strength analysis of hull structure inbulk carriers

CLASSIFICATION NOTES

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The electronic

No. 31.1

Strength Analysis of Hull Structure in Bulk Carriers

DECEMBER 2012

DET NORSKE VERITAS AS

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FOREWORD

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Classification NotesClassification Notes are publications that give practical information on classification of ships and other objects. Examplesof design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for somecomponents are given as interpretations of the more general rule requirements.

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Classification Notes - No. 31.1, December 2012

Changes –

CHANGES

GeneralThis document supersedes Classification Notes No. 31.1, June 2011.

Text affected by the main changes in this edition is highlighted in red colour. However, if the changes involvea whole chapter, section or sub-section, normally only the title will be in red colour.

Main ChangesItems related to Ore Carriers are removed from this Classification Note and used as a basis for a newClassification Note No. 31.10 Strength Analysis of Hull Structures in Ore Carriers.



Contents –

CONTENTS

1. General.................................................................................................................................................... 51.1 Introduction...............................................................................................................................................51.2 Bulk Carriers.............................................................................................................................................51.3 Procedure ..................................................................................................................................................61.4 Definitions.................................................................................................................................................7

2. Design Loads......................................................................................................................................... 102.1 General....................................................................................................................................................102.2 Bulk cargo filling part of hold (heavy cargo) .........................................................................................102.3 Bulk cargo expanded to fill hold.............................................................................................................11

3. Design Loading Conditions – Local Strength.................................................................................... 123.1 General ...................................................................................................................................................123.2 Summary for Bulk Carriers.....................................................................................................................123.3 Design Loading Conditions for Bulk Carriers ........................................................................................163.4 Fatigue Loads..........................................................................................................................................23

4. Cargo Hold Analysis ............................................................................................................................ 244.1 General....................................................................................................................................................244.2 Model Extent...........................................................................................................................................244.3 Modelling of geometry ...........................................................................................................................254.4 Elements and Mesh Size .........................................................................................................................264.5 Boundary Conditions ..............................................................................................................................294.6 Loading Conditions.................................................................................................................................314.7 Presentation of input and results .............................................................................................................324.8 Evaluation of results and applicable acceptance criteria ........................................................................33

5. Local Structure Analysis ..................................................................................................................... 365.1 General....................................................................................................................................................365.2 Stiffeners subject to large deformations .................................................................................................365.3 Other fine mesh models ..........................................................................................................................385.4 Documentation and result presentation...................................................................................................385.5 Acceptance Criteria.................................................................................................................................39

6. Additional Requirements Considering Flooding .............................................................................. 396.1 General....................................................................................................................................................396.2 Global Bending Moment and Shear Force Limitation............................................................................396.3 Transverse Bulkhead Strength ................................................................................................................406.4 Diaphragm and shear plates in double bottom below bulkhead stool, considering flooding

(evaluation of the effectiveness) .............................................................................................................416.5 Limit to Hold Loading, Considering Flooding .......................................................................................42

7. Cargo Hold Load Limitations............................................................................................................. 427.1 General....................................................................................................................................................427.2 Definitions...............................................................................................................................................427.3 Procedure for preparation of Hold Mass Diagrams ...............................................................................437.4 Hold mass diagrams................................................................................................................................497.5 Local Tank Top Loading ........................................................................................................................54

8. Wave Torsion Induced Stresses ......................................................................................................... 578.1 General....................................................................................................................................................57

9. Shear Force Correction ....................................................................................................................... 579.1 General....................................................................................................................................................579.2 Definitions...............................................................................................................................................579.3 Rule Requirement ...................................................................................................................................579.4 Allowable Shear Force............................................................................................................................589.5 Corrected Shear Force.............................................................................................................................59

Appendix A.Checklist for Finite Element Analysis .......................................................................................................... 62

Appendix B.Beam Modelling.............................................................................................................................................. 65



Sec.1. General –

1. General

1.1 Introduction

1.1.1 This Classification Note covers only the strength analysis of hull structure in non CSR bulk carriers. Forbulk carriers with CSR notation, the strength analysis of hull structure is covered in Rules Pt.8 Ch.2.

This Classification Note is applicable for ships with class notation HC-A, HC-B, HC-C and HC-B.

For ships with class notation HC-M, design load cases are given in Rules Pt.5 Ch.2 Sec.5 Table C1 based onthe ships’ loading manual. For application of sea pressure load, cargo load and hold mass diagrams, relevantparts of this Classification Note may be applied.

1.1.2 The “Rules for Classification of Ships” require a direct structural analysis to be carried out in order tocope with the complexity in the loading of bulk carriers and the many possible loading conditions. The scopefor the analysis is to verify that stresses in the girder structure are within specified limits when the structure isloaded in accordance with the specified design load conditions.

1.1.3 The structural analysis is generally related to primary strength members of the midship region of bulkcarriers arranged with double bottom and single or double side. However, additional calculations may have tobe carried out for fore- and aftmost holds as the hopper/top wing tank construction normally is changedsignificantly compared to the midship construction.

1.1.4 Where in the text it is referred to the Rules, the references refer to the July 2011 edition of “Rules forClassification of Ships”.

1.1.5 Any recognised calculation method or computer program may be applied provided the effects ofbending, shear axial and torsion deformations are considered when relevant.

1.1.6 Strength analysis carried out in accordance with the procedure outlined in the Classification Note willnormally be accepted as basis for class approval.

Nauticus Hull is a computer program offered by DNV that is suitable for the calculations specified in thisClassification Note.

1.2 Bulk Carriers

1.2.1 Bulk carriers are ships designed primarily for the transportation of solid bulk cargoes. Such cargoes aregenerally uniform in composition, and are loaded directly into the cargo space without any intermediate formof containment. The range of cargoes carried in bulk carriers is considerable. Leading bulk cargoes in the worldtrade are iron ore, coal, grain, bauxite/alumina and phosphate rock, along with substantial quantities ofconcentrates, petroleum coke, steel, ores, cement, sugar, quarts, salt, fertilisers, sulphur, scrap, aggregates andforestry products. Further, the receivers of bulk cargoes have very varied requirements for tonnage deliveredper month or per year. The size of vessels that they choose to carry their cargoes and the frequency that suchvessels are employed will be influenced by a variety of factors, including the receivers’ storage capacity, depthof water in the berth, regularity of the demand for the commodity and the financing of its purchase. This largevariety in demand and the variety in pattern of international trade have created a versatile world fleet of veryvaried ship sizes. These may be categorised as follows:

Handy-size bulkers: This is the most common size of bulk carriers with a deadweight of 25 000 to 35 000 tonnesand a draught less than 11.5 m. The handy-sized bulker is so called because her comparatively modestdimensions permit her to enter a considerable number of ports, world-wide. Such vessels are used in manytrades in which the loading or discharging port imposes a restriction upon the vessel’s size, or where thequantity of cargo to be transported requires only a ship able to carry 35 000 tonnes or less.

Handymax bulkers: The trend is for each category of bulker to increase in size, and some commentators nowconsider the larger handy-sized bulkers, in the 35 000 to 50 000 tonnes range, to be a separate category, thehandy-max bulker.

Panamax bulkers: Larger than the handy-sized vessel is the Panamax bulk carrier, so named because she isdesigned to the maximum dimensions (particularly the maximum breadth) which can pass through the PanamaCanal. The limiting dimensions for canal transit are Loa 289.5 m, extreme breadth 32.2 m and maximumdraught 12.04 m. The typical tonnage range is 50 000 to 100 000 tonnes. Panamax bulkers are extensivelyemployed in the transport of large volume bulk cargoes such as coal, grain, bauxite and iron ore in the long haultrades.

Cape-sized bulkers: Cape-sized bulk carriers have dead weights in the range of 100 000 to 180 000 tonnes.While most lie within the range of 100 000 to 140 000 tonnes, new-building in recent years have been



Sec.1. General –

concentrated in the 140 000 to 180 000 tonnes range. Cape-sized vessels, with loaded draughts usually in excessof 17 m can be accepted fully laden at only a small number of ports world-wide and are engaged in the longhaul iron ore and coal trades. The range of ports which they visit is increased by the use of two port discharges,the ship being only part laden on reaching the second discharge port.

Very Large Bulk Carriers (VLBCs): VLBCs are bulkers greater than 180 000 tonnes dead weight. These aremainly employed on the Brazil/Europe and the Australia/Japan routes.

1.2.2 In light of the variety both in cargoes, vessel size, hold arrangement and not least the trading routes,including multi port loading and discharging it is evident that the masters and officers of such vessels, will bein great need of information about relevant loading limitations of the vessel, such as:

— maximum allowable/minimum required mass in each individual hold as a function of draught— maximum allowable/minimum required mass in two (or more) adjacent holds. i.e. block loading as a

function of draught— maximum allowable mass on deck and hatch cover loading— allowable container loading arrangement both in holds and on deck/hatch cover— maximum allowable tank top pressure (steel coil loading)— still water bending moment and shear force limitations— still water torsion moment limitations.

In Sec.1.2.3 and 1.2.4 the most important local load limitations and those most frequently not adhered to havebeen highlighted.

1.2.3 In order to exemplify the need for information about limitations related to the maximum allowable massin each individual hold we have described below two situations in which the master may decide to place anexcessive tonnage of cargo in a particular hold.

— Many bulk carriers load iron ore in ports, which are located within the tropical zone (Brazil, Australia, WestAfrica, India). When such vessels are loaded to tropical marks, and take only small quantities of bunkers,the total cargo tonnage carried will be substantially (5 to 10%) larger than the standard loading shown inthe loading manual. In this situation each alternately loaded hold is likely to be overloaded by tonnageapproaching 5 to 10%.

— When a ship is asked to load two or more different grades or consignments of ore (e.g. fines and pellets) itis sometimes necessary to juggle with the quantities in each hold, to take account of draught, trim andlongitudinal strength at each stage in the voyage. In these circumstances it is easy to decide to load anexcessive tonnage in one or several holds, if the maximum permitted tonnage is not prominently displayedand well known aboard ship.

1.2.4 In recent years there has been reported structural damages in which there are reason to believe thatincorrect adjacent hold loading, (block loading), has caused such structural damages. The reason for such mal-operation is not easy to explain exactly; however, below we have indicated some arguments which should besufficient to justify the need for proper instruction for such load limitations.

— there are reasons to believe that the vast majority of ship operators and ships’ personnel are completelyunaware that adjacent hold loading (block loading) can cause problems

— a ship can be incorrectly block loaded without creating excessive hull girder shear forces or bendingmoments, so there is normally no evidence to warn the ship’s officer that his loading may cause damage

— adjacent hold loading (block loading) is likely to be considered as a method of loading when several gradesof ore are to be loaded, or several consignments of cargo carried, and has recently been used increasingly,for a third reason.

In order to cope with the above need for information a procedure for calculating the necessary cargo hold loadlimitations is given in Sec.7.

1.3 ProcedureThis classification note describes methods for performing calculations with respect to structural strength ofbulk carriers with conventional design. The calculations are based on requirements given in Rules forClassification of Ships. For vessels with notation NAUTICUS(Newbuilding), it is required that FEM analysisis carried out, while for other vessels beam analysis may be acceptable. The flow chart in Fig.1-1 gives anoverview of the applicable chapters depending on the method of calculation.

The chapters are briefly described in the following:

Sec.2. Design Loads, gives description or references to the applicable local loads, like sea pressure and pressurefrom cargo.

Sec.3. Loading Conditions, gives a description of applicable loading conditions. The conditions described in



Sec.1. General –

detail here are normally covering all relevant conditions for a typical design of bulk carriers. Some conditionsrepresent the Rule minimum loading while others represent the extreme loading conditions as defined in theloading manual. Steel coil loading and container loading are to be evaluated separately.

Sec.4. Cargo Hold Analysis, gives a description of an acceptable procedure for Finite Element Analysis for bulkcarriers. It is here focused on extent of model, the structure that shall be included, boundary conditions, meshtopology and results that shall be evaluated.

Sec.5. Local Structure, Analysis gives a description of how to perform Finite Element Analysis of localstructures of bulk carriers.

Sec.6. Flooding Conditions, gives a description of additional requirements for vessels where this is applicable.These requirements ascribe from unified rules given by IACS (International Association of ClassificationSocieties) and are applicable to bulk carriers above 150 meters carrying heavy cargoes with density above 1.0ton/m3, according to Rules Pt.5 Ch.2 Sec.5 Table A3.

Figure 1-1Flowchart of applicable sections in this Classification Note depending of calculation method

Sec.7. Cargo Hold Limitations, gives a procedure for preparation of local load diagrams for individual holdsand for any two adjacent holds. Such limitations do generally define maximum allowable and minimumrequired mass as a function of the vessel draught.

Sec.8. Wave Torsion induced Bending Stresses gives a method to calculate torsion induced stresses.

Sec.9. Shear force correction, describes the method and background for shear force corrections.

Appendix A, Checklist for FE Analysis, gives checklists related to modelling of Finite Element Models. Thechecklists are suitable for verification of the model.

Appendix B, Beam Modelling, gives a description of acceptable methods for performing structural strengthcalculations by use of 2- or 3-dimensional beam models for bulk carriers.

1.4 Definitions

1.4.1 Symbols not mentioned in the following list are given in connection with relevant formulae. The generalsymbols may be repeated when additional definition is found necessary in connection with specific formulae.

L = Rule length in m. *B = Rule moulded breadth in m. *

Finite element analysis Beam analysis

Sec.2Design loads

Sec.3Load conditions

Sec.4Cargo hold analysis

Sec.5Local structure analysis

Sec.6Flooding conditions

Sec.7Cargo hold load limitations

Sec.8Torsional stress calculations

Sec.9Shear force correction

Appendix BBeam modelling general

Floodingcalculations

required

Yes

No

Finite element analysis Beam analysis

Sec.2Design loads

Sec.3Load conditions

Sec.4Cargo hold analysis

Sec.5Local structure analysis

Sec.6Flooding conditions

Sec.7Cargo hold load limitations

Sec.8Torsional stress calculations

Sec.9Shear force correction

Appendix BBeam modelling general

Floodingcalculations

required

Yes

No



Sec.1. General –

D = Rule moulded depth in m. *T = Mean moulded summer draught in m. *CB = Block coefficient. *V = Maximum service speed in knots on draught T.h = Cargo or ballast head in m.hdb = Height of double bottom in m.E = Modulus of elasticity = 2.06·105 N/mm2 for steel.go = Acceleration of gravity. go = 9.81 m/s2.Cw = Wave coefficient. **av = Combined vertical acceleration in m/s2. **at = Combined transverse acceleration in m/s2. **σ = Normal stress.τ = Shear stress.

* For details see the Rules for Classification of Ships Pt.3 Ch.1 Sec.1.

** For details see the Rules for Classification of Ships Pt.3 Ch.1 Sec.4B.

= as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 C.ρ, δ



Sec.1. General –

1.4.2 The structural terminology adopted in this Note is illustrated in Fig.1-2, showing a typical structuralarrangement of a bulk carrier in the midship area.

Figure 1-2Typical nomenclature for bulk carrier sections in way of cargo hold and transverse bulkhead

Top wing tankwebframe

Hopper sidewebframe

Double bottomfloor

Keel plateDouble

bottom tank

Bottom plating

Bottomlongitudinal

Side plating

Double bottomlongitudinal girder

Inner bottomplating

Inner bottomlongitudinal

Hopper tank slopingplating longitudinal

Hopper tanksloping plating

Bilgeplating

Sidelongitudinal

CARGO HOLD

Top wing tank slopingplating longitudial

Top wing tanksloping plating

Sidelongitudinal

Top wingtank

Strength decklongitudinal

Strength deckplating

Hatch coaming

Top wing tank platingvertical strake

Main frame

Hopper tank

Bilgelongitudinal

Cross deck structureHatch and coaming

Hatch and beam

Upper stool bottom plate

Corrugated transversebulkhead

Cross deckstructuretransverse beam

Cross deck structurecantilever beam

Shedder plate

Lower stooldiaphragm

Bottom stool top plate

Lower stool

Inner bottom

Double bottomlongitudinalgirder

Upper stool



Sec.2. Design Loads –

2. Design Loads

2.1 General

2.1.1 Design pressure loads applied in direct calculations representing external sea pressure, liquid in tanksand cargo in holds, are to be taken as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12. Loadsfrom cargo in holds are further specified in 2.2 to 2.3 in the following.

2.2 Bulk cargo filling part of hold (heavy cargo)

2.2.1 Design pressure: The design lateral pressures with bulk cargo filling partly of hold are in accordancewith Rules for Classification of Ships Pt.3 Ch.1 Sec.12 and shall be taken as:

P = ρ (go + 0.5av) K hc (kN/m2)K = sin2α tan2(45 − 0.5 δ) + cos2α, minimum cos α α = Angle between panel in question and the horizontal plane in degrees.δ = Angle of repose. In general to be taken as 20° for light bulk cargo (grain etc.), 25° for cement cargo

(associated cargo density 1.3 t/m3) and 35° for heavy bulk cargo (associated cargo density ≥ 1.78 t/m3). Otherwise it is to be taken as 30°.

hc = Assumed height of cargo surface above the inner bottom in hold, see the Rules for Classification ofShips Pt.5 Ch.2 Sec.5, see also Fig.2-1. For bulk carriers, it is to be taken as 0.3 H + 0.14 bf within60% of the middle length and breadth of hold, and linearly reduced to a level 0.3 H at hold sides andto 0.3 H + 0.07 bf at transverse bulkheads.

H = Height of hold (including hatchway) above plane part of inner bottom in m bf = Breadth of hold in m at level 0.3 H above inner bottom at hold midlength.ρ = M / VHR, as given in Pt.5 Ch.2 Sec.5 B104.M = Mass of cargo in hold, in (t), in accordance with the Rules for Classification of Ships Pt.5 Ch.2 Sec.5.VHR = Volume of cargo hold below the level of hc. Specially for conventional bulk carriers, it may be taken

as V0.3H + 0.10267 bf2 lh for regularly shaped cargo holds. For irregularly shaped holds, VHR may be

specially considered.V0.3H = Volume of hold in m3 below level 0.3 H above inner bottom.lh = Length of hold above lower stool in m, measured to the middle of corrugation depth.

See also Fig.2-1.

Figure 2-1Cargo distribution filling part of cargo hold of bulk carriers

H

0.3 H

lh

0.6 bf

0.6 lh

bf

hc

hc

0.14 bf

0.07 bf



Sec.2. Design Loads –

2.2.2 Shear load: A design shear load, ps, has been added in order to obtain the correct total downward forcein way of sloping elements i.e. transverse bulkhead stools and hopper tank construction, corresponding to thecargo mass, see also Fig.2-2. The shear load, ps acting on sloping parts of bulkheads is to be taken as:

ρ, α, K, hc = as given in 2.2.1.

Figure 2-2Cargo shear load on sloping elements

2.3 Bulk cargo expanded to fill hold

2.3.1 Design pressure: The below pressure distribution assumes that the hold is filled completely up to the topof hatch coaming with bulk cargo. The mass in the hold is then expanded giving a different definition of hccompared with Ch 2.2. The design lateral pressures are to be taken as:

p = ρ (go + 0.5av) K hc (kN/m2)K = As defined in Sec.2.2.1.hc = Vertical distance in m from the load point to the highest point of the hold including hatchway in general.

