Strength analysis of hull structure in liquefied gas carriers with membrane tanks

Transcription

1 CLASSIFICATION NOTES No Strength analysis of hull structure in liquefied gas carriers with membrane tanks JULY 2016 The electronic pdf version of this document found through is the officially binding version The content of this service document is the subject of intellectual property rights reserved by Det Norske Veritas AS (DNV). The user accepts that it is prohibited by anyone else but DNV and/or its licensees to offer and/or perform classification, certification and/or verification services, including the issuance of certificates and/or declarations of conformity, wholly or partly, on the basis of and/or pursuant to this document whether free of charge or chargeable, without DNV's prior written consent. DNV is not responsible for the consequences arising from any use of this document by others.

2 FOREWORD DNV is a global provider of knowledge for managing risk. Today, safe and responsible business conduct is both a license to operate and a competitive advantage. Our core competence is to identify, assess, and advise on risk management. From our leading position in certification, classification, verification, and training, we develop and apply standards and best practices. This helps our customers safely and responsibly improve their business performance. DNV is an independent organisation with dedicated risk professionals in more than 100 countries, with the purpose of safeguarding life, property and the environment. Classification Notes Classification Notes are publications that give practical information on classification of ships and other objects. Examples of design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some components are given as interpretations of the more general rule requirements. Det Norske Veritas AS July 2016 Any comments may be sent by to rules@dnvgl.com If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million. In this provision "Det Norske Veritas" shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalf of Det Norske Veritas.

3 CHANGES CURRENT Page 3 CHANGES CURRENT General This document supersedes Classification note No. 31.9, October Text affected by the main changes in this edition is highlighted in red colour. However, if the changes involve a whole chapter, section or sub-section, normally only the title will be in red colour. Det Norske Veritas AS, company registration number , has on 27 th November 2013 changed its name to DNV GL AS. For further information, see Any reference in this document to Det Norske Veritas AS or DNV shall therefore also be a reference to DNV GL AS. Main changes July 2016 General Cross references in this document have been updated accordingly due to the rule change of DNV Rules for Classification of Ships, Pt.5 Ch.5. Sec.3 Design loads [3.2]: Collision case has been added. Sec.6 Strength analysis of cargo holds [6.2]: Collision case has been added in the load case to be considered for cargo hold analysis. [6.6.5], [6.6.6]: Criteria for collision case have been added for buckling and yielding assessment. Editorial corrections In addition to the above stated main changes, editorial corrections may have been made.

4 Contents Page 4 CONTENTS CHANGES CURRENT General Introduction LNG membrane tank designs Arrangement of cargo area General requirements Design requirements for cargo containment system Definitions Units Definitions Material selection Introduction General Means of heating Steel significant temperature Outer hull structures General Port-state requirements At supports Inner hull structures General Calculation of the inner hull temperatures Connecting members Material selection Corrosion additions Design loads Introduction Loading conditions Rule loads General Inner hull Sloshing Stern slamming Local strength Introduction Scantlings of plates and stiffeners Hull girder strength Loads Bending moments and shear forces Requirements for hull girder stresses Hull girder section modulus Buckling strength Other Requirements for inner hull stress limits Vessels with GTT MARK III containment system Vessels with GTT NO96 System Allowable stress of inner hull Strength analysis of cargo holds Introduction Loads Modelling Procedure Model extent General model idealisation... 21

5 Contents Page Girders Elements and mesh size Stiffeners Plating Boundary conditions Presentation of input and results Presentation of input data Presentation of results Strength assessment Evaluation of results and applicable acceptance criteria Longitudinal stress Mean shear stress Shear stress in the hull girder Buckling control and related acceptance criteria Stress control and related acceptance criteria Local structure analysis Model Stiffeners with brackets subjected to large deformations Other fine mesh models Documentation and result presentation Acceptance criteria Forward and aft end cargo hold analysis Fatigue assessment General Locations to be checked Hopper knuckle connections Inner bottom connection to cofferdam bulkhead Stringer connection to cofferdam bulkhead Liquid dome connection Chamfer knuckles Knuckles outside midship area Loads to be considered Dynamic load cases Load application Fatigue damage calculations Damage accumulation Part time at sea Weld improvement Weld toe grinding Weld profiling Weld details Strength assessment based on direct calculated wave loads General Requirements for the CSA-FLS and CSA(2) analysis General Locations to be checked Loading conditions Allowable stress and strength criteria Stress and buckling check (ULS analysis) General Selection of design sea state Design load cases Verification of structural loads Simplified direct strength assessment Fatigue analysis (FLS) Modelling Panel model for wave load analysis Global Structural model Mass model Wave load analysis General Objectives... 43

6 Contents Page Type of analysis Linear vs. non-linear analysis Wave load analysis parameters Numerical tools References... 45

7 Sec.1 General Page 7 1 General 1.1 Introduction This Classification Note should be considered in connection with DNV Rules for Classification of Ships, Pt.3 Ch.1, Hull Structural Design, Ships with Length 100 metres and above /1/, and Pt.5 Ch.5, Liquefied Gas Carriers /2/. The aim of this Classification Note is to describe procedures for strength analysis of liquefied gas carriers with membrane tanks. In general liquefied gas carriers with membrane tanks should satisfy the strength criteria to main class 1A1 as given in the Rules Pt.3 Ch.1 /1/. Additionally the criteria for classification notation Tanker for Liquefied Gas as given in the Rules Pt.5 Ch.5 /2/ should be complied with for the inner hull, supporting the cargo tank insulation and membranes. The requirements of DNV Rules Pt.5 Ch.5 /2/ are considered to meet the requirements of the International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk, IGC Code /3/. Optional classification notations given in the Rules Pt.3 Ch.1 Sec.15 such as PLUS-1 or PLUS-2, and CSA- FLS or CSA(2) may also be relevant. Additionally applicable requirements given by the USCG, /4/, should be satisfied for LNG vessels trading to US ports or operating under US flag. 1.2 LNG membrane tank designs In accordance with the International Code for Construction and Equipment of Ships Carrying Liquefied Gases in Bulk, the IGC Code, /3/, membrane tanks are defined as follows: Membrane tanks are non-self-supporting tanks which consist of a thin layer (membrane) supported through insulation by the adjacent hull structure. The membrane is designed in such a way that thermal and other expansion or contraction is compensated for without undue stressing of the membrane. The design vapour pressure p 0 is normally not to exceed 0.25 bar. If, however, the hull scantlings are increased accordingly and consideration is given, where appropriate, to strength of the supporting insulation, p 0 may be increased to a higher value but not exceeding 0.7 bar. The definition of membrane tanks does not exclude designs such as those in which non-metallic membranes are used or in which membranes are included or incorporated in the insulation. Such designs require, however, special consideration by the Flag Administration. In any case, the thickness of the membranes should normally not exceed 10 mm. Currently there are three membrane LNG containment systems in use in LNG vessels: GTT MARK III (Austenitic stainless steel primary barrier and composite secondary barrier) GTT NO 96 (36% Ni invar for both primary and secondary barrier) GTT CS 1 (36% Ni invar primary barrier and composite secondary barrier). The membrane and insulation arrangement of GTT Mark III LNG tank design is shown in Figure 1-1 and Figure 1-2.

