DNVGL-CG-0152 Plus - extended fatigue analysis of ship · PDF fileLow cycle fatigue analysis shall be performed according to procedure given in DNVGL CG 0129. 3 Symbols and abbreviations

The electronic pdf version of this document, available free of chargefrom http://www.dnvgl.com, is the officially binding version.

DNV GL AS

CLASS GUIDELINE

DNVGL-CG-0152 Edition April 2016

Plus - extended fatigue analysis of shipdetails

FOREWORD

DNV GL class guidelines contain methods, technical requirements, principles and acceptancecriteria related to classed objects as referred to from the rules.

© DNV GL AS April 2016

Any comments may be sent by e-mail to [email protected]

If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of DNV GL, then DNV GL shallpay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to tentimes the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million.

In this provision "DNV GL" shall mean DNV GL AS, its direct and indirect owners as well as all its affiliates, subsidiaries, directors, officers,employees, agents and any other acting on behalf of DNV GL.

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Class guideline — DNVGL-CG-0152. Edition April 2016 Page 3Plus - extended fatigue analysis of ship details

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CONTENTS

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Section 1 Introduction............................................................................................ 61 Objective..............................................................................................62 General................................................................................................ 63 Symbols and abbreviations..................................................................6

Section 2 Scope of class notation Plus................................................................... 71 Longitudinal stiffener-frame connections............................................ 72 Bottom and side shell plating............................................................103 Stringer heel and toe details............................................................. 104 Deck openings and deck details........................................................ 115 Ship specific details...........................................................................116 Low cycle fatigue...............................................................................12

Section 3 Analysis procedure analysis procedure................................................. 131 Fatigue analysis.................................................................................132 Stress analysis...................................................................................133 Finite element analysis......................................................................134 Corrosion additions............................................................................13

Section 4 Stress analysis of stiffener-frame connections......................................141 General.............................................................................................. 142 Calculation of stress components...................................................... 143 Loading conditions.............................................................................14

Section 5 Finite element modelling of stiffener-frame connections.......................151 General.............................................................................................. 152 Semi-nominal stress model............................................................... 153 Stress concentration models..............................................................184 Loads................................................................................................. 215 Stress read out from FE models........................................................ 236 Screening procedure..........................................................................28

Section 6 Documentation of Plus analysis............................................................ 301 FE-models.......................................................................................... 302 Stresses............................................................................................. 30

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3 Fatigue calculations........................................................................... 304 Stress concentration factor analysis..................................................30

Section 7 References.............................................................................................311 General.............................................................................................. 31

Appendix A Stress concentration factors.............................................................. 321 General.............................................................................................. 322 Establish stress concentration factors............................................... 323 Example of establishing stress concentration factors........................ 334 Stress concentration factors for typical longitudinal endconnection details.................................................................................365 Semi-nominal finite element mesh of stiffener-frame connections.....48

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SECTION 1 INTRODUCTION

1 ObjectiveThis class guideline provides guidance on how to perform and document analyses required for compliancewith the class notation Plus as described in the RU SHIP Pt.6 Ch.1 Sec.6. The class notation providesenhanced scope for fatigue strength and ensures that specific critical structural details are adequatelydesigned to meet specified fatigue requirements.

2 GeneralThe Plus notation is an optional class notation mainly intended for vessels operating in harsh areas andincludes extended scope of fatigue strength verification for hull structural details.This class guideline covers a description of the following:

— Scope— Procedures for— Modelling— Structural analysis— Stress read out— Fatigue analysis— Stress concentration factors— Documentation of the analysis.

Calculations documenting compliance with requirements in this section shall be submitted for verification.The fatigue strength evaluation shall be carried out based on the target fatigue life, service area and loadsspecified by the CSR for CSR ships and RU SHIP Pt.3 for other ship types. The method of fatigue assessmentis given in DNVGL CG 0129.The following details in the cargo area are to be considered in the fatigue strength assessment in addition tothose required for other class notations:

— Longitudinal stiffener-frame connections located in the bottom, inner bottom, side and inner side includingconnected web stiffener, cut-out and collar plate, Sec.2 Figure 1.

— Strength deck plating including stress concentrations from openings, scallops, pipe penetrations andattachments

— Bottom and side shell plating connection to web frames and stiffeners— Stringer heels and toes— Ship specific details as specified in Sec.2 [5].

The effect of low cycle fatigue is to be considered for details subjected to large stress variations duringloading and unloading. Low cycle fatigue analysis shall be performed according to procedure given in DNVGLCG 0129.

3 Symbols and abbreviationsThe symbols following symbols and abbreviations are used in this class guideline. For symbols not defined inthis class guideline, reference is made to RU SHIP Pt.3 Ch.1 Sec.4, RU SHIP Pt.3 Ch.9 and DNVGL CG 0129.

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SECTION 2 SCOPE OF CLASS NOTATION PLUS

1 Longitudinal stiffener-frame connections

1.1 GeneralIn general it shall be demonstrated that the fatigue analysis for all stiffener-frame connections in themidship-, forward-, and aft-cargo areas are in compliance with the requirements for notation Plus.Compliance can be demonstrated based on direct analysis or by simplified method, as described below, or acombination of those.