For sloping hopper, lower stool, bulkhead and shipside plating the distance may be measured to the decklevel only, unless the hatch coaming is in line with or close to the panel considered. (Note that slopinghopper, lower stool, bulkhead and shipside may be taken to be close to the hatch coaming when it is lessthan 10° out of line from the vertical when measured from the deck, see also Fig.2-3.) Pressure onoverhang structure like sloping topwing tank and upper stool may be disregarded.

ρ = M/VH, as given in Pt.5 Ch.2 Sec.5 B104.M = Mass of cargo in hold (t). Defined as the mass, according to the loading manual, combined with the

corresponding angle of repose that gives the largest nominal lateral pressure on the bulkhead. This isexpressed by the largest effective lateral mass, ME, where ME = M tan2 (45 – 0.5δ). ME is not to be lessthan 0.43 VH, which correspond to a cargo density of 0.88 t/m3 and an angle of repose of 20°. Ref theRules for Classification of Ships Pt.5 Ch.2 Sec.5 B104 and B203.

VH = Cargo hold volume including hatch in m3.

ps ρ go 0.5av+( ) 1 K–( )hc

αtan----------------------- kN m

2⁄( )=

Ps2

Ps1Ps1

2

1

2Ps2



Sec.3. Design Loading Conditions – Local Strength –

Figure 2-3Design load pressure height for cargo bulkhead

2.3.2 Design shear load: The design shear load, ps, described in 2.2.2, is to be applied for sloping parts ofbulkheads.

3. Design Loading Conditions – Local Strength

3.1 General

3.1.1 The following definitions apply:

TDAM = damaged water line (m) from damage stability calculations. May be assumed equal to ship’s mouldeddepth D.

TLB = shallowest ballast draught (m) in all seagoing loading conditions. Other definitions refer to Ch 7.2.

3.2 Summary for Bulk Carriers

3.2.1 Table 3-1 and 3-2, lists applicable design loading conditions given in the Rules Pt.5 Ch.2 Sec.5 withindication regarding their applicability with respect to typical class notations, structural part and analysis.

These design loading conditions are normally covering all relevant loading conditions for a typical bulk carrierdesign. The design loading conditions cover the Rule “minimum conditions” in which the intention is to ensuresufficient operational flexibility of the vessel, independent of the specified loading conditions. The loadingmanual may, however, specify loading conditions for the vessel in question, which are not represented in Table3-2, such as steel coils, container, lumber, non homogenous loading etc. It is therefore of outmost importancethat the loading manual is carefully reviewed prior to defining the final design loading conditions.

3.2.2 Flooding conditions applicable for vessels as described in Sec.1.3, are additionally described in Sec.6.The structure is in general not dimensioned by direct calculations for such conditions.

hh

10o

Load points




3.2.3 Design loading conditions are further explained in Sec.3.3.

Table 3-1 Applicable design loading conditions for bulk carriers

LCClass notations

HC-A HC-B HC-C HC-A No MP HC-B No MP HC-C No MP HC-B*

1 X X X - - - -2 X X X - - - -3a X 1) - - X 1) - - -3b X 2) - - X 2) - - -4 - - - - - - X5 - - - X X X -6a X 1) - - X 1) - - -6b and 6c X 2) - - X 2) X X -7 X X X - - - X8 X 3) - - X 3) - - -9 - - - X X X -10 X X X - - - X11 - - - X X X -12 X X X X X X X13 X 4) X 4) X 4) X 4) X 4) X 4) X 4)

14 X 4) X 4) X 4) X 4) X 4) X 4) X 4)

15 X X X X X X X16 X X X X X X X17 X X X X X X X18 X X X X X X XX: Applicable -: Not applicable

1) applicable to ore holds only

2) applicable to empty holds only

3) applicable only when block loading specified in loading manual. Ref. Sec.7.2

4) applicable only when cargo hold(s) is/are designed for ballast in seagoing conditions

Table 3-2 Design loading conditions for bulk carriersExplanation of illustrations shown in Table 3-2:

1. Double bottom tanks: If fuel oil tanks - fullIf water ballast tanks - empty

If fuel oil tanks - fullIf water ballast tanks - full

2. Cargo holds:




Description Application Draught Illustration1 Multiport Condi-

tion – Any Single HoldLoaded

Double bottom struc-tureMainframes

0.67 T

2 Multiport Condi-tion – Any Single HoldEmpty


0.83 T

3 HC-A Condition –Loading Condition with Specified Holds Empty


T a)

b)

4 HC-B* Condition–Any Single HoldEmpty or Loaded


0.67T and T

a)

b)

5 No MP Condition Double bottom struc-tureMainframes

T a)

b)

Table 3-2 Design loading conditions for bulk carriers (Continued)

0.67T M

0.83T MFULL

T MHD + 0.1MH

MHD+0.1MH

0.67T

1.2MFULL

T 1.2 MFULL




6 Harbour Condition Double bottom struc-tureMainframes

0.67 T a)

b)

c)

7 Multiport and HC-B* Condition – Adjacent Holds Loaded

Compression of transverse deckTransverse bulkheads

0.67 T

8 HC-A Condition – Adjacent Holds Loaded


T

9 No MP Harbour Condition – Adjacent Holds Loaded


0.67 T

10 Multiport and HC-B* Condition – Adjacent Holds Empty

Transverse bulkhead.Tensile strength of cross deck

0.75 T

11 No MP Condition – Adjacent Holds Empty

Transverse bulkheadTop wing tank

THB

12 Bulk Cargo With Filled Hold

Transverse bulkhead lateral strength

T


0.67T MHD

0.67T M

T MHD + 0.1 MH

0.67T MFULL

0.75TMFULL

THB

MFULL

T




3.3 Design Loading Conditions for Bulk Carriers

3.3.1 LC1 – Multiport Condition – Single Hold Loaded

3.3.1.1 LC1 is applicable for class notations HC-A, HC-B, and HC-C.

3.3.1.2 Any cargo hold is to be capable of carrying M at 67% of maximum draught (0.67T), where,

M = MFULL (in loaded hold)

3.3.1.3 Fuel oil tanks in double bottom in way of the loaded cargo hold, if any are to be full, and ballast water tanks inthe double bottom in way of the loaded cargo hold are to be empty. All double bottom tanks in way of the emptycargo hold are to be empty.

3.3.1.4 The cargo mass and sea pressure load is to be in accordance with Sec.2.1 and Sec.2.2, with density ρ=M/VHR.

13 Heavy Ballast Condition

Transverse bulkheadTop wing tank

THB

14 Heavy Ballast – Heeled Condition

Hopper tank girdersTop wing tank

THB

15 Ballast inTop Wing Tank

Top wing tank construction

THB

16 Ballast in Top Wing Tank – Heeled Condition

Top wing tank construction

THB

17 Watertight Bulk-head Loading

Transverse bulkhead lateral strength

TDAM

18 Cargo on Deck Top wing tank, cross deck cantilevers, hatch end and side coamings

T 1)

Note:1) When load restriction on upper deck in the loading manual is clearly specified, the actual draught for the correspond-ing loading condition may be used instead of the scantling draught T.


THB

THB

THB

THB

TDAM




3.3.1.5 This loading condition is applied primarily for the strength evaluation of the double bottom structure. Note thatthe double bottom strength shall be evaluated on the basis of allowable hull girder still water bending moment.It may however also be decisive for the side frame ends, if rotation of hopper/top wing tank constructionbecomes significant.

3.3.2 LC2 –Multiport Condition – Single Hold Empty

3.3.2.1 LC2 is applicable for class notations HC-A, HC-B and HC-C.

3.3.2.2 Any cargo hold is to be capable of being empty, with the next cargo holds carrying M, at 83% of maximumdraught (0.83 T), where,



3.3.2.4 The cargo mass and sea pressure load is to be in accordance with Sec.2.1 and Sec.2.2, with density ρ = M/VHR.


3.3.3 LC3 – HC-A Condition

3.3.3.1 LC3 is applicable for class notations HC-A and HC-A No MP, and is to cover a loading condition with specifiedholds empty. In LC3a, the midhold is ore hold. In LC3b, the midhold is empty hold.

3.3.3.2 In LC3a, ore holds, are to be capable of carrying M at maximum draught (T), and in LC3b, empty holds are tobe capable of being empty with the next cargo holds carrying M, where,

M = MHD + 0.1MH (in loaded hold)



3.3.3.5 A specified reduced allowable hull girder still water bending moment may be applied for the alternative loadingcondition with empty holds. The limit is defined by the maximum bending moment in hogging and sagging (= 0.5 MSO as given in Pt.3 Ch.1 Sec.5 B), minimum occurrence for these loading conditions, unless higherlimits are specified to be used.





3.3.4 LC4 – HC-B* Condition

3.3.4.1 LC4a and LC4b are applicable for class notations HC-B*.

3.3.4.2 In LC4a, any cargo hold is to be capable of carrying M at 67% of maximum draught (0.67T), where,

M = 1.2MFULL (in loaded hold)

In LC4b, any cargo hold is to be capable of being empty with the next cargo holds carrying M, at maximumdraught (T), where,

M = 1.2MFULL (in loaded hold)




3.3.5 LC5 – No MP Condition

3.3.5.1 LC5a and LC5b are applicable for the class notations HC-A No MP, HC-B No MP and HC-C No MP, i.e. vesselswhich have not been designed for loading and unloading in multiple ports.

3.3.5.2 Any single cargo hold is to be capable of carrying M at maximum draught (T), where

M = MFULL (in full hold)

and the less of

M = 0.5 MH (in slack hold) = 1.025 l b (T - THB) (in slack hold)




3.3.6 LC6 – Harbour Condition

3.3.6.1 LC6a is applicable for class notation HC-A and HC-A No MP. The midhold is ore hold.

LC6b and LC6c are applicable for class notations HC-A No MP, HC-B No MP and HC-C No MP, i.e. vesselswhich have not been designed for loading and unloading in multiple ports.




3.3.6.2 For HC-A and HC-A No MP notations, LC6a, any single cargo hold is to be capable of carrying maximumallowable seagoing mass M at 67% of maximum draught (0.67 T) where

M = MHD (in loaded hold)and for HC-A No MP, HC-B No MP and HC-C No MP notations, LC6b and LC6c, where

M = MFULL (in loaded hold)and the lesser of

M = 0.5 MH − 1.025 l b 0.33 T − 0.15 MFULL (in slack hold) = 1.025 l b (0.67 T − THB) − 0.15 MFULL (in slack hold) = minimum 0


3.3.6.4 The cargo mass and sea pressure load is to be in accordance with Sec.2.1 and Sec.2.2 without dynamic values,with density ρ = M/VHR.


3.3.7 LC7 – Multiport and HC-B* Condition – Adjacent Holds Loaded

3.3.7.1 LC7 is applicable for class notations HC-A, HC-B, HC-C and HC-B*.

3.3.7.2 Any two adjacent cargo holds are to be capable of carrying M at 67% of maximum draught (0.67 T), where,

M = MFULL (in loaded hold for HC-A, HC-B and HC-C) = 1.1 MFULL (in loaded hold for HC-B*)


3.3.7.4 The cargo mass and sea pressure load in any cargo hold is to be in accordance with Sec.2.1 and Sec.2.2, withdensity ρ = M/VHR.

3.3.7.5 This loading condition is applied primarily for the compression strength of the transverse deck structurebetween hatches and for the shear strength of the transverse bulkheads. Note that the double bottom strengthshall be evaluated on the basis of allowable hull girder still water bending moment.

3.3.8 LC8 – HC-A Condition – Adjacent Holds Loaded

3.3.8.1 LC8 is applicable for class notation HC-A and HC-A No MP, if two adjacent cargo holds, which according toa design loading condition may be loaded with the next hold being empty.

3.3.8.2 Any two adjacent cargo holds are to be capable of carrying 10% of MH in each hold in addition to the maximumcargo load according to that design loading condition, at maximum draught (T), where,

M = based on MHD, adj + 0.1MH, adj (in loaded hold,)





3.3.8.4 The cargo mass and sea pressure load in any cargo hold is to be in accordance with Sec.2.1 and Sec.2.2, withdensity ρ = M/VHR.

3.3.8.5 This loading condition is applied primarily for the compression strength of the transverse deck structurebetween the hatches and for the shear strength of the transverse bulkheads. Note that the double bottom strengthshall be evaluated on the basis of allowable hull girder still water bending moment.

3.3.9 LC9 – No MP Harbour Condition – Adjacent Holds Loaded

3.3.9.1 LC9 is applicable for class notations HC-A No MP, HC-B No MP and HC-C No MP, i.e. vessels which have notbeen designed for loading and unloading in multiple ports.

3.3.9.2 Any two adjacent cargo holds are to be capable of carrying MFULL at 67% of maximum draught (0.67 T),where,



3.3.9.4 The cargo mass and sea pressure load is to be in accordance with Sec.2.1 and Sec.2.2 without dynamic values,with density ρ = M/VHR.

3.3.9.5 This loading condition is applied primarily for the compression strength of the transverse deck structurebetween hatches and for the shear strength of the transverse bulkheads. Note that the double bottom strengthshall be evaluated on the basis of allowable hull girder still water bending moment.

3.3.10 LC10 – Multiport and HC-B* Condition – Adjacent Holds Empty

3.3.10.1 LC10 is applicable for class notations HC-A, HC-B, HC-C, and HC-B*.

3.3.10.2 Any two adjacent cargo holds are to be capable of being empty at 75% of maximum draught (0.75 T), where,



3.3.10.4 The cargo mass and sea pressure load is to be in accordance with Sec.2.1, Sec.2.2, with density ρ=M/VHR.

3.3.10.5 This loading condition is applied primarily for the tensile strength of the cross deck between the hatches andfor the shear strength of the transverse bulkheads. Note that the double bottom strength shall be evaluated onthe basis of allowable hull girder still water bending moment.




3.3.11 LC11 – No MP Condition – Adjacent Holds Empty

3.3.11.1 LC11 is applicable for class notations HC-A No MP, HC-B No MP and HC-C No MP, i.e. vessels which havenot been designed for loading and unloading in multiple ports.

3.3.11.2 Any two adjacent cargo holds are to be capable of being empty at deepest ballast draught (THB), where,



3.3.11.4 The sea pressure load is to be in accordance with Sec.2.1 and Sec.2.2, with density ρ = M/VHR.

3.3.11.5 This loading condition is applied primarily for the tensile strength of the cross deck between the hatches andfor the shear strength of the transverse bulkheads. Note that the double bottom strength shall be evaluated onthe basis of allowable hull girder still water bending moment.

3.3.12 LC12 – Bulk Cargo With Filled Hold Condition

3.3.12.1 LC12 is applicable to all bulk carriers.

3.3.12.2 Any transverse bulkhead is to be capable of withstand lateral pressure due to M, where,

M = MHD + 0.1MH (HC-A) = MFULL (HC-B or HC-C) = 1.2MFULL (HC-B*)

3.3.12.3 The cargo pressure is to be taken according to Sec.2.3 and the sea pressure according to Sec.2.1. The draughtis to be taken at maximum draught (T).

3.3.12.4 The load condition is applicable primarily for the transverse bulkhead structure including stool diaphragmplates and in-line shear plates inside double bottom and for local design of the hopper tank.

3.3.13 LC13 – Heavy Ballast Condition

3.3.13.1 LC13 shall be considered if ballast in holds has been specified for the vessel.

3.3.13.2 Cargo holds, which are designed as ballast holds, are to be capable of being full of ballast water includinghatchways, with all double bottom tanks being filled, at heavy ballast draught (THB). If data for the ballastdraught are not available, the draught may be taken as 0.45T.

3.3.13.3 The ballast and sea pressure load is to be in accordance with Sec.2.1. Load from ballast pressure acting on thehatch cover shall be included as appropriate.

3.3.13.4 This loading condition is applied primarily for the strength evaluation of the transverse bulkhead and for hopperand top wing tank structures, in addition to the double bottom structure of the ballast hold. Note that the doublebottom strength shall be evaluated on the basis of allowable hull girder still water bending moment.




3.3.14 LC14 – Heavy Ballast – Heeled Condition

3.3.14.1 LC14 is similar to LC13, and shall be considered if ballast in holds has been specified for the vessel.

3.3.14.2 The ballast and sea pressure load is to be taken according to the Rules Pt.3 Ch.1 Sec.12 for heeled condition.Load from ballast pressure acting on the hatch cover shall be included as appropriate.

3.3.14.3 This loading condition is applied primarily for the top wing tank structure adjacent to the ballast hold, sidestructure and local scantlings of the transverse bulkhead.

3.3.15 LC15 – Ballast in Top Wing Tank

3.3.15.1 LC15 is applicable for bulk carriers with top wing tank.

3.3.15.2 Top wing tanks are to be filled, with adjacent top wing tanks being empty; draught may be taken according tothe heavy ballast draught (THB) when considered relevant.

3.3.15.3 The sea pressure loads may normally be disregarded in this condition, but the ballast pressure load is to be takenin accordance with Sec.2.1.

3.3.15.4 The intention of this condition is to check the top wing tank structure only. Consequently, application of arealistic pressure distribution on the double bottom construction is not necessary.

3.3.16 LC16 – Ballast in Top Wing Tank – Heeled Condition

3.3.16.1 LC16 is similar to LC15, and is applicable for bulk carriers with top wing tank.

3.3.16.2 The ballast pressure load is to be taken according to the Rules Pt.3.Ch.1 Sec.12 for heeled condition.

3.3.16.3 The intention of this condition is to check the top wing tank structure only. Consequently, application of arealistic pressure distribution on the double bottom construction is not necessary.

3.3.17 LC17 – Watertight Bulkhead Loading

3.3.17.1 LC17 is intended to ensure that the watertight subdivision is maintained in case of an emergency flooding.

3.3.17.2 Flooded sea water load is to be according to the Rules, Pt.3 Ch.1 Sec.9 B, with filling of the hold up to thedamaged waterline.

3.3.17.3 The sea pressure load may be taken at a draught equal to the damaged waterline, TDAM. Further design criteriaare given in the Rules, Pt.3 Ch.1 Sec.9.

3.3.17.4 This loading condition is generally applicable for watertight bulkhead structures including stool diaphragmplates and in-line shear plates inside double bottom.

3.3.18 LC18 – Cargo on Deck

3.3.18.1 LC18 is applicable for bulk carriers with a distinct top wing tank arrangement, where a deck cargo loadingcapacity has been specified.




3.3.18.2 Forces due to specified cargo load on hatches should be included in the consideration, ref. Rules Pt.3 Ch.1 Sec.4 C.

3.3.18.3 The sea pressure load is to be in accordance with Sec.2.1, at full draught (T). When load restriction on upperdeck in the loading manual is clearly specified, the actual draught for the corresponding loading condition maybe used instead of the scantling draught T.

3.4 Fatigue Loads

3.4.1 In order to include stresses caused by relative deflection in the fatigue assessment of longitudinals, dynamicload cases as specified in Table 3-3 are to be applied to the cargo hold model for bulk carriers. The results fromthese load cases may also be used for fatigue assessment of other structural parts e.g. hopper knuckles.

The external and internal dynamic pressures are to be calculated according to Classification Note 30.7 “FatigueAssessment of Ship Structures”.

