Guidelines-no.19 Guidelines for Fatigue Strength of Ship Structure%2c 2007

8/12/2019 Guidelines-no.19 Guidelines for Fatigue Strength of Ship Structure%2c 2007

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GUIDANCE NOTES

GD 11-2007

CHINA CLASSIFICATION SOCIETY

GUIDELINES FOR FATIGUE

STRENGTH OF SHIP STRUCTURE

2007

BeiJing


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CONTENTS

CHAPTER 1 GENERAL...................................................................................................................1

1.1 Introduction.....................................................................................................................................1

1.2 Application......................................................................................................................................1

1.3 Denitions.......................................................................................................................................1

1.4 Fatigue analysis method..................................................................................................................2

1.5 Hull structural details......................................................................................................................3

CHAPTER 2 FATIGUE ANALYSIS.................................................................................................5

2.1 Locations for fatigue check.............................................................................................................5

2.2 Selection of design S-N curves.......................................................................................................5

2.3 Weibull distribution of stress ranges in hull structures.................................................................10

2.4 Allowable stress ranges.................................................................................................................10

2.5 Calculation of cumulative damage................................................................................................13

CHAPTER 3 FATIGUE LOAD.......................................................................................................15

3.1 General requirements....................................................................................................................15

3.2 Wave bending moment and torsional moment..............................................................................15

3.3 Sea water dynamic pressure...........................................................................................................17

3.4 Ship motions and accelerations.....................................................................................................21

3.5 Cargo pressure in holds.................................................................................................................23

CHAPTER 4 CALCULATION OF NOMINAL STRESS RANGES...........................................26

4.1 General requirements....................................................................................................................26

4.2 Simplied calculations of stress ranges........................................................................................26

4.3 Combined global stress ranges......................................................................................................31

4.4 Nominal stress range calculations.................................................................................................33

4.5 Direct calculations of local nominal stress ranges........................................................................33

CHAPTER 5 CALCULATION OF HOT SPOT STRESS............................................................37

5.1 Hot spot stress assessment method................................................................................................375.2 Stress concentration factors of typical detail.................................................................................37

5.3 Calculation method of stress concentration factors.......................................................................39

5.4 Direct calculation of hot spot stress..............................................................................................39

Appendix 1 GAMMA FUNCTION TABLES................................................................................43

Appendix 2 EXAMPLE CALCULATION FOR STRUCTURE FATIGUE STRENGTH.......52

Appendix 3 HULL STRUCTURAL DETAILS..............................................................................57


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CHAPTER 1 GENERAL

1.1 Introduction

1.1.1 When ships navigate at sea, the ship structures are always affected by wave forces and inertial

forces resulted from ships movements. Because both wave forces and inertial forces are continuously

variable dynamic loads, they produce alternating stresses in the interior of ship structure, rendering

fatigue damages on ship structure.

1.1.2 Fatigue damages are one of the main damages to the ship structures. Especially for large ships

and those of high tensile steel the fatigue problems are outstanding.

1.1.3 The design of structural details may be improved by the fatigue strength check as to ensure

members bearing alternating dynamic loads in hull structure to have sufcient fatigue life.

1.1.4 The class notation COMPASS(F) may be assigned to classed ships complying with the

assessment requirements of the Guidelines.

1.2 Application

1.2.1 For the following ships the fatigue strength of structures in cargo hold areas is to be checked

in accordance with the requirements of the Guidelines:

(1) bulk carriers of 150 m and over in length, including ore carriers;

(2) container ships of 150 m and over in length;

(3) oil tankers of 190 m and over in length.

1.2.2 The fatigue strength assessment for oil tankers with CSR class notation is to be carried out in

accordance with relevant provisions of PART NINE of Rules for Classication of Sea-Going Steel Ships.

1.2.3 The fatigue strength assessment for bulk carriers with CSR class notation is to be carried out in

accordance with relevant provisions of PART TEN of Rules for Classication of Sea-Going Steel Ships.

1.2.4 For ships other than those specied in 1.2.1 above the fatigue strength of the structures may

be checked in accordance with the Guidelines.

1.2.5 For ships carrying out fatigue strength check in accordance with the requirements of the

Guidelines, their structural design, construction workmanship and quality are to comply with the

requirements of CCS Rules for Classication of Sea-Going Steel Ships and other relevant standards

accepted by CCS.

1.3 Denitions

1.3.1 The denitions in the Guidelines are as follows:

(1) Length of ship L(m) is the distance on the summer load waterline from the forward side ofthe stem to the after side of the rudder post, or to the centre of the rudder stock if there is no rudder

post, but it is to be not less than 96%, and need not be greater than 97%, of the extreme length on the

summer load waterline.

(2) Breadth of ship B(m) is the horizontal distance measured over the main frames at the widest

part of the ship.

(3) Moulded depth of ship D (m) is the vertical distance measured at the middle of the length

L from top of keel to top of the deck beam at side on the uppermost continuous deck. When a

rounded gunwale is arranged, the moulded depth is to be measured to the point of intersection of the

continuation of the moulded deck line and side shell plating.


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(4) Draught d(m) is the vertical distance measured at the middle of the lengthLfrom top of plate

keel to the summer load waterline.

(5) Draught d1

(m) is the vertical distance measured at the middle of the lengthLfrom top of plate

keel to the waterline under calculated condition.

(6) Block coefcient Cbis to be determined by the following formula:

CLBd

b =

where: moulded displacement in m3at draught corresponding to summer load waterline; Llength of ship, in m;

Bbreadth of ship, in m;

d draught, in m.

(7) Large openings: deck openings complying with any of the following conditions are large

opening:

b

B10.7

l

l

H

BH

0.89

1B

b0.6and

l

l

H

BH0.7

where: b width of opening, in m; where several hatches are in parallel, b is the total breadth of

the hatches;

B1 maximum deck width, including openings, in m, at the middle of the opening length;

lH

length of hatch, in m;

lBHdistance, in m, between the centreline of transverse deck strips at the hatch ends;

where no other hatch forward or after the hatch, lBH

is measured to the bulkhead.

(8) Stress range S(N/mm2): stress range resulted from alternating stress of structure fatigue is to be

determined by the following formula:

S= maxmin

where: max

maximum value of stress circulation, in N/mm2;

min

minimum value of stress circulation, in N/mm2.

(9) Design stressis the calculated stress for fatigue assessment. It may either be nominal stress or

hot spot stress.

1.4 Fatigue analysis method

1.4.1 Fatigue analysis of ship structure may be carried out by means of simplified and direct

calculations.


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1.4.2 The simplied and direct calculation methods are mainly composed of the following:

(1) fatigue load calculations;

(2) calculation of stress range components;

(3) determination of stress concentration factor;

(4) combination of stress ranges;

(5) calculations and criteria for cumulative damage.

1.4.3 Fatigue load corresponding to transcendental probability level is taken as 10-4

and corresponding

ship design service life is 20 years.

1.4.4 The total cycles of stress range circulation within the ship design service life is 0.6108.

1.4.5 Long-term distribution of stress range may be represented by a 2-parameter Weibull

probability distribution.

1.4.6 S-Ncurves are the basic S-Ncurves for non-tubular joints consisting of eight curves, as

amended by U.K. Department of Energy. Such curves are applicable to steel material of minimum

yield stress less than 400 N/mm2

.1.4.7 Calculations of cumulative damages are based upon Palmgren-Miner linear cumulative

damage theory. Cumulative damageDis to be obtained by the following formula:

( )( )

D Nf S

N SdST=

0

where: NTstress total circulation cycles for structure in its design service life;

Sstress ranges;

f(S)probability density factor of long-term distribution of stress range;

N(S)number of cycles when failure of structure fatigue corresponding to stress range S.

1.4.8 When fatigue analyses are to be carried out, the full load and ballast conditions are to be taken

into account.

1.4.9 When calculating design stress ranges, corrosion effect is to be considered, i.e. as-built

structure scantlings are to deduct the relevant corrosion allowance. Because fatigue is a cumulative

process throughout the ship service life, the corrosion allowance used in fatigue analysis may take a

half of that in ship design service life.

1.5 Hull structural details

1.5.1 Denitions

(1) Critical areas are defined as locations where, by reason of stress concentration, alignment/

discontinuity and corrosion will have a higher probability of failure during the life of the ship than

the surrounding structures.

(2) Critical locations are dened as the specic locations within the critical area that can be prone

to fatigue damage for which design improvements are provided.

1.5.2 In general the following methods are used to improve welded structural details of critical

locations, in order to improve fatigue strength of hull structure at the design stage:

(1) To reduce the nominal stress level: increasing the local scantling to reduce the nominal stress

level, and hence the hot spot stress for a given structural detail;


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(2) To reduce the geometrical stress concentration: the adoption of a good detail design conguration

by the provision of soft connections reduces the geometrical stress concentration factor due to the

geometrical discontinuity;

(3) To control building misalignment: reducing misalignment to minimize resultant stress

concentration factor;

(4) To improve weld geometry: special attention is given to achieving a favourable geometry and

smooth transition at the weld toe to minimise resultant stress concentration factor.

1.5.3 Structural details designs of bulk carriers, oil tankers and container ships are given in Appendix

3 to the Guidelines for the purpose of providing technical guidance (non-mandatory requirements)

for designers in the design improvement of structural details of critical locations in order to increase

structural fatigue life. It may also be used as a reference for other types of ships.


