Section 5 - Longitudinal Strength A 5 - 1

Section 5

Longitudinal Strength

A. General

1. Scope

1.1 For ships of categories I - II according to 4.1.3, thescantlings of the longitudinal hull structure are to bedetermined on the basis of longitudinal strength calculations.For ships which do not belong to these categories i.e. ingeneral for ships of less than 65 m in length, see alsoSection 7, A. 4.

1.2 The wave bending moments and shear forcesspecified under B.2 and 4. are design values which, inconnection with the scantling formulae, correspond to aprobability level Q = 10-8. Reduced values may be usedfor the purpose of determining combined stresses asspecified under E.4.

2. Calculation Particulars

The curves of the still water bending moments and stillwater shear forces for the envisaged loading and ballastconditions are to be calculated.

3. Assumptions for calculation, loading conditions

3.1 The calculation of still water bending moments andshear forces is to be carried out for the following loadingconditions:

.1 departure condition

.2 arrival condition

.3 intermediate conditions.

For determining the scantlings of the longitudinal hullstructure the maximum values of the still water bendingmoments and shear forces calculated for the loadingconditions .1 to .3 are to be used.

3.2 In general, the loading conditions specified in 4.4.2are to be investigated.

3.3 For other ship types and special ships, the calculationof bending moments and shear forces for other loadingconditions according to the intended service may be requiredto be investigated.

3.4 Where for ships of unusual design and form as wellas for ships with large deck openings a complex stressanalysis of the ship in the seaway becomes necessary, theanalysis will normally be done by using computer programsapproved by the Society.

4. Loading guidance information

4.1 General, definitions

4.1.1 Loading guidance information is a means inaccordance with Regulation 10(1) of LLC 66 which enablesthe master to load and ballast the ship in a safe mannerwithout exceeding the permissible stresses.

4.1.2 An approved loading manual is to be supplied forall ships except those of Category II with length less than90 m in which the deadweight does not exceed 30 % ofthe displacement at the summer loadline draft.

In addition, an approved loading instrument is to be suppliedfor all ships of Category I of 100 m in length and above.In special cases, e. g. extreme loading conditions or unusualstructural configurations, BKI may also require an approvedloading instrument for ships of Category I less than 100m in length.

Special requirements for bulk carriers, ore carriers andcombination carriers are given in Section 23, B.10.

4.1.3 The following definitions apply:

A loading manual is a document which describes:

– the loading conditions on which the design of theship has been based, including permissible limitsof still water bending moment and shear force,

– the results of the calculations of still water bendingmoments, shear forces and where applicable,limitations due to torsional and lateral loads, seealso F.,

– the allowable local loading for the structure (hatchcovers, decks, double bottom, etc.).

A loading instrument is an approved analog or digitalinstrument consisting of

– loading computer (Hardware) and

– loading program (Software)

by means of which it can be easily and quickly ascertainedthat, at specified read-out points, the still water bendingmoments, shear forces, and the still water torsional momentsand lateral loads, where applicable, in any load or ballastcondition will not exceed the specified permissible values.

An approved operational manual is always to be providedfor the loading instrument.

Loading computers must be type tested and certified, seealso 4.5.1. Type approved hardware may be waived, if

Section 5 - Longitudinal Strength A5 - 2

redundancy is ensured by a second certified loadinginstrument.

Type approval is required if S the computers are installed on the bridge or in

adjacent spaces S interfaces to other systems of ship operation are

provided

For type approval the relevant rules and guidelines areto be observed.

Loading programs must be approved and certified, see also4.3.1 and 4.5.2. Single point loading programs are notacceptable.

Ship categories for the purpose of this paragraph aredefined for all classed seagoing ships of 65 m in lengthand above which are contracted for construction on or after1st July 1998 as follows:

Category I Ships:

Ships with large deck openings where, according to F.,combined stresses due to vertical and horizontal hull girderbending and torsional and lateral loads have to beconsidered.

Chemical tankers and gas carriers.

Ships more than 120 metres in length, where the cargoand/or ballast may be unevenly distributed.

Ships less than 120 metres in length, when their designtakes into account uneven distribution of cargo or ballast,belong to Category II.

Category II Ships:

Ships with arrangement giving small possibilities forvariation in the distribution of cargo and ballast (e.g.passenger vessels) and ships on regular and fixed tradingpatterns where the loading manual gives sufficient guidance,and in addition those exceptions given under Category I.

4.2 Conditions of approval of loading manuals

The approved loading manual is to be based on the finaldata of the ship. The manual is to include the design loadingand ballast conditions upon which the approval of the hullscantlings is based.

4.4.2 contains as guidance only a list of the loadingconditions which normally are to be included in the loadingmanual.

In case of modifications resulting in changes in the maindata of the ship, a new approved loading manual is to beissued.

The loading manual must be prepared in a languageunderstood by the users. If this language is not English,a translation into English is to be included.

4.3 Conditions of approval of loading instruments

4.3.1 The approval of the loading instrument is to include:

– verification of type approval,

– verification that the final data of the ship has beenused,

– acceptance of number and position of read-outpoints,

– acceptance of relevant limits for all read-out points,

– checking of proper installation and operation of theinstrument on board in accordance with agreed testconditions, and that a copy of the approved operationmanual is available.

4.3.2 4.5 contains information on approval proceduresfor loading instruments.

4.3.3 In case of modifications implying changes in themain data of the ship, the loading program is to be modifiedaccordingly and approved.

4.3.4 The operation manual and the instrument outputmust be prepared in a language understood by the users.If this language is not English, a translation into Englishis to be included.

4.3.5 The operation of the loading instrument is to beverified upon installation. It is to be checked that the agreedtest conditions and the operation manual for the instrumentare available on board.

