No. 34.2
PLUS - EXTENDED FATIGUE ANALYSIS OF SHIP DETAILS
JUNE 2010
DET NORSKE VERITAS
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FOREWORD
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 and consultancyservices relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out researchin relation to these functions.
Classification Notes
Classification Notes are publications that give practical information on classification of ships and other objects. Examples of de-sign solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some componentsare given as interpretations of the more general rule requirements.
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The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note.
Main changes
This issue of CN 34.2 replaces the April 2009 issue.
—the CSR correction factor for corrosive environment should be used for CSR vessels with PLUS notation—a screening procedure for fatigue assessment of all frame positions, is also included—scope of low cycle fatigue is elaborated. (2.7.1).
More detailed guidance given for:—shell plating (2.3.1)—deck details (2.5.1)—stringer heels (2.4.1)
—ship specific details (2.6.1)—load calculation (3.4.1)—global model (5.2.1)
—screening procedure (2.2.1 and 5.7)
—shape of semi-nominal element mesh (8.5: new Table 8.7).
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Classification Notes - No. 34.2, June 2010
Page 3
CONTENTS
1.1.11.21.32.2.12.22.32.42.52.62.73.3.13.23.33.43.53.63.73.84.4.14.24.34.44.54.65.5.15.25.3
INTRODUCTION.................................................... 5Objective......................................................................5General.........................................................................5Symbols and abbreviations..........................................5SCOPE OF CLASS NOTATION PLUS................ 6General.........................................................................6Longitudinal stiffener-frame connections....................6Bottom and side shell plating......................................7Stringer heel and toe details.........................................7Deck openings and deck details...................................8Ship specific details.....................................................8Low cycle fatigue........................................................8PLUS ANALYSIS PROCEDURE.......................... 9PLUS analysis flowchart............................................9Fatigue analysis...........................................................9Stress analysis..............................................................9Load calculation...........................................................9Finite element analysis................................................9Corrosion additions......................................................9Effect of corrosive environment..................................9Longitudinal stiffener-frame connections....................9STRESS ANALYSIS OF STIFFENER-FRAME CONNECTIONS..................................... 11General.......................................................................11Long term distribution of stresses .............................11Stresses to be considered...........................................11Combination of stresses.............................................11Calculation of stress components..............................11Load calculation ........................................................11FINITE ELEMENT MODELLING
OF STIFFENER-FRAME CONNECTIONS....... 13General ......................................................................13Global model.............................................................13Semi-nominal stress model........................................13
5.45.55.65.76.6.16.26.36.47.8.8.18.28.38.48.59.9.19.29.39.49.59.69.79.89.99.10
Stress concentration models......................................14Loads.........................................................................16Stress read out from FE models................................17Screening procedure .................................................19DOCUMENTATION OF PLUS ANALYSIS...... 21FE-Models.................................................................21Stresses......................................................................21Fatigue calculations...................................................21Stress concentration factor analysis..........................21REFERENCES....................................................... 21APPENDIX A - STRESS CONCENTRATION FACTORS............................................................... 22General......................................................................22Establish stress concentration factors........................22Example of establishing stress concentration
factors........................................................................22Stress concentration factors for typical longitudinal end connection details...............................................25Semi-nominal finite element mesh
of stiffener-frame connections...................................33APPENDIX B - CALCULATION EXAMPLE: LONGITUDINAL STIFFENER FRAME
CONNECTION OF AN OIL TANKER............... 37Introduction...............................................................37Fatigue loads.............................................................37Global stress analysis................................................37Semi-nominal stress analysis....................................37Read out of semi-nominal stress...............................37Stress concentration factor........................................38Combination of stresses............................................38Long term stress distribution ....................................39Fatigue damage calculation.......................................39Total fatigue damage.................................................39
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1. Introduction
1.1 Objective
1.1.1
This Classification Note provides guidance on how to performand document analyses required for compliance with the classnotation PLUS as described in the DNV Rules Pt.3 Sec.1Ch.15 E. The class notation provides enhanced scope for fa-tigue strength and ensures that specific critical structural de-tails are adequately designed to meet specified fatiguerequirements.
1.3 Symbols and abbreviations
1.3.1
The following general symbols are used in this ClassificationNote:
Aft perpendicular Base lineCentreline
IACS Common Structural Rules for Bulk Carriers and Oil Tankers
HSHotspotGMMetacentre heightKrRoll radius of gyration
Dfull loadFatigue damage in fully loaded conditionDballastFatigue damage in ballast condition
Dnon-corrFatigue damage in non-corrosive environment DcorrFatigue damage in corrosive environment SCFStress concentration factor KGGeometric stress concentration factorLRule length of ship in m, see Rules Pt.3 Ch.1 Sec.1. TdDesign fatigue lifeTCEffective coating lifeTFatigue lifeTfullDraught in full load conditionTballDraught in ballast conditiont/2Stress read out position at distance half plate
thickness from hotspot
feEnvironmental reduction factor fmMean stress reduction factor hWeibull shape parameterhoBasic Weibull shape parameterhaAdditional shape factor depending on motion re-sponse period log( )10th logarithm mS-N fatigue parameter
S-N fatigue parameteraqWeibull scale parametervoLong-term average zero up-crossing frequency σeStress amplitude due to external pressureσiStress amplitude due to internal pressureσtTensional stress for mean stress reductionσcCompressive stress for mean stress reduction
σsemi-nomSemi-nominal stress amplitude, e.g. stress derived
from 50×50 mm model
Δσ0Combined local hotspot stress range before mean
stress correction
ΔσlCombined local hotspot stress rangeP1First principal stress directionP2Second principal stressσmMembrane stressσBBending stressσHSPrincipal hotspot stress amplitudeσt/2Principal stress amplitude at t/2 positionΓ( )Gamma function [-]γ( )Incomplete gamma function [-]S1Stress range for which change in SN slope occurs APBLCLCSR
1.2 General
1.2.1
The PLUS notation is an optional class notation mainly intend-ed for vessels operating in harsh areas and includes extendedscope of fatigue strength verification for hull structural details.The scope of PLUS notation require additional calculations tothose specified in the NAUTICUS (Newbuilding) and CSR. This Classification Note covers a description of the following:—————————
scope
procedures formodelling
structural analysisstress read outfatigue analysis
stress concentration factorsexample calculations
documentation of the analysis.
Calculations documenting compliance with requirements inthis section shall be submitted for verification.
The PLUS notation is primarily intended for tankers, gas carri-ers and container carriers of conventional design, but can alsobe applied to other types of vessel. Generally the vessels shallcomply with: class notation CSR or NAUTICUS (Newbuild-ing).
The fatigue strength evaluation shall be carried out based onthe target fatigue life and service area specified by the CSR orNAUTICUS (Newbuilding) notation.
The following details in the cargo area are to be considered inthe fatigue strength assessment in addition to those required forother class notations:
—longitudinal stiffener-frame connections located in the
bottom, inner bottom, side and inner side including con-nected web stiffener, cut-out and collar plate. (See illustra-tion in Fig. 2-2)
—deck plating including stress concentrations from open-ings, scallops, pipe penetrations and attachments
—bottom and side shell plating connection to frames and
stiffeners.
—stringer heels and toes.
—specified ship specific details as specified in section 2.6.The effect of low cycle fatigue is to be considered for detailssubjected to large stress variations during loading and unload-ing. Low cycle fatigue analysis shall be performed accordingto procedure given in Classification Note 30.7/1/.
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2. Scope of Class Notation PLUS
2.1 General
2.1.1
An overview of the different additional class notations used todocument structural compliance is illustrated in Fig.2-1.
Only calculations for stiffener-frame connections and low cy-cle fatigue needs to be performed if the vessel is to complywith both PLUS-notation and CSA-FLS or CSA-2 notation.Other requirements of the PLUS notation need not to be per-formed if compliance with the CSA notation is documentedand confirmed.
