NKK-Guidelines for Direct Strength Analysis

Guidelines for Direct Strength Analysis ClassNK

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Guidelines for Direct Strength Analysis

Contents

1 General ････････････････････････････････････････････････････････････････････････ 11.1 Application･････････････････････････････････････････････････････････････････ 11.2 Procedure for Evaluation ･･････････････････････････････････････････････････････ 11.3 Minimum Thickness･･････････････････････････････････････････････････････････ 2

2 Applicable Members ･････････････････････････････････････････････････････････････ 22.1 Applicable Members ･････････････････････････････････････････････････････････ 2

3 Loading Conditions ･･････････････････････････････････････････････････････････････ 23.1 Loading Conditions ･･････････････････････････････････････････････････････････ 2

4 Design Conditions････････････････････････････････････････････････････････････････ 44.1 General ････････････････････････････････････････････････････････････････････ 44.2 Design Sea Conditions ････････････････････････････････････････････････････････ 4

4.2.1 General ･･････････････････････････････････････････････････････････････ 44.2.2 Setting the Design Sea Conditions ･････････････････････････････････････････ 5

4.3 Design Regular Waves ････････････････････････････････････････････････････････ 54.3.1 General ･･････････････････････････････････････････････････････････････ 54.3.2 Setting the Design Regular Waves ･････････････････････････････････････････ 6

5 Design Loads････････････････････････････････････････････････････････････････････ 75.1 General ････････････････････････････････････････････････････････････････････ 75.2 Ship Motions and Accelerations･････････････････････････････････････････････････ 8

5.2.1 Ship Motions ･････････････････････････････････････････････････････････ 85.2.2 Acceleration of the Center of Gravity of the Ship ･････････････････････････････ 85.2.3 Acceleration of the Center of Gravity of the Tank ･････････････････････････････ 9

5.3 Pressure Acting on the Hull ･･･････････････････････････････････････････････････ 105.3.1 Sea Water Pressure ････････････････････････････････････････････････････ 105.3.2 Pressure due to Liquid Cargo and Ballast ･･････････････････････････････････ 13

6 Direct Load Analysis ････････････････････････････････････････････････････････････ 156.1 General ･･･････････････････････････････････････････････････････････････････ 156.2. Setting Method for Design Loads ･･････････････････････････････････････････････ 15

7 Considerations for Corrosion ･････････････････････････････････････････････････････ 167.1 General ･･･････････････････････････････････････････････････････････････････ 167.2 Corrosion Deduction ････････････････････････････････････････････････････････ 16

ClassNK Guidelines for Direct Strength Analysis

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8 Structural Analysis･･････････････････････････････････････････････････････････････ 178.1 General ･･･････････････････････････････････････････････････････････････････ 178.2 Analysis Model ････････････････････････････････････････････････････････････ 17

8.2.1 Extent of the Modeling･････････････････････････････････････････････････ 178.2.2 Members Considered ･･････････････････････････････････････････････････ 178.2.3 Mesh Size ･･･････････････････････････････････････････････････････････ 17

8.3 Loads and Boundary Conditions ･･･････････････････････････････････････････････ 178.3.1 Loads ･･････････････････････････････････････････････････････････････ 178.3.2 Supports ････････････････････････････････････････････････････････････ 17

8.4 Results of Analysis･･････････････････････････････････････････････････････････ 18

9 Considerations of Hull Girder Stresses ･････････････････････････････････････････････ 199.1 General ･･･････････････････････････････････････････････････････････････････ 199.2 Stresses due to Hull Girder Moments････････････････････････････････････････････ 19

9.2.1 Stress due to Vertical Bending Moment ････････････････････････････････････ 199.2.2 Stress due to Horizontal Bending Moment･･････････････････････････････････ 19

9.3 Superimposition of Stresses ･･･････････････････････････････････････････････････ 20

10 Evaluation of Yielding Strength ･･････････････････････････････････････････････････ 2110.1 Reference Stresses ････････････････････････････････････････････････････････ 2110.2 Allowable Stresses ････････････････････････････････････････････････････････ 21

11 Evaluation of Buckling Strength･･････････････････････････････････････････････････ 2211.1 General ･････････････････････････････････････････････････････････････････ 2211.2 Reference Stresses ････････････････････････････････････････････････････････ 2211.3 Buckling Stress of Plate Panel ･･･････････････････････････････････････････････ 24

11.3.1 Elastic Buckling Stress Vectors ･･･････････････････････････････････････ 2411.3.2 Considerations for Influential Factors ･･････････････････････････････････ 2711.3.3 Buckling Stress････････････････････････････････････････････････････ 28

11.4 Buckling Stress of Cross-tie Structure ･････････････････････････････････････････ 2811.5 Buckling Strength Criteria ･･････････････････････････････････････････････････ 29

12 Evaluation of ultimate strength･･･････････････････････････････････････････････････ 3012.1 General ･････････････････････････････････････････････････････････････････ 3012.2 Reference Stress ･･････････････････････････････････････････････････････････ 3012.3 Ultimate Strength of Plate Panel ･････････････････････････････････････････････ 3012.4 Ultimate Strength Criteria ･･････････････････････････････････････････････････ 31


