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Introduction

Guidelines for Direct Strength Analysis

Guidelines for Fatigue Strength Assessment

Guidelines for Ultimate Hull Girder Strength Assessment

Guidelines for Bulk Carrier StructuresAugust 2002

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i

Introduction

Since total losses of bulk carriers due to structural failures that have occurred continuously after 1990,

demands are increasingly being made on the shipbuilding, marine and other related industries to enhance

the structural safety of ships. In response to such changes, ClassNK has decided to contribute to the

promotion of the structural safety by improving the existing Rules related to structural strength of ships.

This decision is based on the need to offer better transparency and rationality in the Rules by putting

together advanced technologies and technical information accumulated until now.

The fundamental requirements related to structural strength were re-constructed based on past experience

and current technical knowledge to ensure the structural safety of ships. These efforts were compiled as the

“Technical Guide Regarding the Strength Evaluation of Hull Structures” at the end of 1999. Based on the

Technical Guide, Guidelines for Bulk Carrier Structures have been newly developed as practical standardsfor structural strength of bulk carriers making full use of the results of ongoing research. The guidelines

consist of the following three components:




The Guidelines for Direct Strength Analysis have been developed for evaluating the yielding strength and

buckling strength of primary structural members (including hold frames) considering the corrosion

deduction amount of bulk carriers to be used for direct strength analysis. These guidelines introduce the

wide results of ongoing research on loads due to waves and bulk cargoes, structural response to the loads

and strength assessment of hull structures, corrosion deduction amount and so on.

The Guidelines for Fatigue Strength Assessment have been developed for assessing the fatigue strength

of primary structural members (including hold frames) of bulk carriers. Design loads and structural analysis

methods in these guidelines generally conform to the Guidelines for Direct Strength Analysis.These

guidelines have succeeded in developing a practical standard with higher reliability for assessing fatigue

strength through consideration of significant effect of welding residual stresses and mean stresses, standard

route for bulk carriers and so on.

The Guidelines for Ultimate Hull Girder Strength have been developed with the aim of preventing hull

girder fractures (jack-knife casualties) of bulk carriers. These guidelines can be used to confirm that hull

girder in the corroded condition are sufficient their lives to withstand the hull girder fractures in severe sea

conditions that they may encounter during its service life. The ultimate hull girder strength is confirmed by

assessing the hull girder bending moment capacity of transverse sections of the hull applying ultimate

strength assessment considering post-buckling.



ii

ClassNK has already published "Guidelines for Tanker structures" on November 2001. These guidelines for

tanker or bulk carrier can be applied to the hull structures of ore carrier or bulk carrier with double side

skins.

These guidelines will be incorporated henceforth in the Rules for the Survey and Construction of

Steel Ships after carrying out necessary revisions. Consequently, these guidelines are to be used

flexibly as optional standards at this stage.



For information on this publication, please contact the followings;

Development Department, Nippon Kaiji Kyokai

1-8-3, Ohnodai, Midoriku, Chiba 267-0056

Tel : +81-43-294-6672

Fax : +81-43-294-6699

e-mail : [email protected]

Copyright © 2002 ClassNK

All rights reserved



Guidelines for Direct Strength Analysis ClassNK

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Contents

1 General･･･････････････････････････････････････････････････････････････････････ 1

1.1 Application ････････････････････････････････････････････････････････････････ 1

1.2 Procedure for Evaluation ･････････････････････････････････････････････････････ 1

1.3 Minimum Thickness ･････････････････････････････････････････････････････････ 2

2 Applicable Members････････････････････････････････････････････････････････････ 2

2.1 Applicable Members･････････････････････････････････････････････････････････ 2

3 Loading Conditions ････････････････････････････････････････････････････････････ 2

3.1 Loading Conditions･･････････････････････････････････････････････････････････ 2

4 Design Conditions･･････････････････････････････････････････････････････････････ 4

4.1 General ･･･････････････････････････････････････････････････････････････････ 4

4.2 Design Sea Conditions ･･･････････････････････････････････････････････････････ 4

4.2.1 General ･････････････････････････････････････････････････････････････ 4

4.2.2 Setting the Design Sea Conditions ････････････････････････････････････････ 5

4.3 Design Regular Waves ･･･････････････････････････････････････････････････････ 5

4.3.1 General ･････････････････････････････････････････････････････････････ 54.3.2 Setting the Design Regular Waves ････････････････････････････････････････ 6

5 Design Loads ･･････････････････････････････････････････････････････････････････ 7

5.1 General ･･･････････････････････････････････････････････････････････････････ 7

5.2 Ship Motions and Accelerations ････････････････････････････････････････････････ 9

5.2.1 Ship Motions･････････････････････････････････････････････････････････ 9

5.2.2 Acceleration at the Center of Gravity of the Ship ････････････････････････････ 9

5.2.3 Acceleration at the Center of Gravity of the Hold and Tank ･･･････････････････ 10

5.3 Pressure Acting on the Hull ･･････････････････････････････････････････････････ 11

5.3.1 Sea Water Pressure ･･･････････････････････････････････････････････････ 11

5.3.2 Pressure due to Bulk Cargo･････････････････････････････････････････････ 14

5.3.3 Pressure due to Ballast ････････････････････････････････････････････････ 15

6 Direct Load Analysis ･･････････････････････････････････････････････････････････ 18

6.1 General ･･････････････････････････････････････････････････････････････････ 18

6.2 Setting Method for Design Loads･･････････････････････････････････････････････ 18

7 Considerations for Corrosion ･･･････････････････････････････････････････････････ 19

7.1 General ･･････････････････････････････････････････････････････････････････ 19

7.2 Corrosion Deduction････････････････････････････････････････････････････････ 19



ClassNK Guidelines for Direct Strength Analysis

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8 Structural Analysis ････････････････････････････････････････････････････････････ 21

8.1 General ･･････････････････････････････････････････････････････････････････ 21

8.2 Analysis Model････････････････････････････････････････････････････････････ 21

8.2.1 Extent of the Modeling ････････････････････････････････････････････････ 21

8.2.2 Members Considered ･････････････････････････････････････････････････ 21

8.2.3 Mesh Size ･･････････････････････････････････････････････････････････ 21

8.3 Loads and Boundary Conditions･･･････････････････････････････････････････････ 21

8.3.1 Loads･･････････････････････････････････････････････････････････････ 21

8.3.2 Supports ･･･････････････････････････････････････････････････････････ 21

8.4 Results of Analysis ･････････････････････････････････････････････････････････ 22

9 Considerations of Hull Girder Stresses････････････････････････････････････････････ 23

9.1 General ･･････････････････････････････････････････････････････････････････ 23

9.2 Stresses due to Hull Girder Moments･･･････････････････････････････････････････

239.2.1 Stress due to Vertical Bending Moment ･･･････････････････････････････････ 23

9.2.2 Stress due to Horizontal Bending Moment･････････････････････････････････ 23

9.3 Superimposition of Stresses ･･････････････････････････････････････････････････ 24

10 Evaluation of Yielding Strength･････････････････････････････････････････････････ 25

10.1 Reference Stresses ･･･････････････････････････････････････････････････････ 25

10.2 Allowable Stresses ･･･････････････････････････････････････････････････････ 25

11 Evaluation of Buckling Strength ････････････････････････････････････････････････ 26

11.1 General ････････････････････････････････････････････････････････････････ 26

11.2 Reference Stresses ･･･････････････････････････････････････････････････････ 26

11.3 Buckling Stress of Plate Panel ･･････････････････････････････････････････････ 27

11.3.1 Elastic Buckling Stress Vectors･･･････････････････････････････････････ 27

11.3.2 Considerations for Influential Factors ･････････････････････････････････ 30

11.3.3 Buckling Stress ･･･････････････････････････････････････････････････ 31

11.4 Buckling Strength Criteria ･････････････････････････････････････････････････ 31

12 Evaluation of ultimate strength･････････････････････････････････････････････････ 32

12.1 General ････････････････････････････････････････････････････････････････ 32

12.2 Reference Stress ･････････････････････････････････････････････････････････ 32

12.3 Ultimate Strength of Plate Panel･････････････････････････････････････････････ 32

12.4 Ultimate Strength Criteria･･････････････････････････････････････････････････ 33




- iii -

Symbols

L : Scantling length of ship m

B : Greatest moulded breadth of ship m

D : Moulded depth of ship m

d f : Design moulded draught of ship m

d i : Draught amidships for the relevant loading condition m

C b : Block coefficient corresponding to design moulded draught of ship -

V : Design speed knots

g : Acceleration due to gravity (= 9.81) m/s2

ρ C : Density of cargo t/m3

ρ B : Density of sea water (= 1.025) t/m3

σ Y : Yield stress

σ Y =235 for MS

σ Y =315 for HT 32 σ Y =355 for HT 36

N/mm2

K : Material coefficient corresponding to yielding strength of material -

E

K =1.0 for MS

K =0.78 for HT 32

K =0.72 for HT 36

: Young’s modulus of steel (= 206,000) N/mm2

υ : Poisson’s ratio (= 0.3) -




- 1 -


1 General

1.1 Application

-1. The structural arrangement and scantlings of primary members in the cargo hold areas of bulk carriers to which Chapter 31, Part C of the Rules are applied, can be determined by theseGuidelines.

-2. Even if the scantlings of structural members of the hull are determined based on the direct strengthcalculation, the said scantlings should also satisfy the requirements given below.

(1) Requirements related to longitudinal strength prescribed in Chapter 15, Part C of the Rules

(2) Requirements related to hull strength in flooded condition prescribed in Chapter 13 and31A, Part C of the Rules

(3) Requirements related to plating and longitudinals prescribed for local loads

(4) Requirements related to fatigue strength.

1.2 Procedure for Evaluation

The overview of the procedure for evaluation is given in Fig. 1.1.

Note: Numbers in arentheses indicate cha ter numbers

Fig. 1.1 Procedure for Evaluation

Loading Conditions

3

Design Sea Conditions

4.2

Design Regular Waves

4.3

Design Loads

5

Structural Analysis

8

Direct Load Analysis

6

Corrosion Deduction

7

Superimposition with Hull Girder Stresses

9

Evaluation of

Yielding Strength

10

Evaluation of

Buckling Strength

11

Evaluation of

Ultimate Strength

12




- 2 -

1.3 Minimum Thickness

-1. The thickness of structural members in cargo holds and deep tanks such as bulkhead plating, floors,

girders and their end brackets shall be greater than the values given in Table 1.1 according to thelength of ship.

-2. The thickness of structural members in cargo holds and deep tanks shall be greater than 7mm.

Table 1.1 Minimum Thickness

More than 90 105 120 135 150 180 195 225 275 325 375 L(m)

Less than 105 120 135 150 180 195 225 275 325 375

Thickness (mm) 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0

2 Applicable Members

2.1 Applicable MembersThe structural members whose structural arrangement can be determined based on these guidelines are

given in (1) to (7) below.

(1) Shell platings, inner bottom plating, hopper plates of bilge hopper tanks constituting the double bottom and sloping plate of topside tanks

(2) Floors and girders in the double bottom

(3) Transverse rings in the bilge hopper tanks

(4) Transverse rings in the topside tanks

(5) Transverse bulkhead platings (including stools and girders in stools)

(6) Hold frames

(7) Cross decks

3 Loading Conditions

3.1 Loading Conditions

Loading conditions to be considered are according to (1), (2) and (3) below.

(1) From the planned loading conditions, select the loading conditions, which are expected to besevere on the yielding and buckling strengths.

(2) In principle, the full load condition and the ballast condition are taken as the loading conditions.When special loading conditions such as alternate loading or two-port loading, or loading of

cargo of specially high density are predicted, such conditions are to be included in the

calculations.(3) Table 3.1 shows the standard loading conditions.




- 3 -

Table 3.1 Standard Loading Conditions

Loading Condition Loading pattern draught

L o w

D e n s i t y

C a r g

o F

1

H o m o g e n e o u s L o a

d i n g

H i g h

D e n s i t y

C a r g o

F

2

F u l l L o a d i n g C o n d i t i o n

A l t e r n a t e

L o a d i n g

H i g h

D e n s i t y

C a r g o

F

3

d f (draught of

DesignMaximum

Load)

L o w

D e n s i t y

C a r g o M

1

M u l t i p l e P o r t L o a d i n g

H i g h

D e n s i t y

C a r g o M

2

d m(draught of

MultiplePort

Loading)

L o w

D

e n s i t y

C a r g o

A

1

T w o - P o r t s L o a d i n g

H i g h

D e n s i t y

C a r g o

A

2

d a(draught of Two-Ports

Loading)

N o r m a l

B a l l a s t

B

1

d bn

(draught of

NormalBallast)

B a l l a s t C o n d i t i o n

H e a v y

B a l l a s

tB2

d bh

(draught of Heavy

Ballast)

H y d r o -

s t a t i c T e s t

C o n d i t i o n

T

1d t = d f /3

NOTE:

(1) Low Density Cargo means the density of cargo is under 1.0 (t/m3).

(2) High Density Cargo means the density of cargo is 1.0 (t/m3) or more.(3) h of water head of a tank being subjected to hydraulic pressure test is vertical distance between the

considered point and a point at height of 2.45 (m) above the top of tank at ship's side (h = hc+2.45).hc: Vertical distance from the considered point to the upper deck.

df

df

df

dm

dm

da

da

dbh

dt

h

dbn

d f

d f

d f

d m

d m

d a

d a

d bn

d bh

h

d t




- 4 -

4 Design Conditions

Symbols

T 01( j) : Mean wave period corresponding to each design sea condition sec.

H max( j) : Maximum wave height corresponding to each design sea condition m

λ j : Wave length of design regular wave corresponding to each design sea condition m

χ j : Wave encountering angle corresponding to each design sea condition or each

design regular wave

deg.

H j : Wave height of design regular wave corresponding to each design sea condition m

j : Subscript representing each design condition; stands for L-180, L-0, R and P -

4.1 General

-1. In principle, unrestricted service area is considered assuming that the ship encounters 108 waves

when navigating the North Atlantic Ocean. However, the design conditions could be set based onthe sea conditions in restricted service area, if the ship is planned for service in smooth water area or coasting area and is registered in the condition of restricted area.

-2. The design conditions may be suitably changed when loading conditions are restricted to sea areaswhere the effect of waves is small, such as in enclosed seas or harbours.

-3. When the structural strengths are evaluated, the number of the design sea conditions or the designregular wave conditions may be suitably reduced with the consent of the Society.

4.2 Design Sea Conditions

4.2.1 General

-1. Short-term sea conditions considered to be the most severe for the hull structure are set as thedesign sea conditions under the conditions of 4.1.

-2. Design sea conditions are taken as the short-term sea conditions shown in the following (a) to (d).

(a) Design condition L-180 : Short-term sea condition at which the vertical wave bending

moment becomes maximum (head sea condition)

(b) Design condition L-0 : Short-term sea condition at which the vertical wave bendingmoment becomes maximum (following sea condition)

(c) Design condition R : Short-term condition at which rolling becomes maximum

(d) Design condition P : Short-term sea condition at which the hydrodynamic pressure atthe waterline becomes maximum




- 5 -

4.2.2 Setting the Design Sea Conditions

The design sea conditions are specified in Table 4.1.

Table 4.1 Design Sea Conditions

Designcondition

Waveencountering

angle χ j (deg.)

Mean wave period T 01( j) ( s) Maximum wave height H max( j) (m)

L-180180

Head sea

L-00

Following sea

R90

Beam sea

P 90

Beam sea

g T

j

j

πλ 2

85.0)(01 =

j : Stands for L-180, L-0,

R and P

)(3/13)max( j j H C H ⋅=

C 3 : 1.9

)(3/1 j H : Significant wave height, as given

by the following equations

)(21)(3/1 j j C C H ⋅= (m)

C 1

5.1

100

30075.10

−−=

Lfor L ≤ 300 m

75.10= for 300 m < L ≤ 350 m5.1

150

35075.10

−−= L

for 350 m < L

L

LC

j

j

25)(2

−+=

λ

4.3 Design Regular Waves

4.3.1 General

-1. Regular waves that generate response values equivalent to the response values generated in irregular waves under design sea conditions are set as design regular waves.