1.2 Direct analysisThe connections in bottom, inner bottom, side, inner side and hopper tank may be assessed with finiteelement analysis according to Sec.5. Figure 1 illustrates the typical hotspots at a stiffener-frame connection.The hotspots include locations on the web-frame, stiffener lug and the web stiffener. The analyses shouldcover the entire cargo area of the selected vessel. See Figure 2 for an overview.Connections in double side and bottom at one web-frame in the middle of the forward-, amidships- and aft-tank may be analysed according to the procedure described in this class guideline.The fatigue calculations should be performed for the mid-frame of:

— Amidships cargo area— Aft cargo area— Forward cargo area.

The fatigue capacity of the other frames where fatigue calculation is not performed may be assessed with thescreening procedure described in Sec.5 [6].

1.3 Simplified methodLNG membrane and LPG carrier (with independent tanks of type A or type C):

— Design for cut outs in case where the web stiffener is omitted or not connected to the longitudinal arerequired to adopt a full tight collar plate for the following members:

— Side shell below 1.1Tsc

— Inner hull longitudinal bulkhead below 1.1Tsc

— Top side tank sloping plate below 1.1Tsc

— Hopper and inner bottom— Bottom.

— For cut outs in case where the web stiffener is connected to the longitudinal stiffener flange, the collarplate is to be extended to the attached plate. In addition, for LNG carriers with membrane tanks, keyholetype scallop and soft toe is to be provided for web stiffener unless back bracket is fitted.

— Where the web stiffener is located on side shell below the lowest stringer and hopper plate, the webstiffener is to have soft toe (LNG membrane carrier only).

— Longitudinal stiffener on side shell and topside tank which supports the upper connecting side framebrackets shall have a full tight collar plate and web stiffener with soft toed, if any. (LPG carrier only).

— A full tight collar plate is to be provided for the area prone to high shear stress in way of opening eitherdouble bottom or double side structures.

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Oil tankers with plane bulkheads in way of cargo tanks:

— Cut outs where the web stiffener is not connected to the longitudinal full tight collar plate shall be appliedthe following areas:

— Side shell below 0.9D— Inner hull longitudinal bulkhead below 0.9D— Top side tank sloping plate below 0.9D— Hopper and inner bottom— Bottom.

— Cut outs in case where the web stiffener is connected to the longitudinal stiffener flange shall have collarplate extended to the attached plate and keyhole type scallop and soft toe is to be provided for webstiffener (unless back bracket is fitted) for the following members:

— Side shell below 1.1Tsc— Inner hull longitudinal bulkhead below 1.1Tsc— Top side tank sloping plate below 1.1Tsc— Hopper and inner bottom— Bottom.

— Full tight collar plate is to be provided for the area with high shear stress in way of openings in doublebottom and double side structures.

— Full tight collar plate is to be provided for the longitudinal stiffener in way of bracket toe of primarysupport member.

— For bottom and inner bottom longitudinals, full tight collar plate is to be provided for stiffeners within 20%– 30% of effective shear span.

— For forward and aft cargo tanks, full tight collar plate or improved cut-out is to be provided for thelongitudinal stiffeners between 0.9D and the lowest stringer as well as in way of longitudinal stiffeners inthe hopper tank.

Alternative design verified by direct analysis may be accepted on a case by case basis.Ship types not covered shall be based on special consideration.Application of structural details described above may be specially considered case-by-case for designs whichis different from typical arrangement.

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Figure 1 Hot spots at stiffener-frame connections

Figure 2 View of ship and location of areas to be analysed

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Figure 3 Web frames in cargo area

2 Bottom and side shell platingThe fatigue capacity of the bottom and side shell plating between two web-frame positions in midship-,forward- and aft-cargo area shall be assessed using the prescriptive fatigue analysis. Both the transversestress at stiffener mid-length and the longitudinal stress at the plate-transverse frame intersection should beassessed. It is sufficient to use simplified stress formulas for plate bending due to lateral pressure given inDNVGL CG 0129.The plate field should be subjected to internal and external rule pressure loads as given in RU SHIP Pt.3 Ch.4or according to CSR BC&OT Pt.1 Ch.4, whichever is relevant.The fatigue analysis shall be based on maximum effective stress range from the considered dynamic loadcases and stress concentration factors according to procedures of DNVGL CG 0129.

3 Stringer heel and toe detailsFatigue calculations should be carried out for the stringers in the midship area, forward and aft hold. The heeland toe of the stringers are normally the critical locations to be assessed. This is illustrated in Figure 4. Thefatigue calculations should be performed using a fine mesh finite element model with appropriate t × t meshin order to capture the hotspot stress. The procedures for modelling and stress read-out from fine mesh finiteelement models are described in DNVGL CG 0127 and DNVGL CG 0129. The analysis is typically performedusing a cargo hold model and a local fine mesh model together with the sub-modelling technique.

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Figure 4 Critical locations on stringers

4 Deck openings and deck detailsDeck openings and deck details in the cargo area should be analysed with respect to fatigue. Normally it issufficient to use stress concentration factors for deck details as given in DNVGL CG 0129. The details thatshould be included are:

— Openings— Pipe penetrations— Attachments— Scallops.

