous. If they are attached by welding, such weldsmust also comply with the relevant joint classification requirements (note particularly that tack welds, unlesssubsequently ground out or covered by a continuous weld, would reduce the joint to class F)

b) Edge distance

An edge distance criterion exists to limit the possibility of local stress concentrations occurring at unweldededges as a result, for example, of undercut, weld spatter, or accidental overweave in manual fillet welding (seealso notes in Table 7). Although an edge distance can be specified only for the “width” direction of anelement, it is equally important to ensure that no accidental undercutting occurs on the unwelded corners of,for example cover plates or box girder flanges. If undercutting occurs it should subsequently be groundsmooth.


1. Automatic butt weldscarried out from bothsides. If a specialistinspectiondemonstrates thatlongitudinal welds arefree from significantflaws, category B2may be used.

C 1.

2.2. Automatic fillet welds.

Cover plate ends shallbe verified using detail5. in Table 8

1. and 2.:

- No start-stop positionis permitted exceptwhen the repair isperformed by aspecialist andinspection carried outto verify the properexecution of the repair.


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42


3. Automatic fillet or buttwelds carried out fromboth sides butcontaining stop-startpositions.

C1 3.

4.

4. Automatic butt weldsmade from one sideonly, with a backingbar, but without start-stop positions.

4.:- When the detail

contains start-stoppositions use categoryC2

5. Manual fillet or buttwelds.

C2

6. Manual or automaticbutt welds carried outfrom one side only,particularly for boxgirders

6.:- A very good fit

between the flange andweb plates is essential.Prepare the web edgesuch that the root faceis adequate for theachievement of regularroot penetration without brake-out.

C2 7. Repaired automatic ormanual fillet or buttwelds

7.:- Improvement methods

that are adequatelyverified may restorethe original category.


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Table 4 Intermittent welds and welds at cope holesDetailcategory Constructional details Description Requirement

E 1. 1.Stitch or tack weldsnot subsequentlycovered by acontinuous weld

1.:- Intermittent fillet

weld with gap ratiog/h � 2.5.

F 2. 2.Ends of continuouswelds at copeholes.

2.:- Cope hole not to be

filled with weldmaterial.

3. 3.Cope hole andtransverse buttweld.

3.:- For butt weld in

material with copehole advice onfatigue assessmentmay be found inCN 30.7.

- The SCF (or K-factor) from CN30.7 may be usedtogether with the Ccurve.


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Table 5 Transverse butt welds, welded from both sidesNotes on potential modes of failureWith the weld ends machined flush with the plate edges, fatigue cracks in the as-welded condition normallyinitiate at the weld toe, so that the fatigue strength depends largely upon the shape of the weld overfill. If theoverfill is dressed flush, the stress concentration caused by it is removed, and failure is then associated withweld defects.

Design stresses

In the design of butt welds that are not symmetric about the root and are not aligned, the stresses must includethe effect of any eccentricity (see section 2.5 to 2.9).

With connections that are supported laterally, e.g. flanges of a beam that are supported by the web,eccentricity may be neglected.


C1 1.

2.

3.

41

4

1

1. Transverse splices inplates flats and rolledsections

2. Flange splices in plategirders.

3. Transverse splices inplates or flats taperedin width or in thicknesswhere the slope is notgreater than 1:4.

1. and 2.:- Details 1. and 2. may

be increased toCategory C when highquality welding isachieved and the weldis proved free fromsignificant defects bynon-destructiveexamination (it isassumed that this isfulfilled by inspectioncategory I).

1., 2. and 3.:- All welds ground flush

to plate surface parallelto direction of thearrow.

- Weld run-off pieces tobe used andsubsequently removed,plate edges to beground flush indirection of stress.

- All welds welded inhorizontal position inshop.


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D 4.

5.

6.

41

4 1

4.Transverse splices inplates and flats.

5.Transverse splices inrolled sections orwelded plate girders

6.Transverse splices inplates or flats taperedin width or inthickness where theslope is not greaterthan 1:4.

4., 5. and 6.:- The height of the weld

convexity to be notgreater than 10% of theweld width, with smoothtransitions to the platesurface.

- Welds made in flatposition in shop.

- Weld run-off pieces tobe used andsubsequently removed,plate edges to be groundflush in direction ofstress.


October 2001

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46


E 7.

41

4 1

7.Transverse splices inplates, flats, rolledsections or plategirders made at site.(Detail category Dmay be used forwelds made in flatposition at sitemeeting therequirements under4., 5. and 6.)

7.:- The height of the weld

convexity to be notgreater than 20% of theweld width.

- Weld run-off pieces tobe used andsubsequently removed,plate edges to be groundflush in direction ofstress.

8.

F1 0.16hr�

F311.0

hr�

8.Transverse splicebetween plates ofunequal width, withthe weld ends groundto a radius.

8.:- The stress concentration

has been accounted forin the joint classification.

- The width ratio H/hshould be less than 2.


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Table 6 Transverse butt welds, welded from one sideNotes on potential modes of failureWith the weld ends machined flush with the plate edges, fatigue cracks in the as-welded condition normallyinitiate at the weld toe, so that the fatigue strength depends largely upon the shape of the weld overfill. If theoverfill is dressed flush, the stress concentration caused by it is removed, and failure is then associated withweld defects. In welds made on permanent backing strip, fatigue cracks most likely initiate at the weldmetal/strip junction.

Design stresses

In the design of butt welds that are not symmetric about the root and are not aligned, the stresses must includethe effect of any eccentricity (see section 2.5 to 2.9).

With connections that are supported laterally, e.g. flanges of a beam that are supported by the web,eccentricity may be neglected.


W3 1. 1.Butt weld madefrom one side onlyand withoutbacking strip.

1.:With the root proved freefrom defects larger than 1-2mm (in the thicknessdirection) by non-destructivetesting, detail 1 may berecategorised to F3 (it isassumed that this is fulfilledby inspection category I). If itis likely that larger defectsmay be present after theinspection the detail may bedowngraded from F3 based onfatigue life calculation usingfracture mechanics. Theanalysis should then be basedon a relevant defect size.