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Symbols

L : Scantling length of ship mB : Greatest moulded breadth of ship mD : Moulded depth of ship mdf : Design moulded draft of ship mdi : Draft amidships for the relevant loading condition mCb : Block coefficient corresponding to design moulded draft of ship -V : Design speed knotsg : Acceleration due to gravity (= 9.81) m/s2

ρC : Design maximum specific gravity of cargo t/m3

ρB : Specific gravity of sea water (= 1.025) t/m3

σY : Yield stress σY =235 for MS

σY =315 for HT32

σY =355 for HT36

N/mm2

K : Material coefficient corresponding to yielding strength of material -

E

K=1.0 for MS K=0.78 for HT32 K=0.72 for HT36: Young’s modulus of steel (= 206,000) N/mm2

υ : Poisson’s ratio (= 0.3) -


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Guidelines for Direct Strength Analysis

1 General1.1 Application

-1. The structural arrangement and scantlings of primary members in the cargo oil tank areas of tankersto which Chapter 29, Part C of the Rules are applied, can be determined by these Guidelines.

-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 plating and longitudinals prescribed for local loads(3) Requirements related to fatigue strength.

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

Loading Conditions(3)

Design Sea Conditions(4.2)

Design Regular Waves(4.3)

Design Loads(5)

Direct Load Analysis(6)

Structural Analysis(8)

Corrosion Deduction(7)

Superimposition with Hull Girder Stresses(9)

Evaluation ofYielding Strength

(10)

Evaluation ofBuckling Strength

(11)

Evaluation ofUltimate Strength

(12)

(Note: Numbers in parentheses indicate chapter numbers)

Fig. 1.1 Procedure for Evaluation


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1.3 Minimum Thickness-1. The thickness of structural members in cargo oil tanks and deep tanks such as bulkhead plating,

floors, girders including struts and their end brackets shall be greater than the values given in Table1.1 according to the length of ship.

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

Table 1.1 Minimum ThicknessGreater

than 90 105 120 135 150 180 195 225 275 325 375L(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 Members2.1 Applicable Members

The structural members whose structural arrangement and scantlings can be determined based theseguidelines are given in (1) to (8) below.

(1) Shell platings and longitudinal bulkhead platings constituting the double bottom and the doublesides (including the inner bottom platings and hopper platings)

(2) Floors and girders in the double bottom(3) Webs and stringers in double sides(4) Transverse rings in the bilge hopper tanks(5) Transverse rings and longitudinal girders in the cargo oil tanks and the ballast tanks(6) Transverse bulkhead platings (including corrugated bulkheads) and stools(7) Horizontal girders attached to transverse bulkheads(8) Cross-ties

3 Loading Conditions3.1 Loading Conditions

Loading conditions to be considered are the sea-going condition and the hydrostatic test condition.They are according to –1. and –2. below.

-1. Sea-going condition(1) From the planned loading conditions, select the loading conditions, which are expected to be

severe on the yielding and buckling strengths.(2) In principle, the full load condition and the ballast condition are taken as the loading conditions.

Loading conditions such as multiple port loading/unloading conditions considered to be severe onthe hull strength are also included.

(3) Tables 3.1, 3.2 and 3.3 show the standard examples of loading conditions to be considered.-2. Hydrostatic test condition

Table 3.1 to Table 3.3 show the standards for loading conditions in the hydrostatic test condition.


- 3 -

Table 3.1 Two Rows of Longitudinal Bulkheads Table 3.2 Three Rows of Longitudinal Bulkheads

Table 3.3 Four Rows of Longitudinal Bulkheads

Center tank Fore & aft tanksLoading pattern

Bal

last

con

ditio

nFu

ll lo

adin

g an

d sp

ecia

l loa

ding

con

ditio

nsH

ydro

stat

ic te

st c

ondi

tion

Case

T-1

F-1

F-2

F-3

B-1

B-2


Bal

last

con

ditio

nFu

ll lo

adin

g an

d sp

ecia

l loa

ding

con

ditio

nsH

ydro

stat

ic te

st c

ondi

tion

Case

T-1

F-1

F-2

F-3

B-1

B-2


Full

load

ing

and

spec

ial l

oadi

ng c

ondi

tions

Hyd

rost

atic

test

con

ditio

n

Case

T-1

F-1

F-2

F-3

F-4

F-5


Bal

last

con

ditio

nFu

ll lo

adin

g an

d sp

ecia

l lo

adin

g co

nditi

ons

Case

F-6

F-7

B-1

B-2

B-3


- 4 -

4 Design Conditions

Symbols

T01(j) : Mean wave period corresponding to each design sea condition sec.Hmax(j) : Maximum wave height corresponding to each design sea condition mλj : Wave length of design regular wave corresponding to each design sea condition m

χj : Wave encountering angle corresponding to each design sea condition or eachdesign regular wave deg.

Hj : Wave height of design regular wave corresponding to each design sea condition mj : Subscript indicating each design condition, stand 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 ships is planned for service in smooth water areaor 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 Conditions4.2.1 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 above.

