Strength Analysis of Hull Structures in Container Ships

Transcription

1 CLASSIFICATION NOTES No Strength Analysis of Hull Structures in Container Ships JULY 2011 This Classification Note includes all amendments and corrections up to August 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 DET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, property and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancy services relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out research in relation to these functions. 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. All publications may be downloaded from the Society s Web site The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note. The electronic pdf version of this document found through is the officially binding version Det Norske Veritas AS July 2011 Any comments may be sent by to rules@dnv.com For subscription orders or information about subscription terms, please use distribution@dnv.com Computer Typesetting (Adobe Frame Maker) by Det Norske Veritas 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 - Page 3 CHANGES This document replaces the April 2010 edition. Text affected by the main changes is highlighted in red colour in the electronic pdf version. However, where the changes involve a larger section, only the title may be in red colour. Main changes Table 1-1: Analysis Level 3 in existing class note has been removed resulting in reduction from 4 to 3 possible analysis level scopes for container ships. The calculation scope for the different analyses Levels is now more precisely defined in Sec.1.6 to 1.8. Rule torsion loads are now more clearly defined in Sec.2.5. In the current class note, the Rule-defined design load cases for FE cargo hold model is a repeat of Pt.5 Ch.2 Sec.6 C400. The figures for these load cases in this proposal have been removed, with a reference to the Rules in Sec Buckling requirements to the FE cargo hold model have been updated in Table 4-2: Requirements in flooded damage condition. For inner bottom and longitudinal girders in way of transverse bulkheads, elastic buckling may be accepted. Longitudinal structures shall also be checked for uni-axial buckling in longitudinal direction. The changes in procedures and requirements to Level 1 Rule torsion analysis are mainly editorial with the following exemptions: Sec.5.4.3: The procedure for calculating the combined global stress range for fatigue assessment of hatch covers has been changed. Sec.5.6.3: Stress concentration factors for hatch corners have been made dependant of the radius and thickness. Scope of ULS hot spot stress and FLS in way of all hatch corners for Level 2 and 3 analyses has been modified to include all hatch corners and critical stringer corners. The changes in procedures and requirements to Level 2 global analysis are mainly editorial with the following exemptions: Sec.6.4.2: The procedure for calculating the combined global stress range for fatigue assessment of hatch covers has been changed. Sec.6.6.2: Fatigue load cases to be applied to the global FE model have been aligned with the procedures for calculating the combined global stress range for fatigue assessment of hatch covers. Sec.6.8.2: The required locations for fine-mesh models are now clearly defined. Sec.6.8.3: A general procedure has been established for assessing hot spot stresses for hatch corners with no fine-mesh models. Sec : A general procedure has been established for establishing generic stress concentration factors in way of hatch corners with no fine-mesh models. Sec : A screening criterion has been introduced for check of nominal stress levels in way of stringer corners. If not complying with this screening criterion, then ULS hot spot stress and FLS assessment need to be carried out. The procedures and requirements to Level 3 global analysis (Level 4 in the current class note) have been changed as follows: Sec.7.2: Hydrodynamic analysis is in general same as for CSA-2 class notation (as defined in Class note No. 34-1) with some Level 3 specific items. Sec.7.3: Global structural FE model is in general same as for CSA-2 class notation (as defined in Class note No. 34-1) with some Level 3 specific items. Sec.7.5 to 7.10: Scope for result evaluation (ULS and FLS) is significantly reduced compared to CSA- 2 class notation, and is same as for Level 2 global analysis with the following additional requirements: - Sec.7.6: ULS check of transverse strength fore and aft body. - Sec.7.10: Component stochastic FLS of stiffener end connections amidships. Sec : A screening criterion has been introduced for check of nominal stress levels in way of stringer corners. If not complying with this screening criterion, then ULS hot spot stress and FLS assessment need to be carried out. Amendments In addition to some editorial corrections, superfluous text on page 2 was removed.

4 Page 4 CONTENTS 1. Introduction General Container ship characteristics Objectives Application and scope Mandatory scope of calculation/analysis Detailed scope for Level 1 Rule torsion analysis Detailed scope for Level 2 global analysis Detailed scope for Level 3 wave load analysis Definition of symbols and abbreviations Design Loads Definition of units Design loads Container forces Sea pressure load Torsion moments for Level 1 Rule torsion analysis and Level 2 global analysis Hull Girder Strength Calculation for Vertical Bending Moments and Vertical Shear Forces, and Local Rule Scantlings Limits for design stillwater bending moment Limits for stillwater shear force Scantling check positions Cargo Hold Analysis Based on Rule-Defined Load Cases General Analysis model Boundary conditions Load cases Acceptance criteria Level 1 Rule Torsion Analysis General principles Combined nominal stress evaluation Combined hot spot stress evaluation Fatigue assessment Calculation procedure Stress concentration factors for hot spot stress evaluation Acceptance criteria Level 2 Global Analysis General principles Combined nominal stress evaluation Combined hot spot stress evaluation Fatigue assessment Global coarse FE modelling Load cases Load application General procedures for obtaining hot spot stress Hot spot stress evaluation by fine-mesh models Stress concentration factors for hot spot stress evaluation Acceptance criteria Level 3 Wave Load Analysis General principles Hydrodynamic analysis Structural modelling principles Methodology for ultimate limit state (ULS) assessment Combined nominal stress evaluation (ULS) Transverse strength of the fore and aft body Combined hot spot stress evaluation (ULS) Methodology for fatigue limit state (FLS) assessment Fatigue assessment of hatch corners and stringer corners Fatigue assessment of stiffener end connections amidships Documentation and verification Acceptance criteria...50

5 Page 5 8. References Appendix A. Structural Verification Procedure for Lashing Bridge Structure Appendix B. Structural Verification Procedure for Hatch Cover Stoppers Appendix C. Structural Verification Procedure for Hatch Cover Guide Post Appendix D. Structural Verification Procedure for Hatch Covers Appendix E. Strength Analysis for Fuel Oil Deep Tank Structure in Container Hold... 59

6 Page 6 1. Introduction 1.1 General This Classification Note describes the scope and methods required for structural analysis of container ships and the background for how such analyses should be carried out. The description is based on relevant Rules for Classification of Ships, guidance and software. The DNV Rules for Classification of Ships may require direct structural strength analyses in case of a complex structural arrangement, or unusual vessel size. Structural analyses carried out in accordance with the procedure outlined in this Classification Note will normally be accepted as basis for plan approval. Where the text refers to the Rules for Classification of Ships, the references refer to the latest edition of the Rules for Classification of Ships. Any recognised calculation method or computer program may be utilised provided that the effects of bending, shear, axial and torsion deformations are considered, when relevant. If wave loads are calculated from a hydrodynamic analysis, it is required to use recognised software. As recognised software is considered all wave load programs that can show results to the satisfaction of the Society. 1.2 Container ship characteristics Container ship categories Container ships are ships designed exclusively for the transportation of container cargoes and arranged with cell guides in holds. Containers are standardised in several sizes, e.g. 20, 40, 45 and 48 containers are common. The most common sizes are 20 (TEU: Twenty-foot Equivalent Unit) and 40 (FEU: Forty-foot Equivalent Unit) containers. The size of the container ship will be influenced by the characteristics of the route and trade pattern for which the ship is employed. The ships may be categorised as follows according to the size group: Feeder container ship: A container ship which can carry approximately 100 TEU TEU and is mainly deployed for short voyages between hub ports and small ports in the local area. The ships may be equipped with cranes for serving smaller ports where gantry cranes are not available. Service speed range is normally between 18 to 22 knots. Panamax: A container ship which can carry up to about TEU. Main dimensions are limited to the Panama Canal (B=32.2 m, Loa=294 m, T=12.0). Ballast requirements to maintain acceptable stability are a concern of the Panamax due to its high length to beam ratio. Most of these ships were designed for the long haul trade routes, e.g. Asia-Europe, Asia-USA and Europe-USA with a design speed of 24 knots. However, the traditional Panamax fleet is gradually being replaced by Post-Panamax container ships on these trade routes. Post-Panamax: A container ship exceeding the Panama Canal limits. Post-Panamax container ships typically have a capacity of TEU and upwards and design speed around 25 knots. NPX, New Panamax: A container ship with dimensions allowing it to pass the new Panama Canal locks. (Loa=366 m, B=49 m, T=15.2) and approximate size of TEU. Design speed knots. Ultra Large Container Ships (ULCS): designs exceeding the NPX limits. The biggest container ships deployed have continuously increased in size over the decades, the driver being economy of scale Operational patterns that may have impact on the design Container ships are normally operated on regular routes between designated ports. The time schedule is extremely important for the operation of container ships. The weather and sea conditions vary, depending on where the ship is trading. Variations in the loading conditions will also affect the behaviour of the ship at sea, making it complex to predict the actual long-term loading on the hull structure. This Classification Note focuses on typical loading conditions and load cases established to prevent structural problems during regular trade around the world. Ship owners and operators, if they have specific knowledge about possible loading conditions, trade routes, preferred GM values during operation etc., should give such information to the designers in shipyards and Class as early as possible when planning a new project. By providing such information, the amount of assumptions made during the construction phase may be reduced, giving increased confidence in the validity of the design calculation.

7 Page Torsion response Container ships having large hatch openings are subject to large torsion response compared to ships having closed cross-sections. Only considering the vertical hull girder force components is therefore not sufficient to decide the required hull girder strength. The torsion (stillwater torsion induced by cargo and unsymmetrical tank arrangement etc., and wave torsion induced by oblique wave encounter) and the horizontal wave bending moment should therefore also be included in the hull girder strength assessments. The criticality of the torsion response will heavily depend on the ship size. This Classification Note describes three different levels for longitudinal hull girder strength assessments including torsion analysis, depending on the ship size, as shown in Table Objectives The objective of this Classification Note is: To give a guidance for design and assessment of the hull structures of container ships in accordance with the Rules for Classification of Ships To give a general description on how to carry out relevant calculations and analyses To suggest alternative methods for torsion response calculation To achieve a reliable design by adopting rational design and analysis procedures. 1.4 Application and scope Overview of different analysis levels In order to achieve the objectives described in Sec.1.3, three different analysis levels are defined. The three different analysis levels are applicable for the design of container ships according to the vessel characteristics as described in Table 1-1. Level 1 analysis should normally be carried out as part of the mandatory procedure for the NAUTICUS(Newbuilding) notation. However, strengthening required by the Level 1 analysis may be overruled by findings from more comprehensive analyses according to Level 2 and Level 3. Table 1-1 Analysis levels versus calculation/analysis scope Level Rules calculation Level 1 Analysis Extended Rule calculation Level 2 Analysis Applicable Notation Mandatory scope of calculation/analysis Supplementary scope of analysis Remarks NAUTICUS (Newbuilding)* NAUTICUS (Newbuilding) Comprehensive Level 3 Analysis NAUTICUS (Newbuilding) Hull girder strength calculation for vertical bending moments and vertical shear forces, and local Rules scantlings Rule check of hull girder ultimate strength according Rule fatigue strength calculation for longitudinal connections ** Cargo hold analysis based on Rule-defined loading conditions ** Rule torsion calculation (ULS) for longitudinal members and hatch corners Rule torsion calculation (FLS) for hatch corners Global FE analysis for Global FE analysis with Rule torsion load cases direct calculated wave (ULS and FLS) loads (ULS and FLS) Fine-mesh analysis for selected hatch corners and stringer corners (ULS and FLS) Suitable for small ships less than Panamax size and with normal design, or for designs for which DNV or designer have experience Required for large ships from Panamax size Recommended for Extraordinary Design * NAUTICUS(Newbuilding) notation is mandatory for Container Carriers of length greater than 190 m. ** For designs where the NAUTICUS(Newbuilding) notation is mandatory, the structural verification procedures require the use of FEA in the evaluation of the midship cargo hold region. In addition, extended fatigue evaluations of end structures of longitudinals within the cargo region are required Calculation tools The following tools may be used, depending upon the characteristics of the vessel and the required analysis scope as shown in Table 1-1:

8 Page 8 NAUTICUS Hull 1) Section Scantlings can be used for typical midship section and other necessary crosssections in order to calculate: Local Rule scantlings Hull girder strength calculation for vertical bending moments and vertical shear forces Rule check of hull girder ultimate strength Rule fatigue strength calculation for longitudinal connections. Cargo hold analysis for the assessment of primary structures in the midship area using NAUTICUS Hull 1) FE modelling and analysis tools Rule torsion calculation using NAUTICUS Hull 1) Section Scantlings, 3D Beam and Simplified Torsion Calculation Tool Global analysis modelling the complete ship length using NAUTICUS Hull 1) FE modelling and analysis tools, and using load cases obtained either by direct wave load analysis or Rule-defined loads Verification of applied loads to the global model using NAUTICUS Hull1) CUTRES Wave load analysis 2) as part of a global analysis using WASIM 3) or equivalent Hatch corner analysis, Ultimate Limit State (ULS) and Fatigue Limit State (FLS), with fine-mesh model for selected hatch corner locations. Evaluation of the remaining hatch corners based on established stress concentration factors and nominal stress. 1) NAUTICUS Hull is a computer program, offered by DNV, that is suitable for the calculations of Rules required scantlings and cargo hold analysis, etc. 2) Direct wave load analysis is not part of the mandatory requirement for NAUTICUS (Newbuilding) class notation, and is therefore to be carried out at owner s and/or builder s discretion. However for extraordinary vessel design, such comprehensive analysis scope including wave load/global analysis is recommended. 3) WASIM is a linear/nonlinear time domain computational tool for sea keeping and load analysis of ships. The complete 3D interaction between waves and hull at forward speed is included. The computer program is not limited to small waves but can simulate also extreme wave conditions. 1.5 Mandatory scope of calculation/analysis Hull girder strength calculation for vertical bending moments and vertical shear forces, and local Rule scantlings Longitudinal strength of the vessel for vertical bending moments and vertical shear forces, and local Rule scantlings can be verified by the Rule-defined calculation procedure as further described in Sec.3. NAUTICUS Hull Section Scantlings should be utilised for a suitable number of cross-sections along the length of the ship. Special attention should be given to sections where the arrangement of longitudinal material changes. Sections close to the aft and forward quarter-length and at the transition between the engine room and cargo hold area need to be specially considered Rule check of hull girder ultimate strength A global ULS hull girder criterion has been introduced for container ships in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B This implies that the whole length of the ship is verified to have an ultimate yield and buckling strength to withstand an extreme vertical wave hogging moment, through an advanced buckling analysis method. All relevant cross-sections are to be considered, also outside 0.4 L. Hull cross-sections with transversely stiffened areas, such as engine rooms, are considered to be especially important to be checked. Cross-sections modelled in NAUTICUS Hull Section Scantlings in order to comply with requirements in accordance with Sec can be utilized for strength verification according to the global ULS hull girder criterion Rule fatigue strength calculation for longitudinal connections For container ships where the NAUTICUS(Newbuilding) notation is mandatory (see Rules for Classification of Ships Pt.5 Ch.2 Sec.6 A 106), the fatigue characteristics of end structures of longitudinals in bottom, inner bottom, side, inner side/longitudinal bulkheads and decks should be assessed as specified in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 C 309. For other designs where the NAUTICUS(Newbuilding) notation is not mandatory, as a minimum the fatigue characteristics of side shell longitudinal connections as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.7 E 400 should be evaluated Cargo hold analysis based on Rule-defined load cases Strength of the typical primary structural members in the midship area is to be assessed through a cargo hold analysis using NAUTICUS Hull FE modelling and analysis tools or equivalent. The complete analysis including modelling, load cases, strength assessment, allowable stresses, and buckling control should be carried out according to the procedures given in Sec.3.