F 2. 2.Transverse buttweld on apermanent backingstrip without filletwelds.

G 3. 3.Transverse buttweld on a backingstrip fillet weldedto the plate.


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Table 7 Welded attachments on the surface or the edge of a stressed memberNotes on potential modes of failureWhen the weld is parallel to the direction of the applied stress, fatigue cracks normally initiate at the weldends. When the weld is transverse to direction of stressing, cracks usually initiate at the weld toe; forattachments involving a single, as opposed to a double, weld cracks may also initiate at the weld root. Thecracks then propagate into the stressed member. When the welds are on or adjacent to the edge of the stressedmember the stress concentration is increased and the fatigue strength is reduced; this is the reason forspecifying an “edge distance” in some of this joints (see also note on edge distance in table Table 3).


1.

E l � 50mm

F 50 < l � 120mmF1 120 < l � 300mmF3 l > 300mm

1.Welded longitudinalattachment

1. The detail category isgiven for:- Edge distance � 10mm- For edge distance

< 10mm the detailcategory shall bedowngraded with oneSN-curve

2.

D150mmr ,

Wr

31

��

F

31

Wr

61

��

F1

61

Wr

101

��

F3

101

Wr

161

��

G

161

Wr

251

��

2.Gusset plate with aradius welded to theedge of a plate or beamflange.


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3.

G l � 150mm

W1 150 < l � 300mm

W2 l > 300mm

3.Gusset plate welded tothe edge of a plate orbeam flange.

4.

t

5.

6.

E t � 12mm

F t > 12mm

4.Transverse attachmentswith edge distance �10mm

5.Vertical stiffener weldedto a beam or a plategirder.

6.Diaphragms of boxgirders welded to theflange or web

5.:- The stress range

should be calculatedusing principal stressesif the stiffenerterminates in the web.

5. and 6.: The detailcategory is given for:- Edge distance � 10mm- For edge distance

< 10mm the detailcategory shall bedowngraded with oneSN-curve


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7.

E Edge distance � 10mm

G Edge distance < 10mm

7.Welded shear connectorto base material.

G 8. 8. Welded attachment withedge distance < 10mm


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Table 8 Welded joints with load carrying weldsNotes on potential modes of failureFailure in cruciform or T joints with full penetration welds will normally initiate at the weld toe. In joints made withload-carrying fillet or partial penetration butt welds, cracking may initiate either at the weld toe and propagate intothe plate, or at the weld root and propagate through the weld. In welds parallel to the direction of the applied stress,however, weld failure is uncommon. In this case, cracks normally initiate at the weld end and propagate into the plateperpendicular to the direction of applied stress. The stress concentration is increased, and the fatigue strength istherefore reduced, if the weld end is located on or adjacent to the edge of a stressed member rather than on itssurface.

Design stresses

In the design of cruciform joints, which are not aligned the stresses, must include the effect of any eccentricity. Themaximum value of the eccentricity may normally be taken from the fabrication tolerances. The design stress may beobtained as the nominal stress multiplied by the stress concentration factor due to the eccentricity.


F 1. 1.Full penetration buttwelded cruciform joint

1.:- Inspected and found free from

significant defects.

The detail category is given for:- Edge distance � 10mm- For edge distance < 10mm the

detail category shall bedowngraded with oneSN-curve

W3 2.

t<20mm

2.Partial penetration tee-butt joint or filletwelded joint andeffective fullpenetration in tee-buttjoint. See also section2.7.

2.:- Two fatigue assessments are

required. Firstly, rootcracking is evaluated takingCategory W3 for �w. �w isdefined in section 2.2.Secondly, toe cracking isevaluated by determining thestress range in the load-carrying plates and useCategory G.

- If the requirements in section2.10 are fulfilled and the edgedistance � 10mm, CategoryF1 may be used for partialpenetration welds and F3 forfillet welds.


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52


F1 3.

>10 mm

of main plateStressed area

2

1

3.Fillet welded overlapjoint. Crack in mainplate.

3.:- Stress in the main plate to be

calculated on the basis of areashown in the sketch.

- Weld termination more than10 mm from plate edge.

- Shear cracking in the weldshould be verified using detail7.

W1 4. 4.Fillet welded overlapjoint. Crack inoverlapping plate.

4.:- Stress to be calculated in the

overlapping plate elements- Weld termination more than

10 mm from plate edge.- Shear cracking in the weld

should be verified using detail7.

5.

tt c

tt

c

G t and tc � 20 mmW3 t and tc > 20 mm

5.End zones of single ormultiple welded coverplates in beams andplate girders. Coverplates with or withoutfrontal weld.

5.:- When the cover plate is wider

than the flange, a frontalweld, carefully ground toremove undercut, isnecessary.

E 6. and 7. 6.Continuous fillet weldstransmitting a shearflow, such as web toflange welds in plategirders. For continuousfull penetration buttweld in shear useCategory C2.

7.Fillet welded lap joint.

6.:- Stress range to be calculated

from the weld throat area.7.:- Stress range to be calculated

from the weld throat areaconsidering the total length ofthe weld.

- Weld terminations more than10 mm from the plate edge.


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E 8. 8.Stud connectors(failure in the weld orheat affected zone).

8.:- The shear stress to be

calculated on the nominalcross section of the stud.

9.

F

G

9.Trapezoidal stiffenerwelded to deck platewith fillet weld or fullor partial penetrationbutt weld.

9.:- For a full penetration butt

weld, the bending stress rangeshall be calculated on thebasis of the thickness of thestiffener.

- For a fillet weld or a partialpenetration butt weld, thebending stress range shall becalculated on the basis of thethroat thickness of the weld,or the thickness of thestiffener if smaller.


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Table 9 Hollow sectionsDetailcategory Constructional details Description Requirement

B1 1. 1.Non-welded sections 1.:Sharp edges and surface flaws to beimproved by grinding

B2 2. 2.Automaticlongitudinal seamwelds (for all othercases, see Table 3)

2.:- No stop /start positions, and free

from defects outside the tolerancesof OS-C401 Fabrication andTesting of Offshore Structures.