It is emphasised that this is pure dynamic load cases for evaluation of the structures fatigue life. The static partis therefore not included in this chapter. However, static load cases for alternate full load sea, homogeneousfull load sea and ballast sea as applicable shall be used to calculate the mean stress factor.

Further procedure for fatigue calculations is given in the Classification Note 30.7.

Table 3-3 Dynamic load cases for bulk carriersLC Description Draught External

pressureInternal pressure Illustration

F1 Alternate Full Load Sea

Full Dynamic -

F2 Alternate Full Load Sea

Full - Dynamic

F3 Homoge-nous Full Load Sea

Full Dynamic -

F4 Homoge-nous Full Load Sea

Full - Dynamic

F5 Ballast Sea Normal ballast

Dynamic -

F6 Ballast Sea Normal ballast

- Dynamic



Sec.4. Cargo Hold Analysis –

4. Cargo Hold Analysis

4.1 General

4.1.1 This chapter gives guidance on how to perform finite element calculations for the girder system withinthe midship area of bulk carriers.

4.1.2 In general the finite element model shall provide results suitable for evaluating the strength of the girdersystem and for performing buckling analysis of plate flanges and girder webs. This may be done by using a 3Dfinite element model of the midship area. Several approaches may be applied; ranging from a detailed 3D-model of the cargo holds to a coarse mesh 3D-model, supported by finer mesh sub models. Coarse mesh modelscan be used for calculating deformations and stresses typically suited for buckling control. The deformationsmay be applied as boundary conditions on sub models for finding the stress level in more detail.

The same principles may normally be used on structures outside the midship area but within the cargo area,provided special precautions are taken regarding model extent and boundary conditions.

4.1.3 Fig.4-1 shows a typical 3D-model of a conventional bulk carrier. Whichever approach is used, the modelor set of models applied shall give a proper presentation of the following structure:

— Typical web frames in hopper and top wing tanks or wing tanks, including floors and mainframes atmidhold in midship area

— Typical corrugation section of transverse bulkhead with connection to upper and lower stool— Transverse section in way of pipe duct in line with the lower transverse bulkhead stool side— Typical stringer in double side tanks or wing tanks— Typical longitudinal girder in double bottom.

In the model description and examples given in the following all these structures are included in one 3D-modelof the cargo hold for evaluating the results in these areas directly. This implies that the “cargo hold analysis”and “frame and girder analysis”, in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12 are combined intoone model.

4.1.4 In addition, analyses of local structure can be made for determining the detailed stress level in stiffenerssubject to large relative support deflections. Such analyses are described in Sec.5 “Local structure analysis”.

It is emphasised that this represents one acceptable approach for performing such calculations, and thatalternative methods may be equally applicable.

Figure 4-1Example of a 3D-model of a conventional bulk carrier

4.2 Model Extent

4.2.1 General: The extent of the model does in general depend on the structure and the loading conditions, andwhether these are symmetric in the longitudinal and transverse direction.

The extent of the recommended model is visualized in Table 4-1.

4.2.2 Transverse extent: Normally the structure is symmetric in the transverse direction while the load patternin the heeled condition, LC14, is not symmetric. This implies that a full breadth model should be made:




For vessels without symmetry about centreline with respect to structure or loads, the analysis model amidshipsshould comprise full breadth of the model.

However, even for the heeled condition a half breadth model may be satisfactory if due concern is shown toboundary conditions and their influence of the results in the structure. In the examples in the following, a fullbreadth model is applied.

4.2.3 Longitudinal extent: Often the transverse bulkheads with upper and lower stools stool are not symmetricin the longitudinal direction. In order to represent this correctly the model must have an extent including onefull length cargo hold:

For vessels without symmetry about the transverse bulkhead, the analysis model amidships should comprisetwo hold lengths (½ + 1 + ½).

For vessels with symmetry about the transverse bulkhead, the model may be limited to ½ + ½ hold models.

4.3 Modelling of geometry

4.3.1 General model idealisation: All main longitudinal and transverse geometry shall be included in themodel. The scantlings shall, according to the Rules for Classification of Ships, be modelled with reducedscantlings; i.e. corrosion addition according to the Rules for Classification of Ships shall be deducted from theactual scantlings.

When reduced effectivity of curved flanges is not represented by the model formulation itself, the reducedeffectivity shall be defined by assigning reduced thickness of plate elements or cross sectional areas of beamand rod elements. Such reduced effectivity may be calculated as given in the Rules for Classification of ShipsPt.3 Ch.1 Sec.3. Typical structures are:

— Curved plate flanges (e.g. bilge plating).— Curved face plates on hopper tank web frame and top wing tank web frame.

Half thicknesses shall be applied on plates in symmetry planes on the boundaries of the model.

4.3.2 GirdersFree flanges of girders shall be included in the model: In ship structures, openings in the girder webs will bepresent for access and pipe penetrations. If such cut-outs affect the overall force distribution or stiffness of thegirder, the cut-out shall be reflected in the model. This may be done by either; reducing the thickness accordingto the formula below or by geometrical modelling of the cut-out. The mean girder web thickness may for thefirst approach be taken as follows:

Figure 4-2Mean girder web thickness

tw = web thickness

rco =

hhcotw

tmean

Ico

tmean

h hco–

h rco----------------- tw=

11co

2

2.6 h hco–( )2--------------------------------+




lco = length of cut-out hco = height of cut-out h = height of girder web

When rco is larger than 1.2, (rco > 1.2), it is advised that the cut-out is included in the model in one of the twoways given above. When rco is larger than 2, (rco > 2), it is advised that the cut out is geometrically included inthe model.

Smaller openings for access and piping may be ignored. However, when such openings are ignored this mustbe considered when evaluating the results see Sec.4.8.2.

4.3.3 Stiffeners: Continuous stiffeners oriented in the direction of the girders contribute to the overall bendingstiffness of the girders and shall be included in the model in such a way that the bending stiffness of the girderis correctly modelled.

Non-continuous stiffeners may be included in the model as beam element with reduced effectivity. Sectionalarea of such stiffeners may be calculated as follows:

Stiffeners on girders perpendicular to the flanges may be included in the model when considered important,alternatively by transferring them to the nearest nodes instead of introducing additional nodes. Bucklingstiffeners considered less important for the stress distribution, as sniped buckling stiffeners, may be ignored.

4.3.4 Corrugated bulkhead and stools: Corrugated bulkheads shall be included in the model. Slanted plates(shedder plates) shall, if present, be included in the model as they transfer loads from the flange of thecorrugations to the opposite side of the stool.

Normally it is difficult to match the mesh from the corrugations directly with the mesh from the stool, so apractical approach is to adjust the mesh of the stools in to the corrugations. The corrugations will then havetheir true geometrical shape.

Diaphragms in the stools and vertical stiffeners on the stool side plating are to be included in the model.

It is proposed to use one or two 4-noded element over the depth of the corrugation web. This model formulationgives a good representation of the response of the corrugated bulkhead provided supporting brackets are fittedin line with the corrugations. Modelling of these brackets does normally not change the load transfer from thecorrugations to the stool significantly as the vertical flanges are well supported by the vertical or slanted stoolplate. Such brackets do therefore not have to be included in a cargo hold analysis due to the fact that finiteelements tends to transmit forces more than the real structure through the nodes sheared by the neighbouringelements.

The calculated response for designs without such brackets should however be adjusted to represent the reducedefficiency of the web. Alternatively, a model with a fine element mesh, or a separate evaluation, may be used.

4.3.5 Main frames, supporting brackets and connected longitudinals: The cargo hold model shall give a properrepresentation of deflection of mainframes. In order to achieve this, the mainframes, the supporting brackets inthe hopper tank and top wing tank and the connected longitudinals must be represented in the model. Apractical approach is to include all the mainframes in the model. In order to evaluate the mainframes,supporting bracket and connected longitudinals, in detail, a fine mesh model must be made.

4.3.6 Hatch coamings, hatch corners and hatches: The hatch coamings shall be included in the model. Whenit is necessary to evaluate the strength of hatch corners a separate fine meshed model must be made. Hatchcovers shall not be included in the model. Unless load conditions including torsional loading of the hull girderis included, the results in these areas will be limited to stress concentrations mainly caused by global hull girderforces. In such cases these forces must be applied to the model.

4.4 Elements and Mesh Size

4.4.1 General: The performance of the model is closely linked to the type-, shape- and aspect ratio of elements,and the mesh topology that is used. The mesh described here is adequate for representing the cargo hold modeland frame and girder model as defined in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12. The followingguidance on mesh size etc. is based on the assumption that 4-noded shell or membrane elements in combinationwith 2-noded beam or truss elements are used.

Sniped at both ends 30% of actual areaSniped at one end 70% of actual areaConnected at both ends 100% of actual area




Higher order elements such as 8-noded or 6-noded elements with a coarser mesh than described below may beused provided that the structure and the load distribution are properly described.

In general the mesh size should be decided on the basis of proper stiffness representation and load distributionof tank and sea pressure on shell- or membrane elements.

4.4.2 Plating: 4-noded shell or membrane elements may be used in connection with mesh size as describedbelow. 3-noded shell or membrane elements with constant strain shall normally not be used. It may howeverbe used to a limited extent for avoiding poor mesh transitions.

The element mesh should preferably represent the actual plate panels between stiffeners so that the stresses forthe control of yield and buckling strength can be read and averaged from the results without interpolation orextrapolation.

In practise, the following may be applied:

— there should be minimum three elements over the height of girders. The mesh should in general and as faras practical follow the stiffener system on the girder. For main frames, one element over the web height isacceptable. See Fig.4-3.

— one, two or three elements between transverse girders. By using three elements it normally matches withthe mainframes. Some local stiffener bending will be included in the results. See comments given inSec.4.8. Flanges on brackets shall not be connected to the plating, in order to simulate the snipped flangeat bracket toe. This applies also to main frame lower and upper end brackets. See Fig.4-4.

— one element between longitudinals. See Fig.4-3 and 4-4. This contributes to a correct load transfer from thelongitudinal to the transverse frame.

— inside hopper tank, top wing areas and wing tanks the mesh are normally limited by the longitudinals insurrounding structures. The mesh should follow the stiffener system on transverse girder webs as far aspracticable. The mesh should be fine enough to represent the shape of large openings in the web frameinside the hopper tank. See Fig.4-3 and 4-4.

— one element or more on each web and flange on the corrugations in corrugated bulkheads. Two elementsare suggested. This is satisfactory for determining the stress level in the bulkhead. An example of mesh oncorrugated bulkheads is shown in Fig.4-5. See also Sec.4.3.4.

Figure 4-3Mesh on transverse webframe of a bulk carrier




Figure 4-4Mesh on lower bracket of main frame in single side skin bulk carriers

Figure 4-5Mesh on corrugated transverse bulkhead of a bulk carrier

4.4.3 Longitudinals and stiffeners: Longitudinals and other continuous stiffeners should be included in themodel. These are preferably to be represented by 2-noded eccentric beam elements.

If the program used can not consider eccentricity of profiles, precautions shall be taken so that the model givesthe correct section modulus for double and single skin structures. However, axial area and shear area of suchstiffeners should only represent the profile without the plate flange.

Flange not to be connected to the plating




Figure 4-6Overlap of beam elements and shell elements

Special attention should be paid when connecting a beam element to one node of a shell or membrane element.The end of the beam elements may then be assumed as hinged in the calculation. This will affect the loaddistribution. The mentioned effect may be avoided by an overlap between the beam and shell elements. SeeFig.4-6.

Other stiffeners including buckling stiffeners and free flanges of girders may be modelled as 2-noded beam- ortruss elements with effective cross sectional areas calculated according to the Rules.

Curved flanges are to be represented with their true effectivity in the model.

Stiffeners inside stools may in general be represented by beam elements or alternatively by shell or membraneelements.

4.5 Boundary Conditions

4.5.1 Boundary conditions for the application of local loadSymmetric boundary conditions are in general to be applied at the ends of the model. If half breadth modelsare used, symmetry shall be applied along the centreline of the model.

The model may be supported in vertical direction by applying vertical springs in the vertical direction at theline forming the intersection between side and transverse bulkhead. Bulk carriers with double side shall beadditionally supported by vertical springs at the intersection between inner side and transverse bulkheads. Thespring constant may be calculated as follows, ignoring the effect of bending deflection:

ASi = shear area for side, inner side or longitudinal bulkheadlh = length of one cargo hold.Alternatively, vertical forces applied in the same intersections may be applied. The model must then berestrained from rigid body translation in the vertical direction.

Boundary conditions for the application of local loads for bulk carriers of ordinary design are given in Table4-1, applying symmetry conditions in one end and, symmetry and linear dependency in the other end. Theseboundary conditions introduce a horizontal force applied at one of the ends. The purpose of this force is tocompensate for the fictitious compression of the hull girder when the mid hold is empty and the holds fore andaft are full. In order to keep the nodes in “plane A” in one plane, the nodes must be linearly dependent in thelongitudinal direction of the point (point c) where the force is applied. The magnitude of the force will vary oneach load case but shall in general be equal to the net load on the transverse bulkhead.

Line C is defined as the intersection between the vertical part of the side shell and the transverse bulkhead. Pointa is the point of intersection between the bottom, centreline and transverse bulkhead.

As an alternative, boundary conditions with pure symmetry at the ends (Plane A also fixed in the longitudinaldirection) without a counteracting force may be applied. The longitudinal stresses should then be corrected forthe mentioned fictitious compression.

Beam element

Beam element

Lower stool

"Overlap

h

Si

l

EAK

38.7

8

⋅=




4.5.2 Boundary conditions for the application of hull girder loadsWhen hull girder loads, i.e. bending moment and shear forces, are intended applied to the model, it is advisedthat such loads are applied as separate load cases with separate boundary conditions. The resulting stresses maythen be manually superimposed to the relevant stresses from the local load model. The described boundaryconditions and load application are summarised in Table 4-2 and Table 4-3.

Bending moment - boundary conditions: One end should be restricted as shown in Table 4-2. The other endshould be kept plane and the displacements of the plane should be as a rigid body. The latter is necessary toapply the hull girder bending moment. In order to keep the nodes in one plane they are to be linearly dependentof each other as a rigid body.

Symmetry conditions along the centreline of the model are to be applied for models covering a half breadth ofthe ship.

Application of hull girder bending moment: In general a bending moment shall be applied to the end of themodel. The bending moment at the end may be applied as a force pair acting in the opposite direction appliedat two points. The points should be positioned vertically above each other with one point in the deck and onepoint in bottom. The size of the bending moment shall be such that the vertical hull girder bending moment, asdescribed in the Rules, is achieved in the middle of the model. Some modifications to the size of this bendingmoment are however necessary. The background for this is that the allowable hull girder bending moment (MS+ MW) is based on gross scantlings. The FEM model is based on net scantlings (gross scantling reduced by tk).It is therefore necessary to reduce the Hull girder bending moment by a factor of Zmod / Zgross. Where Zmod isthe hull girder section modulus as modelled (i.e gross scantling reduced by the corrosion addition, tk) andZgross, the hull girder section modulus based on actual scantlings. In addition to this bending moment the localloads will also set up a “semi-global hull girder bending moment” that may be compensated for when applyingthe bending moment. (It is advised that the loads are adjusted to match the acceptance criteria and not theopposite.)

The magnitude of the force pair will be as follows:

F = Magnitude of force at points in deck and bottomM = Modified bending moment as described aboveh = Height from base line to point in deck.

Table 4-1 Boundary conditions for an ordinary bulk carrier with unsymmetrical stool structureLocation Displacement Rotation

δx δy δz θx θy θzPlane A L - - - X XPlane B X - - - X XLine C SPoint a, b XPoint c FhX = Restricted from displacement or rotationL = Linearly dependant of point c- = FreeS = SpringsFV = Vertical forces. When vertical forces are

applied the model must in addition be restricted from translation in the vertical direction by fixing it in one node.

Fh = Counteracting horizontal force

Lin

e C

Lin

e C

Lin

e C

Lin

e C

zx

y

b

a

cFh

F Mh-----=




Shear force - boundary conditions: The boundary conditions are given in Table 4-3. Symmetrical boundaryconditions are to be applied at ends. Symmetry conditions along the centreline of the model are to be appliedfor models covering a half breadth of the ship. For models covering the full breadth of the ship the model mustbe fixed in the transverse direction at the intersections between the transverse bulkhead and the longitudinalcentreline girder at inner bottom.

Application of shear forces: The shear forces are to be applied at the outer shell at the ends of the model (LineC and F). The shear forces are to be applied as vertical line loads. The forces are to be distributed according toa shear flow calculation with the forces acting in opposite directions at the two ends as shown in Table 4-3. Themagnitude of the shear force shall be such that the maximum allowable shear force is achieved within themodel. Springs shall be applied at one end.

4.6 Loading Conditions

4.6.1 General: Normally the basic loading conditions as described in the Rules for Classification of Ships Pt.5Ch.2 of the Rules, shall be considered. These loading conditions are further elaborated in Sec.3 of thisClassification Note.

The loading should be applied in the form of lateral pressure on shell elements, (or line loads on membraneelements). Alternative load application may be specially considered.

4.6.2 Fatigue loads: For vessels subject to the class notation NAUTICUS (Newbuilding), see the Rules forClassification of Ships Pt.5 Ch 2 Sec 5A, fatigue strength assessment are in general to be carried out for endstructures of longitudinals in bottom, inner bottom, side, inner side and deck in the midship area. For thatpurpose any deformation of the said longitudinals caused by relative deformation by the supporting strengthmembers may have to be calculated.

It is emphasized that such deformations are to reflect dynamic loading only. The dynamic pressure loads are tobe calculated according to the Classification Note 30.7 “Fatigue Assessment of Ship Structure”, see Sec.3.6.

Table 4-2 Boundary conditions for bulk carrier cargo hold analysis when hull girder bending moments are appliedLocation Displacement Rotation

δx δy δz θx θy θzPlane A L L L L L LPlane B X X X X X XCentreline (when applica-ble)

X X X

Point a,b Fa,bX Fixed.L Rigid body linearly dependent.Fa,b Force according to the above. Forces act-

ing in opposite direction at point a and b.

Table 4-3 Boundary conditions for bulk carrier cargo hold analysis when global shear forces are appliedLocation Displacement Rotation

δx δy δz θx θy θzPlane A X X XPlane B X X XCentreline (when applica-ble)

X X X

Line S , Fv

Line F FvX Fixed.S Springs.Fv Vertical forces acting in opposite directions at

the ends.

Pointa

zx

y

Force FbPoint

b

Force Fa

Lin

e C

Line

C

Lin

e F

Line

F

zx

y




4.7 Presentation of input and results

4.7.1 The requirements given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12 regarding properdocumentation of the model shall be followed. A practical guidance is given in the following. In appendix A,examples of checklists for internal verification of FEM analyses are given.

4.7.2 Presentation of input data: A reference to the set of drawings the model is meant to represent should begiven. The modelled geometry is to be documented, preferably as an extract directly from the generated model.The following input shall be reflected:

— plate thickness — free flange sectional area considering efficiency of curved flanges— beam section properties— boundary conditions— load cases.

4.7.3 Presentation of results: The stress presentation should be based on element membrane stresses or gaussmembrane stresses at the middle of element thickness, excluding plate bending stress, in the form of iso-stresscontours in general. Numerical values should also be presented for highly stressed areas (e.g. areas where stressexceeds 60% of allowable limits or areas in way of openings not included in the model).

