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ShipRight Design and Construction Structural Design Assessment Primary Structure of Container Ships September 2016

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Document History

Date:

Notes:

May 2000 Preliminary release.

November 2001 Preliminary editorial revisions.

July 2002 Final release.

October 2002 Editorial revisions.

May 2004 Revisions as identified in Notice – ‘Changes incorporated in May 2004 version’.

May 2006 Revisions as identified in Notice – ‘Changes incorporated in May 2006 version’.

March 2016 Revisions as identified in ‘Notice 1 – SDA Primary Structure of Container Ships, March 2016 version’.

September 2016

Consolidated version incorporating: ‘Notice 1 – SDA Primary Structure of Container Ships, March 2016 version’, IACS Unified Requirement S34 (May 2015) and Corrigenda.

© Lloyd's Register Group Limited 2016. All rights reserved. Except as permitted under current legislation no part of this work may be photocopied, stored in a retrieval system, published, performed in public, adapted, broadcast, transmitted, recorded or reproduced in any form or by any means, without the prior permission of the copyright owner. Enquiries should be addressed to Lloyd's Register Group Limited, 71 Fenchurch Street, London, EC3M 4BS.

Primary Structure of Container Ship, September 2016

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CONTENTS

INTRODUCTION Section 1: Application .................................................................................................................. 3

Section 2: Symbols ....................................................................................................................... 4

Section 3: Direct calculation procedures report .......................................................................... 6

PART A: Global Model of Complete Ship ................................................................................................ 8

Chapter 1: Analysis of Global Loads .................................................................................................... 8

Section 1: Application .................................................................................................................. 8

Section 2: Objectives .................................................................................................................... 8

Section 3: Structural modelling .................................................................................................... 9

Section 4: Loading conditions .................................................................................................... 13

Section 5: Boundary conditions ................................................................................................. 22

Section 6: Acceptance criteria ................................................................................................... 24

PART B: Verification of Structural Components and Details ................................................................. 28

Chapter 1: Analysis of Global Loads on Local Details........................................................................ 28

Section 1: Application ................................................................................................................ 28

Section 2: Objectives .................................................................................................................. 28

Section 3: Structural modelling .................................................................................................. 29

Section 4: Loading and boundary conditions ............................................................................. 33


PART C: Verification of Primary Structure ............................................................................................ 39

Chapter 1: Verification of Double Bottom and Transverse Strength ................................................ 39








Chapter 2: Transverse Bulkhead and Mid-Hold Support Structures: Surge (Fore and Aft) Loading . 58




Primary Structure of Container Ship, September 2016

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Chapter 3: Transverse Watertight Bulkhead Assessment in Damaged (Flooded Hold) Condition ... 61






Chapter 4: Transverse Bulkhead Structures: Additional Requirements for Fuel Oil Deep Tanks ...... 68








Chapter 5: Surge (Fore and Aft) Loading: Additional Requirements for Fuel Oil Deep Tanks ........... 90



Section 3: Loading condition ...................................................................................................... 90

Appendix A: Procedure to Apply Transverse Asymmetric Loads to a Half-Breadth Model……………….92

Appendix B: Combined Stresses Analysis in Oblique Sea Based on Equivalent Design Waves………….94

Appendix C: Rule Equivalent Design Wave Hydrodynamic Torque, Vertical and Horizontal Bending Moment Distributions...............................................................................………….....…...……………………98

Appendix D: Combined Direct Stresses in Oblique Sea (Alternative Method)…………………………………104

Introduction Primary Structure of Container Ship, September 2016

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INTRODUCTION Section 1: Application

Section 2: Symbols

Section 3: Direct calculation procedures report

Section 1: Application

1.1. The ShipRight Structural Design Assessment (SDA) and Construction Monitoring (CM) procedures are mandatory for container ships with a beam greater than 32 m or a length greater than 150 m and for other container ships of abnormal hull form, or of unusual structural configuration or complexity, see Pt 4, Ch 8,1.3 of Lloyd’s Register’s Rules and Regulations for the Classification of Ships (hereinafter referred to as the Rules for Ships).

1.2. For container ships other than those defined in 1.1, the SDA and CM procedures may be applied on a voluntary basis.

1.3. The SDA procedure requires the following:

• A detailed analysis of the ship’s structural response to specified load scenarios using finite element analysis.

• Other direct calculations as applicable.

1.4. Container ships are defined as ships which are dedicated to the carriage of containers within cellular guide systems installed in the holds and to which the requirements of Pt 4, Ch 8 of Lloyd’s Register’s Rules and Regulations for the Classification of Ships (hereinafter referred to as the Rules for Ships) apply. These procedures are not intended for application to multipurpose or hybrid ship designs.

1.5. The direct calculation of the ship’s structural response is to be based on a three-dimensional (3-D) shell finite element analysis carried out in accordance with the procedures contained in these guidance notes.

1.6. The full finite element (FE) analysis procedure comprises three parts:

• PART A: verification of global strength using a mathematical model of the entire hull.

• PART B: verification of structural components and details, using follow-up fine mesh models.

• PART C: verification of the strength of transverse, side and double bottom structures using a mathematical model of the cargo holds amidships.


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1.7. PART C procedures are required to be carried out for all container ships for which the ShipRight SDA class notation is required. In general, the whole of PART C is to be applied. The exception to this is PART C, Ch 4 which is only required when the ship configuration dictates.

1.8. PART A and PART B procedures, in addition to PART C procedures, are required to be carried out for container ships which:

• Do not comply fully with Pt 4, Ch 8 of the Rules for Ships, especially with regard to cross-deck dimensions, hatchway deck and coaming corner radii and thickness of plate inserts in way.

• Have a beam greater than 32 m or a length greater than 290 m.

• Have wing-wall side structures with a width between side shell and longitudinal bulkhead less than 1.6 m.

• Incorporate features, scantlings or construction arrangements that are considered to be significantly different from normal design.

1.9. A detailed report of the calculations is to be submitted and must include the information detailed in Section 3. The report must show compliance with the specified structural design criteria detailed in the relevant PARTS of this procedure.

1.10. If the computer programs employed are not recognised by Lloyd’s Register, full particulars of the programs will also be required to be submitted, see Pt 3, Ch 1,3.1 of the Rules for Ships.

1.11. Lloyd’s Register may, in certain circumstances, require the submission of computer input and output to further verify the adequacy of the calculations carried out.

1.12. Where alternative procedures are proposed, these are to be agreed with Lloyd’s Register before commencement.

1.13. Container ships of unusual form or structural arrangements may need special consideration, and additional calculations to those contained in this procedure may be required.

1.14. It is recommended that the designer discusses the SDA analysis requirements with Lloyd’s Register early on in the design cycle.

Section 2: Symbols

2.1. The symbols used in these guidance notes are defined as follows:

L = Rule length, as defined in Pt 3, Ch 1,6 of the Rules for Ships

B = moulded breadth, as defined in Pt 3, Ch 1,6 of the Rules for Ships

D = depth of ship, as defined in Pt 3, Ch 1,6 of the Rules for Ships


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kL, k = higher tensile steel factor, see Pt 3, Ch 2,1 of the Rules for Ships

SWBM = still water bending moment

Mw(hog) = Design hogging vertical wave bending moment as defined in Pt 4, Ch 8,16.6 of the Rules for Ships. Also see Pt 4, Ch 8,3.2.1 and 3.2.2.

Mw(sag) = Design sagging vertical wave bending moment as defined in Pt 4, Ch 8,16.6 of the Rules for Ships. Also see Pt 4, Ch 8,3.2.1 and 3.2.2.

Qw+ = Design positive vertical wave shear force as defined in Pt 4, Ch 8,16.7 of the Rules for Ships.

Qw- = Design negative vertical wave shear force as defined in Pt 4, Ch 8,16.7 of the Rules for Ships.

MWC1, MWC2 = Rule design vertical wave bending moment, as defined in Pt 4, Ch 8,15.3.1 of the Rules for Ships

MHC1, MHC2 = Rule design horizontal wave bending moment, as defined in Pt 4, Ch 8,15.3.2 of the Rules for Ships

MWTC1, MWTC2 = Rule design hydrodynamic torque, as defined in Pt 4, Ch 8,15.3.3 of the Rules for Ships

MSTC = Rule design static cargo torque, as defined in Pt 4, Ch 8,15.3.4 of the Rules for Ships

𝑓fH, 𝑓fS = Non-linear correction factors for determining hogging wave bending moment, Mw(hog), and sagging wave bending moment, Mw(sag). See Pt 4, Ch 8,3.2.2 of the Rules for Ships.

LPP = length between perpendiculars

LCG = longitudinal centre of gravity

TSC = scantling draught

g = acceleration due to gravity

ρ = density of sea-water

h = local head for pressure evaluation

σo = specified minimum yield stress of material

σu = ultimate buckling capability of a panel of plating

λ = buckling factor of safety

σe = von Mises or equivalent stress

= �σex2 + σey2 − σexσey + 3τexy2

σex = direct stress in element x direction

σey = direct stress in element y direction


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σx = direct stress in the global longitudinal direction

σy = direct stress measured normal to the global longitudinal direction

τ = shear stress

τexy = shear stress in element x-y plane

t = thickness of plating

tc = thickness deduction for corrosion.

2.2. Consistent units are to be used throughout the analysis.

2.3. Units used in all Rule equations are to be as defined in the Rules for Ships.

Section 3: Direct calculation procedures report

3.1. A report is to be submitted to Lloyd’s Register for the approval of the primary structure of the ship and is to contain:

• list of plans used, including dates and versions;

• detailed description of structural modelling, including all modelling assumptions;

• plots to demonstrate correct structural modelling and assigned properties;

• details of material properties used;

• details of displacement boundary conditions;

• details of all still water and dynamic loading conditions reviewed with calculated shear force (SF) and bending moment (BM) distributions;

• details of the calculations for the waterlines used for the dynamic loading conditions;

• details of the acceleration factors for each loading condition;

• details of applied loadings and confirmation that individual and total applied loads are correct;

• details of boundary support forces and moments;

• plots and results that demonstrate the correct behaviour of the structural model in response to the applied loads;

• summaries and plots of global and local deflections;

• summaries and sufficient plots of von Mises, directional and shear stresses to demonstrate that the design criteria are not exceeded in any member;

• plate buckling analysis and results;


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• tabulated results showing compliance, or otherwise, with the design criteria; and

• proposed amendments to structure where necessary, including revised assessment of stresses and buckling properties.

Part A, Chapter 1 Primary Structure of Container Ship, September 2016

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PART A:

Global Model of Complete Ship

Chapter 1:

Analysis of Global Loads Section 1: Application

Section 2: Objectives

Section 3: Structural modelling

Section 4: Loading conditions

Section 5: Boundary conditions

Section 6: Acceptance criteria


1.1. For the application of PART A, see INTRODUCTION, 1.8.


2.1. The objectives of PART A are

a) To ensure that the global hull stress response with particular reference to its torsional capability complies with Pt 4, Ch 8 of the Rules for Ships. b) To provide boundary conditions for the fine mesh models required by PART B for the investigation of the detailed stress response of the following important structural details:

• Hatch corner radii at the connection of the container hold area with the engine room and deckhouse structure, if applicable.

• Hatch corner radii at the connection of the upper deck and hatch side coamings with the transverse structure of watertight bulkheads and open transverse bulkheads.

• Scarphing and integration details of the hatch side coamings with the superstructure and engine room construction

• Hatch corner arrangements at fore-end of the ship.

c) To provide boundary conditions for fine mesh models of unusual structural arrangement.


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3.1. The torsional response of a container ship is governed by the structural arrangements and loading distributions over the complete length of the ship. In particular, the torsional stress levels within the open length of the hull (container hold area) are greatly influenced by the degree of warping constraint provided by the closed engine room and deckhouse structure, if applicable, and the closed forward and after ends of the hull.

3.2. A 3-D shell finite element model of the complete ship length is required. This model should extend over the full breadth and depth of the ship and represent, with reasonable accuracy, the actual geometric shape of the hull. All effective longitudinal material is to be included. Similarly, all transverse primary structures (i.e. watertight bulkheads, open bulkheads (mid-hold support structure), web frames and cross-deck structures) are to be represented in the model.

3.3. The FE model is to be represented using a right-handed Cartesian co-ordinate system with:

• X measured in the longitudinal direction, positive forward;

• Y measured in the transverse direction, positive to port from the centreline; and

• Z measured in the vertical direction, positive upwards from the baseline.

3.4. The size and type of shell elements selected are to provide a satisfactory representation of the deflections and stress distributions within the ship’s structure. In general, the shell element mesh is to follow the primary stiffening arrangement. Hence, it is anticipated that there will be:

• transversely, one element between longitudinal girders;

• longitudinally, one element between double bottom floors; and

• vertically, one element between stringers or decks.

3.5. For ships in which a non-standard spacing of primary members is proposed, it may be necessary to refine this mesh arrangement, in order to achieve satisfactory element aspect ratios.

3.6. The ship’s superstructure or deckhouse is to be included in the model. This is to be represented using shell elements with a mesh arrangement similar to that used for the hull in way, and which adequately represent the structural arrangement of the deckhouse. However, for deckhouse tiers higher than the second deck above the level of the hatch coamings, a coarser mesh idealisation may be used.

3.7. The proposed scantlings, excluding Owner’s extras and any additional thicknesses fitted to comply with the optional ShipRight Enhanced Scantlings descriptive note, ES, are to be incorporated in the model. All primary structure is to be represented by membrane shell elements. This includes the deck plating, bottom and side shell plating, longitudinal girders, longitudinal and transverse bulkhead plating, transverse floors, side web plating, stringer plates, etc.

3.8. Secondary stiffening members may be modelled using line elements, grouped at plate boundaries, positioned in the plane of the plating having an axial property. Where appropriate, a single line element may represent more than one secondary stiffener. The line elements are to have a cross-sectional area representing the stiffener area.

3.9. Face plate and plate panel stiffeners of primary members may be represented by line elements having an axial property.


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3.10. Figs. 1.3.1 to 1.3.5 indicate acceptable mesh arrangements for the various structural components of a typical girderless container ship.

3.11. The modelling, load cases and boundary conditions of PART A are based on the assumption of a full-breadth model.

3.12. If the designer does not have sufficient resources to undertake a full-breadth FE analysis, then a half-breadth ship model, using asymmetric loading techniques, is acceptable.


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Fig.

1.3

.1

3-D

fini

te e

lem

ent m

odel

of c

ompl

ete

cont

aine

r sh

ip

Fig.

1.3

.2

3-D

fini

te e

lem

ent m

odel

sho

win

g th

e po

rt s

ide

of th

e sh

ip


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Fig. 1.3.3

Typical FE model of a transverse web frame

Fig. 1.3.4

Typical FE model of an open bulkhead frame


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Fig. 1.3.5

Typical FE model of a watertight or closed bulkhead frame


4.1. A number of standard load cases are to be considered. The purpose of these load cases is to ensure that the longitudinal strength of the hull structure complies with the loading combinations specified in Pt 4, Ch 8 of the Rules for Ships.

4.2. Where required by Pt 4, Ch 8,14.1.2 of the Rules for Ships, non-linear ship motion analysis is to be used to calculate the vertical, horizontal and torsional loads in oblique sea conditions. These vertical, horizontal and torsional loads obtained are to be used for the analysis in PART A and PART B. Guidance for the application of the direct calculated loads is described in Appendix B.

4.3. The sign conventions adopted for the analysis in PART A and PART B are shown in Fig. 1.4.1. Load cases representing the following load components are required to be analysed for the construction of the combined load cases:

4.3.1. Hogging still water bending moment A special load case is to be prepared which fulfils the following criteria:

• Ship to be upright at or near to the scantling draught.

• All bays are to be filled with containers.

• Fuel oil deep tanks constructed in transverse bulkhead structures or fuel oil deep tanks constructed in container cargo hold, where fitted, are to be filled.


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• A condition which results in the still water bending moment distribution applied to the model being approximately the same as the assigned, or specified, permissible hogging still water bending moment distribution. The maximum permissible still water bending moment within 0.4L amidships is to be achieved.

• Incremental vertical forces may be applied to the side shell of the FE model for adjusting the bending moment to meet the required distribution along the ship length. Alternatively, the stresses may be adjusted using the method described in 6.4.

4.3.2. Sagging still water bending moment A special load case is to be prepared which fulfils the following criteria:

• Ship to be upright at light draught which results in a maximum sagging or minimum hogging still water bending moment.

• Fuel oil deep tanks constructed in transverse bulkhead structures or fuel oil deep tanks constructed in container cargo hold, where fitted, are to be filled.

• All bays are to be filled with containers.

• A condition which results in the still water bending moment distribution applied to the model being approximately the same as the assigned, or specified, permissible sagging or minimum hogging still water bending moment distribution. The maximum permissible sagging or minimum hogging still water bending moment within 0.4L amidships is to be achieved.

• Incremental vertical forces may be applied to the side shell of the FE model for adjusting the bending moment to meet the required distribution along the ship length. Alternatively, the stresses may be adjusted using the method described in 6.4.

4.3.3. Head sea (Hog) This load case is intended to represent the design hogging vertical bending condition. This is to comprise the following:

a) The hogging still water load case as specified in 4.3.1.

b) A distribution of forces or pressures which induce the hogging design vertical wave bending moment, Mw(hog) as defined in 2.1 of INTRODUCTION, along the model length. The required wave bending moment may be generated by use of a hogging wave with the following characteristics:

• a wavelength equal to LPP;

• the wave crest amidships;

• a sinusoidal wave profile; and

• a height sufficient to induce the required hogging design vertical wave bending moment (VWBM) amidships.

The wave height required to induce the required bending moment will need to be derived by trial and error using a suitable still water loads program. The ship is to be balanced on the wave and the resulting draft, trim and wave parameters are to be used for determination of the external pressure distribution. The wave bending moment achieved in the model using this technique will only be correct at the midship location. Hence, it will be necessary to adjust the vertical bending to meet the required distribution along the ship length. This may be achieved by applying incremental vertical forces to the side shell of the FE model. Alternately, as indicated in 6.4, the longitudinal stress results at each frame location may be


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factored prior to comparing with the acceptance criteria. Alternative methods of generating the wave bending moment distribution will be considered.

4.3.4. Head sea (Sag) This load case is intended to represent the design sagging vertical bending condition. This is to comprise the following:

a) The sagging (or minimum hogging) still water load case as specified in 4.3.2.

b) A distribution of forces or pressures which induce the sagging design vertical wave bending moment, Mw(sag) as defined in 2.1 of INTRODUCTION, along the model length. The required wave bending moment may be generated by use of a sagging wave with the following characteristics:

• a wavelength equal to LPP;

• the wave trough amidships;

• a sinusoidal wave profile; and

• a height sufficient to induce the required sagging design vertical wave bending moment (VWBM) amidships.

The wave height required to induce the required bending moment will need to be derived by a trial and error procedure described in 4.3.3.

4.3.5. Head sea vertical wave bending moment (Mw(hog)) The ship is subjected only to wave pressure loads which generate the hogging design vertical wave bending moment, Mw(hog) as defined in 2.1 of INTRODUCTION, along the model length. This load case may be constructed by subtracting the still water load case (4.3.1) from the head sea (hog) load case (4.3.3). This load case is used for PART B’s analysis only.