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CHAPTER 2 FATIGUE ANALYSIS

2.1 Locations for fatigue check

2.1.1 For the following structural members in cargo hold area, fatigue strength check is to be carried

out:

(1) connections of longitudinals (bottom, side, deck and inner shell) to transverse web frames;

(2) connections of longitudinals (bottom, side, deck and inner shell) to transverse bulkheads;

(3) for bulk carriers and ore carriers, hatch corners with higher stress levels, connections of inner

bottoms to lower stool sloping plates, connections of transverse bulkheads to lower stool top plates,

connections of transverse bulkheads to upper stool sloping plates, connections of frames to top side

tanks and hopper tanks of single hull bulk carriers are to be selected;

(4) for ships with large openings (e.g. container ships), hatch corners are to be selected in way of

large opening ends and midship area;(5) knuckle areas of connections of hopper tanks to inner bottoms and of hopper tanks to sides.

2.2 Selection of designS-Ncurves

2.2.1 S-Ncurves (see Fig. 2.2.1) are composed of Curves B, C, D, E, F, F2, G, W and each shows a

kind of relationship of structural details bearing alternating stress range values Sand the number of

stress cyclesN, which may be represented by:

)log()log()log( SmKN =

where: minverse slope of the S-Ncurve, taken as 3;

Kfactors for S-Ncurves. See Table 2.5.1(2).

B

C

D

EF

F2G

WStressrange

S

(N/mm2)

1000

100

10

104

105

106

107

Number of stress cyelesN

Fig. 2.2.1


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2.2.2 A general principle for selecting S-Ncurves is shown in Table 2.2.2.

Table 2.2.2

Types Description of joints Sketches S-N curves

1 Plates and sections with no ame-cut edges and free from

cracks and cut

B

2 Plates with ame-cut edges but free from cracks and cut

C

3 Two-sided full penetration butt welds (perpendicular to

the direction of load)

E

4 Continuous fillet welds parallel to the direction of load

based on stress range of face plate adjacent to the weld

D

5 Intermittent fillet welds parallel to the direction of load

based on stress range of face plate adjacent to the weld

endsE

6 Butt, fillet or intermittent fillet welds with cope holes,

parallel to the direction of load based on stress range of

face plate adjacent to the weld ends F

7 Fillet welded bracket with load direction parallel to the

welds:

l 150 mml 150 mm

l

F

F2

8 Bracket with smooth transitions (scarfing or circular)

welded to the face plates of beams, c2 t, maximum is

25 mm:

r0.5 h

r0.5h or 20

if 20, see Type 7

c

r(t)

h

F

F2


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Types Description of joints Sketches S-N curves

9 Fillet welded bracket with load perpendicular to the welds

E

10 Stiffeners welded on girder webs based on principle stress

range of girder webs in way of weld ends

E

11 Stiffeners welded on girder webs based on principle stress

range of face plates of girders in way of weld toesF

12 Cross or T joints, full penetration welded

F

13 Cross or T joints, llet welded

F2

2.2.3 When calculating the fatigue strength of hull structural details, suitable S-N curves are

to be selected in accordance with the general principles and types, directions of bearing forces

and construction workmanship of structural details given in 2.2.2. Table 2.2.3 shows S-N curves

applicable to typical hull structural details.

2.2.4 When hot spot stress method is used in fatigue assessment, E curves are selected for welded

details and C curves for non-welded details in hull structures.


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Table 2.2.3

Locations Types of Joints Remarks

Frame ends in holds of

bulk carriers

E

F2

When E curve is selected, hot spot

stress is to be used.

E

F2



E

F2



E

F2





E

G



E

F2




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Joints of longitudinals

to t r ansve rse r ing

frames

F2

F2

F

E

E



E

E

When E curve is selected, hot spotstress is to be used.

Joints of vertical web

frames of transverse

bulkheads in oil tankers

t o d o u b l e b o t t o m

girders E

E



Joints of vertical web

frames of transverse

bulkheads in oil tankers

to deck girders EE




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Joints of horizontal

girders in oil tankers

to side longitudinals or

longitudinal stiffeners

o f l o n g i t u d i n a l

bulkheads

E



E



Rounded hatch corners

C

When C curve is selected, hot spotstress is to be used.

Elliptical hatch corners

C

When C curve is selected, hot spot


2.3 Weibull distribution of stress ranges in hull structures

2.3.1 Long-term distribution of stress range of hull structures is assumed as a 2-parameter Weibull

distribution, shape parameter of Weibull distribution is determined by the following formula:

1.45 - 0.036f L

where:L length of ship, in m;

f= 1-0.08z/d1 forzd1;

f= 0.92 + 0.08(z- d1)/(D - d

1) forz d

1;

where the calculated points are on transverse bulkheads,f = 0.92;

D moulded depth, in m;

d1 draught at calculated working condition, in m;

z height from calculated points to the base line, in m.

2.4 Allowable stress ranges

2.4.1 Allowable stress ranges may be applied for the check of hull structural fatigue strength with

design stress ranges at full load conditions. Where the requirements in 2.4.4 are not complied with,

further check is to be carried out by calculating the fatigue cumulative damage level of the structures

in accordance with the requirements in 2.5.


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2.4.2 Shape parameter of Weibull distribution is to be calculated in accordance with the

requirements of 2.3.1.

2.4.3 S-Ncurves adopted in the check are to be selected in accordance with the requirements of 2.2

and the joint classication.

2.4.4 Fatigue strength of hull structures is to comply with the requirements of following formula:

SL [S

L]

where: SL design stress ranges under full load conditions, in N/mm2, to be calculated in accordance

with the requirements of Chapter 4;

[SL] allowable stress ranges, in N/mm2, to be obtained from Table 2.4.1 based upon the

selected S-Ncurves and .

Allowable stress ranges [SL], in N/mm2 Table 2.4.1

S-NCurve

B C D E F F2

G W

.60 1253.57 1055.68 802.21 703.69 598.72 527.84 438.42 315.86

.61 1214.51 1022.78 777.21 681.77 580.06 511.40 424.76 306.02

.62 1177.47 991.59 753.51 660.97 562.37 495.80 411.80 296.69

.63 1142.30 961.97 731.00 641.23 545.57 480.99 399.50 287.83

.64 1108.89 933.83 709.62 622.48 529.61 466.92 387.82 279.41

.65 1077.13 907.08 689.29 604.64 514.44 453.55 376.71 271.40

.66 1046.90 881.62 669.95 587.67 500.00 440.82 366.13 263.79

.67 1018.11 857.38 651.53 571.51 486.25 428.70 356.07 256.53

.68 990.67 834.27 633.97 556.11 473.15 417.14 346.47 249.62

.69 964.50 812.24 617.22 541.42 460.65 406.13 337.32 243.02

.70 939.52 791.20 601.24 527.40 448.72 395.61 328.58 236.73

.71 915.67 771.11 585.97 514.01 437.33 385.56 320.24 230.72

.72 892.87 751.91 571.38 501.21 426.44 375.96 312.27 224.97

.73 871.06 733.54 557.42 488.96 416.02 366.78 304.64 219.48

.74 850.18 715.97 544.06 477.25 406.05 357.99 297.34 214.22

.75 830.19 699.13 531.27 466.03 396.51 349.57 290.35 209.18

.76 811.04 683.00 519.01 455.27 387.36 341.51 283.65 204.35

.77 792.67 667.53 507.26 444.96 378.58 333.77 277.22 199.73

.78 775.05 652.69 495.98 435.07 370.17 326.35 271.06 195.29

.79 758.13 638.44 485.15 425.57 362.09 319.23 265.14 191.02

.80 741.88 624.76 474.75 416.45 354.32 312.38 259.46 186.93

.81 726.26 611.60 464.76 407.68 346.86 305.81 254.00 182.99

.82 711.23 598.95 455.15 399.25 339.69 299.48 248.74 179.21

.83 696.78 586.78 445.90 391.13 332.79 293.40 243.69 175.57

.84 682.87 575.06 436.99 383.32 326.14 287.54 238.82 172.06

.85 669.47 563.78 428.42 375.80 319.74 281.90 234.14 168.68

.86 656.56 552.90 420.15 368.55 313.57 276.46 229.62 165.43

.87 644.11 542.42 412.19 361.56 307.63 271.22 225.27 162.29


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Allowable stress ranges [SL], in N/mm2 Table 2.4.1(continued)

S-NCurve

B C D E F F2 G W.88 632.10 532.31 404.50 354.82 301.89 266.16 221.07 159.27

.89 620.51 522.55 397.09 348.32 296.36 261.28 217.01 156.35

.90 609.32 513.13 389.93 342.04 291.01 256.57 213.10 153.53

.91 598.51 504.03 383.01 335.97 285.85 252.02 209.32 150.80

.92 588.07 495.23 376.33 330.11 280.86 247.62 205.67 148.17

.93 577.98 486.73 369.87 324.44 276.04 243.37 202.14 145.63

.94 568.21 478.51 363.62 318.96 271.38 239.26 198.72 143.17

.95 558.76 470.55 357.57 313.66 266.87 235.28 195.42 140.79

.96 549.62 462.85 351.72 308.52 262.50 231.43 192.22 138.48

.97 540.77 455.39 346.06 303.55 258.27 227.70 189.13 136.25

.98 532.19 448.17 340.57 298.74 254.18 224.09 186.13 134.09

.99 523.88 441.17 335.25 294.07 250.21 220.59 183.22 132.00

1.00 515.82 434.39 330.09 289.55 246.36 217.20 180.40 129.97

1.01 508.01 427.80 325.09 285.16 242.62 213.91 177.67 128.00

1.02 500.42 421.42 320.24 280.91 239.00 210.72 175.02 126.09

1.03 493.07 415.23 315.53 276.78 235.49 207.62 172.44 124.23

1.04 485.93 409.21 310.96 272.77 232.08 204.61 169.95 122.44

1.05 478.99 403.37 306.52 268.88 228.77 201.69 167.52 120.69

1.06 472.25 397.70 302.21 265.09 225.55 198.86 165.16 118.991.07 465.71 392.18 298.02 261.42 222.42 196.10 162.87 117.34