9 Page 9 For fuel oil deep tanks arranged in the cargo area, i.e. fuel oil deep tanks located inboard of the inner side, above the inner bottom, and between adjacent transverse bulkheads, additional strength analysis should be carried out in order to determine the required scantling of primary structures. Applicable procedures are described in Appendix E. 1.6 Detailed scope for Level 1 Rule torsion analysis General The Level 1 Rule torsion analysis is in line with the standard Rule scope and provides a fast and reliable method for torsion response assessment. This procedure may also be used at an early design stage for larger designs and novel designs in order to obtain preliminary torsion response results Application For ships up to about Panamax size, a Level 1 Rule torsion analysis may be sufficient for the strength assessment. A Level 1 Rule torsion analysis may also be sufficient for Post-Panamax design where either DNV or the designer can document previous experience Objective The objective of a Level 1 Rule torsion analysis is to examine the hull girder structural response due to Rule torsion moments combined with Rule vertical bending moments and Rule horizontal wave bending moment Scope In order to assess torsion response for smaller container ships, a simplified torsion assessment (Level 1 Rule torsion analysis) has been proven reliable. The Level 1 Rule torsion analysis is based on prismatic beam theory, applying Rule-defined loads (vertical bending, horizontal wave bending and torsion). A Level 1 Rule torsion analysis is to be carried out within the cargo hold area where the hatch opening size remains unchanged. The scope of the torsion response evaluation is to carry out, within the Level 1 Rule torsion model range: Yield check of nominal combined stress in way upper deck hatch corners and hatch coaming top corners as given in Sec.5.2 Yield check of combined hot spot stress in way of upper deck hatch corners and hatch coaming top as given in Sec.5.3 Fatigue assessment of upper deck hatch corners and hatch coaming top corners as given in Sec.5.4 Yield check and uni-axial buckling assessment of nominal combined stress of the bilge area and lower stool bench structures, applying nominal combined stress as given in Sec.5.2. The hot spot stress in way of the hatch corners for yield check and fatigue assessment is to be established based on nominal combined stress, combined with predefined stress concentration factors defined in Sec.5.6. The Level 1 Rule torsion response evaluation calculation procedure is further described in Sec Detailed scope for Level 2 global analysis General The Level 2 global analysis includes a more elaborate procedure for obtaining nominal combined stresses. The scope for establishing hot spot stresses is also more detailed compared to Level 1 Rule torsion analysis (see Sec.1.7.4). Acceptance criteria are in general the same as for Level 1 Rule torsion analysis Application This procedure is mainly aimed at a full Panamax size (Panamax length) and Post-Panamax container ships, but may also be applicable for smaller ships having unconventional structural arrangement Objective The objective of a Level 2 global analysis is: To examine hull structural response to Rule torsion moments combined with Rule vertical bending moments and Rule horizontal wave bending moment To obtain hull deflections at the hatch coaming top level Scope A Level 2 global analysis includes a global coarse FE model covering the entire ship length, and fine-mesh models for selected critical locations. The global loads are same loads as for Level 1 Rule torsion analysis (Rule-defined loads). The loads are applied to the global model in a simplified manner by adding point loads throughout the ship length. The scope of the global response evaluation is to carry out, throughout the entire ship length:

10 Page 10 Yield check of nominal combined stress in way of upper deck hatch corners and hatch coaming top corners as given in Sec.6.2 Yield check of combined hot spot stress in way of hatch corners, critical stringer corners in the forward area, and corners in way of HFO deep tank top structures (if applicable) as given in Sec.6.3 Fatigue assessment of hatch corners, critical stringer corners in the forward area, and corners in way of HFO deep tank top structures (if applicable) as given in Sec.6.4 Yield check and uni-axial buckling assessment of nominal combined stress of the bilge area and lower stool bench structures, applying nominal combined stress as given in Sec.6.2 Assessment of hull deflections at the hatch coaming top and the upper deck levels, as guidance to the hatch cover manufacturer. The hot spot stress for yield check and fatigue assessment is for certain critical areas, as specified in Sec.6.8.2, to be established based on fine-mesh models. For the remaining locations, the simplified procedure as outlined in Sec should be used. 1.8 Detailed scope for Level 3 wave load analysis General The Level 3 wave load analysis involves a comprehensive analysis scope requiring direct calculation of wave load and response. The scope of hydrodynamic analysis and structural modelling principles for the coarse global FE model is comparable to that required for the CSA-2 class notation according to the Rules for Classification of Ships Pt.3 Ch.1 Sec.15 E. The scope for Ultimate Limit State (ULS) assessment and Fatigue Limit State (FLS) assessment is quite limited compared to the CSA-2 class notation, as shown in Sec and Sec Application This analysis will be adopted as an option by the shipyard or ship owner and is not mandatory for the NAUTICUS(Newbuilding) notation. This analysis is recommended for container ships having extraordinary structural arrangement or main dimensions, as well as vessels of novel design Objective The aim of the analysis is to ensure that all critical structural details are adequately designed to meet fatigue and strength requirements. The objective of a Level 3 wave load analysis is: To calculate the design wave for maximum vertical wave bending moment in upright condition To calculate, along the hull girder, the maximum combined hull girder stress and stress range induced by wave torsion moment, wave horizontal bending moment and wave vertical bending moment in oblique waves To examine hull structural response against the chosen maximum conditions as above, with regard to buckling, yield and fatigue To obtain hull deformations at hatch coaming top level To assess the transverse strength of the fore and aft body Scope Hydrodynamic analysis Typically, two different types of hydrodynamic analyses are to be carried out. These are: ULS (Ultimate Limit State) analysis intended to calculate hull girder loads, local sea pressure and motions in extreme environmental conditions FLS (Fatigue Limit State) analysis intended for calculation of dynamic loads used for fatigue assessment of critical details of the structure. The objectives of the wave load analysis are: To calculate the sea-keeping characteristics of the vessel, including accelerations To calculate the global hull girder loads distributed over the vessel length To establish design waves for ULS conditions for further nonlinear wave load calculations To calculate ULS load cases for global strength, buckling and yield checks To calculate FLS load cases for hatch corners, HFO deep tank structure (where applicable), critical stringer corners in the forward area, and for longitudinal connection in side shell and bilge area in the midship. The procedures for hydrodynamic analysis are further described in Sec Structural modelling principles A Level 3 wave load analysis includes a global coarse FE structural model covering the entire ship length. The procedures for structural modelling are further described in Sec.7.3. The global coarse FE model is similar to

11 Page 11 that for Level 2 global analysis, with a more detailed load application (pressure loads transferred from the hydrodynamic analysis), and with mass modelling in order to obtain equilibrium. The scope for establishing hot spot stress is the same as for Level 2 global analysis as shown in Sec Ultimate Limit State (ULS) assessment The procedures for obtaining nominal stresses in the coarse FE structural model are similar to the procedures outlined in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures, Sec.5. The methodology is further specified in Sec.7.4. The scope and procedures for result evaluation are somewhat reduced compared to Classification Note No. 34.1, and are therefore further described in the following sections: Combined nominal stress evaluation (ULS) according to Sec.7.5 Transverse strength of the fore and aft body according to Sec.7.6 Combined hot spot stress evaluation (ULS) according to Sec Fatigue Limit State (FLS) assessment The procedures for obtaining nominal stresses in the coarse FE structural model are similar to the procedures as outlined in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures, Sec.4. The methodology is further specified in Sec.7.8. The scope and procedures for fatigue assessment is somewhat reduced compared to Classification Note No. 34.1, and is therefore further described in the following sections: Fatigue assessment of hatch corners and stringer corners according to Sec.7.9 Fatigue assessment of stiffener end connections amidship according to Sec Deformation The deformation of the hatch coaming in the maximum torsion load case is important for the hatch cover design. The deformation should also be considered in connection with lashing, e.g. lashing bridge may take additional force due to relative movement between hatch cover and hatch coamings. 1.9 Definition of symbols and abbreviations Symbols not mentioned in the following list are given in connection with relevant formulae. The general symbols may be repeated when additional definitions are found necessary in connection with specific formulae. L = Rule length in m 1) B = Rule breadth in m 1) D = Rule depth in m 1) T = Rule draught in m 1) T A = draught in m for considered condition T B = draught in m for ballast condition C B = Rule block coefficient 1) C W = wave coefficient 2) V = maximum service speed in knots on draught T E = modulus of elasticity, N/mm 2 for steel G = shear modulus, N/mm 2 for steel a v = combined dynamic vertical acceleration in m/s 2 2) g o = standard acceleration of gravity, 9.81 m/s 2 h db = height of double bottom in m rolling angle 2) pitching angle 2) ULS = Ultimate Limit State (i.e. stress, yield and buckling check) FLS = Fatigue Limit State. 1) For details, see the Rules for Classification of Ships Pt.3 Ch.1 Sec.1. 2) For details, see the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B.

12 Page Design Loads 2.1 Definition of units The following SI units are used in this Classification Note: Table 2-1 Definition of Units Description Unit Symbol Mass tons [t] Length millimetre NOTE: metre [m] is used in some cases as stated in each case [mm] Time second [s] Force kilo Newton [kn] NOTE Newton [N] is used in some cases as stated in each case 2.2 Design loads Design pressure loads due to external sea pressure, liquids in tanks and due to cargo, except as given in sections 2.3 and 2.4, are to be taken as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12 B Container forces Upright condition The vertical force of a container or stack is not to be taken less than: P V = (g o + 0.5a v ) M [kn] a v = Dynamic vertical acceleration according to the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B601 M = mass of container or container stack (tons) Heeled condition The vertical force of a container or stack is not to be taken less than: P V = g o M [kn] The transverse force of a container or a stack is not to be taken less than: P t = 0.5 M a t [kn] a t = dynamic transverse acceleration = 0.4a y + g o sin + a ry [m/s 2 ] a y and a ry are as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4, with R R taken with a negative sign for positions below the centre of rolling. For loading conditions with maximum cargo load on the upper decks, the transverse dynamic acceleration, a t, may be based on the GM value from the loading manual and not on the standard values given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B400. The GM value is not to be taken less than: 0.05B with B < 32.2 m 0.08B with B > 40.0 m. For intermediate values, linear interpolation should be used. The transverse force P t is a dynamic load at probability level 10-4, and the results may be used for simplified fatigue control Pitching condition The vertical force of container/stack is not to be taken less than: P v = g o M [kn] The longitudinal force of a container or stack is not to be taken less than: P t = 0.5 M a l [kn] a l = dynamic longitudinal acceleration = 0.6a x + g o sin + a px [m/s 2 ] a x and a px are as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4, with R P taken with a negative sign for positions below the centre of pitching. The centre is generally not to be taken at a higher level than the considered draught.

13 Page Sea pressure load Upright Condition The sea pressure in upright condition is to be taken as given in the Rules for Classification of Ships Rules for Classification of Ships Pt.3 Ch.1 Sec.12 B Heeled condition The external sea pressure, p, in heeled conditions is normally to be taken as given in the Rules for Classification of Ships Rules for Classification of Ships Pt.5 Ch.2 Sec.6 C406. For external sea pressures in heeled condition to be applied for strength analysis of fuel oil deep tank structure in container hold, please refer to Appendix E. 2.5 Torsion moments for Level 1 Rule torsion analysis and Level 2 global analysis ULS The Rule torsion moments are defined in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B205. In this Classification Note, the two distributions of the torsion moment M WT have been designated as M WT1 and M WT2: M WT1 = K T1 L 5/4 (T+0.3 B) C B z e + K T2 L 4/3 B 2 C SWP M WT2 = K T1 L 5/4 (T+0.3 B) C B z e - K T2 L 4/3 B 2 C SWP where K T1 = 1.40 sin(360 x/l) K T2 = 0.13 (1- cos (360 x/l) = C SWP, and z e as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B205 According to Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B210, the stillwater torsion applied for strength evaluation can be assumed to have a distribution equal to the wave torsion along the hull girder to that of the wave torsion. The maximum value should be equal to: M ST = 0.3 L B 2 [knm] Hence, two different stillwater torsion distributions are to be applied, M ST1 and M ST2 : M ST1 = 0.3 L B 2 M WT1 /M WT1(max) M ST2 = 0.3 L B 2 M WT2 /M WT2(max) Rule wave torsion moments x/l Figure 2-1 Rule wave torsion moment distributions MWT1 MWT FLS For FLS, the Rule-defined wave torsion moments should be reduced to 10-4 probability level by the f r factor as defined in Classification Note No Fatigue Assessment of Ship Structures. Fatigue life should be checked for both Rule-defined torsion cases, M WT1 and M WT2 : M wt1 = f r M WT1 M wt2 = f r M WT2