The permissible limits for the still water bending momentsand shear forces to be applied for the ballast water exchangeat sea are to be determined in accordance with E., whereB.2.1 and B.2.2 are to be used for the wave bendingmoments and B.3., B.4.1 and B.4.2 for the wave shearforces.

4.4 Design cargo and ballast loading conditions

4.4.1 The loading manual should contain the designloading and ballast conditions, subdivided into departureand arrival conditions and ballast exchange at sea conditions,where applicable, upon which the approval of the hullscantlings is based.

Where the amount and disposition of consumables at anytransitory stage of the voyage are considered to result ina more severe loading condition, calculations for suchtransitory conditions are to be submitted in addition to thosefor departure and arrival conditions.

Also, where any ballasting and/or deballasting is intendedduring voyage, calculations of the transitory conditionsbefore and after ballasting and/or deballasting any ballasttank are to be submitted and, after approval, included inthe loading manual for guidance.

Section 5 - Longitudinal Strength A 5 - 3

4.4.1.1Partially filled ballast tanks in ballast loadingcondition

Ballast conditions involving partially filled peak and otherballast tanks are not permitted to be used as designconditions where alternative filling levels would result indesign stress limits being exceeded.

To demonstrate compliance with all filling levels betweenempty and full, it will be acceptable if, in each conditionat departure, arrival and where required by 4.3.2 anyintermediate condition, the tanks intended to be partiallyfilled are assumed to be:

– empty

– full

– partially filled at intended level

Where multiple tanks are intended to be partially filled,all combinations of empty, full or partially filled at intendedlevel for those tanks are to be investigated.

However, for conventional ore carriers with large wingwater ballast tanks in cargo area, where empty or full ballastwater filling levels of one or maximum two pairs of thesetanks lead to the ship's trim exceeding one of the followingconditions, it is sufficient to demonstrate compliance withmaximum, minimum and intended partial filling levels ofthese one or maximum two pairs of ballast tanks such thatthe ship's condition does not exceed any of these trim limits.

Filling levels of all other wing ballast tanks are to beconsidered between empty and full.

The trim conditions mentioned above are:

– trim by stern of 0,03 L, or

– trim by bow of 0,015 L, or

– any trim that cannot maintain propeller immersion(I/D) not less than 25%

I = the distance from propeller centreline to thewaterline

D = propeller diameter

The maximum and minimum filling levels of the abovementioned pairs of side ballast tanks are to be indicatedin the loading manual.

4.4.1.2 Partially filled ballast tanks in combinationwith cargo loading conditions

In such cargo loading conditions, the requirements in 4.4.1.1apply to the peak tanks only. Requirements of 4.4.1.1 and4.4.1.2 are not applicable to ballast water exchange usingthe sequential method.

4.4.2 In particular the following loading conditions shouldbe included:

Cargo Ships, Container Ships, Roll-on/Roll-off andRefrigerated Carriers, Ore Carriers and Bulk Carriers

– homogeneous loading conditions at maximumdraught,

– ballast conditions,

– special loading conditions, e.g. container or lightload conditions at less than the maximum draught,heavy cargo, empty holds or non-homogeneouscargo conditions, deck cargo conditions, etc., whereapplicable,

– short voyage or harbour conditions, whereapplicable,

– docking condition afloat,– loading and unloading transitory conditions, where

applicable.

Oil tankers

– homogeneous loading conditions (excluding dryand segregated ballast tanks) and ballast or partloaded conditions for both departure and arrival,

– any specified non-uniform distribution of loading,

– mid-voyage conditions relating to tank cleaning orother operations where these differ significantlyfrom the ballast conditions,

– docking condition afloat,

– loading and unloading transitory conditions.

Chemical tankers

– conditions as specified for oil tankers,

– conditions for high density or heated cargo, see alsoSection 12, A.6., and

– segregated cargo where these are included in theapproved cargo list.

Liquefied gas carriers

– homogeneous loading conditions for all approvedcargoes for both arrival and departure,

– ballast conditions for both arrival and departure,

– cargo condition where one or more tanks are emptyor partially filled or where more than one type ofcargo having significantly different densities iscarried for both arrival and departure,

– harbour condition for which an increased vapourpressure has been approved (see Rules for ShipsCarrying Liquefied Gas in Bulk, Volume IX,Section 4, 4.2.6.4),

– docking condition afloat.

Combination carriers

– conditions as specified for oil tankers and cargoships

Section 5 - Longitudinal Strength A5 - 4

4.5 Approval procedures of loading instruments

4.5.1 Type test of the loading computer

The type test requires:

– the loading computer to undergo successful testsin simulated conditions to prove its suitability forshipboard operation,

– The testing of a design may be waived if a loadinginstrument has been tested and certified by anindependent and recognized authority, provided thetesting program and results are consideredsatisfactory.

4.5.2 Certification of the loading program

4.5.2.1 After the successful type test of the Hardwarethe producer of the loading program must ask BKI forcertification.

4.5.2.2 The number and location of read-out points areto be to the satisfaction of BKI.

Read-out points should usually be selected at the positionof the transverse bulkheads or other obvious boundaries.Additional read-out points may be required betweenbulkheads of long holds or tanks or between containerstacks.

4.5.2.3 BKI will specify:

– the maximum permissible still water shear forces,bending moments (limits) at the agreed read-outpoints and when applicable, the shear forcecorrection factors at the transverse bulkheads,

– when applicable, the maximum permissible torsionalmoments,

– also when applicable the maximum lateral load.

4.5.2.4 For approval of the loading program the followingdocuments have to be submitted:

– operation manual for the loading program,

– print-outs of the basic ship data like distributionof light ship weight, tank and hold data etc.,

– print-outs of at least 4 test cases,

– diskettes with loading program and stored test cases.