C1 3.Circumferential buttweld made from bothsides dressed flush.

D 4.Circumferential buttweld made from bothsides.

E 5.Circumferential buttweld made from bothsides made at site.

F 6.Circumferential buttweld made from oneside on a backingbar.

3., 4., 5. And 6.:- The applied stress must include the

stress concentration factor to allowfor any thickness change and forfabrication tolerances, ref. section2.8.7.

- The requirements to thecorresponding detail category inTable 5 apply.

F3 7. 7.Circumferential buttweld made from oneside without abacking bar.

7.:- The applied stress should include

the stress concentration factor toallow for any thickness change andfor fabrication tolerances, ref.section 2.8.7.

- The weld root proved free fromdefects larger than 1-2mm.


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C1 8. Circumferentialbutt welds betweentubular and conicalsections, weldmade from bothsides dressed flush.

D 9. Circumferentialbutt welds betweentubular and conicalsections, weldmade from bothsides.

E 10. Circumferentialbutt welds betweentubular and conicalsections, weldmade from bothsides made at site.

F

8., 9., 10 and 11.

11. Circumferentialbutt welds betweentubular and conicalsections, weldmade from one sideon a backing bar.

8, 9., 10., and 11.:- The applied stress must also

include the stress concentrationfactor due to the overall form of thejoint, ref. section 2.8.9.

- The requirements to thecorresponding detail category inTable 5 apply.

F3 12. 12. Circumferentialbutt welds betweentubular and conicalsections, weldmade from one sidewithout a backingbar.

12.:- The applied stress must also

include the stress concentrationfactor due to the overall form of thejoint

- The weld root proved free fromdefects larger than 1-2mm.

F3 13. 13. Butt welded end toend connection ofrectangular hollowsections.

13.:- With the weld root proved free

from defects larger than 1-2 mm


October 2001

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56


F 14. 14. Circular orrectangular hollowsection, filletwelded to anothersection.

14.:- Non load carrying welds.- Section width parallel to stress

direction � 100mm.- All other cases, see Table 7

G 15. 15. Circular hollowsection butt weldedend to end with anintermediate plate.

15.:- Load carrying welds.- Welds inspected and found free

from defects outside the tolerancesof OS-C401 Fabricationand testingof Offshore Structures

- Details with wall thickness greaterthan 8mm may be classifiedCategory F3.

W1 16. 16. Rectangular hollowsection butt weldedend to end with anintermediate plate.

16.:- Load carrying welds.- Welds inspected and found free

from defects outside the tolerancesof OS-C401 Fabrication andTesting of Offshore Structures

- Details with wall thickness greaterthan 8mm may be classified asCategory G.


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Table 10 Details relating to tubular membersDetailcategory Constructional details Description Requirement

T 1.Parent materialadjacent to the toes offull penetration weldedtubular joints.

1.:- The design should be based

on the hot spot stress.

F1 2. 2.Welded rungs.

F1 3.Gusseted connectionsmade with fullpenetration welds.

3.:- The design stress must

include the stressconcentration factor due tothe overall form of the joint.

F3

3. and 4.

4.Gusseted connectionsmade with fillet welds.

4.:- The design stress must

include the stressconcentration factor due tothe overall form of the joint.

F 5. 5.Parent material at thetoe of a weld attachinga diaphragm to atubular member.

The nominal design stress forthe inside may be determinedfrom section 2.8.8.


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58


E to G,seeTable 7

6. 6.Parent material (of thestressed member)adjacent to the toes ofa bevel butt or filletwelded attachments inregion of stressconcentration.

6.:-Class depends on attachmentlength (see Table 7) but stressmust include the stressconcentration factor due to theoverall shape of adjoiningstructure.

D 7. 7.Parent material to, orweld metal in weldsaround a penetrationthrough a wall of amember (on a planeessentiallyperpendicular to thedirection of stress)

7.:In this situation the relevantstress must include the stressconcentration factor due to theoverall geometry of the detail.

W1 8.Weld metal in partialpenetration or filletwelded joints around apenetration through thewall of a member (on aplane essentiallyparallel to the plane ofstress).

8.:- The stress in the weld should

include an appropriate stressconcentration factor to allowfor the overall joint geometry.Reference is also made toAppendix 3.

Recommended Practice DNV-RP-C203Appendix 2October 2001

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59

APPENDIX 2 SCF’S FOR TUBULAR JOINTS

Stress concentration factors for simple tubular joints and overlap joints

Stress concentration factors for tubular joints for joint types T/Y are given in Table 1, for joint types X in Table 2, forjoint types K in Table 3 and Table 4 and for joint types KT in Table 5. Stress concentration factors are based on“Development of SCF Formulae and Generalised Influence Functions for use in Fatigue Analysis", ref /2/.

Joint classification is the process whereby the axial force in a given brace is subdivided into K, X and Y components ofactions corresponding to the three joint types for which stress concentration equations exists. Such subdivision normallyconsiders all of the members in one plane at a joint. For purposes of this provision, brace planes within ±15º of eachother may be considered as being in a common plane. Each brace in the plane can have a unique classification thatcould vary with action condition. The classification can be a mixture between the above three joint types.

Figure 1 provides some simple examples of joint classification. For a brace to be considered as K-joint classification,the axial force in the brace should be balanced to within 10% by forces in other braces in the same plane and on thesame side of the joint. For Y-joint classification, the axial force in the brace is reacted as beam shear in the chord. ForX-joint classification, the axial force in the brace is carried through the chord to braces on the opposite side. Figure 1 c),e) and h) shows joints with a combination of classifications. In c) 50% of the diagonal force is balanced with a force inthe horizontal in a K-joint and 50% of the diagonal force is balanced with a beam shear force in the chord in an Y-joint.In e) 33% of the incoming diagonal force is balanced with a force in the horizontal in a K-joint with gap 1 and 67% ofthe incoming diagonal force is balanced with a force in the other diagonal in a K-joint with gap 2. In h) 50% of thediagonal force is balanced with a force in the horizontal on the same side of the chord in a K-joint and 50% of thediagonal force is balanced with a force in the horizontal on the opposite side of the chord in a X-joint.