4.3.6. Head sea vertical wave bending moment (Mw(sag)) The ship is subjected only to wave pressure loads which generate the sagging design vertical wave bending moment, Mw(sag) as defined in 2.1 of INTRODUCTION, along the model length. This load case may be constructed by subtracting the still water load case (4.3.2) from the head sea (sag) load case (4.3.4). This load case is used for PART B’s analysis only.

4.3.7. Oblique sea vertical wave bending moments (MVWi) The vertical wave bending moment load cases specified in Appendix C are required. The ship is subjected only to the vertical wave bending moments which generate the required vertical wave bending distributions.

4.3.8. Oblique sea hydrodynamic torques (MTWi) The hydrodynamic torque load cases specified in Appendix C are required. The ship is subjected to pure torsional moments which generate the required hydrodynamic torque distributions.

4.3.9. Cargo torque (MSTC) The ship is subjected to pure torsional moments which generate the Rule cargo torque distribution given in Pt 4, Ch 8,15.3.4 of the Rules for Ships, or the specified cargo torque, if this is larger.

4.3.10. Oblique sea horizontal wave bending moments (MHWi) The horizontal wave bending moment load cases as specified in Appendix C are required. The ship is subjected to pure bending moments which generate the required horizontal bending moment distributions.


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4.3.11. Longitudinal (surge) acceleration The following Inertia loads due to longitudinal acceleration are to be considered:

• Containers: Longitudinal component of container loads, arising from the effect of ship motions, acting on the transverse bulkheads and cross deck structure. See PART C, Ch 2, for definition of this load component.

• Fuel Oil (or other liquids): Longitudinal component of fuel oil (or other liquid) loads, arising from the effect of ship motions, acting on the transverse bulkheads. If the ship carries fuel oil (or other liquids) in deep tanks constructed in the transverse bulkhead structures or deep tanks within the container cargo holds then these additional load components are required to be included in the analysis of these structures. Similarly, if analysing the arrangements forward and aft of the engine room for a ship which carries fuel oil (or other liquids) in deep tanks constructed within the container cargo holds immediately aft or forward of the engine room, then these additional load components are required to be included in the analysis. Hydrostatic loading is also to be included if this component was omitted from the still water load case of PART A. See PART C, Ch 5 for definition of this load component.

This longitudinal load is required for the assessment of cross deck box and transverse bulkhead structures, see Table 1.6.1, and PART B’s analysis.

4.4. In constructing the load cases referred to in 4.3, the load components given in Table 1.4.1 are to be included. Alternative methods of achieving the load cases described in 4.3 will be considered.

4.5. For a half-breadth model, only the loads applicable to one half of the model are to be applied. These loads are to be derived in the same manner as that required for a full-breadth model.


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NOTES

1. Vertical bending moment – hogging vertical bending moment is positive and produces tensile stresses at the deck.

2. Horizontal bending moment - positive horizontal bending moment produces tensile stresses at starboard side of the ship.

3. Hydrodynamic and cargo torques are to be applied so that the warping stresses on the port side deck in way of the engine room are in compression, see Fig. 1.4.2.

Fig. 1.4.1 The sign conventions adopted for the analysis in PART A and PART


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In phase hydrodynamic torque MTW1

Out of phase hydrodynamic torque MTW6

Fig. 1.4.2 Application of incremental torsional moments to generate hydrodynamic torque distributions

NOTE: The in phase and out of phase hydrodynamic torque distributions, 𝑀TW1and𝑀TW6, given in Appendix C, are the same distributions as 𝑀WTC1and 𝑀WTC2 in Pt 4, Ch 8,15.3.3 of the Rules for Ships.


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Table 1.4.1 Summary of load components for the full ship FE model

Load case Load component Remarks

Hogging still water See 4.3.1 Sagging still water See 4.3.2 Head sea (Hog) See 4.3.3 Head sea (Sag) See 4.3.4

Steelweight

As generated from the modelled hull structure, suitably factored to achieve the specified steelweight, including the position of the LCG. In this respect, it may be useful to divide the model longitudinally into a number of material zones, each of which can have a separate factored value for the steel density.

Machinery and outfit All major items to be applied as point loads or pressure loads at their correct locations. Minor or unknown items may be included in the steelweight.

Containers above deck (on hatches)

Vertical loads to be applied to the hatch coamings of cross-deck structure in way of the stack corners.

Containers in holds and above deck in open hatch (hatch coverless) ships

Vertical loads to be applied to longitudinal structure at the stack base.

Buoyancy loads

To be applied as pressure loads, ρgh, on wetted shell elements, where h is the distance of the element centroid below the still waterline or wave profile as appropriate.

Additional forces or pressures

As necessary to achieve the required still water and wave bending moment distributions.

Ballast and fuel oil To be applied as pressure loads or nodal forces on tank boundaries, based on the actual liquid head. Any over-pressurisation of the tank is to be omitted.

Head sea vertical wave bending moment (Mw(hog)) See 4.3.5

Hogging design vertical wave bending moment distribution, as defined in 2.1 of INTRODUCTION.

Combined load case as follows: Head sea (Hog) – Hogging still water

Head sea vertical wave bending moment (Mw(sag)) See 4.3.6

Sagging design vertical wave bending moment distribution, as defined in 2.1 of INTRODUCTION.

Combined load case as follows: Head sea (Sag) – Sagging or minimum hogging still water

Oblique sea vertical wave bending moment (MVWi) See 4.3.7

Vertical wave bending moment, MVWi, as specified in Appendix C

Incremental vertical forces are to be applied to the side shell (port and starboard) at each frame position to generate the required vertical wave bending moment distribution. No other load components are to be included.

Oblique sea hydrodynamic torque (MTWi) See 4.3.8

Hydrodynamic torque distribution, MTWi, as specified in Appendix C

Incremental torsional moments are to be applied along the length of the ship as forces acting in the plane of the side shell. When integrated along the ship length, the incremental torsional moments are to generate the Rule hydrodynamic torque distribution. No other load components are to be included.

Cargo torque (MSTC) See 4.3.9

Cargo torque distribution, MSTC, as given in Pt 4, Ch 8,15.3.4 of the Rules for Ships

Incremental torsional moments are to be applied along the length of the ship as forces acting in the plane of the side shell. When integrated along the ship length, the incremental torsional moments are to generate the Rule cargo torque distribution. No other load components are to be included.

Oblique sea horizontal wave bending moment (MHWi) See 4.3.10

Horizontal wave bending moment distribution, MHWi, as specified in Appendix C

Incremental longitudinal forces are to be applied to the side shell port and starboard at the bulkhead positions to generate a moment couple at each bulkhead. When integrated along the ship length, the incremental moment couples are to generate the Rule horizontal wave bending moment distribution. No other load components are to be included.


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4.6. The following load cases are to be compared with the assessment criteria specified in Section 6:

• Head sea load cases (see Table 1.4.2);

• Oblique sea load cases (see Table 1.4.3). Alternatively, the stress combinations given in Appendix D may be used to obtain the maximum and minimum longitudinal direct stresses if the hydrodynamic loads specified in Appendix C are applied. However, if non-linear ship motion analysis is used to determine the hydrodynamic loads, see 4.2, the load combinations given in Table 1.4.3 must be used.

Table 1.4.2 Load combinations for head sea condition

Load case Wave direction Wave Still water load case

(see Note 4)

Longitudinal Acceleration, see Note 1 (Containers, see Note 2 and/or FO, see Note 3)

Still water hogging condition

H1a Head Sea 𝑀w(ℎ𝑜𝑜) Hog 1 (see Note 5) H1b (see Note 6) Head Sea 𝑀w(𝑠𝑠𝑜) Hog 1 (see Note 5) H2a Head Sea 𝑀w(ℎ𝑜𝑜) Hog -1 (see Note 5) H2b (see Note 6) Head Sea 𝑀w(𝑠𝑠𝑜) Hog -1 (see Note 5) Still water sagging condition

H3a Head Sea 𝑀w(𝑠𝑠𝑜) Sag 1 (see Note 5) H3b (see Note 6) Head Sea 𝑀w(ℎ𝑜𝑜) Sag 1 (see Note 5) H4a Head Sea 𝑀w(𝑠𝑠𝑜) Sag -1 (see Note 5) H4b (see Note 6) Head Sea 𝑀w(ℎ𝑜𝑜) Sag -1 (see Note 5)

Symbols

Still water (Hog) Still water load case with required hogging permissible still water bending moment as described in 4.3.1.

Still water (Sag) Still water load case with required sagging or minimum hogging permissible still water bending moment as described in 4.3.2.

𝑀w(hog) Head Sea hogging vertical wave bending moment (Mw(hog)) load case as described in 4.3.5. Note that the hogging vertical bending moment is to be in accordance with that specified in 2.1 of INTRODUCTION.

𝑀w(sag) Head Sea sagging vertical wave bending moment (Mw(sag)) load case as described in 4.3.6. Note that the sagging vertical bending moment is to be in accordance with that specified in 2.1 of INTRODUCTION.

NOTES 1. Longitudinal acceleration load component is required to be applied in the assessment of transverse bulkhead and cross deck

structures, see Table 1.6.1, and the analysis in PART B. 2. Containers - longitudinal component of container loads, arising from the effect of ship motions, acting on the transverse

bulkheads and cross deck structure. See 4.1 and PART C, Ch 2, for definition of this load component. 3. FO - longitudinal component of fuel oil (or other liquid) loads, arising from the effect of ship motions, acting on the transverse

bulkheads. See 4.1 and PART C, Ch 5, for definition of this load component. 4. Hogging and sagging (or minimum hogging) still water load cases as specified in 4.3.1 and 4.3.2 are to be considered. 5. Inertia force due to longitudinal acceleration of containers and/or fuel oil, see 4.3.11.

1: application of head sea positive pitch acceleration case MC1 (HS_1) -1: application of head sea negative pitch acceleration case MC1 (HS_2)

6. This case is only required for PART B’s analysis.


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Table 1.4.3 Load combinations for oblique sea condition

Load case Wave direction

Load Combination (at step i)

ID

Wave Static

𝑀VWi 𝑀HWi 𝑀TWi Container and/or FO

(see Notes 6 & 7)

Still water load case

(see Note 4)

𝑀STC (see Note 5)

Still water hogging OS1

Starboard

OS1i 1 1 1 1 Hog 1 OS2 OS2i 1 1 1 1 Hog -1 OS3 OS3i 1 1 1 -1 Hog 1 OS4 OS4i 1 1 1 -1 Hog -1 OP1

Port

OP1i 1 -1 -1 1 Hog 1 OP2 OP2i 1 -1 -1 1 Hog -1 OP3 OP3i 1 -1 -1 -1 Hog 1 OP4 OP4i 1 -1 -1 -1 Hog -1

Still water sagging OS5

Starboard

OS5i 1 1 1 1 Sag 1 OS6 OS6i 1 1 1 1 Sag -1 OS7 OS7i 1 1 1 -1 Sag 1 OS8 OS8i 1 1 1 -1 Sag -1 OP5

Port

OP5i 1 -1 -1 1 Sag 1 OP6 OP6i 1 -1 -1 1 Sag -1 OP7 OP7i 1 -1 -1 -1 Sag 1 OP8 OP8i 1 -1 -1 -1 Sag -1

NOTES 1. The maximum and minimum direct (tangential) stresses over a complete wave cycle (i.e. for all steps i) are obtained as

follows for comparison against the acceptance criteria: σ(OSna) = Max(σ(OSni)) σ(OSnb) = Min(σ(OSni)) σ(OPna) = Max(σ(OPni)) σ(OPnb) = Min(σ(OPni)) where, 𝑛 = 1, 2, 3, 4, 5, 6, 7 and 8

2. The element von Mises stress is to be calculated individually at each step using the corresponding direct and shear stresses at the same step. The maximum von Mises stresses over a complete wave cycle (i.e. for all steps i) are obtained as follows for comparison against the acceptance criteria: σvm(OSn) = Max�σvm(OSni)� σvm(OPn) = Max(σvm(OPni)) where, 𝑛 = 1, 2, 3, 4, 5, 6, 7 and 8

3. The buckling factor of safety is to be calculated individually at each step using the corresponding direct and shear stresses at the same step. The minimum buckling factor of safety over a complete wave cycle (i.e. for all steps i) are to be less than the required criteria: λmin(OSn) = Min(λ(OSni)) λmin(OPn) = Min(λ(OPni)) where, 𝑛 = 1, 2, 3, 4, 5, 6, 7 and 8

4. Hogging and sagging (or minimum hogging) still water load cases as specified in 4.3.1 and 4.3.2 are to be considered. The stress of each still water load case is to be combined with the stresses due to cargo torque and wave loads (including longitudinal acceleration inertia load where required, see Note 6 for assessing against the acceptance criteria).

5. Cargo torque load case, see 4.3.9.

6. Longitudinal acceleration load component is required to be applied for the assessment of transverse bulkhead and cross deck structures, see Table 1.6.1, and PART B’s analysis.

7. Inertial force due to longitudinal acceleration of containers and/or fuel oil, see 4.3.11. • 1 indicates application of oblique sea positive pitch acceleration case MC3 (OS1_1) • -1 indicates application of oblique sea negative pitch acceleration case MC3 (OS1_2) For containers, see PART C, Ch 2, for definition of this load component. For FO, see PART C, Ch 5, for definition of this load component.


22


5.1. The load cases specified in 4.3 require different boundary conditions as given in Table 1.5.1. These boundary conditions are illustrated in Fig. 1.5.1.

5.2. The boundary conditions specified in Table 1.5.2 combined with those in Table 1.5.1 are appropriate for a half-breadth model

5.3. The boundary conditions described in this section are preferred. However, alternative equivalent boundary conditions may be used.

5.4. In Table 1.5.1, ‘open length’ refers to the container hold area of the ship which lies forward of the ‘closed’ engine room section.

Table 1.5.1 Boundary conditions for a full-breadth model

Load case See Paragraph Boundary conditions

Hogging still water Sagging still water Head sea (Hog) Head sea (Sag) Oblique sea vertical wave bending moments

4.3.1 4.3.2

4.3.3 4.3.4

4.3.7

(a) The model is to be free of imposed constraints, except for those necessary to prevent rigid body motion. Rigid body motions may be prevented by the use of free-body constraints (e.g. the Inertia Relief facility in Nastran terminology).

(b) Alternatively, model may be constrained as follows: At the F.P. on the centreline: δy = δz = 0 At the A.P. on the centreline: δx = δy = δz = 0 At the deck on the centreline at the AP: δy = 0

(c) See Notes 1 and 3.

Hydrodynamic torques Cargo torque

4.3.8

4.3.9

(a) At a bulkhead near to mid-length of the open length: • vertical constraint (δz = 0) at the side shell at mid-depth, port and

starboard • longitudinal constraint (δx = 0) at the keel on the centreline • transverse constraint (δy = 0) at the keel on the centreline.

(b) At the aft end of the keel or transom, where appropriate, and at the forward end of the keel on the centreline: • grounded vertical (Z) springs, see Note 2.

(c) At the deck near the F.P. and A.P. on the centreline: • grounded transverse (Y) springs, see Note 2.

(d) See Note 1.

Horizontal wave bending moments 4.3.10

(a) At a bulkhead near to mid-length of the open length: • vertical constraint (δz = 0) at the keel on the centreline • longitudinal constraint (δx = 0) at the deck edge, port and starboard • transverse constraint (δy = 0) at the deck and keel on the centreline.

(b) At the aft end of the keel or transom, where appropriate, and at the forward end of the keel on the centreline: • grounded vertical (Z) springs, see Note 2.

(c) See Note 1.

NOTES 1. Care is to be taken to ensure that, within practicable limits, there is no net imbalance of load or moment in any of the six

degrees of freedom. 2. Spring stiffness is to be small, equivalent to 1 kgf/m. The resultant load in the springs is to be checked to ensure these loads

are not significant. 3. Care is to be taken to ensure that the FE model is not over constrained.


23

Table 1.5.2 Additional boundary conditions for a half-breadth model

Load case See

Paragraph Boundary conditions

Still water

Head sea Oblique sea vertical wave bending moments

4.3.1 and 4.3.2

4.3.3 and 4.3.4

4.3.7

Centreline plane: Symmetry constraints, i.e. δy = θx = θz = 0

Hydrodynamic torque

Cargo torque

4.3.8

4.3.9 Centreline plane: Anti-symmetry constraints, i.e. δx = δz = θy = 0

Horizontal wave bending moment 4.3.10 Centreline plane: Anti-symmetry constraints, i.e. δx = δz = θy = 0

NOTE

These boundary conditions are additional to those given in Table 1.5.1 and take precedence over the requirements of Table 1.5.1 when necessary.


24

(1) Still water, head sea and oblique sea cases

Fig. 1.5.1 Boundary conditions for the global ship FE model: locations of free body constraints


6.1. In accordance with the procedures set out in Pt 4, Ch 8 of the Rules for Ships, the longitudinal direct stress values along the complete ship length are not to be greater than the values indicated in Table 1.6.1 at the following positions:

a) the inboard edge of the strength deck;

b) the point on the bilge where the combined stress is greatest; and

c) the top of continuous hatch coaming.


25

6.2. At the hatch side coaming and upper deck intersections, stress concentrations arise from the inter-connection of the superstructure/closed engine room section and the cross-deck strips. These areas are to be subject to the follow-up analyses indicated in PART B.

6.3. The stresses in the transverse bulkhead and cross deck structures are not to be greater than the values indicated in Table 1.6.1

6.4. The distribution of actual SWBM, Mw(hog) and Mw(sag), obtained over the length of the model are to be compared with the required bending moment distributions. The longitudinal stress value derived from the FE model for each longitudinal location is to be factored by the ratio of the locally required bending moment to the locally achieved moment prior to combining with stresses from other load cases, for comparison with the acceptance criteria specified in Table 1.6.1.

6.5. Figures showing the resulting longitudinal stress distributions are to be produced. An example stress distribution plot is shown in Fig.1.6.1.

6.6. Structures in way of high stress gradients are to be subject to further investigation.

6.7. The buckling strength of the longitudinal and transverse members as indicated in Table 1.6.1 are to be investigated. A minimum factor of safety as given in Table 1.6.1 is to be achieved.

6.8. The buckling capability of plate panels is to be assessed using a plate thickness reduced by the standard thickness deduction values given in PART C, Ch 1, Table 1.6.2.

6.9. The buckling factors of safety of plate panels are to be derived using the procedure that taking into account all relevant direct and shear stress components, such as Lloyd’s Register ShipRight Software’s buckling module. The average stress acting within a single plate panel may be used to assess the buckling capability.

6.10. Where the calculated elastic critical buckling stress exceeds 50% of the specified minimum yield stress, then the buckling stress is to be adjusted for the effects of plasticity using the Johnson-Ostenfeld correction formula, given below:

σcr = σ0 �1 −σ0

4σc�

where

σo = specified minimum yield stress of material

σcr = critical buckling stress corrected for plasticity effects

σc = elastic critical buckling stress.