8 Sec.1 General Page 8 Figure 1-1 Primary membrane, GTT Mark III Figure 1-2 GTT Mark III system

9 Sec.1 General Page 9 The membrane and insulation arrangement of the GTT NO 96 LNG tank design is shown in Figure 1-3, Figure 1-4 and Figure 1-5. Figure 1-3 Standard flat area, building principle of GTT NO 96 Figure 1-4 Corner part of GTT NO 96

10 Sec.1 General Page 10 Figure 1-5 GTT NO 96 system 1.3 Arrangement of cargo area General requirements To facilitate the support of the membrane system, it is necessary to have a double bottom, double side, trunk deck and cofferdam bulkhead. The height of double bottom and double side breadth shall comply with Pt.5 Ch.5 Sec.3 /2/. 1.4 Design requirements for cargo containment system Design requirements given by the manufacturer for the cargo containment system shall be complied with. The following items are normally considered: cargo tank geometrical requirements filling restrictions and operational restrictions hull girder strength (elongation deformations) (see also Sec.4) pump room tower connection to inner bottom (e.g. pump tower tubular structure, pump tower base support and arrangement and details of liquid/gas dome) anchoring bar connection to inner hull, if applicable. 1.5 Definitions Units The following SI-units (International System of units) are used in this Classification Note: Mass: tonnes (t) Length: millimetres (mm) or metres (m), stated in each case Time: seconds (s) Force: kilo-newtons (kn) Acceleration: metres per second square (m/s 2 ) Definitions The following notations have been applied: L = Rule length in m 1) B = Rule moulded breadth in m 1) D = Rule moulded depth in m 1) T = mean moulded summer draught in m 1) T A = min. relevant seagoing draught in m, may be taken as 0.35D if not known C B = block coefficient 1) f 1 = material factor depending on material strength group, see the Rules Pt.3 Ch.1 Sec.2 E = modulus of elasticity of the material N/mm 2 for steel. 1) For details see Rules Pt.3 Ch.1

11 Sec.1 General Page 11 Figure 1-6 shows the nomenclature for a typical midship section. Figure 1-6 Nomenclature for a midship section

12 Sec.2 Material selection Page 12 2 Material selection 2.1 Introduction General Presence of cold cargo will cause lower temperatures for parts of the hull steel structures. Therefore the steel temperatures for all hull structures, and the parts of the containment structure welded to the hull, have to be calculated. The calculation is normally to be based on empty ballast tanks since this assumption gives the lowest steel temperature Means of heating For ambient temperature conditions of 5ºC for air and 0ºC for sea-water, approved means of heating the transverse hull structure material (i.e. transverse bulkhead structure) may be used to ensure that the temperature of this material does not fall below the steel significant temperature. If lower ambient temperatures are specified according to Pt.5 Ch.5 Sec.4 [5.1.1].1.3 /2/, approved means of heating may also be used for the longitudinal hull structural material, provided the material remains suitable for the temperature conditions of 5ºC for air and 0ºC for sea-water without heating. Such means of heating are to comply with the Rules Pt.5 Ch.5 Sec.4 [5.1.1].6 /2/. 2.2 Steel significant temperature Steel significant temperature is the minimum temperature of hull structure based on: the relevant ambient temperature the cargo tanks and secondary barrier for the containment system is at design temperature of cargo tank piping systems are at design temperature of cargo tank insulation material. The matters mentioned above are valid both for outer and inner hull structures. 2.3 Outer hull structures General The outer hull structure includes the shell and deck plating of the ship and all stiffeners attached thereto. The material for the outer hull structure is to be in accordance with Pt.3 Ch.1 Sec.2, unless the calculated temperature of the material in the design condition is below -5ºC due to the effect of low temperature cargo, in which case the material is to be in accordance with the DNV Rules Pt.5 Ch.5 Sec.4 [5.1.1].1 /2/ assuming the ambient air and sea temperatures of 5ºC and 0ºC respectively. For vessels intended to operate for longer periods in areas with low air temperatures and of which the notation DAT (-X C) has been specified, the material selection of exposed members above the ballast waterline of the vessel shall comply with Pt.5 Ch.1 Sec.7 /1/ Port-state requirements In order to travel to US-ports the following requirements to hull plating have to be satisfied along the length of the cargo area /4/. the deck stringer and sheer strake must be at least Grade E steel the strake at the turn of the bilge must be of Grade D or Grade E At supports At supports (e.g. at upper and lower pump tower supports) where cold spots will occur, a local thermal analysis may be carried out in order to establish the steel significant temperature. 2.4 Inner hull structures General The inner hull structure includes inner bottom plating, longitudinal bulkhead plating, transverse bulkhead plating, floors, webs, stringers and all stiffeners attached thereto Calculation of the inner hull temperatures The calculation of the inner hull temperatures should be based on the relevant conditions as follows: IGC Code: ambient temperatures are 5ºC for air and 0ºC for seawater. For the ship to satisfy requirements, For any water in the world except Alaskan waters : ambient temperatures are 5 knots air at -18ºC and still sea water at 0ºC.

13 Sec.2 Material selection Page 13 For the ship to satisfy USCG requirements For Alaskan waters : ambient temperatures are 5 knots air at -29ºC and still sea water at -2ºC Connecting members For members connecting inner and outer hulls, the mean temperature may be taken for determining the steel grade. The load condition giving the lowest draft among load conditions of two tanks empty and the other tanks full may be used for the temperature calculations Material selection Based on the calculated temperatures the material is to be selected in accordance with the DNV Rules Pt.5 Ch.5 Sec.6 /2/. 2.5 Corrosion additions Corrosion addition shall be taken into account according to the DNV Rules Pt.3 Ch.1 /1/. The following figures show corrosion additions in way of trunk deck and cofferdam bulkhead. Figure 2-1 Corrosion additions in way of upper deck and trunk deck Void Void Cofferdam bulkhead 0.0 Void 0.0 Cargo tank Ballast tank Figure 2-2 Corrosion additions in way of transverse cofferdam bulkhead Ballast tank

14 Sec.3 Design loads Page 14 3 Design loads 3.1 Introduction Design loads according the Rules Pt.3 Ch.1, /1/, are applicable for all parts the hull structure. In addition loads from the cargo, based on the Rules Pt.5 Ch.5, /2/, should be applied when analysing local strength of plates and stiffeners of the parts of inner hull supporting the membrane tanks. Design loads and load cases for strength analysis of the cargo hold are described separately in Sec.6. For fatigue assessment the loads applied are described in DNV Classification Note 30.7 Fatigue Assessment of Ship Structures /5/. If direct wave load and sea keeping analysis is requested, e.g. in case of un-proven designs or in case of classification notation CSA-FLS or CSA(2), a guide on such analysis is given in Sec.8. Further details on the application of direct wave loads in fatigue assessment are given in CN Loading conditions At least the following loading conditions shall be examined: Loading condition (ULS, Harbour) resulting in extreme still water hull girder loads. Loading condition (ULS, Seagoing) resulting in a combination of extreme still water hull girder loads and wave induced hull girder loads. Loading condition (ULS, Seagoing) resulting in extreme liquid acceleration levels in the cargo tanks. Loading condition (ALS, Accidental) resulting in collision load. Both harbour and sea-going conditions, inclusive any sequential ballast exchange conditions, are to be reviewed. Based on the above, the following design parameters should be defined: Minimum draft in ballast, at FP, AP and at L/2. Maximum draft with one cargo tank empty. In case of filling of double hull ballast tanks in way of an empty cargo tank this should be noted as an operational limitation to be specified in loading manual. Minimum draft with only one cargo tank full, unless operational limitations, e.g. specifying minimum 2 cargo tanks to be filled in any cargo loading conditions. For fatigue assessment, the following two loading conditions shall normally be taken into account: Fully loaded condition, departure. Normal ballast condition, arrival. 3.3 Rule loads General All parts of the hull should be checked according to the loads as described in the Rules Pt.3 Ch.1 /1/ Inner hull Cargo tank pressures, based on a 10-8 probability level for the North Atlantic, as given in the Rules Pt.5 Ch.5 Sec.4 /2/ shall be applied for the local scantlings for inner hull (plates and stiffeners). The acceleration, a b, is calculated by combining the three component accelerations a x, a y and a z values according to an ellipsoid surface. For different directions of a b in the ellipsoid, the pressure at different corner locations in the cargo tank is calculated. Between corner points the pressure may be found by linear interpolation. The Rule values of a x, a y and a z may be replaced by accelerations calculated from direct wave load analysis. These accelerations shall be on a 10-8 probability level for the North Atlantic and calculated for the loading conditions in the loading manual that give the highest accelerations. As a guidance, the loading conditions with only one tank full, while other tanks are empty are normally considered to produce the largest transverse accelerations Sloshing Large prismatic membrane tanks may be vulnerable with respect to sloshing and sloshing impact loads, for partially filled tanks, in particular. These tanks are therefore subject to filling level restrictions in order to avoid operation with the most critical filling level. For details, see Classification Notes 30.9 Sloshing analysis of LNG membrane tanks /8/. Sloshing analysis is normally required for vessels with unconventional tank size, typically vessels larger than

15 Sec.3 Design loads Page cubic metres, or tank design with no or limited experience. The following locations in no.2 cargo tank should be checked as representative locations for sloshing. Lower chamfer connection at middle of a cargo tank due to roll dominant motion. Lower chamfer connection at transverse bulkhead due to pitch and surge dominant motion. Upper chamfer connection at middle of a cargo tank due to roll dominant motion. Upper chamfer connection at transverse bulkhead due to pitch and surge dominant motion. Upper chamfer connection in way if inner deck due to pitch and surge dominant motion. Results of the analysis shall be applied to the other cargo tanks including no.1 cargo tank, unless a sloshing analysis for the other cargo tanks is carried out Stern slamming For ships with twin skegs impact pressure on the stern should be considered evaluated together with the slamming requirements of DNV Rules Pt.3 Ch.1 Sec.6 /1/. The impact pressures may be obtained by model tests or direct calculations.