2.2 Longitudinal stiffener-frame connections
2.2.1
In general the fatigue analysis should be conducted for all stiff-ener-frame connections in the midship-, forward-, and aft-tank. The connections in bottom, inner bottom, side, inner sideand hopper tank should be assessed with finite element analy-sis according to section 5. Fig.2-2 illustrates the typicalhotspots at a stiffener-frame connection. The hotspots includelocations on the web-frame, stiffener lug and the web stiffener.The analyses should cover the entire cargo area of the selectedvessel. See Fig.2-3 for an overview.
The work scope should minimum include the following:
All types of stiffener-frame connections found in the cargotank area should be covered by the analysis. Every connectionin double side and bottom at one web-frame in the middle ofthe forward-, amidship- and aft-tank should be analysed ac-cording to the procedure described in this Classification Note.If any stiffener-frame connections at other web-frames differfrom the connections in the target web-frame then also theseconnections should be modelled into the target frame. The ob-jective is that all the different types of stiffener-frame connec-tions are covered by the analysis. See Fig.2-4.
The fatigue calculations should be performed for the mid-frame of:
a)Amidship cargo tankb)Aft cargo tank
c)Forward cargo tank.
A screening analysis should be performed in order to assess thefatigue capacity of the all the other frames in the forward-,amidship- and aft cargo tank. The screening procedure is de-scribed in section 5.7.
Scope2PLUS(Enhanced scope )FLS(fatigue)3CSA-FLS1CSR,Nauticus(Newbuilding)(Includes scope fromPLUS,Nauticus(Newbuilding)orCSR)4CSA-2(As CSA-FLS, but alsoyield, buckling and hullgirder capacity)Safety levelULS(yield andbuckling)(Mandatory ClassNotations for certainvessels)Figure 2-1Class notation overview
The PLUS notation require compliance with NAUTICUS (New-building) or CSR notation.
For the class notations NAUTICUS (Newbuilding) and CSRthis implies that all requirements are to be complied with anddocumented independent of PLUS.
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Figure 2-2Hot spots at stiffener-frame connections2.3 Bottom and side shell plating
2.3.1
The fatigue capacity of the bottom and side shell plating be-tween two web-frame positions in midship-, forward- and aft-tank should be assessed using a simplified fatigue analysis.Both the transverse stress at stiffener mid-length and the longi-tudinal stress at the plate-transverse frame intersection shouldbe assessed. It is sufficient to use simplified stress formulas forplate bending due to lateral pressure given in ClassificationNote 30.7 /1/.
The plate field should be subjected to internal and external rulepressure loads as given in Classification Note 30.7 /1/. The fa-tigue analysis should be based on relevant combination ofstress components and stress concentration factors accordingto procedures of Classification Note 30.7 /1/.
Aft hold analysis Midship analysis Fwd. hold analysis Figure 2-3
View of ship and location of details in ship
2.4 Stringer heel and toe details
Target web frameIf the other frames in the cargo hold has different details than on the analysis frame. Analysis should be conducted with these details on the analysis frame.Figure 2-4Frames in cargo tank
2.4.1
Fatigue calculations should be carried out for the stringers inthe midship area, forward and aft hold. The heel and toe of thestringers are normally the critical locations to be assessed. Thisis illustrated in Fig.2-5. The fatigue calculations should be per-formed using a fine mesh finite element model with appropri-ate txt mesh in order to capture the hotspot stress. Theprocedures for modelling and stress read-out from fine meshfinite element models are described in Classification Note 30.7/1/. The analysis is typically performed using a cargo holdmodel and a local fine mesh model together with the sub-mod-elling technique. The stringer model should be subjected toboth lateral pressure loads and global vertical and horizontalbending moments. The global moments may be applied to thecargo hold model as unit moments. The resulting hotspot stressshould be scaled such that the applied moment equal the globalrule moments.
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2.6 Ship specific details
2.6.1
For different ship types there are characteristic fatigue proneareas. Critical areas of attention should be included in the fa-tigue analysis for PLUS notation. Since these details may varyfrom vessel type to vessel type these ship specific detailsshould be discussed at an early stage for clarification. Detailsthat require fatigue analysis are:LPG carriers:
—lower and upper side brackets—dome opening and coaming. LNG membrane carriers: ————
upper hopper knuckle
longitudinal girders at transverse bulkheadsupper and lower chamfer knucklesdome opening and coaming.
Figure 2-5
Critical locations on stringers
In general a finite element analysis is required to verify the fa-tigue strength of these details. The procedures for modellingand stress read-out are described in Classification Note 30.7 /1/.2.7 Low cycle fatigue
2.7.1
Low cycle fatigue strength of highly stressed locations underrepeated cyclic static loads, mainly due to cargo loading andunloading, should be considered as significant yielding cancause cracks at hotspots even though the dynamic stress fromwave loading is low.
A procedure for calculating the combined damage due to lowcycle and high cycle fatigue is described in Classification Note30.7 /1/. The low cycle stress range due to loading and unload-ing is based on the use of a pseudo-elastic hot spot stress rangederived by use of a plasticity correction factor on the elasticstress range. The method enables use of standard hotspot SN-curve.
For compliance with the PLUS-notation the following loca-tions should be verified with respect to low cycle fatigue: —Web stiffener on top of inner bottom longitudinal and hop-per slope longitudinals when wide frame space is em-ployed.
—Web-frame hotspots at the stiffener-frame connections in
areas of high girder shear stress or where web stiffener isnot fitted on top of longitudinal flange.
—Heel and toe of horizontal stringer of transverse bulkhead
for frequent alternate loading anticipated.
—Inner bottom connection to transverse bulkhead for fre-quent alternate loading anticipated.
—Lower stool connection to inner bottom for a loading con-dition with one side tank empty and the other tank full.
2.5 Deck openings and deck details
2.5.1
Deck openings and deck details in the cargo area should be an-alysed with respect to fatigue. Normally it is sufficient to usestress concentration factors for deck details as given in Classi-fication Note 30.7. The details that should be included are:————
openings
pipe penetrationsattachmentsscallops.
The fatigue requirements for the deck plating will normally besatisfied provided that the target fatigue life is obtained with astress concentration factor KG = 3.0. Stress concentration mod-el should be made if KG of the target detail is not found inClassification Note 30.7.
The fatigue calculation is performed using the nominal stressdue to hull girder bending together with relevant stress concen-tration factor to obtain the hotspot stress. The nominal stresslevel may be established using simplified formulas given inClassification Note 30.7 /1/.
The control of the deck openings and deck details may have di-rect impact on the hull girder cross section, ref. Pt.3 Ch.1 Sec.5C305.
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3. PLUS Analysis Procedure
3.1 PLUS analysis flowchart
3.1.1
Stringer heel and toe Ship specific Deck details Fatigue loads, CN30.7 Shell Plating Stiffener-frame connections 3.3 Stress analysis
3.3.1
The long term stress ranges for fatigue calculations of PLUSdetails are in general to be calculated according to the proce-dure given in Classification Note 30.7 except for the stiffener-frame connections. The stress analysis procedure for the longi-tudinal stiffener-frame connections is described in section 3.8.
3.4 Load calculation
Plate bending CN30.7 Cargo hold model Global stress analysis (cargo hold model) Global stress CN30.7 3.4.1
The procedure for calculation of loads is given in Classifica-tion Note 30.7 /1/.
The following loads should be considered:
Location
Stiffener-frame connectionStringer
Deck openings and detailsShell plating
Hopper/chamfer knuckleWeb-frame bracketsDome openings
Inner bottom – bulkhead connection
Loads
Pressure
Pressure + global momentsGlobal moments
Pressure + global momentsPressurePressure
Global moments
Pressure + global moments
Fine mesh model (txt-mm mesh) SCF CN30.7 SCF CN30.7 Semi-nominal stress model (50x50mesh)SCF CN34.2 Hotspot stress Combination of stresses, CN30.7 Combination of stresses, CN34.23.5 Finite element analysis
3.5.1
Finite element models and analysis for all details included inthe scope of PLUS notation except the stiffener-frame connec-tions should be according to Classification Note 30.7 /1/. Theprocedure for modelling of longitudinal stiffener-frame con-nections is given in section 5.
Long term distribution CN30.7 Long term distribution CN34.2Simplified fatigue damage CN30.7 3.6 Corrosion additions
Figure 3-1
PLUS Analysis flowchart
3.6.1
Net scantlings as defined by NAUTICUS (Newbuilding) orCSR-notation, whichever is relevant, shall be used.