-2. Nonlinear effects in large waves and three-dimensional effects are considered when setting thedesign regular waves.

-3. To perform practical strength evaluation within the elastic range, the design wave height is

corrected to a level corresponding to elastic design. This level taken as the level at which adequatestrength can be ensured against the maximum load considering residual strength until ultimatestrength.




- 6 -

4.3.2 Setting the Design Regular Waves

Design regular waves are set corresponding to each design sea condition are specified in Table 4.2.

Table 4.2 Design Regular Waves

Regular wave height H j (m)Design

conditions

Encountering

angle χ j

(deg.)

Wave length λ j (m)

4C 5C 6C

L-180 180 Ld

d

f

i L

+=− 16.0180λ

L-0 0 Ld

d

f

i L

+=−

3

216.00λ

0.65 0.9

R 902

2 R R T g

π λ = 0.42 0.8

P 90 Ld

d

f

i P

+= 4.02.0λ

)(654 jmax j H C C C H ⋅⋅⋅=

4C : Correction coefficient

for regular waveheight


for nonlinear and 3Deffects


for elastic design0.70 0.7

0.67

NOTE:

GM

K C T xx

R

2= ( s)

15.1=C

K xx

: Roll radius of gyration (m); given as below according to the loading condition

K xx = 0.35 B for full loading condition

= 0.40 B for ballast condition and partial loading condition

GM : Metacenter height (m); if the value of GM is not available beforehand, it may be calculatedfrom the equation below.

GM = KM – KG

−−

−=

f

i

f

i

d

d

d

d B KM 17242.0

6.0136.04.054.0 +

−+

+=

f

i

f

i

d

d

d

d D KG

In case of loading condition F2 given in Table 3.1, KG is 0.55 times KG above.

The draught is corrected as shown below for partial loading condition.

2

f P

i

d d d

+= (m)

pd : Draught amidships in partial condition (m)




- 7 -

5 Design Loads

Symbols

K xx : Roll radius of gyration; according to 4.3 above m

GM : Metacenter height; according to 4.3 above m

T R : Natural period of roll motion sec.

T P : Natural period of pitch motion sec.

φ : Roll angle rad.

θ : Pitch angle rad.

aheave : Acceleration at the center of gravity of ship due to heave motion m/s2

a pitch : Acceleration at the center of gravity of ship due to pitch motion rad./s2

aroll : Acceleration at the center of gravity of ship due to roll motion rad./s2

at : Transverse acceleration at the center of gravity of cargo hold and tank m/s2

av : Vertical acceleration at the center of gravity of cargo hold and tank m/s2

P C : Internal dynamic pressure in bulk cargo caused by ship motions and accelerations kN/m2

P B : Internal dynamic pressure in ballast tank caused by ship motions and

accelerations

kN/m2

P L : Hydrodynamic pressure corresponding to design condition L kN/m2

P P : Hydrodynamic pressure corresponding to design condition P kN/m2

P R : Hydrodynamic pressure corresponding to design condition R kN/m2

5.1 General

-1. Loads acting on the hull under design regular wave conditions are set as design loads.

-2. Loads in still water and in waves are considered as loads acting on the hull. External hydrostatic pressure and internal static pressure due to bulk cargo and ballast are considered as loads in still

water. External hydrodynamic pressure and internal dynamic pressure due to bulk cargo and ballast are considered as wave-induced loads.

-3. The hull girder stresses caused by bending moments acting on the hull girder are separatelysuperimposed on the stresses obtained from structural analysis using the design loads descried thischapter. The details are given in Chapter 9.

-4. The wave length of the design regular wave corresponding to L-180 may be used as the wave lengthof the design regular waves corresponding to L-0 given in Table 4.2 in the application of thischapter.

-5. The values of design loads obtained at the center of length of the considered hold are used.

-6. In case of condition L-180, if the strength using design loads at the transverse section 0.15 L forwardof the midship section is investigated, the strength investigations at all other locations may beomitted except in holds where locations to be investigated are specified in longitudinal direction.

-7 The definitions of wave crest and wave trough in the L-180 and L-0 design conditions are accordingto Fig. 5.1. Furthermore, the definitions of weather side down and weather side up for the R and P design conditions are according to Fig. 5.2.




- 8 -

(a) For design condition L-180 (b) For design condition L-0

: Wave crest : Waterline

: Wave trough

Fig. 5.1 Definition of Wave Crest and Wave Trough (for full loading condition)

(a) Weather side down (b) Weather side up

Fig. 5.2 Definitions of Weather Side Down and Weather Side Up

P P

P P

Lee sideWeather side Weather side Lee side

C L C L




- 9 -

5.2 Ship Motions and Accelerations

5.2.1 Ship Motions

Table 5.1 gives the natural period of pitch motion T P , the pitch angle θ , the natural period of roll motion

T R, and the roll angle φ .

Table 5.1 Ship Motions

Natural period ( s) Angle (rad.)

Pitch g

T L P

1802 −= πλ

( )

1802.1

2.053

−+

= L

b

H C L

V θ

180− L H : Regular wave height corresponding to the

design condition L-180 (m)

Roll GM

K C T xx

R

2=

C = 1.15

R

R

H BT

4=φ

R H : Regular wave height corresponding to the design

condition R (m)

5.2.2 Acceleration at the Center of Gravity of the Ship

Table 5.2 gives the acceleration at the center of gravity of the ship due to pitch motion a pitch, roll motionaroll and heave motion aheave.

Table 5.2 Acceleration at the Center of Gravity of Ship

Acceleration at the center of gravity

of ship due to pitch motion

22

=

P

pitchT a

π θ (rad./s

2

)

Acceleration at the center of gravity

of ship due to roll motion

22

=

R

roll T

a π φ (rad./s2)

Acceleration at the center of gravityof ship due to heave motion

( )

( ) P

b

heave H C L B

V g a

6.0

2.05

3⋅

+= (m/s2)

H P : Regular wave height corresponding to the design

condition P (m)




- 10 -

5.2.3 Acceleration at the Center of Gravity of the Hold and Tank

The vertical acceleration av and the transverse acceleration at at the center of gravity of the hold and tank

are given in Table 5.3 corresponding to each design condition. The longitudinal acceleration need not beconsidered.

Table 5.3 Acceleration at the Center of Gravity of Hold and Tank

Design

condition

Acceleration at the center of gravityof hold and tank (m/s2)

(Wave crest in head sea and weather side down in beam sea)

Acceleration at the center of gravityof hold and tank (m/s2)

(Wave trough in head sea andweather side up in beam sea)

Remarks

－－－

L-180va− pitch g iheave

f

iv a x xa

d

d a −+= positive upward

－－

L-0－－

－

φ g at = t a− positive lee side R

roll iheavev a ya La += )40/( va− positive upward

φ g at 5.0= t a− positive lee side P

roll iheavev a yaa 5.0+= va− positive upward

NOTE: x g : Longitudinal distance from A.P. to the rotation center of pitch motion (= 0.45 L) (m)

xi : Longitudinal distance from A.P. to the considered center of gravity of tank (m)

yi : Transverse horizontal distance from the centerline of the hull to the considered center of gravity

of tank (m) ; positive when the considered center of gravity of the tank is on the weather side andnegative when the considered center of gravity of the tank is on the lee side

FPAP

Pi

yi<0

Weather side

Pia

t>0

xg(=0.45L)

xi

av>0

Lee side

Fig. 5.3 Definition of Coordinates for Calculating Accelerations at the Center of Gravity of the Tank

C L




- 11 -

5.3 Pressure Acting on the Hull

5.3.1 Sea Water Pressure

-1. Hydrostatic pressure

The pressure corresponding to the draught in still water is considered as the hydrostatic pressure for

each loading condition.

-2. Hydrodynamic pressure

(1) The hydrodynamic pressure P L (kN/m2) corresponding to the design conditions L-180 and L-0 is

given by the following equation and Fig. 5.4. At any section, P L is taken as positive for wavecrest and negative for wave trough.

L

i

L H B

y

d

z C P

++±= 1

23.2 7

C 7 : Distribution coefficient in the longitudinal direction of the ship: according to the

equation given below.

7C L

b

c L

x

B

y

C

−+=

3'43

61 Design condition L-180 (forward part of ship)

L

b

c L

x

B

y

C

−+=3'2

112

1 Design condition L-180 (aft part of ship)

1= Design condition L-0

25.02

cos25.1 +−

−=

f

i

f

i L

d

d

L

x

d

d c

π

d i : Draught amidships for the relevant loading condition (m)

x : Longitudinal distance from the midship section to the considered cross section (m)

y : Transverse horizontal distance from the centerline of the ship to the considered point in the midship section (m)

y' : Transverse horizontal distance from the centerline of the ship to the considered point in the considered section (m)

z : Vertical distance from the bottom of the ship to the considered point in midship

section (m); max. ( z ) = d i

H L : Wave height of regular wave corresponding to the design conditions L-180 and L-0,

in meter; H L-180 may be taken as the typical wave height of regular wavecorresponding to L-180 and L-0.




- 12 -

Fig. 5.4 Hydrodynamic Pressure Distribution at the Midship Section

(In Case of Design condition L-0, Wave Crest)

(2) The dynamic pressure P R (kN/m2) corresponding to the design condition R is given by thefollowing equation and Fig. 5.5. At any section, P R is taken as positive when the weather side isdownwards, and negative when upwards.

++±= R R H

B

y y P 1

21.0sin10 φ

y : Transverse horizontal distance from the centerline of the ship to the considered point in the considered section (m), positive weather side

φ : Roll angle (rad.), as defined in 5.2.1.

H

-10(B/2)sinφ+2H

φ

Weather side Lee side

10(B/2)sinφ+2H

Fig. 5.5 Hydrodynamic Pressure Distribution at the Midship Section(In case of Weather Side Downward)

(3) The dynamic pressure P P (kN/m2) corresponding to the design condition P is given by the

following equation and Fig. 5.6. At any section, P P is taken as positive when the weather side isdownwards, and negative when upwards.

P

i

PW H B

y

d

z P

+±=

2323 for weather side

3

PW PL

P P = for lee side

y : Transverse horizontal distance from the centerline of the ship to the considered point in the considered section (m)

6.9 H 6.9 H

4.6 H 4.6 H

2.3 H

C L

C L




- 13 -

z : Vertical distance from the bottom of the ship to the considered point in the

considered section (m); max.( z ) = d i

Fig. 5.6 Hydrodynamic Pressure Distribution at the Midship Section

(In case of Weather Side Downward)

(4) Correction to hydrodynamic pressure

(a) The hydrodynamic pressure may be considered to have a uniform distribution in thelongitudinal direction of the ship within the range of the hold model.

(b) When the hydrodynamic pressure at the waterline is positive, the hydrodynamic pressure is

converted to water head firstly, and then the pressure is assumed as acting linearly from thewaterline up to the position of the converted water head for the hydrodynamic pressure abovethe waterline (see Fig. 5.7).

(c) When the hydrodynamic pressure at the waterline is a negative, the combined pressure of the

hydrodynamic and hydrostatic pressure is not taken as negative value for the hydrodynamic pressure below the waterline (see Fig. 5.7).

(d) In sea areas where the effect of waves is small such as in harbours, the hydrodynamic pressuremay be reasonably altered.

Weather side

45

P

P/( Bg)

Hydrostatic

pressure

Bgd

i

P

d

i

Weather side

Hydrodynamic

pressure

When hydrodynamic pressure is positive When hydrodynamic pressure is negative

Fig. 5.7 Correction to Hydrodynamic Pressure

5H


15H

3H9H

C L C L

C L




- 14 -

5.3.2 Pressure due to Bulk Cargo

-1. Shape of bulk cargo surface

(1) The shape of bulk cargo surface indicated by (L-a) in L of Table 5.4 is taken as the shape of the bulk cargo surface to be assessed. Where loading of high density cargo is anticipated, the shape

of bulk cargo surface indicated by (H-a) in H of Table 5.4 is taken as the shape of surface to beassessed.

(2) To obtain the pressure due to dry bulk cargo for strength assessment, the shapes L and Hindicated in (1) above are corrected to the shapes indicated by (L-b) and (H-b) of Table 5.4.

(3) It is assumed that cargo pressure does not act on the shell plating in the case of the shape of bulk cargo surface (H-b) for strength assessment, obtained in (2) above.

-2. Static pressure due to bulk cargo

(1) The static pressure P S (kN/m2) due to bulk cargo acting on the vertical walls of cargo hold isgiven by the following equation.

C C C S gz K P ρ = K C : Coefficient corresponding to the angle of inclination of the vertical wall of the

cargo hold given by the equation below.

α α 2

02

sincos K K C +=

α : Angle of inclination of said panel on the side not facing the cargo holdwith respect to the horizontal plane (deg.) (See Fig. 5.8.)

K 0 : Coefficient of earth pressure at rest given by the equation below.

ψ sin10 −= K

ψ : Angle of repose of cargo (deg.) given in Table 5.5.

z C : Vertical distance from the said panel to the upper shape of bulk cargosurface for strength assessment (m) (See shape of bulk cargo surface (L-b)and (H-b) in Table 5.4.)

Fig. 5.8 Definition of Angle of Inclination of Vertical Wall

-3. Dynamic pressure due to bulk cargo

(1) The dynamic pressure P C (kN/m2) due to bulk cargo acting on the vertical wall of the cargo holdfor each design condition is given in Table 5.6.

(2) In sea areas where the effect of waves is negligible, such as within ports (during cargo handling),dynamic pressure P C of the bulk cargo may be suitably reduced.

α

Cargo hold side




- 15 -

5.3.3 Pressure due to Ballast

-1. Static pressure due to ballast

(1) The pressure due to ballast in still water (kN/m2) is considered as the static pressure.

-2. Internal dynamic pressure due to ballast

(1) The internal dynamic pressure due to ballast P B is shown in Table 5.6 for each design condition.

(2) In sea areas where the effect of waves is negligible, such as within ports (during cargo handling),dynamic pressure due to ballast, P B may be suitably altered.




- 16 -

Table 5.4 Shapes of bulk cargo surfaces

Shape of cargo surface L Shape of cargo surface H

NOTES:

(1) It is assumed that the cargo is loaded up to theupper deck plating in each shape of dry bulk

cargo surface considered. For the shape of dry bulk cargo surface for strength assessment,the top side tanks are ignored and the shape is

taken as horizontal in both longitudinal andtransverse directions.

(2) The cargo loading height for strength

assessment z C is determined from the mass of the cargo loaded.

(3) The density of the cargo ρ C can bedetermined from the equation below.

ρ C

W

V =

W : Mass of cargo loaded (t )

V : Volume of cargo hold excluding thevolume enclosed by hatch coaming

(m3)

NOTES:(1) The shape of dry bulk cargo surface is taken

to be horizontal in the transverse andlongitudinal directions near the ship's

centerline, but is assumed to vary linearlyfrom the centerline towards the ship sides

considering the angle of repose ψ . The shapeof dry bulk cargo surface for strength

assessment is taken to be horizontal in thelongitudinal and transverse directions near theship’s centerline, but is assumed to vary

linearly from the centerline towards the ship's

sides considering half the angle of repose (ψ /2). The width of the transverse part is takenas half the width of the cargo hold.

(2) The cargo loading height z C is determinedfrom the mass of the cargo loaded, the angle

of repose and the density of the cargo. Theshape of dry bulk cargo surface may be takenas horizontal in the longitudinal direction.

(3) The density of cargo is taken as the maximumdesigned density of the cargo. Unless

particularly specified, the density of the cargois taken as 3.0 (t/m3).

(4) The values of angle of repose of cargo ψ ,given in Table 5.5 may be taken as standard

values. Unless particularly specified, theangle of repose is taken as 30°.