16 Sec.4 Local strength Page 16 4 Local strength 4.1 Introduction All parts of the vessel should be checked with respect to the Rule requirements for main class as given in Pt.3 Ch.1 /1/. This includes also the inner hull members supporting the membrane tanks. 4.2 Scantlings of plates and stiffeners The local scantlings of plates and stiffeners of inner hull supporting membrane tanks shall satisfy the following: The required plate thickness for the inner hull is: The required section modulus for stiffeners for the inner hull is: where: p 15 t [mm] σ k eq t =,8k a s l sp Z = mσ eq p eq = cargo tank pressures, given in DNV Rules Pt.5 Ch.5 Sec.4 [6.1.1] s = stiffener spacing [m] l = effective stiffener span [m], i.e., distance between web frames taking web stiffener on top into account σ = 0.8σ f for plates σ = 0.75σ f for stiffeners, but not to be taken greater than σ f - σ L - σ D/H σ f = minimum upper yield stress [N/mm 2 ] σ L = sum of longitudinal stresses based on wave bending moment with a probability level of 10-8 and maximum hogging/sagging still water bending moments in the considered loaded cargo tank [N/ mm 2 ] m = bending moment factor, may be determined based on direct stress calculations = 7.5 for vertical stiffeners simply supported at one or both ends = 12 for continuous longitudinal stiffeners = 10 for horizontal or vertical stiffeners at transverse bulkheads t k = corrosion addition (mm), see the Rules Pt.3 Ch.1 Sec.2 D w k = corrosion addition for stiffeners, see the Rules Pt.3 Ch.1 Sec.3 C1004 σ D/H = double hull stress in N/mm 2 taken from plate flange of the girders perpendicular to the stiffener direction at the considered position. The stress is based on maximum bending stress from the cargo tank loaded conditions k a = correction factor for aspect ratio of plate field = ( s l)2 = maximum 1.0 for s/l = 0.4 = minimum 0.72 for s/l = 1.0. w k [cm 3 ]

17 Sec.5 Hull girder strength Page 17 5 Hull girder strength 5.1 Loads Bending moments and shear forces Hull girder bending moments and hull girder shear forces shall be applied according to the Rules Pt.3 Ch.1 Sec.5 /1/. The hull girder strength assessment shall be made by applying permissible still water bending moments and still water shear forces given in the loading manual. When considering actual still water bending moments and shear forces, all combination of empty and full cargo tanks shall be considered including ballast exchange. The permissible still water bending moments shall in general not be lower than the standard Rule values. If the maximum still water bending moments are well below the standard Rule values, smaller values may be used as design basis but no less than 50% of the standard Rule values. This requires that all relevant loaded conditions as well as ballast conditions are checked, and that the loading manual shall consider possibilities for variation of the distribution of cargo and ballast exceeding the conditions considered. In case that any of the maximum still water bending moments and still water shear forces exceed the standard Rule values the maximum value(s) shall be applied. 5.2 Requirements for hull girder stresses Hull girder section modulus The requirements to hull girder section modulus are given in the Rules Pt.3 Ch.1 Sec.5 C303 /1/. The hull girder section modulus as well as the hull girder shear properties should be based on gross scantlings (no deduction of the Rule corrosion addition). Alternatively a global FE model i.e. of the entire ship may be used to determine the hull girder stresses. If the FE-model is based on net-scantlings, the requirement may be adjusted to account for the difference on net and gross scantlings Buckling strength Buckling strength check shall be carried out according to the Rules Pt.3 Ch.1 Sec.12 /1/ Other In case of the optional classification notation CSA(2) the hull girder strength shall satisfy criteria given in the Rules Pt.3 Ch.1 Sec.15 /1/. This includes both yield and ultimate panel strength criteria. Details are given in Sec Requirements for inner hull stress limits Vessels with GTT MARK III containment system As the primary barrier of stainless steel is double corrugated, the in plane stiffness is very low. Thus this type of membrane is less sensitive to hull deformations than plane membranes. The following design limitation is applicable with respect to acceptable longitudinal elongation of inner hull structure due to hull girder bending. /6/. 2 σ + σ + σ 185 N / mm where: st dyn loc σ st = hull girder bending stress due to maximum still water bending moment σ dyn = hull girder bending stress due to maximum wave water bending moment corresponding to 10-8 probability in winter North Atlantic σ loc = Maximum bending stress of inner hull due to double hull deflection when considering alternate loading cases. The bending stress may be taken in the middle between the floors/transverse frames Vessels with GTT NO96 System Invar membrane may in the longitudinal direction of the ship be considered as a plane plate rigidly connected to the cofferdam bulkhead structure. In order to keep the total stress level in the membrane at an acceptable level, the cargo containment system designer has given the following restrictions to be complied with when evaluating the necessary section modulus for the hull girder in the cargo area. /7/ σ + σ st dyn 120 N / mm 2

18 Sec.5 Hull girder strength Page 18 where: σ st = hull girder bending stress due to the maximum still water moment calculated for the most severe loaded condition or ballast seagoing condition σ dyn = hull girder bending stress due to a wave corresponding to a 10-8 probability in winter North Atlantic operation Allowable stress of inner hull The requirement of inner hull stress given in [5.3] above and others if relevant shall be confirmed by the designer of the cargo containment system for each project.

19 Sec.6 Strength analysis of cargo holds Page 19 6 Strength analysis of cargo holds 6.1 Introduction The following describes acceptable methods for the strength analysis, with focus on finite element models of the midship area. The analysis shall confirm that the stress levels are acceptable when the structures are loaded in accordance with the described design conditions. Any recognised calculation method or computer program may be applied, provided the effects of bending, shear, axial, and torsional deformations are adequately considered. 6.2 Loads The basic loading conditions as described in [3.2] shall normally be considered. The load patterns given in Table 6-1 are based on these conditions, and are regarded as the minimum conditions. Other conditions may be considered when relevant. Based on operational limitations, e.g. if surrounding ballast tanks in way of empty or filled cargo tank are always filled, the standard load cases shown in Table 6-1 may be modified. Relevant loads according to the Rules Pt.3 Ch.1 Sec.12 /1/ should be analysed. These load cases are shown in Table 6-1. The following hull girder bending moments should be applied to each load case. LC1: design still water hogging bending moment + max rule wave hogging bending moment amidships according to Pt.3 Ch.1 Sec.5 B204 LC2: design still water sagging bending moment + max rule wave sagging bending moment amidships according to Pt.3 Ch.1 Sec.5 B204 LC3: design still water sagging bending moment LC4: no bending moment LC5: no bending moment. Table 6-1 Load cases for strength analysis of cargo holds LC No Draught Condition External pressure Internal pressure Figure LC1 T 1) Sea Dynamic Static 2) LC2 T A Sea Static Dynamic 3) LC3 T A 6) Harbour Static Static 2) LC4 T A Sea Dynamic 4) Dynamic 5) LC5 T Accidental Static Accidental 0.5 g 0 forward Notes: 1) Maximum draft with one cargo tank empty may be used instead of scantling draft T, if this is stated as an operational limitation in the loading manual 2) Pressure should include overpressure, p 0 ; p = ρ g 0 h s + p 0 3) Pressure should include vertical acceleration and overpressure, p 0 ; p = ρ (g a v ) h s + p 0 4) External pressure in accordance with Rules Pt.3 Ch.1 Sec.12 B300 5) Internal pressure in accordance with Rules Pt.3 Ch.1 Sec.12 B300, overpressure p 0 to be added 6) Draught not to be taken greater than minimum of L and the minimum ballast draught where: T A = Minimum relevant seagoing draught in m, may be taken as 0.35D if not known.