Definitions of geometrical parameters can be found in Figure 2.

A classification of joints can be based on a deterministic analysis using a wave height corresponding to that with thelargest contribution to fatigue damage. A conservative classification may be used keeping in mind that

SCFX > SCFY > SCFK


October 2001

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Figure 1 Classification of simple joints.


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61

saddleD

T

crown crown

L

t

d

�

T

t

d

D

�

Ddβ �

D2Lα �

2TDγ �

Ttτ �

Ddβ A

A �

Ddβ B

B �

Ttτ A

A �

Ttτ B

B �

T

BRACE A

D

g

d

BRACE B

A

t A

Bt

dB

A��B 2T

Dγ �Dg

��

Ddβ A

A � Dd

β BB �

Dd

β CC �

Ttτ A

A �

Ttτ B

B �

Tt

τ CC �

AB

T

t

d

B

A t

BC

D

B

t

C

d

d

B

B

C

CA

A

A C

��

g g2TDγ �

Dgζ AB

AB �

Dgζ BC

BC �

Figure 2 Definition of geometrical parameters.


October 2001

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62

The validity range for the equations in Table 1 to Table 5 are as follows:

0.2 � � � 1.0

0.2 � � � 1.0

8 � � � 32

4 � � � 40

20� � � � 90�

sinθβ0.6�

� � � 1.0

Reference is made to section 2.13.2 if actual geometry is outside validity range.


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63

Table 1 Stress Concentration Factors for Simple Tubular T/Y JointsLoad type and fixityconditions

SCF equations Eqn. No. Shortchordcorrection

Chord saddle:

� �� 1.621.1 θsin0.52β31.11τγ ��

(1) F1

Chord crown:

� �� θsin3α0.25βτ0.65β52.65τγ 20.2��

(2) None

Brace saddle:

� �� 0.01α-2.71.10.10.52 θsin0.96β1.25β0.187ατγ1.3 ��(3) F1

Axial load-Chord ends fixed

Brace crown:

� �� 1.2α0.1τβ0.0450.011β4β0.12expγ3 21.2��

(4) None

Chord saddle:

(Eqn.(1)) � � � � � �20.5221 sin2θβ1βτ6α0.8C ��

(5) F2

Chord crown:

� �� sinθ3αCβτ0.65β52.65τγ 220.2

��(6) None

Brace saddle:(Eqn.(3)) F2

Axial load-General fixityconditions

Brace crown:� �� 1.2αCτβ0.0450.011ββ4exp0.12γ3 3

21.2�� (7) None

Chord crown:� � � �0.70.68β10.85 θsinγτ1.45β � (8) None

In-plane bending

Brace crown:� � � �� 1.16-0.06γ0.77β1.090.4 θsinγτ0.65β1 �

�(9) None

Chord saddle:

� �� 1.63 θsin1.05β1.7βτγ �(10) F3

Out-of-plane bending

Brace saddle:� � ��

�� 40.050.54 β0.08β0.470.99γτ (Eqn.(10)) (11) F3

Short chord correction factors (� < 12)� � � �2.5-1.160.232 αγ0.21-expγ0.02β0.56-β0.83-1F1 ��

� � � �2.5-1.380.042 αγ0.71-expγ0.03β0.97-β1.43-1F2 ��

� �1.8-0.890.161.8 αγ0.49-expγ0.55 β-1F3 �

where exp(x) = ex

Chord-end fixity parameterC1 = 2(C-0.5)C2 = C/2C3 = C/5C = chord end fixity parameter0.5 � C � 1.0, Typically C = 0.7


October 2001

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Table 2 Stress Concentration Factors for Simple X Tubular JointsLoad type and fixityconditions

SCF equation Eqn. no.

Chord saddle:

� � � �1.71.8 θsinβ1.10βτγ3.87 �

(12)

Chord crown:

� �� θsinβτ30.65β52.65τγ 20.2��

(13)

Brace saddle:

� � � �2.51.70.90.5 θsinβ1.09βτγ1.91 ��(14)

Axial load (balanced)

Brace crown:� �� 0.0450.011β4β0.12expγ3 21.2

�� (15)

In joints with short cords (� < 12) the saddle SCF can be reducedby the factor F1 (fixed chord ends) or F2 (pinned chord ends)where

� � � �2.5-1.160.232 αγ0.21-expγ0.02β0.56-β0.83-1F1 ��

� � � �2.5-1.380.042 αγ0.71-expγ0.03β0.97-β1.43-1F2 ��

Chord crown:(Eqn.(8))

In plane bending

Brace crown:(Eqn. (9))

Chord saddle:

� �� 1.64 θsin1.34β1.56βτγ �(16)

Brace saddle:� � ��

�� 40.050.54 β0.08β0.470.99γτ (Eqn.(16)) (17)

Out of plane bending(balanced)

In joints with short chords (� < 12) eqns. (16) and (17) can bereduced by the factor F3 where:

� �1.8-0.890.161.8 αγ0.49-expγβ0.55-1F3 �


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65

Load type and fixityconditions

SCF equation Eqn. no.

Chord saddle:� � ��

3β0.261 (Eqn. (5)) (18)

Chord crown:(Eqn. (6))Brace saddle� � ��

3β0.261 (Eqn. (3)) (19)

Brace crown:(Eqn.(7))

Axial load in one braceonly

In joints with short chords (� < 12) the saddle SCFs can be reducedby the factor F1 (fixed chord ends) or F2 (pinned chord ends)where:

� � � �2.5-1.160.232 αγ0.21-expγ0.02β0.56-β0.83-1F1 ��

� � � �2.5-1.380.042 αγ0.71-expγ0.03β0.97-β1.43-1F2 ��

Chord saddle:(Eqn. (10))

Brace saddle:(Eqn. (11))

Out-of-plane bending onone brace only:

In joints with short chords (� < 12) eqns. (10) and (11) can bereduced by the factor F3 where:

� �1.8-0.890.161.8 αγ0.49-expγβ0.55-1F3 �


October 2001

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66

Table 3 Stress Concentration Factors for Simple Tubular K Joints and Overlap K JointsLoad type and fixityconditions

SCF equation Eqn.no.