The fatigue requirements for the deck plating will normally be satisfied provided that the target fatigue life isobtained with a stress concentration factor Kg = 3.0. Stress concentration model should be made if Kg of thetarget detail is not found in DNVGL CG 0129 App.A.The fatigue calculation is performed using the nominal stress due to hull girder bending together withrelevant stress concentration factor to obtain the hotspot stress. The nominal stress level may be establishedusing the prescriptive method given in DNVGL CG 0129 Sec.4.The control of the deck openings and deck details may have direct impact on the hull girder cross sectionmodulus, ref. RU SHIP Pt.3 Ch.5.

5 Ship specific detailsFor different ship types there are characteristic critical areas of attention which are prone to fatigue andthese areas should be included in the fatigue analysis for Plus notation. Since these details vary from vesseltype to vessel type these ship specific details need to be selected at an early stage for clarification. Detailsthat require fatigue analysis are:

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LPG carriers (prismatic A-type tanks):

— Lower and upper side brackets— Dome opening and coaming.

LNG membrane carriers:

— Upper hopper knuckle— Longitudinal girders at transverse bulkheads— Upper and lower chamfer knuckles— Dome opening and coaming.

In general very fine mesh finite element analysis is required to verify the fatigue strength of these details.

6 Low cycle fatigueLow cycle fatigue strength of highly stressed locations under repeated cyclic static loads, mainly due to cargoloading and unloading, should be considered as significant yielding can cause cracks at hotspots even thoughthe dynamic stress from wave loading is low.A procedure for calculating the combined damage due to low cycle and high cycle fatigue is described inDNVGL CG 0129 App.H. The low cycle stress range due to loading and unloading is based on the use of apseudo-elastic hot spot stress range derived by use of a plasticity correction factor on the elastic stressrange. The method enables use of standard hotspot SN-curve.For compliance with the Plus-notation the following locations need to be verified with respect to low cyclefatigue:

— Web stiffener on top of inner bottom longitudinal and hopper slope longitudinals when wide frame space isemployed.

— Web-frame hotspots at the stiffener-frame connections in areas of high girder shear stress or where webstiffener is not connected to top of longitudinal stiffener.

— Heel and toe of horizontal stringer of transverse bulkhead for which frequent alternate loading isanticipated.

— Inner bottom connection to transverse bulkhead for which frequent alternate loading is anticipated.— Lower transverse stool connection to inner bottom for a loading condition with one tank empty and the

tank on opposite side full.

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SECTION 3 ANALYSIS PROCEDURE ANALYSIS PROCEDURE

1 Fatigue analysisIn order to obtain the class notation Plus all structural details described in the scope should comply with afatigue damage ratio equal or below 1.0 for the specified design fatigue life. The environmental reductionfactor, fe, is not to be taken less than the following:

f e = 1.0 for ships with class notation CSRf e = 0.8 for other ship types.

2 Stress analysisThe long term stress ranges for fatigue calculations of Plus details are to be calculated according to theprocedure given in DNVGL CG 0129. The hot spot stress range calculation will be based on the maximumstress range from the considered dynamic load cases:

∆σ = maxi (∆σFS, i(j))

where

∆σ = Fatique stress range, in N/mm2, for load case (i) of loading condition (j).

Further details for fatigue stress range calculation are described in DNVGL CG 0129 Sec.6.

3 Finite element analysisFinite element models and analysis for all details in the scope of Plus notation except the stiffener-frameconnections shall be according to DNVGL CG 0129 Sec.6. The procedure for modelling of longitudinalstiffener-frame connections is given in Sec.5.

4 Corrosion additionsNet scantlings as defined by RU SHIP Pt.3 Ch.3 or CSR, whichever is relevant, shall be used in the finiteelement model.For vessels with the class notation ESP and CSR the stresses are to be calculated for a thickness equaltn50. For other vessels the stresses will be based on the modelled gross offered thickness, tgr. The scantlingapproach factor for correction of stress according to net scantlings approach, fc, are to be applied, see DNVGLCG 0129 Sec.3 [2.2].

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SECTION 4 STRESS ANALYSIS OF STIFFENER-FRAME CONNECTIONS

1 GeneralThe stress analysis is to be done in accordance with hot spot stress approach given in DNVGL CG 0129.The local loads from sea pressure, ballast pressure and cargo loads will be dominating in way of theseconnections and the hull girder loads will have little influence if any. Hence the dynamic load casesrepresenting beam sea for midship area will be sufficient. For forward and aft cargo areas both beam sea andoblique sea cases need to be considered.

2 Calculation of stress componentsThe calculation of the stress range is performed by finite element analysis of a semi-nominal 50×50 mmmesh size model. Hotspot stress range for fatigue calculations is found by multiplying the semi-nominalstress with stress concentration factors. Sec.5 describes the procedure for finite element analysis.

3 Loading conditionsFatigue analyses should be carried out for representative loading conditions. The following two loadingconditions are normally sufficient for documentation for analysis of oil tankers, container vessels and gascarriers.

— Normal full load departure condition— Normal ballast arrival condition.

Other ship types may require other representative loading conditions in addition to these two conditions, seeRU SHIP Pt.3 Ch.9 Sec.4 and CSR Pt.1 Ch.4 Sec.8 [5].

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SECTION 5 FINITE ELEMENT MODELLING OF STIFFENER-FRAMECONNECTIONS

1 GeneralThis section applies to the longitudinal stiffener-frame connection details. A finite element analysis witha semi-nominal stress model (50×50 mm mesh) is required for stress calculations of the stiffener-frameconnections. For all the other details reference is made to DNVGL CG 0127 for guidance on the finite elementmodelling of fine mesh model and partial ship model.