6.11. In calculating the buckling factors of safety, the edge restraint factor, c, defined in Pt 3, Ch 4,7 of the Rules for Ships, may be taken into account in calculating the critical buckling stress of wide panels subjected to compressive loading on the long edge of the panel. The edge restraint factor, c, may not be used in the calculation of critical buckling stress for compression applied on the short edge.

6.12. Buckling assessment based on the first principle direct calculation method may be specially considered.


26

Table 1.6.1 Maximum permissible membrane stresses

Maximum permissible membrane stresses (N/mm2)

See Note 1 Minimum Buckling Factor of Safety

Load case Structural item Von-Mises stress Direct stress (See Note 2)

Shear stress

Head sea (Hog) See 4.3.3 Head sea (Sag) See 4.3.4

Longitudinal hatch coaming Upper deck plating

- 0,745σL - -

Bottom shell Turn of bilge Inner bottom

- 0,92σL - 1,1

See Note 5

Cross deck box (See Note 3) 0,75σ0 - - 1,1

Longitudinal structural members elsewhere - 0,745σL -

1,1 See Note 5

Oblique sea See 6.4

Longitudinal hatch coaming - 0,745σL - -

Upper deck plating - 0,67σL - -

Bottom shell Turn of bilge Inner bottom

- 0,845σL - 1,1

Cross deck box (See Note 3) 0,75σ0 - - 1,1

Transverse bulkhead structure (See Note 3) 0,75σ0 - 0,35σ0 1,1

Longitudinal structural members elsewhere - 0,67σL - -

where σL=235/kL N/mm2

NOTES 1. See also 6.4. 2. The magnitude of the direct stress is to be less than the permissible value. 3. For the assessment of cross deck box and transverse bulkhead structure, inertial loads due to longitudinal acceleration are

to be considered, see 4.3.11. 4. See 4.6 for load cases for assessment 5. The buckling strength of the longitudinal members, outside the extent covered or assessed by PART C, are to be

investigated.


27

Fig.

1.6

.1

Long

itud

inal

dis

trib

utio

n of

str

ess

in a

hat

ch s

ide

coam

ing

(For

illu

stra

tive

pur

pose

s)

Part B, Chapter 1 Primary Structure of Container Ship, September 2016

28

PART B:

Verification of Structural Components and Details

Chapter 1:

Analysis of Global Loads on Local Details Section 1: Application



Section 4: Loading and boundary conditions



1.1. For the application of PART B, see INTRODUCTION, 1.8.


2.1. The objective of PART B is to ensure that the structural responses of the following structural details are within acceptable limits:

a) Hatch corner radii at the connection of the container hold area with the engine room and deckhouse structure, if applicable (see 3.4 and 3.5).

b) Hatch corner radii at the connection of the lower decks, upper deck and hatch side coamings with the transverse structure of the watertight bulkheads and open transverse bulkheads (see 3.3).

c) For container ships with fuel oil deep tanks located inboard of the inner skin and above the double bottom: the arrangements of the connection of the crown of the fuel oil deep tanks to the side structure (see 3.7).

d) Scarphing and integration details of the hatch side coamings with the superstructure and engine room construction (see 3.4 and 3.5).

e) Connection of the forward open length with the forward end of the ship (see 3.6).

f) Structure in way of high stress gradients or areas exceeding the stress criteria specified in PART A.

g) Any other unusual feature.


29


3.1. The structural details specified in 2.1 are to be represented by fine mesh in the PART A global model. Alternatively, separate detailed fine mesh models covering the structural details are to be prepared and loaded with enforced displacements obtained from the full ship global analysis.

3.2. Fine mesh models will be required for the areas detailed below. Typical models are indicated in Figs. 1.3.1 and 1.3.2.

3.3. Midship cross-deck strip and hatch corner detail

3.3.1. A model of the midship cross-deck strip at approximately the position of maximum warping displacement. A typical model is shown in Fig. 1.3.1 and modelling guidance is given in 3.8.

3.3.2. If the scantlings and/or structural arrangement of the hatch corner cross-deck structure and the hatch coaming arrangement differ between the watertight bulkheads and the open bulkheads, then models of both bulkhead arrangements will be required. Similarly, if there are different bulkhead design arrangements, then a model is to be made of each design variant.

3.3.3. For container ships with fuel oil deep tanks arranged between the inner skin and above the double bottom, a fine mesh model of the connection of the cross-deck arrangements to the side structure will be required in way of the hatch coaming and upper deck levels and also at the tank crown level. This model is additional to that described in 3.3.1 and 3.3.2.

3.4. Connection of the forward open length with the forward end of the engine room

3.4.1. A model of the integration of the open length with the forward end of the engine room encompassing the hatch way radius at upper deck level, the hatch corner radius at hatch coaming top level and, if applicable, the integration of the hatch side coamings with the superstructure side. A typical model is shown in Fig. 1.3.2 and modelling guidance is given in 3.8.

3.4.2. The model description has been framed on the basis that the longitudinal hatch side coamings are integrated with the superstructure. If, however, a separate deckhouse is proposed with discontinuous hatch side coamings, then the model should permit examination, using a suitable fine mesh, of the discontinuities introduced by such an arrangement.

3.5. Connection of the aft open length with the aft end of the engine room

3.5.1. A model of the integration of the aft open length with the engine room/superstructure arrangement, similar to that described in 3.4, is also to be made.

3.5.2. This requirement will be waived if the scantlings and arrangements of the aft integration are the same as the forward integration and the stress levels, obtained from PART A, of the full ship global analyses are lower.

3.6. Connection of the forward open length with the forward end of the ship

3.6.1. A model of the integration of the forward open length with the fore-ship is also to be made.

3.6.2. The extent and position of this model is to be decided on review of the PART A results. Agreement of the local plan approval office to the modelling proposals should be obtained prior to commencing the analysis. General modelling guidance is given in 3.8.

3.7. Connection of open lengths with fuel oil deep tanks constructed within container hold


30

3.7.1. In cases where fuel oil deep tanks are arranged inboard of the inner skin and above the inner bottom and have length exceeding four times the width of the cross-deck strip specified in Pt 4, Ch 8,4.3.1 of the Rules for Ships, analysis of the integration with the adjacent hull structure is to be carried out.

3.7.2. The models are to be as described in 3.4, 3.5, 3.6 and 3.8.

3.7.3. If the crown of the fuel oil tank is not in line with the coaming top or upper deck, the vertical extent of the model is to be increased so that the model extends from one stringer level below the crown of the tank to the coaming top. The corner arrangements in adjacent container holds in line with the crown of the tank are to be modelled in fine mesh and results are to comply with the requirements of Sec 5.

3.8. Modelling Requirements

3.8.1. These models are to include a fine mesh in way of the hatch corner radii at the upper and lower decks and hatch coaming top levels. Similarly, a suitably fine mesh is to be included at the scarphing and integration details of the hatch side coamings with the superstructure and engine room constructions.

3.8.2. The level of refinement is to be such as to enable stress concentrations to be identified. Where finite element analysis programs do not supply nodal stresses, a line element of small (nominal) area is to be incorporated to obtain the peak edge stresses at the following locations:

• along the plate edge of hatch corners at the lower decks, upper deck and hatch coaming,

• along the superstructure to hatch side coaming scarphing brackets.

3.8.3. The extent of these models is to be such that the application of boundary displacements (taken from the global analysis) will not affect the response at the relevant points of the local fine mesh model. In general, it is recommended that the model extends:

• transversely over the half-breadth of the ship,

• longitudinally from the midpoint of one 40 ft container bay to the midpoint of the next 40 ft container bay,

• vertically from the coaming top plate to the deck or stringers below the intersection of the bottom of the cross-deck strip with the longitudinal bulkhead.

3.8.4. In respect of the model described in 3.4 and 3.5, a similar extent should be used, but with the vertical extent encompassing the superstructure deck above the top of any scarphing brackets.

3.8.5. The primary structure and coaming stays are to be represented by shell finite elements having both membrane and bending capability.

3.8.6. The structural geometry, particularly in areas of concern, is to be accurately represented. In this respect, a minimum of 15 elements in a 90 degree arc are to be used to describe the curvature of the hatchway radius plating. However, the element edge dimensions along the free edge of the radius should not be less than the thickness of the plating being represented and also should not be greater than 1.5 times the thickness of the plating being represented. Except where necessary from practical meshing considerations, this level of idealisation is to be maintained over the bracket plating and is to extend into the stringer plating, deck plating and coaming. Mesh transitions should not be arranged close to bracket toes.

3.8.7. All cut-outs (e.g. for ventilation systems, access openings) are to be represented in the model.


31

3.8.8. Secondary stiffening may be represented by line elements, except in way of the ending of primary structure, e.g. longitudinal bulkhead longitudinal stiffener in way of cross-deck box bottom plating.

3.8.9. The extent of models required for 2.1(e), (f) and (g) will be subject to special consideration. However, the modelling philosophy outlined in the preceding paragraphs will generally apply.

Fig.

1.3

.1

Cros

s-de

ck s

trip

– F

ine

mes

h m

odel

sho

win

g co

rner

det

ails


32

Fig.

1.3

.2

Engi

ne r

oom

bul

khea

d fo

rwar

d –

Fine

mes

h m

odel


33

Section 4: Loading and boundary conditions

4.1. The loads specified in PART A, Ch 1,4.3, including inertial loads due to longitudinal acceleration, are to be considered in PART B’s analysis.

4.2. Where separate fine mesh models are used to derive the stress responses for the load cases as defined in 4.1 and PART A, Ch 1,4.3, the models are to be loaded at their boundaries with enforced displacements obtained from the results of the PART A global model, together with local loads within the region of the fine mesh model, where appropriate. The translational enforced displacements are to be adjusted as follows:

a) For the still water cases (see PART A, Ch 1,4.3.1 and 4.3.2) the enforced displacements are to be corrected by the ratio of the required permissible SWBM value to the actual bending moment applied to the global model at the fine mesh model location.

b) For the head sea cases (see PART A, Ch 1,4.3.3 and 4.3.4) and oblique sea cases (see PART A, Ch 1,4.3.7 to 4.3.10) the enforced displacements are to be corrected by the ratio of the required wave bending moment to the actual bending moment applied to the global model at the fine mesh model location.

4.3. Where the structural details are represented by embedded fine meshes in the global model, the stress result for the load cases described in 4.2(a) and 4.2(b) is to be corrected by the ratio of the required wave bending moment to the actual bending moment applied to the global model at the location of the element under consideration.

4.4. If the structural arrangement is symmetrical about the ship’s centreline, then it is only necessary to analyse the structural details on either the port or the starboard side of the ship. The enforced displacements should be taken from locations on the side of the global model where the details are represented by the fine mesh models.

4.5. For the head sea condition, the load combinations given in PART A, Ch 1, Table 1.4.2 are to be considered for PART B’s analysis.

4.6. For the oblique sea condition, the load combinations given in PART A, Ch 1, Table 1.4.3 are to be considered for PART B’s analysis.

4.7. Alternatively the stress combinations given in Appendix D may be used to obtain the maximum and minimum longitudinal direct stresses, such as the tangential stresses in way of hatch corner free edges, if the hydrodynamic loads specified in Appendix C are applied. However, if non-linear ship motion analysis is used to determine the hydrodynamic loads, see PART A, Ch 1,4.2, the load combinations given in PART A, Ch 1, Table 1.4.3 must be used.

4.8. The load case combinations may be obtained by:

a) Extracting the stress results from selected fine mesh elements for each individual load case as defined in 4.1 and PART A, Ch 1,4.3.

b) If separate fine mesh models are used, unadjusted displacement results from PART A load cases described in 4.2(a) and 4.2(b) may be used and the correction applied to the stress result.

c) Use a spreadsheet, or equivalent method, to combine the stress results of all specified load components.


34

d) Von Mises stresses are to be calculated based on the sum of the direct stresses and the sum of the shear stresses from all load components specified.


5.1. The direct (tangential) stresses at the following locations are to comply with the acceptance criteria in Table 1.5.1:

• at the free edge of the hatch corner radii at the upper deck,

• at the free edge of the hatch coaming top,

• at the free edge of scarphing brackets between the superstructure side plating and the top of the hatch coaming,

• at other critical locations within the connection.

5.2. Elsewhere, stress levels are to comply with the acceptance criteria detailed in Table 1.5.2.

5.3. The factors jBOSna, jBOSnb, jBOPna and jBOPnb, where n = 1 to 8, specified in the combination cases in Table 1.5.1 are to be individually determined for each element.

5.4. Separate hatch corner radius plates formed by insert brackets welded to the transverse and longitudinal structures are not recommended. If such brackets are proposed in these locations, acceptance will be subject to special consideration. Similarly, proposals to omit corner radii will be subject to special consideration.

5.5. In respect of the superstructure to coaming top scarphing brackets, it may be necessary for the weld at the toe of the bracket at its connection with the coaming top plate to be ground into a suitable radius and be verified free of surface imperfections. This is in addition to the requirements specified in Note 1 of Table 1.5.1.


35

Table 1.5.1 Acceptance criteria for free edges of hatch corner radii and scarphing brackets

Wave direction Stresses for assessment Allowable Stress, N/mm2

(see Notes 1, 2 and 4)

Head Sea

Peak stresses (see PART A, Ch 1, Table 1.4.2)

|σ(H1a)| |σ(H2a)| |σ(H3a)| |σ(H4a)|

1.5 𝑗 σ0 (Theoretical peak stress,

see Note 3)

Dynamic stress ranges (see Note 6)

𝑗sa|𝑗BH1a σ(H1a) − 𝑗BH2b σ(H2b)| 𝑗sa|𝑗BH2a σ(H2a) − 𝑗BH1b σ(H1b)| 𝑗sa|𝑗BH3a σ(H3a) − 𝑗BH4b σ(H4b)| 𝑗sa|𝑗BH4a σ(H4a) − 𝑗BH3b σ(H3b)|

600 𝑗 𝑗dl 𝑗w (N/mm2) (see Note 1)

Oblique Sea

Peak stresses (see PART A, Ch 1, Table 1.4.3)

|σ(OSna)| |σ(OSnb)| |σ(OPna)| |σ(OPnb)| 𝑛 = 1, 2 ,3, 4, 5, 6, 7 and 8

1.5 𝑗 σ0 (Theoretical peak stress,

see Note 3)

Dynamic stress ranges (see Note 6)

𝑗sa|𝑗BOS1a σ(OS1a) − 𝑗BOS3b σ(OS3b)| 𝑗sa|𝑗BOS3a σ(OS3a) − 𝑗BOS1b σ(OS1b)| 𝑗sa|𝑗BOS2a σ(OS2a) − 𝑗BOS4b σ(OS4b)| 𝑗sa|𝑗BOS4a σ(OS4a) − 𝑗BOS2b σ(OS2b)| 𝑗sa|𝑗BOP1a σ(OP1a)− 𝑗BOP3b σ(OP3b)| 𝑗sa|𝑗BOP3a σ(OP3a) − 𝑗BOP1b σ(OP1b)| 𝑗sa|𝑗BOP2a σ(OP2a)− 𝑗BOP4b σ(OP4b)| 𝑗sa|𝑗BOP4a σ(OP4a) − 𝑗BOP2b σ(OP2b)|

𝑗sa|𝑗BOS1a σ(OS5a) − 𝑗BOS3b σ(OS7b)| 𝑗sa|𝑗BOS3a σ(OS7a) − 𝑗BOS1b σ(OS5b)| 𝑗sa|𝑗BOS2a σ(OS6a) − 𝑗BOS4b σ(OS8b)| 𝑗sa|𝑗BOS4a σ(OS8a) − 𝑗BOS2b σ(OS6b)| 𝑗sa|𝑗BOP1a σ(OP5a)− 𝑗BOP3b σ(OP7b)| 𝑗sa|𝑗BOP3a σ(OP7a) − 𝑗BOP1b σ(OP5b)| 𝑗sa|𝑗BOP2a σ(OP6a)− 𝑗BOP4b σ(OP8b)| 𝑗sa|𝑗BOP4a σ(OP8a) − 𝑗BOP2b σ(OP6b)|

600 𝑗 𝑗dl 𝑗w (N/mm2) (see Note 1)

where

For head sea condition: σ(Hna) and σ(Hnb), where 𝑛 can be 1, 2, 3 or 4, are the stresses obtained from load cases Hna and Hnb. See PART A, Ch 1, Table 1.4.2. 𝑗BHna is to be taken as 1,0 in general. If the value of σ(BHna) is negative (i.e. in compression) then 𝑗BHna may be taken as 0,6. 𝑗BHnb is to be taken as 1,0 in general. If the value of σ(BHnb) is negative (i.e. in compression) then 𝑗BHnb may be taken as 0,6.

For oblique sea condition: σ(OSna), σ(OSnb), σ(OPna) and σ(OPnb), where 𝑛 can be 1 to 8, are defined in PART A, Ch 1, Table 1.4.3. 𝑗BOSna is to be taken as 1,0 in general. For free edges and plating clear of welds, if the value of σ(BOSna) is negative (i.e. in compression) then 𝑗BOSna may be taken as 0,6. 𝑗BOSnb is to be taken as 1,0 in general. For free edges and plating clear of welds, if the value of σ(BOSnb) is negative (i.e. in compression) then 𝑗BOSnb may be taken as 0,6. 𝑗BOPna is to be taken as 1,0 in general. For free edges and plating clear of welds, if the value of σ(BOPna) is negative (i.e. in compression) then 𝑗BOPna may be taken as 0,6. 𝑗BOPnb is to be taken as 1,0 in general. For free edges and plating clear of welds, if the value of σ(BOPnb) is negative (i.e. in compression) then 𝑗BOPnb may be taken as 0,6.


36

where

j =

jsa = jdl =

jw =

σ0 = t =

𝑊t = n =

𝑊uts =

0,9 for upper deck hatchway corner forward and aft of the engine room 0,95 for upper deck hatchway corner forward and aft of cross-deck strips which have a width (dimension in the

longitudinal direction) greater than 6w, where w is the width of cross deck strip specified in Pt 4, Ch 8,4.4.5 of the Rules for Ships

1,0 elsewhere 1,0 Factor reflecting the required design fatigue life = (25/FLY)0,25 where, FLY is specified fatigue life in years but not to be taken less than 25 𝑊t × 𝑊uts for free edges and plating in accordance with Note 1 0,7 𝑊t in way of weld of scarphing bracket to hatch coaming top 0,6 𝑊t in way of weld endings Yield stress of material in N/mm2 Thickness of hatch corner plate Thickness correction = (22/𝑡)𝑛 but not to be taken greater than 1,0 0,1 for free edges of plating 0,25 in way of welds High tensile steel correction factor for free edges and plating: 1,0 for all steel grades having a nominal yield stress of 235 N/mm2 1,0 for all steel grades having a nominal yield stress of 270 N/mm2 1,0 for steel grades A and D for all nominal yield stresses 1,056 for steel grades EH32 and FH32 1,12 for steel grades EH36 and FH36 1,15 for steel grades EH40 and FH40 1,23 for steel grades EH47 1,0 for all steel grades in way of welds

NOTES 1. The allowable stress ranges given in the table apply to:

• The FREE EDGE of hatch corner radius plating which is integral with the deck or hatch coaming top plate. See also 5.1. The free edge is to be free of welding (including butts & seams) and ground smooth for a minimum distance of 500 mm clear of the radius tangent points.