-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 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


- 5 -

4.2.2 Setting the Design Sea ConditionsThe design sea conditions are set according to Table 4.1.

Table 4.1 Design Sea Conditions

Designcondition

Waveencountering

angle χj (deg.)Mean wave period T01(j) (s) Maximum wave height Hmax(j) (m)

L-180 180Head sea

L-0 0Following sea

R 90Beam sea

P 90Beam sea

gT j

j

πλ285.0)(01 =

j : Stands for L-180, L-0,R and P

)(3/13)max( jj HCH ⋅=

C3 : 1.9

)(3/1 jH : Significant wave height,calculated as below

)(21)(3/1 jj CCH ⋅= (m)

1C5.1

10030075.10

−

−=L

L ≤ 300m

75.10= for 300m<L ≤ 350m5.1

15035075.10

−

−=L

for 350m<L

LL

C jj

25)(2

−+=

λ

4.3 Design Regular Waves4.3.1 General

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

-2. Nonlinear effects in large waves and 3D effects are considered when setting the design regularwaves.

-3. To perform practical strength evaluation within the elastic range, the design wave height iscorrected to a level corresponding to elastic design. This level is taken as the level at whichadequate strength can be ensured against the maximum load considering residual strength untilultimate strength.


- 6 -

4.3.2 Setting the Design Regular WavesDesign regular waves are set corresponding to each design sea condition, according to Table 4.2.

Table 4.2 Design Regular Waves

Regular wave height Hj (m)Design

conditions

Encounteringangle

χj (deg.)Wave length λj (m)

4C 5C 6C

L-180 180 Ldd

f

iL

+=− 16.0180λ

L-0 0 Ldd.

f

iL

+=− 3

21600λ

0.65 0.9

R 90 2

2 RR Tgπ

λ = 0.42 0.8

P 90 Ldd

f

iP

+= 4.02.0λ

)max(654 jj HCCCH ⋅⋅⋅=

4C : Correction coefficientfor regular waveheight

5C : Correction coefficientfor nonlinear and 3Deffects

6C : Correction coefficientfor elastic design

0.70 0.7

0.67

NOTE:

GMK

CT xxR

2= (s)

C = 1.15Kxx : Roll radius of gyration (m); given as below according to the loading condition

Kxx = 0.35B for full loading condition= 0.40B for ballast condition and segregation 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

dd

dd

BKM 17242.0

6.0138.02.054.0 +

−+

+=

f

i

f

i

dd

dd

DKG

The draught is corrected as shown below for the segregation loading condition.

2fP

idd

d+

= (m)

pd : Draught amidships in the segregation loading condition (m)


- 7 -

5 Design Loads

Symbols

Kxx : Roll radius of gyration; defined in 4.3 mGM : Metacentric height, defined in 4.3 mTR : Natural period of roll motion sec.TP : 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

apitch : 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 tank m/s2

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

PC : Internal dynamic pressure in cargo tank caused by ship motions andaccelerations

kN/m2

PB : Internal dynamic pressure in ballast tank caused by ship motions andaccelerations

kN/m2

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

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

PR : 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 liquid cargo and ballast are considered as loads in stillwater. External hydrodynamic pressure and internal dynamic pressure due to liquid cargo andballast 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 described inthis chapter. The detail 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.


- 8 -

5.2 Ship Motions and Accelerations5.2.1 Ship Motions

Table 5.1 gives the natural period of pitch motion Tp, the pitch angle θ, the natural period of roll motionTR, and the roll angle φ.

Table 5.1 Ship Motions

Natural period (s) Angle (rad.)

Pitchg

T LP

1802 −=πλ

( )1802.1

2.053−

+= L

b

HCL

Vθ

HL-180 : Regular wave height corresponding to the designcondition L-180 (m)

Roll GMK

CT xxR

2=

C = 1.15

RR

HBT

4=φ

HR : Regular wave height corresponding to the designcondition R (m)

5.2.2 Acceleration of the Center of Gravity of the ShipTable 5.2 gives the acceleration of the center of gravity of the ship due to pitch motion apitch, roll motion

aroll and heave motion aheave.

Table 5.2 Acceleration of the Center of Gravity of Ship

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

22

=

Ppitch T

a πθ (rad./s2)

Acceleration of the center of gravityof the ship due to roll motion

22

=

Rroll T

a πφ (rad./s2)

Acceleration of the center of gravityof the ship due to heave motion

( )

( ) Pb

heave HCLB

Vga 6.0

2.053⋅

+= (m/s2)

HP : Regular wave height corresponding to the designcondition P (m)


- 9 -

5.2.3 Acceleration of the Center of Gravity of the TankThe vertical acceleration av and the transverse acceleration at of the center of gravity of the tank are

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

Table 5.3 Acceleration of Center of Gravity of Tank

Designcondition

Acceleration of the center of gravityof the tank (m/s2)

(Wave crest in head sea and weatherside down in beam sea)

Acceleration of the center of gravityof the tank (m/s2)