1.08 459.34 386.82 293.95 257.85 219.38 193.42 160.65 115.74

1.09 453.15 381.61 289.99 254.37 216.43 190.81 158.48 114.18

1.10 447.14 376.54 286.14 250.99 213.55 188.28 156.38 112.66

1.11 441.28 371.61 282.39 247.71 210.76 185.81 154.33 111.19

1.12 435.58 366.81 278.74 244.51 208.03 183.41 152.34 109.75

1.13 430.03 362.14 275.19 241.39 205.38 181.08 150.40 108.35

1.14 424.63 357.59 271.74 238.36 202.80 178.80 148.51 106.99

1.15 419.37 353.16 268.37 235.40 200.29 176.59 146.67 105.66

1.16 414.24 348.84 265.09 232.53 197.84 174.43 144.87 104.37

1.17 409.24 344.63 261.89 229.72 195.45 172.32 143.13 103.11

1.18 404.37 340.53 258.77 226.99 193.13 170.27 141.42 101.89

1.19 399.62 336.53 255.73 224.32 190.86 168.27 139.76 100.69

1.20 394.99 332.63 252.77 221.72 188.65 166.32 138.14 99.52

Note: Intermediate values may be obtained by linear interpolation.


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2.5 Calculation of cumulative damage

2.5.1 Cumulative damageDof hull structures is to be obtained by the following formula:

8

/3

3

10)1(42.18

6.0

i

i

i

Liiii

m

Kf

SD

i

where: itime distribution factor in corresponding calculated conditions, to be obtained from

Table 2.5.1(1), i=1 for full load conditions, and i= 2 for ballast calculated conditions;

Kfactors for S-N curves to be obtained from Table 2.5.1(2);

SLi

design stress ranges in corresponding calculated conditions, in N/mm2, to be calculated

in accordance with the requirements of Chapter 4 and Chapter 5;

i shape parameter in corresponding calculated conditions, to be calculated according to

the requirements of 2.3.1;

)1(

,2

1),1(

0.1

/2

i

i

i

ii

i

i m

mmi

i

L

qi

iS

Sf

42.18

fi plate thickness correction factors to be obtained from the following formulae:

fi= 1.0 for t22

fi=

223 4

t

/

for t 22

where: t plate thickness in way of calculated point, in mm;

(a,x) incomplete GAMMA function values, to be taken from Tables GAMMA functions

of Appendix 1;

complete GAMMA function values, to be taken from Tables GAMMA functions of

Appendix 1;where: S

qstress amplitude values at intersection point of two-slope S-N curves to be taken from

Table 2.5.1(2).

Time distribution factor Table 2.5.1(1)

Full load Ballast

Bulk carriers 0.6 0.4

Oil tankers 0.5 0.5

Container ships 0.75 0.25


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Kand Sqof S-Ncurves Table 2.5.1(2)

S-N curves K Sq

B 5.800 x 1012 83.3955

C 3.464 x 1012 70.2305

D 1.520 x 1012 53.3680

E 1.026 x 1012 46.8147

F 6.319 x 1011 39.8305

F2

4.330 x 1011 35.1153

G 2.481 x 1011 29.1659

W 9.279 x 1010 21.0136

2.5.2 Cumulative damage D in design service life is to be determined according to the following

formula:

=

=2

1i

iDD

where: iD cumulative damage of structures in corresponding calculated conditions is to be

calculated in accordance with 2.5.1.

2.5.3 Cumulative damageDof structures in design service life is to be determined as follows:

D1.0


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CHAPTER 3 FATIGUE LOAD

3.1 General requirements

3.1.1 In the Guidelines only the following wave induced loads are considered as external loads of

fatigue analysis:

(1) load of hull girder (wave bending moment and torsional moment);

(2) sea water dynamic pressure;

(3) cargo pressure in holds resulting from acceleration of hull movement.

3.1.2 External loads of fatigue may be calculated by methods from 3.2 to 3.5 of this Chapter, or by

direct calculations specied in relevant CCS guidelines for direct calculations.

3.1.3 For ships navigating in restricted services, the wave bending moment in 3.2 of this Chapter

may be reduced by:

(1) 5% for ships intended for service category 1;(2) 10% for ships intended for service category 2;

(3) 15% for ships intended for service category 3.

3.2 Wave bending moment and torsional moment

3.2.1 Wave hogging bending momentMW(+) and wave sagging bending momentMW(-) in various

transverse sections along the ship length are to be determined in accordance with the following

formulae:

( )M MCL BCW b+ = 190 102 3 kN m

( ) ( )M MCL B CW b = + 110 0 7 102 3. kN m


B breadth of ship, in m;

Cbblock coefcient, but not to be less than 0.6; Mdistribution factor of bending moments along the ship length, see Fig. 3.2.1;

Ccoefcient to be calculated in accordance with the following formulae respectively:

( )

C

L

=

1075300

100

1 5

.

.

for 90 m L300 m;

C= 1075. for 300 mL350 m;

( )

CL

=

1075

350

150

1 5

.

.

for 350 m L500 m.


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M

1.0

0.0 L

0.0 0.4L 0.65L

Fig. 3.2.1

3.2.2 Horizontal wave bending momentMHin various transverse sections along the ship length are

to be determined in accordance with the following formula:

)2000

3.0( 12+= bH CdMCL

LM kNm


d1 draught under calculated conditions, in m; Cbblock coefcient;

Ccoefcient, same as 3.2.1; Mdistribution factor of bending moments along the ship length, to be obtained from

Fig. 3.2.1.

3.2.3 Wave torsional moment ( )M xT in various transverse sections along the ship length are to be

determined in accordance with the following two formulae:

(1) Wave torsional moment ( )M xT in bowing quartering condition is to be calculated in accordancewith the following formula:

( )M e LB C xL

L Bd Cd

x

L

T

L

T

b

=

+

0 00123 12

113 1 1432

0 00295 3

1 25

1

3

1

. cos

. . sin

.

.kN m


B breadth of ship, in m;

1d draught under calculated conditions, in m;Cbblock coefcient;

distance from shearing centre under ship base line to the ship base line, in m;x distance from calculated section to aft perpendicular, in m;

C C CT W W= +13 2 43 4 78 92. . .

where: CW waterline plane coefcient.


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(2) Wave torsional moment ( )M xT in quarter following sea is to be calculated in accordance withthe following formula:

( )M e LB C xL

L Bd Cd

x

L

T

L

T

b

=

+ +

0 00123 12

113 1 1432

0 00295 3

1 25

1

3

1

. cos

. . sin

.

. kN m

where:L,B, d1, Cb, ,x, CTsee 3.2.3(1).

3.2.4 Where calculating the hull bimomentBcaused by bow quartering and quarter following sea

by means of direct calculation method, the greater value is to be taken.

3.2.5 The wave bending moment and bimoment ranges are to be determined by the following

formulae.(1) The vertical wave bending moment range MWis to be determined as follows:

( ) ( )M M Mw w w= + kN m

where: ( )Mw + wave hogging bending moment, in kNm, calculated according to 3.2.1; ( )Mw wave sagging bending moment, in kNm, calculated according to 3.2.1.(2) The horizontal wave bending moment range MHis to be determined as follows:

M MH H= 2 kN m

where: MHhorizontal wave bending moment, in kNm, calculated according to 3.2.2.

(3) Bimoment range B is to be determined as follows:

B B

= 2 kN m2

where: Bbimoment, in kNm2, calculated according to 3.2.4.

3.3 Sea water dynamic pressure

3.3.1 The sea water dynamic pressure values around hull cross sections within 0.2 to 0.7Lare to be

determined by the following formulae:

(1) Sea water dynamic pressure pWL in way of water line at side is to be calculated by the followingtwo formulae and the greater value is to be taken:

p B CC dWL b10 66

12 3 0 4= + +. . kN/m2

p p BWL WL m2 10 5 5= +. kN/m2

where: B breadth of ship, in m;

1d draught under calculated conditions, in m;


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-8-

Cbblock coefcient;

Ccoefcient, same as 3.2.1;

m

maximum roll angle, in rad, calculated according to 3.4.1(2).

(2) Sea water dynamic pressure pBSin way of bottom side (the bilge) is to be calculated by the

following two formulae, the greater value is to be taken:

p p dBS WL1 1 112= . kN m2

p p d B eBS WL m

d

L2 1 1

3 14

0 5 0 6 51

= +

. .

.

kN m2

where:pWL1

, d1,B, msee 3.3.1(1);

Llength of ship, in m.