2 Semi-nominal stress model

2.1 ModellingFor calculation of the stress level at the longitudinal stiffener-frame connections a semi-nominal stress finiteelement model should be made. The purpose of the semi-nominal model is to capture the local geometricstress flow and effect of cut-outs, web frame-toes and tripping brackets. The model also captures moreaccurately the shear stress distribution from longitudinal stiffeners to web frame.The stress results are used together with stress concentration factors to obtain the hotspot stress range foruse in fatigue calculation.The model should have approximately 50 mm elements at the critical hotspots for each longitudinal stiffener-frame connection in side, inner side, bottom, inner bottom and hopper. The longitudinal extent of the modelshould be at least one frame spacing on each side of the target frame. Examples of models are shown inFigure 1 and Figure 2.The element types to be used are:

Quad elements: 8 node

Triangular elements: 6 node

Beam elements: 3 node.

The semi-nominal stress model may be included in the cargo hold model or sub-modelling may be used.The slot geometry should be modelled as described in [3], see Figure 3. It is important that the area aroundall hotspot locations is modelled with 50 mm size elements. In cases where it is impossible to create square50 mm elements an aspect ratio of 4 should not be exceeded. If elements different from 50×50 mm sizeare needed these elements should preferably be placed away from the hotspots i.e. at mid-span of cut-outopening. Away from the hotspots the mesh can gradually become coarser. The rounded corners of the slotshould be modelled as “square” elements.Eccentric lugs are not to be modelled as eccentric but as in-plane shell elements, and the plate thicknessshould not be increased to account for the overlapping plates. The effect of eccentric lug induced bendingstresses will be captured by the stress concentration factors. The cut-out should be modelled as at is ondrawings with correct width and height. As a consequence will the distance from the longitudinal top flangeto cut-out edge increase with half the thickness of top flange. The stiffener is idealized with plate elements inthe centre of the actual stiffener.Guidance on meshing of the slot geometry is given for all connection types in App.A [3]. It is important thatthe finite element mesh is similar in order to ensure correct hotspot stress.The loads are to be the same pressure loads as applied to the cargo tank model. If a sub-modelling analysisis to be used, the applied loads will also include either prescribed displacements or prescribed forces/stresses.

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2.2 All types of stiffener-frame connections in the cargo area should be analysed using semi-nominal models.If the mid-hold target web-frame does not include all types of connections then the remaining shouldbe included in another model based on the mid-hold web-frame model. This should also be done for allconnections in the forward and aft cargo holds. Since a vessel does not have parallel body in the forwardand aft tank area some simplification will be necessary. The remaining frames of the cargo tanks should beassessed based on a screening procedure described in [6].

Figure 1 FE-model with 50 mm mesh, whole model

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Figure 2 FE-model with 50 mm mesh, hopper tank

Figure 3 Slot geometry with stress read out points

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3 Stress concentration models

3.1 If the design of a longitudinal stiffener-frame connections is not found among the typical designs listed inApp.A [4] a very fine mesh model (stress concentration model) should be made in order to establish thestress concentration factor of that particular design. The stress concentration models should be modelledaccording to the procedure given in this section. App.A [2] describes how the stress concentration factors arecalculated while Sec.6 describes necessary documentation.

3.2 Two models are needed if additional stress concentration factors 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 calculate the hotspot stress.

The stress concentration factor will be the stress ratio between the models. The models are made to simulatethe behaviour of double side and double bottom. The models should have a vertical extent of 3 stiffeners, i.e.4 stiffener spacing, and the longitudinal extent should be ½ frame spacing in both forward and aft direction.Two typical models are shown in Figure 4 and Figure 5. No cut-outs for manholes should be included in thestress concentration models. Both models should include the typical hotspots for the target detail. Sec.2Figure 1 shows typical hotspots to be assessed.The element types to be used are:

Quad elements: 8 node

Triangular elements: 6 node

Beam elements: 3 node.

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Figure 4 FE-Model with 50 mm mesh, SCF analysis

Figure 5 FE-Model with t×t mesh, SCF analysis

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For the 50×50 mm mesh model, the mesh density in the area of the web frame slots, including webstiffeners, is to be approximately 50×50 mm but adjusted to fit the slot geometry. Outside this area themesh size may be increased to reduce the size of the model. The element aspect ratio should however notexceed 4. Smooth corners are to be modelled as sharp corners and the eccentricity of the stiffener lug is tobe ignored. An example of a detail is shown in Figure 7.For the t×t mesh model the mesh density in the area of the web frame slots, including web stiffeners, isto be approximately the plate thickness. The mesh with plate thickness size should extend at least fourelements in all directions at all relevant hotspots. Outside this area the mesh density may be increased toreduce the size of the model. The element aspect ratio should however not exceed 4. The eccentricity of thestiffener lug is to be included in the model and modelled according to Figure 8. Figure 6 shows an example ofa stiffener lug detail modelled with t×t mesh.

Figure 6 Stiffener and lug details – with web stiffener on top, t×t mesh

Figure 7 Stiffener and lug details – with web stiffener on top, 50×50 mesh

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Figure 8 Modelling of eccentric collar plate

4 LoadsThree load effects are to be modelled in both models.

LC1: External pressure

LC2: Shear stress

LC3: Axial load

Each load effect will result in a stress concentration factor. In order to combine the stress concentrationfactors into one stress concentration factor, weighting of the different load effects should be used. Theweighting is to be conducted by scaling the applied load according to the following criteria:

LC1: External pressure, nominal shear stress in the middle of the stiffener web of 100 N/mm2.