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

Remarks

0=ta ta− －L-180

va− pitchgiheavefiv axxadda −+= )/( positive upward

0=ta ta− －L-0

0=va va− －

φgat = ta− positive lee sideR

rolliheavev aya)/L(a += 40 va− positive upward

φg.at 50= ta− positive lee sideP

rolliheavev ay.aa 50+= va− positive upward

NOTE:xg : Longitudinal distance from AP to the center of rotation of pitch motion (= 0.45L) (m)xi : Longitudinal distance from AP to the considered center of gravity of the tank (m)yi : Transverse horizontal distance from the centerline of the hull to the considered center of gravity of

the 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

Weather side Lee side

Weather side down Weather side up


Fig. 5.1 Difinition of Weather Side Down and Weather Side Up

FPAP

Pi

yi<0

Weather side

Piat>0

xg(=0.45L)xi

av>0Lee side

Fig. 5.2 Definition of Coordinates for Calculating Accelerations of the Center of Gravity of the Tank

CL


- 10 -

5.3 Pressure Acting on the Hull5.3.1 Sea Water Pressure

-1. Hydrostatic pressure(1) The pressure corresponding to the draught in still water is considered as the hydrostatic pressure

for each loading condition.(2) The hydrostatic pressure in the hydrostatic test condition is taken as equivalent to the hydrostatic

pressure at 1/3 of the designed full load draught.

-2. Hydrodynamic pressure(1) Hydrodynamic pressure corresponding to design conditions L-180 and L-0

The dynamic pressure (kN/m2) shown in Fig. 5.3 and the following equations are considered asthe hydrodynamic pressure PL corresponding to the design conditions L-180 and L-0.

Li

L HBy

dzC.P

++±= 1

232 7

C7 : Distribution coefficient in the longitudinal direction of the ship; according to theequation given below.

7C3'4

361

−+=

Lx

B

y

Cbfor design condition L-180 (forward part of ship)

3'21121

−+=

Lx

B

y

Cbfor design condition L-180 (aft part of ship)

1= for design condition L-0di : 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.= di

HL : Wave height of regular wave corresponding to the design conditions L-180 and L-0,in meter; HL-180 may be taken as the typical wave height of regular wavecorresponding to L-180 and L-0.

6.9 H 6.9 H

4.6 H 4.6 H2.3 H

Fig. 5.3 Hydrodynamic Pressure Distribution at the Midship Section (In Case of Wave Crest)CL


- 11 -

(2) Hydrodynamic pressure corresponding to the design condition RThe dynamic pressure (kN/m2) shown in Fig. 5.4 and the following equations are considered asthe hydrodynamic pressure PR corresponding to the design condition R.

++±= RR H

By

.sinyP 12

1010 φ

y : Transverse horizontal distance from the centerline of the ship to the considered pointin the considered section (m); weather side is taken as positive.

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

H

-10(B/2)sinφ+2H

φ


10(B/2)sinφ+2H

Fig. 5.4 Hydrodynamic Pressure Distribution at the Midship Section(In case of Weather Side Downward)

(3) Hydrodynamic pressure corresponding to the design condition PThe dynamic pressure (kN/m2) shown in Fig. 5.5 and the following equations are considered asthe hydrodynamic pressure PP corresponding to the design condition P.

Pi

PW HBy

dzP

+±=

2323 for weather side

3PW

PLP

P = for lee side

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

z : Vertical distance from the bottom of the ship to the considered point in the consideredsection (m); zmax.= di

5H


15H

3H9H

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

CL


- 12 -

(4) Correction to hydrodynamic pressure(a) 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, thehydrodynamic pressure acting on the cross section located at the longitudinal center ofconsidered hold is used.

(b) When the hydrodynamic pressure at the waterline is positive, the hydrodynamic pressure isconverted 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. 5.6)

(c) When the hydrodynamic pressure at the waterline is negative, the combined pressure of thehydrodynamic and hydrostatic pressure is not taken as a negative value for the hydrodynamicpressure below the waterline. (See Fig. 5.6)

(d) In sea areas where the effect of waves is small such as in harbours, the hydrodynamicpressure may be reduced to 1/3 of its original value.

(e) The hydrodynamic pressure may not be considered in the hydrostatic test condition.

Weather side

45°

P

P/(ρBg)

Hydrostaticpressure

ρBgdi

P

d i

Weather sideHydrodynamic

pressure

When hydrodynamic pressure is positive When hydrodynamic pressure is negative

Fig. 5.6 Correction to Hydrodynamic Pressure

CL CL


- 13 -

5.3.2 Pressure due to Liquid Cargo and Ballast-1. Static pressure due to liquid cargo and ballast

(1) The pressure due to liquid cargo and ballast in still water (kN/m2) is considered as the staticpressure.

(2) The pressure in the hydrostatic test condition is the hydrostatic pressure (kN/m2) equivalent to thewater head of the vertical distance from each position to a point 2.45m above the deck at theship’s side.

(3) If a venting system has been provided for the protection of cargo oil tanks, vapour pressure(kN/m2) equivalent to the setting pressure of the venting system is considered.