Table 5.5 Angle of repose of typical cargoes

Cargo Angle of repose (deg.)

General 30

Iron, ore and coal 35

Cement 25

(L-a) Shape of cargo surface (H-a) Shape of cargo surface

(L-b) Shape of cargo surface

for strength assessment

(H-b) Shape of cargo surface for strength assessment

z

C

z

C

ψ

B 2

ψ

ψ 2

B 2

z

CC

ψ




- 17 -

Table 5.6 Dynamic pressures due to dry bulk cargo and ballast

Dynamic pressure due to bulk cargo and ballast (kN/m2)設計条件

bulk cargo ballast Remarks

L-180 C vC C C z a K P ρ 75.0= Bv B B z a P ρ =

L-0 0=C P 0= B P

＋: positive pressure

－: negative pressure

R

P )25.075.0( C t C vC C C ya z a K P += ρ )( Bt Bv B B ya z a P += ρ ＋: positive pressure

－: negative pressure

NOTE:

yC : Transverse horizontal distance from the center of the tank to the considered point (m)

（The distance is taken as positive if the considered point is located at the weather side from the

transverse center of the tank, or as negative if the considered point is located at the lee side from

the transverse center of the tank, see Fig. 5.7.）

z C : Vertical distance from the top of the tank to the considered point (m)

(a) Shape of bulk cargo surface L (b) Shape of bulk cargo surface H

Fig. 5.9 Definition of yC

NOTE: y B : Transverse distance from the considered point to the top of tank located at the most lee-side

when the weather side is downward, or at the most weather side when the weather side isupward (m)

(When the weather side is downward, the distance is taken as positive if the point is located atthe weather side, or as negative if the point is located at the lee side, from the top of tank at themost lee side; see Fig. 5.10.)

(When the weather side is upward, the distance is taken as positive if the point is located at theweather side, or as negative if the point is located at the lee side, from the top of tank at the

most weather side; see Fig. 5.10.)

z B : Vertical distance measured from the middle point of the overflow pipe on the top of tank to the

considered point (m), vertical distance from the considered position to the top of hatchcoaming for heavy ballast hold (m)

Fig. 5.10 Definition of y B and z B

z

C

z

C

波上側波下側C

< 0

C

> 0


z

C

z

C

y

C

> 0

y

C

< 0

波上側波下側Weather side Lee side

波上側波下側

zB

yB

> 0

yB

> 0

zB

zB

yB

> 0

Weather side Lee side 波上側波下側

yB

< 0

yB

< 0

zB

zB

zB

yB

< 0





- 18 -

6 Direct Load Analysis

6.1 General

-1. Design loads in waves can also be set for each ship using direct load analysis without using thedesign loads described in Chapter 5.

-2. The standard method for setting design loads using direct load analysis is shown in 6.2.

-3. In addition to the standard method given in 6.2, the design loads may also be set using a more

sophisticated method based on the design sea conditions given in 4.2 or based on the design regular wave conditions given in 4.3.

6.2 Setting Method for Design Loads

-1. Direct load analysis is performed under design regular wave conditions given in 4.3 for setting the

design loads. The internal dynamic pressures due to the liquid cargo and ballast and thehydrodynamic pressures at the time shown in Table 6.1 are set as the design loads.

-2. It is preferable to set the wave lengths of design regular waves using the results of direct load

analysis by the strip method in the design regular wave conditions given in 4.3. In this case, thewave length of design regular waves is taken as the wave length when the response of the dominantload given in 4.2 becomes maximum in regular waves.

-3. It is necessary to make the correction of nonlinearity for the hydrodynamic pressure near thewaterline based on the method given in 5.3.1-2(4)(b) and (c).

-4. For details of direct load analysis, the “Technical Guide Regarding the Strength Evaluation of

Hull Structures (Dec. 1999)” could be referred to.

Table 6.1 Time to be Considered in Design Regular Wave Conditions

Design

conditionsTime to be considered

L-180

・Time when the vertical wave bending moment (Hog.) at midship becomes maximum

・Time when the vertical wave bending moment (Sag.) at midship becomes maximum

・Time when the vertical acceleration at the center of gravity of the investigated hold

becomes maximum

・Time when the vertical acceleration at the center of gravity of the investigated hold

becomes minimum

L-0・Time when the vertical wave bending moment (Hog.) at midship becomes maximum

・Time when the vertical wave bending moment (Sag.) at midship becomes maximum

R

・Time when the rolling motion (weather side is downward) becomes maximum

・Time when the rolling motion (weather side is upward) becomes maximum

P ・Time when the hydrodynamic pressure at the waterline amidships becomes maximum

・Time when the hydrodynamic pressure at the waterline amidships becomes minimum




- 19 -

7 Considerations for Corrosion

7.1 General

-1. Considerations for corrosion are made by performing strength evaluation based on net thickness. Net thickness is obtained by subtracting the corrosion deduction assumed for direct strength

calculations from the gross thickness (thickness shown on the plans).-2. For hull girder stress calculations, the gross thickness is used. To consider the effect of corrosion,

this stress is then multiplied by the stress incremental factor due to corrosion.

7.2 Corrosion Deduction

Fig 7.1 and Fig. 7.2 show the values of corrosion deduction for various structural members according tothe length of a ship.

Fig. 7.1 Corrosion Deduction (These values are applied to ships 200m or more)




- 21 -

8 Structural Analysis

8.1 General

-1. Structural analysis is performed by the Finite Element Method. The members to be analyzed aremodeled using plate elements.

-2. An approved analysis program having adequate accuracy should be used. If deemed necessary,documents related to systems used in the analysis and documents for confirming the accuracy may be required to be submitted to the Society.

8.2 Analysis Model

8.2.1 Extent of the Modeling

-1. The extent of analysis is decided such that the actual stress conditions of the ship can be reproduced

by considering the arrangement of cargo oil and ballast tanks, the loading pattern and thearrangement of members near the bulkhead.

-2. The model extends at least a hold lengthwise (21

21 + holds), and full depth and full breadth (refer to

Fig. 8.1).

8.2.2 Members Considered

The members to be considered are the members to be evaluated and all primary members within theextent of the model. Load transmitting members such as longitudinal stiffeners and watertight bulkheadstiffeners should also be included in the model.

8.2.3 Mesh Size

The size of the mesh is selected considering the stress condition in the model and the meshing of elements is performed rationally so as to avoid meshes with large aspect ratios (see Fig. 8.1). The

standard size of an element in the stress evaluation area is decided by taking one side of the element asapproximately equal to the spacing of the nearby stiffeners.

8.3 Loads and Boundary Conditions

8.3.1 Loads

Loads are applied such that the load transmitting to the primary members is faithfully reproducedconsidering the arrangement of stiffeners.

8.3.2 Supports

-1. The model is supported in the depth and breadth directions at the position of the transverse

bulkhead. Members near the support points are excluded from the evaluation members.-2. When members near the point of support are necessary to be evaluated, analysis is performed

separately by supporting the model at locations away from the bulkhead.

-3. The model is supported at its forward and aft ends in the length direction applying symmetryconditions.




- 22 -

8.4 Results of Analysis

The stress distributions in each member are output and checked for the correctness of analysis beforestrength evaluation is carried out.

Fig. 8.1 Example of Structural Model of Bulk Carrier




- 23 -

9 Considerations of Hull Girder Stresses

Symbols

σ S : Stress due to still water vertical bending moment N/mm2

σ WV : Stress due to wave-induced vertical bending moment N/mm2

σ WH : Stress due to wave-induced horizontal bending moment N/mm2

σ G : Sum of the stresses σ S , σ WV and σ WH N/mm2

9.1 General

-1. To consider the effect of hull girder moment, the hull girder stress is added to the stress in the lengthdirection of the ship obtained from structural analysis for the longitudinal members.

-2. Firstly, the maximum hull girder moment is converted to the stress using beam theory. Next, the

hull girder stress is determined by multiplying this stress by the stress superimposition ratio set for each design condition.

9.2 Stresses due to Hull Girder Moments

9.2.1 Stress due to Vertical Bending Moment

The stress due to still water vertical bending moment σ S and the stress due to wave-induced vertical

bending moment σ WV are calculated as given below.

510×⋅= V

V

S S f

I

M σ ( N/mm2)

510×⋅= V

V

WV WV f

I

M σ ( N/mm2)

M S : Still water vertical bending moment corresponding to each loading condition; takenas the mean value of the two bulkhead positions located on both sides of theevaluation position (kN-m).

M WV : Wave-induced vertical bending moment at the considered section according to 15.2.1,Part C of the Rules (kN-m).

I V : Moment of inertia of the cross section about the horizontal neutral axis of thetransverse section to be evaluated (cm4)

f V : Vertical distance from the horizontal neutral axis to the evaluation position (m)

9.2.2 Stress due to Horizontal Bending MomentThe stress due to horizontal bending moment is calculated as given below.

510×⋅= H

H

WH WH f

I

M σ ( N/mm2)

M WH : Wave-induced horizontal bending moment at the considered section (kN-m), as given by the following equation

L

Ld LC C M iWH

3532.0 2

81

−=

C 1 : According to Table 4.1

C 8 : Distribution coefficient of the horizontal bending moment in the length direction of the ship, which is determined by linear interpolation using the equation belowaccording to the position of the considered cross section.




- 24 -

C 8 = 0 at AP

= 1.0 between 0.35 L and 0.65 L

= 0 at FP

I H : Moment of inertia of the cross section about the vertical neutral axis of the transverse

section to be evaluated (cm4)

f H : Horizontal distance from the neutral axis to the evaluation position (m)

9.3 Superimposition of Stresses

The hull girder stressσG determined by the equation below is superimposed on the stress in the length

direction of the ship obtained from structural analysis.

( ( ) )WH WV S G C C C C σσσ ⋅+⋅⋅+⋅= 111069 σ ( N/mm2)

C 9 : Correction coefficient considering stress increment due to corrosion; taken as 1.1

C 6 : Correction coefficient for elastic design; taken as 0.67

C 10 : Superimposition ratio of wave-induced vertical bending stress

σ WV , as defined in Table 9.1

C 11 : Superimposition ratio of horizontal bending stress σ WH , as defined in Table 9.1

Table 9.1 Superimposition Ratio of Wave-induced Hull Girder Stresses

Design conditions C 10 C 11

Wave crest Hogging L-180

Wave trough1.0

Sagging－－

Wave crest Hogging L-0

Wave trough

1.0

Sagging

－－

Weather side isdownward

Weather side(compression)

RWeather side is

upward

－－ f

i

d

d −2.1

Weather side(tension)

Weather side isdownward

Sagging

P Weather side is

upward

4.0− f

i

d

d

Hogging

－－




- 25 -

10 Evaluation of Yielding Strength

10.1 Reference Stresses

-1. The equivalent stress and axial stress are used as reference stresses for the evaluation of yielding

strength. The equivalent stress σ eq is used for shell elements and membrane elements, while the

axial stress σ a is used for rod elements.

-2. The equivalent stress is taken as the Mises’ equivalent stress using the following equation.

212

2221

21 3τ σ σ σ σ σ ++⋅−=eq

σ 1, σ 2 : In-plane normal stresses ( N/mm2); hull girder stress determined in Chapter 9 issuperimposed on the normal stress in longitudinal members in the lengthdirection of the ship

12τ : Shear stress corresponding toσ 1, σ 2 ( N/mm2)

-3. The stress at the center of the element is used as the reference stress for shell elements and

membrane elements. However, when fine mesh is used rather than the standard mesh given inChapter 8 the mean stress corresponding to the standard mesh may be used.

-4. If a girder has openings, the effect of openings is considered in the stress evaluation.

10.2 Allowable Stress

The reference stresses determined in 10.1 should not exceed the allowable stresses specified in Table10.1.

Table 10.1 Allowable Stresses

σ eq and σ a ( N/mm2

)Members

Sea-going conditionDuring cargo handling or

Hydrostatic test condition

All members to be evaluated 195/ K 215/ K




- 26 -

11 Evaluation of Buckling Strength

Symbols

a : Length of longer side of plate panel mm

b : Length of shorter side of plate panel mm

α : Aspect ratio of plate panel (α = a / b) -

t : Thickness of plate panel mm

σ ref : Reference stress N/mm2

σ ecr : Equivalent elastic buckling stress N/mm2

σ pcr : Equivalent plastic buckling stress N/mm2

11.1 General

-1. Corrosion deduction specified in Fig.7.1 and Fig.7.2 is deducted from the thickness of the plate

panel for the evaluation of buckling strength.

-2. Analytical procedures other than those specified in this Guideline may be used for buckling strengthevaluation if deemed appropriate by the Society.

11.2 Reference Stresses

-1. Plate panel

The reference stress σ ref for the evaluation of buckling strength of the plate panel is the representativeequivalent stress combining the four in-plane stress components of shell elements or membrane elements

in the element coordinate system shown in Fig.11.1 and is obtained by the equation given below. In caseof longitudinal members with one of the element coordinate axes in the length direction of the ship, thehull girder stress determined in Chapter 9 above is considered.

2

2

23

4

3

4

3

2

1τ σ σ σ σ σ σ σ +

++

+−= by yby y x xref ( N/mm2)

Fig. 11.1 Four In-plane Stress Components

σ x : Compressive stress in x direction

σ y : Compressive stress in y direction

σ by : In-plane bending stress in y direction

τ : Shear stress

(Unit: N/mm2）

σ y

σ by

σ x

x

y

τ

τ




- 27 -

11.3 Buckling Stress of Plate Panel

11.3.1 Elastic Buckling Stress Vectors

The elastic buckling stress vectors (σ xB, σ yB, τ B, σ byB) are determined using the elastic bucklinginteraction equations given in Table 11.1.

Table 11.1 Elastic Buckling Interaction Equations

1321 =++ g z k yk xk )101( ≤≤α (1)

17.1

64.1

52.1

4 =++ z k yk xk )102( ≤≤α (2)

g

21 ≤≤α 8.12.0 +α

42 ≤≤α 0.16.0 +α

104 ≤≤α 0.31.0 +α xcr x

xB xσ γ

σ = ,

ycr y

yB y

σ γ

σ = ,

cr s

yB z

τ γ

τ = ,

bycr

byBby

σ

σ =

NOTES:

1. The smaller of the two solutions obtained from equation (1) and (2) is taken as the buckling stressvector.

2. The value of buckling stress components (σ xcr , σ ycr , τ cr , σ bycr ) under one single stress component isgiven in Table 11.2.

3. The reduction factors due to in-plane bending stress (k 1 to k 6) are given in Table 11.3.

4. The reduction factors due to opening (γ x, γ y, γ s) are given in Table 11.4.

Table 11.2 Buckling Stress under One Single Stress Component

Stress components Buckling stress σ cr Buckling coefficient K

E x xcr K σ σ =

2

+= mm K x α α

E y ycr K σ σ =2

2

11

+=α

y K

E scr K σ τ =2

434.5

α += s K

E bybycr K σ σ =426.887.1587.1

α α ++=by K

9.23= whichever is the smaller

NOTES:

1. m, an integer, is the number of half-waves of buckling mode in the direction of the

longer side of the panel that satisfies )1()1( +≤≤− mmmm α

2. σ E is taken as

2

2

2

)1(12

− b

t E

ν

π




- 28 -

Table 11.3 Reduction Factors due to In-plane Bending Stress

e1 α e2 α e3

311 .≤≤α 032391 .. +− α 311 .≤≤ α 432671 .. −α 311 .≤≤α 01.