(3) Sea water dynamic pressure pBCat bottom centreline is to be calculated as follows:

p p dBC WL= 1 112. kN m2

where: pWL1 , d1 see 3.3.1(1).

(4) Sea water dynamic pressure phdat any point around hull cross section is to be determined asfollows:

p p z d

hhd WL=

1 1

1

kN m2 for d1+ h1zd1;

( ) ( )p p p p zd

p p y

Bhd WL BS WL BC BS = +

+

1 1

2

1

kN m2 forz d1;

phd = 0 kN/mm2 forzd1+ h1

where: pWL to be calculated according to 3.3.1(1) above;

pBSto be calculated according to 3.3.1(2) above; pBCto be calculated according to 3.3.1(3) above; B breadth of ship, in m;

1

d draught under calculated conditions, in m; y distance from calculated point to longitudinal central section, in m; zvertical distance from calculated point to base line, in m; h

1sea water dynamic pressure acting height (see Fig. 3.3.1) above waterline at side is to

be calculated by the following two formulae and the lesser value is taken:

ph WL

1011

dDh 112

where: Dmoulded depth, in m.

m

m


21/120

-9-

The distribution of sea water dynamic pressure phd around the hull cross section may be referred inFig. 3.3.1.

pWL

pBS

pBC

z

h1

Fig. 3.3.1

3.3.2 The sea water dynamic pressure range paround hull cross sections within 0.2 to 0.7Lare to

be determined by the following formulae:

p phd= 21 kN m2 for d1zd1+ h1;

{1

2 pp= hd

-10(z-d1)} kN/m2 for d1- h2zd1;

p phd= 2 21

kN m2

for 0 z d1- h2;

where: shape parameter of Weibull distribution calculated according to 2.3.1;

phdcalculated according to 3.3.1(4);

h1 sea water dynamic pressure acting height above waterline at side, in m, calculated

according to 3.3.1(4);

z vertical distance from calculated point to base line, in m;

1d draught under calculated conditions, in m;

h2vertical distance between maximum value point of sea water dynamic pressure at side

and waterline (see Fig. 3.3.2) is to be calculated according to the following formula,

but not greater than d1:

h p dp p d

WL

WL BS

21

110= +

m

where: pWLto be calculated according to 3.3.1(1);

pBSto be calculated according to 3.3.1(2).

The distribution of sea water dynamic pressure range p around the hull cross section may be

referred in Fig. 3.3.2.


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-0-

h

h

p = 2pBC BC

p = 2p

p = 2p

WL WL

BS BS

Fig. 3.3.2

3.3.3 The mean values pmof sea water dynamic pressure range around hull cross sections within0.2 to 0.7Lare to be determined by the following formulae:

(1) The mean values pmof sea water dynamic pressure range at side are to be determined as follows:

p p d

Dm = 2

11 ( )max kN m2


d1draught under calculated conditions, in m;

Dmoulded depth, in m;

pmaxmaximum value referred to in Fig.3.3.2 of sea water dynamic pressure range in d1 h2

at side are to be determined by the following two formulae:

p hmax= 20 2 kN m2

for h d2 1< ;

p d pBSmax= +10 1 kN m2 for h d2 1= ;

where: h2vertical distance between maximum value point of sea water dynamic pressure at side

and waterline is to be determined according to 3.3.2;

pBS

to be determined according to 3.3.1(2).

(2) The mean values pmof sea water dynamic pressure range at bottom are to be determined by

the following two formulae:

p p pm BS BC = +21 ( ) kN m2 for h d2 1< ;

p d p pm BS BC = + +

2 10

1

2

1

1

( ) kN m

2 for h d2 1= ;


pBS

to be calculated according to 3.3.1(2);

pBC

to be calculated according to 3.3.1(3);

d1 draught under calculated conditions, in m.


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3.4 Ship motions and accelerations

3.4.1 Roll periods and amplitude under ship relative motions are to be obtained from the following

formulae:

(1) Roll period TRis to be determined by the following formula:

T k GM R r= 2 sec

where: kr roll rotation radius, in m, when no actual values found, assumption may be made by

the following formulae:

kr= 0.35B, for oil tankers under ballasting conditions;

kr= 0.25B, for ships carrying ores between longitudinal bulkheads;

kr= 0.39B, for other cases;

where:Bbreadth of ship, in m;

GMinitial metacentric height at calculated conditions, in m, when no actual values found,

assumption may be made by the following formulae:

GM= 0.12B, for oil tankers and bulk carriers; GM= 0.07B, for other kinds of ships.

where:Bbreadth of ship, in m.

(2) Maximum roll amplitude mis to be determined from the following formula, but not exceed 0.523:

m

Rk T

B=

+

62 5 125

75

. .rad

where: TRsee 3.4.1(1);


kcoefcient to be determined by the following formulae:

k= 1.2 for ships with no bilge keels;

k= 1.0 for ships with bilge keels;k= 0.8 for ships with anti-rolling stabilizers.

(3) Pitch period TPis to be determined by the following formula:

T LP= 180 10. sec

where: L length of ship, in m.

(4) Maximum pitch amplitude mis to be determined by the following formula, but not to exceed 0.14:

m ba C= 0 25 0. rad

where: Cbblock coefcient; a

0acceleration factor, to be calculated according to the following formula:

a C L C V LV0 3= +

where: C LV = 50 , to be taken not greater than 0.2; L length of ship, in m;

V ship velocity, in kn;

C coefcient to be calculated according to 3.2.1 above.


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3.4.2 Accelerations of ship motions are to be determined by the following formulae:

(1) Surge acceleration axis to be determined by the following formula:

a a Cx b= 2 0 m s2

where: Cb coefcient of block;

a0 acceleration factor referred to 3.4.1 (4) above.

(2) Sway acceleration ayis to be determined by the following formula:

a ay = 3 0 m s2

where: a0 see 3.4.2 (1) above.

(3) Heave acceleration azis to be determined by the following formula:

a a Cz b= 7 0 m s2

where: a0, Cb see 3.4.2 (1) above.

(4) Roll acceleration aris to be determined by the following formula:

ar= ( )Tm R6 282

. rad s2

where: TR roll period, in s, to be determined according to 3.4.1 (1) above;

m maximum roll amplitude, in rad, to be determined according to 3.4.1 (2) above.

(5) Pitch acceleration apis to be determined by the following formula:

ap= ( )Tm p6 282

. rad s2

where: Tp pitch period, in s, to be determined according to 3.4.1 (3) above;

m maximum pitch amplitude, in rad, to be determined according to 3.4.1 (4).

(6) Transverse combined acceleration atis to be determined by the following formula:

a a a z z t y r rp m 22

10sin m s2

where: ay sway acceleration, see 3.4.2 (2);

ar roll acceleration, 3.4.2 (4); m maximum roll amplitude, in rad, see 3.4.1 (2);

z vertical distance from cargo centroid to base line, in m;

zrp vertical distance from roll rotary axial and pitch rotary axial to base line, in m, to be

calculated according to the following two formulae, whichever the lesser is to be taken:

zrp1dD

24+= m;

zrp2

D

2= m;


25/120

--

where: D moulded depth of ship, in m;

d draught, in m.

(7) Longitudinal combined acceleration al

is to be determined by the following formula:

a a a z z l x p rp m 22

10sin m s2

where: zrp,z see 3.4.2 (6);

ax surge acceleration, see 3.4.2 (1);

ap pitch acceleration, see 3.4.2 (5);

mmaximum pitch amplitude, see 3.4.1 (4).

(8) Vertical combined acceleration avis to be determined by the following two formulae, whichever

the greater is to be taken:

2222

1 smyaaa rzv +=

22222 sm45.0 Lxaaa pzv

where: az heave acceleration, see 3.4.2 (3);

ar roll acceleration, see 3.4.2 (4);

ap pitch acceleration, see 3.4.2 (5);

x longitudinal distance from cargo centroid to after perpendicular, in m;

y transverse distance from cargo centroid to central line section, in m;

L length of ship, in m.

3.5 Cargo pressure in holds

3.5.1 The pressure acting on ship sides, bottom and bulkheads due to liquid cargoes is to be

determined by the following formulae respectively:

(1) The pressurepacting on ship sides, inner bottom and only one bulkhead due to liquid cargoes is

to be determined by the following three formulae, whichever the greatest is to be taken:

p1 a zv kN m

2 p2 a yt kN m

2 p3 a xl kN m

2

where: cargo mass density, in t/m3; x longitudinal distance, in m, from calculated point to free surface centre in holds;

y transverse distance, in m, from calculated point to free surface centre in holds;

z vertical distance, in m, from calculated point to free surface centre in holds;

at transverse combined acceleration, in m/s2, to be calculated according to 3.4.2 (6);

al longitudinal combined acceleration, in m/s2, to be calculated according to 3.4.2 (7);

av vertical combined acceleration, in m/s2, to be calculated according to 3.4.2 (8).


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--

(2) Liquid pressurepon the transverse bulkheads of fore and aft tanks carrying the same liquid is

to be determined by the following formula:

p= 2alx kN/m2

where: , al,x see 3.5.1 (1) above.

(3) Liquid pressurepon the longitudinal bulkheads of tanks at sides carrying the same liquid is to

be determined by the following formula:

p= 2aty kN/m2

where: , at,y see 3.5.1 (1) above.