-2. Internal dynamic pressures due to liquid cargo and ballast(1) Internal dynamic pressures due to liquid cargo and ballast

The internal dynamic pressures due to liquid cargo PC and due to ballast PB are shown in Table5.4 for each design condition.

(2) Correction to internal dynamic pressures due to liquid cargo and ballast(a) In sea areas where the effects of waves is small such as in harbours, the internal dynamic

pressures due to liquid cargo and ballast may be reduced to 1/3 of their original value.(b) The internal dynamic pressure due to ballast may not be considered in the hydrostatic test

condition.


- 14 -

Table 5.4 Internal Dynamic Pressures due to Liquid Cargo and Ballast

Internal dynamic pressure (kN/m2)Designcondition Liquid cargo Ballast Remarks

L-180 CvCC zaP ρ= BvBB zaP ρ=

L-0 0=CP 0=BP＋: positive pressure－: negative pressure

R

P( )CtCvCC yazaP += ρ ( )BtBvBB yazaP += 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 fromthe 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. 5.7.)

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

zC

yC> 0

Weather side

Tankcenter

Lee side

zC

yC< 0


Tankcenter

Fig. 5.7 Definition of yC and zC

yB : 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 isupward (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 atthe most lee side; see Fig. 5.8.)(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 atthe most weather side; see Fig. 5.8.)

zB : Vertical distance measured from the middle point of the overflow pipe on the top of tank tothe considered point (m).

yB < 0

yB < 0yB > 0

zB

zB


zB

yB > 0yB < 0

zB

yB > 0

zB


Fig. 5.8 Definition of yB and zB

CL

CL CL

CL


- 15 -

6 Direct Load Analysis6.1 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 Section 6.2.-3. In addition to the standard method given in Section 6.2, the design loads may also be set using a

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

6.2 Setting Method for Design Loads-1. Direct load analysis is performed using the strip method under design regular wave conditions given

in 4.3 for setting the design loads. The internal dynamic pressures due to the liquid cargo andballast and the hydrodynamic 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 loadanalysis by the strip method in the design regular wave conditions given in Section 4.3. In thiscase, the wave length of design regular waves is taken as the wave length when the response of thedominant load given in Section 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 Section 5.3.1-2(4)(b) and (c).

-4. For details of direct load analysis, the “Technical Guide Regarding the Strength Evaluation ofHull Structures (Dec. 1999)” could be referred to.

Table 6.1 Time to be Considered in Design Regular Wave Conditions

Designconditions Time to be considered

L-180

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• Time when the hydrodynamic pressure at the bottom centerline of the cross section

located at the middle of the investigated hold becomes maximum• Time when the hydrodynamic pressure at the bottom centerline of the cross section

located at the middle of the investigated hold becomes minimum

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


- 16 -

7 Considerations for Corrosion7.1 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 strengthcalculations 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 DeductionFig 7.1 shows the values of corrosion deduction for various structural members.

Fig. 7.1 Corrosion Deduction

CL


- 17 -

8 Structural Analysis8.1 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 maybe required to be submitted to the Society.

8.2 Analysis Model8.2.1 Extent of the Modeling

-1. The extent of analysis is decided such that the actual stress conditions of the ship can be reproducedby 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 inclusive of thetotal height and total width of the hold. (See Fig. 8.1 and Fig. 8.2).

8.2.2 Members ConsideredThe 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 bulkheadstiffeners should also be included in the model.

8.2.3 Mesh SizeThe 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 and Fig. 8.2).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 Conditions8.3.1 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 end in the length direction applying symmetry

conditions.


- 18 -

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 Three-tank Type Tanker

Fig. 8.2 Example of Structural Model of Two-tank Type Tanker

3Y11

of

3Y11

3Y11


- 19 -

9 Considerations of Hull Girder Stresses

Symbols

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

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

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

σG : Sum of the stresses σS , σWV and σWH 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 length

direction of the ship obtained from structural analysis for the longitudinal members.-2. Firstly, the maximum hull girder moment is converted to stress using beam theory. Next, the hull

girder stress is determined by multiplying this stress by the stress superimposition ratio set for eachdesign condition.

9.2 Stresses due to Hull Girder Moments9.2.1 Stress due to Vertical Bending Moment

The stress due to still water vertical bending moment σS and the stress due to wave-induced verticalbending moment σWV are calculated as given below.

510×⋅= VV

SS f

IM

σ (N/mm2)

510×⋅= VV

WVWV f

IM

σ (N/mm2)

MS : Still water vertical bending moment corresponding to each loading condition; taken as themean value of the two bulkhead positions located on both sides of the evaluation position(kN-m).

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

IV : Moment of inertia of cross section about the horizontal neutral axis of the transversesection of the hull to be evaluated (cm4)

fV : 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×⋅= HH

WHWH f

IMσ (N/mm2)

MWH : Wave-induced horizontal bending moment at the considered section (kN-m), which iscalculated by the equation given below.

LLdLCCM iWH

3532.0 281

−=

C1 : According to Table 4.1C8 : 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.