4131 .. ≤≤α 123232 .. +− α 4131 .. ≤≤α 812691 .. −α 4131 .. ≤≤α 421320 .. +− α

5241 .. ≤≤α 00. 5241 .. ≤≤α 9450630 .. −α 241 ≤≤α . 781580 .. +− α

552 ≤≤ α . 00. 552 ≤≤α . 630. 522 .≤≤α 22130 .. +− α

105 ≤≤α 00. 105 ≤≤α 680010 .. +− α 352 ≤≤α . 071240 .. +− α

43 ≤≤α 710120 .. +− α

64 ≤≤α 470060 .. +− α

by

ebyebyek

−++

=1

)()( 322

11

106 ≤≤α 200150 .. +− α

α e1 e2

31 ≤≤ α 940140 .. +− α 61 ≤≤α 850050 .. +− α

63 ≤≤α 7400730 .. +− α 106 ≤≤α 562001250 .. +− α )1}(1)({

12

1

2bybye

k e −+

=

106 ≤≤α 4500250 .. +− α

α e1

41 ≤≤α 680170 .. +− α bybyek

−−= 1)(1 1

3

104 ≤≤α 00.

α e1 e2

522 .≤≤α 0550030 .. +α 32 ≤≤α 50 .

352 ≤≤α . 520260 .. −α 63 ≤≤α 2010 .. +α

43 ≤≤α 160140 .. −α 106 ≤≤α 50050 .. +α )1}(1)({

1

2

1

4bybye

k e −+

=

104 ≤≤α α 10.

α e1 e2

522 .≤≤α 360. 322 .≤≤α 530060 .. +α

352 ≤≤α . 241640 .. −α 5232 .. ≤≤α 8750090 .. +− α

43 ≤≤α 440080 .. +α 352 ≤≤α . 15120 .. +− α

54 ≤≤α 720010 .. +α 43 ≤≤α 790080 .. +− α

105 ≤≤α 920030 .. +− α 64 ≤≤α 510010 .. +− α

by

ebyek

−

+=

1

)( 215

106 ≤≤α 4800050 .. +− α

α e1

32 ≤≤α 440040 .. +α

63 ≤≤ α 410050 .. +α by

byek

−

−=

1

)(1 16

106 ≤≤α 590020 .. +α




- 29 -

Table 11.4 Reduction Factors due to Opening

Circular opening Elliptical opening

2)(1

1,,,,

11

000 f

s y x s y x

b

d f +

== γ γ γ γ γ γ

2)(1

1,,,,

21

000 f

s y x s y x

b

d f +

== γ γ γ γ γ γ

γ x0 (γ x0<0.8 ,γ x0=0.8) γ x0 (γ x0<0.8,γ x0=0.8) f 1 f 2 f 1 f 2

0.7 1.0

0.7 1.0

γ y0 γ y0

f 1 f 2 f 1 f 2

21 ≤≤α 1-0.3α 21 ≤≤α 0.9-0.2α

2≥α 0.41.0

2≥α 0.5 1.0

γ s0 γ s0

f 1 f 2 f 1 f 2

551 .≤≤α 58

752250 2

.

..

+− α α

1.8 551 .≤≤α )5.8

75.225.0(6.1 2

+− α α

1.8

55.≥α 93750. 1.8

55.≥α 51. 1.8

Circular or elliptical opening with slot

xs x x . γ γ γ 021=

(0 x x γ γ ≥ ,

0 x x γ γ = )

ys y y γ γ γ 0=

ss s s γ γ γ 02=

(0 s s γ γ ≥ ,

0 s s γ γ = )

NOTES: 1. Parameters are according to the figures below.

Circular opening Elliptica

Here, d 1 is the diameter of circular opening (mm), d 2 is the sm(mm) and h s is the length of the slot (mm).

2. If there are two slots in the direction of the longer side of th

16.0 +−=b

h s ysγ

3. If the slot is reinforced by a collar plate, then the following

a

bd 1

h s




- 30 -

11.3.2 Considerations for Influential Factors

-1. General

The effects of stiffener and water pressure may be considered as influential factors that affect the buckling strength.

-2. Effects of stiffener

The effect of stiffener can be considered by correcting the buckling stress ratio y to y’ in equation (1)or (2) in Table 11.1 using the following equation.

y

y y

κ =

y : Buckling stress ratio shown in Table 11.1

κ y : Influential factor of stiffener in y direction in Fig.11.1 and given by the equation below.

If different kinds of stiffeners are arranged on the longer side of the plate panel, themean value of the influential factors of the two stiffeners is taken.

1

3

+

=

t

t c w

yκ 0.1<t t w ， 01.t t w ≥ , then 01.t t w =

c : Coefficient given in Table 11.5 according to the type of the stiffener

t w : Thickness of web plating of stiffener (mm)

Table 11.5 Coefficient c

Type of stiffener c

21 ≤≤α 1030 .. +α

72 ≤≤α 980140 .. +− α Angle stiffener

107 ≤≤α 00.

21 ≤≤α 10350 .. −α

32 ≤≤α 60.

63 ≤≤α 11330 +− α .

T-shaped stiffener,girder

106 ≤≤ α 50050 .. +− α

61 ≤≤α 120020 .. +− α Flat bar, bulb plate

106 ≤≤ α 00.

-3. Effects of water pressure

The effect of water pressure can be considered by correcting the buckling stress ratios x and y to x′and y′ respectively in equation (1) or (2) in Table 11.1 using the following equations

xq

x

x =′ ，

yq

y

y =′

x, y : Buckling stress ratios shown in Table 11.1.

q x, q y : Influential factors of water pressure in x and y direction shown in Fig.11.1

respectively given by the following equations. q x, and q y are applied for plate panels of thickness greater than 13mm and aspect ratio greater than 2.

5761

6.1

4

4

+= Et

qb

q x ，95.0

75.1

4

4

160

1

+=

b

a

Et

qb

q y




- 31 -

q x, q y : Load due to water pressure acting on the plate panel

( N/mm2) is taken as the difference between internal andexternal pressures.

11.3.3 Buckling Stress

-1. The equivalent elastic buckling stress is determined from the following equation using the elastic buckling stress vectors obtained in 11.3.2 above.

2

2

23

4

3

4

3

2

1 BbyB yBbyB yB xB xBecr τ σ σ σ σ σ σ σ +

++

+−= （ N/mm2）

-2. If the value of the equivalent elastic buckling stress σ ecr is greater than half the value of the yield

stress σ Y , the equivalent plastic buckling stress σ pcr is determined from the equation below.

−=

ecr

Y Y pcr

σ

σ σ σ

41 （ N/mm2）

11.4 Buckling Strength Criteria

-1. Plate Panel

The results obtained in 11.2 -1 and 11.3 above are necessary to satisfy the conditions below. Here, λ isthe buckling criterion given in Table 11.6.

(1) When the value of the equivalent elastic buckling stress σ ecr is greater than half the value of the

yield stress σ Y

λ σ

σ ≥

ref

pcr

(2) When the value of the equivalent elastic buckling stress σ ecr is less than half the value of the yield

stress σ Y

λ σ

σ ≥

ref

ecr

Table 11.6 Buckling Strength Criteria of Plate Panel

Buckling criterion λ Members

Sea-going conditionDuring cargo handling or

Hydrostatic test condition

All members to be evaluated 1.1 1.0




- 32 -

12 Evaluation of Ultimate Strength

Symbols

a : Length of longer side of plate panel mm

b : Length of shorter side of plate panel mm

α : Aspect ratio of plate panel (α =a/b) -

t : Thickness of plate panel mm

β : Slenderness ratio of plate panel ( E t b Y /)/( σ β ×= ) -

σ ref : Reference stress N/mm2

σ us : Ultimate strength for strength evaluation N/mm2

12.1 General

-1. Strength evaluation of plate flange members of girders connected to bottom shell plating and inner

bottom plating which are subjected mainly to bi-axial compressive stress may be carried out byultimate strength evaluation regardless of Chapter 11.

-2. Corrosion deduction specified in Fig.7.1 and Fig.7.2 is deducted from the thickness of the plate panel for the evaluation of ultimate strength.

-3. Analytical procedures other than those specified in this section may be used for ultimate strengthevaluation if deemed appropriate by the Society.

12.2 Reference Stress

-1. The reference stress σ ref for the evaluation of ultimate strength is taken as the representativeequivalent stress given in the following equation. In case of longitudinal members with one of the

element coordinate axes in the length direction of the ship, the hull girder stress determined in

Chapter 9 is considered.

22 y xref σ σ σ += ( N/mm2)

Here, σ x and σ y are the normal stresses shown in Fig.11.1 ( N/mm2)

12.3 Ultimate Strength of Plate Panel

-1 Ultimate strength under bi-axial compressive stress

The ultimate strength σ xU and σ yU under bi-axial compressive stress is determined by the ultimatestrength interaction equations given in Table 12.1.

Table 12.1 Ultimate Strength Interaction Equations

Slenderness ratio β Interaction equation

10 ≤≤ β )(1 x y y ≥= )(1 x y x ≤=

31 ≤≤ β 1=+ δ δ y x ,1

4

−= β

δ

β ≤3 122 =+ y x

xus

xU xσ

σ = ，

yus

yU y

σ

σ =

NOTE:

The ultimate strength σ xus and σ yus under one single stress component is given in Table 12.2.




- 33 -

Table 12.2 Ultimate Strength under One Single Stress Component

Stress component Ultimate strength σ xus, σ yus

2

25.125.2

β β σ

σ −=

Y

xus 0.1≥ β

0.1=Y

xus

σ σ 0.1≤ β

−=

a

b

Y

yus

2

25.125.2

β β σ

σ

−

−+

−+

a

b1

)2.0(

6.0

2.0

06.08.0

2 β β

-2. Ultimate strength for strength evaluation

The ultimate strength σ us for the strength evaluation is determined from the equation given belowusing the ultimate strength under bi-axial compression in item –1. above.

22 yU xU us σ σ σ += （ N/mm2）

12.4 Ultimate Strength Criteria

The ultimate strength criterion λ is satisfied using the result obtained from 12.2 and 12.3 as follows, and based on Table 12.3.

λ σ

σ ≥

ref

us

Table 12.3 Ultimate Strength Criteria

Ultimate strength criterion λ

MembersSea-going condition

During cargo handling or Hydrostatic test condition

Members that are mainly subjected to bi-axial

compressive stress such as the bottom shell platings and the inner bottom platings

1.2 1.1



Guidelines for Fatigue Strength Assessment ClassNK

- i -


Contents

1 General ･････････････････････････････････････････････････････････････････････････ 1

1.1 Application･･････････････････････････････････････････････････････････････････ 1

1.2 Documents for Submission ･････････････････････････････････････････････････････ 1

2 Members and Locations to be Assessed ･･･････････････････････････････････････････････ 2

2.1 General･････････････････････････････････････････････････････････････････････ 2

2.2 Members subjected to Fatigue Strength Assessment ･･････････････････････････････････ 2

3 Assessment Procedure ･････････････････････････････････････････････････････････････ 4

3.1 General･････････････････････････････････････････････････････････････････････ 4

3.2 Overview of Procedure･････････････････････････････････････････････････････････ 4

4 Design Loads･････････････････････････････････････････････････････････････････････ 6

4.1 General ･････････････････････････････････････････････････････････････････････ 6

4.2 Loading Conditions ･･･････････････････････････････････････････････････････････ 7

4.3 Loads in Still Water ･･･････････････････････････････････････････････････････････ 7

4.3.1 General ･･･････････････････････････････････････････････････････････････ 7

4.3.2 Hydrostatic Pressure･････････････････････････････････････････････････････ 7

4.3.3 Static Pressure due to Ballast Weights ･･･････････････････････････････････････ 7

4.3.4 Static pressure due to bulk cargo ･･･････････････････････････････････････････ 7

4.4 Dynamic Loads ･･････････････････････････････････････････････････････････････ 8

4.4.1 General ･･･････････････････････････････････････････････････････････････ 8

4.4.2 Hydrodynamic Pressure ･･････････････････････････････････････････････････ 9

4.4.3 Dynamic Pressures due to Bulk Cargo and Ballast ････････････････････････････ 15

5 Direct Load Analysis ････････････････････････････････････････････････････････････ 17

5.1 General ････････････････････････････････････････････････････････････････････ 17

5.2 Method of Setting Design Loads ････････････････････････････････････････････････ 17

6 Structural analysis ･･･････････････････････････････････････････････････････････････ 18

6.1 General ････････････････････････････････････････････････････････････････････ 18

6.2 Analysis Modeling ･･･････････････････････････････････････････････････････････ 18

6.2.1 Extent of the modeling ･･････････････････････････････････････････････････ 18

6.2.2 Members Considered ･･･････････････････････････････････････････････････ 18

6.2.3 Mesh Size････････････････････････････････････････････････････････････ 18

6.3 Loads and Boundary Conditions ････････････････････････････････････････････････ 18

6.3.1 Loads ･･･････････････････････････････････････････････････････････････ 18



ClassNK Guidelines for Fatigue Strength Assessment

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6.3.2 Supports ･････････････････････････････････････････････････････････････ 18

6.4 Results of Analysis･･･････････････････････････････････････････････････････････ 19

7 Superimposition of Hull Girder Stresses ･･･････････････････････････････････････････ 21

7.1 General････････････････････････････････････････････････････････････････････ 21

7.2 Stress due to Hull Girder Moment ･･･････････････････････････････････････････････ 21

7.3 Superimposition of Stresses ････････････････････････････････････････････････････ 22

8 Evaluation of Stress ･･････････････････････････････････････････････････････････････ 23

8.1 General････････････････････････････････････････････････････････････････････ 23

8.2 Nominal Stress ･･････････････････････････････････････････････････････････････ 23

8.2.1 General ･･････････････････････････････････････････････････････････････ 23

8.2.2 Evaluation Method･････････････････････････････････････････････････････ 23

8.3 Hot-spot Stress ･･････････････････････････････････････････････････････････････ 25

8.3.1 General ･･････････････････････････････････････････････････････････････ 25

8.3.2 Evaluation Method･････････････････････････････････････････････････････ 25

8.4 Stress Concentration Factor ････････････････････････････････････････････････････ 26

8.4.1 General ･･････････････････････････････････････････････････････････････ 26

8.4.2 Bilge Hopper Knuckle ･･････････････････････････････････････････････････ 26

8.4.3 Intersection of Plate and Girder ･･･････････････････････････････････････････ 27

8.5 Long-term Distribution of the Stress Range････････････････････････････････････････ 28

8.5.1 General ･･････････････････････････････････････････････････････････････ 28

8.5.2 Long-term Distribution･･････････････････････････････････････････････････ 28

9 Fatigue Strength Assessment ･･･････････････････････････････････････････････････････ 29

9.1 General････････････････････････････････････････････････････････････････････ 29

9.2 Design Curves ･･････････････････････････････････････････････････････････････ 29

9.3 Mean Stress Effects ･･････････････････････････････････････････････････････････ 30

9.3.1 General ･･････････････････････････････････････････････････････････････ 30

9.3.2 Methods for Considering the Mean Stress Effects･････････････････････････････ 30

9.4 Cumulative Fatigue Damage ･･･････････････････････････････････････････････････ 31




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Appendices: Examples of Structural Details

A.1 General･･･････････････････････････････････････････････････････････････････････ 33

A.2 Extent ････････････････････････････････････････････････････････････････････････ 33

A.3 Workmanship Standards･･････････････････････････････････････････････････････････ 33

A.4 Welding Standards ･･････････････････････････････････････････････････････････････ 34

A.5 Examples of Structural Details･････････････････････････････････････････････････････ 34

A.5.1 Upper/Lower Ends of Hold Frame････････････････････････････････････････････ 35

A.5.2 Intersection of Inner Bottom Plating and Hopper Plating in BHT････････････････････ 36

A.5.3 Intersections in the Lower Stool and Connection between Lower Stool and Transverse

Bulkhead ･･･････････････････････････････････････････････････････････････ 37

A.5.4 Connection between Upper Part of Transverse Bulkhead and TST Slant Plating or Upper

Stool ･･･････････････････････････････････････････････････････････････････ 38

A.5.5 Bilge Keel Ends (Connections at Bilge Shell Plating) ･････････････････････････････ 39

A.5.6 Bulwark Gusset Plate and Bulwark Stay ･･･････････････････････････････････････ 40

A.5.7 Hatch Coaming End Bracket Ends and Coaming Stay･････････････････････････････ 41

A.5.8 Around the Hatch Corner ･･･････････････････････････････････････････････････ 42




- 1 -


1 General

1.1 Application

-1. The fatigue strength of principal members in the cargo hold area of bulk carriers to which Chapter 31, Part C of the Rules can be assessed according to these Guidelines. The above requirementneed not be applied however, if the fatigue strength is assessed by a more sophisticated method.