Shortchordcorrection

Chord:

� �

� �� ζ8ATANβ0.291.64ββ

sinθsinθ

sinθβ1.16β0.67γτ

0.380.30

min

max

0.30

min

max20.50.9

��

��

�

��

��

��

(20) None

Brace:

� � � � �� 0.70.140.25 θsinτβ1.571.971 (Eqn. (20))+

� � � �� 1.220.51.5

minmax1.8

τγβC

β4.2ζ14ATAN0.0840.131θθsin�

��

(21) None

Balanced axial load

Where:C = 0 for gap jointsC = 1 for the through braceC = 0.5 for the overlapping braceNote that �, �, � and the nominal stress relate to the braceunder considerationATAN is arctangent evaluated in radians

Chord crown:(Eqn. (8))(for overlaps exceeding 30% of contact length use1.2�(Eqn. (8)))

Gap joint brace crown:(Eqn. (9))

Unbalanced in planebending

Overlap joint brace crown:(Eqn. (9))�(0.9+0.4�) (22)

Chord saddle SCF adjacent to brace A:

(Eqn. (10))A � � � �� x0.8-expγβ0.081 0.5B (Eqn. (10))B

� � � �� x1.3-expβ2.05x0.8-expγβ0.081 0.5max

0.5A�

where A

A

βsinθζ

1x ��

(23) F4Unbalanced out-of-planebending

Brace A saddle SCF� ��

�� 40.050.54 β0.08β0.470.99γτ (Eqn. (23)) (24) F4

� �2.4-1.061.88 αγ0.16-expβ1.07-1F4 �

(Eqn. (10))A is the chord SCF adjacent to brace A as estimated from Eqn.(10).Note that the designation of braces A and B is not geometry dependent. It is nominated by the user.


DET NORSKE VERITAS

67

Table 4 Stress Concentration Factors for Simple Tubular K Joints and Overlap K JointsLoad type and fixityconditions

SCF equations Eqn.No.

Shortchordcorrection

Chord saddle:(Eqn. (5)) F1

Chord crown:(Eqn. (6)) -

Brace saddle:(Eqn.(3)) F1

Brace crown:(Eqn. (7)) -

Axial load on one braceonly

Note that all geometric parameters and the resulting SCF’srelate to the loaded brace.

Chord crown:(Eqn. (8))


In-plane-bending on onebrace only

Note that all geometric parameters and the resulting SCF’srelate to the loaded brace.

Chord saddle:

(Eqn. (10))A � � � �� x0.8-expγβ0.081 0.5B��

where A

A

βsinθζ

1x ��

(25) F3Out-of-plane bending onone brace only

Brace saddle:� ��

�� 40.050.54 β0.08β0.470.99γτ (Eqn. (25)) (26) F3

Short chord correction factors:

� � � �2.5-1.160.232 αγ0.21-expγ0.02β0.56-β0.83-1F1 ��

� �1.8-0.890.161.8 αγ0.49-expγβ0.55-1F3 �


October 2001

DET NORSKE VERITAS

68

Table 5 Stress Concentration Factors for Simple KT Tubular Joints and Overlap KT JointsLoad type SCF equation Eqn.

no.Chord:(Eqn. (20))Brace:(Eqn. (21))

Balanced axial load

For the diagonal braces A & C use � = �AB + �BC + �B

For the central brace, B, use � = maximum of �AB, �BC


In-plane bending

Brace crown:(Eqn. (9))Chord saddle SCF adjacent to diagonal brace A:(Eqn. (10))A

� � � �� AC0.5

CAB0.5

B x0.8-expγβ0.081x0.8-expγβ0.081

(Eqn (10))B � � � �� AB0.5maxAB

0.5A 1.3x-expβ2.050.8x-expγβ0.081

(Eqn (10))C � � � �� AC0.5maxAC

0.5A 1.3x-expβ2.050.8x-expγβ0.081��

where

A

AABAB β

θsinζ1x ��

� �

A

ABBCABAC β

θsinβζζ1x

��

��

(27)Unbalanced out-of-plane bending

Chord saddle SCF adjacent to central brace B:

(Eqn. (10))B � � � ��

1PAB

0.5A x0.8-expγβ0.081

� � � �� 2P

BC0.5

C x0.8-expγβ0.081

(Eqn. (10))A � � � �� AB0.5maxAB

0.5B x1.3-expβ2.05x0.8-expγβ0.081

(Eqn. (10))C � � � �� BC0.5maxBC

0.5B x1.3-expβ2.05x0.8-expγβ0.081��

where

B

BABAB β

θsinζ1x ��

B

BBCBC β

θsinζ1x ��

2

B

A1 β

βP ��

�

��

��

2

B

C2 β

βP ��

�

��

��

(28)

Out-of-plane bendingbrace SCFs

Out-of-plane bending brace SCFs are obtained directly from the adjacentchord SCFs using:

� � chord40.050.54 SCFβ0.08β0.470.99γτ ��

��

where SCFchord = (Eqn. (27)) or (Eqn. (28))

(29)


DET NORSKE VERITAS

69

Load type SCF equation Eqn.no.