- 20 -

C8 = 0 at AP= 1.0 between 0.35L and 0.65L= 0 at FP

IH : Moment of inertia of the cross section about the vertical neutral axis of the transverse sectionof the hull to be evaluate (cm4)

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

9.3 Superimposition of StressesThe hull girder stress σG determined by the equation below is superimposed on the stress in the length

direction of the ship obtained from structural analysis.( ( ) )WHWVSG CCCC σσσ ⋅+⋅⋅+⋅= 111069 σ (N/mm2)

C9 : Correction coefficient considering stress increment due to corrosion; taken as 1.1C6 : Correction coefficient for elastic design; taken as 0.67C10 : Superimposition ratio of wave-induced vertical bending stress σWV ; according to Table 9.1.C11 : Superimposition ratio of horizontal bending stress σWH ; according to Table 9.1.

Table 9.1 Superimposition Ratio of Wave-induced Hull Girder Stresses

Design conditions C10 C11

Wave crest Hog.L-180

Wave trough1.0

Sag.－－

Wave crest Hog.L-0

Wave trough1.0

Sag.－－

Weather side isdownward

Weather side(compression)R Weather side

is upward

－－f

i

dd. −21

Weather side(tension)

Weather side isdownward Sag.

P Weather sideis upward

40.dd

f

i −Hog.

－－


- 21 -

10 Evaluation of Yielding Strength10.1 Reference Stresses

-1. The equivalent stress and axial stress are used as reference stresses for the evaluation of yieldingstrength. The equivalent stress σeq is used for shell elements and membrane elements, while theaxial stress σa is used for rod elements.

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

212

2221

21 3τσσσσσ ++⋅−=eq

σ1, σ2 : In-plane normal stresses (N/mm2); hull girder stress determined in Chapter 9 issuperimposed on the normal stress in longitudinal members in the length directionof the ship

12τ : Shear stress corresponding to σ1, σ2 (N/mm2)

-3. The stress at the center of the element is used as the reference stress for shell elements andmembrane 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 StressThe reference stresses determined in Section 10.1 should not exceed the allowable stresses specified in

Table 10.1.

Table 10.1 Allowable Stresses

σeq and σa (N/mm2)Members

Sea-going condition Hydrostatic test condition

All members to be evaluated 195/K 215/K


- 22 -

11 Evaluation of Buckling Strength

Symbols

a : Length of longer side of plate panel mmb : Length of shorter side of plate panel mmα : Aspect ratio of plate panel (α = a/b) -t : Thickness of plate panel mmσref : Reference stress N/mm2

σecr : Equivalent elastic buckling stress N/mm2

σpcr : Equivalent plastic buckling stress N/mm2

11.1 General-1. Corrosion deduction specified in Fig.7.1 is deducted from the thickness of the plate panel for the

evaluation of buckling strength.-2. Buckling strength may be evaluated by a different method if approved by the Society as

appropriate.

11.2 Reference Stresses-1. Plate panel The reference stress σref 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 elementsin the element coordinate system shown in Fig.11.1 and is obtained by the equation given below. Incase of longitudinal members with one of the element coordinate axes in the length direction of the ship,the hull girder stress determined in 9 above is considered.

222 3)43()

43(

21 τσσσσσσσ ++++−= byybyyxxref (N/mm2)

Fig. 11.1 Four In-plane Stress Components

σx : Compressive stress in x directionσy : Compressive stress in y directionσb : In-plane bending stress in y directionτ : Shear stress

(Unit: N/mm2)τ

σy

σby

σx

x

y

τ


- 23 -

-2. Cross-tie structure The reference stress σref for evaluation of buckling strength of the cross-tie structure is taken as themean axial compressive stress σa at the center of the cross-tie span shown in Fig. 11.2.

aref σσ = (N/mm2)

l : Span of cross-tie

Fig. 11.2 Reference Stress in Cross-tie Structure

σa (N/mm2)

Trans. web Trans. web


- 24 -

11.3 Buckling Stress of Plate Panel11.3.1 Elastic Buckling Stress Vectors

The elastic buckling stress vectors (σxB, σyB, τB, σbyB) are determined using the elastic buckling interactionformula given in Table 11.1.

Table 11.1 Elastic Buckling Interaction Equations

)101(1321 ≤≤=++ α　gzkykxk (1))102(17.1

64.1

52.1

4 ≤≤=++ α　zkykxk (2)g

21 ≤≤ α 8120 .. +α42 ≤≤ α 0160 .. +α104 ≤≤ α 0310 .. +α

xcrx

xBxσγ

σ= ,

ycry

yByσγ

σ= ,

crs

Bzτγ

τ= ,

bycr

byBbyσσ

=

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

stress vector.2. The buckling stress components (σxcr, σycr, τcr, σbycr) under uni-axial stress field is given in

Table 11.2.3. The reduction factors due to in-plane bending stress (k1 to k6) are given in Table 11.3.4. The reduction factors due to opening (γx, γy, γs) are given in Table 11.4.