-2. When the hull structural scantlings are determined based on these Guidelines, prior approval of the

Society is to be obtained with respect to the type of members, the rules to be applied and the scopeof the applicability of the formulae in the procedure.

1.2 Documents for Submission

Documents which clearly state the conditions of calculation and which summarize the calculated results

of assessments on fatigue strength according to these Guidelines are to be submitted to the Society.




- 2 -

2 Members and Locations to be Assessed

2.1 General

-1. Members to be subjected to fatigue strength assessments are selected after considering the structuralarrangement of the ship, and the importance, functions, etc. of the members.

-2. Members which are prone to fatigue crack because of stress concentration due to structuraldiscontinuities at the ends of large stiffeners, and members at locations where the problem of watertightness is likely to occur due to cracks in the compartments, are given priority for theassessment.

2.2 Members subjected to Fatigue Strength Assessment

-1. Members and locations that required to be assessed for fatigue strength in accordance with theseGuidelines are given in Table 2.1 and illustrated in Fig. 2.1.

-2. Locations with high stresses are selected from among the locations mentioned in item -1 above for fatigue strength assessment.

Table 2.1 Members and Locations to be Assessed for Fatigue Strength

Members Locations

Intersection of sloping plate of lower stool, girder, floor plate and inner bottom plating

Inner bottom platingIntersection of sloping plate of bilge hopper tanks, girder,

floor plate and inner bottom plating

Intersection of lower end of hold frame and sloping plateof bilge hopper tank

Sloping plate of bilge hopper tanksIntersection of inner bottom plating and sloping plate of

bilge hopper tanks

Intersection of sloping plate of lower stool and transverse bulkhead

Intersection of sloping plate of upper stool and upper part of

transverse bulkheadTransverse bulkhead

Intersection of slant plating of topside tanks and upper partof transverse bulkhead

Intersection of upper end of hold frame and sloping plate

of topside tanksSloping plate of topside tank

Intersection of end of hatch coaming and sloping plate of topside tanks

Sloping plate of lower stoolIntersection of inner bottom plate and sloping plate of lower

stool




- 3 -

Fig. 2.1 Members and Locations to be Assessed for Fatigue Strength




- 4 -

3 Assessment Procedure

3.1 General

-1. The conditions of a ship to be considered when assessing the fatigue strength are the full loadcondition and the ballast condition during normal operation.

-2. Any condition in which, the ship is planned to have a long-term operation other than the full loadand ballast conditions, is also to be considered.

-3. The fatigue strength should be assessed by the evaluation of cumulative fatigue damage for stresscycles of 108.

-4. The calculation of cumulative fatigue damage is performed by using the long-term distribution of hot-spot stress range in the S-N curve.

3.2 Overview of Procedure

The fatigue strength is assessed by the procedure given below, in accordance with the method shownschematically in Fig. 3.1.

-1. Evaluate the dynamic stress at the location under investigation by structural analysis(1) Perform structural analysis applying design loads relevant to the design conditions and loading

conditions of the ship, and determine the nominal stress.

(2) Perform the above for the wave crest (or weather side downward) and wave trough (or weather side upward) of the design load, and determine the nominal stress range.

(3) And also determine the nominal mean stress.

(4) Multiply these stresses by the stress concentration factor and find the hot-spot stress range andthe hot-spot mean stress due to design loads.

-2. Evaluate the stress at the location under investigation due to hull girder moment.(if an effect of hullgirder moment on the fatigue strength is not negligible)

(1) Use the midship section modulus in the wave-induced bending moment on the hull girder applicable to the loading condition of the ship at the location being evaluated, and determinethe nominal stress due to the hull girder moment.

(2) Perform the above for the hogging and sagging conditions (in case of design condition R, twoconditions in hull girder horizontal bending), and determine the nominal stress range due to thehull girder moment.

(3) And also determine the nominal mean stress due to the hull girder moment.

(4) Multiply these stresses by the stress concentration factor and find the hot-spot stress range andthe hot-spot mean stress due to the hull girder moment.

(5) Add the hot-spot stress range and the hot-spot mean stress due to the hull girder moment in thehot-spot stress range and the hot-spot mean stress due to design loads respectively and

determine the hot-spot stress range and the hot-spot mean stress of the structure.-3. Evaluate the cumulative fatigue damage.

(1) Apply the Weibull shape parameter to the obtained hot-spot stress range to determine the long-term distribution of hot-spot stress range.

(2) For each loading condition of the ship, evaluate the equivalent stress range considering theresidual stress at the location to be evaluated, the mean stress and the long-term response valueof the stress range.

(3) Use the long-term distribution of the equivalent stress range in the design S-N curve andcalculate the cumulative fatigue damage.

(4) Add the cumulative fatigue damages calculated for each loading condition of the ship.

(5) Compare the maximum value of the calculated cumulative fatigue damage against the

allowable value to confirm that it is within the limit.




- 5 -

Fig. 3.1 Overview of Fatigue Strength Assessment Procedure

Object Ship

Structural Analysis

Cumulative Fatigue Damage

Decision

Nominal Stress Range

Long Term Distribution of

Hot-Spot Stress Range

Max. Hot-Spot Stress Range

Stress

Concentration

Factor

Weibull

parameter

NO Change of

Structural Details

Y E S

S-N Curve

Design Loads

(wave crest, wave trough)Hull Girder Moment

Nominal Mean

Stress

Nominal Stress RangeNominal Mean

Stress

Hot-Spot Stress RangeHot-Spot Mean

StressHot-Spot Stress Range

Hot-Spot MeanStress

Hot-Spot Mean Stress

Long Term Distribution of Equivalent

Hot-Spot Stress Range




- 6 -

4 Design Loads

Symbols

L : Scantling length of ship m

B : Greatest moulded breadth of ship m

D : Moulded depth of ship m

d f : Design moulded draught of ship m

d i : Draught amidships for the relevant loading condition m

C b : Block coefficient corresponding to design moulded draught of ship -

V : Design speed of ship knots

g : Acceleration due to gravity (= 9.81) m/s2

ρ B : Density of sea water (= 1.025) t/m3

H j : Wave height of design regular wave corresponding to each design sea condition m

j : Subscript representing each design condition; stands for L-180, L-0, R and P - K xx : Roll radius of gyration m

GM : Metacentric height m

T R : Natural period of roll motion sec.

T P : Natural period of pitch motion sec.

φ : Roll angle rad.

θ : Pitch angle rad.

aheave : Acceleration of the center of gravity of ship due to heave motion m/s2

a pitch : Acceleration of the center of gravity of ship due to pitch motion rad./s2

aroll : Acceleration of the center of gravity of ship due to roll motion rad./s2

at : Transverse acceleration at the center of gravity of cargo hold or tank m/s

2

av : Vertical acceleration at the center of gravity of cargo hold or tank m/s2

P C : Internal dynamic pressure in bulk cargo caused by ship motions and

accelerations

kN/m2

P B : Internal dynamic pressure in ballast water tank caused by ship motions and

accelerationskN/m2

P L : Hydrodynamic pressure corresponding to design condition L-180 or L-0 kN/m2

P P : Hydrodynamic pressure corresponding to design condition P kN/m2

P R : Hydrodynamic pressure corresponding to design condition R kN/m2

4.1 General

-1. Loads in still water and in waves are considered as loads acting on the hull. However, if other loadsare expected to play important roles in the structural strength of the ship according to the structuralconfiguration, service conditions and properties of cargo, these loads are also considered.

-2. External hydrostatic pressure and internal static pressure due to bulk cargo and ballast are

considered as loads in still water. External hydrodynamic pressure and internal dynamic pressuredue to bulk cargo and ballast are considered as wave-induced loads.

-3. If the effect of hull girder moment on the fatigue strength is not negligible, the hull girder stressesare separately superimposed on the stresses determined from structural analysis and consideringhull girder sectional forces and moments.




- 7 -


-1. In the full loading conditions, homogeneous and alternate loading conditions are to be contained inthe calculations.

-2. In the ballast conditions, normal and heavy ballast conditions are to be considered in the

calculations.-3. When the conditions other than the above -1. and -2. are planned, they are also taken into

consideration.

4.3 Loads in Still Water

4.3.1 General

If necessary, the loads indicated below may be considered as loads in still water.

(a) Hydrostatic pressure

(b) Bulk Cargo and ballast

(c) Other static loads

4.3.2 Hydrostatic Pressure

The pressure corresponding to the draught in still water is considered as the hydrostatic pressure for eachloading condition. The density of the seawater is to be taken as 1.025 (t/m3).

4.3.3 Static Pressure due to Ballast

The pressure due to ballast in still water is considered as the static pressure. In this case, the density of ballast water is taken as 1.025 (t/m3).

4.3.4 Static Pressure due to Bulk Cargo-1. The static pressure P S (kN/m2) due to bulk cargo acting on the vertical walls of cargo hold is

according to the equation given below

C C C S gz K P ρ =

K C : Coefficient corresponding to the angle of inclination of the vertical wall of the cargohold given by the equation below

α α 20

2 sincos K K C +=

α : Angle of inclination of said panel on the side not facing the cargo holdwith respect to the horizontal plane (deg.)

0 K : Coefficient of earth pressure at rest given by the equation below

ψ sin10 −= K

ψ : Angle of repose of cargo (deg.) according to Table 4.1

ρ C : Density of the cargo (t/m3)

z C : Vertical distance from the said panel to the upper shape of bulk cargo surface for strength assessment in m




- 8 -

Table 4.1 Angle of repose of typical cargoes

CargoAngle of repose

(deg.)

Iron Ore and Coal 35

Cement 25Others 30

-2. When density of cargo taken into consideration is less than 1.0 (t/m3), shape of cargo surface is based on the following points.

(1) The cargo loading height for strength assessment z C is determined from the mass of the cargo in ahomogeneous loading condition.

(2) The density of the cargo ρ C can be determined from the equation below.

V

W C = ρ

W : Mass of cargo loaded (t )

V : Volume of cargo hold excluding the volume enclosed by hatch coaming (m3)

-3. When density of cargo that takes into consideration is 1.0 (t/m3) or more, shape of cargo surface is based on the following points.

(1) The shape of dry bulk cargo surface is taken to be horizontal in the transverse and longitudinaldirections near the ship's centerline, but is assumed to vary linearly from the centerline towards

the ship sides considering half the angle of repose (ψ /2). The width of the transverse part is takenas half the width of the cargo hold.

(2) The cargo loading height z C is determined from the mass of the cargo loaded, the angle of reposeand density of the cargo. The shape of dry bulk cargo surface may be taken as horizontal in thelongitudinal direction.

(3) The density of cargo is taken as the maximum designed density of the cargo. Unless particularlyspecified, the density of the cargo is taken as 3.0 (t/m3).

(4) The pressure due to bulk cargo shall not be applied to the side plating.

Low Density Cargo High Density Cargo

Fig 4.1 Shape of bulk cargo surface

4.4 Dynamic Loads

4.4.1 General

-1. In principle, unrestricted service area is considered assuming that the ship encounters 108 waves.

-2. In determining the long-term distribution of hot-spot stress range by applying the Weibull shape parameter, design loads are set to be the maximum loads in 104 waves.

-3. From the loads determined according to the design conditions given below, dynamic loads with theseverest loading conditions on the member to be investigated, are selected and used.

z

C

z

C

ψ 2

B 2

z

CC




- 9 -

(a) Design condition L-180 : Short-term sea condition at which the vertical wave bending

moment becomes maximum (head sea condition)

(b) Design condition L-0 : Short-term sea condition at which the vertical wave bending

moment becomes maximum (following sea condition)

(c) Design condition R : Short-term condition at which rolling becomes maximum

(d) Design condition P : Short-term sea condition at which the hydrodynamic pressure at

the waterline becomes maximum

-4. Notwithstanding the dynamic loads specified here in Section 4.4, the design loads mentioned in the

“Guidelines for Direct Strength Analysis” may also be used for the assessment. In such a case,however, the stresses used in the evaluation should be corrected according to the method given inSection 8.2.2-6. and -7.

4.4.2 Hydrodynamic Pressure

-1. The hydrodynamic pressure P L (kN/m2) corresponding to the design conditions L-180 and L-0 isgiven by the following equation and Fig. 4.2. At any section, P L is taken as positive for wave crestand negative for wave trough.

L

i

L H B

y

d

z C P

++±= 1

23.2 7 (kN/m2)

C 7 : Distribution coefficient in the longitudinal direction of the ship; according to theequation given below.

7C L

b

C L

x

B

y

C

34

36

1

′−+= Design condition L-180 (forward part of ship)

Lb

C L

x

B

y

C

32

1

12

1

′

−+= Design condition L-180 (aft part of ship)

1= Design condition L-0

25.02

cos25.1 +−

−=

f

i

f

i L

d

d

L

x

d

d C

π

d i : Draught amidships for the relevant loading condition (m)

x : Longitudinal distance from the midship section to the considered cross section (m)

y : Transverse horizontal distance from the centerline of the ship to the considered point in the midship section (m)

y' : Transverse horizontal distance from the centerline of the ship to the considered point in the considered section (m)

z : Vertical distance from the bottom of the ship to the considered point in midship

section, (m) zmax= d i

H L : Wave height of regular wave corresponding to the design conditions L-180 and L-

0 (m), H L-180 may be taken as the typical wave height of regular wavecorresponding to L-180 and L-0 ; according to Table 4.2.




- 10 -

6.9 H 6.9 H

4.6 H 4.6 H

2.3 H

Fig. 4.2 Hydrodynamic Pressure Distribution at the Midship Section (In case of wave Crest)

-2 The dynamic pressure P R (kN/m2) corresponding to the design condition R is given by the followingequation and Fig. 4.3. At any section, P R is taken as positive when the weather side is downwards,and negative when upwards.

R R H B

y y P

+±±= 1

2sin10 φ (kN/m2)

y : Transverse horizontal distance from the centerline of the ship to the considered point in the considered section (m), positive weather side

H R : Wave height of regular wave corresponding to design condition R (m), accordingto Table 4.2.

φ : Roll angle (rad.), according to Table 4.3

H

-10(B/2)sinφ+2H

φ


10(B/2)sinφ+2H

Fig. 4.3 Hydrodynamic Pressure Distribution at the Midship Section (In case of Weather Side Downward)

-3 The dynamic pressure P P (kN/m2) corresponding to the design condition P is given by the following

equation and Fig. 4.4. At any section, P P is taken as positive when the weather side is downwards,and negative when upwards.

P P P

i

H B

y

d

z

+±=

2320.3 for weather side




- 11 -

P

i

H B

y

d

z

+±=

232 for lee side

H P : Wave height of regular wave corresponding to design condition P (m); according

to Table 4.2. y : Transverse horizontal distance from the centerline of the ship to the considered

point in the considered section (m)

z : Vertical distance from the bottom of the ship to the considered point in the

considered section (m); zmax = d i

Fig. 4.4 Hydrodynamic Pressure Distribution at the Midship Section (In case of Weather Side Downward)

-4. The hydrodynamic pressure may be considered to have a uniform distribution in the longitudinal

direction of the ship within the range of the hold model. In this case, the hydrodynamic pressureacting on the cross section located at the longitudinal center of considered hold is used.