LC2: Shear stress, nominal stress in the middle of the web frame of 100 N/mm2.

LC3: Axial stress, nominal stress in the middle of the web frame of 100 N/mm2.

The applied pressure and prescribed displacements should be used to obtain the nominal stress criteria in theareas indicated in Figure 9 (areas shaded in grey).The different load effects and boundary conditions are shown in Figure 10 through Figure 12. The forwardand aft part of the finite element model should have symmetry condition describing the behaviour in a doubleside or double bottom.

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Figure 9 Nominal stress criteria

Figure 10 Load application and boundary conditions for LC1, external pressure

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Figure 11 Load application and boundary conditions for LC2, shear stress

Figure 12 Load application and boundary conditions for LC3, axial stress

5 Stress read out from FE models

5.1 The maximum principal element stress within ±45º of the normal to the weld should be used for the analysis.As a conservative approach the absolute maximum principal stress could be used regardless of direction tothe weld.

5.2 The semi-nominal stress should be the maximum principal membrane stress at the considered hotspotlocation.The stress read point on the semi-nominal model is to be at the hotspot node location. Among all theelements that have a result at the considered hotspot node it is the element result with maximum principalstress value that should be used for damage calculation. No averaging of nodal stresses is allowed. SeeFigure 3, Figure 13 and Figure 14 for illustration. If necessary the membrane stress should be calculatedusing the surface stresses at upper and lower surfaces.

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Figure 13 Example of stress read out point from 50×50 mm mesh model

Figure 14 Example of maximum principal membrane stress value among adjacent elements

5.3 The maximum semi-nominal stress value for a certain hotspot node may be found at different elementsamong the various load conditions. The semi-nominal stress values should not necessarily be taken from thesame element in all load conditions. For a certain hotspot the result values should be found at the same nodeposition but they might result from various elements connected to that node.

5.4 The stress read out points in the stress concentration model is to be at a distance t/2 from the hotspot. Theprincipal element stresses at t/2 should be multiplied with a factor 1.12 to calculate the hotspot stress. This

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is one of the two stress extrapolation procedures given in DNVGL CG 0129. See Figure 15 and Figure 16 forillustration.

Figure 15 Example of stress read out point from t×t mesh model

5.5 When extracting stress results from the stress concentration model there could for a given hotspot be manypossible t/2-nodes. The maximum principal stress value at position t/2 away from the hotspot location shouldbe used as the relevant hotspot stress. All t/2-positions will have to be assessed with regard to stress level incombination with principal stress direction in order to locate the maximum relevant stress value. See Figure16 for illustration.

5.6 The maximum principal stress value at t/2-position may occur at different positions for the three consideredload cases. Despite possibly different location of maximum stress location the stress read out node in thestress concentration model should for a given hotspot remain the same for all three load cases: axial, shearand pressure load. The node position giving the absolute maximum value among all three load cases shouldbe used when extracting stress for all three load cases. Note that both upper and lower element surfaceshould be checked in order to find the maximum principal stress.

5.7 At the stress read out node the finite element model will report a result for both upper and lower surfaceand also principal stress in two directions. The principal stress direction that is within 45 degrees to the weldnormal should be used as relevant hotspot stress. If both principal stresses are both at 45 degrees to theweld normal one should choose the maximum of the two directions. Both upper and lower surface stressshould be reported for all three load cases. The surface resulting in the largest total stress when summing upthe contributions from the load cases should be used as basis for calculation of stress concentration factor.

5.8 For a specific hotspot location the stress read out procedure for the stress concentration model can besummarized as follows:

— Locate all possible t/2-nodes with principal stress direction within 45 degrees to weld normal (t/2 nodes:nodes with a distance of t/2 from the hotspot).

— Find the t/2-node with the largest principal surface stress among all load cases.

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— Perform stress read out of both first and second principal stress on upper and lower surface at the samenode for all three load cases.

— For a certain load case locate the largest principal stress among the two principal directions (P1 or P2) forboth upper and lower surface.

— To decide on which surface to use calculate the sum of the three load cases for both upper and lowersurface. The surface with the largest total stress should be used for calculation of the SCF.

— The SCF is calculated according to the expression in App.A [2.2].

Figure 16 Possible stress read out nodes at t/2 position

5.9 In the stress concentration model the collar plate is modelled with eccentricity. In the area where thecollar plate overlaps with the web plate, the stress is normally reduced due to the increase effective platethickness. Some hotspots are located on the boundary between web plate and collar plate. For these hotspotthe stress results in the overlapping area need not be considered. These stress values are assumed not togive rise to fatigue crack growth. Figure 16 illustrates the overlapping area.

5.10 Example of relevant elements to consider for identification of possibly maximum principal stress values att/2 position are shown in Figure 17 for the hotspots of detail type T201. For the hotspots #101, #107, #202,#206, #207 and #208 is the marked element the only relevant to consider regarding t/2-stress values. Forhotspot #104, #105 and #106 which are located at the slit opening edge, several element along the edgeneeds to be considered marked with arrows on Figure 17.Hotspot #102, #103, #204 and #205 are located adjacent to the area where the lug plate and the web-plateare overlapping each other. Elements that are inside this overlapping area will not be necessary to considerwhen locating the relevant t/2-stress result. Normally these elements will have smaller stress values andstresses in this area will not contribute to crack growth in real structures.