The following should be presented:

— deformed shapes— transverse or vertical membrane stress of shell/plate elements in

— bottom plating— inner bottom plating— deck plating— longitudinal bulkhead plating— cross deck/upper stool plating— hopper tank plating— top wing tank bottom plating— transverse floors and web frames in hopper and top wing tank and wing tank — stringers in wing tank— transverse bulkhead plating— upper and lower stool plating— side and inner side if double side skin construction— mainframes

— longitudinal membrane stress of shell/plate elements in

— bottom plating— inner bottom plating— longitudinal girders— cross deck cantilever beams

— shear stresses of shell/plate elements in

— transverse floors— longitudinal girders— longitudinal girders below bulkhead stool— stool diaphragms— lower/upper stools top and bottom plating— transverse bulkhead plating in way of ship side, (inner side if relevant) hopper and top wing tank and

wing tank— hopper plating, hopper girder and longitudinal bulkhead plating adjacent to transverse bulkhead— web frames inside hopper and top wing tank and wing tank, mainframes, upper and lower bracket— stringers inside double side and wing tank— cross deck cantilever beams

— axial stress of free flanges— deformations of supporting brackets for mainframes including longitudinals connected to these— deformation of supports for longitudinals subject to large relative deformation.




4.8 Evaluation of results and applicable acceptance criteria

4.8.1 In the following procedures for handling results and applying acceptance criteria are described.Acceptance criteria are in general given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.12 and Pt.5 Ch.2Sec.5.

4.8.2 Evaluation of results - Longitudinal stress: For buckling control the following longitudinal stresses maynormally be considered:

σL = sum of longitudinal stresses based on wave bending moment with a probability of 10-8 of exceedanceσLR = sum of longitudinal stresses based on wave bending moments with a probability of 10-4 of

exceedanceσDB = longitudinal girder bending stresses resulting from bending of large stiffened panels between

transverse bulkheads, due to local load on an individual cargo hold. These stresses are often referredto as double bottom stresses, as they are typical for double bottom structures, and may be taken asresults from the cargo hold analysis

σS = longitudinal hull girder bending stresses defined as MS/Zi , where MS is the still water bendingmoment and Zi is the section modulus at the considered position (i) based on gross scantling. (Nocorrosion addition deducted). Maximum sagging or hogging moment to be applied as values for MS.MS is defined in the Rules for Classification of Ships Pt.3 Ch.1 Sec.5 and Pt.5 Ch.2 Sec.5

σW = longitudinal hull girder bending stresses caused by wave bending moment MW, which correspond toa probability of exceedance of 10-8. σW = MW/Zi . MW is defined in the Rules for Classification ofShips Pt.3 Ch.1 Sec.5

σWR = longitudinal hull girder bending stresses caused by reduced wave bending moment MWR, whichcorresponds to a probability level of exceedance of 10-4. MWR = 0.59 MW.

Relevant stress components related to hull girder, girders, and stiffeners are defined in Fig.4-7.

Fictitious longitudinal stresses may occur in the model due to assumptions made for the boundary conditions.These effects are due to “semi global bending” of the hull girder and a fictitious compression force when themiddle hold is empty. When the longitudinal girder stresses are evaluated, typically for girders in doublebottom, the magnitude of these effects should be considered as follows:

— ordinary bulk carriers have longitudinal girders in the double bottom. It is advised that the fictitiouscompression force when the mid hold is empty is eliminated by applying boundary conditions as describedin Table 4.1. As an alternative this may be done by manual corrections after the calculation

— the effect of the “semi global bending” depends on the distance between the supports. For an ordinary bulkcarrier, this effect may be significant and should be taken into consideration. Manual corrections should bedone.

σL σDB σS σWor σLR σDB σS σWR+ +=

+ +=




Figure 4-7Stresses identified as hull girder bending stresses, double bottom bending stresses and stiffener bendingstresses, σal = σs + σw, see the Rules for Classification of Ships

It should also be noted that the stiffener bending stress is not a part of the girder bending stresses. Themagnitude of the stiffener bending stress included in the stress results depends on the mesh division and theelement type that is used. This is shown in Fig.4-8 where the stiffener bending stress, as calculated by the FE-model, is shown depending on the mesh size (valid for 4-noded shell elements). One element between floorsresults in zero stiffener bending. Two elements between floors result in a linear distribution with approximatelyzero bending in the middle of the elements. When a relatively fine mesh is used in the longitudinal directionthe effect of stiffener bending stresses should be isolated from the girder bending stresses when buckling andstress level is checked for the plate flange.

Figure 4-8Normal stress caused by local load on the stiffener, depending on number of elements along the stiffener

4.8.3 Mean shear stress: The mean shear stress, τmean, is to be used for the capacity check of a plate. This maybe defined as the shear force divided on the effective shear area. For results from finite element methods themean shear stress may be taken as the average shear stress in elements located within the actual plate field, andcorrected with a factor describing the actual shear area compared to the modelled shear area when this isrelevant. For a plate field with n elements the following apply:

Ai = effective shear area of element iτi = shear stress of element i

Upper deck

N.A. alσ

N.A.

DBσ

stσHull Girder Bending Double Bottom Bending Local Bending of Longitudinal

N.A.

τmean

τi Ai⋅( )

i 1=

i n=

Aw

-----------------------------=




Aw = effective shear area as of the real structure. To be taken in accordance with the Rules for Classificationof Ships Pt.3 Ch.1 Sec.3.

4.8.4 Shear stress in the hull girder: It is not necessary to consider hull girder shear stresses in longitudinalbulkheads and ship side unless special boundary conditions as well as loads are applied. The shear strength ofthe hull girder may normally be evaluated in accordance with the Rules for Classification of Ships Pt.3 Ch.1Sec.5. Detailed procedure for shear force correction is specified in Sec.9.

4.8.5 Buckling control and related acceptance criteria: Table 4-4 gives examples of areas to be checked forbuckling and the applicable method and accept criteria. In case of any differences in the acceptance criteriagiven here compared with those given in the Rules for Classification of Ships, the latter shall apply.

Table 4-4 Examples of areas to be checked and procedure to be used related to buckling controlItem Remarks

Buckling of girder plate flanges in:— double bottom (including bottom

and inner bottom)— side plating (including inner side

when relevant)— deck — longitudinal bulkhead— hopper structure— top wing tank structure— cross deck structure inc. stools

1) Uniaxial buckling in transverse direction to be analysed based on mean transverse compressive stress with ψ = 1 and allowable usage factor, η = 0.8

2) Uniaxial buckling in longitudinal direction to be analysed according to the Rules for Classification of Ships Pt.3 Ch.1 Sec.13 based on hull girder stress σal = σS + σW.

3) Bi-axial buckling to be analysed based on longitudinal stress and mean transverse stress. When the longitudinal stresses are obtained from hull girder loads on a probability of exceedance of 10-4, usage factors ηx= ηy = 0.85 shall be used. For a probability of exceedance of 10-8, usage factors ηx = ηy = 1.0 shall be used.

Comment:Mean transverse compressive stress is to be calculated from a group of elements representing one plate field between stiffeners.Longitudinal stresses are to be taken as described in 4.8.2.

Buckling of girder plate flanges in:— plane transverse bulkhead— upper and lower stools and the

web of these girders

1) Buckling to be analysed based on mean compressive stress with ψ = 1 and allowable usage factor, η = 0.8.

2) Bi-axial buckling to be checked when relevant.

Comment:Mean compressive stress are to be calculated from a group of elements represent-ing one plate field between stiffeners.

Buckling of cross tie 1) Buckling to be analysed based on axial stress with usage factor according to Rules, against column buckling, torsion buckling and web buckling.Note:Axial stress in cross tie may normally be taken as the stress at the mid height and at the mid span. The effective span of the cross tie may normally be taken as: Breadth of side tank – ½ Depth of both vertical girders

2) Buckling of local plate panels on cross ties to be checked according to buckling of girder webs with one or two plate flanges as appropriate.

3) Buckling of free flanges on the cross tie to be calculated according to Rules Pt.3 Ch.1 Sec.13

Buckling of corrugated bulkheads Buckling to be analysed based on mean compressive stress with kl = 5 (Pt.3 Ch.1 Sec.14) and allowable usage factor, η = 0.8.

Buckling of girder webs in: — double bottom— double side (when relevant)— deck— longitudinal bulkhead— plane transverse bulkhead— hopper tank— topwing tank— stools

Buckling of girder webs with one plate flange:

1) Buckling to be calculated as for girder plate flanges

2) Buckling to be analysed based on mean shear stress with allowable usage factor, η = 0.85.

3) Bi-axial buckling with shear.Buckling of girder webs with two plate flanges:

4) Buckling to be analysed based on mean shear stress with allowable usage factor, η = 0.85.

5) Buckling caused by compression loads from sea and cargo, alternatively together with shear, to be checked when relevant.

Comment:Mean shear stress to be taken as described in 4.8.3, representing one plate field between stiffeners.



Sec.5. Local Structure Analysis –

4.8.6 Stress control and related acceptance criteria: Table 4-5 gives examples of areas where the stress levelshall be controlled, together with the applicable method and accept criteria. In case of any differences in theacceptance criteria given here compared with those given in the Rules for Classification of Ships, the latter shallapply.

5. Local Structure Analysis

5.1 GeneralLocal structure analysis may be used to analyse local nominal stresses in laterally loaded local stiffeners andtheir connecting brackets, subjected to relative deformations between supports. See Fig.5-1. The model andanalysis described in the following are suitable for calculating:

— nominal stresses in stiffeners— nominal stresses in longitudinals supporting main frames.

These models may be included in the 3D cargo hold analysis model, or run separately as sub models withprescribed boundary deformations from a 3D-analysis. Local pressure loads must be applied to the localmodels.

5.2 Stiffeners subject to large deformations

5.2.1 General: Relative deformations between stiffener supports may give rise to high stresses in local areas.Typical areas to be considered are;

— longitudinals in double bottom towards transverse bulkheads or partial girders— longitudinals connected to main frame supporting brackets. See Fig. 5-1.

A method for the first example is shown in the following. For the other example, similar method applies.

Table 4-5 Examples of areas to be checked and procedure to be used related to control of nominal membrane stresses. All stresses in N/mm2

Item RemarksStresses in longitudinal girders

1) Allowable reduced longitudinal nominal stress, σ = 190 f1. Based on a probability of exceedance of 10-4. (Reduced longitudinal stress, σLR = σDB + σS + σWR < 190 f1, Ref 4.8.2)

2) Allowable mean shear stress τ = 90 f1 (sea) and τ = 100 f1 (harbour) for girders with one plate flange, and τ = 100 f1 (sea) and τ = 110 f1 (harbour) for girders with two plate flanges. Shear stress in way of openings not included in the calculation to be evaluated in terms of mean shear stress See 4.8.3.

Stresses in transverse and vertical girders with two plate flanges (Double skin constructions) like:— Double bottom— Double side

1) Allowable nominal normal stress in flanges of girders σ = 160 f1 (sea) and σ = 180 f1 (harbour) in general.

2) Allowable mean shear stress of girder webs, τ = 100 f1 (sea) and 110 f1 (harbour). Shear stress in way of openings not included in the calculation to be evaluated in terms of mean shear stress See 4.8.3.

3) Allowable equivalent stress, σe = 180 f1 for seagoing conditions and σe = 200 f1 for harbour conditions.

Stresses in transverse and vertical girders with one plate flange like:— Main frames— Side tank web frame— Stringer in wing tank— Deck partial girder— Cross tie— Top wing tank web

frame— Hopper tank web

frame

1) Allowable nominal normal stress, σ = 160 f1 (sea) and σ = 180 f1 (harbour) in general.

2) Allowable mean shear stress τ = 90 f1 (sea) and 100 f1 (harbour). Shear stress in way of openings not included in the calculation to be evaluated in terms of mean shear stress See 4.8.3.

3) Allowable equivalent stress, σe = 180 f1 for seagoing conditions and σe = 200 f1 for harbour conditions.

4) Allowable nominal normal stress in flooded condition, σ = 220 f1 (Not applicable for mainframes).




Figure 5-1Main frames, connecting brackets and longitudinals in bulk carriers

5.2.2 Model extent: In general, the model of a longitudinal in double bottom towards transverse bulkheads orpartial girder is recommended to have the following extent:

— The stiffener model shall extend to a stiffener support at least two frame spacings outside the area subjectto the study.

— The width of the model shall be at least ½ + ½ stiffener spacing. See Fig.5-3.

Fig.5-2 shows the extent of a model of an inner bottom longitudinal and bottom longitudinal. Here the extentcovering the full length is used for checking both sides of the unsymmetrical stools simultaneously.

Figure 5-2Extent of stiffener model for checking both sides of the unsymmetrical stool

5.2.3 Elements and element mesh: Normally three (3) 4-noded elements are to be used over the web height ofthe stiffeners. Corresponding sizes are to be used for the plate flange. The face plate shall normally be modelledwith 2-noded beam elements. Effective flange in curved areas should however be represented properly. Anexample of a model as described is shown in Fig.5-3 and Fig.5-4. Generally, the element fineness along thestiffener shall be fine enough for providing a good aspect ratio of the elements.

The two last elements towards the point of interest shall not be larger than 2% of the stiffener’s span length ifthe results are to be used directly. However, the elements may be up to 8% of the span length if extrapolationof the results towards the point of interest is carried out. A method for extrapolation is given in Ch.5.4.

Figure 5-3View of element model




Figure 5-4Acceptable element mesh. The size of elements does in this case require extrapolation of results towardsthe point of interest

5.2.4 Boundary conditions: If the model is run separately, prescribed displacements or forces are to be takenfrom the cargo hold analysis (or frame and girder analysis when relevant). These displacements or forces areto be applied to the boundaries of the local structure model in points where the results from the global modelare representative. See Table 5-1.

5.3 Other fine mesh modelsOther fine mesh models may be made for the study of critical details. If the accept criteria are based onmaximum allowable nominal stresses the modelling principles described above should be followed.

5.4 Documentation and result presentationWhen extrapolation of results is required, see 5.2.3, this shall normally be based on the results in the two lastelements towards the point of interest. The results in the Gauss point in the middle of the element representingthe flange of the longitudinal shall be used for the extrapolation. The extrapolation method is indicated in Fig.5-5.

Table 5-1 Boundary conditions for model of longitudinals in double bottom

Location Displacement Rotationδx δy δz θx θy θz

Free edge of plate flanges forming the bottom, in-ner bottom and stool sides.

- - - X - X

Free edges of:Double bottom floors.Top of stool.Double bottom floors in line with stool.

D D D D D D

X-D

Restricted from displacement or rotation. Free.Displacements transferred from cargo tank model or frame and girder model.



Sec.6. Additional Requirements Considering Flooding –

Figure 5-5Extrapolation towards point of interest based on results in elements representing the flange

Documentation and result presentation is to follow the principles given in Sec.4.7.

The following stresses shall be given:

a) Normal stresses and shear stresses of plate/membrane elements.

b) Axial stress of truss/beam elements.

5.5 Acceptance CriteriaAcceptance criteria for stress results from local structure analysis are given in the Rules for Classification ofShips Pt.3 Ch.1 Sec.12 and in Pt.5 Ch.2.

6. Additional Requirements Considering Flooding

6.1 General

6.1.1 Generally the Rules require that damage stability calculations are carried out to control that the ship hassufficient residual stability for given damage scenarios without reference to the ship’s actual loading conditionsand without controlling the ships overall strength for such damage conditions.

However, for vessels subject to the requirements as given in the Rules for Classification of Ships Pt.5 Ch.2Sec.5 Table A3, the ships overall strength (hull girder shear and bending strength) are to be controlled forflooding of each cargo hold for all actual seagoing cargo and ballast conditions. I.e. the loading conditionsgiven in the loading manual and those evaluated by the loading instrument only. The determination of the massof water ingress should reflect the damaged waterline. A permeability of 0.3 for the volume occupied by cargomay be used. For the remaining flooded volume in the loaded hold and for empty holds a permeability of 0.95to be used. For the loaded holds a permeability of 0.9 for the whole volume below the damaged waterline maybe used as an alternative to the above. Realistic data for the cargo mass volume and density to be applied.

6.2 Global Bending Moment and Shear Force Limitation

6.2.1 Generally the maximum allowable still water bending moment in a flooded condition, MSf, is describedby below formula, provided adequate uni-axial buckling capacity of the cross section is available. See the Rulesfor Classification of Ships Pt.3 Ch.1 Sec.13.

Zz = hull girder section modulus at the considered positionMw = wave bending moment according to the Rules for Classification of Ships.

When the hull girder capacity is fully utilised, the maximum allowable still water bending moment at theconsidered section, in flooded condition, MSf, is described by:

σ2σ

1σ

Msf 175 f1 Zz 0.8 Mw–=

Msf Ms 0.2 Mw+=




Ms = Allowable still water bending moment according to the Rules for Classification of Ships in intactcondition.

6.2.2 It should be noted that there is only one limitation curve in a flooded condition, irrespective of possiblereduced bending moment limits applied in an alternate intact condition.

6.2.3 The three typical bending moment limits are given in the illustration Fig.6-1 following.

Figure 6-1Typical bending moment limitation curves for intact and flooded conditions

6.2.4 The maximum allowable shear force capacity at the considered section in flooding condition, QSf , isdescribed by:

QS = Allowable still water shear force according to the Rules for Classification of Ships in intact condition.See also 9.4.

QW = Maximum vertical wave shear force according to the Rules for Classification of Ships.

6.3 Transverse Bulkhead Strength

6.3.1 Generally the Rules for Classification of Ships require that the strength of transverse bulkhead structuresubjected to flooding loads have been controlled using a pressure head corresponding to the deepestequilibrium waterline in the damage condition, and pressure load from water alone only.

6.3.2 For vessels subject to the requirements as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.5Table A3, the transverse bulkheads are to be checked according to Pt.5 Ch.2 Sec.8 D. The pressure loads in thiscase reflects the effect of mixed cargo and water.

The following load cases may be applied:

— water alone— filled cargo hold to deck at centre line with mass corresponding to the hold’s maximum allowable mass— cargo hold filled to a level corresponding to its maximum allowable mass and applying cargo density of

1.78 t/m3 — cargo hold filled to a level corresponding to its maximum allowable mass and applying cargo density of 3.0

t/m3.

Flooding head shall be as required in above referred Rules. A most severe combination of angle of repose andcargo density should be applied for the case of filled cargo hold (ref. Sec.2.3).

6.3.3 It should be noted that the rule check program “Section Scantling” in the Nauticus Hull package may beused for checking corrugation girder, shedder and gusset plates, stool plating and stiffeners as relevant.However, diaphragm plates and in line shear plates inside double bottom is to be checked separately.Acceptable procedure is described in 6.4.