-5. When the hydrodynamic pressure at the waterline is positive, the hydrodynamic pressure is

converted to water head firstly, and then the pressure is assumed as acting linearly from thewaterline up to the position of the converted water head for the hydrodynamic pressure above thewaterline. (See Fig. 4.5)

-6. When the hydrodynamic pressure at the waterline is negative, the combined pressure of the

hydrodynamic pressure and hydrostatic pressure is not taken as negative value for the hydrodynamic pressure below the waterline. (See Fig. 4.5)

5H


15H

3H9H




- 12 -

Weather side

45

P

P/( Bg)

Hydrostatic

pressure

Bgd

i

P

d i

Weather side

Hydrodynamic

pressure

When hydrodynamic pressure is positive When hydrodynamic pressure is negative

Fig. 4.5 Correction to Hydrodynamic Pressure




- 13 -

Table 4.2 Design Regular Waves

Design

Conditions

Encounter-

ing angle

χ j (deg.)

Wave length λ j (m) Regular wave height H j (m) pC 4C

L-180 180 Ld

d

f

i L

+=− 16.0180λ

L-0 0 Ld

d

f

i L

+=−

3

216.00λ

0.65

R 90

2

2 R R T

g

π λ =

0.42

P 90 Ld

d

f

i P

+= 4.02.0λ

L

LC C C H

j

p j

259.1 14

−+=

λ

pC : Correction coefficient for

exceedance probability level

4C : Correction coefficient for

regular wave height

1C : As specified in Chapter 15

2.1-1, Part C of the Rule

0.5

0.70

NOTE:

GM

K C T xx

R

2= ( s)

15.1=C K xx : Roll radius of gyration (m); given as below according to the loading condition

K xx = 0.35 B for full loading condition

= 0.40 B for ballast condition and partial loading condition

GM : Metacentric height (m), if the value of GM is not available beforehand, it may becalculated from the equation given below.

GM = KM – KG

−−

−=

f

i

f

i

d

d

d

d B KM 17242.0

6.0136.04.054.0 +

−+

+= f

i

f

i

d

d

d

d

D KG

0.55 times is applied to the case in the uniform (homogeneous) loading conditionwhose density exceeds 1.0 (t/m3) by full loading condition.




- 14 -

Table 4.3 Ship Motions

Natural period ( s) Angle (rad.)

Pitch g T L

P 1802 −

=πλ

( )1802.1

2.053

−+

= L

b

H

C L

V θ

H L-180 : Regular Wave height corresponding to

the design condition L-180 (m)

Roll GM

K C T xx

R

2=

C = 1.15

R

R

H BT

4=φ

H R : Regular Wave height corresponding tothe design condition R (m)




- 15 -

4.4.3 Dynamic Pressures due to Bulk Cargo and Ballast

The dynamic pressures due to bulk cargo and ballast are shown in Tables 4.4 for each design condition.

Table 4.4 Fluctuating Dynamic Pressures due to Bulk Cargo and Ballast

Dynamic pressure due to bulk cargo and ballast weights (kN/m2)DesignConditions Bulk Cargo Ballast Remarks

L-180 C vC C C z a K P ρ 75.0= Bv B B z a P ρ =

L-0 0=C P 0= B P

+ : positive- : negative

R

P ( )C t C vC C C ya z a K P 25.075.0 += ρ ( ) Bt Bv B B ya z a P += ρ + : positive

- : negative

NOTE:av, at : Acceleration of the center of gravity of tank according to Table 4.5

yC : Transverse horizontal distance from the center of the tank to the considered point (m)(The distance is taken as positive if the considered point is located at the weather side from

the transverse center of the tank, or as negative if the considered point is located at the leeside from the transverse center of the tank, see Fig. 4.6.)

z C : Vertical distance from the top of the tank to the considered point (m)

y B: : Transverse distance from the considered point to the top of tank located at the most lee-sidewhen the weather side is downward, or at the most weather side when the weather side is

upward (m) (When the weather side is downward, the distance is taken as positive if the point is locatedat the weather side, or as negative if the point is located at the lee side, from the top of tank at

the most lee side; see Fig.4.7.)

(When the weather side is upward, the distance is taken as positive if the point is located atthe weather side, or as negative if the point is located at the lee side, from the top of tank at

the most weather side; see Fig. 4.7.)

z B : Vertical distance measured from the middle point of the overflow pipe on the top of tank toconsidered point (m)

Low density cargo High density cargo

Fig. 4.6 Definition of yC

Fig. 4.7 Definition of y B and z B

z

C

z

C

波上側波下側C

< 0

C

> 0

z

C

z

C

y

C

> 0

y

C

< 0

波上側波下側Weather side Lee side Lee sideWeather side

波上側波下側

zB

yB

> 0

yB

> 0

zB

zB

yB

> 0

Weather side Lee side 波上側波下側

yB

< 0

yB

< 0

zB

zB

zB

yB

< 0

Lee sideWeather side




- 16 -

Table 4.5 Acceleration of the Centre of Gravity of Tank

DesignConditions

Acceleration of the center of

gravity of the hold or tank (m/s2)(Wave crest in head sea and

weather side down in beam sea)

Acceleration of the center of

gravity of the hold or tank (m/s2)(Wave trough in head sea and

weather side up in bean sea)

Remarks

－－－

L-180va− pitch g iheave

f

iv a x xa

d

d a −+= Positive upward

－－－

L-0－－－

φ g at = t a− Positive lee side

Rroll iheavev a ya

La +=

40va− Positive upward

φ g at 5.0= t a− Positive lee side

P roll iheavev a yaa 5.0+= va− Positive upward

NOTE:

x g : Longitudinal distance from the A.P. to the rotation center of pitch motion (=0.45 L) (m)

xi : Longitudinal distance from the A.P. to the considered center of gravity of tank (m)

yi : Transverse horizontal distance from the centerline of the hull to the considered center of gravity of

tank (m); positive when the considered center of gravity of the tank is on the weather side andnegative when the considered center of gravity of the tank is on the lee side (Refer to Fig.4.8)

aheave : Acceleration of the center of gravity of ship due to heave motion; according to Table 4.6

a pitch : Acceleration of the center of gravity of ship due to pitch motion; according to Table 4.6aroll : Acceleration of the center of gravity of ship due to roll motion; according to Table 4.6

φ : Roll angle; according to Table 4.3

FPAP

Pi

yi<0

Weather side

Piat>0

xg(=0.45L)

xi

av>0

Lee side

Fig. 4.8 Definitions of Coordinates for Calculating Accelerations of the Center of Gravity of the Tank

Table 4.6 Acceleration of the Center of Gravity of the Ship

Acceleration of the center of gravity of the ship due to pitch motion

22

=

P

pitchT

aπ

θ (rad./s2)

θ : Pitch angle, according to Table 4.3

Acceleration of the center of gravity of

the ship due to roll motion

22

=

R

roll T

aπ

φ (rad./s2)

Acceleration of the center of gravity of

the ship due to heave motion

( )

( ) P

b

heave H C L B

V g a

6.0

2.05

3⋅

+= (m/s2)

H P : Regular Wave height corresponding to the designcondition P (m)




- 17 -

5 Direct Load Analysis

5.1 General

-1. Design loads in waves can also be set for each ship using direct load analysis without using thedesign loads described Chapter 4 for wave-induced loads and Chapter 7 for hull girder stresses.

-2. The standard method for setting design loads using direct load analysis is given in Section 5.2.

-3. In addition to the standard method given in Section 5.2., the design loads may also be set using a

more sophisticated method based on the design sea conditions or on the design regular waveconditions.

5.2 Method of Setting Design Loads

-1. Direct load analysis is performed using the strip method under design regular wave conditions given

in Table 4.1 for setting the design loads. The internal dynamic pressure due to the bulk cargo and ballast and the hydrodynamic pressures at the time shown in Table 5.1 are set as the design loads.

-2. It is preferable to set the wave length of design regular waves using the results of direct load

analysis by the strip method in the design regular wave conditions given in Table 4.1. In this case,the wavelength of design regular wave is taken as the wavelength when the response of thedominant load given in Section 4.4.1-3. becomes maximum in regular waves.

-3. It is necessary to make the correction of nonlinearly for the hydrodynamic pressure near thewaterline based on the method given in Section 4.4.2.-5 and -6 above.

-4. For details of direct load analysis, the “Technical Guide Regarding the Strength Evaluation of

Hull Structures (Dec. 1999)” could be referred to.

Table 5.1 Time to be Considered in Design Regular Wave Conditions

Design

ConditionsTime to be Considered

L-180

• Time when the vertical wave bending moment (Hog.) at midship becomes maximum

• Time when the vertical bending moment (Sag.) at midship becomes maximum

• Time when the vertical acceleration at the center of gravity of the investigated hold becomes maximum

• Time when the vertical acceleration at the center of gravity of the investigated hold becomes minimum

L-0 • Time when the vertical wave bending moment (Hog.) at midship becomes maximum

• Time when the vertical bending moment (Sag.) at midship becomes maximum

R • Time when the rolling motion (weather side is downward) becomes maximum

• Time when the rolling motion (weather side is upward) becomes minimum

P • Time when the hydrodynamic pressure at the waterline amidships becomes maximum

• Time when the hydrodynamic pressure at the waterline amidships becomes minimum




- 18 -

6 Structural analysis

6.1 General

-1. Cross scantlings in the drawings are used in the model for structural analysis.

-2. Structural analysis is to be performed by the Finite Element Method. The members to be analyzed

are to be modeled using plate elements.

-3. An approved analysis program having adequate accuracy should be used. If deemed necessary,

documents related to systems used in the analysis and documents for confirming the accuracy may be required to be submitted to the Society.

6.2 Analysis Model

6.2.1 Extent of the model

-1. The extent of model is decided such that the actual stress conditions of the ship can be reproduced

by considering the arrangement of cargo oil and ballast tanks, the loading pattern and thearrangement of members near the bulkhead.

-2. The model extends at least half the hold on both sides of the transverse bulkhead , and full depthand full breadth. (Refer to Fig. 6.1)

-3. When the hot-spot stress is evaluated directly by the finite element analysis, fine meshes are to be

used appropriately so that the stress concentration at local discontinuity can be evaluated withsufficient accuracy. (Refer to Fig. 6.2.)

6.2.2 Members Considered

-1. The members to be considered are the members to be evaluated and all primary members within the

extent of the model. Load transmitting members such as longitudinal stiffeners and watertight bulkhead stiffeners should also be included in the model.

-2. When the hot-spot stress is evaluated directly by the finite element analysis, secondary members

around the hot-spot are to be included in the model.

6.2.3 Mesh Size

-1. The size of the mesh is selected considering the stress condition in the model and the meshing of

elements is performed rationally, so as to avoid meshes with large aspect ratios (See Fig. 6.1). Thestandard size of an element in the stress evaluation area is decided by taking one side of the elementas approximately equal to the spacing of the nearby stiffeners.

-2. When the hot-spot stress is evaluated directly by the finite element analysis, secondary membersaround the hot-spot are to be included in the model. The standard size of an element around the hot-

spot is decided by taking one side of the element as approximately equal to the plate thickness. Thesize of mesh is changed gradually. (Refer to Fig. 6.2)

6.3 Loads and Boundary Conditions

6.3.1 Loads

Loads are applied such that the load transmitted to the primary members is faithfully reproducedconsidering the arrangement of stiffeners.

6.3.2 Supports

-1. The model is supported in the vertical and transverse directions at the position of the transverse bulkhead. Members near the support points are excluded from being evaluated.

-2. When members near the support points are to be evaluated, analysis is performed separately bysupporting the model at locations away from the bulkhead.

-3. The model is supported at its forward and aft ends in the length direction applying symmetryconditions.




- 20 -

Fig. 6.2 Example of Fine Mesh Model




- 21 -

7 Superimposition of Hull Girder Stresses

Symbols

σ GS : Stress due to still water vertical bending moment N/mm2

σ WV : Stress due to wave-induced vertical bending moment N/mm2

σ WH : Stress due to wave-induced horizontal bending moment N/mm2

σ GW : Sum of the stresses σ WV and σ WH N/mm2

7.1 General

-1. The hull girder stress of members in which the hull girder stress cannot be ignored is to bedetermined. This stress is then added to the stress determined by applying the design loads.

-2. The hull girder stress is evaluated based on gross scantlings (scantlings in the drawings).

-3. The maximum value of the hull girder moment is converted to hull girder stress using beam theory.

This stress is multiplied by the stress superimposition ratio set for each design condition todetermine the hull girder stresses due to vertical bending and horizontal bending of the hull.

-4. The hull girder stress is added to the stress in the length direction of the ship obtained fromstructural analysis, and the stress considering the effect of the hull girder moment is determined.

-5. The stress concentration factor for the hull girder stress is 1.0.

7.2 Stress due to Hull Girder Moments

-1. The stress due to still water vertical bending moment of the hull is calculated as shown below.

510×⋅= V

V

S

GS f I

M σ ( N/mm2)

M S : Still water vertical bending moment corresponding to each loading condition; the mean

value of the two bulkhead positions located at both sides of the evaluation position istaken. (kN-m)

I V : Moment of inertia of the cross section about the horizontal neutral axis of thetransverse section to be evaluated (cm4)

f V : Vertical distance from the horizontal neutral axis to the evaluation position (m)

-2. The stress due to the wave-induced vertical bending moment of the hull is calculated as given below.

510

2×⋅= V

V

WV WV f

I

M σ ( N/mm2)

M WV : Wave-induced vertical bending moment at the considered section (kN-m); according to

15.2.1, Part C of the Rules. M WV is M W(HOG), or M W(SAG) according to the conditions

-3. The stress due to wave-induced horizontal bending moment of the hull is calculated as shown below.

5102

×⋅= H

H

WH WH f

I

M σ ( N/mm2)

M WH : Wave-induced horizontal bending moment at the considered section (kN-m):calculated by the equation given below.

L

Ld LC C M iWH

3532.0 2

81

−=

C 1 : According to Chapter 15.2.1-1, Part C of the Rule




- 23 -

8 Evaluation Stress

Symbols

σ 0 : Nominal Stress N/mm2

C C1 : Correction coefficient for corrosion ‐

C C2 : Correction coefficient for corrosion ‐

σ hot : Hot-spot stress N/mm2

K t : Stress concentration factor ‐

8.1 General

-1. In fatigue strength assessment, at the locations where the fatigue crack may initiate (hot-spot

location), the stress range and mean stress are determined based on the stress obtained from thedifference in the maximum and minimum values of the stress when a unit-cycle dynamic load is

applied.-2. Stress on the plate surface at the hot-spot location that includes the stress increment (hot-spot stress)

due to effects of local structural discontinuity is used for fatigue strength assessment.

-3. The hot-spot stress may be determined by multiplying the nominal stress at the hot-spot location bythe stress concentration factor.

8.2 Nominal Stress

8.2.1 General

-1. The nominal stress, σ n , is the stress at the hot-spot location considering the stress increment due tothe effects of overall structural discontinuities.

-2. Use the stress component perpendicular to the weld bead at the hot spot for evaluating the weld part.

-3. The effects of secondary bending stress are to be considered if they are too large to be ignored.

-4. Fatigue strength may be assessed based on the evaluated stress according to the “ Guidelines for

Direct Strength Analysis”.

8.2.2 Evaluation Method

-1. The nominal stress may be determined by using the beam theory or may be taken as the valuedetermined by the “Guidelines for Direct Strength Analysis”.

-2. When determining the nominal stress of the plate surface from the results of FEM calculation, use

the stresses at positions that are 1.5 times the frame spacing and 2.5 times the frame spacing fromthe hot spot. Then determine the stress at the hot-spot position by extrapolation. (Refer to Fig. 8.1)

-3. When determining the nominal stress at the ends of large stiffeners from the results of FEMcalculation, use the axial stress at the center of the free flange of the bracket. (Refer to Fig. 8.2)

-4. The nominal stress due to hull girder moment is evaluated according to 7.2.




- 24 -

Fig. 8.1 Definition of Nominal Stress (example of intersection of double bottom floor and bilge hopper)

Fig. 8.2 Definition of Nominal Stress at the End of Large Stiffener

-5. Correction considering the effects of corrosive environment to members exposed to suchenvironments.

1

0

C C

σ σ =

σ 0 : Stress evaluated from structural analysis used design loads in 4.4.2 and 4.4.3.