The calculated strength results at the fixed read-out pointsmust not differ from the results of the test cases by morethan 5 % related to the approved limits.

4.5.3 Final approval of the loading instrument will begranted when the accuracy of the loading instrument hasbeen checked in the presence of the Surveyor afterinstallation on board ship using the approved test conditions.

If the performance of the loading instrument is foundsatisfactory, the Surveyor will stamp his signature and datea self-adhering label for approval plate provided for thispurpose, which shall be fixed to the loading instrumentscasing in a prominent position. The date of approval (month,year) and the number of corresponding approval certificateare stated on proof label.

A certificate will then be issued. A copy of the certificateis to be included in the operation manual.

4.6 Class maintenance of loading guidanceinformation

At each Annual and Class Renewal Survey, it is to bechecked that the approved loading guidance informationis available on board.

The loading instrument is to be checked for accuracy atregular intervals by the ship's Master by applying testloading conditions.

At each Class Renewal Survey this checking is to be donein the presence of the Surveyor.

5. Definitions

k = material factor according to Section 2, B.2.

CB = block coefficient as defined in Section 1,H.4.CB is not to be taken less than 0,6

x = distance in [m] between aft end of length L andthe position considered

v0 = speed of the ship in [kn] according to Section.1,H.5.

Iy = moment of inertia of the midship section in [m4]around the horizontal axis at the position x/L

eB = distance in [m] between neutral axis of hullsection and base line

eD = distance in [m] between neutral axis of hullsection and deck line at side

ez = vertical distance of the structural elementconsidered from the horizontal neutral axis [m](positive sign for above the neutral axis, negativesign for below)

WB = section modulus of section in [m3] related tobase line

WD = section modulus of section in [m3] related todeck line at side

S = first moment of the sectional area consideredin [m3] related to the neutral axis

MT = total bending moment in the seaway in [kNm]

= MSW + MWV

MSW = permissible vertical still water bending moment

Section 5 - Longitudinal Strength B 5 - 5

in [kNm] (positive sign for hogging, negativesign for sagging condition)

MWV = vertical wave bending moment in [kNm](positive sign for hogging, MWVhog, negativesign for sagging condition, MWVsag)

MWH = horizontal wave bending moment [kNm](positive sign for tension in starboard side,negative for compression in starboard side)

MST = static torsional moment in [kNm]

MWT = wave induced torsional moment in [kNm]

QT = total vertical shear force in the seaway in [kN]

= QSW + QWV

QSW = permissible vertical still water shear force in[kN]

QWV = vertical wave shear force in [kN]

QWH = horizontal wave shear force in [kN].

The sign rule see Fig. 5.1

Fig. 5.1 Sign rule

B. Loads on the Ship’s Hull

1. General

In general the global loads on the hull in a seaway can becalculated with the formulas stated below.

For ships of unusual form and design (e.g. L/B # 5, B/H$ 2,5, L $ 500 m or CB < 0,6) and for ships with a speedof:

v0 $1,6 @ [kn]L

as well as for ships with large bow and stern flare and withcargo on deck in these areas BKI may require determinationof wave bending moments as well as their distribution overthe ship's length by approved calculation procedures. Suchcalculation procedures must take into account the ship'smotions in a natural seaway.

2. Still Water Loads

2.1 General

Due to the provided loading cases the vertical longitudinal

bending moments and shear forces are to be (MSW, QSW).If statical torsional moments are likely to be expected fromthe loading or construction of the ship, they have to be takeninto account.

Still water loads have to be superimposed with the waveinduced loads according to 3.

2.2 Guidance values for containerships with randomloading

2.2.1 Still water bending moments

When determining the required section modulus of themidship section of containerships in the range:

= 0,3 to = 0,55xL

xL

it is recommended to use at least the following initial valuefor the hogging still water bending moment:

MSW ini = n1 @ c0 @ L2 @ B @ (0,123 ! 0,015 @ CB)

n1 = # 1,21,07 · 1 % 15 · n105

2

n = according to 2.2.2

MSWini shall be graduated regularly to ship’s ends.

2.2.2 Static torsional moment

The maximum static torsional moment may be determinedby:

MST max = [kNm]± 20 · B · CC

CC = maximum permissible cargo capacity of theship [t]

= n . G

n = maximum number of 20'-containers (TEU) ofthe mass G the ship can carry

G = mean mass of a single 20'-container [t]

For the purpose of a direct calculation the followingenvelopping curve of the static torsional moment over theship's length are to be taken:

MST = [kNm]0,568 · MSTmax *cT1*%cT2

cT1, cT2 = distribution factors, see also Fig. 5.2

cT1 = for sin0,5 2π xL

0# xL

<0,25

= forsin 2π xL

0,25# xL#1,0

cT2 = for sin π xL

0# xL

<0,5

= forsin2 π xL

0,5# xL#1,0

Section 5 - Longitudinal Strength B5 - 6

Fig. 5.2 Distribution factors cT1 and cT2 fortorsional moments

3. Wave induced loads

3.1 Vertical wave bending moments

The vertical wave bending moment amidships is to bedetermined by the following formula:

MWV = L2 @ B @ c0 @ c1 @ cL @ cM [kNm]

c0 = wave coefficient as follows:

= + 4,1 for L < 90 mL25

= 10,75 ! for 90 L 300 m300 S L100

1,5<– <–

= 10,75 for L > 300 mc1 = hogging/sagging factor as follows:

c1H = 0,19 @ CB hogging condition

c1S = S 0,11 (CB + 0,7)sagging condition

cL = for L < 90 mL90

= 1,0 for L 90m>–

cM = distribution factor, see also Fig. 5.3cMH = hogging condition

= for < 0,42,5 @ xL

xL

= 1,0 for 0,4 0,65<–xL

<–

= for > 0,651 S

xL

0,35xL

cMS = sagging condition

= cv @ for < 0,42,5 @ xL

xL

= cv for 0,4 0,65 @ cv<–xL

<–

= for > 0,65 @ cvcv !

xL

! 0,65 @ cv

1 ! 0,65 @ cv

xL

cv = influence with regard to speed v0 of the vessel

= 1,0 for 1, 4 · the value3 v0

1,4 @ L>– L

need not be less than 14

= 1,0 for damaged condition.