Bendingmoment[tm]

Max. allowable still water bendingmoment in flooded conditionMax. allowable still water bendingmoment in intact condition

Possible reduced limit for bendingmoment in intact alternate condition

Length

20% of wave bending moment

LFP

Qsf Qs 0.2 Qw+=




6.4 Diaphragm and shear plates in double bottom below bulkhead stool, considering flooding (evaluation of the effectiveness)

6.4.1 The shear strength of diaphragm - and shear plates is to be checked with respect to the bending moment,MLS, from the lower stool as given by:

Zle = as given in the Rules for Classificationof Ships Pt.5 Ch.2 Sec.8 D303

σa,le = as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.10 D305

Q = as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.8 D209

s1,hLS = as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.8 D203

pc,fl = pc,f as given in the Rules for Classification of Ships Pt.5 ch.2 Sec.8 D204 with h1 = d1 – hDBpc,fu = pc,f as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.8 D204 with h1 = d1 – (hDB +

hLS)d1, hDB = as given in the Rules for Classification of Ships Pt.5 Ch.2 Sec.8 D203

τf =

σf = minimum upper yield stress.The shear moment capacity, Mt, of longitudinal double bottom girders and shear plates below the lowerbulkhead stool, are within a load breadth of each longitudinal double bottom girder, bl, generally given by:

The shear moment capacity, Mt, may generally be determined as follows:

MτL =

Mτs =

n = number of effective shear plates including longitudinal double bottom girders within the loadbreadth bl.

6.4.2 For the determination of Mts, smaller size access holes in the shear plates within the length of the lowerstool may generally be disregarded.

Access holes etc. in shear plates and double bottom girder webs below the lower bulkhead stool are assumedto be arranged with effective edge stiffening.

hLS2

pc fl,2

----------- pc fu,+

3--------------------------------------------- kNm

m------------ MLS

Zleσa le, 103–

QhLS+( )s1

--------------------------------------------------------- +=

σf

3-------

Mτ MLSbl=

Mτ MτLMτs

+=

lls τf tla 2–( ) hDB hoa–( ) τf tlf 2–( )hDB hof–( )

+()

[]/2

τf ts 2–( )lshDB l

n



Sec.7. Cargo Hold Load Limitations –

Figure 6-2Diaphragm and shear plates in double bottom below bulkhead stool and longitudinal girder

6.5 Limit to Hold Loading, Considering Flooding

6.5.1 Generally the Rules require that the strength of the double bottom construction is based on the mostunfavourable loading conditions as given in the loading manual and the minimum loading as given in the Rules.The individual holds net loading (shear) and/or the most unfavourable combination of net loading and bendingmoment (buckling, longitudinals) will then decide the scantling. When first the extreme loadings have beenchecked they serve as basis for the Local Strength Diagrams giving the maximum allowable/minimum requiredmass as a function of the draught. See Sec.7 for further details. Typical for this approach is that it is based onintact loading only.

6.5.2 However, for vessels subjected to the requirements as given in the Rules for Classification of Ships Pt.5Ch.2 Sec.5 Table A3, the double bottom shear strength are also to be checked for above loads in floodingcondition. See the Rules for Classification of Ships Pt.5 Ch.2 Sec.8 E. It should be noted that the rule checkprogram “Allowable Hold Loading” in the Nauticus Hull package may be used for this purpose.

Further, the highest cargo density will give the strictest requirement and a cargo density of 3.0 t/m3 shouldgenerally serve as the extreme condition in combination with permeability of 0.3 for the volume occupied bythe cargo.

7. Cargo Hold Load Limitations

7.1 General

7.1.1 The design loading conditions of the ship as defined in the loading manual, ref. Sec.3, (and also RulesPt.5 Ch.2 Sec.5), refers to a given cargo mass and a given draught. These design loading conditions are, inaddition to being used for scantling check, also utilised to define limits to the cargo mass of holds for otherdraughts.

7.1.2 Generally the allowable mass of cargo in a given hold or adjacent holds is related to the net loading onthe double bottom of the considered hold(s). This implies that the allowable mass of cargo in the hold(s) willvary linearly with the buoyancy pressure acting on the bottom of the ship.

7.1.3 In any actual loading condition longitudinal hull girder bending moments and shear forces are to bewithin the limits defined in the loading manual/loading instrument.

7.2 Definitions

MMAX = maximum allowable mass curveMMIN = minimum required mass curveMH = the actual cargo mass (t) in a cargo hold corresponding to a homogeneously loaded

condition at maximum draughtMH, ADJ. = sum of MH for the two adjacent holds




MFULL = the cargo mass (t) in a cargo hold corresponding to cargo with virtual density (homogenousmass / hold cubic capacity = MH / VH = minimum 1.0 t/m3) filled to the top of the hatchcoming. MFULL shall not be less than MH.

MFULL, ADJ. = sum of MFULL for the two adjacent holdsMHD = the maximum cargo mass (t) allowed to be carried in a cargo hold according to design

alternative loading condition(s), i.e. specified in the loading manual, with specified holdsempty

MHD, ADJ. = the maximum cargo mass (t) allowed to be carried in adjacent holds according to designblock loading conditions, i.e. specified in the loading manual, with cargo mass larger thanMFULL, ADJ.

VH = hold volume in m3 including volume of hatchT = maximum draught (m), i.e. scantling draughtTA = draught (m) at mid-hold position of the cargo hold or the adjacent cargo holds in m

associated with cargo massTHB = deepest ballast draught, usually heavy ballast draughtl = length of the considered hold(s) in m, see Figure 7-1b = mean breadth of the considered cargo hold(s) in m at the level of the top of the hopper tank,

see Figure 7-1.

In general, the above symbols are defined for a single cargo hold in seagoing conditions, unless clearlyspecified otherwise. When the symbols have a subscript of “adj.” and/or “harbour”, it means that they aredefined for adjacent cargo holds and/or in harbour conditions.

Figure 7-1Definition of length and breadth to be used in calculation of local strength diagrams

7.3 Procedure for preparation of Hold Mass Diagrams

7.3.1 The procedures for determining limits to the loading of cargo hold(s), given in the following, areapplicable for ships with class notation HC-A, HC-B, HC-C, HC-A No MP, HC-B No MP, HC-C No MP, andHC-B*. The procedures have been based on the assumption that the structure comply with class requirementsfor the ship’s design load conditions, but not necessarily utilising any strength margin, in particular at reduceddraughts. In case such strength margins exist, the hold mass diagrams may alternatively be based on the stressresponse from the direct strength calculations reflecting the design mass and relevant draught.The limit to the mass of cargo in hold is primarily related to the shear response of the double-bottom floors andgirders, and is largely given by the net pressure load exerted by cargo, other dead-weight and buoyancy on thedouble bottom structure. Ballast water in double bottom ballast tanks with in the extent of l times b as shownin Figure 7-1should be considered as a part of mass of cargo in hold(s).

In the design stage, hold mass diagrams are prepared based on a preliminary loading manual. Very often thedraught changes for the same loading condition in the final loading manual, which may make the conditionunacceptable with respect to hold mass diagrams. It is therefore suggested to keep some margin in the holdmass diagrams. This may be achieved by round up of MH, MFull, MHD, etc.

Examples of hold mass diagrams are shown in 7.4.




7.3.2 Single Hold Loading

7.3.2.1 Applicable for HC-B No MP and HC-C No MPAny cargo hold is:

— to be capable of carrying MFULL at maximum draught (T)— to be capable of carrying minimum 50% of MH at maximum draught (T)— to be capable of being empty at deepest ballast draught (THB).

The maximum allowable mass curve may be taken as:

MMAX = MFULL − 1.025 l b (T − TA) = maximum MFULL

The minimum required mass curve may be taken as the less of:

MMIN = 1.025 l b (TA −THB)MMIN = 0.5 MH − 1.025 l b (T − TA)

In harbour conditions, any cargo hold is:

— to be capable of holding the maximum allowable seagoing mass at 67% of maximum draught (0.67 T)— to be capable of increasing the maximum allowable mass in a cargo hold at reduced draught during loading

and unloading in harbour, by 15% of the maximum mass allowed at the maximum draught in sea-goingcondition, but shall not exceed the mass allowed at maximum draught in the sea-going condition. Theminimum required mass may be reduced by the same amount.

The maximum allowable mass curve (harbour) may be taken as the larger of:

MMAX, harbour = MFULL − 1.025 l b (0.67T − TA)MMAX, harbour = MMAX + 0.15 MFULL = maximum MFULL

The minimum required mass curve (harbour) may be taken as:

MMIN, harbour = MMIN − 0.15 MFULL

7.3.2.2 Applicable for HC-A No MP onlyFor ships where a specified reduced bending moment limit has been assigned for the condition with emptycargo holds at maximum draught, both limits, according to 7.3.2.1 and 7.3.2.2, to the mass of cargo in the holdsshould be included in the local strength diagram. If the vessel is loaded in between the two curves, the actualbending moment is not to be greater than the specified reduced bending moment.

In addition to the requirements given in 7.3.2.1, any cargo hold is:

— to be capable of carrying MHD + 0.1MH at maximum draught (T) (for ore holds)— to be capable of being empty at maximum draught (T). (for empty holds)

For ore holds:


MMAX = MHD + 0.1 MH – 1.025 l b (T − TA) = maximum MHD

The minimum required mass curve may be taken same as in 7.3.2.1.

For empty holds:

The maximum allowable mass curve may be taken same as in 7.3.2.1.

The minimum required mass may be taken as:

MMIN = 0 at T

In harbour conditions, similar to the requirements given in 7.3.2.1:

For ore holds:


MMAX, harbour = MHD − 1.025 l b (0.67T − TA)MMAX, harbour = MMAX + 0.15 MHD = maximum MHD





MMIN, harbour = MMIN − 0.15 MHD

For empty holds:

The maximum allowable mass curve (harbour) may be taken same as in 7.3.2.1.



7.3.2.3 Applicable for HC-B and HC-C

Any cargo hold is:

— to be capable of carrying MFULL at 67% of maximum draught (0.67 T)— to be capable of being empty at 83% of maximum draught (0.83 T).


MMAX = MFULL − 1.025 l b (0.67 T − TA) = maximum MFULL

The minimum required mass curve may be taken as:

MMIN = 1.025 l b (TA − 0.83 T)


— to be capable of increasing the maximum allowable mass in a cargo hold at reduced draught during loadingand unloading in harbour, by 15% of the maximum mass allowed at the maximum draught in sea-goingcondition, but shall not exceed the mass allowed at maximum draught in the sea-going condition. Theminimum required mass may be reduced by the same amount.

The maximum allowable mass curve (harbour) may be taken as:

MMAX, harbour = MMAX + 0.15 MFULL = maximum MFULL



7.3.2.4 Applicable for HC-A onlyFor ships where a specified reduced bending moment limit has been assigned for the condition with emptycargo holds at maximum draught, both limits, according to 7.3.2.3 and 7.3.2.4, to the mass of cargo in the holdsshould be included in the local strength diagram. If the vessel is loaded in between the two curves, the actualbending moment is not to be greater than the specified reduced bending moment.

In addition to the requirements given in 7.3.2.3, any cargo hold is:

— to be capable of carrying MHD + 0.1MH at maximum draught (T) (for ore holds)— to be capable of being empty at maximum draught (T) (for empty holds).

For ore holds:


MMAX = MHD + 0.1 MH – 1.025 l b (T − TA) = maximum MHD

The minimum required mass curve may be taken as same in 7.3.2.3.

For empty holds:

The maximum allowable mass curve may be taken as same in 7.3.2.3.

The minimum required mass may be taken as:

MMIN = 0 at T

In harbour conditions, similar to the requirements given in 7.3.2.3:

For ore holds:





MMAX, harbour = MHD − 1.025 l b (0.67T − TA)MMAX, harbour = MMAX + 0.15 MHD = maximum MHD



For empty holds:

The maximum allowable mass curve (harbour) may be taken same as in 7.3.2.3.



7.3.2.5 Applicable for HC-B* onlyAny cargo hold is:

— to be capable of carrying 1.2 MFULL at 67% of maximum draught (0.67 T)— to be capable of being empty at maximum draught (T).


MMAX = 1.2 MFULL − 1.025 l b (0.67 T − TA) = maximum 1.2 MFULL

The minimum required mass curve may be taken as:

MMIN = 0 at T




MMAX, harbour = MMAX + 0.18 MFULL

= maximum 1.2 MFULL



7.3.3 Adjacent Hold Loading

7.3.3.1 Applicable for HC-B No MP and HC-C No MPAny two adjacent cargo holds are:

— to be capable of carrying MFULL, adj., at maximum draught (T)— to be capable of carrying minimum 0.5 MH, adj., at maximum draught (T)— to be capable of being empty at deepest ballast draught (THB).


MMAX, adj. = MFULL, adj. − 1.025 l b (T − TA) = maximum MFULL, adj.

The minimum allowable mass curve may be taken as the less of:

MMIN, adj. = 0.5MH,adj. − 1.025 l b (T − TA)MMIN, adj. = 1.025 l b (TA −THB)

In harbour conditions, any two adjacent cargo holds are:

— to be capable of carrying the MFULL, adj. at 67% of maximum draught (0.67 T)— to be capable of increasing the maximum allowable mass in a cargo hold at reduced draught during loading

and unloading in harbour, by 15% of the maximum mass allowed at the maximum draught in sea-going




condition, but shall not exceed the mass allowed at maximum draught in the sea-going condition. Theminimum required mass may be reduced by the same amount.


MMAX, harbour = MFULL, adj. − 1.025 l b (0.67T − TA)MMAX, harbour = MMAX + 0.15 MFULL, adj. = maximum MFULL, adj.


MMIN, harbour = MMIN − 0.15 MFULL, adj.

7.3.3.2 Applicable for HC-A No MP onlyIn addition to the requirements given in 7.3.3.1, any two adjacent cargo holds:

— which according to a design loading condition may be loaded with the next holds empty, are to be capableof carrying 0.1 MH, adj. in addition to the maximum cargo load according to that design loading condition,MHD, adj., at maximum draught (T).

The maximum allowable mass curve may be taken as the larger of:

MMAX, adj. = MHD, adj. + 0.1 MH, adj. − 1.025 l b (T − TA) (only when MHD, adj. applicable) = maximum MHD, adj.

The maximum allowable mass curve as given in 7.3.3.1.

The minimum required mass curve may be taken same as in 7.3.3.1.In harbour conditions, similar to therequirements given in 7.3.3.1:


MMAX, adj., harbour = MMAX, adj. + 0.15 MHD, adj. (only when MHD, adj. applicable) = maximum MHD, adj.

The maximum allowable mass curve (harbour) as given in 7.3.3.1

The minimum required mass curve (harbour) may be taken as the less of:

MMIN, harbour = MMIN − 0.15 MHD, adj. (only when MHD, adj. applicable)

The minimum required mass curve (harbour) as given in 7.3.3.1.

7.3.3.3 Applicable for HC-B and HC-CAny two adjacent cargo holds are:

— to be capable of carrying MFULL, adj., at 67% of maximum draught (0.67 T)— to be capable of being empty at 75% of maximum draught (0.75 T).


MMAX, adj. = MFULL, adj. − 1.025 l b (0.67 T − TA) = maximum MFULL, adj.

The minimum allowable mass curve may be taken as:

MMIN, adj. = 1.025 l b (TA − 0.75 T)

In harbour conditions, any two adjacent cargo holds are:



MMAX, harbour = MMAX + 0.15 MFULL, adj. = maximum MFULL, adj.


MMIN, harbour = MMIN − 0.15 MFULL, adj.




7.3.3.4 Applicable for HC-A onlyIn addition to the requirements given in 7.3.3.3, any two adjacent cargo holds:

— which according to a design loading condition may be loaded with the next holds empty, are to be capableof carrying 0.1 MH, adj. in addition to the maximum cargo load according to that design loading condition,MHD, adj., at maximum draught (T).

The maximum allowable mass curve may be taken as the larger of:

MMAX, adj. = MHD, adj. + 0.1 MH, adj. − 1.025 l b (T − TA) (only when MHD, adj. applicable) = maximum MHD, adj.

The maximum allowable mass curve as given in 7.3.3.3

The minimum required mass curve may be taken same as in 7.3.3.3. In harbour conditions, similar to therequirements given in 7.3.3.3:


MMAX, adj., harbour =MMAX, adj. + 0.15 MHD, adj. (only when MHD, adj. applicable) = maximum MHD, adj.

The maximum allowable mass curve (harbour) as given in 7.3.3.3

The minimum required mass curve (harbour) may be taken as the less of:

MMIN, harbour = MMIN − 0.15 MHD, adj. (only when MHD, adj. applicable)The minimum required mass curve (harbour) as given in 7.3.3.3

7.3.3.5 Applicable for HC-B* onlyAny two adjacent cargo holds are:

— to be capable of carrying 1.1 MFULL, adj. at 67% of maximum draught (0.67 T)— to be capable of being empty at 75% of maximum draught (0.75 T).


MMAX, adj. = 1.1 MFULL, adj. − 1.025 l b (0.67 T − TA) = maximum 1.1 MFULL, adj.

The minimum allowable mass curve may be taken as:

MMIN, adj. = 1.025 l b (TA − 0.75 T)In harbour conditions, any two adjacent cargo holds are:



MMAX, adj., harbour =MMAX, adj. + 0.165 MFULL, adj. = maximum 1.1 MFULL, adj.


MMIN, adj., harbour =MMIN, adj. − 0.165 MFULL, adj.




7.4 Hold mass diagrams

7.4.1 Single Hold Loading

Applicable for HC-B No MP and HC-C No MP(Reference is made to 7.3.2.1 + LC5 and 6 in Chapter 3)Maximum seagoing curve:


Minimum seagoing curve (the less of):

MMIN = 1.025 l b (TA −THB)MMIN = 0.5 MH − 1.025 l b (T − TA)

Maximum harbour curve (the larger of):

MMAX, harbour = MFULL − 1.025 l b (0.67 T − TA)MMAX, harbour = MMAX + 0.15 MFULL = maximum MFULL

Minimum harbour curve:


Applicable for HC-A No MP - Ore Hold(Reference is made to7.3.2.2 + LC3, 5 and 6 in Chapter 3)Maximum seagoing curve:

MMAX = MHD + 0.1 MH − 1.025 l b (T − TA) = maximum MHD


MMIN = 1.025 l b (TA − THB)MMIN = 0.5 MH − 1.025 l b (T − TA)


MMAX, harbour = MHD − 1.025 l b (0.67 T − TA)MMAX, harbour = MMAX + 0.15MHD = maximum MHD


MMIN, harbour = MMIN − 0.15MHD




Applicable for HC-A No MP – Empty Hold(Reference is made to 7.3.2.2 + LC3, 5 and 6 in Chapter 3)Maximum seagoing curve:


Minimum seagoing curve:

MMIN = 0 at T


MMAX, harbour = MFULL − 1.025 l b (0.67 T − TA)MMAX, harbour = MMAX + 0.15MFULL = maximum MFULL



Applicable for HC-B and HC-C(Reference is made to 7.3.2.3 + LC1 and 2 in Chapter 3)Maximum seagoing curve:



MMIN = 1.025 l b (TA − 0.83 T)

Maximum harbour curve:

MMAX, harbour = MMAX + 0.15 ΜFULL = maximum MFULL






Applicable for HC-A - Ore Hold(Reference is made to 7.3.2.4 + LC1, 2, 3 and 6 in Chapter 3)Maximum seagoing curve:

MMAX = MHD + 0.1 MH − 1.025 l b (T − TA) = maximum MHD


MMIN = 1.025 l b (TA − 0.83 T)


MMAX, harbour = MHD − 1.025 l b (0.67 T − TA)MMAX, harbour = MMAX + 0.15MHD = maximum MHD



Applicable for HC-A – Empty Hold(Reference is made to 7.3.2.4 + LC1, 2 and 3 in Chapter 3)Maximum seagoing curve:



MMIN = 0 at T


MMAX, harbour = MMAX + 0.15 MFULL = maximum MFULL



Applicable for HC-B* only(Reference is made to 7.3.2.5 + LC4 in Chapter 3)Maximum seagoing curve:

MMAX = 1.2 MFULL − 1.025 l b (0.67 T − TA) = maximum 1.2 MFULL


MMIN = 0 at T


MMAX, harbour = MMAX + 0.18 MFULL = maximum 1.2 MFULL






7.4.2 Adjacent Hold Loading

Applicable for HC-B No MP and HC-C No MP(Reference is made to 7.3.3.1 + LC9 and 11 in Chapter 3)Maximum seagoing curve:



MMIN, adj. = 1.025 l b (TA − THB)MMIN, adj. = 0.5MH, adj. - 1.025 l b (T − TA)


MMAX, adj., harbour = MFULL, adj. − 1.025 l b (0.67 T − TA)MMAX, adj., harbour = MMAX, adj. + 0.15 MFULL, adj. = maximum MFULL, adj.