20 Sec.6 Strength analysis of cargo holds Page 20 The design cargo density shall not be taken less than the maximum acceptable cargo density (usually 0.5 t/m 3 ) and the design overpressure (p 0 ) shall not be less than 25 kn/m 2 and shall be applied for all loaded cargo tanks. The loading should be applied in the form of lateral pressure on shell elements, (or line loads on membrane elements). Alternative load application may be specially considered. Self weigh of hull structures and cargo containment system shall be taken into account. 6.3 Modelling Procedure In general a finite element model shall provide results suitable for performing buckling analysis and for evaluating the strength of the girder system. This may be achieved by using a three dimensional finite element model of the midship area, alternatively supported by one or more levels of sub-models. In the Rules Pt.3 Ch.1 Sec.12 /1/, types of analyses called cargo tank analysis and frame and girder analysis are described. Two different approaches may be applied. Whichever approach is used, the model or sets of models applied shall give a proper presentation of the following structure: typical web frame at middle of tanks web frame adjacent to transverse bulkhead transverse bulkhead horizontal stringer including longitudinal stringers in double side transverse bulkhead vertical girders including longitudinal girders in double bottom and trunk deck. In addition, analyses of local structure may be made for determining the detailed stress level in stiffeners subject to relative support deflections. Such analyses may also be necessary in way of girder webs with high stress level and/or large cut-outs i.e. hopper tank area Model extent The extent of the model of the tank structures amidships covers two tank lengths (½+1+½) and full breadth of the vessel. Figure 6-1 Example of a cargo hold model For vessels with unconventional design/size, it should be considered to use a model covering three cargo tanks including foremost cargo tank. Alternatively, two separate models, i.e. a midship model of ½ ½ cargo tanks and a no.1 cargo tank model may be used.

21 Sec.6 Strength analysis of cargo holds Page General model idealisation All main longitudinal and transverse geometry shall be included in the model. The scantlings shall be modelled with net scantlings. Half thicknesses shall be applied in symmetry planes in case of odd numbers of web frames Girders Openings in the girder webs will be present in ship structures for access and pipe penetrations. If such cut outs affect the overall force distribution or stiffness of the girder, the cut out shall be accounted for in the model. This may be done by either: reducing the thickness according to the formula below, or by geometrical modelling of the cut out. For the first approach the mean girder web thickness may be taken as follows: where: t w = web thickness t mean h h = h r co co t W l co h co h r co = l 2 co ( h h ) 2 = length of cut-out = height of cut-out = height of girder web. co When r co is larger than 1.2, (r co > 1.2), it is advised that the cut-out is included in the model in one of the two ways given above. When r co is larger than 2, (r co > 2), it is advised that the cut out is geometrically included in the model. t w l co h co h Figure 6-2 Cut-out in web Smaller openings for access and piping may be ignored. However, when such openings are ignored this must be considered when evaluating the results. The reduced efficiency of curved flanges shall be accounted for in the calculations. This may be included by reduced thickness of plate elements or cross sectional areas of beam and rod elements unless already accounted for by other means. Such reduced efficiency may be calculated as given in Pt.3 Ch.1 Sec Elements and mesh size The performance of the model is closely linked to the type of elements and the mesh topology that is used. The mesh described here is adequate for representing the cargo tank model and frame and girder model as defined in the Rules Pt.3 Ch.1 Sec.12. The following guidance on mesh size etc. is based on the assumption that 4-noded shell or membrane elements in combination with 2-noded beam or truss elements are used. Higher order elements such as 8-noded or 6-noded elements with a coarser mesh than described below may be used provided that the structure and the load distribution are properly described. In general the mesh size should be decided considering proper stiffness representation and load distribution of tank and sea pressure on shell- or membrane elements.

22 Sec.6 Strength analysis of cargo holds Page Stiffeners Continuous stiffeners oriented in the direction of the girders contribute to the overall bending stiffness of the girders and shall be included in the model in such a way that the bending stiffness of the girder is correctly modelled. Non-continuous stiffeners may be included in the model as beam element with reduced efficiency. Sectional area of such stiffeners may be calculated as follows: Sniped at both ends: 30% of actual area Sniped at one end: 70% of actual area Connected at both ends: 100% of actual area. Stiffeners on girders perpendicular to the plate flanges may be included in the model when considered important. Buckling stiffeners considered less important for the stress distribution, as sniped buckling stiffeners, may be ignored. Longitudinals and other continuous stiffeners including stiffeners on transverse bulkheads should be included in the model. These structural parts may be represented by 2-noded eccentric beam elements. If the program used can not consider eccentricity of profiles, precautions shall be taken so that the model gives the correct section modulus for double and single skin structures. However, axial area and shear area of such stiffeners should only represent the profile without the plate flange. Special attention should be paid when connecting a beam element to one node of a shell or membrane element. The end of the beam elements may then be assumed as hinged in the calculation. This will affect the load distribution. The mentioned effect may be avoided by introducing an overlap between the beam and shell elements. Other stiffeners including buckling stiffeners and free flanges of girders may be modelled as 2-noded beam- or truss elements with effective cross sectional areas calculated according to the Rules Plating 4-noded shell or membrane elements may be used in connection with mesh size as described below. 3-noded shell or membrane elements should normally not be used in areas where stresses should be checked. The panel mesh should preferably represent actual plate panel between stiffeners so that the stresses for the control of yield and buckling strength can be read and averaged from the results without interpolation or extrapolation. In practise, the following mesh density may be applied: There may be only one element between longitudinals. There should be a minimum of three elements over the height of girders, the mesh should in general and as far as practical follow the stiffener system on the girder. Two elements between transverse girders. A more refined mesh may be considered for easier description of the geometry. Inside hopper tank areas, the mesh should in general follow the stiffener system. The mesh should be fine enough to represent the shape of large openings in the web frame inside the hopper tank. See Figure 6-3.

23 Sec.6 Strength analysis of cargo holds Page 23 Figure 6-3 Meshes on a typical web frame 6.4 Boundary conditions Boundary conditions are in general to be applied as given in Table 6-2. The model may be supported in vertical direction by applying vertical springs and horizontal springs at the intersection between the double side and the middle line of the transverse double bulkheads. The spring constant may be calculated as follows, ignoring the effect of bending deflection: where: A Si l t i = net shear area for of plate = the length of one cargo tank = is the side or inner side. K i = 0.5 8A Si E 7.8 l t Alternatively, unbalanced vertical forces and horizontal forces for each loading condition may be applied at the intersections between double side and the middle line of the transverse double bulkheads. The boundary conditions in Table 6-2 introduce a counteracting force in the longitudinal direction, for load case LC1. The magnitude of the force will vary for each load case but shall in general be equal to the net load on the transverse bulkhead. If this counteracting force is not applied, the stress results may be adjusted for the compression caused by the net load on the transverse bulkheads.

24 Sec.6 Strength analysis of cargo holds Page 24 Table 6-2 Boundary conditions for cargo tank analysis Plane B Plane A Neutral axis Independent point d F x Central Line y z x δx δy δz θx θy θz Plane A RL RL RL Plane B RL RL RL Point d at neutral axis in plane A F X BM Point d at neutral axis in plane B X Deck, inner deck, bottom, inner bottom springs Side, inner side springs where: X RL BM F x Fixed. Nodal points of all longitudinal elements rigidly linked to independent point at neutral axis on centreline. Bending moment according to the above. Counteracting longitudinal force When vertical springs are applied at side/inner side connection to transverse bulkheads to obtain equilibrium in the vertical direction, the model should be restricted from translation in vertical direction by fixed boundary condition in one node.