Table 11.2 Buckling Stress under One Single Stress ComponentStress components Buckling stress σcr Buckling coefficient K

Exxcr K σσ =2

+=

mmK x

αα

Eyycr K σσ =2

211

+=

αyK

Escr K στ = 2434.5

α+=sK

Ebybycr K σσ =426.887.1587.1

αα++=byK

9.23=

whichever is smaller

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

panel that satisfies )1()1( +≤≤− mmmm α .

2. σe is taken as 2

2

2

)1(12

− btE

νπ


- 25 -

Table 11.3 Reduction Factors due to In-plane Bending Stressα 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 .. +− α552 ≤≤ 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

byebyebyek

−++

=1

)()( 322

11

106 ≤≤ α 200150 .. +− α

α e1 α e2

31 ≤≤ α 940140 .. +− α 61 ≤≤ α 850050 .. +− α63 ≤≤ α 7400730 .. +− α 106 ≤≤ α 562001250 .. +− α)1}(1)({

12

12 bybye

k e −+=

106 ≤≤ α 4500250 .. +− α

α e1

41 ≤≤ α 680170 .. +− αby

)by(ek−

−=

11 1

3

104 ≤≤ α 00.

α e1 α e2

522 .≤≤ α 0550030 .. +α 32 ≤≤ α 50 .

352 ≤≤ α. 520260 .. −α 63 ≤≤ α 2010 .. +α43 ≤≤ α 160140 .. −α 106 ≤≤ α 50050 .. +α

)1}(1)({1

21

4 bybyek e −+

=

104 ≤≤ α α10.

α e1 α e2

522 .≤≤ α 360. 322 .≤≤ α 530060 .. +α352 ≤≤ α. 241640 .. −α 5232 .. ≤≤ α 8750090 .. +− α

43 ≤≤ α 440080 .. +α 352 ≤≤ α. 15120 .. +− α54 ≤≤ α 720010 .. +α 43 ≤≤ α 790080 .. +− α

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

byebye

k−

+=

1)( 21

5

106 ≤≤ α 4800050 .. +− α

α e1

32 ≤≤ α 440040 .. +α63 ≤≤ α 410050 .. +αby

byek

−−

=1

)(1 16

106 ≤≤ α 590020 .. +α


- 26 -

Table 11.4 Reduction Factors due to Opening Circular opening Elliptical opening Slot

2)(1

1,,,,1

1

000f

syxsyx

bdf+

== γγγγγγ 2)(1

1,,,,2

1

000f

syxsyx

bdf+

== γγγγγγssysxssyx ,,,, γγγγγγ =

γx0 (γx0<0.8,γx0=0.8) γx0 (γx0<0.8,γx0=0.8)f1 f2 f1 f2

0.7 1.0

0.7 1.0160 +−=

bh

. sxsγ

γy0 γy0

f1 f2 f1 f2

21 ≤≤ α 1-0.3α 21 ≤≤ α 0.9-0.2α

2≥α 0.41.0

2≥α 0.5 1.0

130 +−=bh

. sysγ

γs0 γs0

f1 f2 f1 f2

551 .≤≤α 58752250 2

...

+− αα 1.8 551 .≤≤α )5.8

75.225.0(6.1 2

+− αα 1.8

55.≥α 93750. 1.8

55.≥α 51. 1.8

1)(7

15.1 +

=

bhs

ssγ

Circular or elliptical opening with slot

xsxx . γγγ 021=(

0xx γγ ≥ , 0xx γγ = )

ysyy γγγ 0=

ssss γγγ 02=

( 0ss γγ ≥ , 0ss γγ = )

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

　　　　　Circular opening 　　Elliptical openingHere, d1 is the diameter of circular opening (mm), d2 is the smaller diameter of elliptical opening(mm) and hs is the length of the slot (mm).2. If there are two slots in the direction of the longer side of the panel, only ysγ is replaced by

　 16.0 +−=bhs

ysγ

3. If the slot is reinforced by a collar plate, then the following may be assumed: 01.,, ssysxs =γγγ

a

b d1

hs

d2


- 27 -

11.3.2 Considerations for Influential Factors-1. General

The effects of stiffener and water pressure may be considered as influential factors that affect thebuckling 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

yyκ

=′

y : Buckling stress ratio shown in Table 11.1κy : 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, the meanvalue of the influential factors of the stiffeners is taken.

13

+

=

tt

c wyκ 01.ttw < , if 01.ttw ≥ then 01.ttw =

c : Coefficient given in Table 11.5 according to the type of the stiffenertw : Thickness of web plating of stiffener (mm)

Table 11.5 Coefficient c

Type of stiffener c21 ≤≤ α 1030 .. +α72 ≤≤ α 980140 .. +− αAngle stiffener107 ≤≤ α 00.21 ≤≤ α 10350 .. −α32 ≤≤ α 60.63 ≤≤ α 11330 +− α.

T-shaped stiffener,girder

106 ≤≤ α 50050 .. +− α61 ≤≤ α 120020 .. +− αFlat bar, bulb plate 106 ≤≤ α 00.

-3. Effects of water pressureThe 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.

xqxx =′ ,

yqyy =′

x, y : Buckling stress ratios shown in Table 11.1qx, qy : Influential factors of water pressure in x and y direction shown in Fig.11.1

respectively given by the following equations. qx, and qy are applied for plate panelsof thickness greater than 13mm and aspect ratio greater than 2.