MMIN, adj., harbour = MMIN, adj. − 0.15 MFULL, adj.

Applicable for HC-A No MP(Reference is made to 7.3.3.2 + LC8, 9 and 11 in Chapter 3)

Maximum seagoing curve (the larger of):

MMAX, adj. = MHD, adj. + 0.1 MH, adj. − 1.025 l b (T − TA) = maximum MHD, adj.(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)



MMIN, adj. = 1.025 l b (TA − THB)MMIN, adj. = 0.5 MH, adj. − 1.025 l b (T − TA)


MMAX, adj., harbour = MMAX, adj. + 0.15 MHD, adj. = maximum MHD, adj.(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)The larger of:

MMAX, adj. harbour = MFULL, adj − 1.025 l b (0.67 T − TA)MMAX, adj. harbour = MMAX, adj. + 0.15 MFULL, adj = maximum MFULL, adj.

Minimum harbour curve (the less of):

MMIN, adj., harbour = MMIN, adj. − 0.15 MHD, adj.(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)





Applicable for HC-B and HC-C(Reference is made to 7.3.3.3 + LC7 and 10 in Chapter 3)Maximum seagoing curve:



MMIN, adj. = 1.025 l b (TA − 0.75 T)


MMAX, adj., harbour = MMAX, adj. + 0.15 MFULL, adj. = maximum MFULL, adj.



Applicable for HC-A(Reference is made to 7.3.3.4 + LC7, 8 and 10 in Chapter 3)Maximum seagoing curve (the larger of):

MMAX, adj. = MHD, adj. + 0.1 MH, adj. − 1.025 l b (T − TA) = maximum MHD, adj.(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)



MMIN, adj. = 1.025 l b (TA − 0.75 T)


MMAX, adj., harbour = MMAX, adj. + 0.15 MHD, adj. = maximum MHD(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)

MMAX, adj. harbour = MMAX, adj. + 0.15 MFULL, adj. = maximum MFULL, adj.

Minimum harbour curve (the less of):

MMIN, adj., harbour = MMIN, adj. − 0.15 MHD, adj.(MHD, adj. is applicable only if design block loading condi-tion specified in the loading manual)

MMIN, adj., harbour = MMIN, adj. − 0.15 MFULL, adj.Applicable for HC-B* only(Reference is made to 7.3.3.5 + LC7 and 10 in Chapter 3)Maximum seagoing curves:

MMAX, adj. = 1.1 MFULL, adj. − 1.025 l b (0.67 T − TA) = maximum 1.1 MFULL, adj.

Minimum seagoing curves:

MMIN, adj. = 1.025 l b (TA − 0.75 T)


MMAX, adj., harbour = MMAX, adj. + 0.165 MFULL, adj. = maximum 1.1 MFULL, adj.






7.5 Local Tank Top Loading

7.5.1 Bulk Carriers are often designed to carry general cargo on inner bottom, e.g. steel coils, aluminium ingotsetc., in addition to the normal homogeneous, alternate and block-loading mode. For that reason owners mayhave specified a maximum tank top pressure without specifying the purpose. If such tank top pressure is usedas basis for calculating the maximum mass in the holds, see formula given in the Rules for Classification ofShips Pt.5 Ch.2 Sec.5 B100, this maximum mass may exceed the maximum mass applied for the differentloading conditions in the loading manual.

For the purpose of handling such cases the following procedure may be applied:

1) For girder strength control the hold maximum mass should reflect the extreme loading conditions as givenin the loading manual. See Sec.3 in this Note.

2) Inner bottom plating and stiffeners are to be designed for the specified maximum tank top pressure. Thelatter assume that this pressure is greater than pressure caused by the cargo mass given in the loadingmanual.

Regarding loading of slabs and ingots such cargoes is normally stowed on dunnage and the amount of suchcargoes is rarely specified. However, if strength calculations or load limitations are requested, such strengthcalculations should be based on the actual footprint loading.

If steel coil loading has been specified the requirement to thickness of inner bottom plating and stiffeners willbe related to the mass, breadth, the number of tiers of steel coils and the number of dunnages arranged beneatheach coil

All above load limitations are to be clearly stated in the appendix to class certificate.

7.5.2 Local Scantlings of Inner Bottom Plating and Longitudinals for Steel Coil LoadingThe following procedure is an acceptable calculation method for verifying local scantlings of inner bottomplating and longitudinals for vessels intended to carry steel coils. Other equivalent methods will also beaccepted as basis for approval.

7.5.2.1 Assumptions

— Longitudinal stiffening is assumed with the coils stowed with the axis in the longitudinal direction. Itshould be noted that the method is not applicable for transverse stowage, which will be subject to specialconsideration.

— The distance between two adjacent steel coils is a fraction (Cs) of the steel coil length.— The distance between two adjacent dunnages supporting a steel coil is the same.— The distance between the end of the steel coil and the nearest dunnage is half of the distance between two

adjacent dunnages.— If plywood sheets are used instead of plank dunnages the point loads on the plate and longitudinal should

be replaced by a line load. This effect may be approximated by specifying a large number of dunnages inthe formulae.

Figure 7-2Assumptions

sd

sd = lc / nd

0.5 sd

nd = number of dunnages

lcCs lc




7.5.2.2 Calculation procedureThis procedure is in general valid for the flat part of the inner bottom, for the hopper top plating forces must berecalculated at right angels to the plate, combining forces in accordance with the Rules Pt.3 Ch.1 Sec.4 C500.

Inner bottom plating

The thickness of the inner bottom plating (longitudinally stiffened) is not to be less than:

K =av = vertical acceleration in centre of hold as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4Q = total force by steel coils on one plate field

= [t]

W = mass of steel coil in tlf = plate length in mlc = length of coil in mnt = number of tiers of steel coils = 1.4 for a single tier of coils that are secured with a key coilnd = number of dunnages per coiltk = corrosion addition as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.2f1 = material factor as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.2s = spacing of inner bottom longitudinals in m.ka = aspect ratio of plate field = lf /s = 3.0 maxsd = lc/ndCs = 0.2 in general, however Cs lc is not to be taken larger than 0.3 mnp = number of patch loads acting on one plate field, the following assumption may be used, direct

calculation for a given arrangement will also be acceptable

in general = > np = roundup {(lf - Cs lc (nc - 1))/sd}

if (nd - 1) sd < lf - (1 + Cs) lc (nc - 1) => np = nc nd

nc = number of coils on one plate field = roundup {lf / ((1 + Cs) lc)}β = ratio of distance between outmost load point on plate and plate length. Unless calculated directly the

following assumptions may be used:

= n p = 1 = >

when np > 1 =>

bd = breadth of dunnage in m

Inner bottom longitudinals

The section modulus of inner bottom longitudinals is not to be less than:

Z = 103 ks M wk /σall [cm3]ks = 1.0 in general = 0.65 for longitudinals with strut fitted at mid spanwk = corrosion addition as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.3

σall =

tK Q⋅

f1------------- 1.65β 2.3–( )ka 6β 12.2+–( ) tk [mm]+=

1.1 1av

g-----+

Wntnp

nd----------------

β bd lf⁄=

βnp 1–( )sd Cslc nc 1–( )+{ }

lf-------------------------------------------------------------------=

225 f1 100 f2b 0.7σdb

within 0.4 L (maximum 160 f1 ) [N/mm2 ]

––




= 160 f1 within 0.1 L from the perpendiculars. Between specified regions the σ -value may be variedlinearly

f1 = material factor as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.2f2b = stress factor bottom as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.6, utilising

Stillwater Bending Moment as applicable for steel coil loading (Min 0.5 MSO).σdb = mean double bottom stress (in homogenous loading condition) [N/mm2] = 20 f1 minimum

The stiffener bending moment at the fixation is found by direct calculation for a given arrangement oraccording to the following simplified formulae.

For one patch load, see Fig.7-3.

a = l / 3l = Stiffener span as given in the Rules for Classification of Ships Pt.3 Sec.3 C100.

Figure 7-3One patch load

For multiple patch loads, see Fig.7-4.

Figure 7-4Multiple patch loads

P = force on one dunnage in kN = Wnt (9.81 + 0.5 · av)/ndav = vertical acceleration in centre of hold as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4l = stiffener span as given in the Rules for Classification of Ships Pt.3 Sec.3 C100

ai : a1 = sd / 2ai = a1 + (i - 1) sd + Cs lc (round down {(i - 1) / nd})for i = 2, 3, 4, 5 ... ... ...

As long as ai < l

End connections of longitudinals are to be evaluated according to the Rules for Classification of Ships Pt.3 Ch.1Sec.12 C400.

M Pa l a–( )2l2⁄=

aP

M

l

MP Σai l ai–( )2( )

l2

------------------------------------=

a1

M

sd

P PP P

l



Sec.8. Wave Torsion Induced Stresses –

8. Wave Torsion Induced Stresses

8.1 General

8.1.1 For bulk carriers of conventional type, the tensional stiffness of the hull is mainly related to the effectiveSt Venants' moment of inertia of the hull, which is greatly increased, compared to that of the typically openship. Consequently, wave torsion induced stresses are in general not necessarily to be considered.

8.1.2 For ships with large deck openings (total width of hatch openings in one transverse section exceeding65% of the ship's breadth or length of hatch opening exceeding 75% of hold length), for example, open hatchbulk carriers, the wave torsion induced stresses shall be considered. An acceptable procedure is specified inClassification Note. 31.7 Strength Analysis of Hull Structures in Container ships (CN31.7). All calculation/analysis specified in the CN31.7 should be carried out depending on ship’s size, except the cargo hold analysiswhich may be waived.

If such kind of ships are designed with asymmetrical (to ship’s centre line) loading conditions, for examplecontainer loading conditions, hull girder still water torsion moment limitations shall be specified in the loadingmanual and shall envelope all asymmetrical loading conditions. When evaluating torsion induced stress, thestill water torsion moment shall be also included.

9. Shear Force Correction

9.1 General

9.1.1 For ships with several shear carrying elements such as single/double side, longitudinal bulkhead andlongitudinal bottom girders, the nominal shear force distribution among those elements may normally bedecided based on “Shear Flow Calculation”. The typical shear force distribution factors for the main shearcarrying members of the hull, for various type of the vessel can be found from the Table D1 of the Rules forClassification of Ships Pt.3 Ch.1 Sec.5.

However, for ships covered by this Classification Note, the actual shear force distribution of the ship sidestructure for various loading conditions will be different from those calculated by “Shear Flow Calculation”,where the 3-D effect of the load distribution on bottom structure is not considered. Therefore, for a correct shearstrength evaluation, the corrected shear force has to be calculated taking into account the local load distribution.Rules Pt.3 Ch.1 Sec.5 D200 and D300 describe the principle of this shear force correction for bulk carriers.

This part of the note will provide the background and/or additional information to the Rules.

9.2 Definitions

9.2.1 Symbols

IN = moment of inertia in cm4 about the transverse neutral axisSN = first moment of area in cm³ of the longitudinal material above or below the horizontal neutral axis,

taken about this axisQs = conventional (not corrected distribution of local load in hold(s)) stillwater shear force in kNΔQs = shear force correction in kN due to distribution of local loads in hold(s)Qw = rule wave shear force in kN as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.5 B200Φ = shear force distribution factor for the effective longitudinal shear carrying elements in the hull girder

(side, inner side and longitudinal bulkhead). t = thickness of effective longitudinal shear carrying element, in mm.τ = allowable shear stress, the lesser of (110 f1 and 0.9τcr (buckling stress)), in N/mm2.

9.3 Rule Requirement

9.3.1 The rule requirement to thickness of ship side or double side as given in Pt.3 Ch.1 Sec.5 D103 of theRules may be reformulated as follows:

The right hand side of the equation may be considered to express the still water shear force capacity (Qallowable)of the hull in way of the considered section. The method for establishing allowable shear force curves isdescribed in Sec.9.4.

WN

NSS Q

S

ItQQ −

⋅Φ≤Δ

Φ±

100

5.0 τ



Sec.9. Shear Force Correction –

The left hand side express the actual “Corrected Shear Force” which could be further simplified into

Qs ± (KPc)

The procedure to determine (KPc) is described in Sec.9.5.

For bulk carriers with single side or double side construction, corrected shear force for all seagoing conditions,harbour conditions and flooded cases if applicable should be checked within the allowable shear force.

The hull girder shear strength should always be checked for areas around engine room forward bulkhead, wheremany hull structures in cargo hold region normally terminate and hull girder shear capacity normally decreases.

9.4 Allowable Shear Force

9.4.1 Seagoing conditionThe allowable shear force Qallowable shall be calculated based on shear flow. Nauticus Hull Section Scantlingis a tool used for this purpose.

With reference to the formula above the allowable still water shear force can be expressed as follows

In Nauticus Hull, the shear flow q (N/mm) is calculated based on 1N vertical force and therefore satisfy theequation below for each plate panel in side/inner side and longitudinal bulkhead.

Comparing the two equation above,

Obviously, Qallowable based on side plating is decided by minimum of of all plate panels on side,

Qallowable based on inner side or longitudinal bulkhead plating may be calculated similarly.

Therefore, Qallowable is

for single skin bulk carrier,

for double skin bulk carrier,

In general, allowable shear force should be calculated based on shear flow calculations carried out at all frameswhere scantling of plating is changed in side, inner side or longitudinal bulkhead. However, the procedure asfollowing may be acceptable as a simplification,

— In the parallel midship area, shear flow calculation should be carried out at transverse bulkheads. For thearea in between any two transverse bulkheads, the allowable shear force may be based on the larger shearflow q at transverse bulkheads and the actual plating scantling in the area.

— Outside the parallel midship area, shear flow calculation should be carried out at transverse bulkheads. Thecross section where the hull shape starts to change from parallel midship area is considered similar as atransverse bulkhead. For the area in between any two transverse bulkheads, the allowable shear force maybe based on the shear flow q (assumed as linearly varied in between the two transverse bulkheads) and theactual plating scantling in the area.

N

NWallowable S

ItQQ

100⋅Φ=+ τ

N

N

S

Iq

Φ⋅= 10

1

1000⋅=+

q

tQQ Wallowable

τ(kN)

1000⋅q

tτ

W

side

sideallowable Qq

tQ −

⋅

=min,

, 1000

τ

sideallowableallowable QQ ,=

),min( ,, innersideallowablesideallowableallowable QQQ =




9.4.2 Harbour conditionThe allowable still water shear force in harbour conditions will be obtained according to the same formula andprinciples as given in 9.4.1 except that the wave shear force, QW, is reduced to 50% for the sections in question.

9.4.3 Flooded casesThe allowable still water shear force in flooded cases will be obtained according to the same formula andprinciples as given in 9.4.1 except that the wave shear force, QW, is reduced to 80% for the sections in question.

9.5 Corrected Shear Force

9.5.1 GeneralWith reference to the formula in 9.3 the corrected shear force, QS,C, can be expressed as follows

QS is the uncorrected shear force or the shear force normally found in the loading manual (nominal shearforce). The sign convention for QS and QS,C is as described in the Rules for Classification of Ships Pt.3Ch.1 Sec.5 B100 (weight of hull aft of considered section exceeding buoyancy → positive), “ + “ appliesfor the corrected shear force at fore end of the hold, and “-“ applies to the corrected shear force at aftend of the hold.

The shear force correction, (KPC), will be further described below for typical bulk carrier construction,i.e. with single and double side.

The calculated (KPC)-value should be considered in connection with the peak values of the conventionalshear force curve at the transverse cargo hold bulkheads.

9.5.2 Bulk Carriers, single/double side constructionThe correction, (KPC), to the nominal shear force may be expressed as follows:

(KPC) = absolute value of (CP(PH + Σ(KNPN)) – CDT1)PH = cargo or ballast in (t) for the hold in questionPN = bunker or ballast (t) in double bottom tank no. N (port and starboard) situated below considered holdT1 = draught in m at the middle of holdCP = load correction factor in kN/tCD = buoyancy correction factor in kN/mKN = (VH A’N)/(H AN A’B) to be calculated for each filled tankH = height of hold in mVH = volume of hold in m³AN = horizontal cross-sectional area (m²) (port and starboard) at level of inner bottom tank NA’N = horizontal cross-sectional area (m²) (port and starboard) at level of inner bottom of that part of the

double bottom tank no. N which is situated within the length of the considered holdA’B = sum of all A’N.For practical purposes CP and CD may be taken as constants independent of cargo filling height and draughtrespectively.

The following values may be used:

CP = (9.81 C BDB LH H)/VH (kN/t)CD = 10 C BDB LH (kN/m)C = B/(2.2 (B + LH)) (for conventional designs) BDB = breadth of the flat part of the double bottom in m, see Fig. 9-2LH = length of hold in m see Fig. 9-1.

QS,C = QS ± (KPC)




Figure 9-1Longitudinal section

Figure 9-2Transverse section

For bulk carriers with single side or double side construction, the double bottom girders always transfer partsof net load applied on the double bottom structure directly to transverse bulkheads. Therefore the loadtransferred by single side or double side structure are decreased. Consequently the corrected shear force curvein each cargo hold should always have smaller absolute slope ratio comparing to nominal shear force.

Following the above principle, the (KPC) should be added to or deducted from the peak values of the nominalshear force curve at transverse bulkheads in each cargo hold.

It should be also noted that (KPC) due to net loads in fore peak tank and engine room are normally neglected.

See Figure 9-3 and 9-4 for examples of nominal and corrected shear force for an alternative loading conditionand a heavy ballast loading condition respectively.

ANAN

A’N A’N

LH

A’B

BDB

AN , A’N , A’B(pipe duct to be deducted)




Figure 9-3Nominal and corrected shear force for an alternative loading condition

Figure 9-4Nominal and corrected shear force for a heavy ballast loading condition



Appendix A Checklist for Finite Element Analysis –

Appendix AChecklist for Finite Element Analysis

A.1 Guidelines for use of checklist for FE analysis

A.1.1 The checklist is developed as an aid to ensure a satisfactory level of technical quality of work for analysisperformed by the FE method. The checklist may also function as guidance for the process of completing FEanalysis.