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Figure 17 Elements to consider in stress read out

5.11 The hotspots on the edge of the slit opening i.e. hotspot #104, #105 and #106 are located in base material.Stress read out on hotspots in base material should be performed at the hotspot. No extrapolation using t/2stress values should be performed and stress results on the opening edge should be used.The use of dummy beam elements at slit opening edge is not allowed. It is found that significant bendingmay occur at the slit opening hotspots. Since the dummy beam element does not capture bending stressacross the plate thickness they are not allowed to use.Note that the maximum stress position along the slit opening most likely will vary for the various load cases.The position with the largest value among the load cases should be used for stress read out for all three loadcases.

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Figure 18 Possible stress read out nodes at slit opening edge

6 Screening procedureThe below screening procedure should be used to assess the fatigue capacity of the web-frames that are notmodelled using a 50×50 mm element mesh. The screening should be based on the nominal stress level ofthe cargo hold model. The screening analysis should follow the following steps:

1) Establish a scaling factor for each stiffener-frame connection in each load case. The scaling factorsshould be based on maximum element average principal stress from the cargo hold model at thereference connection and at the target connection. The web-frame that has been modelled with 50×50mm element mesh is defined as the reference web-frame. The scaling factor, fs, is defined as the ratiobetween the average value of the absolute principal stress level of four neighbouring elements at therelevant -stiffener-frame connection in the target frame and the reference frame, Figure 18:

2) Establish hotspot stress at target stiffener-frame connection by multiplying the scaling factor withthe hotspot stress of the relevant hotspot location at the reference stiffener-frame connection. Thereference hotspot stress is established by use of the semi-nominal model and stress concentrationfactors according to Sec.3 and App.A [4].

3) Fatigue damage is calculated for the relevant hotspot location at the target stiffener-frame connection.4) The above procedure is repeated for all hotspots at all stiffener-frame connections in all web-frames in

the forward-, aft- and amidship cargo-hold models.

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The above screening procedure is only applicable when comparing similar connections in the target and thereference web-frame. Since the 50×50 mm mesh is similar for many different connections it will be possibleto use the screening procedure for a number of different connections even if the two connections in thetarget and the reference web-frame are somewhat different.Note that when different connections having similar 50×50 mm mesh are compared it is important toaccount for the correct SCF giving the relevant reference hotspot stress.If the connections in the target and reference web-frame would have different 50×50 mm mesh thescreening procedure should be used with care. In such case, the 50×50 mm element mesh for the referenceconnection may be modified to reflect the geometry of the target connection.

Figure 19 Neighbouring elements for screening average stress

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SECTION 6 DOCUMENTATION OF PLUS ANALYSIS

1 FE-modelsAll finite element models should be documented with plots clearly showing the mesh at the various details.The model extension and a thorough description of the applied loads and boundary conditions should bedocumented. Element types should be reported. A description of the analysis flowchart should be included asdocumentation for to explain the analysis flow.

2 StressesThe semi-nominal stress in the web frame should be documented with stress plots showing clearly the stressdistribution at all stiffeners. For validation of the predicted fatigue damages all stress values for all locationsshould be reported in numerical format.

3 Fatigue calculationsThe fatigue calculations should be reported including the following items:

— Choice of SN-Curves— Fraction of time in each loading condition— Fraction of time in non-corrosive/corrosive environment— Number of stress cycles— Mean stress correction factors— Total fatigue damage or fatigue life prediction— Stress concentration factors.

4 Stress concentration factor analysisAnalysis of additional stress concentration factors should be thoroughly documented. A detailed descriptionof the longitudinal stiffener-frame connection geometry is to be provided together with a description andplots of both the t×t-model and the 50×50 mesh finite element models. The applied loads and boundarycondition should also be documented, and plots clearly showing the element mesh around the stiffener-frameconnection should be provided. The nominal stress level and the hotspot stress should be documented withplots for all load-cases in both models. The stresses used in calculation of the stress concentration factor areto be reported together with the resulting stress concentration factor.

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SECTION 7 REFERENCES

1 General1) Det Norske Veritas, Finite element analysis of large scale fatigue test of stiffener web frame connections,

DNV report No. 2007-19-09, T. Lindemark, november 20072) Lotsberg, Inge (et.al) Fatigue Capacity of Stiffener to Web Frame Connections, OMAE2009-79061,

Honolulu, Hawaii, USA, 31 may-5 june 2009.

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APPENDIX A STRESS CONCENTRATION FACTORS

1 GeneralThis section describes the procedure of how to establish stress concentration factors for longitudinal stiffener-frame connection details. [4] lists stress concentration factors for the critical hotspots of typical stiffener-frame connections. If a particular detail is not listed among the typical ones in [4] then the user should followthe procedure in [2] for calculating the stress concentration factors.

2 Establish stress concentration factors

2.1 In order to calculate the stress concentration factor a semi-nominal model with 50×50mm mesh and a stressconcentration model with t×t-mesh should be made. The finite element modelling and analysis should beperformed according to the procedure described in Sec.5.