14 Page 14 where f r h 0 = factor to reduce the load from 10-8 to 10-4 probability level = 0.5 1/h 0 = long-term Weibull shape parameter = log 10 (L) 3. Hull Girder Strength Calculation for Vertical Bending Moments and Vertical Shear Forces, and Local Rule Scantlings 3.1 Limits for design stillwater bending moment In general, the design stillwater bending moment amidships is to be taken as the greater of: Maximum value according to the loading conditions in Trim and Stability Booklet Rule value as given in the Rules for Classification of Ships Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B106. The design stillwater bending moment may, however, subject to acceptance in each case, be based on the envelope curve representing all relevant fully and partly load cargo and ballast conditions as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B101. For other sections along the ship length, the design stillwater bending moment curve should vary smoothly to fore and aft ends with a suitable margin over the maximum values of loading conditions. In general, it is recommended to have a 5% margin over the maximum stillwater bending moment according to the Trim and Stability Booklet. The margin relative to the design bending moment is normally to be decided based on the agreement between the builder and the owner. The longitudinal distributions of the vertical wave bending moment, horizontal wave bending moment and wave torsion moment shall be according to the Rules for Classification of Ships. 3.2 Limits for stillwater shear force The stillwater shear force limits (positive and negative) along the hull should be established for a seagoing and a harbour condition. The stillwater shear force limits are to be established by a shear flow analysis. The shear flow analysis should be carried out at several longitudinal positions in order to establish a shear force limit curve that reflects the hull girder shear force capacity over the length of the ship. The calculated hull girder shear stress is to comply with the yield and buckling criteria specified in the Rules for Classification of Ships P.t3 Ch.1 Sec.5 D101. Shear force correction at the watertight bulkheads need not to be carried out in general. 3.3 Scantling check positions A local Section Scantlings analysis should normally be carried out for the cross-sections where the structural arrangement and the scantlings of longitudinal members are changed. The following cross-sections should, as a minimum, be analysed: Midship section 0.25 L from AP 0.75 L from AP In way of HFO deep tank structure (where relevant) 3-5 frame spaces aft of the forward ER bulkhead. In order to carry out a complete strength assessment, it is recommended to run cross-sectional analyses in way of every transverse bulkhead location within the cargo hold area. In way of stepping of stool bench structures, due consideration should be given when assessing the hull girder bending efficiency. 4. Cargo Hold Analysis Based on Rule-Defined Load Cases 4.1 General The objective of the cargo hold analysis is to determine the scantlings of typical primary structural members of the double bottom, transverse bulkhead and side structure of container holds in the midship area. Normally, a cargo hold model is only carried out for the midship region. However, additional calculations may be carried out for the fore end and the aft end as the hull shape and structural arrangement is changed

15 Page 15 significantly compared to that of the midship region. 4.2 Analysis model Model extent The necessary longitudinal extent of the model will depend on structural arrangement, applied boundary conditions and loading conditions. The analysis model should normally extend over two (2) hold lengths (½ hold + 1 hold + ½ hold, i.e container bays). The model should cover the full breadth of the ship in order to account for unsymmetrical load cases (heeled or unsymmetrical flooding conditions). A half breadth model is acceptable in case of symmetric loading in the transverse direction. Symmetry boundary condition should then be applied at the centre line. Even for the heeled condition a half breadth model may be accepted if due concern is shown to boundary conditions and their influence on the results. The model should represent the holds located around amidships. In principle the actual shape of outer shell may be represented as it is. However, the simplification by using the shape of the midship section unchanged for the whole model length is also acceptable if due consideration is given to the stress evaluation of the changed structures. In general, to avoid inaccuracies in results due to boundary condition effects, the structural evaluation should be based on results away from the model boundary conditions. For a normal model extent as described above, with loading conditions as described in Sec.4.4, the structural evaluation may typically be based on results for the middle hold. The extent of the recommended model is visualised in Figure 4-1. Supp. BHD WT BHD WT BHD Supp. BHD Figure 4-1 Model range of cargo hold analysis Modelling of geometry Decks, shell, inner bottom and longitudinal bulkhead plates should be modelled with shell elements in order to take lateral loads. Transverse webs, floors, girders and stringers may be of membrane elements.

16 Page 16 Figure D view of cargo hold model Face plates of primary structures, e.g. vertical webs and stringers of transverse bulkheads may be represented by either beam elements or truss elements. All continuous longitudinals and stiffeners on shell elements should be of beam element type in order to transfer the internal and external loads to the neighbouring primary structural members. Non-continuous secondary structures such as web stiffeners on girders and floors may be included in the model by truss element when considered important, otherwise they may be ignored. If non-continuous stiffeners are included in the model, then the effective 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 Hatch coamings should be included in the model, but hatch covers can be excluded in the model. The structure should, according to the Rules for Classification of Ships, be modelled with net scantlings, i.e. corrosion addition should be deducted from the actual scantlings. Half thickness should be applied on plates in symmetry plane at the boundaries of the model Element and mesh size The stress and deformation results from the analysis are linked to the type, shape and aspect ratio of the elements, and the mesh topology that is used. The following guidance on mesh size is based on 4-noded shell or membrane elements in combination with 2-noded beam or truss elements. 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. The element mesh should preferably represent the actual shape of the structures so that the stresses for the control of yield and buckling strength can be read and averaged from the results without interpolation or extrapolation. Some secondary stiffeners are therefore recommended to be modelled for mesh control. The following is considered as guidance for the mesh arrangement: Three elements over the web height of the girders, floors in double bottom and over stringer webs in side wing structures One element between each longitudinal Four elements between each floor Access holes and large openings in webs, girders and stringers can be considered in the analysis model in several alternative ways, e.g. by including holes as is in the model, by reducing the web thickness, or by due consideration at the stress evaluation stage.

17 Page 17 Figure 4-3 Typical mesh arrangement of transverse web 4.3 Boundary conditions Symmetric boundary conditions are in general to be applied at the ends of the model. If half breadth model is used, symmetry should be applied along the centreline of the model. The model may be supported in the vertical direction by applying springs at the intersection lines between the side/inner side and the watertight transverse bulkheads. The spring constant may be calculated as follows, ignoring the effect of bending deflection: K = 8 A s E / ( l h ) [N/mm] where: A s = shear area for double side [mm 2 ] E = N/mm 2 l h = length of one cargo hold [mm]. Alternatively, vertical forces may be applied in the same intersections and the total vertical forces should balance the unbalanced force between downward and upward forces in the whole model. The model will then be restrained in vertical direction at the intersections in way of transverse bulkheads. Figure 4-4 Boundary conditions for all load cases 4.4 Load cases Rule-defined design load cases The Rule-defined design load cases that are to be applied to the cargo hold model is further described in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 C400.

18 Page Additional load cases For design with deck hatch girder arrangement, additional load cases may be considered according to special loading patterns Application of loads The hatch covers need not be included in the model, but the container loads on the hatch covers must be properly included in the analysis by consideration of frame and support arrangement of hatch covers. Loads shall be combined as specified in LC1-LC6 given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 C402. In general, the following load components should be included in the cargo hold model: Sea pressure including dynamic loads (when relevant), as surface loads Container loads in terms of concentrated load at each contact point to the hull structure including dynamic loads (when relevant) On-deck container load including the weight of hatch covers; in general, no wind force needs to be considered for container stacks on deck Self-weight of the hull structure. The applied loads should be obtained considering the following: The load transfer from the hatch covers should properly take into account the actual force transfer to the hull structure through the girder system of the hatch cover and the support arrangement on the hatch coaming; for simplification, a uniform distributed line load along the longitudinal and transverse hatch coamings may be assumed. For on-deck containers, the longitudinal and transverse accelerations are calculated at 45% of the height of container stack. The number of tiers in each stack should be based on the maximum given in the specification or the Trim and Stability Booklet. For containers in hold, the transverse and longitudinal forces (i.e. accelerations) are calculated at the centre of each container and applied to the transverse bulkhead members in way of the cell guide. For 20 container loading in 40 bays, it is assumed that 25% of the loading at the free end of the containers without cell guides is transferred to the longitudinal bulkhead in the middle of the hold. For containers in hold, the longitudinal and transverse acceleration will vary for each container; a group consideration can then be applied, i.e. the same longitudinal or transverse acceleration can be applied to several containers within the same group. 4.5 Acceptance criteria Allowable stresses Yield check is to be carried out for the load cases defined in Sec Allowable stresses in typical primary members are shown in Table 4-1. The following should be noted: f 1 is material factor as defined in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B100. Longitudinal hull girder stress due to semi-global bending of the cargo hold model may be deducted. By semi-global bending is meant the vertical bending effect of the cargo hold model when exposed to the load cases described in Sec The allowable shear stress is a mean value of all elements over the web height. In case openings are not modelled, the resultant shear stress should be adjusted according to the actual opening ratio.

19 Page 19 Table 4-1 Allowable stresses of primary members Structural item/ Load case Longitudinal structures: bottom shell, inner bottom, side shell, deck and longitudinal bulkhead longitudinal girders in double bottom and double side Nominal stress, [N/mm 2 ] Shear stress, [N/mm 2 ] One Two plate plate flange flange 190 f 1 1) 90 f f 1 2) 100 f f 1 2) Equiv. stress, e [N/ mm 2 ] Transverse and vertical girders 160 f f 2) 1 90 f f 2) f f 2) f f 2) 1 Face plate of primary members Web stiffeners parallel to the face plate 160 f f 2) 1 Flooded damage condition 220 f f f 1 1) Includes hull girder stress at a probability level of ) For tank test condition as described in Appendix E Buckling control Buckling control is to be carried out for the load cases defined in Sec Table 4-2 gives examples of areas to be checked for buckling, and the applicable method and acceptance criteria based on formulae as given in the Rules for Classification of Ships Rules for Classification of Ships Pt.3 Ch.1 Sec.13. Table 4-2 Acceptance criteria and method Structural item/ Acceptance Criteria Load case Longitudinal structures 1) : Bi-axial buckling to be analysed based on longitudinal stress bottom shell, inner bottom, side and mean transverse stress with = 1 and allowable usage shell, deck and longitudinal bulkhead factors below: longitudinal girders in double bottom X, Y = 1.0 included hull girder stress at a probability level of and double side 10-8 X, Y = 0.85 included hull girder stress at a probability level of 10-4 Uni-axial buckling in longitudinal direction to be analyzed based on allowable usage factors below: X = 1.0 included hull girder stress at a probability level of 10-8 X = 0.8 included hull girder stress at a probability level of 10-4 Uni-axial buckling in transverse direction to be analysed based on mean transverse compressive stress with = 1 and allowable usage factor, = 0.8 Plate of watertight transverse bulkhead Uni-axial buckling for compressive stress perpendicular to the stiffening direction to be analysed based on mean transverse compressive stress with = 1 and allowable usage factor, = 0.8 Bi-axial buckling to be analysed based on mean transverse compressive stress with = 1and allowable usage factor, x, y = 0.85 Shear buckling to be analysed based on mean shear stress with allowable usage factor, = 0.85

20 Page 20 Table 4-2 Acceptance criteria and method (Continued) Transverse and vertical structures: Shear buckling to be analysed based on mean shear stress with D/B floors, side transverses allowable usage factor, = 0.85 cross-deck structures Uni-axial buckling in transverse direction to be analysed based vertical/horizontal girders on on mean transverse compressive stress with = 1 and transverse bulkhead allowable usage factor, = 0.8 Bi-axial buckling to be checked where relevant Flooded damage condition: plate of watertight transverse bulkhead 2) Flooded damage condition: vertical/horizontal girders on transverse bulkhead Uni-axial buckling for compressive stress perpendicular to the stiffening direction to be analysed based on mean transverse compressive stress with = 1 and allowable usage factor, = 1.0 Bi-axial buckling to be analysed based on mean transverse compressive stress with = 1and allowable usage factor, x, y = 1.0 Shear buckling to be analysed based on mean shear stress with allowable usage factor, = 1.0 Shear buckling to be analysed based on mean shear stress with allowable usage factors, = 1.0 1) For inner bottom and longitudinal girder segments located within the longitudinal extent of transverse bulkheads, i.e. between the fore and aft flange of vertical bulkhead girders, elastic buckling ( el < a / ) in plate panels may be accepted. 2) For plate of watertight transverse bulkhead in flooded damage condition, elastic buckling ( el < a / ) in plate panels may be accepted. An acceptable method for evaluating ultimate compressive stresses above the critical buckling stress in the elastic range ( el < 0.5 f ) is given in the Rules for Classification of Ships Pt.3 Ch.1 Appendix A. 5. Level 1 Rule Torsion Analysis 5.1 General principles Level 1 Rule torsion analysis model range The application, objective and scope for Level 1 Rule torsion analysis is described in Sec.1.6. The Level 1 Rule torsion response evaluation should be according to the procedure described in Sec.5.5, applying NAUTICUS Hull Section Scantlings, 3D Beam and Simplified Torsion Calculation Tool. The model range of the Level 1 Rule torsion analysis is shown in Figure 2-1. The model range of Level 1 Rule torsion analysis is terminating where the size of the hatchway openings are changed due to the hull shape. Outside the Level 1 Rule torsion model range, the hatch corners are to comply with prescriptive requirements as given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B200. Additional prescriptive requirements for stringer corners in the forward cargo area are also given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B200. The prescriptive requirements for hatch corners given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B200 within the model range of Level 1 Rule torsion analysis may be disregarded provided that results obtained by applying the Level 1 Rule torsion analysis show acceptable results.

21 Page 21 Figure 5-1 Model range for Level 1 Rule torsion analysis Hull girder stress components in torsion The combined longitudinal stress in torsion is to include the effect of, as shown in Figure 2-1: Design stillwater hogging bending moment and vertical wave hogging bending moment Horizontal wave bending moment Warping due to stillwater torsion moment and wave torsion moment Bending of cross deck induced by stillwater torsion moment and wave torsion moment. vertical bending horizontal bending warping stress due to torsion moment bending stress in cross deck induced by torsion moment Figure 5-2 Hull girder stress components in torsion In a sea condition with maximum torsion moment, the ship encounters oblique waves with wave length normally between 0.6 and 0.8 of ship length. In this circumstance, the maximum vertical wave bending moment is unlikely to appear simultaneously with the maximum of horizontal wave bending moment and wave torsion moment. To compensate for the fact that the maximum values of the stress components do not appear simultaneously, only 45% of maximum vertical wave bending moment is to be used for the combined stress evaluation. Container ships are hogging ships and typically have a low specified design sagging bending moment. It should

22 Page 22 therefore be sufficient to calculate the combined stresses, applying vertical hogging bending moments only. For the combined effect of horizontal bending and warping due to torsion moment, the sign convention as shown in Sec should be followed. The combined effect of horizontal bending and warping will depend on: Longitudinal position along the length of the hull girder Above or below the horizontal neutral axis Port or starboard side Wave torsion moment distribution M WT1 or M WT2 as given in Sec The combined stress in torsion should be calculated for port and starboard side to cover all relevant stress combinations Sign convention for horizontal bending stress and warping stress Figure 5-4 and Figure 5-5 show the combined effect of horizontal bending and warping along the length of the hull girder for upper deck and bilge on port side, taking into account the two different wave torsion moment distributions M WT1 and M WT2 as defined in Sec For starboard side horizontal bending stress and warping stress will have the opposite sign as of port side, as shown in Figure 5-2. The vertical bending stress is always to be taken as positive in the deck structures and negative in the bilge due to the hogging condition. Rule wave torsion moments x/l Figure 5-3 Rule torsion moment distributions MWT1 MWT2 Warping stress and horizontal wave stress: Upper deck x/l σwh σwt,w(wt1) σwt,w(wt2) Figure 5-4 Warping stress and horizontal wave stress distribution, upper deck port side