25 Sec.6 Strength analysis of cargo holds Page 25 In general a bending moment shall be applied to the end of the model. The size of this bending moment shall be such that the vertical hull girder bending moment, as described in the rules, is achieved in the middle of the model. The magnitude of the bending moment may be adjusted to account for differences of gross and net scantlings. The hull girder bending moment can be reduced by a factor of Z mod / Z gross. Where Z mod is the hull girder section modulus as modelled (i.e. gross scantling reduced by the corrosion addition, t k ) and Z gross, the hull girder section modulus based on actual scantlings. As the bottom is critical with respect to buckling, the bending moment correction may normally be based on the section modulus at bottom. In addition to this bending moment the local loads will also set up a semi-global hull girder bending moment that may be compensated for when applying the bending moment. 6.5 Presentation of input and results The requirements given in DNV Rules Pt.3 Ch.1 Sec.12 A300 regarding proper documentation of the model shall be followed Presentation of input data A reference to the set of drawings (drawing numbers and versions) the model is based on should be given. The modelled geometry is to be documented preferably as an extract directly from the generated model. The following input shall be reflected: plate thickness free flange sectional area considering efficiency of curved flanges beam section properties boundary conditions load cases Presentation of results The stress presentation should be based on stresses at the middle of the element thickness, excluding plate bending stress, in the form of ISO-stress contours in general. Numerical values should also be presented for highly stressed areas (e.g. areas where stress exceeds 60% of allowable limits or areas in way of openings not included in the model). The following shall be presented: deformed shapes transverse or vertical membrane stress of shell/plate elements longitudinal membrane stresses where relevant shear stress of transverse, longitudinal and vertical girders membrane stresses of transverse, longitudinal and vertical girders von Mises equivalent stress of transverse girders axial stress of free flanges. in case the flange is represented by a bar only the axial force may be available the unbalanced forces and moments should be given for all load cases. 6.6 Strength assessment Evaluation of results and applicable acceptance criteria In the following procedures for handling results and applicable acceptance criteria are described. Acceptance criteria are in general given in the Rules Pt.3 Ch.1 Sec.12 /1/ Longitudinal stress For buckling control the following longitudinal stresses may normally be considered: or σ L = σ DBL + σ S + σ W where: σ LR = σ DBL + σ S + σ WR σ L = Sum of longitudinal stresses based on wave bending moment with a probability of 10-8 of exceedance. σ LR = Sum of longitudinal stresses based on wave bending moments with a probability of 10-4 of exceedance. σ DBL = Longitudinal girder bending stresses resulting from bending of large stiffened panels between transverse bulkheads, due to local load on an individual cargo tank. These stresses are often referred to as double bottom stresses, and may be taken as results from the cargo tank analysis at one of two adjacent girders giving the maximum longitudinal stress at inner bottom level = Longitudinal hull girder bending stresses defined as M S /Z i, where M S is the still water bending moment σ S

26 Sec.6 Strength analysis of cargo holds Page 26 and Z i is the section modulus at the considered position (i) based on gross scantling. (No corrosion addition deducted). Design limits for sagging or hogging moment to be applied as values for M S. σ W = Longitudinal hull girder bending stresses caused by wave bending moment M W, which correspond to a probability of exceedance of σ W = M W /Z i. M W is defined in DNV Rules Pt.3 Ch.1 Sec.5 σ WR = Longitudinal hull girder bending stresses caused by reduced wave bending moment M WR, which corresponds to a probability of exceedance of M WR = 0.59M W. Relevant stress components related to hull girder, girders and stiffeners are defined in Figure 6-4. Figure 6-4 Stress components related to bending of hull girder, double bottom girders and bottom stiffeners It should also be noted that the stiffener bending stress is not a part of the girder bending stresses. The magnitude of the stiffener bending stress included in the stress results depends on the mesh division and the element type that is used. This is shown in Figure 6-5 where the stiffener bending stress, as calculated by the FE-model, is shown depending on the mesh size (valid for 4-noded shell elements). One element between floors results in zero stiffener bending. Two elements between floors result in a linear distribution with approximately zero bending in the middle of the elements. When a relatively fine mesh is used in the longitudinal direction the effect of stiffener bending stresses should be isolated from the girder bending stresses when buckling and stress level are checked. Figure 6-5 Normal stress caused by local load on the stiffener, depending on number of elements along the stiffener Mean shear stress The mean shear stress, τ mean, is to be used for the capacity check of a plate. This may be defined as the shear force divided by the effective shear area. For results from finite element methods the mean shear stress may be taken as the average shear stress in elements located within the actual plate field, and corrected with a factor

27 Sec.6 Strength analysis of cargo holds Page 27 describing the actual shear area compared to the modelled shear area when this is relevant. For a plate field with n elements the following apply: where: A i τ i A w = the effective shear area of element i = the shear stress of element i = effective shear area according to the Rules Pt.3 Ch.1 Sec Shear stress in the hull girder. It is not necessary to consider hull girder shear stresses in longitudinal bulkhead and side unless special boundary conditions as well as loads are applied. The shear strength of the hull girder may normally be evaluated in accordance with the Rules Pt.3 Ch.1 Sec.5 /1/ Buckling control and related acceptance criteria Table 6-3 gives examples of areas to be checked for buckling and the applicable method and acceptance criteria. In case of any differences in the acceptance criteria given here compared with those given in the Rules for Ships, the latter shall apply. Table 6-3 Examples of areas to be checked and procedure for buckling control Item Remarks Buckling of girder plate flanges in: compressive stress with ψ = 1 and allowable usage factor, η = 0.8 Uniaxial buckling in transverse direction to be analysed based on mean transverse double bottom (including Uniaxial buckling in longitudinal direction to be analysed according to the Rules bottom and inner bottom) Sec.13 /1/ based on hull girder stress σ al = σ S + σ W double side (including side Bi-axial buckling to be analysed based on longitudinal stress and mean transverse and inner side) stress inner deck and trunk deck When the longitudinal stresses are obtained from hull girder loads on a probability of exceedance of 10-4, usage factors η x = η y = 0.85 shall be used. For a probability of exceedance of 10-8, usage factors η x = η y = 1.0 shall be used Remark: Mean transverse compressive stress is to be calculated from a group of elements representing one plate field between stiffeners Longitudinal stresses are to be taken as described in [6.6] Buckling of girder plate flanges in: transverse bulkheads Buckling of girder webs in: double bottom double side inner deck/deck-trunk transverse double bulkhead τ i= n ( τ A ) i = i= 1 mean i= n Buckling to be analysed based on uni-axial compressive stress with ψ = 1 and allowable usage factor, η = 0.8 for harbour and seagoing condition and η = 1.0 for accidental condition Bi-axial buckling to be checked when relevant Remark: Mean uni-axial (transverse) compressive stress are normally to be calculated from a group of elements representing one plate field between stiffeners Buckling of girder webs with two plate flanges: Buckling to be analysed based on mean shear stress with allowable usage factor, η = Buckling caused by compressive loads from sea and cargo, alternatively together with shear, to be checked when relevant Buckling of girder webs with one plate flange: Buckling to be calculated as for girder plate flanges. Buckling to be analysed based on mean shear stress with allowable usage factor, η = Bi-axial buckling especially in the bracket areas with shear Remark: Mean shear stress to be taken as described in [6.6], representing one plate field between stiffeners Stress control and related acceptance criteria Table 6-4 gives examples of areas where stress level shall be controlled together with the applicable method and acceptance criteria. In case of any differences in the acceptance criteria given here compared with those given in the Rules, the latter shall apply. i= 1 A i i