• The FREE EDGE of scarphing brackets between the superstructure side plating and the top of the hatch coaming. The free edge is to be free of welding (including butts & seams) and ground smooth. The weld connection to the hatch coaming top is to be of high quality deep penetration type, with suitable dressing applied to the weld ending and subject to suitable NDE. Ideally such brackets should be integral with the superstructure side plating.

For FREE EDGE that is not ground smooth as indicated above but is cut by machine flame cutting with a controlled procedure or the plate thickness is above 100mm, the allowable stress range is to be reduced by a factor of 0,89.

2. See also 5.5 3. Relevant to the use of linear elastic code only. 4. See also Figure 1.5.1 5. If the stresses are derived from the procedure described in Appendix B, B.4.5. 6. Where a ShipRight FDA Level 3 analysis is carried out and verified sufficient fatigue performance of a structural detail, the

assessment against the dynamic stress range criteria for the structural detail can be waived.


37

Table 1.5.2 Acceptance criteria for primary structure

Structural items

Wave direction

(see Notes 1 and 2)

Allowable stress, N/mm2

Von-Mises stress σvm

Direct

stress σ

Shear stress τ

Deck plating outboard of side coaming, see Fig. 1.5.1

Head sea Peak stress Average stress ̶ σ0

0,75σL ̶

Oblique sea Peak stress Average stress ̶ σ0

0,67σL ̶

Longitudinal hatch coaming top plate

Head sea Oblique sea

Peak stress Average stress ̶ σ0

0,75σL ̶

Longitudinal hatch side coaming plating


Peak stress Average stress ̶ σ0

0,75σL ̶

Superstructure side plating


Peak stresses in scarphing bracket Clear of scarphing bracket

σ0 0,8σ0 ̶ ̶

where

σL =235𝑘L

N/mm2

NOTES

1. See PART A, Ch 1, Table 1.4.2 for head sea load cases. 2. For oblique sea conditions, the following cases are to be assessed:

• Peak and average direct stresses, see PART A, Ch 1, Table 1.4.3 or Appendix B, B.4.5 if the stresses are derived by considering the equivalent design wave(s).

• Maximum von Mises stresses are to be determined by considering the equivalent design wave(s), see 4.6 and Appendix B, B.4.5.


38

Fig.

1.5

.1

Acce

ptan

ce c

rite

ria

for

hatc

h co

rner

s

Part C, Chapter 1 Primary Structure of Container Ship, September 2016

39

PART C:

Verification of Primary Structure

Chapter 1:

Verification of Double Bottom and Transverse Strength Section 1: Application







1.1. PART C is applicable to all container ships for which direct calculations are required, see also INTRODUCTION.

1.2. For ships where the calculation procedures have been performed in accordance with PART A, consideration will be given to using a suitable length of that model (4 bays amidships) with suitable detailed follow-up models.

1.3. For container ships which carry fuel oil in deep tanks constructed in transverse bulkhead structures or in deep tanks constructed in container cargo holds, i.e. fuel tanks located inboard of the inner skin and between adjacent transverse bulkheads, additional requirements are specified in PART C, Ch 4.


2.1. The objective of PART C, Ch 1 is to ensure the structural adequacy of the following primary structure with regard to local load considerations:

• double bottom structure,

• transverse structure,

• side structure.


40

2.2. The global strength of container ships for which the procedures in PART A and PART B have not been carried out is to be in compliance with the relevant sections of the Rules for Ships (e.g. Pt 4, Ch 8) and is to be verified by the application of the appropriate ShipRight programs, contact Lloyd’s Register local office for details.


3.1. A model of four 40 ft container bays (½ hold + 1 hold + ½ hold), located at about amidships, is to be considered. If the ship incorporates a substantial fixed guide system to accommodate 20 ft containers, then the model is to include these structural items.

3.2. A typical FE model arrangement is indicated in Figs. 1.3.1 to 1.3.4. This model is arranged such that the open bulkhead is located at the model mid-length. The alternative arrangement whereby a watertight bulkhead is located at the model mid-length will be accepted, but the requirements of Ch 3,3 should be noted.

3.3. The model is to represent the full depth of the ship and it is recommended that the full breadth be modelled to simplify the analysis of the heeled conditions. It should be noted that Figs. 1.3.1 to 1.3.4 show only the starboard half of the model for clarity.

3.4. Alternatively, a half-breadth model may be used. Symmetry boundary conditions at the ship’s centreline are to be used for the upright cases. The heeled condition can be considered by combining the symmetric and anti-symmetric components into which the heeled condition can be idealised, see Appendix A.

3.5. The FE model is to be represented using a right-handed Cartesian co-ordinate system with:

• X measured in the longitudinal direction, positive forward,

• Y measured in the transverse direction, positive to port from the centreline,

• Z measured in the vertical direction, positive upwards from the baseline.

3.6. The proposed scantlings, excluding owner's extras and any additional thicknesses fitted to comply with the optional ShipRight ES descriptive note, are to be incorporated in the model. All plated areas, e.g. shell, inner skin, girders, horizontal stringers and vertical webs of transverse bulkheads, are to be represented with membrane shell elements. Plate bending properties may be required for regions of the model where element boundaries do not coincide with secondary stiffening in order to eliminate stiffness singularities.

3.7. Secondary stiffening members may be modelled using line elements positioned in the plane of the plating having axial and bending properties. The bar elements are to have:

• a cross-sectional area representing the stiffener area; and

• bending properties representing the combined plating and stiffener criteria.

3.8. Face plates to primary stiffening (e.g. to vertical webs of transverse bulkheads) may be represented by line elements having axial stiffness only. Face plate of transverse bulkhead vertical webs and horizontal stringers are to be modelled as plate elements having bending properties. However, incorporating bending stiffness in line elements may be the optimal method of removing singularities at the free edge of membrane elements.

3.9. The recommended element size is as follows:


41

• 1 element between side and bottom longitudinals,

• 2 or more elements between transverse frames to achieve an aspect ratio close to 1.0,

• 3 elements within the depth of primary stiffening.

3.10. In principle, all openings are to be represented. Normal size access openings in plated webs may be modelled by deleting the appropriate elements.

Fig.

1.3

.1

3-D

fini

te e

lem

ent m

odel

for a

sses

smen

t of t

rans

vers

e an

d do

uble

bot

tom

str

engt

h

(sta

rboa

rd h

alf o

f the

mod

el i

s sh

own

here

for

clar

ity)


42

Fig. 1.3.2 Typical FE model of a transverse web frame

Fig. 1.3.3 Typical FE model of an open bulkhead


43

Fig. 1.3.4 Typical FE model of a watertight or closed bulkhead


4.1. The load cases given in Table 1.4.1 and illustrated in Fig. 1.4.1 are to be considered.

4.2. The load components to be included are:

• static and dynamic inertial loads due to the lightship mass, see 4.5 and 4.6;

• static and dynamic inertial loads due to containers, see 4.5 and 4.6;

• hydrostatic loads due to immersion to the draught specified in Table 1.4.1. The hydrostatic loads are to be applied as pressure loads to the shell envelope, equivalent in the upright condition to ρgh, where h is the distance of the element centroid below the still waterline;

• pressure loads due to a local wave crest or trough, see 4.3; and

• hull girder bending moment as specified in Table 1.4.1.

4.3. The additional pressure head to apply as a consequence of a local wave crest or trough is given in Fig. 1.4.2. This additional pressure is to be applied over the full length of the model.

4.4. For the heeled cases, the loads are to be calculated assuming that the ship is held at the required static heel angle. The transverse load components of containers in holds are to be distributed to suitable locations on the transverse bulkheads. The loads from containers above deck are to be distributed as shear loads to the top of the transverse coaming. The ‘overturning moment’ may be ignored.


44

4.5. For load cases C1, C2a, C2b, C3a and C3b, the inertial force of containers and ship masses, including gravitational effects, are to be calculated based on the following vertical acceleration in m/s2. Positive acceleration generates an upward acting inertia force.

𝑠z = − 𝑓 ⋅ �𝐶ZH ⋅ 𝑠heave − 𝑓ap ⋅ 𝐶ZP ⋅ 𝑠pitch ⋅ 𝑥i� − 𝑜 ⋅ cos (𝐶xG ⋅ ψ)

where 𝑠heave is the vertical acceleration due to heave, in m/s2, given in Pt 3, Ch 14,1.5.1 of the Rules for

Ships 𝑠pitch is the acceleration due to pitch, in rad/s2, for motion case MC1 given in Pt 3, Ch 14,1.5.1 of

the Rules for Ships ψ is the maximum pitch angle, in degrees, for motion case MC1 given in Pt 3, Ch 14,1.5.1 of the

Rules for Ships 𝑥i is the longitudinal distance of the container unit from the longitudinal centre of motion, as

defined in Pt 3, Ch 14,1.5.1 of the Rules for Ships 𝑜 is the acceleration due to gravity equal to 9,81 m/s2

𝑓ap is the hull form coefficient for motion case MC1 given in Pt 3, Ch 14,1.5.1 of the Rules for Ships

𝐶ZH = -0,18 𝐶ZP = 1,00 𝐶xG = -0,85 𝑓 = 1 for load case C3a = -1 for load cases C1, C2a, C2b and C3b

4.6. Each load case may be analysed based on a constant vertical acceleration value. This acceleration can be derived using a distance 𝑥i at the longitudinal centre of gravity of the container stack within the model length where:

• The magnitude of the vertical acceleration is maximum for load case C3a

• The magnitude of the vertical acceleration is minimum for load cases C1, C2a, C2b and C3b

4.7. Inertial load due to vertical acceleration need not be applied to load cases C4, C5, C6 and C7. However, the gravitational effect is to be considered. Longitudinal loads caused by ship longitudinal acceleration is to be applied for load case C6, see Ch 2.

4.8. If the required hull girder bending moment is not achieved by the application of the ship’s loading condition and wave pressure, where required, the FE stresses are to be adjusted as follows:

σx = σx_FE + σx_u ∆BM

σy = σy_FE + σy_u ∆BM

τxy = τxy_FE + τxy_u ∆BM

where

σx, σy and τxy are the adjusted direct stresses and shear stress at the centre of the element

σx_FE, σy_FE and τxy_FE are the FE direct stresses and shear stress at the centre of the element

σx_u, σy_u and τxy_u are the direct stresses and shear stress at the centre of the element due to the unit hull girder bending moment load case.

ΔBM is the difference between the required bending moment, as specified in Table 1.4.1, and resultant bending moment from the FE model at the longitudinal position of the element


45

Values of σx_u, σy_u and τxy_u are to be derived by applying a unit bending moment to the model using the boundary conditions described in Fig. 1.5.2.

4.9. Open hatch (hatch coverless) container ships

4.9.1 For the purpose of this section, containers above the upper deck are to be treated in the same manner as containers below deck within the hold.

4.9.2 Case C2b is not relevant and is to be omitted.

4.9.3 The cell guide support structure above the upper deck is to be additionally considered, with respect to Pt 3, Ch 14 of the Rules for Ships.


46

Table 1.4.1 Standard load cases to be considered

Load case Description (see 4.2) Load case type and boundary conditions to apply

C1

Ship loading condition (ship upright) • Draught equal to the scantling draught, Tsc

• All container bays and hatch covers over the bays are to be filled with 40 ft light containers, see Note 1

• All ballast and fuel oil tanks in way of the cargo hold model are to be empty

Wave pressure • Pressure loads due to a local wave crest, see 4.2 Bending moments • Permissible SWBM (hogging) • Design VWBM (hogging), see Note 3

Symmetric

C2a

Ship loading condition (ship upright), see Note 5 • Draught equal to the scantling draught, Tsc • One 40 ft container bay and hatch covers over the bay are to be empty of

containers • The remaining bays and hatch covers over the bays are to be filled with 40

ft heavy containers to the maximum permitted weight, see Note 2 • All ballast and fuel oil tanks in way of the cargo hold model are to be

empty Wave pressure • Pressure loads due to a local wave crest, see 4.2 Bending moments • Permissible SWBM (hogging) • Design VWBM (hogging), see Note 3

Symmetric

C2b

Ship loading condition (ship upright), see Note 5 As for C2a except as follows: • All hatch covers over the bays are to be filled with 40 ft heavy containers

to the maximum permitted weight, see Note 2 Wave pressure As for C2a Bending moments As for C2a

Symmetric

C3a

Ship loading condition (ship upright) • Ship at light draught, see Note 4 • All container bays and hatch covers over the bays are to be filled with 20 ft

heavy containers to the maximum permitted weight, see Note 2. For containers on hatch cover where Russian Stow Arrangement (see Pt 3, Ch 14,5.4.9 of the Rules for Ships) is adopted, the greater of the stack weights of the Russian Stow Arrangement or combined weight of two 20 ft container stacks is to be used.

• All ballast and fuel oil tanks in way of the cargo hold model are to be empty

Wave pressure • Pressure loads due to a local wave trough, see 4.2 Bending moments • Permissible SWBM (sagging or minimum hogging) • Design VWBM (sagging), see Note 3

Symmetric


47

C3b

Ship loading condition (ship upright) • Draught equal to the scantling draught, Tsc • All container bays and hatch covers over the bays are to be filled with 40 ft

heavy containers to the maximum permitted weight, see Note 2 • All ballast and fuel oil tanks in way of the cargo hold model are to be

empty Wave pressure • Pressure loads due to a local wave crest, see 4.2 Bending moments • Permissible SWBM (hogging) • Design VWBM (hogging), see Note 3

Symmetric

C4

Ship loading condition (ship heeled) As C2a except as follows: • Mean draught at centreline equal to the scantling draught, Tsc • Static heel angle equal to the lesser of φ and tan-1 (2 (D – Tsc) / B), where φ

is the maximum roll angle defined in Pt 3, Ch 14,1.5.1 of the Rules for Ships but not to be taken as less than 22°.

Wave pressure • No wave Bending moments • As actual in FE model (i.e. no adjustment required)

Asymmetric

C5

Ship loading condition (ship heeled) As C3a except as follows: • Mean draught at centreline equal to the scantling draught, Tsc • Static heel angle equal to the lesser of φ and tan-1 (2 (D – Tsc) / B), where φ

is the maximum roll angle defined in Pt 3, Ch 14,1.5.1 of the Rules for Ships but not to be taken as less than 22°.

Wave pressure • No wave Bending moments • As actual in FE model (i.e. no adjustment required)

Asymmetric

C6 Longitudinal loads caused by ship accelerations acting on containers, see Ch 2 Symmetric

C7 Damaged (flooded hold) conditions, see Ch 3 Asymmetric

NOTES 1. The container unit weight may be derived based on the expected cargo weight when light containers are loaded in the

considered holds and hatch covers above. The weight of light container units is not to be more than the following: • In hold: 55% of the weight of a corresponding heavy container unit as defined in Note 2, • On deck and hatch covers: 90% of the weight of a corresponding heavy container unit as defined in Note 2 or 17 metric

tons, whichever is the lesser. 2. The weight of heavy container units is to be calculated as the permissible stacking weight divided by the maximum number

of tiers planned. 3. The design vertical wave bending moments (VWBM) are to be Mw(hog) and Mw(sag) as specified in 2.1 of INTRODUCTION.

See also 4.8. 4. Light draught corresponds to the expected draught amidships when heavy containers are loaded in the considered holds

while lighter containers are loaded in other holds. The light draught is not to be taken as greater than 0.9 Tsc. 5. For one bay empty condition, if the cargo hold consists of two or more bays, then each bay, and the deck and hatch covers

above where required, are to be considered entirely empty in turn as separate load cases. The number of load cases may be reduced if the structural arrangement is symmetrical about mid-hold and the scantling enhancement is applied to all cargo bays.


48

Fig. 1.4.1 (see continuation) Illustration of loading conditions (for definition of wave crest and trough, see Fig. 1.4.2)


49

Fig. 1.4.1 (conclusion) Illustration of loading conditions (for definition of wave crest and trough, see Fig. 1.4.2)


50

Fig. 1.4.2

Pressure head distribution PW for local wave crest and trough


5.1. The boundary conditions to be applied to the FE model are dependent on the load case and structural component to be analysed. Different boundary conditions need to be applied for the symmetric and asymmetric load cases.

5.2. The boundary conditions described in this Section are preferred. Alternative equivalent boundary conditions may be used.

5.3. The following boundary conditions are to be applied to analyse different structural components (see Table 1.5.1):

• Set 1 is to be used to analyse load cases C1, C2a, C2b, C3a, C3b and C6.

• Set 2 is to be used for the application of hull girder bending moment, see 4.8.

• Set 3 is to be used to analyse the heeled condition load cases C4 and C5, and the damaged (flooded hold) load case C7.

5.4. The boundary condition sets to be used for full-breadth and half-breadth FE models are summarised in Table 1.5.1 and illustrated in Figs. 1.5.1 to 1.5.3.


51

5.5. For the heeled load cases, C4 and C5, and the damaged (flooded hold) load case, C7, grounded springs are to be applied to the nodes of the elements in the side shell, inner skin, inner and outer bottom, and the upper deck outside the line of hatches at each end of the model to represent the shear stiffness induced by the unmodelled container bays, see Fig. 1.5.3. The spring stiffness, ks, can be calculated as:

𝑘s = 𝐺𝐴𝑙 𝑁

where

G = modulus of rigidity

l = distance from the bulkhead at the end of the model to the next unmodelled bulkhead

A = average cross-sectional area of side shell, inner skin, inner bottom, outer bottom or upper deck outside the line of hatches, as appropriate

N = number of nodes to which the springs are applied.

5.6. Asymmetric boundary conditions for half-breadth FE models

5.6.1 For asymmetric load cases applied to half-breadth FE models, the symmetric and anti-symmetric load components need to be run as separate load cases and then combined to generate the total asymmetric load case. Different boundary conditions are required for the symmetric and anti-symmetric load components.

5.6.2 The structural response of both sides of the ship for asymmetric load cases will be obtained by combining the results from the symmetric and anti-symmetric load cases as described in Appendix A.

Table 1.5.1 Summary of boundary conditions to apply

Load case type Boundary conditions

Half-breadth FE model

Symmetric load cases Load cases C1, C2a, C2b, C3a, C3b, C6

All load components Set 1 see Fig. 1.5.1

Asymmetric load cases Load cases C4, C5, C7

Symmetric load components Anti-symmetric load components

Set 1 Set 3

see Fig. 1.5.1 see Fig. 1.5.3

Symmetric load cases Hull girder bending moment

Bending moment Set 2 see Fig. 1.5.2

Full-breadth FE model

Symmetric load cases Load cases C1, C2a, C2b, C3a, C3b, C6


Asymmetric load cases Load cases C4, C5, C7


Symmetric load cases Hull girder bending moment

Bending moment Set 2 see Fig. 1.5.2


52

Fig.

1.5

.1

Set 1

bou

ndar

y co

ndit

ions

for

load

cas

es C

1, C

2a, C

2b, C

3a, C

3b a

nd C

6 Bo

unda

ry c

ondi

tion

s fo

r th

e ap

plic

atio

n of

sym

met

ric

load

s


53

Fig.