3.5.2 The pressure acting on ship sides, bottom and bulkheads due to dry cargoes is to be determined

by the following formulae respectively:

(1) Cargo pressurepon ship-side or longitudinal bulkheads is to be determined by the following

formula:

p= 0.7atb kN/m2

where: cargo mass density, in t/m3;

b cargo breadth, in m, in horizontal plane inner holds at calculated point;

attransverse combined acceleration, in m/s2, see 3.5.1 (1) above.

(2) Cargo pressurepon the transverse bulkheads is to be determined by the following formula:

p= 0.7all kN/m2


l cargo length, in m, in horizontal plane inner holds at calculated point;

al longitudinal combined acceleration, in m/s2, see 3.5.1 (1) above.

(3) Cargo pressurepon the horizontal inner bottoms is to be determined by the following formula:

p=av h kN/m2


h vertical distance, in m, from calculated point to cargo upper surface in holds;

av vertical combined acceleration, in m/s2, see 3.5.1 (1) above.

(4) Cargo pressurepon the sloping inner bottoms is to be determined by the following two formulae,

whichever the greater is to be taken:

p1 a hv cos

2 kN m

2 p

2 0 7

2. sina bt kN m

2


b cargo breadth, in m, in horizontal plane inner holds at calculated point;

h vertical distance, in m, from calculated point to cargo upper surface in holds;


27/120

--

at transverse combined acceleration, in m/s2, see 3.5.1 (1) above;

av vertical combined acceleration, in m/s2, see 3.5.1 (1) above;

angle of sloping inner bottom to horizontal plane, in degrees.

3.5.3 Cargo pressure ranges and mean values of pressure range are to be determined by the

following formulae respectively:

(1) Liquid cargo pressure range pis to be determined as follows:

p= 2p kN/m2

where: p liquid cargo pressure, in kN/m2, to be calculated as required in 3.5.1.

(2) The cargo pressure range peffected by dry cargoes on ship sides and only one bulkhead in

holds is to be determined as follows:

p=p kN/m2

where: p dry cargo pressure, in kN/m2, to be calculated as required in 3.5.2.

(3) The cargo pressure range peffected by dry cargoes on inner bottoms and bulkheads in holds

at side is to be determined as follows:

p= 2p kN/m2

where: p dry cargo pressure, in kN/m2, to be calculated as required in 3.5.2.

(4) The mean value of dry cargo pressure ranges on ship sides, inner bottoms and bulkheads is

generally to be taken as that in way of central point of grillage.

(5) The mean value pmof liquid cargo pressure ranges on ship sides and bulkheads is to be

determined as follows:

p p h

Dm h= 2

where: h height of liquid cargo in holds, in m;

ph/2liquid cargo pressure range at z h=2

, in kN/m2, to be calculated as required in 3.5.3 (1);

D moulded depth of ship, in m.


28/120

-6-

CHAPTER 4 CALCULATION OF NOMINAL STRESS RANGES

4.1 General requirements

4.1.1 A simplied calculation method for nominal stress ranges is provided from 4.2 to 4.4 of this

Chapter. However, the nominal stress ranges may be determined by direct calculations in accordance

with the requirements of 4.5.

4.1.2 In the process of calculating nominal stress ranges, the corrosion allowance required in Table

4.1.2 is to be deducted from actual hull structural scantlings.

Corrosion Allowance tkValues Table 4.1.2

Thicknesst Corrosion allowance tk(mm)

10 0.75

10 0.05 t+ 0.25, maximum 1.6

4.1.3 For boundaries of ballast tanks and liquid cargo tanks, their corrosion allowance is not to be

less than 1.25 mm.

4.1.4 For dry spaces (cargo spaces in bulk carriers exclusive), their corrosion allowance may be tk/2

in Table 4.1.2, but not less than 0.5 mm.

4.2 Simplied calculations of stress ranges

4.2.1 The stress ranges SVof hull girders caused by vertical wave bending moment are to be determined

by the following formula:

S M

WV

W

V

= 103 N mm2

where: MWvertical wave bending moment range, in kNm, to be calculated as required in 3.2.5 (1); WV vertical section modulus at calculated point, in cm

3.

4.2.2 The stress ranges SHof hull girders caused by horizontal wave bending moment are to be


S M

WH

H

H

=

103 N mm2

where: MHhorizontal wave bending moment range, in kNm, to be calculated as required in 3.2.5 (2); WH horizontal section modulus at calculated point, in cm

3.

4.2.3 The warping stress ranges Sof hull girders caused by wave torsional moment are to be


S B

W

=

105 N mm2

where: B

bimoment ranges to be calculated in accordance with 3.2.5 (3);


29/120

-7-

W I

= warping section modulus, in cm4;

I segmental moment of inertia of calculated section, in cm6

, by means of calculationaccepted by CCS;

segmental coordinate at calculated point, in cm2, by means of calculation accepted

by CCS.

4.2.4 The ship sides, bulkheads or ship bottoms between transverse bulkheads in one hold block to

be calculated as a grillage, the bending stress ranges of the grillage is to be determined as follows:

(1) The moment of inertia iaof grillage in a unit breadth is to be calculated as follows:

iaI

s

I I

b

na

a

a na+

50cm3

where: b grillage breadth, in m, see Figs.4.2.4 (1) and 4.2.4 (2);

Inamoment of inertia, in cm4, of primary structural members together with attached

plating distributed along the breadth of grillage, see Fig.4.2.4 (2);

Ia moment of inertia, in cm4, of central primary structural members together with attached

plating distributed along the breadth of grillage, see Fig.4.2.4 (2);

Saspacing of primary structural members, in cm, distributed along the breadth of grillage,

see Fig.4.2.4 (2).

(2) The moment of inertia ibof grillage in a unit length is to be calculated as follows:

ibIs

I Ia

nb

b

b nb+ 50

cm3

where: a grillage length, in m, see Figs.4.2.4 (1) and 4.2.4 (2);

Sbspacing of primary structural members , in cm, distributed along the length of grillage,

see Fig.4.2.4 (2);

Inbmoment of inertia, in cm4, of primary structural members together with attached

platings distributed along the length of grillage, see Fig.4.2.4 (2);

Ib moment of inertia, in cm4, of central primary structural members together with attached

platings distributed along the length of grillage, see Fig.4.2.4 (2).

(3) The equivalent aspect ratiois to be calculated as follows:

a

b

i

i

b

a

4

where: a, b, ia, ibsee 4.2.4 (1) and 4.2.4 (2) above.

(4) The torsional stiffness factor is to be determined as follows:

I I

I I

pa pb

a b


30/120

-8-

where: Ia,Ib see 4.2.4 (1) and 4.2.4 (2) above;

Ipa moment of inertia, in cm4, of attached platings of central primary structural members

distributed along the grillage breadth to the neutral axis of the grillage;

Ipb moment of inertia, in cm4, of attached platings of central primary structural members

distributed along the grillage length to the neutral axis of the grillage.

(5) The bending stress ranges S2eon the grillage induced by sea water dynamic pressure is to be


S K K p b r

i ie s b

m a

a b

2

210=

N mm2

where: ia, ib, b see those in 4.2.4 (1) and 4.2.4 (2);

Ks factor,Ks= 1.0 for that in way of bottom plating or ship-side plating;Ks= 0.91 forthat in way of web plating or free wing plating;

Kb factor, to be taken from Table 4.2.4 according to, and boundary condition of the

grillage;

pmmean value of sea water dynamic pressure ranges acting on the grillage, in kN/m2,

to be calculated as required in 3.3.3;

ra distance, in m, from neutral axis of grillage to the calculated point.

(6) The bending stress ranges S2ion the grillage induced by cargo pressure in holds is to be


S K K p b ri i

i s bm a

a b

2

2

10= N mm2

where: Ks,Kb, ra, ia, ib, b see those in 4.2.4 (1), 4.2.4 (2) and 4.2.4 (5);

pm mean value of cargo pressure ranges in holds acting on the grillage, in kN/m2, to

be calculated as required in 3.5.3.

b

b

a

Fig. 4.2.4(1)


31/120

-9-

sa

sb

Ib

Ia

Inb

Ina

b

a

Fig. 4.2.4(2)

Factor Kb Table 4.2.4

Rigidly xed the four sides

a

Longitudinal side simply supported, transverse (vertical) side

rigidly xed

a

= 0.0 = 0.5 = 1.0

0.20 0.0036 0.125 0.0014 0.0014 0.0014

0.30 0.0082 0.25 0.0057 0.0057 0.0057

0.40 0.0146 0.375 0.0129 0.0130 0.0130

0.50 0.0228 0.5 0.0243 0.0238 0.0232

0.60 0.0314 0.75 0.0577 0.0534 0.0494

0.70 0.0395 1.00 0.0952 0.0845 0.0762

0.80 0.0466 1.25 0.1243 0.1100 0.0994

0.90 0.0522 1.50 0.1413 0.1261 0.1152

1.00 0.0564 1.75 0.1455 0.1342 0.1251

1.10 0.0591 2.00 0.1439 0.1374 0.1300

1.20 0.0609 2.5 0.1388 0.1381 0.1356

1.30 0.0619 3.0 0.1371 0.1376 0.1369

1.40 0.0624 3.5 0.1371 0.1373 0.1373

1.50 0.0626 4.0 0.1373 0.1374 0.1373

1.60 0.0627 >4.0 0.1374 0.1374 0.1374

>1.60 0.0627

Note: Intermediate values may be obtained by interpolation.