3.2 Fatigue analysis
3.2.1
The fatigue life of details covered by the scope of PLUS nota-tion as described in section 2 is to be calculated according tothe procedure given in Classification Note 30.7. Fig.3-1 showsthe analysis flow of all details included in the PLUS notation.In order to obtain the class notation PLUS all structural detailsdescribed in the scope should comply with a fatigue damageratio equal or below 1.0 for the specified design fatigue life.
3.7 Effect of corrosive environment
3.7.1
Joints that are located in combined corrosive and non-corro-sive environment should be analysed according to proceduresgive in Classification Note 30.7 /1/. For vessels with CSR-no-tation the effect of corrosive environment could be accountedfor by use of the stress correction factor fsn = 1.06.
3.8 Longitudinal stiffener-frame connections
3.8.1
The analysis of the longitudinal stiffener-frame connectionsfollows a different procedure then the other details included inthe PLUS notation. The flowchart in Fig.3-2 illustrates the dif-ferent steps of the procedure for stiffener-frame connections.
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Fatigue analysis of stiffener-frame connection Stress concentration factor analysis Fatigue loads, CN30.7 Stress concentration model: 50x50 mm mesh model, section 5.4 Global stress analysis, section 5.2 Stress concentration model: t x t mesh model, section 5.4 Semi-nominal stress analysis, section 5.3 Stress concentration factor, chapter 7 Combination of stresses, section 4.4 & CN30.7 Long term stress distribution, section 4.2 & CN30.7 Fatigue damage calculations, CN30.7 Figure 3-2
Analysis flowchart for stiffener-frame connections
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4. Stress Analysis of Stiffener-Frame Connections
4.1 General
4.1.1
The stress analysis differs slightly from Classification Note30.7 on two items. The first item is the combination of stressesfrom external and internal loads which has been revised into asimpler format. Secondly only one Weibull shape parameter inthe long term distribution of stresses is used. The rest of thestress analysis procedure uses the same principles as Classifi-cation Note 30.7. The items which differ are presented below.
counting for the long- term sailing routes of the shipconsidering the average wave climate the vessel will beexposed to during the lifetime. Assuming world wideoperation the factor may be taken as 0.8. For shuttletankers and vessels that frequently operates in theNorth Atlantic or in other harsh environments, fe =1.0should be used. The choice of the environmental valueshould be based on the service area specified by theclass notation NAUTICUS (Newbuilding) or CSR=Reduction factor on derived combined stress range ac-counting for the effect of mean stresses, see CN30.7=total local stress amplitude due to the dynamic seapressure loads (tension = positive)
=total local stress amplitude due to internal pressureloads (tension = positive).
fm
4.2 Long term distribution of stresses
4.2.1
The Weibull shape parameter shall for all longitudinal stiffen-er-frame connections be taken as:
h = ho + hawhere: hoha
=basic shape parameter=2.21 - 0.54 log10(L)=0.05
For all longitudinals
σeσi
4.5 Calculation of stress components
4.5.1
The calculation of the stress range is performed by finite ele-ment analysis of a semi-nominal 50×50 mm mesh size model.Hotspot stress range for fatigue calculations is found by multi-plying the semi-nominal stress with stress concentration fac-tors. Chapter 5 describes the procedure for finite elementanalysis.
4.3 Stresses to be considered
4.3.1
The local dynamic stress range is the only stress to consider forfatigue calculation of longitudinal stiffener-frame connections.Global dynamic stress components are considered small andcan be neglected. Static stress ranges are used for calculationof the mean stress reduction factor.
4.6 Load calculation
4.6.1
For calculation of longitudinal stiffener-frame connections isonly external and internal pressure loads considered. The for-mulas for calculating the pressure loads are defined by Classi-fication Note 30.7.
4.6.2
Fatigue analyses should be carried out for representative load-ing conditions. The following two loading conditions are nor-mally sufficient for documentation for analysis of oil tankers,container vessels and gas carriers.
—normal full load departure condition, Tfull—normal ballast arrival condition, Tball.
Some vessels may require other representative loading condi-tions in addition to these two conditions.
4.6.3
For vessels intended normal world wide trading, the fraction ofdesign life in each loading condition is to be taken as the valuesin Table 4-1.
Bulk Carrierslarger thanPanamax
-0.350.250.25
Bulk carriersPanamax
-0.3500.5
ContainerVessel0.650.20--
4.4 Combination of stresses
4.4.1
For each loading condition is a combined stress range of simul-taneous internal and external stress components to be calculat-ed. The combined local stress range is taken as a linearcombination given as:
⎧σe+0.6σi
Δσl=2*fefm*max⎨
⎩0.6σe+σi
Wherefe
=Reduction factor on derived combined stress range ac-Table 4-1 Fraction of time in each loading condition
OilGas
Vessel typeTankersCarriersLoaded conditionBallast conditionAlternate conditionHomogenous condition
0.4250.425--0.450.40--
4.6.4
The six pressure load cases that should be analysed by finite el-ement analysis are listed below:1.2.3.4.
External pressureInternal pressureExternal pressureInternal pressure
Full load conditionFull load conditionBallast conditionBallast condition
5.6.Static pressureStatic pressureFull load conditionBallast condition
The loads are pressures given at 10-4 probability level. Globalbending moments can be disregarded. The magnitude of theloads is given in Classification Note 30.7. See Fig.4-1andFig.4-2 for illustration.
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Figure 4-1
Distribution of pressure amplitudes for tankers in the fully loaded condition
Figure 4-2
Distribution of pressure amplitudes for tankers in ballast condition
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5. Finite Element Modelling of Stiffener-Frame Connections
5.1 General
5.1.1
This section applies to the longitudinal stiffener-frame connec-tion details. A finite element analysis with a semi-nominalstress model (50×50 mm mesh) is required for stress calcula-tions of the stiffener-frame connections. For all the other de-tails reference is made to Classification Note 30.7 for guidanceon the finite element modelling.
Normally, a ½ + 1 + ½ cargo tank model is sufficient to repre-sent the behaviour of the ship structure. Cargo tank modelsshould be made for analysis of the forward-, amidship-, andaft-tank. The cargo tank models should take into account thechange in hull shape at forward and aft part of the vessel.Fig.5-1 shows a typical amidship cargo tank model of a VLCC.The shell plating is not shown in the figure.
The cargo-tank model is equivalent with the model that is usedfor NAUTICUS (Newbuilding) or CSR notation. This impliesthat net scantlings are to be applied according to DNV rules orCSR rules respectively. Element types to be used:Quad elements:4 or 8 nodeTriangular elements:3 or 6 nodeBeam elements:2 or 3 node.
5.2 Global model
5.2.1
The purpose of the global model is to obtain a description ofthe global stress distribution in the hull. The cargo tank modelshould be modelled according to Classification Note 31.3 /2/.
Figure 5-1
Cargo tank FE-Model
The cargo-hold model should be analysed using the load casesgiven in section 4.6.1. These loads are external and internalpressure loads which means that no inertia forces or globalbending moments need to be analysed. The boundary condi-tions to be used are given in Classification Note 31.3.
models are shown in Fig.5-2 and Fig.5-3.The element types to be used are:
Quad elements:8 nodeTriangular elements:6 nodeBeam elements:3 node.
The semi-nominal stress model should be included in the cargotank model or sub-modelling should be used.
The slot geometry should be modelled as described in section8.5 and Fig.5-4. It is important that the area around all hotspotlocations is modelled with 50 mm size elements. In caseswhere it is impossible to create square 50 mm elements an as-pect ratio of 4 should not be exceeded. If elements differentfrom 50×50 mm size are needed these elements should prefer-ably be placed away from the hotspots i.e. at mid-span of cut-out opening. Away from the hotspots the mesh can graduallybecome coarser. The rounded corners of the slot should bemodelled as “square” elements.