28 Sec.6 Strength analysis of cargo holds Page 28 Table 6-4 Examples of areas to be checked and procedure for control of stresses Item Remarks Stresses in longitudinal girders Allowable longitudinal nominal normal stress, σ = 190f 1. Based on a probability of exceedance of 10-4 (longitudinal stress, σ LR = σ DBL + σ S + σ WR < 190 f 1 ) Allowable mean shear stress τ = 90f 1 (sea) and τ = 100f 1 (harbour) for girders with one plate flange, and τ = 100f 1 (sea) and τ = 110f 1 (harbour) for girders with two plate flanges Shear stress in way of openings not included in the calculation to be evaluated in terms of mean shear stress Ref. [6.6] Stresses in transverse and Allowable nominal normal stress in flanges of girders σ = 160f 1 (sea), σ = 180f 1 vertical girders with two plate (harbour) and σ = 235f 1 (accidental) in general flanges like: Allowable mean shear stress of girder webs, τ = 100f 1 (sea), 110f 1 (harbour) and double bottom τ = 136f 1 (accidental). Shear stress in way of openings not included in the double side calculation to be evaluated in terms of mean shear stress Ref. [6.6] other double skin Allowable equivalent stress, σ e = 180f 1 for seagoing conditions, σ e = 200f 1 for constructions harbour conditions and σ e = 235f 1 for accidental condition Stresses in transverse and vertical girders with one plate flange Stresses in brackets 6.7 Local structure analysis Allowable nominal normal stress, σ = 160f 1 (sea) and σ = 180f 1 (harbour) in general Allowable mean shear stress τ = 90f 1 (sea) and 100f 1 (harbour). Shear stress in way of openings not included in the calculation to be evaluated in terms of mean shear stress. Ref. [6.6] Allowable equivalent stress, σ e = 180f 1 for seagoing conditions and σ e = 200f 1 for harbour conditions Under the assumption that the bracket is of favourable design the allowable axial stress in the middle of the bracket s free edge may be taken as 200f 1 When there is uncertainty related to the local design of the bracket toe areas a fine mesh model is to be made Model Local structure analysis may be used to analyse local nominal stresses in laterally loaded local stiffeners and their connected brackets, subjected to relative deformations between supports. The model and analysis described in the following are suitable for calculating: nominal stresses in stiffeners stresses in brackets free edge. These models may be included in the 3D cargo tank analysis model as described in [6.7.2]-[6.7.5], or run separately as sub-models with prescribed boundary deformations from a 3D-analysis. When using prescribed deformations as boundary conditions for sub-models it very important that the stiffness of the coarse and fine mesh are the same. Comparison of the shear force at characteristic sections in coarse and fine mesh model may be necessary. Local pressure loads shall be applied to the local models Stiffeners with brackets subjected to large deformations Relative deformations between stiffener supports may give rise to high stresses in local areas. Typical areas to be considered are: longitudinals in double bottom and adjoining vertical bulkhead members double side longitudinals and adjoining horizontal bulkhead members. Model extent The model is recommended to have the following extent: the stiffener model shall extend to a stiffener support at least two frame spacing outside the area subject to the study the width of the model shall be at least ½ + ½ stiffener spacing. Elements and element mesh Normally three (3) 4-noded elements are to be used over the web height of the stiffeners. Corresponding sizes are to be used for the plate flange. The flange is to be modelled with one element over the flange width for unsymmetrical profiles and two elements for symmetrical profiles. The face plate may alternatively be modelled with 2-noded beam elements. Effective flange in curved areas should however be represented properly. The element mesh along the stiffener shall be fine enough for providing a good aspect ratio of the elements.

29 Sec.6 Strength analysis of cargo holds Page 29 Boundary conditions If the model is run separately, prescribed displacements or forces are to be taken from the cargo tank analysis (or frame and girder analysis when relevant). These displacements or forces are to be applied to the nodes where the stiffener is intersecting with the supporting structure. In the ends and along the plate edge of the model, symmetry conditions are to be applied Other fine mesh models. Other fine mesh models may be made for the study of critical details. If the accept criteria are based on maximum allowable nominal stresses the modelling principles described above should be followed Documentation and result presentation Documentation and result presentation is to follow the principles given in [6.5]. The following stresses shall be given. normal stresses and shear stresses of plate/membrane elements axial stress of truss/beam elements Acceptance criteria Acceptance criteria for stress results from local structure analysis are given in the Rule Pt.3 Ch.1 Sec.12 Table B Forward and aft end cargo hold analysis In addition finite element analysis for the following areas may be required in order to assess the structural strength based on hull girder bending moments: longitudinal members in deck house between trunk deck and upper deck fore end of the trunk deck for vessels equipped with the Mark III cargo containment system vertical girders in fore end cofferdam bulkhead between trunk deck and upper deck for vessels equipped with the Mark III cargo containment system.

30 Sec.7 Fatigue assessment Page 30 7 Fatigue assessment 7.1 General The fatigue assessment is limited to steel structures in the cargo area excluding the cargo containment system and its components. The inner hull structures supporting the cargo containment system should be designed to satisfy a design fatigue life of minimum 20 years in North Atlantic operation /1/. The outer hull should be designed to satisfy a design fatigue life as given in the Rules Pt.3. Ch.1 Sec.16. Unless otherwise described, details of the fatigue strength assessment are given in DNV Classification Notes 30.7 Fatigue Assessment of Ship Structures. Direct fatigue analysis by using wave loads may be necessary for LNG carriers with membrane types without previous service experiences. Details are given in Sec Locations to be checked The required locations to be checked are described in the DNV Rules Pt.3 Ch.1 Sec.16. Fatigue strength assessment shall be carried out for the following locations: longitudinals in way of end-supports in cargo area lower and upper hopper knuckle connections forming boundary of inner skin amidships inner bottom connection to transverse cofferdam bulkhead double side stringer connection to transverse cofferdam bulkhead liquid dome coaming connection to deck, if applicable termination of aft end of no.1 inner longitudinal bulkhead, if applicable. Locations for special notations, such as PLUS and CSA notations are described in DNV rules Pt.3 Ch.1 Sec.15. The following locations shall be checked in addition to locations above: longitudinal stiffener connections to web plating in ballast tanks in the cargo area including forward ballast tank lower and upper chamfer knuckle connections longitudinal bulkhead knuckle in way of cofferdam bulkhead large openings, e.g. gas dome, access opening greater than or equal to 600 mm 800 mm in upper and trunk decks in cargo area fore and aft end of trunk deck terminations. Structural elements in the cargo area being of possible interest for fatigue evaluation are described as follows, see also Sec.8: motor room structure supports doors and openings in deck house subject to hull girder stress pump tower base support connection to inner bottom any attachment to inner hull that may lead to abrupt collapse of hull primary structures or pump tower before gas detection other location subject to high dynamic stress and/or high stress concentration Hopper knuckle connections Fatigue strength of lower and upper hopper knuckle connections for LNG carriers is normally critical. The double side and bottom structures of LNG carriers are long, thus hull bending stresses are therefore normally significant. Figure 7-1 shows an example of a fine element model with plate thickness size meshes. Figure 7-2 and Figure 7-3 illustrate the hotspots to be evaluated for lower and upper hotspot respectively.

31 Sec.7 Fatigue assessment Page 31 Figure 7-1 A finite element model of lower and upper hopper knuckles HS2 B HS6 HS1 HS5 HS4 B HS5 A HS4 HS3 A A HS3 A Section A-A Section B-B Floor HS6 HS5 HS4 HS3 Girder Figure 7-2 Hot spots to be checked, lower hopper knuckle B B HS1 A HS5 A HS1 HS5 HS3 HS2 HS6 HS4 Stringer A Section A-A HS3 Web B A HS5 HS6 HS2 B Section B-B HS6 HS4 Figure 7-3 Hot spots to be checked, upper hopper knuckle

32 Sec.7 Fatigue assessment Page Inner bottom connection to cofferdam bulkhead The inner bottom connection to transverse bulkhead shall be checked, since the dynamic pressure due to pitch is high in the long cargo tanks, see Figure 7-4. An example of finite element model is shown in Figure 7-5. Cofferdam bulkhead Weld HS9 HS7 HS5 HS6 HS8 HS10 Inner Bottom or L. BHD. HS1 HS2 A HS3 HS11 Weld HS12 HS4 A PLAN A-A Transverse Web HS3 HS11 HS12 HS4 Girder or Stringer Figure 7-4 Some examples of hot spots within +/- 150 mm from a web frame Figure 7-5 A finite element model of inner bottom connection to transverse bulkhead Stringer connection to cofferdam bulkhead The fatigue strength of a stinger connection may be estimated by comparing nominal stress between inner bottom connection to cofferdam bulkhead and a stringer connection from the midship cargo tank analysis.

33 Sec.7 Fatigue assessment Page Liquid dome connection For the liquid dome, the fatigue strength shall be checked for the hot spots at forward and aft coamings and the deck opening, as shown in Figure 7-6. Detail B Section A-A Fore and aft corners Trunk deck D<1,0, N.A. D<1,0, N.A. A Detail B Fore and aft corners A D<1,0, N.A. Figure 7-6 Hot spots in way of liquid dome Fatigue strength of the other liquid domes may be estimated by comparing nominal stress level. Special attention shall be given to liquid dome coaming top and opening in way of cofferdam bulkhead, for a recess type liquid dome corner. Figure 7-7 shows a finite element model with thickness size mesh. Figure 7-7 A finite element model of dome Chamfer knuckles For lower and upper chamfer connection, fatigue strength of a chamfer connection may be estimated by comparing nominal stress of the chamfer knuckle connections with a hopper knuckle connection of similar type from the midship cargo tank analysis Knuckles outside midship area If a fine mesh models outside the midship region are not available, comparative stress estimation may be made between the midship web-frame and a representative web-frame for the location to be checked as shown in Figure 7-8.