32/120

-0-

4.2.5 Where the bending stress ranges of secondary structural members are calculated, the fatigue

load is to be calculated according to the requirements in Chapter 3 and based on the determined

boundary conditions of the structure (e.g. ends of longitudinals to be rigidly fixed), adopting

theoretical calculations for bending of a single span girder; and where the fatigue load is evenly

distributed on secondary members with the two ends rigidly xed, they may be determined by the

following formulae.

(1) The bending stress ranges S3eon the secondary members effected by sea water dynamic pressure

is to be determined as follows:

23

22

3 mmN1016612

l

x

l

x

W

pslS

s

e

where: s spacing of secondary members, in cm;

l span of secondary members, in cm, to be determined as required in 1.2.3, Chapter 1,PART TWO of CCS Rules for Classication of Sea-going Steel Ships, see Fig. 4.2.5;

Wssection modulus, in cm3, of secondary members with attached plating;

x distance from the end of secondary members to the calculated point, in cm, see Fig. 4.2.5;

psea water dynamic pressure ranges acting on the secondary members, in kN/m2, to

be calculated as required in 3.3.2 above.

x

l

Calculated point

Fig. 4.2.5

(2) The bending stress ranges S3ion the secondary members effected by cargo pressure in holds isto be determined as follows:

S psl

W

x

l

x

li

s

3

2 2

3

126 6 1 10=

+

N mm2

where: s, l, Ws,x see those in 4.2.5 (1) above;

p cargo pressure ranges in holds acting on the secondary members, in kN/m2, to be

calculated as required in 3.5.3 above.


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4.2.6 The bending stress ranges on rectangular plating are to be determined by the following

formulae respectively:

(1) The bending stress ranges S4e

on the plating effected by sea water dynamic pressure is to be

determined by either one of the following formulae:

S K ps t e4 12 2= / N mm2 ( bending stress ranges on mid-point of short sides)

S K ps t e4 22 2= / N mm2 (bending stress ranges on mid-point of long sides)

where: s length of short sides, in cm, see Fig 4.2.6;

t thickness of plating, in mm;

K1,K2 factors, to be taken from Table 4.2.6;

p sea water dynamic pressure ranges, in kN/m2,

acting on the centre of rectangularplating, to be calculated as required in 3.3.2.

Factors K1and K2 Table 4.2.6

l/s 1.0 1.1 1.2 1.3 1.4 1.5 1.7 1.9 2.0

K1

0.0308 0.0323 0.0332 0.0338 0.0341 0.0342 0.0343 0.0343 0.0343

K2

0.0308 0.0349 0.0383 0.0412 0.0436 0.0454 0.0480 0.0493 0.0500

Note: l length of long side of rectangular plating, in cm, see Fig. 4.2.6; intermediate values may be obtained by

interpolation.

s

lFig. 4.2.6

(2) The bending stress ranges S4ion the plating effected by cargo pressure in holds is to be

determined by either of the following two formulae:

S K ps t i4 1 2 2= / N mm2 ( bending stress ranges on mid-point of short sides)

S K ps t i4 22 2= / N mm2 (bending stress ranges on mid-point of long sides)

where: s, t,K1,K2 see those in 4.2.6 (1) above;

p cargo pressure ranges in holds, in kN/m2, acting on the centre of rectangular plating,

to be calculated as required in 3.5.3.

4.3 Combined global stress ranges

4.3.1 The global stress ranges Sgare to be calculated by the following formulae respectively.


34/120

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(1) The global stress ranges Sgof ships with large openings are to be calculated as follows:

S S S S g V H= + +0 6. N mm

2

where: SV stress ranges, in N/mm2, of hull girder induced by vertical wave bending moment, to

be calculated as in 4.2.1;

SH

stress ranges, in N/mm2, of hull girder induced by horizontal wave bending moment,

to be calculated as in 4.2.2;

S warping stress ranges, in N/mm2, of hull girder induced by wave torque, to be

calculated as in 4.2.3. It may also be calculated by means of other methods.

(2) The global stress ranges Sgof other ships are to be calculated as follows:

S S S S S g V H V H= + +2 2 0 2. N mm2

where: SV stress ranges, in N/mm2, of hull girder induced by vertical wave bending moment, to

be calculated as in 4.2.1;

SH

stress ranges, in N/mm2, of hull girder induced by horizontal wave bending moment,

to be calculated as in 4.2.2.

4.3.2 The positive and negative symbols are to be taken into account when combining stress ranges

induced by sea water pressure and cargo pressure in holds. Where stress calculated is tensile one,

the positive value is taken for the corresponding stress ranges and where the stress at the calculated

point is compressive one, the negative value is taken for the corresponding stress ranges. Local stress

ranges Sl are to be determined by the following formulae:

(1) The local stress range Seinduced by sea water dynamic pressure is to be determined by the

following formula:

Se= S2e+ S3e+ S4e N/mm2

where: S2e bending stress ranges of grillage, in N/mm2, taking into account of symbols, the

value calculated as required in 4.2.4(5);

S3e bending stress ranges of beams, in N/mm2, taking into account of symbols, the value

calculated as required in 4.2.5(1);

S4e bending stress ranges of plating, in N/mm2, taking into account of symbols, the value

calculated as required in 4.2.6(1).

(2) The local stress range Siinduced by cargo pressure in holds is to be determined by the following

formula:

Si= S2i+ S3i+ S4i N/mm2

where: S2i bending stress ranges of grillage, in N/mm2, taking into account of symbols, the

value calculated as required in 4.2.4(6);

S3i bending stress ranges of girders, in N/mm2, taking into account of symbols, the value

calculated as required in 4.2.5(2);

S4i bending stress ranges of plating, in N/mm2, taking into account of symbols, the value

calculated as required in 4.2.6(2).


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(3) The local stress ranges Slare to be determined by the following formula:

S S S S S l e i p e i 2 2 2 N mm2

where: Se the local stress range, in N/mm2, induced by sea water dynamic pressure, see 4.3.2 (1);

Si the local stress range, in N/mm2, induced by cargo pressure in holds, see 4.3.2 (1);

p mean corresponding factor between Seand Sito be determined by the following two

formulae:

( )

p

z

d

x L

L

y

B

z x L

Ld= +

05 0 2 0 6

050 2 0 4

05

1 1

. . ..

. ..

forz d1

px L

L

y

B= +

0 3 0 205

0 2. ..

. forz d1

where: Llength of ship, in m;


d1draught at calculated condition, in m;

x distance from calculated point to aft perpendicular, in m;

y distance from calculated point to longitudinal central section, in m;

z vertical distance from calculated point to base line, in m.

4.4 Nominal stress range calculations

4.4.1 The nominal stress range SLof structural members being not taken account into the

longitudinal bending is to be determined by the following formula:

SL=KS

l N/mm2

where: Sllocal stress range, in N/mm2, to be calculated according to 4.3.2(3);

Kstress concentrating factor, to be taken as 1 in this Chapter.

4.4.2 The nominal stress range SLof structural members being taken account into the longitudinal

bending is to be determined by the following two formulae, whichever is the greater:

( )1 6.09.0 SSKS lgL += N/mm2

( )S K S S L g l2 0 9 0 6= +. . N/mm2

where: K, Slsee 4.4.1 above;

Sgglobal stress range, in N/mm2, to be determined as required in 4.3.1.

4.5 Direct calculations of local nominal stress ranges


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The 3-D FE analysis may be applied for direct calculations of local nominal stress ranges. The

net scantling model is applied in FE calculations and the corrosion allowance is to be deducted in

accordance with 4.1.2.

4.5.1 Structural FE model

(1) The extent of the 3-D FE model is to include 1/2 hold length forward and 1 hold length in the

middle and 1/2 hold length aft within mid-ship cargo area in longitudinal direction, and full depth of

the ship in vertical direction. In general, the results of the middle hold are applied for assessment (see

Fig. 4.5.1).

(2) While both primary members and loads are symmetrical to longitudinal centerline plane, only

half breadth, port or starboard side, of the hull structure is required to be modeled.

(3) The meshing of the 3-D FE model of hull structure is to be carried out as the longitudinal

spacing or similar spacing transversely along the hull envelop, and the frame spacing or similar

spacing along hull length. The meshes are to be as square as possible.

(4) In general, all areas of shell plates, deep webs of transverse rings, stringers, plane bulkhead web

stiffeners, frames, other members as well as corrugation bulkheads and bulkhead stools are to be

modeled by 4-node plate (shell) elements. Triangular elements are to be minimized. In high stress

areas and areas of signicant stress changes, such as lightening holes, manholes, connection of stool

to bulkhead, positions adjacent to brackets or structural discontinuities, triangular elements are to be

avoided as practicable as possible.

(5) All stiffeners of plates, which are subject to external sea pressure and cargo pressure, are

modeled by eccentric beam elements. The stiffeners and/or face plates of web transverses, frames,

oors, girders and brackets may be modeled by rod elements. In view of difculty in meshing, one

line element may represent more than one beam or rod elements.

(6) Not less than 3 plate elements are to be arranged in vertical direction for bottom girders and

oors. In general, the elements at the lowest end of bulkhead are to be divided as square as possible.

(7) The web of side frame may be modeled by plate element or beam element. In case the ratio of

web height of frame against size of grid at side is less than 1/3, beam element may be applied.