Eccentric lugs are not to be modelled as eccentric but as in-plane shell elements, and the plate thickness should not be in-creased to account for the overlapping plates. The effect of ec-centric lug induced bending stresses will be captured by thestress concentration factors. The cut-out should be modelled as
5.3 Semi-nominal stress model
5.3.1
For calculation of the stress level at the longitudinal stiffener-frame connections a semi-nominal stress finite element modelshould be made. The purpose of the semi-nominal model is tocapture the local geometric stress flow and effect of cut-outs,web frame-toes and tripping brackets. The model also capturesmore accurately the shear stress distribution from longitudinalstiffeners to web frame.
The stress results are used together with stress concentrationfactors to obtain the hotspot stress range for use in fatigue cal-culation.
The model should have approximately 50 mm elements at thecritical hotspots for each longitudinal stiffener-frame connec-tion in side, inner side, bottom, inner bottom and hopper tank.The longitudinal extent of the model should be at least oneframe spacing on each side of the target frame. Examples of
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at is on drawings with correct width and height. As a conse-quence will the distance from the longitudinal top flange tocut-out edge increase with half the thickness of top flange. Thestiffener is idealized with plate elements in the centre of the ac-tual stiffener.
Guidance on meshing of the slot geometry is given for all con-nection types in section 8.5. It is important that the finite ele-ment mesh is similar in order to ensure correct hotspot stress.The loads are to be the same pressure loads as applied to thecargo tank model specified in section 4.6. If a sub-modellinganalysis is to be used, the applied loads will also include eitherprescribed displacements or prescribed forces/stresses.
5.3.2
All types of stiffener-frame connections in the cargo areashould be analysed using semi-nominal models. If the mid-tank target web-frame does not include all types of connectionsthen the remaining should be included in another model basedon the mid-tank web-frame model. This should also be donefor all connections in the forward and aft tank. Since a vesseldoes not have parallel body in the forward and aft tank areasome simplification will be necessary. The remaining framesof the cargo tanks should be assessed based on a screening pro-cedure described in section 5.7.
Figure 5-2
FE-model with 50 mm mesh, whole model
Figure 5-3
FE-model with 50 mm mesh, hopper tank
5.4 Stress concentration models
5.4.1
If the design of a longitudinal stiffener-frame connections isnot found among the typical designs listed in section 8.4 astress concentration model should be made in order to establishthe stress concentration factor of that particular design. Thestress concentration models should be modelled according tothe procedure given in this section. Section 8.2 describes howthe stress concentration factors are calculated while section 6.4lists requirements to documentation.
5.4.2
Two models are needed if additional stress concentration fac-tors are to be made:
—50×50 mesh model: This model shall be used to predict the
semi-nominal stress.
—t×t mesh model: This model shall be used to predict the
hotspot stress.The stress concentration factor will be the stress ratio betweenthe models. The models are made to simulate the behaviour ofdouble side and double bottom. The models should have a ver-tical extent of 3 stiffeners, i.e. 4 stiffener spacing, and the lon-gitudinal extent should be ½ frame spacing in both forward andaft direction. Two typical models are shown in Fig.5-5 andFig.5-6. No cut-outs for manholes should be included in thestress concentration models. Both models should include thetypical hotspots for the target detail. Fig.2-2 shows typical
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Figure 5-4Slot geometry with stress read out points
Classification Notes - No. 34.2, June 2010
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hotspots to be assessed.
The element types to be used are:
Quad elements:8 nodeTriangular elements:6 nodeBeam elements:3 node.
Figure 5-5
FE-Model with 50 mm mesh, SCF analysis
Figure 5-6
FE-Model with t×t mesh, SCF analysis
For the 50×50 mm mesh model, the mesh density in the area ofthe web frame slots, including web stiffeners, is to be approx-imately 50×50 mm but adjusted to fit the slot geometry. Out-side this area the mesh density may be increased to reduce thesize of the model. The element aspect ratio should however notexceed 4. Smooth corners are to be modelled as sharp cornersand the eccentricity of the stiffener lug is to be ignored. An ex-ample of a detail is shown in Fig.5-8.
For the t×t mesh model the mesh density in the area of the webframe slots, including web stiffeners, is to be approximatelythe plate thickness. The mesh with plate thickness size shouldextend at least four elements in all directions at all relevanthotspots. Outside this area the mesh density may be increasedto reduce the size of the model. The element aspect ratio shouldhowever not exceed 4. The eccentricity of the stiffener lug is tobe included in the model and modelled according to Fig.5-9.Fig.5-7 shows an example of a stiffener lug detail modelledwith t×t mesh.
Figure 5-7
Stiffener and lug details – with web stiffener on top, t×t mesh
Figure 5-8
Stiffener and lug details – with web stiffener on top, 50×50 mesh
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Classification Notes - No. 34.2, June 2010Page 16
Three load effects are to be modelled in both models. LC1:LC2:LC3:
External pressureShear stressAxial load
Each load effect will result in a stress concentration factor. Inorder to combine the stress concentration factors into onestress concentration factor, weighting of the different load ef-fects should be used. The weighting is to be conducted by scal-ing the applied load according to the following criteria:LC1:LC2:
Figure 5-9
Modelling of eccentric collar plate
LC3:
External pressure, nominal shear stress in the middle of the stiffener web of 100 MPa.
Shear stress, nominal stress in the middle of the web frame of 100 MPa.
Axial stress, nominal stress in the middle of the web frame of 100 MPa.
5.5 Loads
The procedure for calculation of loads given in ClassificationNote 30.7 /1/ should be used for both DNV NAUTICUS (New-building) and CSR classed vessels.
The applied pressure and prescribed displacements should beto obtain the nominal stress criteria in the areas indicated inFig.5-10.
The different load effects and boundary conditions are shownin Fig.5-11 through Fig.5-13. The forward and aft part of thefinite element model should have symmetry condition describ-ing the behaviour in a double side or double bottom.
LC 2 and LC3LC1 Figure 5-10Nominal stress criteriaDET NORSKE VERITAS
Classification Notes - No. 34.2, June 2010
Page 17
membrane stress at the considered hotspot location.
Fixation at top The stress read point on the semi-nominal model is to be at thehotspot node location. Among all the elements that have a re-sult at the considered hotspot node it is the element result withmaximum principal stress value that should be used for dam-age calculation. No averaging of nodal stresses is allowed. SeeFig.5-4, Fig.5-14 and Fig.5-15 for illustration. If necessary themembrane stress should be calculated using the surface stress-es at upper and lower surfaces.
Fixation at bottom Figure 5-11
Load application and boundary conditions for LC1, externalpressure
Stress read out point at hotspot. Prescribed displacement transverse direction Zero displacement in vertical direction. Figure 5-14
Example of stress read out point from 50×50 mm mesh model
Fixation at bottom Max among values atHS location = 440 MPa Hotspot locationFigure 5-12
Load application and boundary conditions for LC2, shear stress
Prescribed displacement Vertical direction Fixation at bottom Figure 5-15
Example of maximum principal membrane stress value amongadjacent elements
Figure 5-13
Load application and boundary conditions for LC3, axial stress
5.6 Stress read out from FE models
5.6.1
The maximum principal element stress within ±45º of the nor-mal to the weld should be used for the analysis. As a conserv-ative approach the absolute maximum principal stress could beused regardless of direction to the weld.
5.6.2
The semi-nominal stress should be the maximum principal
5.6.3
The maximum semi-nominal stress value for a certain hotspotnode may be found at different elements among the variousload conditions. The semi-nominal stress values should notnecessarily be taken from the same element in all load condi-tions. For a certain hotspot the result values should be found atthe same node position but they might result from various ele-ments connected to that node.
5.6.4
The stress read out points in the stress concentration model isto be at a distance t/2 from the hotspot. The principal elementstresses at t/2 should be multiplied with a factor 1.12 to calcu-late the hotspot stress. This is one of the two stress extrapola-tion procedures given in Classification Note 30.7. See Fig.5-16and Fig.5-17 for illustration.
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Classification Notes - No. 34.2, June 2010Page 18
—Perform stress read out of both first and second principal
stress on upper and lower surface at the same node for allthree load cases.
—For a certain load case locate the largest principal stress
among the two principal directions (P1 or P2) for both up-per and lower surface.