1.5

.2

Set 2

bou

ndar

y co

ndit

ions

for

appl

icat

ion

of h

ull g

irde

r be

ndin

g m

omen

t


54

Fig.

1.5

.3

Set 3

bou

ndar

y co

ndit

ions

for

load

cas

es C

4, C

5 an

d C7

Bo

unda

ry c

ondi

tion

s fo

r th

e ap

plic

atio

n of

ant

i-sym

met

ric

load

s an

d bo

unda

ry c

ondi

tion

s fo

r th

e ap

plic

atio

n of

asy

mm

etri

c lo

ads (

full-

brea

dth

mod

el)


55


6.1. The structure is to comply with the acceptance criteria given in Table 1.6.1.

6.2. The buckling capability of plate panels is to be assessed using a plate thickness reduced by the corrosion addition, tc, in Table 1.6.2.

6.3. The buckling factors of safety of plate panels are to be derived using a procedure that takes into account all relevant direct and shear stress components, such as Lloyd’s Register ShipRight Software’s buckling module.

6.4. When the calculated elastic critical buckling stress exceeds 50% of the specified minimum yield stress, then the buckling stress is to be adjusted for the effects of plasticity using the Johnson-Ostenfeld correction formula, given below:

𝜎𝑐𝑐 = 𝜎0 �1 −𝜎0

4𝜎𝑐�

where σo = specified minimum yield stress of material σcr = critical buckling stress corrected for plasticity effects σc = elastic critical buckling stress.

6.5. In calculating the buckling factors of safety, the edge restraint factor, c, defined in Pt 3, Ch 4,7 of the Rules for Ships, may be taken into account when determining the critical buckling stress of wide panels subjected to compressive loading on the long edge of the panel. The edge restraint factor, c, may not be used in the calculation of critical buckling stress for compression applied on the short edge.

6.6. Buckling assessment based on the first principle direct calculation method may be considered in special circumstances.


56

Table 1.6.1 Acceptance criteria for primary structure

Structural item Load case

Allowable stress, N/mm2 (see Notes 2 and 3) Buckling Factor of safety λ

(see Note 1) Von Mises

σe Longitudinal

σx

Transverse σy

(see Note 4)

Shear stress τ

(see Note 5)

Bottom shell plating

C1 C2a C3a C3b

— 0,92σL 0,63σ0 — 1,0

Double bottom girders

C1 C2a C2b C3a C3b

σL 0,92σL — 0,46σL 1,0

Inner bottom

C1 C2a C3a C3b

σL 0,92σL 0,63σ0 — 1,0

Double bottom floors

C1 C2a C4 C5

0,75σ0 — 0,63σ0 0,35σ0 1,1

Side shell Longitudinal bulkhead

C1 C2a C3a C3b

σL 0,92σL 0,63σ0 0,46σL 1,0

C4 C5 σL 0,92σL 0,63σ0 0,46σL 1,1

Side stringers

C1 C2a σL 0,92σL — 0,46σL 1,0

C4 C5 σL 0,92σL — 0,46σL 1,1

Side transverses

C1 C2a C4 C5

0,75σ0 — 0,63σ0 0,35σ0 1,1

Transverse bulkheads all structures

C6 C7

see Ch 2 see Ch 3

Transverse bulkhead plating

C1 C2a C2b

0,75σ0 — 0,63σ0 0,35σ0 1,0

Transverse bulkheads: • vertical web plating • vertical face bars • horizontal web plating • horizontal face bars

C1 C2a C2b

0,75σ0 — 0,63σ0 — 1,0

C4 C5

0,75σ0 — 0,63σ0 — 1,1

Cross-deck box transverses

C4 C5

0,75σ0 — 0,63σ0 0,35σ0 1,1


57

Table 1.6.1 (Continuation): Acceptance criteria for primary structure

where σL = 235/kL

NOTES 1. The panel thickness is to be reduced by the amount tc indicated in Table 1.6.2. The local stresses are to be increased

in the ratio of t/(t – tc), where t is the thickness used in the FE model. These local stresses may be obtained by deducing the stresses due to global bending moment generated in the FE model from the FE stresses.

2. For shell elements, the specified allowable stresses are to be compared with the membrane stress in the relevant structural item.

3. In areas where the openings have not been modelled, the resulting shear stress and von Mises stress are to be corrected according to the ratio of the actual to the modelled shear area. If the resulting stress level exceeds 90% of the specified allowable value, further study by means of fine mesh follow-up models may be required.

4. For bottom shell, inner bottom and transverse bulkhead plating, σy is the stress in the plane of the plating in the transverse direction. For side shell and longitudinal bulkhead, σy is the stress in the plane of the plating parallel to the span of the side transverse. For all other members, σy is the direct stress in the direction of the member’s span.

5. The specified values relate to the mean shear stress over the depth of the member. The peak stress is not to exceed 1.1 × allowable value.

Table 1.6.2 Standard thickness deductions to be used to derive critical buckling stresses

Structural item Thickness deduction, tc in mm

Deck plating 1,0

Shell plating 1,0

Inner bottom plating 1,0

Longitudinal bulkhead (inner skin) 1,0

Crown of side tanks (e.g. 2nd Deck) 1,0 Internal structure of double bottom and side tanks 1,0 Transverse bulkheads, watertight and open 0,0

Cross-deck structure (e.g. top box sides and bottom) 0,0


58

PART C:


Chapter 2:

Transverse Bulkhead and Mid-Hold Support Structures: Surge (Fore and Aft) Loading Section 1: Objectives






1.1. The objective of PART C, Ch 2 is to ensure the adequacy of transverse watertight bulkheads and mid-hold support structures (open bulkheads) under the effect of longitudinal loads arising from longitudinal accelerations acting on the containers. The acceptance criteria are given in 5.2.

1.2. This assessment and the inclusion of this load component in the procedures of PART A and PART B are not required for container ships that have continuous longitudinal deck girders arranged such that the span of the cross-deck boxes does not exceed 13.0 m. The span of the cross-deck box is to be calculated taking into account the presence of the continuous longitudinal deck girders, but ignoring end brackets, etc. Longitudinal deck girders or bulkheads are not to be considered continuous if their continuous longitudinal extent is less than a length equivalent to four (4) 40ft container bays.

1.3. If the procedures in PART A and PART B are not required, then the analysis indicated in this chapter is to be carried out, with the exception of ships that have a structural arrangement which satisfies the description in 1.2.

1.4. Where this analysis is carried out in PART A using a full ship FE model, the analysis in this chapter can be waived.


2.1. The model described in PART C, Ch 1 may be used. If PART A’s analysis is carried out using a full ship model then the loads can be applied directly to the full ship model.


59


3.1. This loading assesses the effects of longitudinal loads caused by ship accelerations acting on containers, on the transverse bulkhead and cross-deck structures. The longitudinal acceleration, ax, at the required locations is to be calculated using the longitudinal acceleration formulae given in Pt 3, Ch 14,8.2.5 of the Rules for Ships. The following motion cases, defined in Pt 3, Ch 14, Table 14.8.4 of the Rules for Ships, are to be applied:

• Head sea: MC1 (HS_1) Positive pitch acceleration case

MC1 (HS_2) Negative pitch acceleration case

• Oblique sea: MC3 (OS1_1) Positive pitch acceleration case

MC3 (OS1_2) Negative pitch acceleration case

Note that longitudinal acceleration due to MC1 (HS_2) is equal in magnitude to MC1 (HS_1) but they are in opposite directions. Likewise, longitudinal accelerations due to MC3 (OS1_1) and MC3 (OS1_2) are equal in magnitude but opposite in direction.

3.2. If the longitudinal loads are not required to be considered in the analysis in PART A and PART B, see 1.3, then the loading condition C6 (see Ch 1, Table 1.4.1) may be based on the largest acceleration of the head sea and oblique sea conditions.

3.3. No other loads are to be applied.


60

Table 2.3.1 Assumptions regarding longitudinal loads and their application

Location of containers Assumptions

Containers in hold for all container ships

The longitudinal force is to be calculated at the centre of each container and is to be suitably distributed to the bulkhead primary members in way of the cell guides.

Containers on hatch covers

The longitudinal force is to be calculated at the mid-height of the stack. The following assumptions are to be made: • wind loads may be neglected • self-weight of the hatch cover is to be taken into account • the stack is to contain the maximum number of loaded tiers, as specified in the Loading

Manual (LM) or Cargo Securing Manual (CSM) • the weight of containers is to be taken as the maximum permitted by the Loading

Manual • all loads arising from containers on the hatch covers are to be applied as forces

to the hatch coaming top • the moment about the stack base caused by the longitudinal force may be ignored • longitudinal forces from containers sited between the ship's side and the longitudinal

coaming (i.e. not sited on the hatch covers) may be ignored • 15% of the total force acting on the hatch cover is to be distributed as a line load to the

top of the hatch coamings (transverse and longitudinal) on which the cover rests. This represents the load which could be assumed to be taken by friction at bearing pads and/or sealing arrangements

• the remaining longitudinal forces acting on the hatch cover are to be taken as acting at the hatch cover longitudinal stopper positions. If the stopper positions are unknown, then they are to be located at the mid-breadth of the aft end of the covers. 3 covers are to be assumed if the number of covers is not known.

Containers above deck for hatch coverless ships

The longitudinal force is to be calculated at the centre of each container and is to be suitably distributed to the cell guide support structure and bulkhead primary members as appropriate.

NOTES 1. Positive longitudinal acceleration (forward parallel to deck) generates longitudinal force acting backward. Negative

longitudinal acceleration creates longitudinal acting forward. 2. The centre of gravity position and distribution of longitudinal force of a container due to ship motion is to be in

accordance with Pt 3, Ch 14,9.2 of the Rules for Ships.


4.1. Boundary condition Set 1, see Ch 1, Fig. 1.5.1 is to be used.


5.1. Where the structural items are assessed using PART A’s procedure with a full ship FE model, see 1.4, the acceptance criteria set out in PART A are to be complied with.

5.2. Where PART A’s procedure is not carried out, the von Mises stresses in the bulkhead structures and the cross-deck structures under the loading scenarios defined in this Section are not to exceed 0,25σo. Single element values in way of the application of loads arising from the containers on hatch covers may exceed this value, but are not to exceed 0,4σo. A minimum buckling factor of safety, λ, of 1,2 is to be achieved.


61

PART C:


Chapter 3:

Transverse Watertight Bulkhead Assessment in Damaged (Flooded Hold) Condition Section 1: Objectives





1.1. The purpose of this Chapter is to ensure that the structural integrity of the transverse watertight bulkheads is not compromised if the container hold is flooded as a result of collision or other accidental occurrence.

1.2. The watertight bulkheads are to be capable of resisting the imposed loads caused by flood water, including the effect of ship motions and accelerations in addition to the normal operating loads.

1.3. Watertight bulkhead structures which comply with the simplified loading and acceptance criteria set out in this Chapter are considered to satisfy the requirements of 1.2. Proposals for alternative assessment procedures are to include evidence that the requirements of 1.2 and the acceptance criteria in Section 4 are to be satisfied.


2.1. The model described in Ch 1 is to be used. If the verification of buckling factor of safety of the face plate of the transverse watertight bulkhead vertical webs and the horizontal stringers is to be waived, the face plate thickness in the FE model is to be represented by a reduced thickness equal to 40 per cent of the original thickness.

2.2. Boundary condition Set 3, as given in Ch 1, Fig. 1.5.3, is to be used.


3.1. Sufficient load cases are to be considered to enable assessment of the response of typical transverse watertight bulkheads to flooding and other loads.

3.2. For models which have been arranged with a watertight transverse bulkhead at the mid-length of the FE model, it will be necessary to consider two separate flooding scenarios:


62

a) the after hold is flooded,

b) the forward hold is flooded.

3.3. For models which have been arranged with an open bulkhead at the mid-length of the FE model, see Fig. 1.3.1 in Ch 1, only the scenario with the hold at the mid-length flooded needs to be considered. The response of both watertight bulkheads of this hold is to be compared with the acceptance criteria.

3.4. For the flooding scenarios specified in 3.2 and 3.3, two basic loading conditions are to be analysed:

a) Condition C7a, which assumes that no containers are carried on hatch covers,

b) Condition C7b, which assumes that the hatch covers are fully loaded with containers to the maximum permitted weight by the ship’s Loading Manual.

The ship is assumed to be in a heel condition. The loads to be applied are as specified in Table 3.3.1 and shown in Figs. 3.3.1 and 3.3.2.

3.5. Condition C7b is to be omitted for hatch coverless container ships.


63

Table 3.3.1 Summary of loading conditions with one hold flooded (also see Fig. 3.3.2)

Item Loading condition, C7

Condition C7a Condition C7b

Transverse watertight bulkheads of flooded hold

Pressure based on the sum of 1) the pressure head due to damaged heel waterline and 2) pitch motion. 1) The damaged heel waterline may be determined based on the

damage stability information. The following 2 separate conditions are to be considered: - Maximum draught at centreline of the forward and aft bulkheads

of the flooded hold (𝑇1) - Maximum draught at inner hull longitudinal bulkhead of the

forward and aft bulkheads of the flooded hold (𝑇2) The above flooding conditions may be represented using a single load case if the maximum loads resulting from these conditions are applied. 2) Pressure head due to ship’s pitch motion:

The pressure head ℎpitch is given by:

ℎpitch = 0,35 𝑙H tan(ψ)

𝑙H is the length of the flooded hold ψ is the pitch angle calculated in accordance with Pt 3, Ch 14, Table 14.8.1 of the Rules for Ships

Where no damage stability information is available, 𝑇1 and 𝑇2 can be obtained as follows:

𝑇1 = 𝑇sc + 1,2 × 1,025 × � 𝑉s100 TPC

� (in m)

𝑇2 to be taken at freeboard deck at side (normally 2nd deck) where 𝑉s is the volume of the flooded compartment corresponding to the level of scantling draught (in m3) TPC is the displacement (tonnes) immersion per centimetre as given in the ship’s Loading Manual 𝑇1 needs not to be taken greater than 𝑇2.

Side and bottom shell Pressure based on heeled waterline defined by 𝑇1 and 𝑇2

Watertight longitudinal bulkheads, decks and inner bottom of flooded hold Pressure based on heeled waterline defined by 𝑇1 and 𝑇2

Containers in flooded hold Empty of containers

Containers in non-flooded hold Fully loaded with maximum permitted 40 ft containers

Ballast tanks in way of flooded hold

Flooded to the level of waterline defined by 𝑇1 and 𝑇2

Containers on hatch covers No containers Fully loaded with maximum permitted 40 ft containers

NOTE

The pressure head to be applied to the external shell plating and longitudinal internal plating is different to that specified for the bulkhead. The purpose of these load cases is to impose flood water loads, including the effect of ship motions and accelerations, onto the bulkhead structure; hence the increased pressure head applied to the bulkhead.


64

Fig. 3.3.1

Loading conditions for flooded load cases


65

Fig. 3.3.2 Heads of water for flooded loading conditions


4.1. The transverse watertight bulkheads and their supporting structures must satisfy the acceptance criteria given in Table 3.4.1 when subjected to the loads specified in Section 3.


66

Table 3.4.1 Acceptance criteria for loading conditions with one hold flooded

Structural member of transverse watertight bulkhead

Allowable stress, N/mm2 Buckling factor

of safety λ (see Note 4)

Von Mises σe

Direct stress σ

Shear stress τ (see Note 5)

Bulkhead plating σ0 0,95σ0 0,55σ0 1,1

(see Note 1)

Vertical webs and horizontal stringers: (a) Web plating

(b) Face plates

σ0 0,95σ0 0,55σ0 1,0

(see Notes 2 & 3)

— σ0 — 1,0

(see Notes 3 & 6)

Cross-deck box structure σ0 0,95σ0 0,55σ0 1,0

(see Note 2)

Double bottom girders and side stringers in way of end connections of bulkhead primary members

σ0 0,95σ0 0,55σ0 1,0

(see Note 2)

NOTES 1. The ultimate buckling capability of bulkhead plate panels is to satisfy the following relationship:

σu ≥ λ σ where σ = the direct membrane stress component, normal to the longest side of the panel σu = the ultimate buckling capability of the panel, is given by: = 0,5 (c + 1) β σo where β = coefficient given in Fig. 3.4.1 c = value given in Pt 3, Ch 4, Table 4.7.2 of the Rules for Ships.

2. The elastic buckling capability of plate panels is to be assessed using all relevant direct and shear stress components and a procedure such as Lloyd’s Register ShipRight Software’s buckling module. The edge constraint factor given in Pt 3, Ch 4 of the Rules for Ships may be taken into account. The Johnson-Ostenfeld correction is to be applied as stated in Ch 1,6.4.

3. The overall buckling capability of the vertical web or horizontal stringers is also to be assessed. 4. The buckling capability of plate panels is to be assessed using a plate thickness reduced by the corrosion addition, tc, in Ch

1, Table 1.6.2. 5. Allowable stress related to element shear stresses. 6. Verification of buckling factor of safety of face plate may be waived if the thickness in the FE model is represented by a

reduced thickness equal to 40 per cent of the original thickness.


67

Fig.

3.4

.1

Coef

ficie

nt β


68

PART C:


Chapter 4:

Transverse Bulkhead Structures: Additional Requirements for Fuel Oil Deep Tanks Section 1: Application







1.1. This Chapter is applicable to container ships which carry Fuel Oil (FO) in deep tanks, constructed in transverse bulkhead structures, or in container cargo hold, i.e. fuel tanks located inboard of the inner skin, above the inner bottom, and between adjacent transverse bulkheads.

1.2. For ships where the calculation procedures have been performed in accordance with PART A, consideration will be given to using a suitable length of that model with suitable detailed follow up models.

1.3. The analysis specified in this Chapter is additional to that specified in Ch 1.

1.4. For container ships intended to operate in areas subject to low air temperatures, there may be a requirement to assess the effect of the heated cargo on critical. Where FO is carried in transverse double plated bulkheads in which all the primary structures are connected to both of the bulkhead platings, the structural analysis described in Sections 2 to 6 of this Chapter may be omitted.

1.5. See also Ch 5.


2.1. The objective of Sections 3 to 6 is to verify the structural arrangements of the primary structure of the fuel oil deep tanks.


69

2.2. The local strength of the container hold structure is to be verified by Chapters 1, 2 and 3 as applicable.

2.3. The global strength of a container ship for which PARTS A and B have not been applied must comply with the relevant Sections of the Rules for Ships, (Pt 4, Ch 8) and this is to be verified by the application of the appropriate ShipRight program.

2.4. The objective of Ch 5 is to provide load components for PART B’s analysis. If PART B’s analysis is not required then the analysis described in Ch 5 is also not required.


3.1. A model is to be constructed extending from one 40 ft bay aft of the aftmost fuel oil deep tank bulkhead to one 40 ft bay forward of the foremost fuel oil deep tank bulkhead.

3.2. This model is to be developed in accordance with Ch 1,3.3 to 3.10.

3.3. The face plates and plate stiffeners of primary members are to be represented by line elements with the cross-sectional area modified, where appropriate, in accordance with Table 4.3.1 and Fig. 4.3.1.