Chord saddle:(Eqn. (5))


Brace saddle:(Eqn. (3))

Axial load on onebrace only


Out-of-plane bendingon one brace only

Chord SCF adjacent to diagonal brace A:

(Eqn. (10))A � � � �� AC0.5

CAB0.5

B x0.8-expγβ0.081x0.8-expγβ0.081 ��

where

A

AABAB β

θsinζ1x ��

� �

A

ABBCABAC β

θsinβζζ1x

��

��

(30)

Chord SCF adjacent to central brace B:

(Eqn. (10))B � � � ��

1PAB

0.5A x0.8-expγβ0.081

� � � �� 2PBC

0.5C x0.8-expγβ0.081�

where

B

BABAB β

θsinζ1x ��

B

BBCBC β

θsinζ1x ��

2

B

A1 β

βP ��

�

��

��

2

B

C2 β

βP ��

�

��

��

(31)

Out-of-plane braceSCFs

Out-of-plane brace SCFs are obtained directly from the adjacent chord SCFsusing:

� � chord40.050.54 SCFβ0.08β0.470.99γτ ��

��

(32)


October 2001

DET NORSKE VERITAS

70

APPENDIX 3 SCF’S FOR PENETRATIONS WITH REINFORCEMENTS

Stress concentration factors at holes in plates with inserted tubulars are given in Figure 1-Figure 14.

Stress concentration factors at holes in plates with ring reinforcement are given in Figure 16-Figure 19.

Stress concentration factors at holes in plates with double ring reinforcement given in Figure 20—Figure 23.

The SCFs in these figures may also be used for fatigue assessments of the welds. Stresses in the plate normal tothe weld , n�� and stresses parallel to the weld, t�� , in equation 2.6.4 may be derived from the stresses in

the plate. The total stress range, w�� , from equation 2.6.4 is then used together with the W3 curve to evaluatenumber of cycles until failure.


DET NORSKE VERITAS

71

H

tp

A A

tr

AA

r

tr

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

100

20

10

r/tp

50

Figure 1 SCF at hole with inserted tubular. Stress at outer surface of tubular, parallel withweld. H/tr = 2.


October 2001

72

72

H

tp

A A

tr

AA

r

tr

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

r/tp

100

50

10

20

.Figure 2 SCF at hole with inserted tubular. Stress at outer surface of tubular, parallel withweld. H/tr = 5.


DET NORSKE VERITAS

73

H

tp

A A

tr

AA

r

tr

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 3 SCF at hole with inserted tubular. Stress in plate, parallel with weld. H/tr = 2.


October 2001

74

74

H

tp

A A

tr

AA

r

tr

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

100

50

20

10

r/tp

Figure 4 SCF at hole with inserted tubular. Stress in plate, parallel with weld. H/tr = 5.


DET NORSKE VERITAS

75

H

tp

A A

tr

AA

r

tr

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 5 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 2


October 2001

76

76

H

tp

A A

tr

AA

r

tr

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10



DET NORSKE VERITAS

77

H

tp

A A

tr

AAr

tr

��1

For � see Table 1

0.9

1.0

1.1

1.2

1.3

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 7 SCF at hole with inserted tubular. Principal stress in plate. H/tr = 2


October 2001

78

78

Table 1 � = angle to principal stress. H/tr = 2tr/tp r/tp=10 r/tp=20 r/tp=50 r/tp=1000.0 90 90 90 90

0.5 72 80 86 88

1.0 56 63 75 82

1.5 50 54 64 73

2.0 46 50 57 66


DET NORSKE VERITAS

79

H

tp

A A

tr

AAr

tr

��1

For � see Table 2

0.9

1.0

1.1

1.2

1.3

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 8 SCF at hole with inserted tubular. Principal stress in plate. H/tr = 5


October 2001

80

80

Table 2 � = angle to principal stress. H/tr = 5tr/tp r/tp=10 r/tp=20 r/tp=50 r/tp=1000.0 90 90 90 900.5 66 72 80 851.0 54 58 65 721.5 49 52 56 622.0 46 48 52 56


DET NORSKE VERITAS

81

H

tp

A A

tr

AA

r

tr

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 9 SCF at hole with inserted tubular. Shear stress in plate. H/tr = 2


October 2001

82

82

H

tp

A A

tr

AA

r

tr

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

tr/tp

SCF

r/tp

100

50

20

10

Figure 10 SCF at hole with inserted tubular. Shear stress in plate. H/tr = 5


DET NORSKE VERITAS

83

H

tp

A A

tr

AA

r

tr

-0.10

-0.05

0.00

0.05

0.10

0.15

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

10

50

100

20

r/tp

r/tp

10

20

100

50

Figure 11 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 2.


October 2001

84

84

H

tp

A A

tr

AA

r

tr

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.5 1.0 1.5 2.0

tr/tp

SCF

10

100

50

20

r/tp



DET NORSKE VERITAS

85

R

B A AtR

tp

A A

Kg

3.0

3.1

3.2

3.3

3.4

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

K g

tR/tp

0.5

1.5

1.0

The following relation applies(a = throat-thickness): tR/tp a/tR 0.5 0.71 1.0 0.40 1.5 0.33

Figure 13 Kg at hole with ring reinforcement. Max stress concentration.


October 2001

86

86

R

B A AtR

tp

A A

Kg

1.5

2.0

2.5

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

SCF

tR/tp

0.5

1.5

1.0

The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0

Figure 14 SCF at hole with ring reinforcement. Stress at inner edge of ring.


DET NORSKE VERITAS

87

tRtp

A A

R

B A A

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.2 0.4 0.6 0.8B/R

SCF tR/tp

0.5

1.5

1.0


Figure 15 SCF at hole with ring reinforcement. Stress in plate, parallel with weld.


October 2001

88

88

tRtp

A A

R

B A A

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

SCF

tR/tp

0.5

1.5

1.0


Figure 16 SCF at hole with ring reinforcement. Shear stress in weld


DET NORSKE VERITAS

89

tRtp

A A

R

B A A

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.0 0.2 0.4 0.6 0.8B/R

SCF

0.5

1.5

1.0

tR/tp


Figure 17 SCF at hole with ring reinforcement. Stress in plate, normal to weld


October 2001

90

90

tRtp

A A

R

B A A

1.5

2.0

2.5

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

SCF

tR/tp

0.5

1.5

1.0


Figure 18 SCF at hole with double ring reinforcement. Stress at inner edge of ring.