—To decide on which surface to use calculate the sum of the
three load cases for both upper and lower surface. The sur-face with the largest total stress should be used for calcu-lation of the SCF.
—The SCF is calculated according to the expression in sec-tion 8.2.2.
Stress read out point t/2 from hotspot. Figure 5-16
Example of stress read out point from t×t mesh model
HS103 5.6.5
When extracting stress results from the stress concentrationmodel there could for a given hotspot be many possible t/2-nodes. The maximum principal stress value at position t/2away from the hotspot location should be used as the relevanthotspot stress. All t/2-positions will have to be assessed withregard to stress level in combination with principal stress di-rection in order to locate the maximum relevant stress value.See Fig.5-17 for illustration.
5.6.6
The maximum principal stress value at t/2-position may occurat different positions for the three considered load cases. De-spite possibly different location of maximum stress locationthe stress read out node in the stress concentration modelshould for a given hotspot remain the same for all three loadcases: axial, shear and pressure load. The node position givingthe absolute maximum value among all three load cases shouldbe used when extracting stress for all three load cases. Notethat both upper and lower element surface should be checkedin order to find the maximum principal stress.
5.6.7
At the stress read out node the finite element model will reporta result for both upper and lower surface and also principalstress in two directions. The principal stress direction that iswithin 45 degrees to the weld normal should be used as rele-vant hotspot stress. If both principal stresses are both at 45 de-grees to the weld normal one should choose the maximum ofthe two directions. Both upper and lower surface stress shouldbe reported for all three load cases. The surface resulting in thelargest total stress when summing up the contributions fromthe load cases should be used as basis for calculation of stressconcentration factor.
5.6.8
For a specific hotspot location the stress read out procedure forthe stress concentration model can be summarized as follows:—Locate all possible t/2-nodes with principal stress direc-tion within 45 degrees to weld normal (t/2 nodes: nodeswith a distance of t/2 from the hotspot)
—Find the t/2-node with the largest principal surface stress
among all load cases
t/2 result value positions. Note that for each t/2 position two different element results are possible. In addition should upper and lower surface be considered and both principal directions. For the two indicated positions in theory totally 16 stress values will have to be checked. Figure 5-17Possible stress read out nodes at t/2 position
5.6.9
In the stress concentration model is the collar plate modelledwith eccentricity. In the area with overlapping collar plate andweb plate is the stress normally reduced due to the increase ef-fective plate thickness. Some hotspots are located on theboundary between web plate and collar plate. For these hotspotthe stress results in the overlapping area are not be considered.These stress values are assumed not to give rise to fatiguecrack growth. Fig.5-18 illustrates the overlapping area. 5.6.10
Example of relevant elements to consider for identification ofpossibly maximum principal stress values at t/2 position areshown in Fig.5-18 for the hotspots of detail type T201. For thehotspots #101, #107, #202, #206, #207 and #208 is the markedelement the only relevant to consider regarding t/2-stress val-ues. For hotspot #104, #105 and #106 which are located at theslit opening edge, several element along the edge needs to beconsidered marked with arrows on Fig.5-18.
Hotspot #102, #103, #204 and #205 are located adjacent to thearea where the lug plate and the web-plate are overlappingeach other. Elements that are inside this overlapping area willnot be necessary to consider when locating the relevant t/2-stress result. Normally these elements will have smaller stressvalues and stresses in this area will not contribute to crackgrowth in real structures.
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Classification Notes - No. 34.2, June 2010
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5.6.11
The hotspots on the edge of the slit opening i.e. hotspot #104,#105 and #106 are located in base material. Stress read out onhotspots in base material should be performed at the hotspot.No extrapolation using t/2 stress values should be performedand stress results on the opening edge should be used.
The use of dummy beam elements at slit opening edge is notallowed. It is found that significant bending may occur at theslit opening hotspots. Since the dummy beam element does notcapture bending stress across the plate thickness they are notallowed to use.
Note that the maximum stress position along the slit openingmost likely will vary for the various load cases. The positionwith the largest value among the load cases should be used forstress read out for all three load cases.
Figure 5-18
Elements to consider in stress read out
HS104Figure 5-19Possible stress read out nodes at slit opening edge5.7 Screening procedure
The below screening procedure should be used to assess the fa-tigue capacity of the web-frames that are not modelled using a50×50 mm element mesh. The screening should be based onthe nominal stress level of the cargo hold model. The screeninganalysis should follow the following steps:
1)Establish a scaling factor for each stiffener-frame connec-tion in each load case. The scaling factors should be basedon maximum element average principal stress from thecargo hold model at the reference connection and at thetarget connection. The web-frame that has been modelledwith 50×50 mm element mesh is defined as the referenceweb-frame. The scaling factor, fs, is defined as the ratiobetween the average value of the absolute principal stresslevel of four neighbouring elements at the relevant
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Classification Notes - No. 34.2, June 2010Page 20
stiffener-frame connection in the target frame and the ref-erence frame, figure 5-20:
⎡(σp1+σp2+σp3+σp4)⎤⎢⎥
4⎢⎥⎣⎦TARGET_CONNECTION
fS=
⎡(σp1+σp2+σp3+σp4)⎤⎢⎥4⎢⎥⎣⎦REFERENCE_CONNECTION
2)Establish hotspot stress at target stiffener-frame connec-tion by multiplying the scaling factor with the hotspot
stress of the relevant hotspot location at the reference stiff-ener-frame connection. The reference hotspot stress is es-tablished by use of the semi-nominal model and stressconcentration factors according to section 5.3 and 8.4.3)Fatigue damage is calculated for the relevant hotspot loca-tion at the target stiffener-frame connection. 4)The above procedure is repeated for all hotspots at all stiff-ener-frame connections in all web-frames in the forward-,aft- and amidship cargo-hold models.The above screening procedure is only applicable when com-paring similar connections in the target and the reference web-
frame. Since the 50×50 mm mesh is similar for many differentconnections it will be possible to use the screening procedurefor a number of different connections even if the two connec-tions in the target and the reference web-frame are somewhatdifferent.
Note that when different connections having similar 50×50mm mesh are compared it is important to account for the cor-rect SCF giving the relevant reference hotspot stress. If the connections in the target and reference web-frame wouldhave different 50×50 mm mesh the screening procedure shouldbe used with care. In such case, the 50×50 mm element meshfor the reference connection may be modified to reflect the ge-ometry of the target connection.
Stiffener-frame connection σ1 σ2σ3 σ4Figure 5-20Neighbouring elements for screening average stressDET NORSKE VERITAS
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6. Documentation of PLUS Analysis
6.1 FE-Models
6.1.1
All finite element models should be documented with plotsclearly showing the mesh at the various details. The model ex-tension and a thorough description of the applied loads andboundary conditions should be documented. Element typesshould be reported. A description of the analysis flowchartshould be included as documentation for to understand theanalysis flow.
6.4 Stress concentration factor analysis
6.4.1
Analysis of additional stress concentration factors should bethoroughly documented. A detailed description of the longitu-dinal stiffener-frame connection geometry is to be provided to-gether with a description and plots of both the t×t-model andthe 50×50 mesh finite element models. The applied loads andboundary condition should also be documented, and plotsclearly showing the element mesh around the stiffener-frameconnection should be provided. The nominal stress level andthe hotspot stress should be documented with plots for all load-cases in both models. The stresses used in calculation of thestress concentration factor are to be reported together with theresulting stress concentration factor.
6.2 Stresses
6.2.1
The semi-nominal stress in the web frame should be docu-mented with stress plots showing clearly the stress distributionat all stiffeners. For validation of the predicted fatigue damag-es all stress values for all locations should be reported in tableformats.
7. References
1)Det Norske Veritas, Classification Note no. 30.7 Fatigue
assessment of ship structures, Høvik, October 20082)Det Norske Veritas, Classification Note no. 31.3 Strength
analysis of hull structures in tankers, Høvik, January 19993)Det Norske Veritas, Rules for classification of ships Part 8
Chapter 1, Common structural rules for double hull oiltankers with length 150 meters and above, Høvik, January2006.4)Det Norske Veritas, Finite element analysis of large scale
fatigue test of stiffener web frame connections, DNV Re-port No. 2007-19-09, T. Lindemark, November 20075)Lotsberg, Inge (et.al) Fatigue Caoacity of Stiffener to Web
Frame Connections, OMAE2009-79061, Honolulu, Ha-waii, USA, 31 May-5 June 2009.