C C 1 : Correction coefficient for corrosion; taken as 0.88

-6. Apply correction to the nominal stress determined by structural analysis in the “Guidelines for

Direct Strength Analysis” using the equation given below.

652

*0

2 C C C C

n

σ σ =

σ 0* : Stress evaluated from structural analysis in the “Guidelines for Direct Strength

Analysis”

C C 2 : Correction coefficient considering corrosion; taken as given below

=2C C 1.2 : for members protected against corrosive environment

1.05 : for members exposed to corrosive environment

C 5 : Correction coefficient for non-linear wave height characteristics and three-dimensional

effects; taken as 0.9 for the design conditions L-180 and L-0; and as 0.8 and 0.7 for thedesign conditions P and R respectively.




- 25 -

C 6 : Correction coefficient for elastic structural design; taken as 0.67

-7. Apply correction to the nominal stress due to hull girder moment determined by the “Guidelines

for Direct Strength Analysis” using the equation given below.

5

*0

2C n

σ

σ =

8.3 Hot-spot stress

8.3.1 General

-1. The effect of weld toe shape is ignored in evaluating the hot-spot stress. Consider the stressincrement due to effects of local structured discontinuities because of local reinforcements or other reasons, and evaluate the stress at the hot-spot position.

-2. The effects of secondary bending stress are to be considered if they are too large to be ignored.

-3. Evaluate the hot-spot stress either by direct analysis using FEM or by multiplying the nominal stress by the stress concentration factor.

8.3.2 Evaluation Method

-1. To determine the hot-spot stress by direct analysis, take the weld toe as the hot-spot position.

Linearly extrapolate the respective stress values at positions 0.5 times and 1.5 times the platethickness away from the hot-spot position, and take the extrapolated value at the hot-spot positionas the hot-spot stress (Refer to Fig. 8.3).

Fig. 8.3 Evaluation of Hot-spot Stress by Extrapolation

-2. The hot-spot stress may also be evaluated by multiplying the nominal stress at the hot-spot location by the stress concentration factor.

nt hot K σ σ ×=

σ hot : Hot-spot stress

K t : Stress concentration factor

σ n : Nominal stress

Hot-spot stress

Stress distribution




- 26 -

8.4 Stress Concentration Factor

8.4.1 General

-1. The values of stress concentration factor given in this section are the standard values to bemultiplied by the nominal stress to determine the hot-spot stress.

-2. To use the standard value of stress concentration factor given in this section, the workmanshipstandards and welding standards of Appendix A.3 and A.4 should be adhered to.

-3. Notwithstanding the standards indicated in this section, the hot-spot stress may be determined byany other appropriate method.

-4. If the stress concentration factor has already been determined for a similar structure, then this valuemay be used subject to the approval of the Society.

8.4.2 Bilge Hopper Knuckle

-1. The stress concentration factor for the bilge hopper knuckle is given by the equation:

43210 K K K K K K t ××××=

K 0 : Coefficient depending on the dimensions at the considered location; according to Table8.1.

K 1 : Correction coefficient depending on the plate bending process; according to Table 8.2.

K 2 : Correction coefficient depending on the web thickness increment; according to Table8.2.

K 3 : Correction coefficient depending on the insertion of horizontal gusset or longitudinal rib;according to Table 8.2. (Refer to Fig. 8.4)

K 4 : Correction coefficient depending on the insertion of transverse rib; according to Table8.2. (Refer to Fig. 8.5)

Table 8.1 Stress Concentration Factor

Platethickness

Rising angle (deg.)

(mm) 40 45 50 90

16 3.0 3.2 3.4 4.2

18 2.9 3.1 3.3 4.0

20 2.8 3.0 3.2 3.8

22 2.7 2.9 3.1 3.6

24 2.6 2.8 3.0 3.5

26 2.6 2.7 2.9 3.4

28 2.5 2.7 2.8 3.3

30 2.4 2.6 2.7 3.2

Note : Values for intermediate plate thickness and rising angle may

be interpolated from the values given in the table.




- 27 -

Table 8.2 Correction Coefficients

K 1 K 2 K 3 K 4

Weld Type 1.7 0.9 0.8 0.9

Bend Type 3.1 0.95 0.45 0.8 Note : In using the correction coefficient K 3 , the members should be

arranged such that the bending deformation of the radius part is

effectively suppressed.: The increase in web thickness is taken basedon the plate thickness of the inner bottom plating.

-2. The following reinforcing methods are taken as standards for using the correction coefficients givenin Table 8.2.

(1) To reinforce a welded-type knuckle connection, the horizontal gusset is arranged to ensurecontinuity with the inner bottom plate.

(2) To increase the web plate thickness, insert the plate locally at the knuckle over a range of about 500mm.

(3) To reinforce the transverse rib, install the reinforcement at a position within 300mm from thegirder plate.

8.4.3 Intersection of Plating and Girder

The stress concentration factor for stress in the web of the fillet weld at the intersection of plating andgirder is given by the equation below.

31

32

341 2

161

t

t t

h

ht

e K t +

+××+= l

l

e : Allowable misalignment (mm); ( )3

,min 41 t t e =

t 1 : Thickness of girder web plate (mm)

h : Span of girder plate panel

t 4 : Thickness of supporting girder web plate (mm)

l : Span of the supporting girder plate panel; to be taken as the frame spacing (mm)

t 2 : Principal plate thickness of side plating etc. (mm)

Fig. 8.4 Example of the Insertion of Horizontal Stiffener or Longitudinal Rib

Fig. 8.5 Example of the Insertion of Transverse Rib




- 28 -

Fig. 8.6 How Dimensions are to be taken

8.5 Long-term Distribution of the Stress Range

8.5.1 General

-1. Take the difference in the hot-spot stress determined by applying wave-induced loads in Chapter 4as the stress range.

-2. When the effect of hull girder moment on the fatigue strength is not negligible, maximum andminimum stresses due to hull girder moment are superimposed on the maximum and minimum hot-spot stresses due to design loads respectively.

-3. Take the long-term distribution of stress range as an exponential distribution with a Weibull shape parameter of 1.0.

8.5.2 Long-term Distribution

-1. Determine the long-term distribution of stress range by considering the Weibull shape parameter inthe maximum value of stress range evaluated in 8.3.

-2. While determining the long-term distribution of stress range, revise the maximum value of the stressrange evaluated in Section 8.3 is to be considered as the response value corresponding to theexceedance probability of 10-4.

-3. When the long-term distribution of stress range is expressed by a frequency distribution during the

calculation of cumulative fatigue damage, set the number of blocks of the frequency distributionsuch that the cumulative fatigue damage can be calculated with adequate accuracy.

l

l

h

l

e

t 1

t 4

t 2

Welded part under evaluation




- 29 -

9 Fatigue Strength Assessment

Symbols

σ mean : Mean structural stress N/mm2

σ res : Local residual stress N/mm2

Dall : Allowable fatigue damage ‐

η : Correction coefficient for bulk carriers ‐

9.1 General

-1. The fatigue strength acceptance criterion is it that the calculated cumulative fatigue damage should be less than the allowable damage.

-2. If the calculated cumulative fatigue damage exceeds the allowable fatigue damage, revise thestructural details so that the stress concentration is mitigated and then re-evaluate the fatigue

strength to meet the acceptance criteria.

9.2 Design Curves

-1. To assess the fatigue strength, S-N curves given in Table 9.1 and Fig. 9.1 are used.

( )( )

⋅<∆∆⋅′

⋅≥∆∆⋅=−′−

−−

mm

mm

C C

C C N

17

17

10;

10;

σ σ

σ σ

Table 9.1 S-N Curves

m C m' C' Non-welded part 4 2.34E+15 7 4.44E+21

Welded part 4.63 5.46E+16 8.25 2.35E+24

Fig. 9.1 S-N Curves

10

100

1000

1E+04 1E+05 1E+06 1E+07 1E+08

Fatigue Life ( cycles )

S t r e s s R a n g e

( M P a )

welded part

non-welded part




- 33 -

Appendices: Examples of Structural Details

A.1 General

-1. Fatigue strength at structural discontinuities should be assessed by the workmanship standards

mentioned in this Appendix and by the method mentioned in the “Guidelines for Fatigue StrengthAssessment” to confirm the safety of fatigue strength.

-2. The method of mitigating the increase in stress concentration in the details of structural

discontinuities given in this Appendix should be taken as the standard method for determining thestress concentration factor given in the “Guidelines for Fatigue Strength Assessment”.

-3. Any method approved as appropriate may be used instead of the standard method for mitigating theincrease in stress concentration and mentioned in this Appendix.

A.2 Extent

The extent of the structures given in this Appendix includes the ends of large stiffeners in cargo hold

and the parts in which often generate a crack.

A.3 Workmanship Standards

-1. The misalignment during work associated with the ends of large stiffeners is defined as shown inFig. A.1 taking the centerline of the plate thickness as the reference.

Fig. A.1 Definition of Misalignment between Girder Plates on Either Side of the Inner Hull

-2. The allowable misalignment is as given below. However, the smaller of the thickness of the two

girder plates on either side of the inner hull is considered.

3

t eall ≤

-3. No openings are provided within the range of stress concentration of web bracket supports.

-4. Stress concentration at the sniped ends should be mitigated effectively




- 34 -

A.4 Welding Standards

-1. Full penetration welds are to comply with the Guidance for the Survey and Construction of Steel

Ships C31A.3.5.

-2. Full penetration welds are to comply with the Guidance for the Survey and Construction of Steel

Ships C31B.3.5.

A.5 Examples of Structural Details

Examples of standard measures for mitigating stress concentration in the structures below are given inthis Appendix.

A.5.1 Upper/Lower Ends of Hold Frame

A.5.2 Intersection of Inner Bottom Plating and Hopper Plating in BHT


Bulkhead

A.5.4 Connection between Upper Part of Transverse Bulkhead and TST Slant Plating or Upper

StoolA.5.5 Bilge Keel Ends (Connections at Bilge Shell Plating)

A.5.6 Bulwark Gusset Plate and Bulwark Stay

A.5.7 Hatch Coaming End Bracket Ends and Coaming Stay

A.5.8 Around the Hatch Corner




- 35 -

A.5.1 Upper/Lower Ends of Hold Frame

(1) Characteristics of cracks at the ends of hold frame

• Cracks at the upper end of the hold frame not accompanied by heavy corrosion, initiate in deep tank

holds, which are subjected to high stresses.

• Such cracks initiate because of mutual interaction between structural members in adjacent TST/BHT

and of the stress concentrate due to structural discontinuities or misalignment.

• The dominant load component is the forced displacement from the hold frames.

Fig. A5.1.1 Example of crack at the upper/lower end of hold frame

(2) Example showing measure to prevent cracks at the ends of hold frame

• Use soft corners at the ends of the hold frame. (See Fig. A5.1.2 (a).)

• Make the lower bracket in the topside tank adequately larger than the upper bracket of the hold frame

thereby making it difficult for the lower bracket to receive the effect of forced displacement from the

upper end of the hold frame. (See Fig. A5.1.2 (b).)

• Make the upper bracket in the bilge hopper tank adequately larger than the lower bracket of the hold

frame thereby making it difficult for the upper bracket to receive the effect of forced displacement

from the upper end of the hold frame. (See Fig. A5.1.2 (b).)

(a) Soft corner at the end of bracket (b) Preventing forced displacement at upper/lower end of hold

frame

Fig. A5.1.2 Example showing measure to prevent cracks at the ends of hold frame




- 36 -

A.5.2 Intersection of Inner Bottom Plating and Hopper Plating in BHT

(1) Characteristics of crack in bilge knuckle

• Cracks can be classified into cracks in the inner bottom plating/sloped plating and cracks in

floors/stiffeners attached to floors.

• Cracks initiate frequently in deep tank holds where loading conditions are severe.

• Where the bilge knuckle is welded type, cracks initiate because of workmanship defects such as

misalignment between girder plating and sloped plating.

• Where the bilge knuckle is bending type, if the distance between the side girder and the center of

radius of the rounded part is large, cracks are likely to initiate easily because bending deformation is

constrained by the floor.

Welded type knuckle Bending type knuckle

Fig. A5.2.1 Crack in the bilge hopper knuckle

(2) Example of measure to prevent cracks

Fig. A5.2.2 (a) Controlling misalignment

Fig. A5.2.2 (c) Installing transverse rib Fig. A5.2.2 (b) Installing horizontal gusset




- 37 -


Bulkhead

(1) Characteristics of cracks in the lower stool

Cracks in the lower stool are classified as follows:

• Cracks at the connection between inner bottom plating/ floor/ girder plating/ stool slant plating

• Cracks at the connection of corrugated bulkhead and slant plating

• Cracks at the connection between flange of corrugated plating and stool slant plating and top plating

of lower part of bulkhead

• Cracks at the connection between upper vertical web of lower stool and stool slant plating and top

plating of lower part of bulkhead

The trend of initiation of cracks is generally considered to be as follows:

• Cracks frequently initiate at locations facing the deep tank hold where loading conditions are severe.

• Cracks initiate because of workmanship defects such as misalignment between stool and floor.

Fig. A5.3.1 Cracks in the lower stool


• Use full penetration welds at the connection between upper vertical web of lower stool and the top

plating of lower part of bulkhead.

• Do not cut scallops at the connection between the upper vertical web of the lower stool and stool slant

plating and the top plating of lower part of the bulkhead.

Fig. A5.3.2 Example of reinforcement at intersections in the lower stool




- 38 -

A.5.4 Connection between Upper Part of Transverse Bulkhead and TST Slant Plating or Upper Stool

(1) Characteristics of cracks at the connection between transverse bulkhead and TST slant plating

Cracks mentioned below have been reported at the connections of upper stool, upper part of transverse

bulkhead and topside tank slant plating.

• At the intersection of upper stool slant plating knuckle and topside tank slant plating knuckle

• At the connection of vertical web in the stool and the bulkhead shelf plate

Structures with large rigidity intersect and very high stress concentration exists at these locations. Cracks

also initiate because of defects in welds and misalignment at the connections between transverse bulkhead

and other members.

• Cracks in the welds of carling in the TST at the connection of the transverse bulkhead and topside tank

slant plating are caused either because of misalignment between corrugated bulkhead and vertical web

or stool slant plating, or because of stress concentration in the scallop at the connection.

Fig. A5.4.1 Cracks at the connection of the upper part of transverse bulkhead and TST slant plating

or upper stool

(2) Measures against cracks in the lower part of the upper stool

The measures mentioned below may be adopted for inhibiting deformation at stool corners.

• Install a diaphragm plate in the stool aligned with the hatch side girder.

• Install a bracket in the stool to coincide with the plane of the bulkhead web plate.

Fig. A5.4.2 Example of structural connection of transverse bulkhead at lower part of upper stool




- 39 -

A.5.5 Bilge Keel Ends (Connections at Bilge Shell Plating)

(1) Types of crack in bilge keel

Cracks at the ends of bilge keel initiate due to stress concentration at the ends of the bilge keel because of

the longitudinal bending of hull. Particular care is necessary against cracks that go into the shell plating

from the ends of bilge keel since the watertightness of the compartment may be lost. Typical cracks at the

ends of bilge keel are of the following kinds:

• Crack 1: Crack that goes into the shell plating from the weld joining the ends of doubling plate

• Crack 2: Crack in the welds joining the bilge keel ends to the hull

• Crack 3: Crack at the end of the bilge keel

Fig. A5.5.1 Types of crack in bilge keel


• Terminate the ends of the bilge keel at the floor positions.

Fig. A5.5.2 Example of measure to prevent cracks

• Gradually taper the ends of the bilge keel.

Fig. A5.5.3 Example of measures to prevent cracks

crack 1

crack 3

crack 2

Floor

bilge keel

bilge strake




- 40 -

A.5.6 Bulwark Gusset Plate and Bulwark Stay

(1) Types of cracks in bulwark

Cracks in the bulwark initiate due to shear forces acting between the upper deck and bulwark because of

structural discontinuities, stress flow and deformation due to longitudinal bending of hull.