(8) Corrugated bulkhead and bulkhead stools: each ange plate or web plate is to be taken at least

as a plate element; for the plate elements at the lower end of corrugated bulkhead in the vicinity of

lower stool and for the elements adjacent to stool plate, the aspect ratio of sides of grid is to be closeto 1.

(9) For lightening holes and manholes of primary members, in particular the openings on girders

adjacent to bulkhead and bracket oors adjacent to lower stool in double bottom, plate elements of

equivalent plate thickness may be used to consider the effect of these openings.

(10) One independent point is set respectively in way of intersection of neutral axis with longitudinal

centerline in fore and aft end planes, and the degree of freedom x, z, y, zfor nodes of longitudinal

members in end planes are related to the relevant independent points.


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l1 l1 l2 l2

extent of FE model

Fig. 4.5.1 Extent of 3D FE model

4.5.2 Boundary conditions

(1) The displacements in transverse direction of nodes on longitudinal centerline plane are

constrained, and the rotations about the two coordinate axes on longitudinal centerline plane areconstrained, i.e. y=x=z= 0.

(2) Constraint of end planes: the independent point at one end constraint x, y, z, x, z, and the

independent point at the other end constraint y, z, x, z, as indicated in Table 4.5.2.

Application of boundary conditions (boundary with symmetrical load) Table 4.5.2

Positiondisplacement constraint rotation constraint

x

y

z

x

y

z

Longitudinal centerline section - Cons. - Cons. - Cons.

End plane A Link - Link - Link Link

End plane B Link - Link - Link Link

Rigid point A Cons. Cons. Cons. Cons. BM Cons.

Rigid point B - Cons. Cons. Cons. BM Cons.

Notes: Cons. constraint corresponding to displacement;

Link displacement of relevant nodes within end plane linked to independent node;

BM global bending moment applied on end plane.

4.5.3 Selection of local nominal stress

For plate elements, the principal stress perpendicular to crack propagation direction within 45

range on the checking element surface is to be selected. For beam element, the principal stress

perpendicular to crack propagation direction within 45 range on the face plate or free edge of the

checking element is to be selected.

4.5.4 Calculation of local nominal stress ranges

Where direct calculation is applied for fatigue strength stress, the following two calculated conditions

are to be included:

(1) full load calculated condition;

(2) ballast calculated condition.

Direct calculation of nominal stress ranges in any condition is to be carried out in accordance with

the table below:


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Direct calculation of nominal stress components Table 4.5.4

Load cases Stress ranges Applied loads

L1 Se

External hydrodynamic pressure ranges

corresponding to full load or ballast condition, to

be calculated in accordance with 3.3

L2 Si

In ternal cargo dynamic pressure ranges

corresponding to full load or ballast condition, to

be calculated in accordance with 3.5

The combination of local stress ranges are to be carried out in accordance with steps specied in 4.3.


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CHAPTER 5 CALCULATION OF HOT SPOT STRESS

5.1 Hot spot stress assessment method

5.1.1 The hot spot stress is to be determined by the following formula:

h= nK

where: h hot spot stress, in N/mm2, to be determined in accordance with 5.3.3.

n nominal stress, in N/mm2, to be determined in accordance with Chapter 4.

K stress concentration factor to be determined in accordance with 5.2 or 5.3. It may also

be determined by means of testing.

5.2 Stress concentration factors of typical detail

5.2.1 The stress concentration factors of round hatch corners may be taken from Fig. 5.2.1, where a

is the length, bthe breadth of the hatch and rthe radius of the corner.

Fig. 5.2.1

5.2.2 The stress concentration factors of elliptic hatch corners may be determined by means of nite

element calculations. The stress concentration factors of elliptic hatch corners may be estimated by

means of approximate calculation according to 5.2.1, where radius r of the corner is the one of short

axis of ellipse.


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5.2.3 The stress concentration factors of actual hull longitudinal member details may be calculated

in accordance with 5.3. The approximate values of stress concentration factors of partial joints are

given in Table 5.2.3.

Stress concentration factors Table 5.2.3

Joint type Stress concentration factors

1.30

1.40

1.60

1.50

1.80

1.35

t1

t2

1224 1160

2

1

. ( )+ tt

1.00 (slope 1:5)

1.13 (slope 1:3)

1.27 (slope 1:2)

1.00 (slope 1:5)

1.13 (slope 1:3)

1.27 (slope 1:2)


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5.3 Calculation method of stress concentration factors

5.3.1 Where the stress concentration factors of welded joints are calculated, the calculated points are

to be taken from the place of structure where cracks may likely occur. The stress concentration factor

Kis to be determined by the following formula:

K= h/n

where: n stress, in N/mm2, to be determined according to the requirements in 5.3.2.

h stress, in N/mm2, to be determined according to the requirements in 5.3.3.

5.3.2 Stress n is the maximum principal stress obtained at calculated points by means of coarse

mesh finite element analysis, when calculating a unit load is to be added on the force bearing

direction of the structural detail. The following principles are to be complied with in calculation:

(1) The general geometry of joints (such as the changes of openings, scarngs, bevels, brackets and

scantlings) are to be taken into account but that of welds is not included.

(2) When nite element mesh is developed, uniform change of mesh is to be ensured and abrupt

change of mesh is avoided.

(3) The nite element mesh in the vicinity of calculated points is to be ne enough as to reect the

change of stress gradient. The mesh size is not to be greater than the plate thickness tof the force

bearing structural members.

(4) The aspect ratio of nite element mesh is not to exceed 3.

5.3.3 Stress h is the maximum principal stress obtained at calculated points of structural details bymeans of ne mesh nite element analysis, when calculating a unit load is to be added on the force

bearing direction of the structural detail. For detailed calculation of stress h, see 5.4.6.

5.3.4 The hot spot stress is obtained by interpolation method given in 5.4.6.

5.4 Direct calculation of hot spot stress

5.4.1 General requirements

Fatigue strength assessment of complicated structure requires the use of fatigue hot spot stress

method. The fatigue hot spot stress is to be determined by means of fine finite element direct

calculation. The model is based on principles given in 5.4.2.

5.4.2 Structural modelling

The ne nite element model is to be based on the following principles:

(1) The fatigue hot spot stress may be calculated by means of a separate ne nite element model,

with boundary conditions being obtained from analysis of a coarse mesh finite element model;

alternatively, direct calculation may be performed via a ne nite element model tted into a coarse

mesh nite element model.

(2) The corrosion allowance required in Table 4.1.2 is to be deducted from actual hull structural

scantlings in the ne nite element model.


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-0-

(3) The ne nite element zone is to be such that the hot spot stress will not be affected by the boundary

conditions of displacement and those of forces. The fine finite element model is to be such that its

rened edges are supported by primary members, e.g. girders, horizontal girders and oors in cargo area.

(4) The nite element mesh in the vicinity of calculated points is to be ne enough as to reect the

change of stress gradient. The mesh size is not to be greater than the plate thickness tof the force

bearing structural members. The ne mesh zone is to be such as to extend over at least 10 tin all

directions leading to the fatigue hot spot position. 4-node or 8-node shell elements are to be used and

the use of any triangular element is to be prevented. The weld geometry and structural alignment are

not taken into account. Frames inside the ne mesh zone are to be modeled using shell elements.

(5) The following principles of structural modelling are mainly applicable to hopper knuckles:

(a) Special fatigue strength assessment is at least to be carried out for the knuckle joint between

inner bottom and hopper tank sloping plate in the cargo tank region. The assessment

position may be selected in the midship cargo tank region. Alternatively, it may be

determined via coarse mesh nite element analysis.(b) The rened zone is to be such as to ensure at lest 2 oor spaces along the direction of ship

length, 4 longitudinal spaces at knuckle line along the direction of molded depth and 4

longitudinal spaces at the side of knuckle line along the direction of ship breadth.

(c) Scarng brackets on the oor adjoining the inner bottom plating, the longitudinals adjacent

to knuckles and lapped brackets further away from transverse rings are to be modeled using

shell element. Longitudinals adjacent to knuckles and other brackets are to be modeled by

shell element, where the openings are to be considered on a case by case basis.

A typical knuckle ne nite element mesh is shown in Fig. 5.4.2.

Fig. 5.4.2

5.4.3 Load calculations

Where the fatigue strength stress is determined by means of direct calculations, the following

calculated loads are to be included:

(1) global wave bending moment and range, to be calculated in accordance with 3.2;

(2) external hydrodynamic pressure ranges, to be calculated in accordance with 3.3;

(3) internal cargo dynamic pressure ranges, to be calculated in accordance with 3.5.


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5.4.4 Boundary conditions

Boundary conditions of model are to be simply supported in accordance with Tables 5.4.4(1) and

5.4.4(2).

Rigid-link of both ends Table 5.4.4(1)

Nodes on longitudinal members at both

ends of the model

Translational Rotational

Dx Dy Dz Rx Ry Rz

All longitudinal members RL RL RL - - -

RL means rigidly linked to the relevant degrees of freedom of the independent point

Support condition of the independent point Table 5.4.4(2)

Location of the independent pointTranslational Rotational

Dx Dy Dz Rx Ry Rz

Independent point on aft end of model - Fix Fix - - -

Independent point on fore end of model Fix Fix Fix Fix - -

5.4.5 Calculated condition

Where direct calculation is applied for fatigue strength stress, the following two calculated conditions

are to be included:

(1) full load calculated condition;

(2) ballast calculated condition.