6.3 Fatigue calculations
6.3.1
The fatigue calculations should be reported including the fol-lowing items:———————
choice of SN-Curves
fraction of time in each loading condition
fraction of time in non-corrosive/corrosive environmentWeibull shape factor used in the calculationsnumber of stress cycles
mean stress correction factors
fatigue damages for each loading condition in non-corro-sive/corrosive environment
—total fatigue damage or fatigue life prediction—stress concentration factors.
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Classification Notes - No. 34.2, June 2010Page 22
8. Appendix A - Stress Concentration Factors
8.1 General
8.1.1
This section describes the procedure of how to establish stressconcentration factors for longitudinal stiffener-frame connec-tion details. Section 8.4 lists stress concentration factors for thecritical hotspots of typical stiffener-frame connections. If aparticular detail is not listed among the typical ones in section8.4 then the user should follow the procedure in section 8.2 forcalculating the stress concentration factors.
t/2σ2
σm,1σm,2
maximum second principal element stress at t/2 po-sition
=semi-nominal principal membrane element stress at hotspot node
semi-nominal principal membrane element stress at =hotspot node=
The checked hotspots should normally include the hotspotsmarked in Fig.5-4.
8.2.3
The stress concentration factor for hotspot #102 and #103 seeFig.2-2, should be based on effective hotspot stress accordingto the expression below:
txt−mesh⎛LC3⎞HSHS
maxσorσ⎜∑Upper⎟Effective,1Effective,2LC1⎜⎟max⎜LC3
⎟txt−mesh
HSHS
⎜maxσorσLower⎟⎜∑⎟Effective,1Effective,2LC1⎝⎠KG=50x50−mesh
8.2 Establish stress concentration factors
8.2.1
In order to calculate the stress concentration factor a semi-nominal model with 50×50mm mesh and a stress concentra-tion model with t×t-mesh should be made. The finite elementmodelling and analysis should be performed according to theprocedure described in section 5.
8.2.2
When extracting stress results the maximum element principalstresses should be used and not the node averaged stresses. Thestress read out points should be located:
—At t/2 from the intersection line in the t×t-mesh model, see
Fig.5-17.
—At the node at hotspot in the 50×50mm mesh model, see
Fig.5-14.Note that the stress at t/2 should be multiplied with an extrap-olation factor of 1.12 to find the hotspot stress. See Classifica-tion Note 30.7 /1/ for details on extrapolation procedures. The maximum principal stress within ±45º of the normal to theweld should be used for the analysis. This requirement will inmost cases decide whether first or second principal stressshould be used.
For some hotspots the position of maximum element principalstress could vary among the three load cases. Note that thestress read out position for a given hotspot should be the samefor all load cases. The position giving the maximum stress val-ue among all load cases should be used for stress read out in allload cases.
The SCFs are calculated as the ratio of the principal stressesbetween the semi-nominal model and the fine mesh model.The sum of absolute principal stresses at read out position is tobe used for both models as described in the formula:
∑maxσLC1
LC3
m,1
orσm,2
The effective hotspot stress reduces the bending component ofthe surface stress with a factor of 0.6. Effective stress is calcu-lated according the following expression:
σEffective_HS=σm,HS+0.60σB,HS
σm,HSσB,HS
==
membrane stressbending stress
8.3 Example of establishing stress concentration factors
8.3.1
This example illustrates how to establish stress concentrationfactors for a T-shaped longitudinal through a slot with lug con-nection. The example is based on finite element analysis as de-scribed in section 5.4 and shows how to weight the differentload cases and stresses, and how to establish the stress concen-tration factors.
The stresses from the finite element analysis are found in Table8-1. The magnitude of the sum of the stresses in the t×t-meshmodel is used to predict the criticality of the hotspots. The crit-ical hotspots will vary from detail to detail dependent on thedifferent detailed design.
The weighted stress concentration factors are shown in Table8-1. The weighted stress concentration factors are establishedbased on the columns marked with “sum”, which is basicallythe sum of the different load cases as illustrated in the formulaabove. The weighted stress concentration factors should beused in the fatigue calculations.
8.3.2 Flowchart
The below flowchart shows the main steps of the procedure tobe followed when establishing a stress concentration factor,reference is given to the indicated sections for detailed guid-ance.
⎛⎞HStxt−mesh⎜∑maxσ1HSorσ2Upper⎟LC1⎟max⎜⎜LC3⎟
HSHStxt−mesh
⎜Lower⎟⎜∑maxσ1orσ2⎟LC1⎝⎠KG=50x50−mesh
LC3
∑maxσLC1
1
LC3
m,1
orσm,2
σHS=σ1t/2⋅1.12=hotspot stress in first principal direction
σHS
2
=σt/2
2
⋅1.12=hotspot stress in second principal direction
σ1t/2
=maximum first principal element stress at t/2 position
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Pressure-, axial- and shear loads Section 5.5 8.3.3 Loads
To simulate the stress flow in a double side or bottom the twomodels needed for calculation of stress concentration factorsshould both be subjected to pressure, axial and shear loads asdescribed in section 5.5.
8.3.4 Semi-nominal model
A 50×50 mm mesh model should be made according to the re-quirements given in section 5.3. The model is used to calculatesemi-nominal stresses.
Fig.8-1 shows the membrane principal stress distribution at thestiffener-frame connection and the stress read out position atthe example hotspot #102 for the pressure load case. Table 8-1 lists stress values for all load cases.
Semi-nominal stress model (50x50-mesh) Section 5.3 Stress concentration model (txt-mesh) Section 5.4 Calculation of weighted stress concentration factor (SCF) Section 8.2 Max. membrane principalstress component at HS102 = 647 MPa (LC1)Figure 8-1Semi-nominal membrane principal stress8.3.5 Fine mesh model
A t×t-mm mesh model should be made according to the re-quirements given in section 5.4. The model is used to calculatethe hotspot stresses. Fig.8-2 shows the hotspot principal stressdistribution at the stiffener-frame connection and the stressread out position at the example hotspot #102 for pressure load
case. Table 8-1 lists hotspot stresses for all load cases. Notethat the stress read out point on the t×t-mesh model is at t/2 po-sition away from the hotspot location, and that the maximumelement principal stress within ±45 degree of the weld normalshould be used.
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Classification Notes - No. 34.2, June 2010Page 24
Max. principal stresscomponent at t/2 positionfrom HS 102 = 602 Mpa (LC1)HS#102Figure 8-2Hotspot surface principal stress 8.3.6 Stress concentration factor calculation
The SCFs are calculated as the ratio between the membraneprincipal stresses from the semi-nominal and the surface prin-cipal stress from the fine mesh model. The sum of the absoluteprincipal stresses from pressure, axial and shear loads are to beused for both models as described in the formula:
txt−mesh⎛LC3⎞HSHS
orσ⎜∑maxσEffectiveUpper⎟,1Effective,2
LC1⎟max⎜⎜LC3⎟txt−mesh
HSHS
⎜maxσorσLower⎟⎜∑⎟Effective,1Effective,2⎝LC1⎠KG=50x50−mesh
KG=1.12⋅(683+185+176)txt−mesh1044=1.12⋅=1.12⋅0.78=0.8850x50−mesh(647+502+183)1332Note that fine mesh stress values taken at t/2 position should
be multiplied by an extrapolation factor of 1.12 in order to ob-tain the hotspot stress.