Fig. 5.3 Distribution factor cM and influence factor cv

3.2 Vertical wave shear forces

The vertical wave shear forces are to be determined by thefollowing formula:

QWV = c0 @ cL @ L @ B (CB + 0,7) cQ [kN]

c0, cL = see section 4, A.2.2

cQ = distribution factor according to Table 5.1, seealso Fig. 5.4.

m = Sc1H

c1S

c1H, c1S see 2.1.

3.3 Horizontal bending moments

MWH = 0,32 @ L @ QWHmax @ cM [kNm]

cM = see 3.1, but for cv = 1

QWHmax= see 3.4

Section 5 - Longitudinal Strength B 5 - 7

Table 5.1 Distribution factor cQ

Range Positive shear forces Negative shear forces

0 < 0,2 1,38 @ m S 1,38 <–xL

xL

xL

0,2 < 0,3<–xL 0,276 @ m S 0,276

0,3 < 0,4 1,104 m S 0,63 + (2,1 S 2,76 m)<–xL

xL

S 0,474 S 0,66 xL

0,4 < 0,6<–xL 0,21 S 0,21

0,6 < 0,7<–xL

(3 cv – 2,1) + 0,21xL

– 0,6 S 1,47 S 1,8 m % 3 (m S 0,7) xL

0,7 < 0,85<–xL 0,3 @ cv S 0,3 m

0,85 # 1,0<–xL

13

cv 14 xL

– 11 – 20 xL% 17 S 2 m 1 S

xL

Fig 5.4 Distribution factor cQ

3.4 Horizontal shear forces

QWHmax = [kN]± cN · L·T ·B·CB·c0·cL

cN = 1 % 0,15 · L

B

cNmin = 2

QWH = QWHmax · cQH

cQH = distribution factor according to Table 5.2, seealso Fig. 5.5

Table 5.2 Distribution factor cQH

Range cQH

0 0 1≤ <xL

, 0 4 6, .+xL

0 1 0 3, ,≤ ≤xL

1

0 3 0 4, ,< <xL

1 0 5 0 3, . ,− −⎛⎝⎜

⎞⎠⎟

xL

0 4 0 6, ,≤ ≤xL

0,5

0 6 0 7, ,< <xL

0 5 5 0 6, . ,+ −⎛⎝⎜

⎞⎠⎟

xL

0 7 0 8, ,≤ ≤xL

1,0

0 8 1 0, ,< ≤xL

1 0 4 25 0 8, , . ,− −⎛⎝⎜

⎞⎠⎟

xL

3.5 Torsional moments

The maximum wave induced torsional moment is tobe determined as follows:

MWTmax = [kNm]± L·B2·CB·c0·cL· 0,11% a 2%0,012

Section 5 - Longitudinal Strength C5 - 8

a = TL

·cN · zQ

B

amin = 0,1

cN = see 3.4

ZQ = distance [m] between shear centre and a level

at above the basis0,2· B·HT

When a direct calculation is performed, for the waveinduced torsional moments the following envelopping curveis to be taken:

MWT = [kNm]± L·B2·CB·c0·cL·cWT

cWT = distribution factor, see also Fig. 5.6

= a · *cT1% 0,22 · cT2 · 0,9% 0,08 · a

cT1, cT2 = see 2.2.2

Fig 5.5 Distribution factor cQH

Fig. 5.6 Distribution factor cWT

Note

The envelope can be approximated by superposition of bothdistributions according to Fig. 5.2.

C. Section Moduli, Moments of Inertia, Shear andBuckling Strength

1. Section moduli as function of longitudinalbending moments

1.1 The section moduli related to deck respectively WD’or bottom WB are not to be less than:

W = [m3]fr ·*MSW % MWV*

σp · 103

fr = 1,0 (in general)

= according to F.2. for ships with large openings

Ships, for which also at damaged condition sufficientlongitudinal strength is to be proved, the section modulusis not to be less than:

Wf = [m3]*MSWf % 0,8 · MWV*

σp · 103

see also B.2.1. and G

σp = permissible hull girder bending stress in[N/mm2]

= cs @ σp0

σp0 = 18,5 for L < 90 mLk

= for L $ 90 m175k

cs = 0,5 + for < 0,3053

xL

xL

= 1,0 for 0,30 0,70<–xL

<–

= for > 0,70.53

1,3 SxL

xL

1.2 For the ranges outside 0,4 L amidships the factorcs may be increased up to cs = 1,0, if this is justified underconsideration of combined stresses due to longitudinal hullgirder bending (including bending to impact loads),horizontal bending, torsion and local loads and underconsideration of buckling strength.

2. Minimum midship section modulus

2.1 The section modulus related to deck and bottomis not to be less than the following minimum value:

Wmin = k @ c0 @ L2 @ B ·(CB + 0,7)·10-6 [m3]

c0 according to Section 4, A.2.2 for unlimited service range(crw =1,0)

For ships classed for a restricted range of service, theminimum section modulus may be reduced as follows:

Section 5 - Longitudinal Strength C 5 - 9

P (Restricted Ocean Service) : by 5%

L (Coasting Service) : by 15%

T (Shallow Water Service) : by 25%

2.2 The scantlings of all continuous longitudinalmembers based on the minimum section modulusrequirement are to be maintained within 0,4 L amidships.