Table 4.3.1 Line element effective cross-sectional area

Structure represented by element Effective area, Ae

Primary member face bars Symmetrical Asymmetrical

Ae = 100% An Ae = 100% An

Curved bracket face bars (continuous) Symmetrical Asymmetrical

see Fig. 4.3.1

Straight bracket face bars (discontinuous)

Symmetrical Asymmetrical

Ae = 100% An Ae = 60% An

Straight bracket face bars (continuous around toe curvature)

Straight portion Symmetrical Asymmetrical

Ae = 100% An Ae = 60% An

Curved portion Symmetrical Asymmetrical

see Fig. 4.3.1

Web stiffeners – sniped both ends

Flat bars Ae = 25% stiffener area

Other sections

Ae = p

o

A

rYI

A –2

+

Web stiffeners – sniped one end, connected other end

Flat bars Ae = 75% stiffener area

Other sections

Ae = p

o

A

rYI

A –

2

2

+

Symbols

A = cross-section area of stiffener and associated plating An = average face bar area over length of line element Ap = cross-section area of associated plating I = moment of inertia of stiffener and associated plating Y0 = distance of neutral axis of stiffener and associated plating from median plane of plate

r = radius of gyration =AI


70

Fig. 4.3.1 Effective area of curved face bars


71


4.1. The load cases required are illustrated in Figs. 4.4.1(a) to 4.4.1(d) for arrangement of three, four, five and six abreast fuel oil tanks. If the ship’s Loading Manual consists of loading conditions with two or more adjacent fuel oil tanks filled and other fuel oil tanks empty, these conditions are also to be investigated in addition to those shown in the figure. The load components to be included are:

• static and dynamic inertial loads due to the lightship mass, see 4.7 and 4.8;

• static and dynamic inertial loads due to containers and fluid in tanks, see 4.7 and 4.8;

• the hydrostatic loads due to immersion to the draught specified. The hydrostatic loads are to be applied as pressure loads to the shell envelope, equivalent in the upright condition to ρgh, where h is the distance of the element centroid below the still waterline;

• pressure loads due to a local wave crest or trough, see 4.4;

• over pressure of tanks, see 4.2;

• hull girder bending moments as specified in Table 4.4.1; and

• hull girder shear forces as specified in Table 4.4.1.

4.2. The over pressure head is calculated as follows:

• For load cases D1 to D6 Max(hof, h/2) in metres

• For load cases D7 and D8 Max(2,4, h) in metres

where h is the vertical distance between the crown of the FO tank and the top of the overflow; and hof is the height of the overflow measured from the deck on which it is fitted, see Figs 4.4.1(a) to 4.4.1(d)

4.3. For design purposes, fuel oil is to be assumed to have a specific gravity of 1,0.

4.4. For cases requiring the consideration of wave crest and trough conditions, the wave pressure distribution to be applied is described in Ch 1, Fig 1.4.2, with the draught, Tsc, taken as the scantling draught or lightest loaded draught, as appropriate. The external pressure may be taken as uniform over the model length.

4.5. For the heeled cases, D5 and D6, the static heel angle is to be taken as the lesser of φ and tan-1 (2 (D – Tsc) / B), where φ is the maximum roll angle defined in Pt 3, Ch 14,1.5.1 of the Rules for Ships but not to be taken as less than 22○. The mean draught at centreline is to be taken as the scantling draught.

4.6. For load cases D1 to D8, the effect of hull global bending moment and shear force are to be included as specified in Table 4.4.1.

4.7. For load cases D1, D2, D3 and D4, the inertial force of containers, ship masses and fluid in tanks due to vertical acceleration, including gravitational effect, are to be calculated in accordance with Ch 1,4.5, with the following 𝑓 factor applied:

𝑓 = 1 for load case D4 = -1 for load cases D1, D2 and D3


72

4.8. Inertial load due to vertical acceleration need not be applied to load cases D5, D6, D7 and D8. However, the gravitational effect is to be considered.

4.9. Where the required hull girder bending moment specified in Table 4.4.1 is not achieved by the application of the ship’s loading condition and wave pressure, the FE stresses are to be adjusted as follows:

σx = σx_FE + σx_u ∆BM

σy = σy_FE + σy_u ∆BM

τxy = τxy_FE + τxy_u ∆BM

where

σx, σy and τxy are the adjusted direct stresses and shear stress at the centre of an element

σx_FE, σy_FE and τxy_FE are the finite element direct stresses and shear stress at the centre of the element

σx_u, σy_u and τxy_u are the direct stresses and shear stress at the centre of the element due to the unit hull girder bending moment load case

ΔBM is the difference between the required bending moment, as specified in Table 4.4.1, and the resultant bending moment from the FE model at the longitudinal position of the element.

Values of σx_u, σy_u and τxy_u are to be derived by applying a unit bending moment to the model using boundary conditions of load case D9 as described in Figure 4.4.2.

4.10. Load case D10 (see Figure 4.4.3) represents the loading and boundary conditions to be adopted for determining the stress components due to global shear force for load cases D1 to D4, see Table 4.4.1. The difference between the required shear force in Table 4.4.1 and the shear force due to the application of the ship’s loading condition and wave pressure is to be applied at the model end.

4.11. Loading conditions for common configurations of fuel oil deep tanks are illustrated in Figs. 4.4.1 (a) to (d). Loading conditions for other configurations will be considered, such that similar loading scenarios on the containment structure are achieved.


73

Table 4.4.1 Application of global bending moments and shear forces to load cases

Load case Condition (see Note 3) Wave pressure Global bending moment Global shear force

D1, D2 and D3 Ship upright Wave crest • Permissible SWBM

(seagoing hogging) • Design VWBM

(hogging), see Note 1

—

D4 Ship upright Wave trough

• Permissible SWBM (seagoing sagging or minimum hogging)

• Design VWBM (sagging), see Note 1

—

D5 and D6 Ship heeled — • As actual in FE model

(i.e. no adjustment required)

—

D7 and D8 Ship upright (Test condition) — • Permissible SWBM

(harbour hogging) —

D1, D2 and D3 Ship upright Wave crest • As actual in FE model


At fwd oil-tight bulkhead • Permissible SWSF (-ve) • Design VWSF (-ve)

D1, D2 and D3 Ship upright Wave crest • As actual in FE model


At aft oil-tight bulkhead • Permissible SWSF (+ve) • Design VWSF (+ve)

D4 Ship upright Wave trough • As actual in FE model


At fwd oil-tight bulkhead • Permissible SWSF (+ve) • Design VWSF (+ve)

D4 Ship upright Wave trough • As actual in FE model


At aft oil-tight bulkhead • Permissible SWSF (-ve) • Design VWSF (-ve)

NOTES 1. The design vertical wave bending moments (VWBM) are to be Mw(hog) and Mw(sag) as specified in 2.1 of INTRODUCTION.

See also 4.9. 2. The design vertical wave shear forces (VWSF) are to be Qw+ and Qw- as specified in 2.1 of INTRODUCTION. 3. All ballast tanks in way of the cargo hold model for load cases D1, D2, D3, D5, D6, D7 and D8 are to be empty.


74

Typical arrangement

Load case D1 — scantling draught + wave crest


Fig. 4.4.1(a) (see continuation) Loading conditions — Fuel oil deep tanks with two longitudinal bulkheads


75


Load case D4 — lightest loaded draught + wave trough

Load case D5 — scantling draught + static heel (see 4.5)

Fig. 4.4.1(a) (continued) Loading conditions — Fuel oil deep tanks with two longitudinal bulkheads


76


Load case D7 — tank test condition (draught = 0.25D)


Fig. 4.4.1(a) (conclusion) Loading conditions — Fuel oil deep tanks with two longitudinal bulkheads


77

Typical arrangement

Load case D1 — scantling draught + wave crest (see Notes)


Fig. 4.4.1(b) (see continuation) Loading conditions — Fuel oil deep tanks with three longitudinal bulkheads


78




Fig. 4.4.1(b) (continued) Loading conditions — Fuel oil deep tanks with three longitudinal bulkheads


79




Fig. 4.4.1(b) (conclusion) Loading conditions — Fuel oil deep tanks with three longitudinal bulkheads

NOTES 1. If the ship’s Loading Manual consists of loading conditions with two or more adjacent fuel oil tanks filled and other fuel

oil tanks empty, these conditions are also to be investigated. 2. The actual loading conditions depend on the structural arrangement and may be different to that shown in the figure. It

is recommended that the designer discusses the analysis requirements with Lloyd’s Register early on in the design cycle.


80

Typical arrangements



Fig. 4.4.1(c) (see continuation) Loading conditions — Fuel oil deep tanks with four longitudinal bulkheads


81




Fig. 4.4.1(c) (continued) Loading conditions — Fuel oil deep tanks with four longitudinal bulkheads


82




Fig. 4.4.1(c) (conclusion) Loading conditions — Fuel oil deep tanks with four longitudinal bulkheads





83

Typical arrangements



Fig. 4.4.1(d) (see continuation) Loading conditions — Fuel oil deep tanks with five longitudinal bulkheads


84




Fig. 4.4.1(d) (continued) Loading conditions — Fuel oil deep tanks with five longitudinal bulkheads


85




Fig. 4.4.1(d) (conclusion) Loading conditions — Fuel oil deep tanks with five longitudinal bulkheads





86

Fig.

4.4

.2

Load

cas

e D

9: M

omen

t cas

e Re

sults

of t

his

case

are

to b

e ad

ded

to r

esul

ts o

f loa

d ca

ses

D1,

D2,

D3,

D4,

D7

and

D8

See

Tabl

e 4.

4.1

and

4.6


87

Fig.

4.4

.3

Load

cas

e D

10: S

hear

cas

e Fo

r co

mbi

nati

on w

ith

resu

lts o

f loa

d ca

ses

D1

to D

4 as

spe

cifie

d in

Tab

le 4

.4.1


88


5.1. The boundary conditions to be applied to load cases D1 to D8 are defined in Ch 1,5.

5.2. Boundary conditions for load cases D9 and D10 are given in Figs. 4.4.2 and 4.4.3 respectively. These boundary conditions to be applied are summarised in Table 4.5.1.

Table 4.5.1 Summary of boundary conditions to apply

Load case type Boundary conditions

Half-breadth FE model

Symmetric load cases Load cases D1, D2, D3, D4, D7 and D8

All load components Set 1 see Fig. 1.5.1 of Ch 1,5

Asymmetric load cases Load cases D5 and D6

Symmetric load components Anti-symmetric load components

Set 1 Set 3

see Fig. 1.5.1 of Ch 1,5 see Fig. 1.5.3 of Ch 1,5

Symmetric load cases Hull girder loads

Bending moment D9 see Fig. 4.4.2

Shear force D10 see Fig. 4.4.3 Symmetric load cases Hull girder bending moment Bending moment Set 2 see Fig. 1.5.2 of Ch 1,5

Full-breadth FE model

Symmetric load cases Load cases D1, D2, D3, D4, D7 and D8


Asymmetric load cases Load cases D5 and D6


Symmetric load cases Hull girder loads

Bending moment D9 see Fig. 4.4.2

Shear force D10 see Fig. 4.4.3


6.1. The structure of the fuel oil deep tank is to comply with the acceptance criteria given in Table 4.6.1.

6.2. The buckling capability of plate panels is to be assessed using a plate thickness reduced by the corrosion addition, tc, see Ch 1, Table 1.6.2.

6.3. The procedure to be adopted for the calculation of buckling factors is specified in Ch 1,6.3 to 6.6.


89

Table 4.6.1 Acceptance criteria for primary structure of, and in way of, the fuel oil deep tanks

Structural item Load case

Allowable stress, N/mm2 (see Notes 2 and 3)

Buckling factor of safety

(see Note 1) Von Mises σe

Longitudinal σx

Transverse σy

(see Note 4)

Shear stress

τ (see Note 6)

Bottom shell plating Inner bottom Double bottom girders

D1 to D8 σL 0,92σL 0,63σo 0,46σL 1,0

Oil-tight longitudinal bulkhead

D1 to D4, D7 and D8 0,75σo — 0,63σo 0,35σo

(see Note 7) 1,1

D5 and D6 — — 0,63σo 0,35σo 1,1

Side shell Side stringers Inner hull longitudinal bulkhead

D1 to D4, D7 and D8 σL 0,92σL — 0,46σL

(see Note 7) 1,0

D5 and D6 σL 0,92σL — 0,46σL 1,1

Transverse structure Double bottom floors

D1 to D8 0,75σo — 0,63σo 0,35σo 1,1

Transverse bulkhead structures

D1 to D4, D7 and D8 0,75σo — 0,63σo 0,35σo 1,0

D5 and D6 0,75σo — 0,63σo 0,35σo 1,1

Cross-deck box structure D1 to D8 0,75σo — 0,63σo 0,35σo 1,1

Transverse structure face plate D1 to D8 — 0,75σo — — —

NOTES

1. The panel thickness is to be reduced by the amount tc as indicated in Ch 1, Table 1.6.2. The local stresses are to be increased by the ratio of t / (t – tc), where t is the thickness used in the FE model. These local stresses may be obtained by deducing the stresses due to global bending moment generated in the FE model from the FE stresses.

2. For shell elements, the specified allowable stresses are to be compared with the membrane stresses in the relevant structural item.

3. In areas where the openings have not been modelled, the resulting shear stress and von Mises stress are to be corrected according to the ratio of the actual to the modelled shear area. If the resulting stress level exceeds 90% of the specified allowable value, further study by means of fine mesh follow-up models may be required.

4. For bottom shell and inner bottom plating, σy is the stress in the plane of the plating in the transverse direction. For side shell and longitudinal bulkhead, σy is the stress in the plane of the plating parallel to the span of the side transverse. For the transverse bulkhead plating, σy is the stress in the plane of the plating in the transverse or vertical directions. For all other members, σy is the direct stress in the direction of the member’s span.

5. Consideration is to be given to the combined local and global stress scenario, see Table 4.4.1. 6. The specified values relate to the mean shear stress over the depth of the member. The peak stress is not to exceed 1.1 ×

allowable value. 7. The effect of hull girder still water and wave shear stress is to be considered and added to cases D1 to D4. In general, shear

stress is not to exceed 0,46σL. For side shell and longitudinal bulkhead plating in way of the ends of transverse oil-tight bulkhead stringers, the shear stress is not to exceed 0,57σL.


90

PART C:


Chapter 5:

Surge (Fore and Aft) Loading: Additional Requirements for Fuel Oil Deep Tanks Section 1: Application




1.1. This Chapter is applicable to container ships which carry fuel oil in deep tanks constructed in transverse bulkhead structures or in a container cargo hold, i.e. fuel tanks located inboard of the inner skin, above the inner bottom and between adjacent transverse bulkheads.


2.1. The objective of this Chapter is to define the load to be applied to the boundary of fuel oil tanks in the procedures of PART A and PART B due to longitudinal (surge) acceleration.

2.2. The inclusion of this load component in the procedures of PART A and PART B are not required for container ships having longitudinal deck girders arranged such that the span of the cross-deck boxes does not exceed 13 m. The span of the cross-deck box is to be calculated taking into account the presence of continuous longitudinal deck girders or bulkheads, but ignoring end brackets, etc. Longitudinal deck girders or bulkheads are not to be considered continuous if they do not extend over a length equivalent to four 40 ft container bays.

Section 3: Loading condition

3.1. This loading condition assesses the effects of longitudinal loads caused by ship accelerations acting on the fuel oil in the tank, on the transverse bulkhead and cross-deck structures. The longitudinal acceleration, ax, at the centre of gravity of a tank is to be calculated using the longitudinal acceleration formulae given in Pt 3, Ch 14,8.2.5 of the Rules for Ships. The following motion cases, defined in Pt 3, Ch 14, Table 14.8.4 of the Rules for Ships, are to be applied:


91

• Head sea: MC1 (HS_1) Positive pitch acceleration case

MC1 (HS_2) Negative pitch acceleration case

• Oblique sea: MC3 (OS1_1) Positive pitch acceleration case

MC3 (OS1_2) Negative pitch acceleration case

Note that longitudinal acceleration due to MC1 (HS_2) is equal in magnitude to MC1 (HS_1) but they are in opposite directions. Likewise, longitudinal accelerations due to MC3 (OS1_1) and MC3 (OS1_2) are equal in magnitude but opposite in direction. The pressure load at the tank boundary due to longitudinal acceleration is to be calculated in accordance with Fig. 5.3.1.

3.2. No other loads are to be applied. However, if the hydrostatic pressure caused by the fuel oil was not incorporated in the analyses of PART A and PART B, this component is to be included in the load cases described in this Chapter.

3.3. The effect of container stacks stowed alongside, in adjacent holds to, or over the fuel oil deep tanks, are to be considered in the analyses of PART A and PART B. These effects are to be calculated as described in Ch 2 and in PART B’s analysis.

Pressure due to negative longitudinal acceleration

P = ρ l │ax│ (N/m2) where ρ = 1000 kg/m3 l = distance from aft bulkhead (m)

Pressure due to positive longitudinal acceleration

P = ρ l │ax│ (N/m2) where ρ = 1000 kg/m3 l = distance from fwd bulkhead (m)

Fig. 5.3.1 Pressure on tank boundaries for fuel oil deep tanks

Appendix A Primary Structure of Container Ship, September 2016

92

APPENDIX A: Procedure to Apply Transverse Asymmetric Loads to a Half-Breadth Model

Section A.1: Procedure to apply transverse asymmetric loads to a half-breadth FE model

A.1.1 In order to generate a transverse asymmetric load case for a half-breadth model, it is necessary to apply the transverse loads by combining two separate load cases. These two load cases consist of:

1. The symmetric load case. This case applies symmetric loading components and boundary conditions to the FE model, see Fig. A.1.1.

2. The anti-symmetric load case. This case applies anti-symmetric loading components and boundary conditions to the FE model, see Fig. A.1.1.

A.1.2 If any of the loads do not conform to the above description, or if the structure is not symmetric about the centreline, then this technique is not strictly valid and a full-breadth FE model is required. In this case, it may be necessary to consider individual load cases for ship heeled in port direction and ship heeled in starboard direction.

A.1.3 Using the above two load cases, the different structural response of both sides of the ship to the transverse loads can be derived as follows:

Port asymmetric = symmetric plus anti-symmetric

Starboard asymmetric = symmetric minus anti-symmetric

This is illustrated in Fig. A.1.1.

A.1.4 Application of the external hydrostatic pressure corresponding to the heeled waterline for symmetric and anti-symmetric load cases is illustrated in Fig. A.1.1 and described as follows:

1. The symmetric load component for the hydrostatic pressure is applied as half the sum of the pressures on the port and starboard sides. Note it is necessary to modify the side shell pressure distribution as shown in Fig. A.1.1 to satisfy the symmetric load definition stated above.

2. The anti-symmetric load component for the external hydrostatic pressure is applied as half the difference of pressure on the port and starboard sides.