23 Page 23 Warping stress and horizontal wave stress: Bilge Figure 5-5 Warping stress and horizontal wave stress distribution, bilge port side x/l σwh σwt,w(wt1) σwt,w(wt2) 5.2 Combined nominal stress evaluation General Within the cargo hold area where the hatch opening size remains unchanged, the combined nominal stress level in way of hatch corners on upper deck and hatch coaming top, and bilge is to be checked Combined nominal stress The combined nominal stress is to be taken as: ( S + WR ) + WH + ( ST,w + WT,w ) + ( ST,dl + WT,dl ) (N/mm 2 ) S hull girder stress due to design stillwater hogging bending moment as given in Sec WR hull girder stress due to reduced vertical wave hogging bending moments as given in Sec WH hull girder stress due to horizontal wave bending moment as given in Sec ST,w warping stress due to stillwater torsion moment as given in Sec WT,w warping stress due to wave torsion moment as given in Sec ST,dl bending stress in longitudinal structure due to warping deformation of cross deck induced by stillwater torsion moment as given in Sec for bilge WT,dl bending stress in longitudinal structure due to warping deformation of cross deck induced by wave torsion moment as given in Sec = 0 for bilge For hull girder stress due to horizontal wave bending moment and warping stress due to torsion, the sign convention in Sec should be followed. Two different wave torsion moments are given in Sec Each of the wave torsion moments can be assumed to be combined with a stillwater torsion moment having the same distribution along the hull girder to that of the wave torsion. The combined nominal stress is therefore to be calculated for each of the torsion moment distributions. The maximum combined nominal stress is to be taken as: max Max [ (M WT1, M ST1 ), (M WT2, M ST2 )] (N/mm 2 ) (M WT1, M ST1 ) calculated combined nominal stress applying M WT1 and M ST1 as given in Sec (M WT2, M ST2 ) calculated combined nominal stress applying M WT2 and M ST2 as given in Sec The calculated maximum combined nominal stress is to comply with the acceptance criterion given in Sec Hull girder stress due to design stillwater hogging bending moment and reduced vertical wave hogging bending moment The hull girder stress due to design stillwater bending moment is given by: S M S,h (z n -z a ) 10 5 / I N (N/mm 2 ) M S,h = design stillwater hogging bending moment as given in Sec.3.1 z n = vertical distance in m form base line to neutral axis of the hull girder z a = vertical distance in m form base line to the point in question I N = moment of inertia in cm 4 of hull girder about the horizontal neutral axis The hull girder stress due to reduced vertical wave hogging bending moments is given by:

24 Page 24 WR 0.45M W,h (z n -z a ) 10 5 / I N (N/mm 2 ) M W,h = vertical wave hogging bending moment as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B Hull girder stress due to horizontal wave bending moment The hull girder stress due to horizontal wave bending moment is given by: WH M WH y a 10 5 / I C (N/mm 2 ) M WH = horizontal wave bending moment as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B205 y a = distance in m from centre line to position considered I C = moment of inertia in cm 4 of hull girder about the vertical neutral axis Warping stress due to torsion moment The warping stress due to stillwater torsion moment and wave torsion moment should be calculated by NAUTICUS Hull Section Scantlings using prismatic beam torsion calculation as further described in Sec.5.5. The wave torsion moments for ULS as defined in Sec are to be applied Bending stress due to warping deformation of cross deck The method for calculating the bending stress in longitudinal structures due to warping deformation of cross deck induced by stillwater torsion moment and wave torsion is further described in Sec.5.5, applying the modelling techniques as given in Sec and Sec The wave torsion moments for ULS as defined in Sec are to be applied. The read-out point of stress from the beam calculation should be in accordance with Sec Combined hot spot stress evaluation General Within the cargo hold area where the hatch opening size remains unchanged, the combined hot spot stress level in way of hatch corners on upper deck and hatch coaming top is to be checked. The hot spot stress is to be calculated applying predefined stress concentration factors to the nominal combined stress. As the stress concentrations will vary along the edge of the hatch corner, it is recommended to calculate the combined hot spot stress for 10 positions along the edge of the hatch corner Combined hot spot stress The combined hot spot stress is to be taken as: hs K v ( S + WR ) + K h WH + K tw ( ST,w + WT,w ) + K td ( ST,dt + WT,dt ) (N/mm 2 ) S, WR as given in Sec WH as given in Sec ST,w as given in Sec WT,w as given in Sec ST,dt bending stress in cross decks due to warping deformation induced by stillwater torsion moment as given in Sec WT,dt bending stress in cross decks due to warping deformation induced by wave torsion moment as given in Sec K v = stress concentration factor in way of hatch corners from vertical bending as given in Sec and K h = stress concentration factor in way of hatch corners from horizontal bending as given in Sec and K tw = stress concentration factor in way of hatch corners from warping as given in Sec and K td = stress concentration factor in way of hatch corners from bending stress due to warping deformations of cross decks as given in Sec and For hull girder stress due to horizontal wave bending moment and warping stress due to torsion, the sign convention in Sec should be followed. Two different wave torsion moments are given in Sec Each of the wave torsion moments can be assumed to be combined with a stillwater torsion moment having the same distribution along the hull girder to that of the wave torsion. The combined hot spot stress is therefore to be calculated for each of the torsion moment distributions. The maximum combined hot spot stress is to be taken as: hs max Max [ hs (M WT1, M ST1 ), hs (M WT2, M ST2 )] (N/mm 2 ) hs (M WT1, M ST1 ) calculated combined hot spot stress applying M WT1 and M ST1 as given in Sec hs (M WT2, M ST2 ) calculated combined hot spot stress applying M WT2 and M ST2 as given in Sec.2.5.1

25 Page 25 The calculated maximum combined hot spot stress is to comply with the acceptance criterion as given in Sec Bending stress due to warping deformation of cross deck The method for calculating the bending stress due to warping deformation of cross deck induced by stillwater torsion moment and wave torsion is further described in Sec.5.5, applying the modelling techniques as given in Sec and Sec The wave torsion moments for ULS as defined in Sec are to be applied. The read-out point of stress from the beam calculation should be in accordance with Sec Fatigue assessment General Fatigue of hatch corners in way of upper deck and hatch coaming top within the cargo hold area where the hatch opening size remains unchanged is to be assessed in accordance with Classification Note No. 30.7, including warping stress obtained from wave torsion moment. The hot spot stress range is to be calculated applying predefined stress concentration factors to the nominal combined stress on 10-4 probability level. As the stress concentrations will vary along the edge of the hatch corner, it is recommended to calculate the fatigue life for 10 positions along the edge of the hatch corner Damage calculation Two different wave torsion moments are given in Sec The damage for each hatch corner is therefore to be taken as: D = Max [D(M wt1 ), D(M wt2 )] D(M wt1 ) = calculated fatigue damage applying M wt1 as given in Sec D(M wt2 ) = calculated fatigue damage applying M wt2 as given in Sec The fatigue damage for each hatch corner is to be calculated in accordance with Classification Note No applying: Design criteria as given in Sec Combined local stress range due to lateral pressure loads l = 0 Combined global stress range, g, as given in Sec Combined global stress range The combined global stress range is to be taken as: g 2 v 2 2 hg wt vh v hg wt (N/mm 2 ) v stress range due to vertical wave bending moment as given in Sec ( hg + wt ) stress range due to horizontal wave bending moment and wave torsion moment vh correlation coefficient as given in Classification Note No. 30.7, Sec The stress range due to horizontal wave bending moment and wave torsion moment can be further be described as: ( hg + wt ) 2 ( hg + wt ) (N/mm 2 ) hg hull girder stress due to horizontal wave bending moment as given in Sec wt warping stress and bending stress due to warping deformation of cross deck induced by wave torsion moment The warping stress and bending stress due to warping deformation of cross deck induced by wave torsion moment can be further described as: wt K tw wt,w + K td wt,dt (N/mm 2 ) wt,w warping stress due to wave torsion moment as given in Sec wt,dt bending stress in cross decks due to warping deformation induced by wave torsion moment as given in Sec K tw = stress concentration factor in way of hatch corners due to warping as given in Sec and K td = stress concentration factor in way of hatch corners from bending stress due to warping deformations of cross decks as given in Sec and For hull girder stress due to horizontal wave bending moment and warping stress due to torsion, the sign

26 Page 26 convention in Sec should be followed Stress range due to vertical wave bending moment The stress range due to vertical wave bending moment is to be taken as: v 2 v (N/mm 2 ) The vertical wave hull girder stress is to be taken as: v 0.5 K v [M wo,h M wo,s ] 10 5 z n -z a / I N (N/mm 2 ) M wo,s(h) = vertical wave sagging (hogging) bending moment as given in Classification Note No. 30.7, Sec z n z a I N = as given in Sec K v = stress concentration factor in way of hatch corners due to vertical bending as given in Sec and Stress due to horizontal wave bending moment The horizontal wave hull girder stress is to be taken as: hg K h M h 10 5 y / I C (N/mm 2 ) M h = horizontal wave bending moment as given in Classification Note No. 30.7, Sec y I C = as given in Sec K h = stress concentration factor in way of hatch corners due to horizontal bending as given in Sec and Warping stress due to torsion moment The warping stress due to wave torsion moment should be calculated by NAUTICUS Hull Section Scantlings using prismatic beam torsion calculation as further described in Sec.5.5. The wave torsion moments for FLS as defined in Sec are to be applied Bending stress due to warping deformation of cross deck The method for calculating the bending stress due to warping deformation of cross deck induced by wave torsion is further described in Sec.5.5, applying the modelling techniques as given in Sec and Sec The wave torsion moments for FLS as defined in Sec are to be applied. The read-out point of stress from the beam calculation should be in accordance with Sec Calculation procedure Overview Level 1 Rule torsion response of main hull structures is to be calculated according to the following calculation procedure: 1) NAUTICUS Hull Section Scantlings, applying a prismatic beam calculation method for the midship section, is to be used for establishing of the torsion response of the hull girder in order to establish longitudinal warping stresses and warping deformations along the cargo hold area. 2) 3D Beam (beam analysis) calculation of upper hull structures is to be carried out for the warping deformations obtained by task 1) in order to establish bending stress in way of cross decks induced by warping deformations. 3) Other stress components such as vertical bending stress and horizontal bending stress are to be calculated using NAUTICUS Hull Section Scantlings output, which is transferred to Simplified Torsion spreadsheet. 4) Total stress combination is to be calculated in way of transverse bulkhead locations according to the sign conventions given in Sec ) Hot spot stress calculation by use of predefined stress concentration factors along the edge of hatch corners should be carried out using the stress concentration data found in Sec ) The flowchart in Figure 5-6 describes the procedure and tools that may be used for the torsion calculation.

27 Page 27 Input of torsion data: - Model length - Longitudinal and transverse deck properties Verification/Input of loads including wave and still water torsion Drawings and standard input for section scanltings Section Scantlings Midship section Sections outside midship Output from section scantlings - Torsion response (deformations and stresses) - Applied loads - Parameters used in torsion evaluation - Section properties Output from section scantlings - Section properties Spreadsheet for result evaluation Spreadsheet for combination of stress components and criteria evaluation Input of -Scantlings to be used for 3D-Beam model - Fatigue parameters - Allowable stresses Automatic generation of 3Dbeam model and transfer of torsion deformations Stresses due to torsional warping deformations 3-Beam calculation 3D-beam model of longitudinal and transverse deck structures Figure 5-6 Flowchart for Level 1 Rule torsion calculation Length of torsion model The calculation model extends from B/5 aft of the engine room bulkhead to the bulkhead section in the forward of cargo hold area where the hatch opening size remains unchanged as shown in Figure Beam section properties of longitudinal deck and cross deck structures For the longitudinal deck strip, the flange of the beam may be assumed from 2 nd deck to hatch coaming top level at the longitudinal bulkhead side, and to upper deck for the side shell. If the plate thickness varies in the area, then an equivalent thickness is to be applied. Longitudinal deck strips may be modelled as an I-section, where the deck structures are idealised as in Figure 5-7. Figure 5-7 Idealisation of beam cross-section (example) The transverse deck beams are idealized as I-sections, but both flanges are to be of the same breadth. The flange breadth should be taken from 2 nd deck level to the hatch coaming top level Calculation of bending stress due to warping deformation of cross deck Beam model In order to find the stress component due to relative warping deformations of cross deck, a beam model of the

28 Page 28 upper deck structure is to be established as shown in Figure 5-8. The same cross-sectional properties as used in the NAUTICUS Hull Section Scantlings should in general be used in the beam model. The longitudinal and transverse warping displacements obtained from NAUTICUS Hull Section Scantlings calculation should be applied as forced displacement to each transverse bulkhead location at the sides. The beam model for the upper part of the hull should include the longitudinal and transverse deck strips with relevant width of the side shell (sheer strake), longitudinal bulkhead, hatch coaming and transverse bulkhead as flange. The flange breadth of the beam element should be equivalent to the breadth used in NAUTICUS Hull Section Scantlings for the torsion response calculation. The end parts of the transverse box beam are modelled with increased dimensions to reflect the local strengthening in the hatch corner area, i.e. increased thickness in deck plate and both flange (bulkhead) plates as per actual design. The transverse beam in the beam model should be positioned in the centre line of the transverse box beam. The longitudinal beam in the beam model should be positioned along the inner side. Z Y X Figure 5-8 Example of beam model for calculation of bending stress due to warping deformation of cross deck Loads and boundary conditions The forced displacements should be applied at all nodes at sides as per the results of the torsion calculation. Transverse displacements are to be applied with the same signs on both sides of the ship, while longitudinal displacements are to be applied with opposite signs at each side. The longitudinal displacements from NAUTICUS Hull Section Scantlings are relative displacement between port and starboard side; hence half the displacement will be applied to each node at port and starboard side Read-out point for bending stress due to warping deformations Nominal stress approach ULS ( ST,dl and WT,dl ) The nominal bending stress in longitudinal structures due to warping deformations of cross deck for nominal ULS check, WT,dl and ST,dl, should be taken from the beam model as specified in Sec.5.5.4, applying half of the difference in bending stress level on the side flange in the longitudinal beams forward and aft of the cross deck beam positions as shown in Figure 5-9: W(S)T,dl 1 2 /2 (N/mm 2 ) W(S)T,dl Nominal bending stress in longitudinal structure due to warping deformations of cross deck induced by wave (stillwater) torsion moment on the side flange 1, 2 from beam model