Types of crack in the bulwark are as follows:

• Where expansion joints are present, cracks that initiate in the bulwark stays or in the root of the gusset

plates

• Where expansion joints are not present, cracks that initiate in the bulwark top plate.

Fig. A5.6.1 Types of crack in the bulwark

(2) Measures against cracks in the bulwark

• Align the toe of the bulwark stay with the upper deck longitudinal. (See Fig. A5.6.1 (a).)

• Ensure adequate section area is available to resist shear forces. (See Fig. A5.6.1 (b).)

(a) Elimination of structural discontinuity (b) Ensuring adequate section area

Fig. A5.6.2 Measures against cracks in bulwark




- 41 -

A.5.7 Hatch Coaming End Bracket Ends and Coaming Stay

(1) Characteristics of cracks in hatch coaming stay/end bracket

Cracks in hatch coaming stay/end bracket initiate because of high stress concentration due to improper

shape. Particular care is required to prevent cracks at bracket ends/stay ends because such cracks may

penetrate the upper deck plating.

Fig. A5.7.1 Cracks in hatch coaming stay/end bracket ends


Fig. A5.7.2 Example of relaxing stress concentration at end bracket ends




- 42 -

A.5.8 Around the Hatch Corner

(1) Types of crack at the hatch corner

Cracks at hatch corner initiate because of the following:

• Stress concentration due to the shape of the hatch corner

• Stress concentration at the ends of fittings on the corner plate

• Misalignment and welding defects

• Scratches due to excessive chafing by wires (notches)

Fig. A5.8.1 Cracks at hatch corner


• Insert thicker plate at the hatch corners

• Use elliptical or parabolic-shaped hatch corners

• Keep deck welding joints, holes in deck girder through which pipes pass and other openings at an

adequately safe distance from the hatch corners.



Guidelines for Ultimate Hull Girder Strength Assessment ClassNK

- i -


Contents

1 General ････････････････････････････････････････････････････････････････････････ 1

1.1 Scope of Application ･････････････････････････････････････････････････････････ 1

1.2 Documents to be Submitted ････････････････････････････････････････････････････ 1

2 Location of assessment for Ultimate Hull Girder Strength ･･････････････････････････････

1

3 Methods for Calculating Ultimate Longitudinal Bending Moment Capacity････････････････ 1

3.1 Assessment Method Using Meshed Elements ･･････････････････････････････････････ 1

3.2 Assessment Method Using Simplified Equations ･･･････････････････････････････････ 3

3.3 Assessment Method by Direct Calculation Using Analysis Codes ･･････････････････････ 4

4 Assessment of Ultimate Hull Girder Strength ･････････････････････････････････････････ 4




- 1 -


1 General1.1 Scope of Application

The ultimate hull girder strength of bulk carrier, which comply with Chapter 31, Part C of the Rules, can be assessed using these Guidelines.

1.2 Documents to be Submitted

All calculations, relevant documents and drawings mentioned below and used in the assessment of

ultimate hull girder strength according to these guidelines are to be submitted to the Society.

• General Arrangement Drawing

• Midship Section Drawing

• Longitudinal Strength Calculations

• Longitudinal Bending Moment Calculations

2 Location of assessment for Ultimate Hull Girder Strength

Assessment is to be performed in the condition and position at which the maximum hogging and saggingmoments respectively occur in the midship region (0.4 L midship).

3 Methods for Calculating Ultimate Longitudinal Bending Moment Capacity

The ultimate longitudinal bending moment capacity is to be calculated by any one of the methodsdescribed in 3.1 to 3.3. The moment of inertia of hull transverse section, transverse sectional area of longitudinals, thickness of panel plating and so on, shall be based on the gross thickness that includes thecorrosion margin.

3.1 Assessment Method Using Meshed Elements

-1. All longitudinal strength members in a hull transverse section are divided into stiffened panel

elements (stiffener and half the width of the panel on both sides associated with the stiffener), full-

width panel elements (full-width panel divided by large stiffeners or stiffeners) and half-width panelelements (panels that are half the full-width panel elements). The total of n elements consisting of stiffened panel elements and panel elements are named element 1, element 2, ….. element n. (SeeFig. 3.1.)

-2. Ultimate strength of stiffened panels and panels are to be calculated by the following equations.

usσ s

sYs pYp

Abt

Abt

+

+−=

σ λ σ )0692.01( 2

for 69.2≤ pλ

s

sYs pYp

Abt

Abt

+

+=

σ λ σ )615.3(2

for 69.2> pλ

σ Yp : Yield stress of panel ( N/mm2)

σ Ys : Yield stress of stiffener ( N/mm2)



ClassNK Guidelines for Ultimate Hull Girder Strength Assessment

- 2 -

b : Breadth of panel (mm); however this value is to be double the breadth in caseof half-width panel.

t : Thickness of panel (mm)

A s : Sectional area of longitudinal (mm2); this value is 0 in case of panel elements.

λ p : Slenderness ratio of plate panel, and given by the following equation.

E t

b Yp

p

σ λ =

E : Young’s modulus ( N/mm2)

-3. The ultimate longitudinal bending moment capacity in the hogging condition is given by thefollowing equation.

∑=n

i

iiiu z A M σ ( N-m)

Ai : Sectional area of element i (mm2)

z i : Distance of element i from the elastic neutral axis (m)

σ i : Stress of element i determined from the equation given below. However, this value

is not to exceed σ yi above the elastic neutral axis and σ usi below the elastic neutralaxis.

ρ σ i

i

z E =

σ yi : Mean yield stress of element i ( N/mm2) However, if the yieldstresses of panel and stiffener are different, the mean yield stress is to be calculated according to their sectional area.

σ usi : Ultimate strength of element i as specified in above item -2. ( N/mm2)

ρ : Radius of curvature given by the following equation (m) Theelements that constitute inner bottom plating are defined as set I .

∑

∑=

I

i

i

I

i

iusi

B I A

A

Ez

σ

ρ ..

11

.. B I z : Distance from the elastic neutral axis to the inner

bottom plating (m)

-4. The ultimate longitudinal bending moment capacity in the sagging condition is given by the

following equation.

∑=n

i

iiiu z A M σ

Ai, σ yi, σ usi, z i : according to above –3.

σ i : Stress of element i determined from the equation given below. However, this value

is not to exceed σ usi above the elastic neutral axis and σ yi below the elastic neutralaxis.

ρ σ i

i

z E =

ρ : Radius of curvature given by the following equation. The elements

that constitute upper deck plating are defined as set U .




- 3 -

∑

∑=

U

i

i

U

i

iusi

DU A

A

Ez

σ

ρ ..

11

z U.D. : Distance from the elastic neutral axis to the upper deck plating (m)

Fig3.1 Example of Meshing Hull Transverse Section

3.2 Assessment Method Using Simplified Equations-1. This method shall be applied on condition that the deck longitudinals and bottom longitudinals are

arranged at almost the same interval and that the thickness of deck and bottom plating except keel plating is almost the same.

-2. The ultimate longitudinal bending moment capacity in the hogging condition is given by thefollowing equations.

( )usbottom yupper

bottomupper

u z z

I M σ σ +

+= ( N-m)

I : Moment of inertia of hull transverse section about the elastic neutral axis (cm4)

z upper : Distance of upper deck plating from the elastic neutral axis (cm)

z bottom : Distance of the mid-point between bottom plating and inner bottom platingfrom the elastic neutral axis (cm)

σ usbottom : Mean value of σ usB.P. and σ usI.B. ( N/mm2)

σ usB.P. : Ultimate strength of stiffened panel at bottom plating is given by 3.1-2 above( N/mm2)

σ usI.B. : Ultimate strength of stiffened panel at inner bottom plating is given by 3.1-2above. ( N/mm2)

σ yupper : Yield stress of upper deck plating ( N/mm2)

-3. The ultimate longitudinal bending moment capacity in the sagging condition is given by thefollowing equations.

usupper

upper

u z

I M σ = ( N-m)



ClassNK Guidelines for Ultimate Hull Girder Strength Assessment

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I , z upper : According to item above -1.

σ usupper : Ultimate strength of stiffened panel at upper deck plating is given by above 3.1-2.( N/mm2)

3.3 Assessment Method by Direct Calculation Using Analysis Codes

The progressive collapse analysis codes according to Smith’s method is recommended as the calculation

method for verifying the processes until the collapse of hull girder strength after the progressive bucklingand plastic collapse of longitudinal strength members.

4 Assessment of Ultimate Hull Girder Strength

The assessment of ultimate hull girder strength is introduced by the following. The total longitudinal

bending moment in extreme conditions should not exceed the moment capacity M u in the hogging andsagging conditions. That is, the equation below should be satisfied.

sc

u

extremew s M M M

η η 1000≤+ −

(kN-m)

M s : Longitudinal bending moment in still water, the absolute value of which

becomes maximum in the hogging (+) and sagging (-) conditions respectively(kN-m)

M w-extreme : Wave-induced longitudinal bending moment in extreme sea conditions, given by the equation below.

wextremew M M 1.1=− (kN-m)

w M bC B LC C ′+=212119.0 (kN-m) In the hogging condition

)7.0(11.0 2121 +′−= bC B LC C (kN-m) In the sagging condition

bC LC C ′,,, 121 : According to 15.2.1, Part C of the Rules (kN-m)

M u : Moment capacity of hull transverse section, calculated from any of themethods given in 3.1 to 3.3 above.

η c : Safety factor for corrosion, taken as 1.13

η s : Safety factor for ultimate strength, taken as 1.1



Supplement to Guidelines for Bulk Carrier Structures

The "Guidelines for Bulk Carrier Structures" have been developed based on extensive, advancedresearch on ship structures and it includes the guidelines for structural strength assessment and

fatigue strength assessment. These guidelines are initially focused on single side bulk carriers as

almost all of the bulk carriers are of single side. However, these guidelines can be applied to double

side bulk carriers as well with slight modifications.

Many double side bulk carriers, such as coal carriers, have been in service over the years, and the

number of double side bulk carriers operating on alternate load condition is recently on the increase.

Considering these trends, the "Guidelines for Bulk Carrier Structures" that was initially developed

for single side bulk carriers were augmented to include double side bulk carriers as well. This

supplement details the changes and additions to the guidelines for application to double side bulk

carriers.



- 1 -


(The handling of double hull bulk carriers)

The "Guidelines for Direct Strength Analysis" are to be applied to double hull bulk carriers taking

into account the changes or additions underlined below, and paying attention to the figures for single

hull bulk carriers shown in these guidelines.

1 General

1.1 Application

-1. The structural arrangement and scantlings of primary members in the cargo hold areas of

bulk carriers applying to Chapter 31, Part C of the Rules can be determined by these

Guidelines.

-2. Even if the scantlings of structural members of the hull are determined based upon the direct

strength calculation, the said scantlings should also satisfy the requirements given below.

(1) Requirements related to longitudinal strength prescribed in Chapter 15, Part C of the Rules

(2) Requirements related to hull strength when flooding prescribed in Chapter 13 and, in case of

single side bulk carriers, 31A, Part C of the Rules

(3) Requirements related to plating and longitudinals prescribed for local loads

(4) Requirements related to fatigue strength.

2 Applicable Members

2.1 Applicable Members

The structural arrangement and scantlings of structural members that can be determined based

upon these guidelines are given in (1) to (7) below.

(1) Shell platings, inner bottom plating, longitudinal bulkhead, hopper plates of bilge hopper

tanks constituting the double bottom and the double side and sloping plate of topside tanks

(2) Floors and girders in the double bottom

(3) Transverse rings in the bilge hopper tanks

(4) Transverse rings in the topside tanks

(5) Transverse bulkhead platings (including stools and girders in stools)

(6) Hold frames in the case of single side and webs and stringers in case of double sides

(7) Cross decks



- 2 -

3 Loading Conditions


In Table 3.1, the following (4) has been added in the remarks.(4) In normal ballast condition, all ballast tanks are basically to be assumed to be ballasted for

strength assessment.

5 Design Loads

5.3 Pressure Acting on the Hull

5.3.2 Pressure due to Bulk Cargo

-1. Shape of bulk cargo surface

(1) The shape of bulk cargo surface indicated by (L-a) in L of Table 5.4 is taken as the shape of

the bulk cargo surface to be assessed. Where loading of high density cargo is anticipated, the

shape of bulk cargo surface indicated by (H-a) in H of Table 5.4 is taken as the shape of

surface to be assessed.

(2) To obtain the pressure due to dry bulk cargo for strength assessment, the shapes L and H

indicated in (1) above are corrected to the shapes indicated by (L-b) and (H-b) of Table 5.4.

(3) It is assumed that cargo pressure does not act on the side shell plating of single side and side

longitudinal bulkhead of double sides in the case of the shape of bulk cargo surface (H-b) for

strength assessment, obtained in (2) above.

7 Considerations for Corrosion

7.2 Corrosion Deduction

Fig. 7.1 and Fig. 7.2 show the values of corrosion deduction for various structural members

according to the length of a ship.



- 3 -

Fig. 7.1 Corrosion Deduction for Direct Strength Calculation of Bulk Carriers

(These values apply to ships of 200m or more)



- 4 -

Fig. 7.2 Corrosion Deduction for Direct Strength Calculation of Bulk Carriers

(These values are apply to ships under 200m )



- 5 -


(The handling of double hull bulk carriers)

The "Guidelines for Fatigue Strength Assessment" are to be applied to double hull bulk carriers

taking into account the changes or additions underlined below, and paying attention to the figures for

single hull bulk carriers shown in these guidelines.

2 Members and Parts to be Assessed

2.2 Members subjected to Fatigue Strength Assessment

-1. Members and parts that required to be assessed for fatigue strength in accordance with these

guidelines are given in Table 2.1 and illustrated in Fig. 2.1.

-2. Locations with high stresses are selected from the locations mentioned in -1. above and the

fatigue strength is assessed.

Table 2.1 Members and Locations to be Assessed for Fatigue Strength

Members Locations

Intersection of sloping plate of lower stool, girder, floor plateand inner bottom plating

Inner bottom plating

Intersection of sloping plate of bilge hopper tanks, girder, floor plate and inner bottom plating

Intersection of side longitudinal bulkhead and sloping plate of bilge hopper tanks

Side longitudinal bulkhead plating

Intersection of side longitudinal bulkhead and sloping plate of topside tanks

Intersection of sloping plate of lower stool and transverse bulkhead

Intersection of sloping plate of upper stool and upper part of

transverse bulkhead

Transverse bulkhead

Intersection of slant plating of topside tanks and upper part of transverse bulkhead

Intersection of upper end of hold frame and sloping plate of topside tanks

Sloping plate of topside tank

Intersection of end of hatch coaming and sloping plate of topside tanks

Sloping plate of lower stool Intersection of inner bottom plate and sloping plate of lower

stool



- 6 -

Fig. 2.1

Members and Locations to be Assessed for Fatigue Strength



4 Design Loads

4.3 Loads in Still Water

4.3.4 Static Pressure due to Bulk Cargo-3. When density of cargo taken into consideration is 1.0 (t/m3) or more, shape of cargo

surface is based on the following points.

(1) The shape of dry bulk cargo surface is taken to be horizontal in the transverse and

longitudinal directions near the ship's centerline, but is assumed to vary linearly from the

centerline towards the ship sides considering half the angle of repose ( /2). The width of

the transverse part is taken as half the width of the cargo hold.

(2) The cargo loading height z C is determined from the mass of the cargo loaded, the angle of

repose and density of the cargo. The shape of dry bulk cargo surface may be taken as

horizontal in the longitudinal direction.

(3) The density of cargo is taken as the maximum designed density of the cargo. Unless

particularly specified, the density of the cargo is taken as 3.0 (t/m3).

(4) It is assumed that cargo pressure does not act on the side shell plating of single side and

side longitudinal bulkhead of double sides in strength assessment.