3. Midship section moment of inertia

The moment of inertia related to the horizontal axis is notto be less than:

Iy = 3 @ 10-2 @ W @ [m4]Lk

W see 1.1 and/or 2.1, the greater value is to be taken.

4. Calculation of section moduli

4.1 The bottom section modulus WB and the deck sectionmodulus WD are to be determined by the followingformulae:

WB = [m3]Iy

eB

WD = [m3]Iy

eD

Continuous structural elements above eD (e.g. trunks,longitudinal hatch coamings, decks with a large camber,longitudinal stiffners and longitudinal girders arrangedabove deck, bulwarks contributing to longitudinal strengthetc.) may be considered when determining the sectionmodulus, provided they have shear connection with thehull and are effectively supported by longitudinal bulkheadsor by rigid longitudinal or transverse deep girders.

The fictitious deck section modulus is then to be determinedby the following formula:

W!D = [m3]Iy

e!D

e!D = z (0,9 + 0,2 @ ) [m]yB

z = distance in [m] from neutral axis of the crosssection considered to top of continuous strengthmember

y = distance in [m] from centre line to top ofcontinuous strength member.

It is assumed that e!D > eD.

For ships with multi-hatchways see 5.

4.2 When calculating the midship section modulus,openings of continuous longitudinal strength members maybe taken into account.

Large openings, i.e. openings exceeding 2,5 m in lengthor 1,2 m in breadth and scallops, where scallop-weldingis applied, are always to be deducted from the sectionalareas used in the section modulus calculation. Smalleropenings (manholes, lightening holes, single scallops inway of seams etc.) need not be deducted provided that thesum of their breadths or shadow area breadths in onetransverse section is not reducing the section modulus atdeck or bottom by more than 3 % and provided that theheight of lightening holes, draining holes and single scallopsin longitudinals or longitudinal girders does not exceed25 % of the web depth, for scallops 75 mm at most. (Seefig.5.7.)

A deduction-free sum of smaller opening breadths in onetransverse section in the bottom or deck area of 0,06(B - Gb) (where B = breadth of ship at the consideredtransverse section, Gb = sum of breadth of openings) maybe considered equivalent to the above reduction in sectionmodulus by 3%.

The shadow area will be obtained by drawing two tangentlines with an opening angle of 30E (see Fig. 5.7).

4.3 Where in the upper and lower flange thicknessesof continuous longitudinal structures forming boundariesof oil or ballast tanks have been reduced due to arrangementof an effective corrosion protection system, these thicknessreduction shall not result in a reduction of midship sectionmodulus of more than 5%.

Note

In case of large openings local strengthenings may berequired which will be considered in each individual case(see also Section 7, A.3.1).

Fig 5.7 Shadow area

5. Ships with multi-hatchways

5.1 For the determination of section moduli 100%effectivity of the longitudinal hatchway girders betweenthe hatchways may be assumed, if an effective attachmentof these girders is given.

5.2 An effective attachment of the longitudinal hatchwaygirder must fulfil the following condition:

Section 5 - Longitudinal Strength C5 - 10

The longitudinal displacement fL of the point of attachmentdue to action of a standard longitudinal force PL is not toexceed

fL = [mm]R20

Rs = length of transverse hatchway girder accordingto Fig. 5.8 in [m]

PL = 10 @ ALG [kN]

ALG = entire cross sectional area of the longitudinalhatchway girder in [cm2]

see also Fig. 5.8.

Fig. 5.8 Ship with multi-hatchways

Where the longitudinal displacement exceeds fL = Rs/20,special calculation of the effectivity of the longitudinalhatchway girders may be required.

5.3 For the permissible composed stress see Section.10,E.3.

6. Shear strength

The shear stress in longitudinal structures due to the verticaltransverse forces QT acc. to E.2. and E.3. must not exceed110/k N/mm2.

For ships with large deck openings and/or for ships withlarge static torsional moments, also the shear stresses dueto MSTmax have to be considered adversely, i.e. increasingthe stress level.

For ships, where also in damaged condition sufficientstrength is to be proved, the shear forces QSWf and 0,8 @QWV are to be assumed. The shear stress must not exceed110/k N/mm2.

The shear stresses are to be determined according to D.3.

7. Proof of buckling strength

All longitudinal hull structural elements subjected tocompressive stresses resulting from MT according to E.1and QT according to E.2. are to be examined for sufficientresistance to buckling according to Section 3, F. For this

purpose the following load combinations are to beinvestigated:

.1 MT and 0,7 @ QT

.2 0,7 @ MT and QT .

8. Ultimate load calculation of the ship's transversesections

8.1 In extreme sea states larger loads than referred toin B.3. may occur. Therefore dimensioning of longitudinalstructures is to be verified by proving the ultimate capacityaccording to 8.2 and 8.3. In general, the safety factor shallnot be less than γ = 1,5.

8.2 Ultimate plastic vertical bending moment

γ · MSW%MWV

cs

# MpR,y

= see 8.1γ

= stress factor according to 1.1cs

MpR,y = transferable vertical bending moment [kNm]around the horizontal axis of the ship's plastifiedtransverse section.

For the calculation of MpR,y , in transversesections under compression, the effectivesectional areas are to be considered accordingto Section 3, F.

8.3 Ultimate plastic vertical transverse force

γ · QSW%QWV

cs

# QpR,z

= see 8.1γ

= see 8.2cs

QpR,z = transferable vertical shear force [kN]

= 11000 3 1.