It is recommended that the checklist is used for self-checking by the one performing the analysis, andpreferably by those performing independent verification.

A.1.2 The control may be further adapted to the computer program used in the analysis. In general thefollowing main items should be checked:

— geometry and element mesh— stiffness properties— boundary conditions— loads and pressures— stresses and reaction forces.

CHECKLIST FOR GEOMETRY, MESH AND ELEMENT PROPERTIESSTRUCTURAL PART:Reference drawings:Directory:Input and model file names:FEM file name:Units (have been checked): Controlled by / date:Length: [mm] Mass: [t]Time: [s] Force: [N]Pressure: [N/mm2]Constants (have been checked):Gravity: 9810 [mm/s2]Density (steel): 7.85 E 10-9 [t/mm3]Young's mod.: 2.1 E 105 [N/mm2]Thermal exp. coeff.: 0.0Poisson's ratio: 0.3Scantlings:Net scantlings applied/ not appliedCheck of nodes:Spot checks of co-ordinates for key-nodes and nodes at border lines have been performed.Check of elements:Elements have been checked for having correct material.Elements have been checked for having correct thickness (membrane/shell) or cross section properties (truss/beam).Truss/beam elements have been checked for having correct eccentricity.Free flange sectional area has been checked for efficiency of curved flanges.Secondary elements (buckling stiffeners) been checked for having correct efficiency according to end connection (sniped/welded).Boundary conditions:The boundary conditions given (fixations) have been checked.Spring constants calculated according to prevailing Class Note used / not usedLoads:Load directions are found to be correct




Plots:Plots of element mesh with thickness (colour plots or by numerical value on elements) and boundary conditions are submitted with the checklists.There is conformance between drawings and plots.

Structural part accepted: date:__________ _________________________sign.

CHECKLIST FOR LOADS Structural part: Controlled by / date:Loads:Hand calculations or other program calculation for each basic load case are compared with the results from data check performed by the solver.Load directions are found to be correctThe sum of loads from data check are checkedSuperelements are/are not mirrored or rotated.Loads are checked for mirrored and rotated superelements.Prints with data check of all loadcases is submitted with the checklists

Loads and load application are accepted: date:__________ _________________________

Sign.

CHECKLIST FOR LOAD COMBINATIONS AND RESULTS PRESENTA-TIONSTRUCTURAL PART: Controlled by / date:Plots:Plots of structural part with deformed shape in proper scale are submitted with the checklists.Plots of transverse membrane stresses of shell elements for relevant structural parts are submitted with the checklists (contour plots and/or plots with numerical values).Plots of shear stresses for relevant structural parts are submitted with the checklists (contour plots and/or plots with numerical values).Plots of in plane stresses for relevant structural parts are submitted with the checklists (contour plots and/or plots with numerical values).Plots of equivalent (von-Mises) stresses for relevant structural parts are submitted with the checklists (contour plots and/or plots with numerical values).Plots of axial stress of free flange for relevant structural parts are submitted with the checklists (contour plots and/or plots with numerical values).Stresses / forces:Spot checks of the calculated stresses have been compared to values calculated by simplified methods.Plots have been used to identify peak stresses.Cross sectional forces and moments have been checked with simplified methods.Code checks / acceptance criteria: Yield check of main structure performed based on relevant load cases and stresses. Hull girder stresses added/not added manually.




Yield check of secondary structure performed based on relevant load cases and stresses. Local bending has been taken into account.Buckling check of transverse elements performed based on relevant load cases and stresses.Buckling check of longitudinal elements performed based on relevant load cases and stresses. Hull girder stresses added/not added manually.Fatigue check performed based on relevant load cases, stresses and available stress concentration factors.

Analysis accepted date:__________ _________________________



Appendix B Beam Modelling –

Appendix BBeam Modelling

B.1 Beam modelling, general

B.1.1 The 2-dimensional beam models, which may be applied for conventional bulk carriers, are as follows:

a) Transverse bulkhead structure, which is modelled as a framework model subjected to in plane loading, seeB.2.

b) Double bottom structure, which is modelled as a grillage model, subjected to lateral loading, see B.3. Notethat this calculation may utilise stiffness data and loads as calculated for the transverse bulkhead calculationmentioned under a) above. Alternatively, load and stiffness data for the bulkhead may be based onapproximate formulae.

c) Top wing tank structure, which for ships without specified deck cargo, is calculated by a framework modelof the top wing tank web frame subjected to in plane loading, see B.4.

B.1.2 Three-dimensional modelling may be applied instead of some or all of the 2-dimensional models referredabove. It may be mentioned that 3-dimensional modelling for the double bottom structure may be utilised forimproved description of the hopper and main frame region of conventional bulk carriers.

B.1.3 Three-dimensional models representing the total cargo hold structure of one or more cargo holds, shouldpreferably be carried out as finite element models.

B.1.4 The symbols used in model sketches are described in Fig.B-1.

B.1.5 For the formulae given in this section, consistent units are assumed used. The actual units to be applied,however, may depend on the structural analysis program used in each case.

B.1.6 The models should represent the “net” structure; i.e. the corrosion additions as specified in the Rules forClassification of Ships Pt.3 Ch.1 Sec.2 are to be deducted from the given scantlings.

B.1.7 Beam- and bar elements representing the stiffness of flanges are generally to be adjusted for effective width inaccordance with the Rules for Classification of Ships Pt.3 Ch.1 Sec.3 C400.

For grillage type double skin structures, however, such as double bottoms stiffened by floors and longitudinalgirders, full flange effectivity may normally be assumed for the elements representing the girders of thegrillage.

B.1.8 The increased stiffness of girder elements with bracketed ends is to be properly taken into account by themodelling. The rigid length of beam elements in way of bracket regions, lr, may normally be taken as:

lr = l – d – lτ, see also Fig.B-2 = 0, minimumd = as given in Fig.B-2lτ = represents the shear induced bending flexibility of the bracket

= 0 in general

= if considered element is ⊥ to all other elements representing the bracket region, and the lτ ofthese elements are taken = zero.

I = moment of inertia of considered girder elementA = area of the bracket region including adjacent girder webst = thickness (mean) of bracket and adjacent girder webs.

B.1.9 The additional girder bending flexibility associated with the shear deformation of girder webs in nonbracketedcorners and corners with limited size softening brackets only should normally be included in the models asapplicable.

2.6IA t----------




The bilge region of transverse girders of open type bulk carriers and longitudinal double bottom girderssupporting transverse bulkhead represent typical cases where the web shear deformation of the corner regionmay be of significance to the total girder bending response, see also Fig.B-3. The additional flexibility may beincluded in the model by introducing a rotational spring, KRC, between the vertical bulkhead elements and theattached nodes in the double bottom, or alternatively by introducing beam elements of a short length, l, andwith cross-sectional moment of inertia, I, as given by the following expressions:

KRC = b1 b2 t G

I =

B.1.10 It is important to use a short element with above properties as this approach assumes constant moment over theelement length. The modelling shall generally take into consideration relevant effects due to variation inelement web height over its length as applicable. Unless special beam elements with varying web height areavailable, members with varying height should preferably be represented by a grid as shown in Fig.B-4, whichshows a typical bulkhead lower stools.

The proposed meshes are appropriate for stools, which are stiffened by diaphragm plates with varying sizedlightening holes. The purpose of the horizontal system lines is to connect the elements representing the stoolside plating and stiffeners (flange effect) with the elements representing the web plating of the stool to form anintegrated structural system. The horizontal elements should be made rigid compared to the vertical elementsrepresenting the web plating, but should not have excessive shear area and moment of inertia (in order to avoidnumerical problems in the solution process).

The necessary number of rigid horizontal elements depends on the shape of the structure. Normally, however,4-5 horizontal elements as indicated in Fig.B-4 should be enough for a satisfactory model representation.

B.1.11 In simplified two-dimensional modelling, possible three-dimensional effects caused by supporting girders etc.are normally represented by springs.

The spring stiffness, KG, of axial springs representing supporting girders may normally be given by thefollowing formula:

l = supporting girder span.I = moment of inertia of the supporting girderAs = shear area of supporting girdersm = model breadthc1 = 76.8 for simple end condition for supporting girder = 384 for fixed end condition for supporting girderc2 = 50 for simple support condition for supporting girder = 250 for fixed end condition for supporting girder.

B.1.12 In beam models the torsional stiffness of box structures is normally represented by beam element torsionalstiffness, and in case of three-dimensional modelling sometimes by shear elements representing the variouspanels constituting the box structure. Typical examples where shear elements have been used are shown inFig.B-7, while a conventional beam element torsional stiffness has been applied in Fig.B-8.

The torsional moment of inertia, IT, of a torsion box may generally be determined according to the followingformula, see also Fig.B-5.

m = no. of panels of which the torsion box is composedti = thickness of panel no. isi = breadth of panel no. i

b1b2 t l G

E-------------------------

KG

c1EIsm

l4

1c2I

l2As

-----------+

------------------------------=

IT

Σi 1=

mrisi( )

Σi 1=m si

ti---

----------------------------

2

=




ri = distance from panel no. i to the centre of rotation for the torsion box. Note the centre of rotation mustbe determined with due regard to the restraining effect of major supporting panels (such as ship sideand double bottom) of the box structure.

B.1.13 In two-dimensional modelling, the three-dimensional effect of supporting torsion boxes is normallyrepresented by rotational springs or by axial springs representing the stiffness of the various panels of the box.

The spring stiffness, KT, of a rotational spring representing a supporting torsion box is normally given by thefollowing expression:

sm = breadth l assumed for two-dimensional modell = length of torsion box between supportsIT = as given in B.1.12.

B.1.14 The rotational restraint by torsion boxes (e.g. top wing tank) may be represented by axial springs as indicatedin Fig.B-6. The stiffness of the axial spring(s) is generally given by the following formula:

l = length of torsion box between supportsb = breadth of panel represented by spring consideredt = thickness of panelsm = breadth assumed for two-dimensional model.

In case the axial spring direction may not be correctly defined in the program applied, the spring should bereplaced by an area element of the equivalent cross-sectional area and extending in the desired spring directionto a fixed support. The cross-sectional area, A, of the area element is generally given by:

l = length of element

Figure B-1Symbols

KT

8GsmIT

l2

-------------------=

Ks

4Gtbsm

l2

-------------------=

AKsl

E--------=

ELEMENTS BETWEEN NODES

RIGID END OF ELEMENTS

RIGID ELEMENTS

ELEMENT HINGED AT NODE

FIXED NODE

NODE WITH FIXED IN PLANE ROTATION ANDX-MOVEMENT, FREE Y-MOVEMENT

NODE WITH FIXED X- AND Y-MOVEMENT,FREE IN PLANE ROTATION

NODE WITH FIXED Y-MOVEMENTFREE IN PLANE ROTATION AND X-MOVEMENT

NODE WITH LINEAR IN PLANE RESTRAINT(LINEAR SPRING)

NODE WITH ROTATIONAL IN PLANE RESTRAINT(ROTATIONAL SPRING)

Y

X




Figure B-2Rigid end lengths of beam elements

Figure B-3Nonbracketed corner model

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.30 0.5 1.0 1.5 2.0

(b)

(a)

hh

oh°r,

db

dr

,

l

lI

h

hb

o

r

(a)

l

l I

ho

r

(b)

r

ho

ho

Double bottom

t

b 1

2b

KRC lI




Figure B-4Element mesh representing tapering member (bulkhead stool)

Figure B-5Torsional stiffness of box structure

Figure B-6Spring modelling of supporting panels of torsion boxes

Flange

Web

r

s

1

3

r3

r2

s1

s2

Centre ofrotation

t b

b

KS

KS




Figure B-73-D beam element model covering double bottom structure, hopper region represented by shear panels, bulkhead and deck between hatch structure. Lumped mainframes

Figure B-83D beam element model covering double bottom structure, hopper region,bulkhead and deck between holds. Lumped main frames

B.2 Transverse bulkhead structures

B.2.1 The transverse bulkhead is normally modelled as a two-dimensional structure. In such case the model normallyrepresents the corrugation at centreline. Three-dimensional modelling including also the deck structure may beadvisable in order to determine the variation in the support stresses of the bulkhead corrugation at the lowerand upper stool over the breadth of the hold, or for instance to represent special load conditions including suchas the moment exerted by a crane pedestal and or deck loads.




B.2.2 Fig.B-9 shows a sketch of a typical transverse bulkhead design and the corresponding two-dimensional beammodel. For calculation of the watertight bulkhead loading, LC17, the fixed support condition should generallybe assumed at the lower bulkhead support at the inner bottom. For consideration of bulkhead strength for cargoload as given by load case LC12, the rotational displacement obtained for the double bottom calculation shouldbe applied at the lower bulkhead support.

B.2.3 The element mesh pattern of the stool should generally be made in accordance with B.1.10. Note that in theregions where each stool side is supported by separate webs, the sloping system lines should represent thecomplete stiffness of the webs including the plate flanges.

B.2.4 As indicated in Fig.B-9, it is normally sufficient to represent the bulkhead support at the deck by a simplysupported node. Note, however, that the deck support should in principle be positioned in the shear centreposition of the crossdeck structure, which in cases with a high hatch end coamings or a large upper stool tendsto be below the deck level. If the shear centre position of the crossdeck is not known, a support position at decklevel is generally acceptable.

It should be noted that when an upper stool has been arranged, the torsional stiffness of the stool structure maybe included as a rotational spring, KT, as given in B.1.13, see also Fig.B-10.

The support by the hatch end coamings and transverse beam may be represented as axial springs as indicatedin Fig.B-10, KD, which according to B.1.11 for the corrugation at centreline (assuming simple support at thehatch side coaming) may be expressed as:

b1 = hatchway breadthI = moment of inertia of hatch end coaming about horizontal axisAS = vertical shear area of hatch end coamingsm = model breadth.

B.2.5 The two-dimensional bulkhead model is normally taken at the ships' centreline. The required model breadthwill depend on the actual design in each case. It may be convenient to choose the breadth corresponding to thelongitudinal bottom girder spacing. Note that the stiffness of corrugated bulkhead above the stool is in this caseto be taken as a multiple of the stiffness of one corrugation.

B.2.6 The bulkhead calculation may be utilised in order to determine stiffness- and force data for the bulkhead to beapplied for the double bottom grillage calculation.

In this case the supporting moment at the lower support, MBB, may be applied in the double bottom grillagecalculation as a moment, MBS, per double bottom girder as follows:

sg = effective breadth of the double bottom side girder consideredsm = model breadth of bulkhead model.The rotational constraining stiffness exerted by the bulkhead on the double bottom may be determined bysubjecting the lower bulkhead support to a rotational displacement, φ, as a separate load case. The rotationspring stiffness exerted by the bulkhead is then determined from the calculated supporting moment, M, by theformula:

B.2.7 If three-dimensional modelling is used, the transverse bulkhead model should be joined to the double bottom

KD

77EIsm

b14

150 I

b12AS

-------------+

----------------------------------=

MBS

MBBsg

sm-----------------=

KRB

Msg

φsm----------=




grillage model described in B.3 following. In such case short bending elements representing the shearflexibility of longitudinal double bottom girders below the bulkhead (stool) should be considered introducedas described in principle in B.1.9.

Figure B-9Two-dimensional mesh of bulkhead structure

Figure B-10Spring support by hatch end coamings

B.3 Double bottom structure

B.3.1 The double bottom structure is normally modelled as a grillage or as a part of a three-dimensional modelcovering the hopper and/or the transverse bulkhead and deck, in addition to the double bottom structure.

Three-dimensional modelling is preferable, and should generally be used for the hopper region unless thehopper tank is small. Similarly the inclusion of the transverse bulkhead structure into the double bottom modelmay be important for the correct assessment of shear forces in double bottom longitudinal girders and for thebulkhead member shear and bending response.

B.3.2 Fig.B-11 shows a typical double bottom grillage element mesh with the hopper tank modelled as a threedimensional structure. The model is to extend athwartships from the ship side to the centreline, wheresymmetry is assumed for relevant load conditions.

In the longitudinal direction the model should extend at least from the middle of one hold to the middle of theadjacent hold. Symmetry is assumed at both model ends.

In cases where the considered holds are unsymmetrical, due to an unsymmetrical lower stool, or due to an

Crossdeck shear centre

K D K D K D K D

K T




unsymmetrical floor arrangement, an increased model length extending over one complete hold and two halfhold lengths should be considered. Alternatively, if a model extending over 2 half hold lengths is used, careshould be exerted to ensure that longitudinal double bottom girders are modelled with their true effective spanlength between bulkhead corrugations. This may be obtained by modelling the bulkhead lower stool as anequivalent symmetrical structure, or by rearranging the floor spacing such that the midspan position is locatedat a floor or midway between two floors.

The vertical model support(s) is generally assumed at the transverse bulkhead(s) in the shear centre position ofthe half cross-section of the hull. The shear centre position of the half cross-section may be determined by ashear flow analysis.

For bulk carriers of conventional arrangement the distance of the support position outside of the side shell, ys,is given approximately by the following expression:

b1 = breadth of hatch opening (m)

For open type double skin bulk carriers, the support point may be assumed at the mid-breadth of the wing tank.

B.3.3

The beam elements representing floors extending from centreline to the hopper side and longitudinal doublebottom girders should have a torsional moment of inertia, IT, equal to:

b = member flange breadth (assuming 100% effective flange breadth, see B.1.7 aboveh = web heighttib = thickness of bottom platingtb = thickness of inner bottom plating.

B.3.4 The shear stiffness of double bottom girder elements is in general to be reduced for girders with large webopenings. For normal arrangement of access and lightening holes a factor of 0.8 may be suitable.

B.3.5 Adjacent floor elements of the grillage model are assumed to be separated halfway between floors. The floorsin line with stool sides have not been included in the model.

B.3.6 Transverse elements in way of pipe tunnels with separate bottom and inner bottom stiffening may be modelledas the other floor elements, except for the effective shear area, AS, which should be taken as:

l = span of transverse stiffeners in pipe tunnelΣI = sum of moments of inertia of bottom and inner bottom transverse stiffeners within the floor flange

breadth.ΣAS = sum of shear areas of bottom and inner bottom transverse stiffeners within the floor flange breadth.

B.3.7 The transverse bulkhead elements should represent the shear and bending stiffness of the bulkhead and thetorsional stiffness of the lower stool and that part of the inner bottom below and adjacent to the stool which isnot represented by the neighbouring floor elements.

The cross-sectional properties of the transverse bulkhead elements should generally be based on an assumedeffective flange width for bottom, inner bottom and deck which does not exceed 20% of the vessel breadth. Forcorrugated bulkheads with a lower stool structure, the element moment of inertia and shear area of thetransverse bulkhead may be determined according to B.5.4.

ys

B b1–

16---------------=

ITb h

2

1tib------ 1

tb----+

-----------------=

AS2.6

l2

12ΣI------------ 2.6

ΣAS-----------+

------------------------------=




The torsional moment of inertia, IT, of the bulkhead elements representing the lower stool should (in agreementwith B.1.12) be determined according to the following formula, see also Fig.B-12.

B.3.8 Adjacent longitudinal double bottom elements are assumed to be separated halfway between the girder webs.The sloping hopper side plate and the bottom plating outside of the hopper side girder should be disregardedwhen the hopper side girder element cross-sectional properties are determined.