According to section 8.2.3 the example hotspot #102 in Fig.8-2 should be based on effective stress with a reduction factor of0.6 on the bending stress component. This reduction is ac-counted for in the above example calculation. The effectivestress of HS102 for LC1 will be:
∑maxσLC1
LC3
m,1
orσm,2
σEff,LC1,HS102=σB+0.6⋅σm=602+0.6⋅136=683
Table 8-1 lists resulting SCF (KG) for all hotspots on the ex-ample detail in Fig.8-1.
t × t modelLC2LC3ShearAxial
By using the stress values for the example hotspot is the fol-lowing SCF (KG) calculated:
Table 8-1 Stresses for SCF calculation and SCF (KG) valuesHotspot
Semi-nominal stress model
LC1LC2LC3PressureShearAxial
Sum
LC1
Pressure
Sum
SCF (Kg)
#102Nominal stress
647100
502100
183100
1332-
683100
185100
176100
1044 × 1.12 = 1169-
0.88
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8.4 Stress concentration factors for typical longitudinal end connection details
8.4.1
The stress concentration factors listed below covers typicalstiffener-frame connections found in ship structures. Fig.8-3shows possible hotspot locations and the numbering system.Table 8-2 shows the dimensions of the details used in calcula-
tion of the tabulated SCFs. Stress concentration factors for de-tails without web stiffener, with web stiffener, and withbacking bracket and soft toe are listed in Table 8-4. Stress con-centration factors for hotspots on the web stiffener are listed inTable 8-5.
If the detail to be checked differs significantly from the typicaldetails in Table 8-2 separate analysis should be conducted ac-cording to section 8.2.
Figure 8-3
Numbering of possible hotspots
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Classification Notes - No. 34.2, June 2010Page 26
8.4.2
Table 8-2 Dimensions of calculated stiffener-frame connections 290mm290mm140mm100mmR50mm15mm100mm150mm15mm50mmR50mm12mm425mmT10212mm350mmT201R75mm290mm150mm100mmR50mm15mm50mm290mm150mm100mmR50mm15mm12mm350mmT20212mm350mmT302R75mm290mm150mm100mmR50mm15mm290mm15mm150mm100mmR50mm12mm350mmT30312mm350mmT304R75mmDET NORSKE VERITAS
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Table 8-2 Dimensions of calculated stiffener-frame connections (Continued)290mm150mm100mmR50mm15mm100mm290mm150mm15mm12mm350mmT30512mm350mmT306250mm150mm100mmR50mm15mm100mm250mm150mmR50mm15mm12mm350mmT403R75mm12mm350mmT404250mm150mm100mm15mm100mm290mm150mmR50mm15mm12mm350mmT40612mm350mmT504DET NORSKE VERITAS
Classification Notes - No. 34.2, June 2010Page 28
Table 8-2 Dimensions of calculated stiffener-frame connections (Continued)
290mm150mm100mm150mm 15mm12mm350mmT506350mm T606 Table 8-3 Dimensions of top stiffener connections 75mmWeb stiffener with high scallopR35mm175mmWeb stiffener with keyhole15mmR30mm175mmR600mmWeb stiffener and bracketsR150mm400mm325mmDET NORSKE VERITAS
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Table 8-4 Stress concentration factors for stiffener-frame connections GeometryHotspotK-factor with web stiffener and high scallop K-factorK-factor with soft toe and bracketK-factorK-factor without web stiffenerK-factorT102101102103104105106107201202203204205206207208---0.610.82-1.05-1.38----1.12----0.640.840.851.37-1.35----1.12----0.590.941.001.10-1.43----1.13-T2011011021031041051061072012022032042052062072081.680.87* 2.26*0.780.92-1.49-2.08-2.831.061.461.471.52T202 1011021031041051061072012022032042052062072081.60 0.88* 2.28*0.780.87-1.49-1.72-3.161.341.35--DET NORSKE VERITAS
Classification Notes - No. 34.2, June 2010Page 30
Table 8-4 Stress concentration factors for stiffener-frame connections (Continued)K-factor with web stiffener and GeometryHotspothigh scallop K-factor
K-factor with soft toe and bracketK-factorK-factor without web stiffenerK-factorT302 1011021031041051061072012022032042052062072081.740.942.330.770.93-1.301.281.411.33--1.16--2.010.732.180.860.950.921.321.221.361.04--1.19--1.830.852.170.711.02-1.951.341.340.89--1.17--T3031011021031041051061072012022032042052062072081.740.94*2.33*0.770.930.891.301.33-1.33---1.221.402.070.75*2.23*0.860.960.941.321.22-0.88---1.241.391.890.88*2.21*0.731.060.861.871.30-1.05---1.251.46T3041011021031041051061072012022032042052062072081.740.95*2.33*0.780.930.861.091.32-1.32----1.362.080.77*2.24*0.860.950.871.341.36-1.11----1.311.900.88*2.21*0.731.060.871.921.32-1.01----1.36DET NORSKE VERITAS
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Table 8-4 Stress concentration factors for stiffener-frame connections (Continued)K-factor with web stiffener and GeometryHotspothigh scallop K-factorK-factor with soft toe and bracketK-factorK-factor without web stiffenerK-factorT3051011021031041051061072012022032042052062072082.061.80*2.85*0.780.870.861.861.30-0.76----1.262.571.70*2.94*0.840.870.861.961.35-1.15----1.19T306 1011021031041051061072012022032042052062072081.551.15*2.84*0.760.770.701.081.22-1.17----1.251.390.99*0.81*0.740.840.801.071.21-1.18----1.29T404101102103104105106107201202203204205206207208-0.69-1.00 1.000.691.191.14--------0.85-0.900.900.851.181.55-------DET NORSKE VERITAS
Classification Notes - No. 34.2, June 2010Page 32
Table 8-4 Stress concentration factors for stiffener-frame connections (Continued)K-factor with web stiffener and GeometryHotspothigh scallop K-factor
K-factor with soft toe and bracketK-factorK-factor without web stiffenerK-factorT406 101102103104105106107201202203204205206207208-0.82-0.730.730.820.50--------T5041011021031041051061072012022032042052062072081.291.06-0.710.850.891.191.14------1.10T506 1011021031041051061072012022032042052062072080.811.10-0.690.740.680.811.15------1.13* based on effective stressDET NORSKE VERITAS
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Table 8-5 Stress concentration factors for top stiffener connections to longitudinal
KG-factor with KG-factor with KG-factor with web stiffener for web stiffener for web stiffener and
GeometryHotspothigh scallopkeyholebrackets
KG-factorKG-factorKG-factor
3021.31-0.50T1023011.71-0.423021.430.910.50T3023011.261.090.423021.400.920.51T3033011.241.070.433021.420.910.51T3043011.261.080.59302--0.50T305301--0.423021.530.90-T3063011.331.12-3021.280.85-T4043011.130.98-3020.98--T606 3011.63--
8.5 Semi-nominal finite element mesh of stiffener-frame connections
Table 8-6 shows the semi-nominal element mesh that is used
to calculate the stress concentration factors in Table 8-4 and
Table 8-5. It is important that a similar element mesh configu-ration is used for the respective stiffener-frame connections inthe semi-nominal web-frame model.
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Table 8-6 Semi-nominal element meshT102T202T201 T302 T303 DET NORSKE VERITAS
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Table 8-6 Semi-nominal element mesh (Continued)T304T404T504T306T506T305T406DET NORSKE VERITAS
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Table 8-7 Semi-nominal element mesh at web stiffener
HighscallopKeyholeWeb stiffener and bracketsDET NORSKE VERITAS
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9. Appendix B - Calculation Example: Longitudinal Stiffener Frame Connection of an Oil Tanker
9.1 Introduction
The following calculation example follows the flowchart ofFig.3-2.
The vessel in this calculation example is a very large crude oilcarrier, VLCC built in accordance with the NAUTICUS (New-building) class notation with a target fatigue life of 30 years inworldwide conditions. The considered hotspot is HS102 of thedetail T302, Fig.9-1. The longitudinal is located at the midspanof the hopper tank outer bottom.
9.3 Global stress analysis
The deformation response of the primary members in the mid-ship area is obtained by finite element analysis of a midshipcargo tank model, see section 5.2. The cargo tank model is sub-jected to the six pressure load cases described in section 4.6.The displacement results of the cargo tank analysis are consid-ered to be global results and transferred to the semi-nominalmodel by sub-modelling technique. Fig.9-2 shows the dis-placement results for the external pressure full load condition.