. . . .κτii

ni i eHib t R

=∑

i to n = number of the shear force transmitting panels(in general these are only continuous web areasof the depth H such as shell and longitudinalbulkheads)

bi = vertical breadth of the panel [mm]

ti = thickness of the panel [mm]

ReHi = yield stress of the panel [N/mm2]

= reduction factor according to Section 3, F.κτi

Section 5 - Longitudinal Strength D 5 - 11

D. Design Stresses

1. General

Design stresses for the purpose of this rule are global loadstresses, which are acting:

– as normal stresses σL in ship's longitudinal direction:

– for plates as membrane stresses– for longitudinal profiles and longitudinal girders

in the bar axis

– shear stresses τL in the plate level

The stresses σL and τL are to be considered in the formulasfor dimensioning of plate thicknesses (Section 6, B.1. andC.1. and Section 12, B.1.), longitudinals (Section 9, B.2.)and grillage systems (Section 8, B.8. and Section 10, E.2.).

The calculation of the stresses can be carried out by ananalysis of the complete hull. If no complete hull analysisis carried out, the most unfavourable values of the stresscombinations according to Table 5.3 are to be taken forσL and τL respectively. The formulae in Table 5.3 containσSW, σWV, σWH, σST and σWT according to 2. and τSW, τWV,τWH, τST and τWT according to 3. as well as:

fF = weighting factor for the simultaneousness ofglobal and local loads

= 0,8 for dimensioning of longitudinal structuresaccording to Sections 3 and 6 to 12

= for fatigue strength0,75 %xL

· 1! xL

calculations according to Section 20

fQ = probability factor according to Section 4, Table4.2

fQmin = 0,75 for Q = 10-6

Note

fQ is a function of the planned lifetime. For a lifetime ofn > 20 years, fQ may be determined by the following formulafor a straight-line spectrum of seaway induced stressranges:

fQ = !0,125 · log 2·10&5

n

For greatest vertical wave bending moment:

σNWV = 0,43 % C · σWVhog

τNWV = 0,43 % C · τWVhog

For smallest vertical wave bending moment:

σNWV = 0,43 % C · 0,5 ! C · σWVhog

% C · 0,43 % C · σWVsag

τNWV = 0,43 % C · 0,5 ! C · τWVhog

% C · 0,43 % C · τWVsag

C = xL

! 0,52

Note

For the preliminary determination of the scantlings, it isgenerally sufficient to consider load case 1, assuming thesimultaneous presence of σL1a and τL1b, but disregardingstresses due to torsion.

The stress components (with the proper signs: tensionpositive, compression negative) are to be added such, thatfor σL and τL extreme values are resulting.

1.1 Buckling strength

For structures loaded by compression or shear forces,sufficient buckling strength according to Section 3, F. isto be proved.

1.2 Permissible stresses

The equivalent stress from σL and τL is not to exceedthe following value:

σV = [N/mm2]σL2% 3 · τL

2 # 190k

1.3 Structural design

1.3.1 In general, longitudinal structures are to be designedsuch, that they run through transverse structurescontinuously. Major discontinuities have to be avoided.

If longitudinal structures must be staggered, sufficientshifting elements shall be provided.

1.3.2 The required welding details and classifying ofnotches result from the fatigue strength analysis accordingto Section 20.In the upper respectively lower ship girder, for the weldingjoints the detail categories (see Table 20.3) shall not beless than

∆σR min = [N/mm2]MWVhog!MWVsag ·*ez*

(4825 ! 29 · n) · Iy

MWVhog, MWVsag = vertical wave bending moment forhogging and sagging according toB.3.1

n = expected lifetime of the ship

20 [years]≥

Section 5 - Longitudinal Strength D5 - 12

Table 5.3 Load cases and stress combinations

Load Case Design stresses σ τL L,

L1aσ σ σ σL a SW ST Q WVf1 = + + .

τ τ τ τL a SW ST Q WVf1 0 7 0 7= + +, . , . .

L1bσ σ σ σL b SW ST Q WVf1 0 7 0 7= + +, . , . .

τ τ τ τL b SW ST Q WVf1 = + + .

L2a( )σ σ σ σ σL a SW ST Q WV WHf2 0 6= + + +. , .

( )τ τ τ τ τL a SW ST Q WV WHf2 0 7 0 7 0 6= + + +, . , . . , .

L2b( )σ σ σ σ σL b SW ST Q WV WHf2 0 7 0 7 0 6= + + +, . , . . , .

( )τ τ τ τ τL b SW ST Q WV WHf2 0 6= + + +. , .

L3a

( )[ ]σ σ σ σ σ σL a F SW ST Q WV WH WTf f3 = + + + +. . '

( )[ ]{ }τ τ τ τ τ τL a F SW ST Q WV WH WTf f3 0 7 0 7= + + + +. , . . , . '

L3b( )[ ]{ }σ σ σ σ σ σL b F SW ST Q WV WH WTf f3 0 7 0 7= + + + +. , . . , . '

( )[ ]τ τ τ τ τ τL b F SW ST Q WV WH WTf f3 = + + + +. . '

L1a,b = Load caused by vertical bending and static torsional moment.

L2a,b = Load caused by vertical and horizontal bending moment as well as static torsional moment.