29 Page 29 Sig-My[N/mm2] Beam order: : 105, σ 1 σ 2 Length[mm] Figure 5-9 Read-out point for bending stress due to warping deformations nominal stress approach Read-out point for bending stress due to warping deformation Hot spot stress approach ULS ( ST,dt and WT,dt ) & FLS ( wt,dt) The nominal bending stress due to warping deformations of cross deck for ULS check ( WT,dt and ST,dt ) and FLS check ( wt,dt ) should be taken from the beam model as specified in Sec The stress is to be taken at the end of the transverse box beam, i.e. at the node corresponding to the end point of the curvature, as shown in Figure 5-10: W(S)T,dt Nominal bending stress due to warping deformations of cross deck induced by wave (stillwater) torsion moment Sig-My[N/mm2] Beam order: : 43, Length[mm] Figure 5-10 Nominal bending stress distribution at end of transverse box beam σ W(S)T,dt 5.6 Stress concentration factors for hot spot stress evaluation General This section includes predefined stress concentration factors to be used for hot spot stress analysis of hatch corners. The predefined stress concentration factors in this section may be substituted with ship-specific stress concentration factors, provided that ship-specific stress concentration models are established. The procedure as given in Sec.6.10 may then be utilised Background and application In way of the hatch corner structure in a container ship, stress concentration factor (K factor) varies along the edge of the hatch corners depending upon stress component, i.e. vertical bending, horizontal bending, warping stress and stress due to warping deformation. In order to calculate the hot spot stresses reasonably accurately along the edge of hatch corners, the variations of stress concentration should be taken into account for each stress component along the edge. The stress concentration factors given in Sec and Sec are basically set for normal hatchway arrangement and hatch corner designs, e.g. radius type in the cargo hold area and keyhole type in the engine room bulkhead. Hot spot stress can be calculated by multiplying the nominal stress by the corresponding K-factor that varies along the edge of the hatch corner:

30 Page 30 hotspot K no min al The predefined stress concentration factors for the hatch corners in the cargo hold area and engine room front bulkhead have been established based on parametric investigation over different hatch corner designs, using fine-mesh (about 1.5t mesh arrangement) models with fictitious truss elements along the edges. For the stress concentration factor of the torsion (warping) deformation case, shear force effect was also included in the stress concentration factor Hatch corners in way of cross decks in cargo hold area Normally, local strengthening with insert plate having increased thickness in way of hatch corner and transverse box beam end is fitted. This thicker plating reduces the hot spot stress along the edge of the hatch corner, and this effect should be considered. The hot spot stress along the edge of the hatch corner depends on the hatch corner radius. Increased radius reduces the hot spot stress, and this effect is also to be considered. The hatch corner edges are assumed free from weld, eccentricity and misalignment. Thus only the stress concentration due to the geometry effect is considered in K-factor tables. The predefined stress concentration factors have the following generic formulation: K = K 0 K t K r K 0 = stress concentration factor depending on location along the edge of the curvature K t = stress concentration factor depending on the thickness ratio between the insert plate and the surrounding plate K r = stress concentration factor depending on the radius of the hatch corner Upper deck The predefined stress concentration factors for hatch corners on upper deck in way of cross decks in cargo hold area are given by: 1) vertical bending: K v = K v,0 K t,x K r,x K 0 = as given in Table 5-1 K t,x = t insert /t deck K r,x = R 2) horizontal bending: K h = K h,0, K t,x K r,x K h,0 = as given in Table 5-2 K t,x = t insert /t deck K r,x = R 3) warping: K tw = K tw,0 K t,x K r,x K h,0 = as given in Table 5-1 K t,x = t insert /t deck K r,x = R 4) warping deformation: K td = K td,0 K t,y K r,y K td,0 = as given in Table 5-3 K t,y = t insert /t deck K r,y = R where: t insert = thickness of insert plate t deck = thickness of upper deck plating R = radius of upper deck corner Hatch coaming top The predefined stress concentration factors for hatch corners on hatch coaming top in way of cross decks in cargo hold area are given by:

31 Page 31 1) vertical bending: K v = K v,0 K t,x K r,x K 0 = as given in Table 5-1 K t,x = t insert /t coaming K r,x = R 2) horizontal bending: K h = K h,0 K t,x K r,x K h,0 = as given in Table 5-2 K t,x = t insert /t coaming K r,x = R 3) warping: K tw = K tw,0 K t,x K r,x K h,0 = as given in Table 5-1 K t,x = t insert /t coaming K r,x = R 4) warping deformation: K td = K td,0 K t,y K r,y K td,0 = as given in Table 5-3 K t,y = t insert /t coaming K r,y = R where: t insert t deck R = thickness of insert plate = thickness of hatch coaming top = radius of hatch coaming top The radius part of the hatch corner edge is divided into 10 segments and the corresponding K 0 factors are presented for each stress component in the following tables. The segments are numbered along the hatch corner edge from the longitudinal upper deck (longitudinal hatch coaming top plate) to the upper deck transverse (transverse hatch coaming top plate), as shown in Figure Figure 5-11 Segment numbering along hatch corner edge (cargo hold area) Table 5-1 Stress concentration factor for vertical bending stress (K v,0 ) and warping stress (K tw,0 ) Seg. No Upper Deck Coam. Top

32 Page 32 Table 5-2 Stress concentration factor for horizontal bending stress (K h,0 ) Seg. No Upper Deck Coam. Top Table 5-3 Stress concentration factor for warping deformation (K td,0 ) Seg No. Upper Deck Coam Top Hatch corner in way of engine room bulkhead The predefined stress concentration factors of the hatch corner in way of the engine room bulkhead differ from the hatch corners in the cargo hold area mainly due to the different shape of the hatch corner design, typically with keyhole design instead of radius type. The same procedure as for the cargo hold area can be used to determine the hot spot stress for all relevant stress components, but the stress component by warping deformation can be omitted since relative deflection at the engine room bulkhead is too small to be considered. Longitudinal Direction Figure 5-12 Segment numbering along hatch corner edge (engine room bulkhead) The radius (streamlined) part of the hatch corner edge is divided into 10 segments and the corresponding K- factors are presented for each stress component in the following tables. The segments are numbered along the hatch corner edge from the longitudinal upper deck (longitudinal hatch coaming top plate) to the upper deck transverse (transverse hatch coaming top plate), as shown in Figure Table 5-4 Stress concentration factor for vertical bending stress (K v ) Seg. No Upper Deck Coam Top Table 5-5 Stress concentration factor for horizontal bending Stress (K h ) Seg. No Upper Deck Coam Top

33 Page 33 Table 5-6 Stress concentration factor for warping stress (K tw ) Seg. No Upper Deck Coam Top 5.7 Acceptance criteria Acceptance criteria ULS Table 5-7 Allowable stress Applicable location Allowable combined nominal stress Top of hatch coaming 225f 1 400f 1 Upper deck 225f 1 400f 1 Bilge 195f 1 Not Applicable f 1 = as given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B101 In way of the bilge area and stool bench structures, a uni-axial buckling assessment in accordance with Rules for Classification of Ships Pt.3 Ch.1 Sec.13 B201 is to be carried out, applying: 1.0 a combined nominal stress calculated in accordance with Sec.5.2. Allowable combined hot spot stress Acceptance criteria FLS The fatigue life is to be minimum 20 years, applying world-wide scatter diagram, as defined in Rules for Classification of Ships Pt.3 Ch.1 Sec.16 A Level 2 Global Analysis 6.1 General principles The application, objective and scope for Level 2 global analysis is described in Sec.1.7. A global coarse FE model is to be made in accordance with Sec.6.5. Similar to Level 1 Rule torsion analysis, Rule-defined loads are to be applied. The Rule-defined loads are further described in Sec.6.6. The Rule-defined loads are to be applied to the global coarse FE model as vertical and horizontal forces covering the entire ship length as shown in Sec.6.7. For ships which are symmetrical about the centre line, the stress resulting from horizontal bending and torsion moments will be of equal magnitude but opposite sign at port and starboard side. Therefore, in the global model it is sufficient to apply loads representing oblique waves from one side only. Furthermore, provided that the hull girder stress components are combined in the manner described in subsequent parts of this section, it is sufficient to read out all stress components from one side of the global model only. In order to obtain hot spot stresses for yield check and fatigue assessment, the general procedure as shown in Sec.6.8 is to be applied. The acceptance criteria for Level 2 global analysis are similar as for Level 1 Rule torsion analysis and are given in Sec Results obtained from Level 2 global analysis supersede results from Level 1 Rule torsion analysis and the prescriptive minimum requirements to hatch corners and stringer corners given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B Combined nominal stress evaluation General Within the cargo hold area the combined nominal stress level in way of hatch corners, stringer corners, and bilge is to be checked.

34 Page Combined nominal stress The combined nominal stress is to be taken as: V + H&T (N/mm 2 ) V hull girder stress due to: design stillwater hogging bending moment reduced vertical wave hogging bending moment as given in Sec H&T hull girder stress due to: horizontal wave bending moment stillwater torsion moment wave torsion moment as given in Sec Two different wave torsion moments are given in Sec Each of the wave torsion moments can be assumed to be combined with a stillwater torsion moment having the same distribution along the hull girder as the wave torsion. The combined nominal stress is therefore to be calculated for each of the torsion moment distributions. The maximum combined nominal stress is to be taken as: max Max [ (M WT1, M ST1 ), (M WT2, M ST2 )](N/mm 2 ) (M WT1, M ST1 ) calculated combined nominal stress applying M WT1 and M ST1 as given in Sec (M WT2, M ST2 ) calculated combined nominal stress applying M WT2 and M ST2 as given in Sec The calculated maximum combined nominal stress is to comply with the acceptance criteria given in Sec Hull girder stress due to design stillwater hogging bending moment and reduced vertical wave hogging bending moment The hull girder stress, V, is to be calculated applying the following procedure: Load case LC V,ULS as given in Sec is to be applied to the global coarse FE model following the procedure defined in Sec V is to be obtained from the global coarse FE model. In way of corners, V, is to be calculated in way of the intersection between inner side and cross deck. The stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side Hull girder stress due to horizontal wave bending moment and torsion moment The hull girder stress, H&T, is to be calculated applying the following procedure: Load cases LC H&T1,ULS and LC H&T2,ULS as given in Sec are to be applied to the global coarse FE model following the procedure defined in Sec H&T is to be obtained from the global coarse FE model, with the sign determined in the following manner: Above the horizontal neutral axis of the hull girder, where the vertical hogging moment gives rise to tension, H&T shall be added as a tensile stress, i.e. H&T = H&T Below the horizontal neutral axis of the hull girder, where the vertical hogging moment gives rise to compression, H&T shall be added as a compressive stress, i.e. H&T = - H&T. In way of corners, H&T is to be calculated at the intersection between inner side and cross deck. The stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side. 6.3 Combined hot spot stress evaluation General Within the cargo hold area the combined hot spot stress levels in way of hatch corners are to be checked. In addition, the combined hot spot stress is to be calculated for the most critical stringer corner (with the greatest nominal combined stress calculated, following the procedure as given in Sec.6.2) and corners in way of HFO deep tanks structure (where applicable). Stringer corners not complying with the screening criteria as given in Sec , if any, are also to be checked for combined hot spot stress Combined hot spot stress The combined hot spot stress is to be taken as: hs V,hs + H&T,hs (N/mm 2 ) V,hs hull girder hot spot stress due to:

35 Page 35 design stillwater hogging bending moment reduced vertical wave hogging bending moment as given in Sec H&T,hs hull girder hot spot stress due to: horizontal wave bending moment stillwater torsion moment wave torsion moment as given in Sec Two different wave torsion moments are given in Sec Each of the wave torsion moments can be assumed to be combined with a stillwater torsion moment having the same distribution along the hull girder as the wave torsion. The combined nominal stress is therefore to be calculated for each of the torsion moment distributions. The maximum combined nominal stress is to be taken as: max Max [ (M WT1, M ST1 ), (M WT2, M ST2 )] (N/mm 2 ) (M WT1, M ST1 ) calculated combined nominal stress applying M WT1 and M ST1 as given in Sec (M WT2, M ST2 ) calculated combined nominal stress applying M WT2 and M ST2 as given in Sec The calculated maximum combined nominal stress is to comply with the acceptance criterion given in Sec Hull girder stress due to vertical stillwater hogging bending moment and reduced vertical wave hogging bending moment The hull girder stress, V,hs, is to be calculated applying the following procedure: Load case LC V,ULS as given in Sec is to be applied to the global coarse FE model following the procedure defined in Sec For locations where fine-mesh models have been established, as required by Sec.6.8.2, V,hs is to be calculated following the procedures defined in Sec.6.9. For locations where fine-mesh models have not been established (see Sec.6.8.2), V,hs is to be calculated following the procedures defined in Sec Hull girder stress due to horizontal wave bending moment and torsion moment The hull girder stress, H&T,hs, is to be calculated applying the following procedure: Load case LC H&T1,ULS and LC H&T2,ULS as given in Sec are to be applied to the global coarse FE model following the procedure defined in Sec For locations where fine-mesh models have been established, as required by Sec.6.8.2, H&T,hs is to be calculated following the procedures defined in Sec.6.9. For locations where fine-mesh models have not been established (see Sec.6.8.2), H&T,hs is to be calculated following the procedures defined in Sec Fatigue assessment General The damage calculation is to be carried out following the same principles as for the Level 1 Rule torsion analysis as given in Sec The procedure for calculating the global stress range is, however, more elaborate. The combined global stress range, g, is to be calculated following the procedures as given in Sec Within the cargo hold area the fatigue assessment in way of all hatch corners is to be carried out. In addition, fatigue life is to be calculated for the most critical stringer corner (with the greatest nominal combined stress computed following the procedure as given in Sec.6.2) and corners in way of HFO deep tanks structure (where applicable). Stringer corners not complying with the screening criteria as given in Sec , if any, are also to be checked for fatigue life Combined global stress range The combined global stress range is to be taken as: g 2 v 2 h& t 2 (N/mm 2 ) vh v h& t v stress range due to vertical wave sagging and hogging bending moment as given in Sec h&t stress range due to horizontal wave bending moment and wave torsion moment vh correlation coefficient as given in Classification Note No. 30.7, Sec The stress range due to horizontal wave bending moment and wave torsion moment can be further be described as:

36 Page 36 h&t 2 h&t (N/mm 2 ) h&t hull girder stress amplitude due to horizontal wave bending moment and wave torsion moment as given in Sec Stress range due to vertical wave bending moment The stress range due to vertical wave bending moment is to be taken as: v 2 v (N/mm 2 ) The vertical wave hull girder stress, v, is calculated applying the following procedure: Load case LC v,fls as given in Sec is to be applied to the global coarse FE model following the procedures defined in Sec For locations where fine-mesh models have been established, as required by Sec.6.8.2, v is to be calculated following the procedures defined in Sec.6.9. For locations where fine-mesh models have not been established (see Sec.6.8.2), v is to be calculated following the procedures defined in Sec Stress due to horizontal wave bending moment and wave torsion moment The hull girder stress, h&t, is to be calculated applying the following procedure: Load cases LC h&t1,fls and LC h&t2,fls as given in Sec are to be applied to the global coarse FE model following the procedure defined in Sec For locations where fine-mesh models have been established, as required by Sec.6.8.2, h&t is to be calculated following the procedures defined in Sec.6.9. For locations where fine-mesh models have not been established (see Sec.6.8.2), h&t is to be calculated following the procedures defined in Sec Global coarse FE modelling 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 distributions are assumed to be of less importance Model extent All structural members of the ship that have an impact on the overall hull girder stiffness (bending, shear and torsion) should be included in the model. The model should therefore also include deckhouse and forecastle, as these members are representing torsion constraints. All primary longitudinal members should be included in the model. In addition, all primary transverse members, i.e. watertight bulkheads, non-watertight bulkheads, cross deck structures and transverse webs should be represented in the model. The omission of minor structures may be accepted on the condition that the omission does not significantly change the deflection of structure. Figure 6-1 Global structural analysis model Model idealization All primary longitudinal and transverse structural members, i.e. shell plates, deck plates, bulkhead plates, stringers and girders and transverse webs, should in general be modelled by shell or membrane elements. The scantlings may be modelled with gross scantlings. Beams, longitudinals and stiffeners should be described by beam or truss elements. Buckling stiffeners of less importance for the stress distribution may normally be disregarded.