2.2 When extracting stress results the maximum element principal stresses should be used and not the nodeaveraged stresses. The stress read out points should be located:

— At t/2 from the intersection line in the t×t-mesh model, see Sec.5 Figure 16.— At the node at hotspot in the 50×50mm mesh model, see Sec.5 Figure 13.

Note that the stress at t/2 should be multiplied with an extrapolation factor of 1.12 to find the hotspot stress.See DNVGL CG 0129 for details on extrapolation procedures.

The maximum principal stress within ±45º of the normal to the weld should be used for the analysis. Thisrequirement will in most cases decide whether first or second principal stress should be used.

For some hotspots the position of maximum element principal stress could vary among the three load cases.Note that the stress read out position for a given hotspot should be the same for all load cases. The positiongiving the maximum stress value among all load cases should be used for stress read out in all load cases.

The SCFs are calculated as the ratio of the principal stresses between the semi-nominal model and the finemesh model. The sum of absolute principal stresses at read out position is to be used for both models asdescribed in the formula:

σ1HS = hotspot stress in first principal direction

σ1t/2 · 1.12

σ2HS = hotspot stress in second principal direction

σ2t/2 · 1.12

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σ1t/2 = maximum first principal element stress at t/2 position

σ2t/2 = maximum second principal element stress at t/2 position

σm,1 = semi-nominal principal membrane element stress at hotspot nodeσm,2 = semi-nominal principal membrane element stress at hotspot node.

The checked hotspots should normally include the hotspots marked in Sec.5 Figure 3.

2.3 The stress concentration factor for hotspot #102 and #103 see Sec.2 Figure 1, should be based on effectivehotspot stress according to the expression below:

The effective hotspot stress reduces the bending component of the surface stress with a factor of 0.6.Effective stress is calculated according the following expression:

= membrane stress

= bending stress.

3 Example of establishing stress concentration factors

3.1 This example illustrates how to establish stress concentration factors for a T-shaped longitudinal through aslot with lug connection. The example is based on finite element analysis as described in Sec.5 [4] and showshow to weight the different load cases and stresses, and how to establish the stress concentration factors.The stresses from the finite element analysis are found in Table 1. The magnitude of the sum of the stressesin the t×t-mesh model is used to predict the criticality of the hotspots. The critical hotspots will vary fromdetail to detail dependent on the different detailed design.The weighted stress concentration factors are shown in Table 1. The weighted stress concentration factorsare established based on the columns marked with “sum”, which is basically the sum of the different loadcases as illustrated in the formula above. The weighted stress concentration factors should be used in thefatigue calculations.

3.2 FlowchartThe flowchart, Figure 1, shows the main steps of the procedure to be followed when establishing a stressconcentration factor, reference is given to the indicated sections for detailed guidance.

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Figure 1 Flowchart

3.3 LoadsTo simulate the stress flow in a double side or bottom the two models needed for calculation of stressconcentration factors should both be subjected to pressure, axial and shear loads as described in Sec.5 [5].

3.4 Semi-nominal modelA 50×50 mm mesh model should be made according to the requirements given in Sec.5 [3]. The model isused to calculate semi-nominal stresses.Figure 2 shows the membrane principal stress distribution at the stiffener-frame connection and the stressread out position at the example hotspot #102 for the pressure load case. Table 1 lists stress values for allload cases.

Figure 2 Semi-nominal membrane principal stress

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3.5 Fine mesh modelA t×t-mm mesh model should be made according to the requirements given in Sec.5 [4]. The model is usedto calculate the hotspot stresses. Figure 3 shows the hotspot principal stress distribution at the stiffener-frame connection and the stress read out position at the example hotspot #102 for pressure load case. Table1 lists hotspot stresses for all load cases. Note that the stress read out point on the t×t-mesh model is at t/2position away from the hotspot location, and that the maximum element principal stress within ±45 degreeof the weld normal should be used.

Figure 3 Hotspot surface principal stress

3.6 Stress concentration factor calculationThe SCFs are calculated as the ratio between the membrane principal stresses from the semi-nominal andthe surface principal stress from the fine mesh model. The sum of the absolute principal stresses frompressure, axial and shear loads are to be used for both models as described in the formula:

By using the stress values for the example hotspot is the following SCF (Kg) calculated:

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Note that fine mesh stress values taken at t/2 position should be multiplied by an extrapolation factor of 1.12in order to obtain the hotspot stress.According to [2.3] the example hotspot #102 in Figure 3 should be based on effective stress with a reductionfactor of 0.6 on the bending stress component. This reduction is accounted for in the above examplecalculation. The effective stress of HS102 for LC1 will be:

σEff,LC1,HS102 = σB + 0.6 · σm = 602 + 0.6 · 136 = 683Table 1 summarize the SCF (Kg) values for all hotspots for the example detail shown in Figure 2.

Table 1 Stresses for SCF calculation and SCF (Kg) values

Semi-nominal stress model t × t model

Hotspot LC1Pressure

LC2Shear

LC3Axial

SumLC1

PressureLC2

ShearLC3Axial

SumSCF (Kg)

#102 647 502 183 1332 683 185 176 1044 × 1.12= 1169 0.88

Nominalstress 100 100 100 - 100 100 100 -

4 Stress concentration factors for typical longitudinal endconnection details

4.1 The stress concentration factors listed below covers typical stiffener-frame connections found in shipstructures. Figure 4 shows possible hotspot locations and the numbering system. Table 2 shows thedimensions of the details used in calculation of the tabulated SCFs. Stress concentration factors for detailswithout web stiffener, with web stiffener, and with backing bracket and soft toe are listed in Table 4. Stressconcentration factors for hotspots on the web stiffener are listed in Table 5.If the detail to be checked differs significantly from the typical details in Table 2 separate analysis should beconducted according to [2].