34 Sec.7 Fatigue assessment Page 34 Figure 7-8 Web frame models at the midship and considered locations 7.3 Loads to be considered Dynamic load cases The following dynamic load cases are relevant for the fatigue strength assessment: LC1: LC2: LC3: LC4: External wave pressure Internal pressure ballast pressure cargo pressure due to heaving/rolling cargo pressure due to pitching Vertical wave bending moment Horizontal wave bending moment. The loads for the ballast condition and the fully loaded condition are to be evaluated separately. The loads are to be calculated according to DNV Classification Notes 30.7 for Fatigue Assessment of Ship Structure. The maximum pressure envelope due to heaving and rolling should be applied to the finite element model for internal cargo pressure. The load case for cargo pressure due to pitching is only relevant for the cofferdam connections to inner bottom and inner side. To take into account the total thickness of the insulation, the cargo density, ρ h, for cargo loads may be adjusted as follows: where: V ρh = ρc V ρ c = design cargo density of LNG, 0.5 t/m 3 V C = volume of cargo tank measured in way of primary barrier, in m 3 V H = volume of cargo hold measured in way of moulded dimensions of inner hull, in m Load application For each loading condition, combined local stress components due to simultaneous internal and external pressure loads are to be combined with global stress components induced by hull girder wave bending. Detailed calculations of stress components, stress combination and stress concentration factors are given in CN30.7. Line loads may be applied for longitudinals of inner hull for LC2, when loads are transmitted through the mastics of the cargo containment system. This is applicable for both cargo pressure loads and ballast pressure loads. For longitudinals in way of end supports, LC1 to LC4 applies. For cut-outs, web stiffener on top, lug connection to transverse webs in way of longitudinal connections, if applicable by additional class notation, LC3 and LC4 may be omitted as the hull girder loads are negligible with respect to fatigue life for these details. C H

35 Sec.7 Fatigue assessment Page 35 For deck openings, access openings, cargo tank dome on the decks, forward end of trunk deck connection and end connections of trunk deck to deck house, where local pressures from cargo, ballast or sea may be disregarded, only LC3 and LC4 applies. For inner bottom connection to cofferdam bulkhead internal cargo pressure due to pitching needs to be evaluated in addition to the internal cargo pressure due to heaving/rolling. It is assumed they contribute equally to the fatigue life, hence the stress-range due to cargo pressure is found from 50% heaving/rolling and 50% pitching. 7.4 Fatigue damage calculations Damage accumulation The requirement to fatigue life is stated in the DNV Rules, Pt.5 Ch.5 and DNV Rules Pt.3 Ch.1 Sec.15. The fatigue life may be calculated based on the S-N fatigue approach under the assumption of linear cumulative damage (Palmgren s - Miner rule) in accordance with CN30.7. The required usage factor is given in Table 7-1. Table 7-1 Usage factor, η Location Inner hull structures, e.g. hopper knuckle connections, inner bottom to transverse bulkhead, pump tower base in general, etc. Environment North Atlantic Usage factor, η Outer hull World-wide 1.0 Pump tower supports where insulation is covered, see North 0.1 Figure 7-9 Atlantic For pump tower base supports, crack will propagate in the thickness direction inside the containment system. Such fatigue cracks may lead to rupture of both the primary and secondary barrier. Cracks on secondary barrier cannot be detected before failure is effective, leading to no redundancy of the system. The hotspots shall therefore satisfy a fatigue damage of 0.1 in North Atlantic operation. It is recommended to avoid welded permanent backing in fatigue sensitive areas. If welded steel backing strip is applied as shown in Figure 7-9, the fixation of welding spots to be kept well away from areas with high stresses (away for the areas with supporting structure below inner bottom). 1.0 Primary barrier Secondary barrier Det. K D<0, 1 N. A. D<1, 0 N. A. Det. K D<0, 1 N. A. Backing material, if applied D<1,0 N. A. F.P. Weld Figure 7-9 Pump tower base support Part time at sea The fraction of design life in the fully loaded cargo and ballast conditions, p n is to be taken as defined by the DNV Rules Pt.3 Ch.1 Sec.15 unless other has been stated, see Table 7-2.

36 Sec.7 Fatigue assessment Page 36 Table 7-2 Fraction of time at sea, p n Vessel type Hull structures Fully loaded condition 0.45 Ballast condition 0.40 Sloshing pressures may normally be neglected in fatigue strength assessment of hull structures except for pump tower supports. For calculations of fatigue strength of pump tower supports, see DNV Classification Note Weld improvement Weld toe grinding Weld toe grinding as described in DNV Classification Notes 30.7 is acceptable. Figure 7-10 shows an example of weld profiling. The weld bead should be ground, and the undercut at the weld toe should be removed. It should be noted that the final grinding direction should go across the weld in order to avoid additional notch due to the grinding. Undercut to be removed at weld toe, min. 0,5 mm Figure 7-10 Example of weld profiling at lower hopper knuckle Weld profiling Weld profiling as described in DNV Recommended Practice DNV-RP-C203 Sec.7.2 is acceptable. ϕ R σ membrane σ bending t + Figure 7-11 Geometric parameters for weld profiling If a finite element analysis of the considered connection has been performed, the results from this can be used directly to derive membrane stress and bending stress. 7.6 Weld details The following weld details are generally recommended to be applied.

37 Sec.7 Fatigue assessment Page 37 Lower chamfer joint : - Full penetration A - A Upper chamfer joint: - Full or partial penetration Upper girder : - Partial penetration A A Upper hopper joint: - Full penetration A-A Lower hopper joint: - Full or partial penetration A A Double bottom girder : - Partial penetration Figure 7-12 Welding details at inner hull, within +/- 150 mm from a web frame Different weld details may be employed depending on the stress level at the details.

38 Sec.8 Strength assessment based on direct calculated wave loads Page 38 8 Strength assessment based on direct calculated wave loads 8.1 General A strength assessment based on direct application of wave loads may be required in case of novel designs and application of class notation CSA-FLS and CSA(2). 8.2 Requirements for the CSA-FLS and CSA(2) analysis General The ultimate and fatigue strength shall be checked for compliance with the DNV Rules for Classification of Ships, Pt.3 Ch.1 Sec.15. The following summarises the requirement and application of the procedure for the Class Notations CSA-FLS and CSA(2) in case of a LNG carrier with membrane tanks Locations to be checked Ultimate capacity A global finite element analysis shall be performed, verifying the nominal and buckling strength of the vessel according to the requirements given in DNV Rules Pt.3 Ch.1 Sec.15. Fatigue capacity The following locations shall be checked by full spectral fatigue analysis, in addition to those requirements by DNV Rules Pt.5 Ch.5 and by the class notations NAUTICUS(Newbuilding) and PLUS: dome opening and coaming inner hull knuckles longitudinal girders at transverse bulkhead trunk deck at transverse bulkhead termination of tank no.1 longitudinal bulkhead aft trunk deck termination. The following locations shall be checked by component stochastic analysis: all longitudinal flange connections in cargo area including forward ballast tank plate weld connections to longitudinals in cargo area. The following locations shall be checked by screening using assumed stress concentration factors: plate seams in cargo area taking the normal building tolerances into account lower and upper hopper knuckle connections outside the midships area inner bottom connection to cofferdam bulkhead in the cargo area horizontal stringer connections outside the midships area liquid dome details outside the midships area lower and upper chamfer knuckle connections outside the midships area openings in upper and trunk decks in cargo area longitudinal connection to fore cofferdam bulkhead of no.1 cargo tank in way of upper deck longitudinal connection to aft cofferdam bulkhead of no.1 cargo tank in way of upper deck for LNG carriers of MARK III type inner longitudinal bulkhead knuckle in no.1 cargo tank for LNG carriers of NO96 type fore and aft of trunk deck termination motor room structure supports longitudinal members in deck house subject to hull girder stress Loading conditions Ultimate capacity The loading conditions shall be selected to obtain the following extreme loads: max. midship hogging moment max. midship sagging moment max. vertical acceleration in tank no.1 max. vertical acceleration in tank no.2. The design loading conditions are selected from the vessel s loading manual. The basis for the selection was to maximise the hull stress response. For each design case a corresponding loading condition shall be selected from the loading manual considering still water bending moments, shear forces and draughts.