A.1.5 The boundary conditions for the symmetric load case and the anti-symmetric load are as follows:

1. Symmetric load case: See PART C, Ch 1, Fig. 1.5.1.

2. Anti-symmetric load case: See PART C, Ch 1, Fig. 1.5.3.

Appendix A Primary Structure of Container Ship, September 2016

93

Fig.

A.1

.1

Der

ivat

ion

of th

e as

ymm

etri

c loa

d ca

ses

for

a ha

lf-br

eadt

h m

odel

from

the

sym

met

ric

and

anti

-sym

met

ric

load

cas

es (s

hip

heel

ed c

ondi

tion

)

Appendix B Primary Structure of Container Ship, September 2016

94

APPENDIX B: Combined Stresses Analysis in Oblique Sea based on Equivalent Design Waves

Section B.1 Application B.1.1 Where required by Pt 4, Ch 8,14.1 of the Rules for Ships, the combined stress analysis specified in PART A and PART B in oblique sea condition is to be analysed based on hydrodynamic torque and vertical and horizontal bending moments obtained by non-linear ship motion analysis.

B.1.2 If the hydrodynamic programs employed are not recognised by Lloyd’s Register, full particulars of the programs will be required to be submitted for review, see Pt 3, Ch 1,3.1 of the Rules for Ships.

B.1.3 In addition to the combined stress analysis described in this Appendix, the head sea condition described in PART A and PART B is to be analysed.

Section B.2 Long term statistical analysis B.2.1 Long term statistical analysis is to be used to determine the design probability level of the loads and the Equivalent Design Waves (EDWs) for the combined stress analysis. The short term probability of the load responses in a particular sea condition is to be derived using a spectral analysis. The responses in regular waves may be obtained using linear ship motion analysis based on potential flow theory.

B.2.2 The following loading conditions are to be analysed:

• a fully loaded condition with a ship draught equal or close to the scantling draught; and

• a loading condition with maximum GM.

B.2.3 The long term analysis is to be based on the assumptions given in Table B.2.1 and the North Atlantic wave environment scatter diagram specified in IACS Rec.34 given in Table B.2.2. The Rayleigh probability density function is to be used to represent the peak distribution. Other probability density functions may be considered in special cases.

B.2.4 The long term probability distribution of the vertical wave bending moment amidship is to be calculated. The design probability level of the loads in oblique sea conditions is to be taken as the probability level at which the long term vertical wave bending moment amidship is equal to the wave vertical bending moment, Mwo, given in Pt 4, Ch 2,2.4.1 (referred to in Pt 4, Ch 8,3.2) of the Rules for Ships, see Figure B.2.1.

B.2.5 The long term hydrodynamic torque at the shear centre along the length of the ship, at 0,05 Lpp increments, is to be determined at the probability level established in B.2.4. A constant shear centre position, based on the shear centre in the midship region at a maximum distance below the baseline, may be used for the calculation of hydrodynamic torques.

B.2.6 The equivalent design regular waves to achieve the long term hydrodynamic torque at the following longitudinal positions should be considered for non-linear ship motion analysis:


95

• Maximum torque in the range 0 ≤ x < 0,5 Lpp

• Maximum torque in the range 0,5 Lpp ≤ x ≤ Lpp

B.2.7 The wave frequency and relative heading of an equivalent design wave is to be selected such that the Response Amplitude Operator (RAO) of the hydrodynamic torque is at its maximum. The wave amplitude is obtained by the ratio of the long term hydrodynamic torque to the selected RAO. For each case two equivalent design waves, i.e. waves approaching from the port side and starboard side at the same angle, are to be considered.

Table B.2.1 Wave environment and assumptions for long term statistical analysis

Wave data IACS Rec.34, see Table B.2.2

Wave energy spectrum

ISSC wave spectrum:

𝑆w(ω) = 4π3 ×𝐻S2

𝑇Z4×

1ω5 × exp�

−16π3 ω4 𝑇Z4

�

Wave spreading distribution Cosine-squared

Directionality (wave heading relative to the ship)

All headings equally probable. The heading increment is not to be greater than 15 deg.

Ship speed 25% of the ship’s maximum service speed but not to be taken less than 5 knots.

Table B.2.2 IACS Rec.34 ̶ North Atlantic wave environment scatter diagram

HS/TZ 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 15,5 16,5 17,5 18,5

0,5 1,5 2,5 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 15,5 16,5

1,3 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0

133,7 29,3

2,2 0,2 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0

865,6 986,0 197,5

34,9 6,0 1,0 0,2 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0

1186,0 4976,0 2158,8

695,5 196,1

51,0 12,6

3,0 0,7 0,2 0,0 0,0 0,0 0,0 0,0 0,0 0,0

634,2 7738,0 6230,0 3226,5 1354,3

498,4 167,0

52,1 15,4

4,3 1,2 0,3 0,1 0,0 0,0 0,0 0,0

186,3 5569,7 7449,5 5675,0 3288,5 1602,9

690,3 270,1

97,9 33,2 10,7

3,3 1,0 0,3 0,1 0,0 0,0

36,9 2375,7 4860,4 5099,1 3857,5 2372,7 1257,9

594,4 255,9 101,9

37,9 13,3

4,4 1,4 0,4 0,1 0,0

5,6 703,5

2066,0 2838,0 2685,5 2008,3 1268,6

703,2 350,6 159,9

67,5 26,6

9,9 3,5 1,2 0,4 0,1

0,7 160,7 644,5

1114,1 1275,2 1126,0

825,9 524,9 296,9 152,2

71,7 31,4 12,8

5,0 1,8 0,6 0,2

0,1 30,5

160,2 337,7 455,1 463,6 386,8 276,7 174,6

99,2 51,5 24,7 11,0

4,6 1,8 0,7 0,2

0,0 5,1

33,7 84,3

130,9 150,9 140,8 111,7

77,6 48,3 27,3 14,2

6,8 3,1 1,3 0,5 0,2

0,0 0,8 6,3

18,2 31,9 41,0 42,2 36,7 27,7 18,7 11,4

6,4 3,3 1,6 0,7 0,3 0,1

0,0 0,1 1,1 3,5 6,9 9,7

10,9 10,2

8,4 6,1 4,0 2,4 1,3 0,7 0,3 0,1 0,1

0,0 0,0 0,2 0,6 1,3 2,1 2,5 2,5 2,2 1,7 1,2 0,7 0,4 0,2 0,1 0,1 0,0

0,0 0,0 0,0 0,1 0,2 0,4 0,5 0,6 0,5 0,4 0,3 0,2 0,1 0,1 0,0 0,0 0,0

0,0 0,0 0,0 0,0 0,0 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,0 0,0 0,0 0,0 0,0

NOTES 1. Total 100,000 wave observations. 2. HS is significant wave height in metres. 3. TZ is zero crossing period in seconds.


96

Fig. B.2.1

Determination of design load probability level based on long term probability distribution of the vertical wave bending moment amidship

Fig. B.2.2 Selection of locations and torque from the long term hydrodynamic torque envelope curve, see B.2.6


97

Section B.3 Non-linear ship motion analysis B.3.1 Non-linear time domain ship motion analysis is to be carried out for each equivalent design regular wave identified in Section B.2.

B.3.2 The hydrodynamic torque at the shear centre (see B.2.5) and vertical and horizontal bending moment distributions along the ship length at an increment not greater than 0,05L, are to be obtained for at least 20 steps (i.e. 0–2π, in 0,1π steps) over a complete wave cycle.

B.3.3 Alternatively, the wave pressures and inertial load due to the ship motions may be applied directly to the FE model to generate the required global loads.

B.3.4 In the selection of the wave cycle, care is to be taken to ensure that the time domain simulation has reached a steady state.

Section B.4 Combined stress analysis B.4.1 A full ship FE model developed for PART A’s analysis is to be used for the combined stress analysis to the global hull stress response in oblique sea condition. The FE model(s) developed for PART B is to be used for the analysis of global loads on local structural details. All equivalent design waves identified in Section B.2 are to be analysed.

B.4.2 The dynamic stress responses are to be calculated for at least 20 steps (i.e. 0–2π, in 0,1π steps) over a complete wave cycle. The stress responses can be obtained by applying the hydrodynamic torque, vertical and horizontal bending moment distributions in B.3.2 to the FE model for each step of the wave cycle. Individual load components may be applied separately and the combined stresses are obtained by superimposition. The boundary conditions given in PART A, Ch 1,5 for the full ship model can be used for this analysis. For PART B’s analysis, additional boundary conditions described in PART B, Ch 1,4 are to be considered where appropriate.

B.4.3 Alternatively, the stress responses may be obtained by applying the wave pressures and inertial load due to the ship motions to the FE model, see B.3.3. A suitable inertial relief technique can be used to balance the FE model.

B.4.4 PART A analysis For each equivalent design wave identified in Section B.2, the combined static and dynamic stresses and buckling factors of safety over a complete wave cycle must comply with the criteria (oblique sea condition) given in PART A, Ch 1,6. The load combinations given in PART A, Ch 1, Table 1.4.3 are to be considered.

B.4.5 PART B analysis For each equivalent design wave identified in Section B.2, the combined static and dynamic stresses and dynamic stress ranges over a complete wave cycle must comply with the criteria (oblique sea condition) given in PART B, Ch 1,5. The load combinations given in PART A, Ch 1, Table 1.4.3 are to be considered.

Appendix C Primary Structure of Container Ship, September 2016

98

APPENDIX C: Rule Equivalent Design Wave Hydrodynamic Torque, Vertical and Horizontal Bending Moment Distributions

Section C.1 Application C.1.1 The hydrodynamic torque, vertical and horizontal bending moments given in this Appendix represent the load responses of the equivalent design wave corresponding to the hydrodynamic loads given in Pt 4, Ch 8,15 of the Rules for Ships.

C.1.2 These loads can be used to determine the structural responses over a wave cycle for the analyses in PART A and PART B. These loads are equivalent to the application of the rule load formulae. The procedure is necessary for determining the maximum von Mises stresses and minimum buckling factor of safety over a wave cycle, see PART A, Ch 1, 4.6 and PART B, Ch 1, 4.7.

C.1.3 The hydrodynamic torque, vertical and horizontal bending moment distributions given in this Appendix represent the loads resulting from oblique sea starboard equivalent design wave.

Section C.2 Loads C.2.1 The vertical wave bending moment, MVWi at step i of the wave cycle is given by:

MVWi = 0,0505 C0 C3,i L2 B (Cb + 0,7) kN m

= (0,0052 C0 C3,i L2 B (Cb + 0,7) tonne-f m

where

C3,i = Vertical wave bending moment distribution coefficients depending on the longitudinal position from A.P. given in Table C.2.1.

Other symbols refer to Pt 4, Ch 8,15 of the Rules for Ships.

C.2.2 The horizontal wave bending moment, MHWi at step i of the wave cycle is given by:

MHWi = 0,2063 C0 C4,i L2 T (Cb + 0,7) kN m

= (0,0210 C0 C4,i L2 T (Cb + 0,7) tonne-f m

where

C4,i = Horizontal wave bending moment distribution coefficients depending on the longitudinal position from A.P. given in Table C.2.2.


C.2.3 The hydrodynamic torque, MTWi at step i of the wave cycle is given by:


99

MTWi = 0,0728 C0 C5,i L B2 (Cb + 0,7) – 0,8683 (0,65T + ε) C0 K3,i L T (Cb + 0,7) kN m

= (0,0078 C0 C5,i L B2 (Cb + 0,7) – 0,0886 (0,65T + ε) C0 K3,i L T (Cb + 0,7) tonne-f m

where

C5,i = Hydrodynamic torque distribution coefficients depending on the longitudinal position from A.P. given in Table C.2.3.

K3,i = Horizontal wave shear force distribution coefficients depending on the longitudinal position from A.P. given in Table C.2.4.



100

Table C.2.1 Vertical wave bending moment distribution coefficients

x/LPP 𝐶3,1, 𝐶3,2

, 𝐶3,3, 𝐶3,4

, 𝐶3,5, 𝐶3,6

, 𝐶3,7, 𝐶3,8

, 𝐶3,9, 𝐶3,10

, 𝐶3,11, 𝐶3,12

, 𝐶3,13, 𝐶3,14

, 𝐶3,15, 𝐶3,16

, 𝐶3,17, 𝐶3,18

, 𝐶3,19, 𝐶3,20

,

0,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,05 0,062 0,065 0,061 0,051 0,036 0,018 -0,002 -0,022 -0,040 -0,054 -0,062 -0,065 -0,061 -0,051 -0,036 -0,018 0,002 0,022 0,040 0,054 0,10 0,158 0,156 0,138 0,106 0,065 0,017 -0,033 -0,079 -0,118 -0,145 -0,158 -0,156 -0,138 -0,106 -0,065 -0,017 0,033 0,079 0,118 0,145 0,15 0,305 0,288 0,242 0,173 0,087 -0,008 -0,102 -0,186 -0,251 -0,292 -0,305 -0,288 -0,242 -0,173 -0,087 0,008 0,102 0,186 0,251 0,292 0,20 0,460 0,420 0,338 0,224 0,087 -0,058 -0,197 -0,318 -0,407 -0,456 -0,460 -0,420 -0,338 -0,224 -0,087 0,058 0,197 0,318 0,407 0,456 0,25 0,611 0,539 0,414 0,248 0,058 -0,137 -0,319 -0,470 -0,575 -0,623 -0,611 -0,539 -0,414 -0,248 -0,058 0,137 0,319 0,470 0,575 0,623 0,30 0,732 0,624 0,454 0,240 0,002 -0,235 -0,450 -0,621 -0,731 -0,769 -0,732 -0,624 -0,454 -0,240 -0,002 0,235 0,450 0,621 0,731 0,769 0,35 0,817 0,669 0,456 0,198 -0,080 -0,350 -0,585 -0,763 -0,867 -0,885 -0,817 -0,669 -0,456 -0,198 0,080 0,350 0,585 0,763 0,867 0,885 0,40 0,850 0,667 0,419 0,129 -0,173 -0,458 -0,699 -0,871 -0,957 -0,950 -0,850 -0,667 -0,419 -0,129 0,173 0,458 0,699 0,871 0,957 0,950 0,45 0,836 0,626 0,354 0,048 -0,263 -0,548 -0,780 -0,935 -0,999 -0,965 -0,836 -0,626 -0,354 -0,048 0,263 0,548 0,780 0,935 0,999 0,965 0,50 0,780 0,554 0,274 -0,032 -0,336 -0,607 -0,818 -0,949 -0,987 -0,929 -0,780 -0,554 -0,274 0,032 0,336 0,607 0,818 0,949 0,987 0,929 0,55 0,683 0,459 0,190 -0,097 -0,374 -0,615 -0,796 -0,899 -0,914 -0,839 -0,683 -0,459 -0,190 0,097 0,374 0,615 0,796 0,899 0,914 0,839 0,60 0,555 0,352 0,114 -0,135 -0,371 -0,571 -0,714 -0,788 -0,784 -0,704 -0,555 -0,352 -0,114 0,135 0,371 0,571 0,714 0,788 0,784 0,704 0,65 0,415 0,241 0,043 -0,159 -0,345 -0,498 -0,602 -0,647 -0,628 -0,548 -0,415 -0,241 -0,043 0,159 0,345 0,498 0,602 0,647 0,628 0,548 0,70 0,275 0,137 -0,015 -0,165 -0,300 -0,404 -0,470 -0,489 -0,460 -0,386 -0,275 -0,137 0,015 0,165 0,300 0,404 0,470 0,489 0,460 0,386 0,75 0,165 0,064 -0,044 -0,147 -0,236 -0,302 -0,338 -0,341 -0,311 -0,250 -0,165 -0,064 0,044 0,147 0,236 0,302 0,338 0,341 0,311 0,250 0,80 0,085 0,016 -0,054 -0,119 -0,172 -0,208 -0,224 -0,219 -0,191 -0,145 -0,085 -0,016 0,054 0,119 0,172 0,208 0,224 0,219 0,191 0,145 0,85 0,041 -0,002 -0,044 -0,083 -0,113 -0,132 -0,138 -0,131 -0,111 -0,080 -0,041 0,002 0,044 0,083 0,113 0,132 0,138 0,131 0,111 0,080 0,90 0,022 -0,002 -0,026 -0,047 -0,063 -0,074 -0,077 -0,073 -0,061 -0,044 -0,022 0,002 0,026 0,047 0,063 0,074 0,077 0,073 0,061 0,044 0,95 0,010 0,001 -0,009 -0,017 -0,024 -0,028 -0,030 -0,029 -0,025 -0,018 -0,010 -0,001 0,009 0,017 0,024 0,028 0,030 0,029 0,025 0,018 1,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

NOTES 1. 𝐶3,i = 𝐶3,i

, × 𝑓 where 𝑓 = |𝑓fH| 𝑖𝑓 𝐶3,i

, ≥ 0, 𝑓 = |𝑓fS| 𝑖𝑓 𝐶3,i

, < 0 2. 𝑓fH, 𝑓fS: Hogging and sagging vertical bending moment correction factors, see 2.1 of INTRODUCTION. 3. Intermediate values are to be determined by linear interpolation.