HS102 Figure 9-1
Example detail and hotspot location
Table 9-1 The example ship’s main dimensionsLength O.A. 332.00 mLength B.P.320.00 mBreadth moulded58.00 mDepth moulded31.00 mDraught design20.80 mDraught scantling22.465 m
Figure 9-2
Global displacement analysis – full load external pressure
9.4 Semi-nominal stress analysis
A semi-nominal model is made to capture the local geometricstress flow and effect of cut-outs, web-frame toes and trippingbrackets. The model requires finer mesh and the resultingstresses are used together with stress concentration factors toobtain the hotspot stress range for use in fatigue calculation.Section 5.3 describes the requirements for the semi-nominalmodel. The semi-nominal model is in addition to the six pres-sure load cases also subjected to displacements transferredfrom the cargo hold model. Fig.9-3 shows the stress flow in thehopper area of the semi-nominal model subjected to externalpressure full load condition.
9.2 Fatigue loads
The load conditions to be considered will vary for specific shiptypes. For the considered tanker for oil it is expected to be42.5% of its lifetime in Full Load condition, 42.5%. The re-maining 15% are assumed to be spent in harbour/calm water.
Table 9-2 Fraction of time at seaLoading conditionFull loadBallast
Fraction0.4250.425
For PLUS analysis of longitudinal stiffener-frame connectionsonly external and internal pressure loads should be considered.The formulas for calculating the pressure values are accordingto Classification Note 30.7.
The following six load cases at 10-4 probability level are ap-plied to the cargo tank model for global stress analysis and tothe semi-nominal model for fatigue stress analysis:1)External dynamic pressure, Full load2)Internal dynamic pressure, Full load3)External dynamic pressure, Ballast4)Internal dynamic pressure, Ballast5)Static pressure, Full load6)Static pressure, Ballast
Figure 9-3
Semi-nominal stress analysis – full load external pressure
9.5 Read out of semi-nominal stress
The semi-nominal stress is read out at the hotspot node. Max-imum element membrane principal stress at the hotspot shouldbe used. Averaging is not allowed. Fig.9-4 shows the stressflow and the read out position for the considered hotspotHS102. Table 9-3 lists the semi-nominal stresses for the sixload cases.
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Figure 9-4Stress read out at hotspot location – Full load external pressureTable 9-3 Semi-nominal stress amplitude
Full load [MPa]
External-105Internal16Static-179
according to CN30.7. In this example the environmental factor
is based on worldwide environment, fe = 0.80.
Ballast [MPa]
-9698189
Full load condition:
⎧−99+0.6⋅15
Δσ0=0.8⋅2⋅max⎨=144
990.615−⋅+⎩
9.6 Stress concentration factor
In order to obtain the hotspot stress for use in fatigue calcula-tion the semi-nominal stress result should be multiplied with
stress concentration factors that accounts for the increase instress due to local geometry and weld geometry. The geometrystress concentration factor KG for the considered hotspotHS102 of detail type T302, at the considered detail is taken ac-cording to Table 8-4. Table 9-4 lists the hotspot stresses.
KG (T302 - HS102) = 0.94σhotspot = σsemi-nom · KG
Table 9-4 Hotspot stress amplitude
Full load [MPa]
External-99Internal15Static-168
Ballast [MPa]
-9092178
Ballast condition:
⎧−90+0.6⋅92
Δσ0=0.8⋅2⋅max⎨=60.8
900.692−⋅+⎩
Mean stress correction
The mean stress correction factor fm is based on the static
stresses. The static stresses are listed in Table 9-3.
The compression and tension stress and fm factor is calculatedaccording to CN30.7 /1/:Full load condition:
Δσ144⎧⎫
⎪σstatic+=−179+=−107⎪
σt=max⎨⎬=022
⎪⎪0⎩⎭Δσ144⎧⎫⎪σstatic−=−179−=−251⎪
σc=min⎨⎬=−25122
⎪⎪0⎩⎭
9.7 Combination of stresses
The combined hotspot stress range is taken as a linear combi-nation of external and internal pressure and corrected for mean
stress level and trading route:
Δσl=fm⋅Δσ0
⎧σ+0.6σi
Δσ0=2fe⋅max⎨e
⎩0.6σe+σi
For the mean stress and environmental factor the approach is
fm=σt+0.7σc0+0.7⋅251=0.7=σt+σc0+251Ballast load condition
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7
a1, m1=S-N parameters for N<10 cycles
7
a, m2=S-N parameters for N>10 cycles
2
Δσ61⎫⎧
⎪σstatic+=189+=219.5⎪
σt=max⎨⎬=219.522
⎪⎪0⎩⎭
⎧⎪⎩
61Δσ⎫
−=189−=158.5⎪
⎬=022
⎪0⎭
S1
=Stress range for which change of slope occur
⎪
σc=min⎨σstatic
Corrosive environment:
The corrosive environment is based on the non-corrosive envi-ronment results (SN curve I) with a reduction factor of 2 on thefatigue life.
This gives the fatigue damage:
Dnon-corrosive=0.228
=0.456Dcorrosive
The vessel is assumed to be 30 - 5 = 25 years in non-corrosiveenvironment and 5 years in corrosive environment. Non-corro-sive environment applies for the first 25 years and corrosiveenvironment applies for the remaining time.
This gives the following fatigue damage for the full load con-dition:
⎛(Td−Tc)⎞Tc
⎟Dfulload=pfulload⋅⎜DD⋅+⋅corrosive⎟⎜non−corrosiveTTdd⎠⎝
fm=σt+0.7σc219.5+0.7⋅0=1.0=σt+σc219.5+0Combined hotspot stressFull load condition:
Δσl=0.7⋅144=100.8
Ballast condition:
Δσl=1.0⋅60.8=60.8
Wherepfulload
Tc
=part of design life in full load condition = 0.425=corrosion protection period = 25 years.
9.8 Long term stress distribution
The long term stress is assumed to be Weibull distributed. Acommon Weibull shape parameter is used for all details. Theshape parameter is dependent on the ship length and is in thisexample:
2530−25⎞⎛
Dfulload=0.425⋅⎜0.228⋅+0.456⋅⎟=0.113
3030⎝⎠
h=h0+ha=2.21−0.54*log10(320)+0.05=0.91
Ballast condition:
9.9 Fatigue damage calculation
The fatigue damage over a design life of 30 years is calculated
based on the simplified approach using the stress range at 10-4probability level according to CN 30.7 /1/: Full load condition:
Non-corrosive environment:
⎡qm1⎛
⎜m
D=ν0Td⎢Γ⎜1+1
⎢a1⎜h⎢⎝⎣
⎛S
;⎜1⎜q⎝
⎞⎟⎟⎠
h
2530−25⎞⎛
Dballast=0.425⋅⎜0.026⋅+0.052⋅⎟=0.013
3030⎠⎝
9.10 Total fatigue damage
The total fatigue damage in full load and ballast condition is:
Dtotal = Dfulload + DBallastDtotal = 0.113 + 0.013 = 0.126
Some fatigue parameters and fatigue damage for each loadcondition are shown in Table 9-5. The total fatigue damage of0.126 is acceptable and corresponds to approximately 151years fatigue life.
⎛⎞(0.228+0.026)30
⎟T=25+⎜−25⎜(0.228⋅0.425+0.026⋅0.425)⎟(0.456+0.052)=151.4
⎝⎠
⎞qm2
⎟⎟+a⎟2⎠⎛
⎜mγ⎜1+2
h⎜⎝
⎛S;⎜1⎜q⎝⎞⎟⎟⎠
h
⎞⎤⎟⎥⎟⎥⎟⎠⎥⎦
where
v0Td=
30⋅365⋅24⋅3600
=9.44135⋅107
4Log10(320)Δσ(lnn0)
1h(the number of cycles during 30 years)
q==
100.8(ln104)
10.91
=8.79 N/mm2(the Weibull scale
parameter)
Table 9-5 Fatigue damage results
Load Part time in conditionsloading
condition
Part time in
non-corrosive/corrosive
Number of cyclesSN-CurveFatigue damage
Full loadBallast
0.4250.425
0.83 3.53·1070.17 7.22·1060.833.13·1070.17 6.42·106non-corrosivecorrosive non-corrosivecorrosive
0.0810.0320.0090.0040.126
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