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Figure 4 Numbering of possible hotspots

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4.2 Table 2 Dimensions of calculated stiffener-frame connections

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Table 3 Dimensions of top stiffener connections

Web stiffener with high scallop

Web stiffener with keyhole

Web stiffener and brackets

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Table 4 Stress concentration factors for stiffener-frame connections

Geometry Hotspot

Kg-factorwith web

stiffener andhigh scallop

Kg-factorwith soft toeand bracket

Kg-factorwithout web

stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

--

-

0.61

0.82

-

1.05

-

1.38

-

-

-

-

1.12

-

--

-

0.64

0.84

0.85

1.37

-

1.35

-

-

-

-

1.12

-

--

-

0.59

0.94

1.00

1.10

-

1.43

-

-

-

-

1.13

-

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.680.87*

2.26*

0.78

0.92

-

1.49

-

2.08

-

2.83

1.06

1.46

1.47

1.52

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Geometry Hotspot

Kg-factorwith web




stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.600.88*

2.28*

0.78

0.87

-

1.49

-

1.72

-

3.16

1.34

1.35

-

-

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.740.94

2.33

0.77

0.93

-

1.30

1.28

1.41

1.33

-

-

1.16

-

-

2.010.73

2.18

0.86

0.95

0.92

1.32

1.22

1.36

1.04

-

-

1.19

-

-

1.830.85

2.17

0.71

1.02

-

1.95

1.34

1.34

0.89

-

-

1.17

-

-

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Geometry Hotspot

Kg-factorwith web




stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.740.94*

2.33*

0.77

0.93

0.89

1.30

1.33

-

1.33

-

-

-

1.22

1.40

2.070.75*

2.23*

0.86

0.96

0.94

1.32

1.22

-

0.88

-

-

-

1.24

1.39

1.890.88*

2.21*

0.73

1.06

0.86

1.87

1.30

-

1.05

-

-

-

1.25

1.46

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.740.95*

2.33*

0.78

0.93

0.86

1.09

1.32

-

1.32

-

-

-

-

1.36

2.080.77*

2.24*

0.86

0.95

0.87

1.34

1.36

-

1.11

-

-

-

-

1.31

1.900.88*

2.21*

0.73

1.06

0.87

1.92

1.32

-

1.01

-

-

-

-

1.36

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Geometry Hotspot

Kg-factorwith web




stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

2.061.80*

2.85*

0.78

0.87

0.86

1.86

1.30

-

0.76

-

-

-

-

1.26

2.571.70*

2.94*

0.84

0.87

0.86

1.96

1.35

-

1.15

-

-

-

-

1.19

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.551.15*

2.84*

0.76

0.77

0.70

1.08

1.22

-

1.17

-

-

-

-

1.25

1.390.99*

0.81*

0.74

0.84

0.80

1.07

1.21

-

1.18

-

-

-

-

1.29

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Geometry Hotspot

Kg-factorwith web




stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

-0.69

-

1.00

1.00

0.69

1.19

1.14

-

-

-

-

-

-

-

-0.85

-

0.90

0.90

0.85

1.18

1.55

-

-

-

-

-

-

-

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

-0.82

-

0.73

0.73

0.82

0.50

-

-

-

-

-

-

-

-

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Geometry Hotspot

Kg-factorwith web




stiffener

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

1.291.06

-

0.71

0.85

0.89

1.19

1.14

-

-

-

-

-

-

1.10

101102

103

104

105

106

107

201

202

203

204

205

206

207

208

0.811.10

-

0.69

0.74

0.68

0.81

1.15

-

-

-

-

-

-

1.13

* based on effective stress

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Table 5 Stress concentration factors for web stiffener connections to longitudinal

Geometry HotspotKg-factor withweb stiffener

for high scallop

Kg-factor with webstiffener for keyhole

Kg-factor withweb stiffenerand brackets

T102302301

1.311.71

--

0.500.42

T302302301

1.431.26

0.911.09

0.500.42

T303302301

1.401.24

0.921.07

0.510.43

T304302301

1.421.26

0.911.08

0.510.59

T305302301

--

--

0.500.42

T306302301

1.531.33

0.901.12

--

T404302301

1.281.13

0.850.98

--

T606302301

0.981.63

--

--

5 Semi-nominal finite element mesh of stiffener-frame connectionsFigure 5 and Figure 6 show the semi-nominal element mesh that is used to calculate the stress concentrationfactors in Table 4 and Table 5. It is important that a similar element mesh configuration is used for therespective stiffener-frame connections in the semi-nominal web-frame model.

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Figure 5 Semi-nominal element mesh at web cutout

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Figure 6 Semi-nominal element mesh at web stiffener

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Documents

DNVGL-CG-0152 Plus - extended fatigue analysis of ship · PDF fileLow cycle fatigue analysis shall be performed according to procedure given in DNVGL CG 0129. 3 Symbols and abbreviations