101

Table C.2.2 Horizontal wave bending moment distribution coefficients

x/LPP 𝐶4,1 𝐶4,2 𝐶4,3 𝐶4,4 𝐶4,5 𝐶4,6 𝐶4,7 𝐶4,8 𝐶4,9 𝐶4,10 𝐶4,11 𝐶4,12 𝐶4,13 𝐶4,14 𝐶4,15 𝐶4,16 𝐶4,17 𝐶4,18 𝐶4,19 𝐶4,20

0,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,05 -0,016 -0,012 -0,007 -0,001 0,005 0,010 0,014 0,017 0,019 0,018 0,016 0,012 0,007 0,001 -0,005 -0,010 -0,014 -0,017 -0,019 -0,018 0,10 -0,046 -0,030 -0,010 0,010 0,030 0,046 0,058 0,064 0,064 0,058 0,046 0,030 0,010 -0,010 -0,030 -0,046 -0,058 -0,064 -0,064 -0,058 0,15 -0,097 -0,055 -0,009 0,039 0,083 0,119 0,143 0,153 0,148 0,129 0,097 0,055 0,009 -0,039 -0,083 -0,119 -0,143 -0,153 -0,148 -0,129 0,20 -0,154 -0,076 0,009 0,094 0,169 0,228 0,264 0,275 0,259 0,217 0,154 0,076 -0,009 -0,094 -0,169 -0,228 -0,264 -0,275 -0,259 -0,217 0,25 -0,208 -0,084 0,049 0,176 0,287 0,369 0,415 0,421 0,385 0,312 0,208 0,084 -0,049 -0,176 -0,287 -0,369 -0,415 -0,421 -0,385 -0,312 0,30 -0,242 -0,065 0,118 0,289 0,432 0,533 0,582 0,573 0,509 0,395 0,242 0,065 -0,118 -0,289 -0,432 -0,533 -0,582 -0,573 -0,509 -0,395 0,35 -0,247 -0,019 0,211 0,420 0,588 0,699 0,741 0,711 0,611 0,451 0,247 0,019 -0,211 -0,420 -0,588 -0,699 -0,741 -0,711 -0,611 -0,451 0,40 -0,217 0,055 0,322 0,557 0,738 0,846 0,872 0,812 0,673 0,468 0,217 -0,055 -0,322 -0,557 -0,738 -0,846 -0,872 -0,812 -0,673 -0,468 0,45 -0,153 0,147 0,433 0,677 0,854 0,948 0,949 0,857 0,681 0,438 0,153 -0,147 -0,433 -0,677 -0,854 -0,948 -0,949 -0,857 -0,681 -0,438 0,50 -0,072 0,240 0,528 0,764 0,926 0,997 0,970 0,849 0,644 0,377 0,072 -0,240 -0,528 -0,764 -0,926 -0,997 -0,970 -0,849 -0,644 -0,377 0,55 0,014 0,318 0,590 0,805 0,941 0,985 0,932 0,789 0,568 0,291 -0,014 -0,318 -0,590 -0,805 -0,941 -0,985 -0,932 -0,789 -0,568 -0,291 0,60 0,087 0,365 0,608 0,791 0,897 0,915 0,843 0,689 0,467 0,200 -0,087 -0,365 -0,608 -0,791 -0,897 -0,915 -0,843 -0,689 -0,467 -0,200 0,65 0,136 0,377 0,581 0,729 0,805 0,802 0,721 0,569 0,361 0,118 -0,136 -0,377 -0,581 -0,729 -0,805 -0,802 -0,721 -0,569 -0,361 -0,118 0,70 0,158 0,353 0,514 0,624 0,674 0,657 0,576 0,439 0,258 0,053 -0,158 -0,353 -0,514 -0,624 -0,674 -0,657 -0,576 -0,439 -0,258 -0,053 0,75 0,151 0,299 0,417 0,495 0,524 0,502 0,431 0,317 0,173 0,012 -0,151 -0,299 -0,417 -0,495 -0,524 -0,502 -0,431 -0,317 -0,173 -0,012 0,80 0,123 0,225 0,305 0,355 0,370 0,349 0,294 0,210 0,106 -0,009 -0,123 -0,225 -0,305 -0,355 -0,370 -0,349 -0,294 -0,210 -0,106 0,009 0,85 0,083 0,145 0,193 0,222 0,229 0,214 0,178 0,124 0,059 -0,013 -0,083 -0,145 -0,193 -0,222 -0,229 -0,214 -0,178 -0,124 -0,059 0,013 0,90 0,043 0,074 0,097 0,111 0,114 0,106 0,088 0,060 0,028 -0,008 -0,043 -0,074 -0,097 -0,111 -0,114 -0,106 -0,088 -0,060 -0,028 0,008 0,95 0,013 0,023 0,031 0,035 0,036 0,034 0,028 0,020 0,009 -0,002 -0,013 -0,023 -0,031 -0,035 -0,036 -0,034 -0,028 -0,020 -0,009 0,002 1,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

NOTE 1. Intermediate values are to be determined by linear interpolation.


102

Table C.2.3 Hydrodynamic torque distribution coefficients

x/LPP 𝐶5,1 𝐶5,2 𝐶5,3 𝐶5,4 𝐶5,5 𝐶5,6 𝐶5,7 𝐶5,8 𝐶5,9 𝐶5,10 𝐶5,11 𝐶5,12 𝐶5,13 𝐶5,14 𝐶5,15 𝐶5,16 𝐶5,17 𝐶5,18 𝐶5,19 𝐶5,20

0,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,05 -0,289 -0,202 -0,096 0,020 0,134 0,235 0,313 0,360 0,372 0,348 0,289 0,202 0,096 -0,020 -0,134 -0,235 -0,313 -0,360 -0,372 -0,348 0,10 -0,456 -0,271 -0,060 0,157 0,358 0,525 0,640 0,693 0,677 0,596 0,456 0,271 0,060 -0,157 -0,358 -0,525 -0,640 -0,693 -0,677 -0,596 0,15 -0,455 -0,199 0,075 0,343 0,577 0,754 0,858 0,877 0,811 0,665 0,455 0,199 -0,075 -0,343 -0,577 -0,754 -0,858 -0,877 -0,811 -0,665 0,20 -0,342 -0,044 0,258 0,535 0,760 0,910 0,971 0,937 0,812 0,606 0,342 0,044 -0,258 -0,535 -0,760 -0,910 -0,971 -0,937 -0,812 -0,606 0,25 -0,184 0,130 0,432 0,691 0,883 0,988 0,997 0,908 0,730 0,481 0,184 -0,130 -0,432 -0,691 -0,883 -0,988 -0,997 -0,908 -0,730 -0,481 0,30 -0,022 0,288 0,570 0,796 0,944 1,000 0,958 0,822 0,606 0,330 0,022 -0,288 -0,570 -0,796 -0,944 -1,000 -0,958 -0,822 -0,606 -0,330 0,35 0,169 0,452 0,691 0,863 0,950 0,944 0,846 0,665 0,418 0,131 -0,169 -0,452 -0,691 -0,863 -0,950 -0,944 -0,846 -0,665 -0,418 -0,131 0,40 0,323 0,570 0,761 0,878 0,909 0,851 0,709 0,499 0,239 -0,044 -0,323 -0,570 -0,761 -0,878 -0,909 -0,851 -0,709 -0,499 -0,239 0,044 0,45 0,439 0,642 0,782 0,846 0,827 0,727 0,556 0,330 0,072 -0,193 -0,439 -0,642 -0,782 -0,846 -0,827 -0,727 -0,556 -0,330 -0,072 0,193 0,50 0,522 0,677 0,766 0,780 0,717 0,585 0,395 0,166 -0,078 -0,316 -0,522 -0,677 -0,766 -0,780 -0,717 -0,585 -0,395 -0,166 0,078 0,316 0,55 0,562 0,672 0,715 0,689 0,595 0,443 0,248 0,028 -0,194 -0,397 -0,562 -0,672 -0,715 -0,689 -0,595 -0,443 -0,248 -0,028 0,194 0,397 0,60 0,544 0,606 0,609 0,553 0,442 0,288 0,106 -0,086 -0,271 -0,428 -0,544 -0,606 -0,609 -0,553 -0,442 -0,288 -0,106 0,086 0,271 0,428 0,65 0,472 0,483 0,447 0,368 0,252 0,111 -0,040 -0,187 -0,316 -0,415 -0,472 -0,483 -0,447 -0,368 -0,252 -0,111 0,040 0,187 0,316 0,415 0,70 0,260 0,244 0,204 0,144 0,070 -0,011 -0,091 -0,162 -0,217 -0,251 -0,260 -0,244 -0,204 -0,144 -0,070 0,011 0,091 0,162 0,217 0,251 0,75 -0,074 -0,108 -0,132 -0,142 -0,138 -0,121 -0,092 -0,054 -0,011 0,033 0,074 0,108 0,132 0,142 0,138 0,121 0,092 0,054 0,011 -0,033 0,80 -0,366 -0,373 -0,344 -0,281 -0,191 -0,082 0,035 0,149 0,248 0,323 0,366 0,373 0,344 0,281 0,191 0,082 -0,035 -0,149 -0,248 -0,323 0,85 -0,385 -0,354 -0,288 -0,195 -0,082 0,039 0,156 0,258 0,334 0,378 0,385 0,354 0,288 0,195 0,082 -0,039 -0,156 -0,258 -0,334 -0,378 0,90 -0,198 -0,169 -0,124 -0,066 -0,002 0,062 0,120 0,167 0,197 0,208 0,198 0,169 0,124 0,066 0,002 -0,062 -0,120 -0,167 -0,197 -0,208 0,95 -0,075 -0,056 -0,031 -0,002 0,026 0,052 0,073 0,086 0,091 0,088 0,075 0,056 0,031 0,002 -0,026 -0,052 -0,073 -0,086 -0,091 -0,088 1,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000



103

Table C.2.4 Horizontal wave shear force distribution coefficients

x/LPP 𝐾3,1 𝐾3,2 𝐾3,3 𝐾3,4 𝐾3,5 𝐾3,6 𝐾3,7 𝐾3,8 𝐾3,9 𝐾3,10 𝐾3,11 𝐾3,12 𝐾3,13 𝐾3,14 𝐾3,15 𝐾3,16 𝐾3,17 𝐾3,18 𝐾3,19 𝐾3,20

0,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,05 0,101 0,061 0,015 -0,032 -0,076 -0,113 -0,139 -0,151 -0,148 -0,131 -0,101 -0,061 -0,015 0,032 0,076 0,113 0,139 0,151 0,148 0,131 0,10 0,211 0,107 -0,008 -0,122 -0,224 -0,304 -0,354 -0,370 -0,349 -0,295 -0,211 -0,107 0,008 0,122 0,224 0,304 0,354 0,370 0,349 0,295 0,15 0,276 0,112 -0,062 -0,231 -0,377 -0,486 -0,548 -0,555 -0,509 -0,413 -0,276 -0,112 0,062 0,231 0,377 0,486 0,548 0,555 0,509 0,413 0,20 0,277 0,060 -0,163 -0,370 -0,541 -0,659 -0,712 -0,696 -0,611 -0,467 -0,277 -0,060 0,163 0,370 0,541 0,659 0,712 0,696 0,611 0,467 0,25 0,214 -0,045 -0,299 -0,525 -0,699 -0,804 -0,831 -0,776 -0,646 -0,452 -0,214 0,045 0,299 0,525 0,699 0,804 0,831 0,776 0,646 0,452 0,30 0,089 -0,181 -0,433 -0,643 -0,790 -0,860 -0,845 -0,748 -0,577 -0,350 -0,089 0,181 0,433 0,643 0,790 0,860 0,845 0,748 0,577 0,350 0,35 -0,083 -0,326 -0,538 -0,697 -0,787 -0,801 -0,736 -0,599 -0,404 -0,169 0,083 0,326 0,538 0,697 0,787 0,801 0,736 0,599 0,404 0,169 0,40 -0,268 -0,459 -0,606 -0,693 -0,712 -0,662 -0,547 -0,378 -0,172 0,050 0,268 0,459 0,606 0,693 0,712 0,662 0,547 0,378 0,172 -0,050 0,45 -0,422 -0,526 -0,579 -0,575 -0,515 -0,404 -0,254 -0,079 0,104 0,277 0,422 0,526 0,579 0,575 0,515 0,404 0,254 0,079 -0,104 -0,277 0,50 -0,485 -0,489 -0,445 -0,358 -0,235 -0,090 0,064 0,212 0,339 0,433 0,485 0,489 0,445 0,358 0,235 0,090 -0,064 -0,212 -0,339 -0,433 0,55 -0,447 -0,353 -0,225 -0,075 0,083 0,232 0,359 0,450 0,498 0,497 0,447 0,353 0,225 0,075 -0,083 -0,232 -0,359 -0,450 -0,498 -0,497 0,60 -0,338 -0,172 0,010 0,192 0,355 0,483 0,564 0,589 0,557 0,471 0,338 0,172 -0,010 -0,192 -0,355 -0,483 -0,564 -0,589 -0,557 -0,471 0,65 -0,227 0,011 0,248 0,460 0,628 0,734 0,768 0,727 0,615 0,443 0,227 -0,011 -0,248 -0,460 -0,628 -0,734 -0,768 -0,727 -0,615 -0,443 0,70 -0,094 0,193 0,461 0,683 0,839 0,913 0,897 0,794 0,613 0,372 0,094 -0,193 -0,461 -0,683 -0,839 -0,913 -0,897 -0,794 -0,613 -0,372 0,75 0,067 0,372 0,641 0,847 0,970 0,998 0,928 0,768 0,532 0,245 -0,067 -0,372 -0,641 -0,847 -0,970 -0,998 -0,928 -0,768 -0,532 -0,245 0,80 0,185 0,470 0,709 0,879 0,963 0,952 0,848 0,661 0,410 0,118 -0,185 -0,470 -0,709 -0,879 -0,963 -0,952 -0,848 -0,661 -0,410 -0,118 0,85 0,245 0,487 0,681 0,808 0,857 0,821 0,705 0,520 0,284 0,021 -0,245 -0,487 -0,681 -0,808 -0,857 -0,821 -0,705 -0,520 -0,284 -0,021 0,90 0,220 0,403 0,547 0,637 0,664 0,627 0,528 0,378 0,191 -0,015 -0,220 -0,403 -0,547 -0,637 -0,664 -0,627 -0,528 -0,378 -0,191 0,015 0,95 0,133 0,227 0,299 0,342 0,351 0,326 0,269 0,186 0,084 -0,026 -0,133 -0,227 -0,299 -0,342 -0,351 -0,326 -0,269 -0,186 -0,084 0,026 1,00 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000


Appendix D Primary Structure of Container Ship, September 2016

104

APPENDIX D: Combined Direct Stresses in Oblique Sea (Alternative Method)

Section D.1 Application D.1.1 The stress combinations given in this Appendix can be used as an alternative to PART A, Ch 1, Table 1.4.3 to obtain the maximum and minimum direct stresses and tangential stresses if the hydrodynamic loads in oblique sea condition specified in Appendix C are used in the analysis.

D.1.2 The stress combinations are not applicable if the hydrodynamic loads in oblique sea are obtained using non-linear ship motion analysis, see Appendix B. In this case, the load combinations described in PART A, Ch 1, Table 1.4.3 are to be used.

Section D.2 Stress Combinations D.2.1 The stress combinations are given in Table D.2.1.

D.2.2 However, if non-linear ship motion analysis is used to determine the hydrodynamic loads, see PART A, Ch 1,4.2, the load combinations given in Table 1.4.3 must be used.


105

Table D.2.1 Stress combinations for oblique sea condition (for direct stresses)

Wave (hull girder)

Longitudinal acceleration, see Note 1

(Containers, see Note 2 and/or FO, see Note 3)

Still water (see Note 4)

𝑀STC (see Note 6)

Still water hogging

Load cases

Wave direction σ �σ12 + σ62 σax (see Note 5) σSC σSTC

OS1a Starboard σ(OS1a) 1 1 Hog 1 OS2a Starboard σ(OS2a) 1 1 Hog -1 OS3a Starboard σ(OS3a) 1 -1 Hog 1 OS4a Starboard σ(OS4a) 1 -1 Hog -1 OS1b Starboard σ(OS1b) -1 1 Hog 1 OS2b Starboard σ(OS2b) -1 1 Hog -1 OS3b Starboard σ(OS3b) -1 -1 Hog 1 OS4b Starboard σ(OS4b) -1 -1 Hog -1

Load cases

Wave direction σ �(σ1′ )2 + (σ6′ )2 σax (see Note 5) σSC σSTC

OP1a Port σ(OP1a) 1 1 Hog 1 OP2a Port σ(OP2a) 1 1 Hog -1 OP3a Port σ(OP3a) 1 -1 Hog 1 OP4a Port σ(OP4a) 1 -1 Hog -1 OP1b Port σ(OP1b) -1 1 Hog 1 OP2b Port σ(OP2b) -1 1 Hog -1 OP3b Port σ(OP3b) -1 -1 Hog 1 OP4b Port σ(OP4b) -1 -1 Hog -1

Still water sagging

Load cases

Wave direction σ �σ12 + σ62 σax (see Note 5) σSC σSTC

OS5a Starboard σ(OS5a) 1 1 Sag 1 OS6a Starboard σ(OS6a) 1 1 Sag -1 OS7a Starboard σ(OS7a) 1 -1 Sag 1 OS8a Starboard σ(OS8a) 1 -1 Sag -1 OS5b Starboard σ(OS5b) -1 1 Sag 1 OS6b Starboard σ(OS6b) -1 1 Sag -1 OS7b Starboard σ(OS7b) -1 -1 Sag 1 OS8b Starboard σ(OS8b) -1 -1 Sag -1

Load cases

Wave direction σ �(σ1′ )2 + (σ6′ )2 σax (see Note 5) σSC σSTC

OP5a Port σ(OP5a) 1 1 Sag 1 OP6a Port σ(OP6a) 1 1 Sag -1 OP7a Port σ(OP7a) 1 -1 Sag 1 OP8a Port σ(OP8a) 1 -1 Sag -1 OP5b Port σ(OP5b) -1 1 Sag 1 OP6b Port σ(OP6b) -1 1 Sag -1 OP7b Port σ(OP7b) -1 -1 Sag 1 OP8b Port σ(OP8b) -1 -1 Sag -1

see Continuation for Notes


106

Table D.2.1 (Continuation): Stress combinations for oblique sea condition (for direct stresses)

NOTES 1. Longitudinal acceleration load component is required to be applied for the assessment of transverse bulkhead and cross deck

structures, see PART A, Ch 1, Table 1.6.1, and PART B’s analysis. 2. Containers - longitudinal component of container loads, arising from the effect of ship motions, acting on the transverse

bulkheads and cross deck structure. See PART A, Ch 1,4.3.11 and PART C, Ch 2, for definition of this load component. 3. FO - longitudinal component of fuel oil (or other liquid) loads, arising from the effect of ship motions, acting on the transverse

bulkheads. See PART A, Ch 1,4.3.11 and PART C, Ch 5, for definition of this load component. 4. Hogging and sagging (or minimum hogging) still water load cases as specified in PART A, Ch 1,4.3.1 and 4.3.2 are to be

considered. The stress of each still water load case is to be combined with the stresses due to cargo torque and wave loads (including longitudinal acceleration inertial load where required, see Note 6) for assessment against the acceptance criteria.

5. Inertial force due to longitudinal acceleration of containers and/or fuel oil, see PART A, Ch 1,4.3.11: • 1 indicates application of oblique sea positive pitch acceleration case MC3 (OS1_1) • -1 indicates application of oblique sea negative pitch acceleration case MC3 (OS1_2)

6. Cargo torque load case, see PART A, Ch 1,4.3.9.

Symbols

σ1 = σVW1 + σHW1 + σTW1 σ6 = σVW6 + σHW6 + σTW6 σ1′ = σVW1 − σHW1 − σTW1 σ6′ = σVW6 − σHW6 − σTW6 where

σSTC = Stress due to cargo torque, 𝑀STC, see PART A, Ch 1,4.3.9 σSC = Stress due to the still water load case with required SWBM distribution, see Note 4.

σVW1, σVW6 = Stresses due to oblique sea vertical wave bending moments, 𝑀VW1 and 𝑀VW6, given in Appendix C. σTW1, σTW6 = Stresses due to oblique sea hydrodynamic torques, 𝑀TW1and 𝑀TW6, given in Appendix C.

σHW1, σHW6 = Stresses due to oblique sea horizontal wave bending moments, 𝑀HW1and 𝑀HW6, given in Appendix C.

𝑀VW1and 𝑀VW6 is equivalent to the oblique sea vertical wave bending moments distribution, 𝑀WC1 and 𝑀WC2, given in Pt 4, Ch 8,15.3.1 of the Rules for Ships with the hogging and sagging factors incorporated.

𝑀HW1and 𝑀HW6 is the same distribution as the oblique sea horizontal wave bending moments, 𝑀HC1 and 𝑀HC2, given in Pt 4, Ch 8,15.3.2 of the Rules for Ships.

𝑀TW1and 𝑀TW6 is the same distribution as the oblique sea hydrodynamic torques, 𝑀WTC1and 𝑀WTC2, given in Pt 4, Ch 8,15.3.3 of the Rules for Ships.

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