5761

6.1

4

4

+=Etqb

qx , 95.0

75.1

4

4

1601

+=

ba

Etqb

q y

q : Load due to water pressure acting on the plate panel (N/mm2) taken asthe difference between internal and external pressures.


- 28 -

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

22

2 343

43

21

BbyByBbyByBxBxBecr τσσσσσσσ +

++

+−= (N/mm2)

-2. Equivalent plastic buckling stress If the value of the equivalent elastic buckling stress σecr is greater than half the value of the yield stressσY, the equivalent plastic buckling stress σpcr is determined from the equation below.

−=

ecr

YYpcr σ

σσσ

41 (N/mm2)

11.4 Buckling Stress of Cross-tie Structure-1. Elastic buckling stress

The elastic buckling stress σecr of the cross-tie structure is determined from the equation below.

42

2 10−×

=l

rEecr πσ (N/mm2)

Here, l : Span length of the cross-tie (m); according to Fig. 11.2.

r : Radius of gyration AIr = (cm)

A : Cross section area of the cross-tie (cm2)I : Minimum value of moment of inertia of the cross-tie (cm4)

-2. Plastic buckling stressIf the value of the elastic buckling stress σecr is greater than half the value of the yield stress σY, the

plastic buckling stress σpcr is determined from the equation below.

−=

ecr

YYpcr σ

σσσ

41 (N/mm2)


- 29 -

11.5 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, λis the buckling criterion given in Table 11.6.(1) When the value of the equivalent elastic buckling stress σecr is greater than half the value of the

yield stress σY.

λσσ

≥ref

pcr

(2) When the value of the equivalent elastic buckling stress σecr is less than half the value of the yieldstress σY.

λσσ

≥ref

ecr

Table 11.6 Buckling Strength Criteria of Plate Panel

Buckling criterion λMembers Sea-going

conditionHydrostatic

test condition

All members to be evaluated 1.1 1.0

-2. Cross-tie structure The results obtained in 11.2-2 and 11.4 above are necessary to satisfy the conditions below. Here, λ isthe buckling criterion given in Table 11.7.(1) When the value of the elastic buckling stress σecr is greater than half the value of the yield stress σY.

λσσ

≥ref

pcr

(2) When the value of the elastic buckling stress ecrσ is less than half the value of the yield stress σY.

λσσ

≥ref

ecr

Table 11.7 Buckling Strength Criteria of Cross-tie Structure

Buckling criterion λMembers Sea-going

conditionHydrostatic

test condition

Cross-tie 1.8 1.6


- 30 -

12 Evaluation of Ultimate Strength

Symbols

a : Length of longer side of plate panel mmb : Length of shorter side of plate panel mmα : Aspect ratio of plate panel (α = a/b) -t : Thickness of plate panel mmβ : Slenderness ratio of plate panel ( Etb Y /)/( σβ ×= ) -

σref : Reference stress N/mm2

σus : 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 is deducted from the thickness of the plate panel for theevaluation of ultimate strength.

-3. Ultimate strength may be evaluated by a different method regardless of the requirements of thissection, if the method is approved by the Society as appropriate.

12.2 Reference Stress-1. The reference stress σref for the evaluation of ultimate strength is taken as the representative

equivalent stress given in the following equation. In case of longitudinal members with one of theelement coordinate axes in the length direction of the ship, the hull girder stress determined inChapter 9 is considered.

22yxref σσσ += (N/mm2)

Here, σx and σy 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 σxU and σyU 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 ≤≤ βx)(y1 ≥= 　　yx)(y1 ≤= 　　x

31 ≤≤ β 1=+ δδ yx , 1

4−

=β

δ

β≤3 122 =+ yx

xus

xUxσσ

= , yus

yUyσσ

=

NOTE: The ultimate strength σxus and σyus under uni-axial stress field are given in Table 12.2.


- 31 -

Table 12.2 Ultimate Strength under One Single Stress Component

Stress component Ultimate strength σ xus , σ yus

225.125.2

ββσσ

−=Y

xus , 0.1≥β

0.1=Y

xus

σσ

, 0.1≤β

−=

ab

Y

yus2

25.125.2ββσ

σ

−

−+

−+

ab1

)2.0(6.0

)2(06.08.0 2ββ

-2. Ultimate strength for strength evaluation The ultimate strength σus for the strength evaluation is determined from the following equation usingthe ultimate strength under bi-axial compression in item -1.

22yUxUus σσσ += (N/mm2)

12.4 Ultimate Strength CriteriaThe ultimate strength criterion λ is satisfied using the result obtained from Sections 12.2 and 12.3 as

follows, and based on Table 12.3σσ

λus

ref

≥

Table 12.3 Ultimate Strength Criteria

Ultimate strength criterion λMembers

Sea-going condition Hydrostatic testcondition

Members that mainly become the bi-axialcompressive stress field such as the bottom shell

platings and the inner bottom platings1.2 1.1

Documents

NKK-Guidelines for Direct Strength Analysis