L3a,b = Load caused by vertical and horizontal bending moment as well as static and wave induced torsional moment

2. Normal stresses in the ship's longitudinaldirection

2.1 Normal stresses from vertical bending moments

2.1.1 statical from MSW:

σSW = [N/mm2]MSW · ez

Iy·103

MSW = still water bending moment according to A.5.at the position x/L

2.1.1 dynamical from MWV:

σWV = [N/mm2]MWV · ez

Iy·103

2.2 Normal stresses due to horizontal bendingmoments

dynamical from MWH:

σWH = ! [N/mm2]MWH · ey

Iz·103

MWH = horizontal wave bending moment according toB.3.3 at the position x/L

Iz = moment of inertia [m4] of the transverse shipsection considered around the vertical axis atthe position x/L

ey = horizontal distance of the structure consideredfrom the vertical, neutral axis [m]

Section 5 - Longitudinal Strength D 5 - 13

ey is positive at the port side, negative at thestarboard side

2.3 Normal stresses from torsion of the ship's hull

When assessing the cross sectional properties the effectof wide deck strips between hatches constraining the torsionmay be considered, e.g. by equivalent plates at the decklevel having the same shear deformation as the relevantdeck strips.

2.3.1 statical from MSTmax:

For a distribution of the torsional moments according toB.2.2.2, the stresses can be calculated as follows:

σST = [N/mm2]0,65·CTor·MSTmax·ωi

λ·Iω·103· 1 ! 2

e a%1

MSTmax = max. static torsional moment according toB.2.2.2

see 2.3.2.C I e a C xTor c c A, , , , , , ,ω λ l

For other distributions the stresses have to be determinedby direct calculations.

2.3.2 dynamical from MWTmax:

σWT = [N/mm2]CTor·MWTmax·ωi

λ·Iω·103· 1 ! 2

e a%1

MWTmax = according to B.3.5

= for 0 # < 0,25CTor 4 · CB !0,1 · xL

xL

= for 0,25 # # 0,65CB ! 0,1 xL

= for 0,65 # # 1CB !0,1

0,35· 1! x

LxL

= sectorial inertia moment [m6] of the ship'sIωtransverse section at the position x/L

= sectorial coordinate [m2] of the structureω iconsidered

= warping valueλ

= [l/m]II

T

2 6, . ω

IT = torsional moment of inertia [m4] of the ship'stransverse section at the position x/L

e = Euler number (e = 2,718...)

A = λ.l c

= characteristical torsion length [m]l c

= 2 · CB· 1! 1! 0,5CB

·

LB&1

4,284

2

· L · Cc

for < 5,284LB

= for $ 5,284257 · BL

2,333· B · Cc

LB

Cc = 0,8 !xA

L% 0,5 % 2,5 ·

xA

L· x

L

for 0 # # 0,4 and 0 # # 0,4xL

xA

L

= 1 for 0,4 # # 0,55xL

= for 0,55 < # 11 ! 10,45

· xL!0,55 x

L

xA = 0 for ships without cargo hatches

= distance [m] between the aft end of the lengthL and the aft edge of the hatch forward of theengine room front bulkhead on ships with cargohatches, see also Fig. 5.9

3. Shear stresses

Shear stress distribution should be calculated by calculationprocedures approved by BKI. For ships with multi-celltransverse cross sections (e.g. double hull ships), the useof such a calculation procedure, especially with non-uniformdistribution of the load over the ship's transverse section,may be stipulated.

3.1 Shear stresses due to vertical shear forces

For ships without longitudinal bulkheads or with twolongitudinal bulkheads, distribution in of the shear stressin the shell and in the longitudinal bulkheads can becalculated with the following formula:

statical from QSW:

τSW =QSW @ Sy(z)

Iy @ t(0,5 - α) [N/mm 2]

dynamical from QWV:

τWV =QWV @ Sy(z)

Iy @ t(0,5 - α) [N/mm 2]

Sy(z) = first moment of the sectional area considered[m3], above or below, respectively, the level zconsidered, and related to the horizontal, neutralaxis

Section 5 - Longitudinal Strength E5 - 14

t = thickness of side shell or longitudinal bulkheadplating in [mm] at the section considered

α = 0 for ships having no longitudinal bulkhead

Where 2 (two) longitudinal bulkheads are fitted:

α = 0,16 + 0,08 for the longitudinal bulkheadsAs

AL

= 0,34 - 0,08 for the side shellAs

AL

As = sectional area of side shell plating in [cm2]within the depth H

AL = sectional area of longitudinal bulkhead platingin [cm2] within the depth H.

For ships of normal shape and construction, the ratio S/Iydetermined for the midship section may be used for allsections.

3.2 Shear stresses due to horizontal shear forces

3. is to be applied to correspondingly.

3.3 Shear stresses due to torsional moments

statical from MSTmax :

For a distribution of torsional moments according to B.2.2.2,the stresses can be calculated as follows:

= [N/mm2]τST 0 65, . . ..maxC M

SI tTor ST

i

i

ω

ω

CTor = according to D.2.3.1

MSTmax = according to B.2.2.2

MWTmax = according to B.3.5= according to D.2.3.1Iω

= statical sector moment [m4] of the structureS iωconsidered

ti = thickness [mm] of the plate considered

For other distributions the stresses have to be determinedby direct calculations.

dynamical from MWTmax:

= [N/mm2]τWT C MS

I tTor WTi

i. .

.maxω

ω

E. Permissible Still Water Loads

1. Vertical bending moments

The permissible still water bending moments for a sectionwithin the length L are to be determined by the followingformulae:

MSW = MT S MWV [kNm]

MSWf = MT S 0,8 . MWV [kNm]

MWV see B.3.1

For harbour- and offshore terminal conditions the waveloads may be multiplied with the following factors:

– harbour conditions (normally) : 0,1

– offshore terminal conditions : 0,5

From the following two values for MT:

MT= σp @ WD(a) @ [kNm] 103

fror

MT= σp @ WB(a) @ [kNm]103

fr

the smaller value is to be taken.

WD(a) = actual deck section modulus in [m3] at theposition x

WB(a) = actual bottom section modulus in [m3] at theposition x

σD, σ’D = longitudinal bending stress [N/mm2] for theship’s upper girder

= σSW + σWV

σB = longitudinal bending stress [N/mm2] for theship’s lower girder

= σSW + σWV

fr = 1,0 (in general).