37 Page 37 The model shall not include self-weight or inertia effects Mesh arrangement In general 4-noded shell or membrane elements in combination with 2-noded beam or truss elements should be used. The elements should be rectangular as far as possible. The use of 3-noded shell or membrane elements should be limited as far as practicable. The mesh size should 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, but may be adjusted to achieve the proper stress investigation for fore and aft part of the cargo hold areas. In general the element size may be taken as 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 the standard configuration, the mesh arrangement described above should be reconsidered to provide a proper aspect ratio of the elements and proper mesh arrangement of the model. The deckhouse and forecastle should be modelled using a similar mesh idealisation including primary structures. Local stiffeners should be lumped to neighbouring nodes Boundary conditions Figure 6-2 shows an example of applicable boundary conditions. The global model is supported in three positions, one at the FP bottom (fixed in vertical and transverse direction), one at the Rule AP bottom (fixed for translation along all three axes) and one position at Rule AP upper deck level (fixed in transverse direction). It should be noted that there is, in general, no internal web structure at the Rule AP. It might therefore be advisable to include a dummy web frame in the bottom at the Rule AP, to provide a stiff structure at the boundary condition. Figure 6-2 Boundary conditions 6.6 Load cases ULS Design stillwater hogging bending moment and reduced vertical wave hogging bending moment LC V,ULS = M S M W M S = design stillwater hogging bending moment as given in Sec.3.1 M W = vertical wave hogging bending moment as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B Horizontal wave bending moment and torsion moment LC H&T1 = M WH + M ST1 + M WT1 LC H&T2 = M WH + M ST2 + M WT2 M WH = horizontal wave bending moment as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B205 M ST = stillwater torsion moment as given in Sec M WT = wave torsion moment as given in Sec FLS Vertical wave bending moment range LC v,fls = f r f sag M W f r = as given in Sec.2.5.2

38 Page 38 1 M W, s f sag 1 2 MW, h M W,s(h) = vertical wave sagging(hogging) bending moment as given in Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B Horizontal wave bending moment and torsion moment LC h&t1 = M h + M wt1 LC h&t2 = M h + M wt2 h horizontal wave bending moment as given in Classification Note No. 30.7, Sec wt wave torsion moment as given in Sec Load application General The objective with the load application for Level 2 global analysis is, by applying concentrated shear forces to the model distributed over the entire ship length, to obtain envelopes of hull girder bending moments and torsion moments within a reasonable accuracy. As the objective is to achieve target hull girder bending moments and torsion moments, local loads such as containers in hold and on deck, tank pressure etc. may be omitted in the model Vertical bending moments The vertical bending moments (design stillwater hogging bending moment and vertical wave hogging bending moment) are to be distributed over the entire ship length The vertical bending moments can be applied to the FE model using concentrated loads to the side shell along the ship length. The concentrated forces (shear forces) are to be applied in way of the 2 nd deck (see Figure 6-3). The vertical shear force to be applied in way of transverse girder structures along the ship length can be calculated using numerical integration of the vertical bending moment between transverse girder structures: x x F V = 1 dm v dm v x1 dm v x dx x x dx dx 2 x 1 x 2 = x-s aft /2 = x+s fwd /2 s aft = spacing in m between the web frame in question and the adjacent web frame aft s aft = spacing in m between the web frame in question and the adjacent web frame forward x = distance in m from AP to web frame in question F v F v Figure 6-3 Application of vertical bending moments Horizontal wave bending moment and torsion moments Horizontal wave bending moment The horizontal wave bending moment is to be distributed over the entire ship length The horizontal wave bending moment envelop can be applied to the FE model using horizontal concentrated loads to the side shell along the ship length. The concentrated forces (shear forces) are normally to be applied in way of the stool bench structure top (Figure 6-4).

39 Page 39 The horizontal shear force to be applied in way of transverse girder structures along the ship length can be calculated using numerical integration of the horizontal wave bending moment between transverse girder structures: x x2 dm WH dmwh x2 dmwh x1 F WH = dx dx dx x x x, x 1, x 2 = as given in Sec F WH F WH Figure 6-4 Application of horizontal wave bending moments Torsion moments The application of the horizontal wave bending moment by horizontal shear force, F WH, as given in Sec means that the main part of the first term in the Rule-defined torsion moments as given in Sec.2.5 is already included in the model: M T,FWH = F WH z e,fwh F WH = as given in Sec z e,fwh = distance in m from the shear centre of the midship section to the applied load F WH Any deviation between the torsion induced by the horizontal wave bending moment and the first term in the Rule-defined torsion moment should be compensated for by applying coupled vertical forces to the side shell along the ship length. The concentrated force couples (shear forces) are normally to be applied in way of the 2 nd deck (Figure 6-5): F M1 = M T1 x B M T1 difference in torsion between transverse girder structures: M T1 = M 1 F WH z e,fwh M 1 = first term in the Rule-defined torsion moment F WH z e,fwh = torsion induced by horizontal wave bending moment x distance between transverse girder structures B = Rule breadth The remaining vertical part of the Rule torsion moment (the 2 nd term in the Rule-defined torsion moment) is to be applied using coupled vertical forces to the side shell along the ship length. The concentrated force couples (shear forces) are normally to be applied in way of the 2 nd deck (Figure 6-5): F M2 = M T 2 x B M T2 x B difference in the 2 nd term of the Rule torsion moment between transverse girder structures distance between transverse girder structures = Rule breadth The force application for torsion moment, F M1 and F M2, can be substituted by moment application at the shear centre of the cross-sections with a rigid plane arrangement.

40 Page 40 F M1(2) F M1(2) Figure 6-5 Application of vertical shear force couple Verification of loads applied to the global FE model The applied loads to the coarse-mesh global FE model should be verified. The structural response should be verified by integrating the stress in the FE model. This may be done using NAUTICUS Hull CUTRES as further described in Sec Normally, no more than 5% deviation for the envelopes of hull girder bending moments should be accepted. For torsion moments, the application of the loads is based on the assumption that the distance to the shear centre is constant over the entire ship length. The Rule formulations for the torsion moments in Sec.2.5 apply the midship section distance to the shear centre over the ship length. By integrating the warping stress over cross-sections with an actual distance to the shear centre deviating from the midship value, there will be a mismatch between the CUTRES results for torsion moments and the applied loads for some cross-sections, as shown in Figure 6-6. This is in particular the case in way of ER, cross decks, HFO deep tank structure (where applicable) and cross-sections in forward and aft end of the cargo hold area. However, no more than 5% deviation between the applied torsion moments and the CUTRES results should be accepted in way of the midship section. Rule wave torsion moments - Applied Vs CUTRES x/l CUTRES CUTRES MWT1 MWT2 Figure 6-6 Rule wave torsion moments Applied Vs CUTRES 6.8 General procedures for obtaining hot spot stress General In order to limit the scope, a minimum number of fine-mesh models are to be established for the selected critical areas as defined in Sec In order to predict hot spot stress for locations where no fine-mesh models are requested, a procedure for establishing the hot spot stress by application of geometric stress concentration factors are described in

41 Page 41 Sec This procedure is mainly intended for hatch corners in way of upper deck and hatch coaming top. However, for stringer corners with similar geometry as for the most critical stringer corner (with fine-mesh model), the procedure as described in Sec may be used. If the results obtained by the method with stress concentration factors are close within or exceeding the acceptance criteria as defined in Sec.6.11, it is recommended to further extend the scope by establishing finemesh models. The hatch corner edges are assumed free from weld, eccentricity and misalignment. Thus only the stress concentration due to the geometry effect is considered Fine-mesh models for selected critical areas Fine-mesh models for hot spot stress evaluation are to be made for the following locations: Hatch corners (upper deck and hatch coaming top) in way of ER front bulkhead Hatch corners (upper deck and hatch coaming top) amidships Most critical hatch corners (upper deck and hatch coaming top) in way of fore part of cargo hold area Corners in way of HFO deep tanks structure (where applicable) Critical stringer corner in fore part. For the locations mentioned above, fine-mesh models in accordance with Sec.6.9 are to be established. If the ship has the engine room located at a position forward of the normal position, the global analysis may result in relatively high stresses in the hatch corners located aft of the engine area. A separate fine-mesh analysis should then be made for such areas Assessment of hot spot stress based on generic stress concentration model The combined hot spot stress due to vertical bending is to be taken as: V,hs K x c x V (N/mm 2 ) x stress concentration factor in way of hatch corners due to longitudinal hull girder stress as given in Sec c x ratio of K t,x (see Sec.5.6.3) between the location with no fine-mesh model and the location with fine-mesh model V nominal longitudinal hull girder stress from vertical bending in way of the intersection between inner side and cross deck. The stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side. The combined hot spot stress due to horizontal wave bending moment and torsion moment is to be taken as: H&T,hs K x c x H&T + K y c y T (N/mm 2 ) x stress concentration factor in way of hatch corners due to longitudinal hull girder stress as given in Sec c x ratio of K t,x (see Sec.5.6.3) between the location with no fine-mesh model and the location with fine-mesh model H&T nominal longitudinal hull girder stress due to horizontal bending, and longitudinal hull girder warping stress induced by torsion moment in way of the intersection between inner side and cross deck; the stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side y stress concentration factor in way of hatch corners from bending stress due to warping deformations of cross decks Sec c y ratio of K t,y (see Sec.5.6.3) between the location with no fine-mesh model and the location with fine-mesh model T nominal bending stress due to warping deformation of cross deck induced by torsion moment in way of the intersection between inner side and cross deck. The stress is to be obtained applying an appropriate linear extrapolation of transverse stress along the inner side. 6.9 Hot spot stress evaluation by fine-mesh models Application Fine-mesh models are to be defined for selected critical areas as specified in Sec The intention with the fine-mesh models is to examine the stress response including geometric stress concentrations for ULS hot spot stress evaluation and FLS in way of selected critical corners Modelling It is generally recommended to use sub-modelling techniques for the fine-mesh models where displacements are transferred from the global model to the smaller fine-mesh models. The analysis model in the midship region should extend two web spaces aft and forward of transverse bulkhead

42 Page 42 location in the longitudinal direction, and from the hatch coaming top to 2 nd deck level in vertical direction. If the scantlings and or structural arrangement differ between the watertight bulkhead and the support bulkhead, due consideration will be necessary, i.e. separate modelling may be required. The analysis model of the engine room front bulkhead should extend two web spaces aft and forward of transverse bulkhead location in the longitudinal direction, and downward to 2 nd deck level in vertical direction. The model should also extend up to the suitable level of deckhouse deck, if applicable. The analysis model for stringer corners should extend two web spaces aft and forward of transverse bulkhead in the longitudinal direction. The model should also extend two coarse-size elements above and below the stringer deck level. Mesh arrangement in way of hatch corner area is important. It is recommended that the radius be divided into 8 to 10 divisions, but with an element size of maximum 2t (i.e. twice the plate thickness). It is recommended to utilise fictitious 1x1 mm beam elements along the edge of hatch corner radius for easy read-out of stress. Special attention should be paid where the curvature of the hatch corner starts and ends. In order to obtain a correct read-out of stress for the first and the last element in way of the hatch corner curvature, the beam elements should be extended to the first element outside the hatch corner radius. All the models are to include fine-mesh in way of hatch corners as well as at the scarping and at the end terminations of longitudinal hatch coamings, where relevant. The coaming stays should also be properly represented in the model by shell or membrane elements. All cut-outs, e.g. ventilation opening, access openings, should be included in the model. Secondary stiffeners may be represented by truss elements unless their contribution to the stresses, at the area of concern, is negligible. Figure D view of hatch corner model midship 6.10 Stress concentration factors for hot spot stress evaluation Application The following procedure may be applied in order to establish hot spot stress in hatch corners where no finemesh models have been established. The intention with the method is to establish an estimated hot spot stress for all hatch corners without having to generate fine-mesh models for all locations. The method consists of establishing generic geometric stress concentration factors by applying unit loading to reference fine-mesh models as defined in Sec The method is based on the assumption that the locations to be investigated by this procedure have similar geometry as for the reference fine-mesh models. The procedure is based on the assumption that longitudinal hull girder stresses from vertical bending, horizontal bending and warping stresses have same stress concentration factor. Hot spot bending stress from warping deformation of cross deck is established applying another stress concentration factor.

43 Page Generic stress concentration factors The nominal stress at reference locations should be established by use of a coarse-mesh local model with the same model extent as that prescribed for the fine-mesh models (see Sec.6.9.2). A unit displacement in the longitudinal direction, l, is to be applied to the coarse-mesh model. The nominal stress, x,nom, is to be calculated in way of the intersection between inner side and cross deck, as shown in Figure 6-8. The stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side. Δx σ x,nom Longitudinal direction (Upper deck H/C top) Figure 6-8 Nominal stress from longitudinal displacement of deck structure Similarly, a unit displacement of the transverse deck beam, t, is applied to assess nominal bending stress in transverse direction, y,nom. The stress is to be obtained applying an appropriate linear extrapolation of transverse stress along the inner side. σ y,nom Longitudinal direction (Upper deck H/C top) Figure 6-9 Nominal stress from bending of transverse deck structure Δt Hot spot stresses along the hatch corner curvature are further to be established by use of a fine-mesh model as shown in Figure The same unit displacements are applied to the fine-mesh models in order to establish the hot spot stresses along the edge of the curvature. The nominal stresses from the coarse-mesh local models are compared with the hot spot stress in order to establish stress concentration factors along the edge of the curvature. Separate stress concentration factors for longitudinal stress and transverse stress are to be established. The hot spot stress is to be taken as the stress in each fictitious beam element along the edge of the hatch corner curvature for each of the forced displacements, j.