The bending stiffness contribution of the bottom-and inner bottom longitudinals may be included by increasingthe longitudinal girder web thickness as follows:

AN = sum of net cross-sectional area of bottom longitudinals within flange breadth of girder (corrosionmargin deducted)

AU = sum of net cross-sectional area of inner bottom longitudinals within flange breadth of girder(corrosion margin deducted)

hn = distance from bottom plating to neutral axis of bottom longitudinals (plate flange disregarded)hu = distance from inner bottom plating to neutral axis of inner bottom longitudinals (plate flange

disregarded).The correct effective shear area for the girder is obtained by multiplying the element shear effectivity factor (ifavailable) by:

B.3.9 For the elements representing the ship side and hopper region, an element with bending and shear stiffness inaccordance with the half hull girder cross-section may be used. The torsional moment of inertia of the hoppertank, IT, should be determined in accordance with B.1.12.

B.3.10 The stiffness and load effects from the side frames acting on the double bottom structure may be representedby rotational springs and nodal forces and moments described for the nodes representing the hopper webs atthe hopper top.

B.3.11 In general, a 3-dimensional modelling of the web frames of hopper region should be applied. The torsionalstiffness of the hopper tank should then be represented by shear elements (elements with large bending rigidity)with shear area equal to the cross-sectional area of the hopper side plate. The local axis of these elements shouldbe defined in the plane of the hopper side.

B.3.12 The rotational spring stiffness representing the transverse bulkhead, KRB, in accordance with B.2.6, may foreach longitudinal girder be determined from the transverse bulkhead calculation.

B.3.13 The moment and the forces are to be applied for each longitudinal girder due to the lateral pressure by cargoon the transverse bulkhead may be determined from the transverse bulkhead calculation.

IT

Σi 1=6

risi( )2

Σi 1=6 si

ti---

-----------------------------=

Δtw

3 AN AU+( ) 1hu h+

n

hdb-----------------–

2

hdb------------------------------------------------------------------=

twtw Δtw+---------------------




Figure B-11Double bottom grillage element mesh

Figure B-12Lower stool torsional moment of inertia

Lo

ng

itud

ina

l se

ctio

n

Gird

er

mo

de

l

ys

Floor models

Transverse section

st

r

11

1

t2

t3

t 4

t 5

t6

r2

r3 r4

r5

r6

s2

s 3

s4

s5

s 6




B.4 Top wing tank / Deck structure

B.4.1 The top wing tank web frame structure is in some cases analysed as a two-dimensional structure where theclosed cell torsional supporting stiffness of the top wing tank between transverse bulkheads is modelled assprings. In other cases a three-dimensional model covering the deck structure and sometimes also the mainframes and the transverse bulkhead should preferably be used.

B.4.2 The two-dimensional modelling assumes that every web frame within one hold length is subjected to the sameloading, and that the supporting stiffness of the top wing tank may be reliably defined in terms of axial springsupports as given in B.1.14. This modelling assumption is normally suitable when calculating the load casesLC15 and LC16 with ballast in the top wing tank.

For the load cases LC13 and LC14 with ballast in hold the boundary assumption for the axial spring supportsfor the two-dimensional model of the top wing tank web frame must be specially considered due to theconstraining effect of the transverse bulkhead load. A two-dimensional model based on an assumed support atthe hatch end coamings may, however, be used provided the hatch end coamings are connected by effectivebracket structures to the transverse bulkhead upper stool.

B.4.3 The two-dimensional modelling may be less well suited for bulkcarrier designs intended for cargo on deck andhatch where the hatch cover load is supported on the hatch end coaming structure, and in particular if the deckstructure between hatches is also utilised for support of a deck crane pedestal. The two-dimensional model mayalso be insufficient when calculating the load cases LC13 and LC14 considering ballast in the ballast hold. Inthese cases it is advised that the deck structure including top wing tank is modelled as a three-dimensionalstructure.

B.4.4 In addition, the two-dimensional modelling may be insufficient in such cases where the hull girder bendinggives rise to significant local bending and/or shear stresses in longitudinal deck members. Important in suchrespect could be designs where high hatch side coamings are combined with deep hatch side coaming girderbrackets at transverse bulkheads for effective support of deck cargo loads etc.

B.4.5 Three-dimensional models of the top wing tank and deck structure should normally extend over minimum twohalf cargo hold lengths, and from the ship side to the centreline. The model should in addition include the sidemain frames and the transverse bulkhead structure at least as supporting springs. A finite element model isgenerally preferable, but beam formulations may also be utilised. When a beam model is used, it is importantthat the torsional stiffness of supporting panels of the top wing tank and bulkhead upper stool are properlyincluded in the model in terms of element torsional moment of inertia as given in B.1.12 or by shear elements.

B.5 Stiffness Properties of Transverse Bulkhead Elements, including effect of Lower Stool

B.5.1 The following gives an approximate formula for the determination of cross-sectional data for transversecorrugated bulkheads including the effect of the lower stool structure.

B.5.2 For the corrugated part, the cross-sectional moment of inertia, IB, and the effective shear area, AB, may beobtained as follows:

AD = cross-sectional area of deck partAL = cross-sectional area of lower stool and bottom partH = distance between neutral axis of deck part and lower stool and bottom parttc = mean thickness of bulkhead corrugationbs = breadth of corrugationbc = breadth of corrugation measured along the corrugation profile.

IB H2 ADAL

AD AL+---------------------=

AB tc

Hbs

bc---------=




B.5.3 For the stool and bottom part, see Fig.B-13, the cross-sectional properties, IS and AS, should be determined asnormal. Based on the above, a correction factor, K, may be determined by the formula:

B.5.4 By applying this factor, the cross-sectional moment of inertia, I, and shear area, A, of the transverse bulkheadas a whole are calculated to:

I = K IBA = K AB

B.5.5 The normal stress in the upper deck, σD, due to the bulkhead bending may be determined according to thefollowing formula:

B.5.6 Similarly the normal stress in the lower stool, σls, due to the bulkhead bending may be determined accordingto the following formula:

ZLS = section modulus of lower stool with respect to position consideredks = 1.0 for position below neutral axis of lower stool and bottom part = -1.0 for position above neutral axis of lower stool and bottom part.

Figure B-13Bulkhead double bottom grillage element definition

K 1

IS 1100IB

ABB2

--------------+

IB 1100IS

ASB2

--------------+

-----------------------------------+=

σD

MBHD

K H AD-------------------=

σls

MBHD

K---------------- 1

HAL------------

ks K 1–( )ZLS

-----------------------+ =

I , A , A

b

bc

s c

LSS

L

t

A

AA DD

H

NEUTRAL AXIS, DECK

NEUTRAL AXIS

0.2 B (max)

LOWER STOOL AND BOTTOM PART




B.6 Stress Analysis, general

B.6.1 The analysis procedures described in the following refer to beam calculations carried out in accordance withB.1-B.4.

B.6.2 The described stress analyses generally refer to allowable stress limits given in the Rules. In additioncompressive normal stresses and shear stresses shall be considered with respect to buckling in accordance withPt.3 Ch.1 Sec.14 of the Rules for Classification of Ships, also for cases where no special reference to bucklingcontrol has been included in the text following.

B.6.3 In the following calculated forces and moments are assumed given in N and Nmm, and material scantlingsreferred in formulae are assumed to be net scantlings, i.e. corrosion additions as stated in the Rules forClassification of Ships Pt.3 Ch.1 Sec.2 D400 deducted.

B.7 Double bottom bending strength

B.7.1 Allowable normal girder stresses as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.13 B400 andbuckling requirements given in Pt.3 Ch.1 Sec.14 B200 and B400 are generally to be complied with. For thesum of longitudinal normal stress due to hull girder bending and longitudinal double bottom stress innonhomogeneous loading conditions (Rule allowable stress = 190 f1 (N⁄mm2), the still water hull girder stressmay generally be based on the mean still water bending moment value, MSM, which for the middle of holdposition is given by:

MS1, MS2 denote still water hull girder bending moments calculated for the aft and forward transverse bulkheadpositions of the cargo hold for the loading condition being considered.

B.7.2 The transverse axial force of the double bottom structure due to external sea pressure on the sides need not beconsidered when the bottom panel is evaluated with respect to biaxial buckling in accordance with Pt.3 Ch.1Sec.14B of the Rules, provided the inner bottom structure is able to effectively support the external sea pressureload.

B.8 Pipe tunnel strength

B.8.1 The modelling technique applied normally reflects the transverse stiffness of the combined bottom and innerbottom structure in the pipe tunnel. Consequently, special stress analysis will be required to determine the localstress response.

B.8.2 The shear area of the pipe tunnel transverse members may normally be expressed as follows:

Inner bottom transverse member:

Bottom transverse member:

F = mean calculated shear force (N) in floor in way of pipe tunnel.

=

MSM

MS1 MS2+

2----------------------------=

τ2F 1 k–( ) 1000pisl+

200AI--------------------------------------------------- N mm

2⁄( )=

τ2Fk 1000pesl+

200AE-------------------------------------- N mm

2⁄( )=

F1 F2+( )s

2sf-------------------------




= 0 for pipe tunnels in the ships' centreline

k =

s = spacing in m of transverse stiffening members of in pipe tunnelsf = mean spacing in m of double bottom floors in way of the considered transverse tunnel membersl = span of transverse pipe tunnel members in m.IE, II denote moment of inertia of stiffeners including plate flange in cm4.

AE, AI denote shear area of stiffeners in cm2.

Other symbols are illustrated in Fig.B-14.

Note the allowable shear stress is to be taken according to the Rules for Classification of Ships Pt3 Ch.1 Sec.13D400 (= 90 f1 N/mm2).

B.8.3 The total normal stress of pipe tunnel transverse members may normally be determined according to thefollowing formula:

Inner bottom transverse member:

Bottom transverse member:

F,l,s = as given in B.8.2σib = transverse stress (N/mm2) in inner bottom in way of pipe tunnel according to double bottom

calculationσb = transverse stress (N/mm2) in bottom in way of pipe tunnel according to double bottom calculationhib = height in m of transverse inner bottom pipe tunnel memberhb = height in m of transverse bottom pipe tunnel memberhdb = height of double bottom at pipe tunnel in mpi = internal pressure from cargo as given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 C400

for the load case consideredpe = external lateral sea pressure according to the load case consideredZe, Zi = section modulus of pipe tunnel members (cm3).Other symbols are defined under B.8.2 and in Fig.B-14.

Note the allowable normal stress is to be taken according to the Rules for Classification of Ships Pt.3 Ch.1Sec.13 B400 (= 160 f1 N/mm2 in general).

IE

IE II+---------------

σ

Fl 1 k–( )2

----------------------pisl

210

3

12--------------------+

Zi--------------------------------------------------

σib hdb 2hib–( )

hdb------------------------------------ N/mm

2( )+=

σ

Flk2

--------pesl

210

3

12---------------------+

Ze-------------------------------------

σb hdb 2hb–( )hdb

---------------------------------- N/mm2( )+=




Figure B-14Analysis of pipe tunnel transverse members

B.9 Strength of double bottom below transverse bulkhead stool

B.9.1 When vertically corrugated transverse bulkheads are subjected to lateral load, large support forces, PF, occursby the bulkhead bending at the lower stool side or the corrugation flange (if no lower stool is fitted) attachmentto the double bottom as illustrated in Fig.B-15.

The force, PF, may be determined from the calculated bending moment of the transverse bulkhead at the innerbottom, MB (Nmm), as follows:

bs = breadth (mm) of stool at inner bottom.For wide stools the force PF will be balanced by the shear forces, FS1 and FS2, in the adjoining longitudinalbottom girder. For narrow stools the vertical stool side force may become very large giving rise to high shearstress in the web area below the stool. The nominal shear stress in the web may normally be determined as thelarger of:

τ =

=

P =

AS = the (vertical) shear area of the longitudinal girder below stool in cm = 10 t(hdb – hl)AH = the (horizontal) shear area of the longitudinal girder below the stool in cm2. = 10 t(bs – bl)hdb = as given in B.8.3hl = breadth in m of lightening hole arranged in double bottom girder below stoolbl = breadth in m of lightening hole arranged in double bottom girder below stoolt = thickness of longitudinal double bottom girder below stool in mm.FS1 and FS2 denote shear forces (N) of the longitudnal girder at the bulkhead stool, taken from the doublebottom grillage calculation.

The allowable nominal shear stress is to be taken in accordance with the Rules for Classification of Ships Pt.3Ch.1 Sec.13 B400 (= 100 f1 N/mm2).

l

h I A Zib i i i

h I A Zb e e e

, ,,

, , ,

STRUCTURALDESIGN

FF1 2

p

p

i

e

DISTR. PRESSURESFORCES

PF

MB

bs-------- (N)=

P100AS----------------

Pbs

100hdbAh------------------------- N mm

2⁄( )

2PF FS1 FS2+( )–( ) 2⁄ (N)




B.9.2 Where the floors below the stool side are discontinuous, e.g. at pipe tunnels, large stress concentrations mayoccur when the normal force, P, is transmitted from the stool to the double bottom. With reference to Fig.B-16,the nominal normal stress of the stool side, σ, at inner bottom may be calculated to:

P = force (N) transmitted between stool side and double bottom in way of the longitudinal girderconsidered

=

b = breadth of stool side in mm corresponding to longitudinal girder

=

be = effective breadth considering continuityts = thickness of stool side plating in mmtw = thickness of diaphragm plate in stool in line with considered longitudinal double bottom girderPF = as given in B.9.1.

The allowable normal stress may be taken in accordance with the Rules for Classification of Ships Pt.3 Ch.1Sec.13 B400 (= 160 f1 N/mm2).

The nominal shear stress, τ, at the intersection between floor and longitudinal girder may be calculated to:

AS1, AS2 denotes shear areas as indicated in Fig.B-16.

The allowable nominal shear stress may be taken in accordance with the Rules for Classification of Ships Pt.3Ch.1 Sec.13 B400 (= 90 f1 N/mm2).

Figure B-15Stress analysis of longitudinal web below transverse bulkhead (stool)

σ3b be–( )P

2b bets-------------------------- N mm

2⁄( )=

PF 1bstw

6tsb----------–

N( )

b1 b2+

2-----------------

τPF

100 AS1 AS2+( )---------------------------------------- N mm

2⁄( )=

hdb

PF

PF

FS1 FS2

hl

bl

bs




Figure B-16Stress analysis of floors below stool sides in way of double bottom tunnel

B.10 Shear strength of webs with cutouts

B.10.1 The nominal shear stress, τ, in webs in way of scalops and holes may in general calculated as:

FS = calculated shear force in N at section considered.The allowable nominal shear stress for double bottom webs is to be taken in accordance with the Rules forClassification of Ships Pt.3 Ch.1 Sec.13 B400 (= 100 f1 N/mm2).

B.10.2 For floor panels, a section parallel to the element axis may be decisive for the design shear stress. Withreference to Fig.B-17 the nominal shear stress for the horizontal sections at neutral axis and at bottom / resp.inner bottom may be calculated according to the following formulae:

τ = nominal shear stress between stiffeners at neutral axis

=

τ = nominal shear stress between stiffeners at bottom (or at inner bottom)

=

The allowable nominal shear stress is to be taken as given in B.10.1.

2

bbb 21 +=

be

30o

P

b1 b2

STRUCTURALDESIGN

EFFECTIVE BREADTHAT INNER BOTTOM

EFFECTIVE SHEARAREA

AS1

AS2

τFS

100hAS------------------- N mm

2⁄( )=

sFS

100hdb AS1

----------------------------- N mm2⁄( )

0.9sFS

100hdbAS2---------------------------- N mm

2⁄( )




Figure B-17Shear stress analysis of girder webs with cutouts

B.11 Strength of transverse bulkhead

B.11.1 The shear connection of the transverse bulkhead structure to the side shell, and compressive / tensile stressesin the transverse deck structure are matters of importance when the overall strength of the transverse bulkheadis evaluated. Both are of particular interest when the bulkhead is of the vertically corrugated type, and whenspecial load conditions with two adjacent holds empty on a large draught or with two adjacent holds loaded(combined with one or more of remaining holds empty) have been specified.

Such load conditions have been calculated with respect to the double bottom strength as described in thefollowing. The consideration of the bulkhead strength with respect to these load cases may therefore be basedon the double bottom calculation results.

B.11.2 The nominal shear stress of transverse bulkheads (above the lower stool) is generally given by:

FBHD = maximum calculated shear force in the transverse bulkhead at the section considered according to thedouble bottom (or quivalent) calculation, see B1-B.4

K = as given in B.5hs = height of lower stool (m)te = effective thickness of bulkhead plating = thickness of corrugation in way of corrugated part of bulkhead

= for diaphragm plate fitted in top wing tank in line with bulkhead corrugation

t = plate thickness of diaphragm plate in the top wing tank.ht = height of top wing tank in way of considered sectionhl = height of lightening holes in diaphragm plate in way of considered section.

The allowable nominal shear stress is to be taken in accordance with the Rules for Classification of Ships Pt.3Ch.1 Sec.13 B 400 (= 90 f1 N/mm2). Within the top wing tank (above the top wing tank bottom), the nominalshear stress as calculated according to the above formula may generally be reduced by a factor = 1.5, byconsideration of the partial support exerted by the top wing tank bottom panel.

B.11.3 The strength of the bulkhead corrugation in way of its attachment to the lower stool shall generally beconsidered in accordance with the Rules for Classification of Ships Pt.3 Ch.1 Sec.9 C 305. For stools withsloping stool top plate note in addition that the bending moment applicable for the control of stresses in way ofthe attachment of the corrugation to the stool need generally only be related to the bending moment at the levelof the top of the sloped stool top plate.

s

hdb

AS1

AS2

CRITICAL HORIZONTALSECTIONS OF SHEARSTRUCTURAL DESIGN

τFBHD

100K D hdb hs––( )te----------------------------------------------------- N mm

2⁄( )=

t ht hl–( )ht

----------------------




B.11.4 The stress of the stool side plate at the attachment to the bulkhead corrugation may generally be determinedbased on the following formula:

σcorr = nominal bending stress in bulkhead corrugation at attachment to stooltcorr = thickness of bulkhead corrugation, corrosion margin tk deductedtstool = thickness of stool side plate, corrosion addition tk deductedβ = angle of stool side plate with the vertical.Generally the σstool should not exceed 1.2 σ, where σ denotes the allowable stress given in the Rules forClassification of Ships Pt.3 Ch.1 Sec.9 C 302.

B.12 Strength of main frames

B.12.1 Generally the main frames of bulkcarriers are to comply with section modulus requirements as given in theRules for Classification of Ships Pt.5 Ch.2 Sec.10 B. For ships with long cargo holds, the main frames willnormally be subjected to considerable prescribed deformation caused by the rotational deformation of thehopper and top wing tanks. Such prescribed deformation occurs in particular for the empty holds and the oreholds in bulkcarriers in the alternate loading condition and for the condition with ballast cargo hold filled.

B.12.2 Main frames subjected to prescribed deformations shall comply with the allowable stress given in Pt.3 Ch.1Sec.13 B400. The occurring stresses may be determined by including the main frames in the double bottom-or wing tank models described in B.1-B.4, or by separate direct calculation.

σstool

σcorr tcorr

tstool βcos---------------------------=


strength analysis of hull structure inbulk carriers

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