39 Sec.8 Strength assessment based on direct calculated wave loads Page 39 The following loading conditions from the loading manual shall be taken into account for ultimate capacity: LC1: Full load at scantling draught in departure condition (S.G. of 0.5 for cargoes) LC2: Normal ballast arrival condition (S.G. of for ballast) LC3: One condition with cargo tank no.1 full and cargo tank no.2 empty LC4: One condition with cargo tank no.1 empty and cargo tank no.2 full LC5: One condition with cargo tank no.2 empty and cargo tank nos. 1 and 3 full LC6: One condition with cargo tank no.2 full and cargo tank nos. 1 and 3 empty LC7: Max shear force, if necessary. The structural analysis should cover the following design load cases /11/: Table 8-1 Design load cases Design Load Case Figure LC1: Max hull girder hogging moment amidships LC2: Max hull girder sagging moment amidships LC3: Max vertical acceleration in tank no.1 LC4: Max bottom pressure in tank no.1 LC5: Max midship hog with mid tank empty, adjacent tanks full, which may be skipped if vertical bending moment is significantly lower than (1). LC6: Max midship sagging with mid tank full, adjacent tanks empty, which may be skipped if vertical bending moment is significantly lower than case (1) LC7: Max shear force in aft most tanks (and/or no.1 tank if found critical) Additional loading conditions may be required if the above load cases does not give the most extreme loads. The ultimate limit state design loads for the vessel will be based on: extreme loads at 10-8 probability level (long term loads) North Atlantic wave environment Pierson-Moskowitz wave spectrum

40 Sec.8 Strength assessment based on direct calculated wave loads Page 40 equal probability of headings cos 2 wave spreading vessel speed of 5 knots. Fatigue capacity The following two loading conditions will be considered for fatigue capacity: full load at scantling draught in departure condition normal ballast in arrival condition. The fatigue load calculations will be based on: wave scatter diagrams for North Atlantic IACS scatter diagram Pierson-Moskowitz wave spectrum equal probability of headings cos 2 wave spreading vessel speed: 2/3 of the design speed Allowable stress and strength criteria The Rules Pt.3 Ch.1 Sec.15 shall be applied. 8.3 Stress and buckling check (ULS analysis) General The stress and buckling checks are carried out for the defined load cases. The load cases are established based on long term loads at selected reference positions along the hull girder. The long term hull girder loads are calculated at the reference positions. A design sea state is defined to reproduce the (linear) long term response in the reference positions. Subsequently, a non-linear wave load analysis is carried out for the design sea states Selection of design sea state A design sea state in this context is a regular design wave with given wave direction, wave period and wave height. The design sea-state (in this context a regular design wave) is determined as follows: wave heading is selected as the wave heading where the long term value for the given response is maximum wave period is selected as the wave period where the transfer function is maximum wave height is calculated as two times the linear long term response divided by the transfer function value for the above wave period and wave direction. The design sea state may also be established using a procedure similar to, or better than the design wave approach Design load cases A design load case is defined as a consistent load set, i.e. the external sea pressure is in balance with the inertia loads on the global FE model. This ensures that the FE model is well balanced and that the reaction forces in the position for boundary conditions are minimized. The design load cases are extracted as snap shots from the time series of the hull girder loads Verification of structural loads The hull girder loads (forces and bending moments) distributions obtained by stress integration of the FE model should be compared with the forces and moments from the wave load analysis. A difference of 5% is usually accepted. The maximum hull girder loads according to the direct wave load analysis should be compared with those of the Rules Simplified direct strength assessment As a first assessment a simplified direct strength analysis may be performed (initial CSA(2)), where ULS (yield and buckling) capacity is evaluated based on loads from non-linear hydro dynamical analysis. Wave load analysis shall be carried out for two critical loading conditions from the loading manual, in addition to the full load and ballast condition used for fatigue strength. From the design sea-states the simultaneous acting loads at the time of the maximised response at the reference position, are applied to the midship model. The global longitudinal stresses are found from the direct calculated hull girder moments, while the direct calculated local pressures at the reference cross-section are applied along the midship model to obtain the transverse and double side/bottom stresses.

41 Sec.8 Strength assessment based on direct calculated wave loads Page Fatigue analysis (FLS) The fatigue analysis should follow a procedure described as the full stochastic fatigue approach or a component stochastic procedure, as given in CN30.7. A linear wave load analysis can be used as basis for the fatigue analysis. In case of a full stochastic fatigue analysis, the sea pressure and accelerations (inertia loads) for unit wave amplitude should be transferred to the structure for wave directions and wave periods as recommended earlier in this section. The phase difference between the pressure at different locations and the acceleration in six degrees of freedom should be accounted for. This can be done efficiently by representing the pressure and the accelerations as complex number. 8.5 Modelling Panel model for wave load analysis The element size of the 3D hydrodynamic mesh has to be sufficiently small to avoid numerical inaccuracies. A good representation in areas with large transitions in shape (bow area, aft area, around the bilge) should be ensured. This will require that a higher density of elements around the bilge and close to the still water level are to be applied. Figure 8-1 shows an example of a hydrodynamic panel model. The size of panels was selected to describe the hull shape and resolve the pressure gradients. As the frequencies of the radiated waves are depending on the encounter frequency, the vessel s speed also has to be considered. Figure 8-1 Hydrodynamic panel model Global Structural model General The global analysis model is a relatively coarse FE model. The purpose of the global hull model is to obtain a reliable description of the overall hull girder stiffness to determine the global stress distribution in primary hull members. The local stress distribution is assumed to be of less importance. Stresses in girders, frames, transverse webs, etc. will be utilised for yield assessments as well as for buckling assessment for major parts of the ship. Model extent All structural parts of the ship shall be included in the model. The model should also include the deckhouse, to extend over the full breadth and depth of the vessel and to represent the actual geometry of the vessel with reasonable accuracy. All primary longitudinal members shall be included and all primary transverse members, i.e. watertight bulkhead, non-watertight bulkhead, cross deck structures and transverse webs shall be represented in the model. Structures not contributing to the global strength may be disregarded. The omission of minor structures may be acceptable on the condition that the omission does not significantly change the deflection of structure.

42 Sec.8 Strength assessment based on direct calculated wave loads Page 42 Figure 8-2 Global structural analysis model Model idealization All primary longitudinal and transverse structural members, i.e. shell plates, deck plates, bulkhead plates, stringers, girders and transverse webs shall in general be modelled by shell or membrane elements. All members should be modelled with net scantlings, i.e. corrosion addition according to the Rules shall be deducted from the actual scantlings. Otherwise, these need to be taken into account during the stress evaluation. Longitudinals and stiffeners shall be described by beam or truss elements. Buckling stiffeners of less importance for the stress distribution may normally be disregarded. Mesh arrangement In general 4-node shell or membrane elements in combination with 2-node beam or truss elements shall be used. The elements shall be rectangular as far as possible. The use of 3-nodes shell or membrane elements shall be limited as far as practicable. The mesh size shall be decided considering proper stiffness representation and load distribution. The standard mesh arrangement is normally to be such that the grid points are located at the intersection of primary members. In general there is one element between longitudinal girders, one element between transverse webs and one element between stringers and decks. If the spacing of primary members deviates much from normal, the mesh arrangement described above shall be re-considered to provide a proper aspect ratio of the elements and proper mesh arrangement of the model. The deckhouse shall be modelled using a similar mesh idealisation including primary structures. Local stiffeners which are considered not important for the overall design check, will be lumped to neighbouring nodes. Boundary conditions To eliminate the rigid body motions of the analysis model, a total of six (6) boundary constraints will be introduced. Other boundary conditions may be used if desirable. The fixation points shall be located away from the areas where the stress is of interest, as the loads transferred from the wave load analysis may lead to unbalance, although small, in the model. However, special care shall be taken to ensure that there is, within practical limits, little or no unbalanced forces and moments of the six boundary constraints. The global model is supported in three positions, one at the bow bottom (fixed in vertical and transverse direction), one at the aft bottom (fixed for translation along all three axes) and one position at upper deck level aft (fixed in transverse direction). The out of balance forces at constraints may be avoided using an inertia relief function or an equivalent means provided by the analysis software. The applied forces shall be well balanced by inertia loads distributed throughout the analysis model induced by an acceleration field.