44 Page 44 Figure 6-10 Fine-mesh model of hatch corner for establishing hot spot stresses for unit displacements The stress concentration for each element and stress component is to be taken as: K K x,i y,i hs, l,i hot spot stress for beam element i from longitudinal displacement of deck structure x, nom nominal stress from longitudinal displacement of deck structure hs, t,i hot spot stress for beam element i from bending of transverse deck structure y, nom nominal stress from bending of transverse deck structure i = the element number along the edge of the curvature 6.11 Acceptance criteria Acceptance criteria ULS Table 6-1 Allowable stress Applicable location Allowable combined nominal stress In way of the bilge area and stool bench structures, a uni-axial buckling assessment in accordance with Rules for Classification of Ships Pt.3 Ch.1 Sec.13 B 201 is to be carried out, applying: 1.0 a combined nominal stress calculated in accordance with Sec.5.2. Allowable combined hot spot stress Top of hatch coaming 225f 1 400f 1 Upper deck 225f 1 400f 1 Stringer corners f 1) 2) 1 400f 1 (where applicable) Bilge 195f 1 Not Applicable 1) f 1 is to be taken for the material surrounding the insert plate in way of the cross deck, if any. 2) To be considered as a screening criterion. If the nominal stress exceeds f 1, fine-mesh modelling for hot spot stress analysis and fatigue assessment is to be carried out. f 1 = σ σ σ hs,δl,i x, nom hs, t,i K x, i σ y, nom x, nom material factor as given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B101

45 Page Acceptance criteria FLS The fatigue life is to be minimum 20 years, applying world wide-scatter diagram, as defined in Rules for Classification of Ships Pt.3 Ch.1 Sec.16 A Level 3 Wave Load Analysis 7.1 General principles The application, objective and scope for Level 3 wave load analysis is described in Sec.1.8. A hydrodynamic analysis, with similar scope as for the CSA-2 class notation is to be carried out. The loads for FLS and design loads for ULS are further described in Sec.7.2. A global coarse FE structural model, with similar scope as for CSA-2 class notation is to be made in accordance with Sec.7.3. The mesh size and the modelling technique for the global FE model is similar as for Level 2 global analysis, with a more elaborate application of loads (pressure loads) and mass tuning. The scope for ULS assessment is quite limited compared to the CSA-2 class notation (more in line with Level 2 global analysis) and is further described in Sec.7.4 to 7.7. Similar as for ULS, the scope for FLS assessment is quite limited compared to the CSA-2 class notation (more in line with Level 2 global analysis) and is further described in Sec.s 7.8 to In order to obtain hot spot stresses for yield check and fatigue assessment, the general procedure as shown in Sec.6.8 are to be applied. The acceptance criteria for Level 3 wave load analysis are given in Sec Results obtained from Level 3 wave load analysis supersede results from Level 2 global analysis and the prescriptive minimum requirements to hatch corners and stringer corners given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B Hydrodynamic analysis General The wave load analysis is in general to be carried out as outlined in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures, Sec.4, applying: Loads for FLS as defined in Sec Design loads for ULS as defined in Sec Structural modelling principles General The global coarse model is in general to be generated as outlined in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures, Sec.6.3 and Sec.6.5. Sub-models are to be established for the critical locations as specified in Sec.6.8.2, applying the modelling techniques as described in Sec Methodology for ultimate limit state (ULS) assessment General For ULS, the procedures according to Sec.5 in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures are to be applied, with the following exemptions: Relevant application of Sec.5.1 in Classification Note No is further described in Sec Relevant application of Sec in Classification Note No is further described in Sec Sec and are in Classification Note No covering result evaluation, and are to be disregarded. The scope for result evaluation according to Level 3 wave load analysis is further described in Sec Sec.5.3 in Classification Note No is not applicable Principal overview Sec in Classification Note No (General) The scope for result evaluation is to be according to Sec Sec in Classification Note No (Global FE analysis local ULS) For a Level 3 wave load analysis, cargo hold modelling, including yield check and buckling control of the cargo hold model, is not applicable.

46 Page 46 Sec in Classification Note No (Hull girder collapse global ULS) Hull girder collapse global ULS is not applicable for Level 3 wave load analysis Design loads Sec in Classification Note No (General) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Design condition and selection of critical loading conditions) The following loading conditions (mass distribution) should be analysed: Maximum stillwater hogging moment amidships (scantling draught) Maximum stillwater sagging moment (or minimum stillwater hogging moment if applicable) amidships (scantling draught). The loading conditions for the ULS analysis should represent the design stillwater moment for the vessel. These loading conditions are usually not included in the trim and stability booklet. Sec in Classification Note No (Hydrodynamic analysis) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Design life and wave environment) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Design waves) Nonlinear wave load analyses are to be carried out for the design sea states. A design load wave 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 ensured that the FE model is well balanced and that the reaction forces in the position for boundary conditions are minimized. The design load waves are extracted as snapshots from the time series of the hull girder loads. The design load waves for the vertical bending moment at the reference positions is straight forward to determine by extracting the loads at the time corresponding to the maximum vertical bending moment for the selected reference position. The time instant corresponding to the maximum torsion moment will not necessarily give the highest stresses in the structure and the largest hatch cover deflection. Selection of design load cases for the torsion moment cases needs careful consideration. It is therefore recommended to extract several design load waves (i.e. snapshots) covering the complete oscillation cycle for the torsion moment and the horizontal bending moment. In general, the following instances are deemed sufficient for selection of snapshots in time domain: Maximum torsion Maximum vertical wave bending Minimum vertical wave bending 2 additional snapshots in between maximum and minimum vertical wave bending. Sec in Classification Note No (Load transfer) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Combined nominal stress evaluation (ULS) General Within the cargo hold area the combined nominal stress level in way of hatch corners, stringer corners, and bilge is to be checked Combined nominal stress As all relevant stress components are included for each design wave, the combined nominal stress can be extracted directly from each load case in the global FE model, and are to comply with the acceptance criteria according to Sec For stringer corners not complying with the screening criterion as given in to Sec , the nominal stress levels may be accepted provided that local fine-mesh modelling is carried out. The results from the fine-mesh

47 Page 47 model should then comply with the requirements according to Sec.7.7 and Sec.7.9. In way of corners the nominal combined stress is to be calculated in way of the intersection between inner side and cross deck. The stress is to be obtained applying an appropriate linear extrapolation of longitudinal stress along the inner side. The buckling control is limited to reading out compressive nominal membrane stress in way of the bilge area and stool bench structures form the coarse global FE model, and carry out a uni-axial buckling assessment in accordance with the requirement given in Sec Transverse strength of the fore and aft body General Sea pressures are applied to the global coarse structural FE model. As the FEM cargo hold analysis according to Sec.4 does not accurately represent the transverse girder structures in the fore and aft body, the transverse strength of thee members should be checked Nominal stress As all relevant stress components are included for each design wave, the combined nominal stress can be extracted directly from each load case in the global model, and are to comply with the acceptance criteria according to Sec Combined hot spot stress evaluation (ULS) General Within the cargo hold area the combined hot spot stress level in way of hatch corners are to be checked. In addition, the combined hot spot stress is to be calculated for the most critical stringer corner. The most critical stringer corner may be identified applying the screening procedure as described in Sec.7.5. Stringer corners not complying with the screening criteria as given in Sec , if any, are also to be checked for combined hot spot stress Combined hot spot stress For locations where fine-mesh models have been established, as required by Sec.6.8.2, the combined hot spot stress is to be calculated following the procedures defined in Sec.6.9. For locations where fine-mesh models have not been established (see Sec.6.8.2), the combined hot spot stress is to be calculated following the procedures defined in Sec The calculated maximum combined nominal stress is to comply with the acceptance criterion given in Sec Methodology for fatigue limit state (FLS) assessment General For FLS, the procedures according to Sec.4 in Classification Note No. 34.1, CSA Direct Analysis of Ship Structures are to be applied, with the following exemptions: Relevant application 4.2 in Classification Note No. 34. is further described Sec Relevant application 4.4 in Classification Note No is further described Sec Sec.4.5 in Classification Note No to be applied to stiffener end connections only (not plate connections to stiffeners and frames) The scope in Sec in Classification Note No.34.1 to be limited as described in Sec.7.5 and Sec.7.6 Relevant application of Sec in Classification Note No is further described in Sec Relevant application of Sec in Classification Note No is further described in Sec Sec in Classification Note No is not applicable Locations for fatigue analysis Sec in Classification Note No (General) Fatigue calculations should for Level 3 wave load analysis be limited to the locations as shown in Table 7-1.

48 Page 48 Table 7-1 Overview of fatigue critical details Detail Location Method Stiffeners end connection One frame amidships Component stochastic Upper deck hatch corner All hatch corners within cargo Full stochastic hold area Hatch coaming top corner All hatch corners within cargo Full stochastic hold area Stringer corner Critical stringer corner in foreship Full stochastic * * Stringer corners not complying with the screening criterion, if any, (see Sec.7.5.2) are also subject to FLS. For stiffener end connections, it is normally sufficient to perform component stochastic fatigue analysis using predefined stress concentration factors. Sec in Classification Note No (Details for fine-mesh analysis) Fine-mesh full stochastic fatigue analysis is to be carried out for the locations as specified in Sec Loads Sec in Classification Note No (Loading conditions) The following loading conditions (mass distribution) should be analysed: Homogenous loading condition with high GM (design draught) Ballast condition. Due attention should be paid to the GM value. Amongst several homogenous loading conditions with similar stillwater hogging moment amidships, the condition with the higher GM value should be selected. The reason for this is to have larger roll motions and therefore higher torsion moment on the hull girder. Sec in Classification Note No (Time at sea) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Wave environment) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Hydrodynamic analysis) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Sec in Classification Note No (Load application) Level 3 wave load analysis is to comply with the procedures outlined in Classification Note No. 34.1, Sec Global screening analysis Sec in Classification Note No (Allowable stress concentration in deck) As the fatigue scope of Level 3 wave load analysis is limited to hatch corners and critical stringer corners, the screening procedure for allowable stress concentration in deck as described in Sec in Classification Note No is therefore not applicable. Sec in Classification Note No (Finding the most critical location for a detail) Fine-mesh models are as a minimum to be carried out for the locations as specified in Sec The fine-mesh models are to be modelled as specified in Sec.6.9. In order to identify the most critical hatch corner location in way of upper deck and the most critical stringer connection in foreship, the screening criteria as specified in Sec in Classification Note No may be applied. Sec in Classification Note No (Fatigue ratio between different positions) In order to predict the fatigue ratio between hatch corners with no fine-mesh models, and hatch corners with no fine-mesh models, the procedure described in Sec should be followed Local fatigue analysis The fine-mesh modelling is to follow the procedures as described in Sec Determination of hot spot stress Sec in Classification Note No (General) The fine-mesh modelling of the hatch corners is to follow the procedures as described in Sec.6.9.

49 Page 49 Sec in Classification Note No (Cruciform connections) Fatigue assessment of cruciform joints is not applicable to container ships applying Level 3 wave load analysis procedure. Sec in Classification Note No (Stress concentration factor) In order to establish stress concentration factors for hatch corners, and to predict fatigue life for locations with no fine-mesh model, the procedure as specified in Sec are to be followed. 7.9 Fatigue assessment of hatch corners and stringer corners General Within the cargo hold area full stochastic fatigue assessment in way of all hatch corners are to be carried out. For hatch corners with fine-mesh models (see Sec.6.8.2), the hot spot stresses are to be extracted directly from the fine-mesh model. For locations with no fine-mesh model, the hot spot stresses are to be predicted applying the procedure described in Sec In addition, fatigue life is to be calculated for the most critical stringer corner. The most critical stringer corner may be identified applying the screening procedure described in Sec.7.5. Stringer corners not complying with the screening criteria as given in Sec , if any, are also to be checked for fatigue Damage calculation The damage calculations are to be carried out, applying the procedures specified in Classification Note No.34.1, Sec.4.7. As the stress concentrations will vary along the edge of the hatch corner, it is recommended to calculate the fatigue life for 10 positions along the edge of the hatch corner Fatigue assessment of stiffener end connections amidships General Component stochastic fatigue assessment for stiffener end connections in way of one frame amidships is to be carried out Damage calculation The damage calculations are to be carried out, applying the procedures specified in Classification Note No.34.1, Sec.4.7. Stress concentration factors according to Classification Note No. 30.7, Appendix A.2 may be applied. The predefined stress concentration factors according to A.2 may be overruled by stress concentration models Documentation and verification General Documentation and verification should be documented in accordance with Classification Note No. 34.1, Sec Comparison of hull girder loads with Rules for Classification of Ships In addition to Sec , the maximum hull girder loads according to the hydrodynamic analysis should be compared with those of the Rules for Classification of Ships. The simultaneous values for the torsion moment, vertical bending moment and the horizontal bending moment should be compared with those of the Rules for Classification of Ships. Care should be taken in selection of the critical load combinations. To evaluate the strength of deck and coaming structures, the wave torsion cases should be added to the stillwater hogging moment. To evaluate the bilge longitudinals, the wave torsion cases should be combined with the stillwater sagging moment Acceptance criteria General The allowable nominal stresses as explained in this section should only be used when loads are based on hydrodynamic analysis that is applied as sea pressure and inertial loads on the FE model. Allowable stress criteria of the global analysis are as outlined below, but the stresses have to be finally assessed considering the local structural design, location, element fineness, etc.