DET NORSKE VERITAS

91

tRtp

A A

R

B A A

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

SCF

tR/tp

0.5

1.51.0


Figure 19 SCF at hole with double ring reinforcement. Stress in plate, parallel with weld


October 2001

92

92

tRtp

A A

R

B A A

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

B/R

SCF

tR/tp

0.5

1.5

1.0


Figure 20 SCF at hole with double ring reinforcement. Shear stress in weld.


DET NORSKE VERITAS

93

tRtp

A A

R

B A A

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8B/R

SCF 0.5

1.5

1.0

tR/tp


Figure 21 SCF at hole with double ring reinforcement. Stress in plate, normal to weld.


October 2001

DET NORSKE VERITAS

94

APPENDIX 4 COMMENTARYComm. 1.3 Methods for fatigue analysisImportant part of action historyThe contribution to fatigue damage for different regions of an Weibull distribution is shown in Figure 1 for a fatiguedamage equal 1.0 (and 0.5) for a 20-year period. The calculation is based on a Weibull long term stress rangedistribution with h = 1.0 (in the range that is typical for a semisubmersible and an S-N curve with slope m = 3.0 for N�107 for and m = 5.0 for N � 107 cycles (Typical S-N curve for air condition).

It is noted that the most important part of the long-term stress range is for actions having a probability of exceedance inthe range 10-3 to 10-1. This corresponds to logn = 5-7 in Figure 1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5 6 7 8 9log n

Rel

ativ

e fa

tigue

dam

age

Relative damage h = 1.0 and D = 1.0

Relative damage h = 1.0 and D = 0.5

Figure 1 Relative fatigue damage in Weibull distribution of stress ranges


DET NORSKE VERITAS

95

Comm. 2.3 S-N curvesSize effectThe size effect may be explained by a number of different parameters:� Thickness of plate – which is explained by a more severe notch with increasing plate thickness at the region where

the fatigue cracks are normally initiated.� Attachment length – which is explained by a more severe notch stress due to more flow of stress into a thick

attachment than a short.� Volume effect – which for surface defects can be explained by increased weld length and therefore increased

possibility for imperfections that can be initiated into fatigue cracks.

It might be added that some authors group all these 3 effects into one group of “thickness effect” or size effect. In thisRP, the thickness exponent is assumed to cover the first item in the list above and partly the second, although also anincreased attachment length reduces the S-N class as shown in Appendix 1 of this Recommended Practice. Examples ofthe third effect and how it can be accounted for in an actual design is explained in more detail in the following.Reference may also be made to /12/, /19/ and /18/ for more background and explanation of the thickness effect.

Test specimens used for fatigue testing are normally smaller than actual structural components used in structures. Thecorrespondence in S-N data depends on the stress distribution at the hot spot region. For traditional tubular joints thereis one local hot spot region, while at e. g. circumferential welds of TLP tethers there is a length significantly longer thanin the test specimens having the similar order of stress range. Crack growth is normally initiated from small defects atthe transition zone from weld to base material. The longer the weld, the larger is the probability of a large defect. Thus,a specimen having a long weld region is expected to have a shorter fatigue life than a short weld. This can be accountedfor in an actual design by probabilistic analysis of a series system, ref. e. g. “Methods of Structural Safety” ref. /21/.Weld length in a tether system is one example where such analysis should be considered to achieve a reliable fatiguedesign. A mooring line consisting of chains is another example where reliability methods may be used to properlyaccount for the size effect in addition to that prescribed in this document.

For threaded bolts, the stress concentration at the root of the threads increases with increasing diameter. Based onfatigue tests, it is recommended to use k = 0.40 which can be assumed to include size effects both due to the notchitself, and due to increased length of notch around circumference with increased diameter. The thickness exponent maybe less for rolled threads. Thus for purpose made bolts with large diameters, it may be recommendable to performtesting of some bolts to verify a fatigue capacity to be used for design. It should be remembered that the design S-N datais obtained as mean minus 2 standard deviation in a log S-log N diagram.

The design S-N curve with thickness effect included is given by:

Curve part (1), see Figure 2.

��

�

�

��

�

�� loglogaloglog 111 m

ttkmNref

Part (2) of the curve is established assuming continuity at N1=106 or 107 cycles depending on the S-N curve is given forseawater with cathodic protection or in air is given by

��

�

�

��

�

��

�

��

�� loglog1logaloglog 22

1

211

1

2 mt

tkmmm

Nmm

Nref

where 1a is for S-N curve without thickness effect included. log 1a is given in Table 2.3.1, 2.3.2 and 2.3.3.


October 2001

DET NORSKE VERITAS

96

10

100

1000

1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

Number of cycles

Stre

ss ra

nge

(MPa

)

2

1

Figure 2 Typical S-N curve with thickness effect included

S-N curvesThe relationship between S-N curves in this document and those given by IIW, ref. /30/, Eurocode 3, ref. /3/, for airenvironment is given in . It should be noted that the correspondence between S-N curves in this document IIW andEurocode 3 relates only to number of cycles less than 5*106.

Table 1 DNV notation in relation to Eurocode 3DNV

notationIIW and

Eurocode 3notation

B1 160B2 140C 125

C1 112C2 100D 90E 80F 71

F1 63F3 56G 50

W1 45W2 40W3 36T


DET NORSKE VERITAS

97

Comm. 2.8 Stress concentration factorsReference is made to “An Analytical study of Stress Concentration Effects in Multibrace Joints under CombinedLoading”, ref. /9/, for further background on this procedure of calculating a resulting hot spot stress from superpositionof stress components.

The formula for SCF at a tubular butt weld can be outlined based on theory for thin walled structures, ref. /25/.

Comm. 2.8.3 Tubular joints welded from one sideThe fatigue design of the root area of tubular joints welded from one side may be considered as follows:� Lack of penetration is hard to control by non-destructive examination and it is considered more difficult to detect

possible defects at a root area of a tubular joint welded from one side, than for a butt weld welded from one side.� For butt welds welded from one side the joint may be classified as F3. The defect size inherent in this curve is less

than 1-2 mm (This defect size may be evaluated by fracture mechanics calculations and the calculated value willdepend on plate thickness. A long defect should be considered here with the defect size measured in the thicknessdirection of the tubular). Defect sizes up to 5 mm may be present without being detected even with a detailedexamination of the root of a tubular joint. A factor for reduction of fatigue life due to a possible large root defect ina tubular joint compared to a butt weld may be evaluated based on fracture mechanics analysis.