= according to F.2. for ships with large openings

In the range x/L = 0,3 to x/L = 0,7 the permissible still waterbending moment should generally not exceed the valueobtained for x/L = 0,5.

2. Vertical shear forces

The permissible still water shear forces for any cross sectionwithin the length L are to be determined by the followingformulae:

QSW = QT S QWV [kN]

QSWf = QT S 0,8 . QWV [kN]

Section 5 - Longitudinal Strength F 5 - 15

QT = permissible total shear force in [kN], for whichthe permissible shear stress τ = τSW + τWVwill be reached but not exceeded at any pointof the section considered.

τ = permissible shear stress [N/mm2]

QWV = according to B.3.2

For harbour and offshore terminal conditions, see 1.

2.1 Correction of still water shear force curve

In case of alternate loading the conventional shear forcecurve may be corrected according to the direct loadtransmission by the longitudinal structure at the transversebulkheads. See also Fig. 5.9.

Fig. 5.9 Correction of the shear force curve

2.2 The supporting forces of the bottom grillage at thetransverse bulkheads may either be determined by directcalculation or by approximation, according to 2.3.

2.3 The sum of the supporting forces of the bottomgrillage at the aft or forward boundary bulkhead of the holdconsidered may be determined by the following formulae:

∆Q = u @ P S v @ T* [kN]

P = mass of cargo or ballast in [t] in the holdconsidered, including any contents of bottomtanks within the flat part of the double bottom

T* = draught in [m] at the centre of the hold

u, v = correction coefficients for cargo and buoyancyas follows:

u = [kN/t]10 @ κ @ R @ b @ hV

v = 10 @ κ @ R @ b [kN/m]

κ = B2,3 (B % R)

R = length of the flat part of the double bottom in[m]

b = breadth of the flat part of the double bottom in[m]

h = height of the hold in [m]

V = volume of the hold in [m3].

3. Static torsional moments

The permissible static torsional moments have to bedetermined according to Table 5.3.

3.1 For ships with torsional moments according to B.2.it has to be proved by means of the loading computer, thatthe maximum permissible values are exceeded at nolocation. Excess values are permissible, if the actualtorsional moments at the adjacent calculation points arecorrespondingly less than the permissible values.

3.2 Unless shown by a particular proof, during loadingand unloading the static torsional moments shall not behigher than 75 % of the wave induced torsional momentaccording to B.3.5.

F. Ships with Large Deck Openings

1. General

1.1 From the displacement of the ship's upper girder,additional bending moments and forces are resulting inthe deck girders around its vertical axes.

After consultation with BKI the stresses resulting from thathave to be calculated for the longitudinal and transversegirders and to be taken into account for the dimensioning.

The calculation of these stresses can be dispensed with,if the guidance values according to 2. and 3. are observed.

1.2 A ship is regarded as one with large deck openingsif one of the following conditions applies to one or morehatch openings:

.1 > 0,6bL

BM

.2 > 0,7RLRM

bL = breadth of hatchway, in case of multi hatchways,bL is the sum of the individualhatchway-breadths

RL = length of hatchway

BM = breadth of deck measured at the mid length ofhatchway

RM = distance between centres of transverse deckstrips at each end of hatchway. Where there isno further hatchway beyond the one underconsideration, RM will be specially considered.

Section 5 - Longitudinal Strength F5 - 16

2. Guidance values for the determination of thesection modulus

The section moduli of the transverse sections of the shipare to be determined according to C.1. and C.2.

The factor fr amounts to:

fr =σL1

σSW% 0,75·σWV

according to D. for the ship's upperσ σ σL SW WV1, ,respectively lower girder. The greater value is to be taken.

The calculation of the factor fr may be dispensed with,if fr is selected according to Fig. 5.10.

Fig. 5.10 Correction factor fr and distribution factor cu

3. Guidance values for the design of transverse boxgirders of container ships

The scantlings of the transverse box girders are to bedetermined by using the following design criteria:

S support forces of hatch covers, see Section 17, C.1.4,

S support forces of the containers stowed in the holdspace,

S stresses due to the torsional deformations of the hull,

S stresses resulting from the water pressure, if thetransverse box girder forms part of a watertightbulkhead, see Section 11.

In general the plate thickness shall not be less than obtainedfrom the following formulae (see also Fig. 5.11):

t1 = [mm] ; orL

t1 = 0,5 t0 [mm]

t0 = thickness of longitudinal hatch coaming or ofthe uppermost strake of the longitudinalbulkhead

t2 = 0,85 [mm]L

or

t2 = 12 @ a [mm]

a = spacing of stiffeners in [m].

The larger of the values t1 or t2 is to be taken.

L need not be taken greater than 200 m.

For coamings on the open deck see also Section 17, B.1.

Fig. 5.11 Joint of the transverse box girder

4. Guidance values for the displacements of theupper girder of the ship

In general, the relative displacement ∆u between the shipsides is to be determined by direct calculations. For thedimensioning of hatch cover bearings and seals, thefollowing value may be used for the displacement:

= ∆u 6·10&5 · MSTmax%MWTmax · 1! L450

[mm]· 4 % 0,1· LB

2· cu % 20

MSTmax, MWTmax according to B.2.2.2 or B.3.5, respectively

cu = distribution factor according to Fig. 5.10

cA = value for cu at the aft part of the open region,see also Fig. 5.10

= # 101,25 ! L400

· 1,6 !3 · xA

L

xA = according to D.2.3.1; for xA no smaller valuethan 0,15 L and no greater value than 0,3 L isto be taken.