50 Page Criteria for nominal stress Allowable von Mises membrane stress in longitudinal members: all 0.9 f (N/mm 2 ) if interaction between hatch cover and main hull structure is not included in stress calculation all 0.95 f (N/mm 2 ) if interaction between hatch cover and main hull structure is included in stress calculation Allowable von Mises membrane in transverse members: all 0.85 f (N/mm 2 ) f minimum upper yield stress of the material Screening criterion for nominal stress in way of stringer corners in fore ship Allowable von Mises membrane stress in way of stringer corners in foreship: all 0.8 f (N/mm 2 ) f minimum upper yield stress of the material surrounding the insert plate, if any Hot spot stress in way of hatch corners When loads are based on 20-year North Atlantic operation, the allowable local peak stresses (equivalent stress) in the hatch corners may be taken as: all 400 f 1 (N/mm 2 ) f 1 = as given in Rules for Classification of Ships Pt.5 Ch.2 Sec.6 B Buckling Strength The ultimate buckling strength is checked for compliance with the Rules for Classification of Ships Pt.3 Ch.1 Sec.13 irrespective of whether loads based on Rules of direct wave loads analysis. 8. References /1/ Det Norske Veritas, Rules for Classification of Ships, Høvik. /2/ Det Norske Veritas, Classification Note No Fatigue Assessment of Ship Structure, Høvik. /3/ Det Norske Veritas, Classification Note No CSA Direct Analysis of Ship Structures, Høvik

51 Page 51 Appendix A Structural Verification Procedure for Lashing Bridge Structure A.1 Introduction A.1.1 Post-Panamax containerships are normally equipped with lashing bridges in order to simplify the securing of high stacks and large number of cargo containers on hatch covers/deck space. A.1.2 Design loads from the container securing equipment acting on the lashing bridge are described in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E300. A.1.3 Forces in container securing equipment and the working load of the securing device are to be less than half the breaking load of the item. In this regard, half the breaking load of the lashing bar (safe working load) is a theoretical maximum load to be taken by the lashing bridge for strength verification. A.1.4 This simple force definition is suitable for the verification of local strength of items like lashing eyes and their welding connection, etc. It seems to be a too conservative approach to apply half the breaking load for all lashing bars connected to the lashing bridge simultaneously. The more lashing bars applied to distribute lashing forces, the higher total load will be applied to the lashing bridge. A.1.5 In order to have a more realistic force application, the following procedure is recommended for lashing bridge design. A.2 Assumption A.2.1 Total container stack weight should be assumed evenly distributed to the container in the stack, i.e. homogeneous weight distribution. However, container lashing arrangement will be taken as per the actual lashing arrangement scheme in the container securing manual. A.2.2 Lashing force will be calculated for the lashing bars securing the stack to the lashing bridge, and the lashing force should be applied to the lashing bridge at the lashing eye locations. A.2.3 Relative displacement between hatch cover and hull structure is to be considered as given in the Rules for Classification of Ships Pt.3 Ch.3 Sec.6 F203. However, this is in normal cases covered by applying case 4 as given in Appendix A A.3 Loading conditions A.3.1 Accelerations Accelerations a t and a l are to be calculated as given in the Rule for Classification of Ships Pt.5 Ch.2 Sec.6 G300. For simplification, the accelerations may be calculated at half the height of the mid stack. Longitudinal position of the lashing bridge is also to be considered to get proper acceleration factors. A.3.2 Lashing force calculation to lashing bridge Lashing force for container stack is to be calculated for maximum container stack weight based on homogeneous weight distribution. The actual container weight distribution that is normal for 40 container stack should not be used. A.3.3 Load cases A Case 1 Lashing force for simultaneous loading in fore and aft space: Lashing forces are to be applied to fore and aft part of the lashing bridge in line with the connected lashing bars along the same direction. For simple application, the lashing force can be decomposed into force components in longitudinal, transverse and vertical direction.

52 Page 52 A Case 2 Lashing force for container loading in fore space only. A Case 3 Lashing force for container loading in aft space only. A Case 4 Lashing force for container loading in fore space only: Safety working load (250 kn) is to be applied to short lashing bars and half the safe working load (125kN) is to be applied to long lashing bars. This case will cover the relative displacement between hatch covers and main hull structures, i.e. lashing bridge. A.4 Allowable stress Normal stress : = 210 f 1 [N/mm 2 ] Shear stress : = 120 f 1 [N/mm 2 ]

53 Page 53 Appendix B Structural Verification Procedure for Hatch Cover Stoppers B.1 Introduction B.1.1 Hatch cover stoppers can either be rolling stoppers which are fixations against transverse movement (one way fix for longitudinal shifting) or rolling/ pitching stoppers (pin stopper) which are fixations against movement in both directions. B.1.2 To prevent damage to the hatch covers and ship structures, the location and type of stoppers is to be harmonised with the relative movements between the hatch covers and ship structure. B.1.3 The number of stoppers is to be as small as possible, preferably only one stopper at each end of the hatch cover panel. B.1.4 A common arrangement for hatch covers, are one rolling stopper at one end and rolling/pitching rolling stopper (pin stopper) at the other end. B.2 Assumption B.2.1 If the container stack is attached/secured to other structures (i.e. lashing bridge) than the hatch cover, the horizontal force on hatch cover may be reduced. However, to be conservative, this may not be considered in the force calculation. B.2.2 Friction force at bearing pads may reduce the horizontal force by about 10% as given the Rules for Classification of Ships Pt.3 Ch.3 Sec.6 F601. However, this should be decided based on bearing pad material. If the bearing pad is of low-friction material, it is recommended not to reduce the horizontal forces. B.2.3 Hatch coaming and supporting structures are to be adequately stiffened to accommodate the loading from hatch covers. B.2.4 Relative displacement between hatch cover and hull structure is to be considered as given in the Rules for Classification Pt.3 Ch.3 Sec.6 F203 in connection with the strength of stopper. However, this may in the normal case be covered by applying longitudinal force to the pin stopper. B.3 Loading conditions B.3.1 Accelerations Accelerations a t and a l are to be calculated as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E300. The accelerations will be calculated for a level corresponding to half the height of the mid stack. B.3.2 Force application All container loads and hatch cover weight are to be considered in the horizontal force calculation. Total container weight is normally maximum for 20 container stack loading. The horizontal force is to be applied to the level of the highest contact point between the hatch cover and the rolling stopper. For pin stopper, the force is to be applied to the middle of the contact area. B.3.3 Load cases B Case 1 (Transverse force) Pt (total) = 0.67 a t (Total no. for 20 container stacks weight [tons] + hatch cover weight [tons]) [kn] Horizontal force will be taken by two stoppers at both ends of the hatch cover and thus half of Pt is to be applied to each stopper.

54 Page 54 B Case 2 (Longitudinal force) Pl (total) = 0.67 a l (Total no. for 20 container stacks weight [tons] + hatch cover weight [tons]) [kn] Pin stopper will take the whole force. B.4 Allowable stress Normal stress : =120 f 1 [N/mm 2 ] Shear stress : = 80 f 1 [N/mm 2 ] Equivalent stress : e =150 f 1 [N/mm 2 ]

55 Page 55 Appendix C Structural Verification Procedure for Hatch Cover Guide Post In case of deleting anti-lifting devices of non-weathertight hatch covers. C.1 Introduction C.1.1 Hatch cover on deck can be non-weather tight and weathertight hatch covers. C.1.2 Securing devices (i.e. anti-lifting device) that locks the hatch cover to the main hull structure are fitted to the hatch covers to maintain integrity during extreme conditions. C.1.3 The anti-lifting device should be fitted for non-weathertight hatch covers. C.1.4 In case there are not lashing bridge, it is recommended to keep anti-lifting device as per normal requirement also for non-weathertight hatch covers. C.1.5 If the lashing bridges are arranged and the anti-lifting devices are omitted, the following evaluation procedure is recommended to ensure the structural integrity in extreme condition. C.1.6 In general, there are two guideposts for each panel of hatch cover, one at fore and aft end. This procedure is aimed at providing the required minimum strength of the guide post in way of deleting the anti-lifting device. C.2 Assumptions C.2.1 The lashing bars are to secure the container stacks on the hatch cover firmly to the lashing bridge. The cargo securing calculation should be done according to DNV requirement. C.2.2 When the vessel is listing, the transverse force due to the on-deck containers can be taken by lashing bars, bearing pads through friction and hatch cover stoppers. However, for strength check, the total force is to be assumed to be taken by the hatch cover stoppers. C.2.3 This means that the guidepost will never be exposed to horizontal force in operation unless all lashing bars are broken and coincidentally hatch covers are lifted up beyond the functioning level of the hatch cover stoppers. C.2.4 Even without anti-lifting device, lifting-up of hatch covers is unlikely to occur even in extreme operation if the lashing is done properly. However, the strength of the guidepost should be designed for a certain unrealistic condition in order to have safety redundancy in extreme conditions. C.3 Loading cases C.3.1 Acceleration Transverse acceleration a t is to be calculated as specified in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E300. The acceleration will be calculated at a vertical position corresponding to the mid stack height. C.3.2 Force application All container load and hatch cover weight are to be considered in the transverse force calculation. Total container weight is normally maximum for 20 container stacks. The transverse force is to be applied at a level corresponding to the half the hatch cover height or the highest contact point between the hatch cover and the guidepost, whichever is highest. C.3.3 Load Pt (total) = a t (Total no. for 20 container stacks weight [tons] + hatch cover weight [tons]) [kn] This transverse force can be taken by two guideposts at fore and aft ends of hatch cover. Thus, half Pt is to be applied for strength check.

56 Page 56 C.4 Allowable stresses Normal stress : = 210 f 1 [N/mm 2 ] Shear stress : = 120 f 1 [N/mm 2 ]

57 Page 57 Appendix D Structural Verification Procedure for Hatch Covers D.1 Introduction D.1.1 Hatch cover structures consist of grillage system in way of container ships. D.1.2 Hatch cover is mounted on the bearing pads which take vertical force, whilst the stoppers take transverse force. D.2 Assumption D.2.1 Total container stack weight should be assumed evenly distributed to the container in the stack, i.e. homogeneous weight distribution. D.2.2 The vertical centre of gravity of each container in the stack is 45% of the container height. D.2.3 Although the container stack is secured to other structures than the hatch cover, for example lashing bridge, no effect is to be considered on force calculation D.2.4 Hatch coaming and supporting structures are to be adequately stiffened to accommodate the loading from hatch covers. D.2.5 Relative movements between hatch cover and hull structure is to be considered as given in the Rules for Classification of Ships Pt.3 Ch.3 Sec.6 F203 in connection with the strength of stopper. However this may in the normal cases be covered by applying longitudinal force to the pin stopper. D.3 Loading conditions D.3.1 Accelerations Accelerations a t and a l are to be calculated as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E300. In general, a homogeneous weight distribution of the container stack is recommended used. For stacks of homogeneous weight distribution, the accelerations will be calculated based on a vertical centre of gravity for the stack corresponding to a VCG of the individual containers of 45% of the container height. D.3.2 Force application All container loads and hatch cover weight are to be considered in the horizontal force calculation. Total container weight is always maximum for 20 container stack loading in connection with hatch cover strength design. Total stack load will be split into 4 container corners. The following load cases will be limited to 20 container loading. D.3.3 Load cases D Case 1: Full stacks and vertical acceleration in upright condition Pv (stack) = (g a v ) (container stacks weight [tons]) [kn] D Case 2: Full stacks and combined vertical with transverse acceleration: Pv (stack) = g 0 (container stacks weight [tons]) [kn] Pt (stack) = 0.67 at (container stacks weight [tons]) [kn] Pv (transverse) = Pt H / Container width H : A distance from the bottom of container stack to the vertical centre of gravity of the stack

58 Page 58 D Case 3: One empty stack and vertical acceleration in upright condition: This case will be similar to Case 1 except one full empty container stack abreast. D Case 4: One empty stack and combined with vertical and transverse acceleration. This case will be similar to Case 2 except one empty container stack abreast. D.4 Allowable stress (Rules for Classification of Ships Pt.3 Ch.3 Sec.6 E700) Normal stress : = 0.58 f [N/mm 2 ] Shear stress : = 0.33 f [N/mm 2 ] Shear buckling : = 0.87 cr Due to the relatively thin and high web plates of the hatch cover girder system. The shear buckling criteria as per the Rules for Classification of Ships Pt.3. Ch.1 Sec.13 B300 needs to be considered. Plate Critical Buckling Stress c a / 0.87

59 Page 59 Appendix E Strength Analysis for Fuel Oil Deep Tank Structure in Container Hold E.1 General The objective of the strength analysis is to determine the scantling of primary structure of the fuel oil deep tanks arranged in container hold, i.e. fuel oil deep tanks located inboard of the inner skin, above the inner bottom, and between adjacent transverse bulkheads. Strength analysis by use of finite element methods is mandatory for container ships with the NAUTICUS(Newbuilding) notation and should be carried out in accordance with principles described in Sec.4. E.2 Analysis Model The analysis model should extend from one 40 bay aft of the aftermost fuel oil tank bulkhead to one 40 bay forward of the foremost fuel oil tank bulkhead. The model should normally cover the full breadth of the ship in order to account for unsymmetrical load cases (Heeled or unsymmetrical tank test conditions). In principle the actual shape of outer shell may be represented as it is. However, the simplification by using the shape of the midship section unchanged for the whole model length is acceptable if due consideration is given to the stress evaluation of the changed structure. Modelling of geometry, element and mesh size are given in Sec and E.3 Boundary Conditions Selection of boundary conditions and calculation of spring constant are given in Sec.4.3. E.4 Design Load Design container forces are given in Sec.3.3. Design liquid pressures in tank are given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 C302 [5] and Pt.3 Ch.1 Sec.12 B310, and the density of fuel oil used in the calculation should in general not be less than t/m 3. In case the actual overflow height is used to define the internal pressure head for the tank test conditions, the allowable stress is subject to special consideration. The sea pressures in upright conditions and tank test conditions are given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 C200. In heeled conditions, the sea pressures are normally to be taken as: P = 10 (T A z) y tan ( /2) [kn/m 2 ] on submerged side and P = 10 (T A z) + 10 y tan ( /2) [kn/m 2 ] on emerged side = 0 minimum T A = actual considered draught in m z = vertical distance in m from base line to considered position y = transverse distance in m from centre line to considered position as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B E.5 Load Cases The load cases as described in the text below are to be examined. The container load above fuel oil tanks, on hatches above container holds, aft bay and fore bay may in general be for 40 container stacks. For two (2) F.O. tanks with one (1) longitudinal bulkhead arranged in container hold, the load cases of LC-4F and LC-6F are to be omitted. For one (1) F.O. tank with no longitudinal bulkhead, four (4) F.O. tanks with three (3) longitudinal bulkheads, or for arrangements where more F.O. tanks are arranged in container hold, the load cases to be specially considered. E.5.1 Full F.O. tanks at reduced draught (LC-1F) All F.O. tanks are to be full, and cargo mass above F.O. tank tops in hold and on deck in seagoing upright condition at reduced draught. In case F.O. tank top is arranged below the 2nd deck level, the maximum cargo mass is to be applied in order to check supporting structures of F.O. tank top 20 or 40 containers to be applied as relevant.

60 Page 60 The adjacent holds and decks are to be assumed empty. The reduced draught is in general to be actual draught as describe in Trim and Stability Booklet, may be taken as 0.8T, if not known. E.5.2 Empty F.O. tanks at scantling draught (LC-2F) All F.O. tanks are to be empty, and the container space above F.O. tank tops in hold and on deck is to be empty. Cargo mass adjacent in holds and decks in sea going upright condition at scantling draught. E.5.3 Heeled condition, side tank full (LC-3F) One(1) side F.O. tank is to be full in heeled condition at reduced draught. The adjacent holds and decks are to be assumed empty. The reduced draught is generally not to be considered larger than 0.8T. E.5.4 Heeled condition, centre tank full (LC-4F) One(1) centre F.O. tank is to be full in heeled condition at reduced draught. The adjacent holds and decks are to be assumed empty. The reduced draught is generally not to be considered larger than 0.8T. E.5.5 Tank test condition, side tanks full (LC-5F) Side F.O. tanks are to be full in harbour condition at minimum ballast draught.