� The stress field at the root may be derived from a finite element analysis. The crack growth may be assumed to benormal to the direction of the maximum principal stress. The fatigue life is first calculated for an initial defect sizecorresponding to that of the F3 curve: F(Life ai = 1 mm). Then the fatigue life is calculated for an initial defect sizecorresponding to that of a tubular joint welded from one side: F(Life ai = 5 mm). The fatigue life reduction factor,R, is obtained from equation .

� A modified S-N curve below F3 is calculated from equation . An S-N curve corresponding to this log a value (orbelow) may now be used for fatigue life analysis based on nominal stress at the root as calculated by a detailedfinite element analysis.

� Fatigue cracking from the root is harder to discover by in service inspection than crack growth from the toe.Therefore, an additional factor on fatigue life should be considered for crack growth from the root.

mm)1aF(Lifemm)5aF(Life

Ri

i

�

�

�

(1)

(R)log11.546alog �� (2)

The following simplified approach for fatigue life assessment of the weld root may be performed as an alternativeprocedure:� As noted above an additional factor on fatigue life should be considered for crack growth from the root.� Normally the stress on the outside of the brace at the hot spot is larger than at the root area. Hence it is considered

to be conservative to use the brace SCF for evaluation of fatigue life at the root. As an approximation the SCF forthe inside can be calculated as

2.0SCFSCF braceinside �� (3)

� The fatigue life for the root may now be calculated using the W3 curve.This procedure is applicalbe for simple tubular joints only.

Comm. 2.14 Simplified fatigue analysisWeibull distributed Stress Range and Bilinear S-N curvesWhen a bi-linear or two-slope S-N curve is used, the fatigue damage expression is

given by


October 2001

DET NORSKE VERITAS

98

ηqS

;hm

1γa

qqS

;h

m1Γ

aq

TνDh

12

2

mh

11

1

m

d0

21

��

�

�

��

�

�

��

��

�

��

��

�

��

��

��

�

��

��

�

��

(4)

where

S1 = Stress range for which change of slope of S-N curve occur

11 m ,a = S-N fatigue parameters for N < 107 cycles (air condition)

22 m ,a = S-N fatigue parameters for N > 107 cycles (air condition)

�( ) = Incomplete Gamma function, to be found in standard tables

�( ; ) = Complementary Incomplete Gamma function, to be found in standard tables

For definitions see also section 2.14.

Alternatively the damage may be calculated by a direct integration of damage below each part of the bilinear S-Ncurves:

dS(S)N

h),∆σ(S,fTvdS

(S)Nh),∆σ(S,fTv

D0

1

1 ∆σ

S 1

0d0S

0 2

0d0��

(5)

Where the density Weibull function is given by

��

�

�

��

�

�

��

��

��

�

h

0h

0

1h

0 h),q(∆Sexp

h),q(∆Shh),∆σf(S,

��

(6)

1/h0

00

))(ln(nh),q(∆

�

�

��

(7)

S-N curves for air condition is assumed here such that the crossing point of S-N curves is here at 107 cycles. The stressrange corresponding to this number of cycles is

1m1

71

1 10aS �

�

��

��

(8)

The left part of S-N curve is described by notation 1, while the right part is described by notation 2.

Short term Rayleigh distribution and linear S-N curveWhen the long term stress range distribution is defined through a short term Rayleigh distribution within each shortterm period for the different loading conditions, and a one-slope S-N curve is used, the fatigue criterion reads,

η)2m(2r)2mΓ(1

aTν

Dheadings allseastates all

1j1,i

m0ijij

d0 ��

(9)

where

rij = the relative number of stress cycles in short-term condition i, j


DET NORSKE VERITAS

99

�o = long-term average zero-crossing-frequency (Hz)

moij = zero spectral moment of stress response process

The Gamma function, )2mΓ(1� is equal to 1.33 for m = 3.0.

Short term Rayleigh distribution and bilinear S-N curveWhen a bi-linear or two-slope S-N curve is applied, the fatigue damage expression is given as,

��

�

�

��

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

� ��

��

2

0ij

02

2

m0ij

2

0ij

01

1

m0ijheadings all

seastates all

1j1,iijd0 2m2

S;

2m1γ

a

)2m(2

2m2S

;2

m1Γa

)2m(2rTνD

21

Comm. 2.13 Calculation of hot spot stress by finite element analysisThis procedure has been tested against known target values for a typical F detail, and a cut-out in a web for longitudinaltransfer, “Fatigue Assessment of Floating Production Vessels “, ref. /4/. Acceptable results were achieved using 8-nodeshell elements and 20 node volume elements with size equal to the thickness. However, this methodology is experiencebased, and caution is advisable when using it for details which differ from those for which it was calibrated.

Based on experience with use of different finite element programs, it is considered difficult to arrive at a firmcalculation procedure that can be applied in general for all type of details. It is therefore recommended that the analysismethod is tested against a well known detail, or that the fatigue detail should be modelled by a very fine element meshincluding the weld notch to determine a target for the analysis, prior to use for fatigue assessment.

Comm. 4 Improvement of fatigue life by fabricationReference is made to “Improvement in Fatigue Life of welded Joints Due to Grinding, Tig Dressing, Weld ShapeControl and Shot Peening”, ref. /16/, for effect of weld improvements on fatigue life. Reference is also made to “APIProvisions for SCF, S-N, and Size-Profile Effects”, ref. /22/, for effect of weld profiling on thickness effect. Referenceis made to “Fatigue of Welded Joints Peened Underwater”, ref. /13/, for fatigue of welded joints peened underwater.

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DNV-RP-C203: Fatigue Strength Analysis of Offshore … · recommended practice rp-c203 fatigue strength analysis of offshore steel structures october 2001 det norske veritas

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