Direct calculation of hot spot stress ranges in any condition is to be carried out in accordance with

the table below:

Direct calculation of hot spot stress components Table 5.4.5

Load cases Stress ranges Applied loads

L1 Sv

Global vertical wave bending moment ranges in full load or ballast

condition, to be calculated in accordance with 3.2

L2 Sh

Global horizontal wave bending moment ranges in full load or

ballast condition, to be calculated in accordance with 3.2

L3 Se

External hydrodynamic pressure ranges corresponding to full load

or ballast condition, to be calculated in accordance with 3.3

L4 Si

Internal cargo dynamic pressure ranges corresponding to full load or

ballast condition, to be calculated in accordance with 3.5

The local stress ranges are to be combined in accordance with steps specied in 4.3 of the Guidelines.

5.4.6 Interpolation of hot spot stress

Stress his to be determined as follows:

h

t t

3

2

2 3 2/ /

where: t/2 maximum principal stress, in N/mm2, at the place with a distance of t/2 from weld

toe calculated in accordance with 5.4.7, where t being the plate thickness, in mm;


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3t/2 maximum principal stress, in N/mm2, at the place with a distance of 3t/2 from weld

toe calculated in accordance with 5.4.7, where t being the plate thickness, in mm.

5.4.7 Four nite element nodes (see Fig. 5.4.7) are selected on the member surface bearing force

in way of welds, the maximum principal stress in way of interpolated point is to be obtained

by Lagrange interpolation based upon the maximum principal stress in way of finite element

nodes selected. But the interpolated point is to be located between the 4 nite element nodes. The

maximum principal stress is to be determined as follows:

44332211 CCCC

where: 1 the maximum principal stress, in N/mm2, in way of nite element node 1;

2 the maximum principal stress, in N/mm2, in way of nite element node 2;

3 the maximum principal stress, in N/mm2, in way of nite element node 3;

4 the maximum principal stress, in N/mm2

, in way of nite element node 4; C

1, C

2, C

3, and C

4are to be calculated as follows respectively:

C x x x x x x

x x x x x x1

2 3 4

1 2 1 3 1 4

=

( )( )( )

( )( )( )

C x x x x x x

x x x x x x2

1 3 4

2 1 2 3 2 4

=

( )( )( )

( )( )( )

C x x x x x x

x x x x x x3

1 2 4

3 1 3 2 3 4

=

( )( )( )

( )( )( )

C x x x x x x

x x x x x x4

1 2 3

4 1 4 2 4 3

=

( )( )( )

( )( )( )

where: x the distance from interpolated point to weld toe, in mm;

x1 the distance of nite element node 1 to weld toe, in mm;



x4 the distance of nite element node 4 to weld toe, in mm.

h

x1 x2x3

x4

t

1.5t0.5t

Fig. 5.4.7


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Appendix 1 GAMMA FUNCTION TABLES

x= ux

10

eu

du x,= ux 10

eu

du Table 1

0.5 1.0 1.5 2.0 2.5

x

3.4 2.9812064 0.0190124 0.1381650 0.3811613 0.7117815 1.0789950

3.6 3.7170238 0.0155505 0.1290610 0.3836591 0.7535631 1.1853485

3.8 4.6941742 0.0127638 0.1210418 0.3879346 0.8019018 1.3096973

4.0 6.0000000 0.0105097 0.1139289 0.3938547 0.8572592 1.4545432

4.2 7.7566895 0.0086783 0.1075803 0.4013258 0.9202110 1.6228694

4.4 10.136101 0.0071845 0.1018817 0.4102855 0.9914495 1.81820814.6 13.381285 0.0059617 0.0967402 0.4206966 1.0717878 2.0447238

4.8 17.837861 0.0049576 0.0920794 0.4325421 1.1621682 2.3073136

5.0 24.000000 0.0041307 0.0878363 0.4458224 1.2636724 2.6117275

5.2 32.578096 0.0034479 0.0839580 0.4605528 1.3775355 2.9647117

5.4 44.598848 0.0028828 0.0804003 0.4767617 1.5051620 3.3741776

5.6 61.553915 0.0024140 0.0771256 0.4944895 1.6481451 3.8494023

5.8 85.621737 0.0020243 0.0741020 0.5137876 1.8082888 4.4012647

6.0 120.00000 0.0016997 0.0713021 0.5347176 1.9876330 5.0425245

6.2 169.40609 0.0014290 0.0687024 0.5573517 2.1884833 5.7881516

6.4 240.83377 0.0012028 0.0662823 0.5817716 2.4134438 6.6557137

6.6 344.70192 0.0010134 0.0640242 0.6080692 2.6654553 7.6658343

6.8 496.60607 0.0008548 0.0619125 0.6363460 2.9478378 8.8427335

7.0 720.00000 0.0007217 0.0599336 0.6667141 3.2643399 10.214864

7.2 1050.3178 0.0006098 0.0580755 0.6992962 3.6191938 11.815666

7.4 1541.3361 0.0005157 0.0563276 0.7342258 4.0171782 13.684453

7.6 2275.0326 0.0004365 0.0546804 0.7716479 4.4636896 15.867460

7.8 3376.9213 0.0003698 0.0531257 0.8117197 4.9648230 18.419083

8.0 5040.0000 0.0003134 0.0516559 0.8546112 5.5274635 21.403345

8.2 7562.2882 0.0002659 0.0502643 0.9005059 6.1593903 24.895617

8.4 11405.887 0.0002256 0.0489449 0.9496015 6.8693938 28.984669

8.6 17290.248 0.0001916 0.0476922 1.0021112 7.6674099 33.775079

8.8 26339.986 0.0001629 0.0465015 1.0582645 8.5646706 39.390092

9.0 40320.000 0.0001385 0.0453681 1.1183082 9.5738762 45.974994

9.2 62010.763 0.0001178 0.0442882 1.1825077 10.709389 53.701106

9.4 95809.457 0.0001003 0.0432580 1.2511485 11.987458 62.770511

9.6 148696.13 0.0000854 0.0422742 1.3245373 13.426463 73.421645

9.8 231791.87 0.0000727 0.0413338 1.4030034 15.047203 85.935914

10.0 362879.99 0.0000620 0.0404340 1.4869011 16.873221 100.64552


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Table 2

3.0 3.5 4.0 4.5 5.0 5.5

x3.4 1.4401492 1.7677242 2.0481720 2.2781069 2.4603952 2.6010785

3.6 1.6273063 2.0417582 2.4068759 2.7138190 2.9626345 3.1585466

3.8 1.8505973 2.3750080 2.8503873 3.2601479 3.5997824 3.8726130

4.0 2.1166086 2.7802039 3.3991792 3.9462242 4.4098445 4.7898048

4.2 2.4333315 3.2731189 4.0791134 4.8094715 5.4423626 5.9715340

4.4 2.8104382 3.8732825 4.9228649 5.8980088 6.7620044 7.4990046

4.6 3.2596216 4.6048754 5.9717440 7.2737758 8.4533090 9.4797923

4.8 3.7950117 5.4978485 7.2780236 9.0166030 10.626969 12.056684

5.0 4.4336821 6.5893211 8.9079135 11.229514 13.428161 15.419567

5.2 5.1962679 7.9253287 10.945362 14.045640 17.047581 19.821436

5.4 6.1077189 9.5630095 13.496924 17.637241 21.736119 25.599972

5.6 7.1982149 11.573335 16.697980 22.227490 27.824342 33.206676

5.8 8.5042824 14.044535 20.720719 28.105875 35.748433 43.246230

6.0 10.070153 17.086373 25.784353 35.648347 46.084721 56.529757

6.2 11.949419 20.835512 32.168233 45.343697 59.595720 74.146938

6.4 14.207054 25.462234 40.228666 57.828112 77.291547 97.563791

6.6 16.921869 31.178861 50.420523 73.930492 100.51192 128.75535

6.8 20.189515 38.250326 63.324992 94.731894 131.03580 170.38593

7.0 24.126145 47.007429 79.685264 121.64358 171.22790 226.054097.2 28.872880 57.863486 100.45243 156.50958 224.23494 300.62609

7.4 34.601266 71.335237 126.84456 201.74147 294.24841 400.68993

7.6 41.519933 88.069117 160.42278 260.49571 386.85677 535.17423

7.8 49.882736 108.87428 203.18923 336.90704 509.51793 716.19226

8.0 59.998699 134.76416 257.71342 436.39581 672.19323 960.19417

8.2 72.244178 167.00868 327.29506 566.07295 888.19902 1289.5407

8.4 87.077727 207.20004 416.17422 735.27386 1175.3508 1734.6547

8.6 105.05828 257.33550 529.80250 956.26251 1557.5017 2336.9628

8.8 126.86743 319.92168 675.19321 1245.1607 2066.6121 3152.9230

9.0 153.33663 398.10589 861.37367 1623.1748 2745.5353 4259.5387

9.2 185.48057 495.84174 1099.9696 2118.2161 3651.7689 5761.9154

9.4 224.53797 618.09784 1405.9610 2767.0418 4862.5095 7803.6205

9.6 272.02164 771.12108 1798.6588 3618.0854 6481.4660 10580.893

9.8 329.77974 962.76861 2302.9689 4735.2001 8648.0483 14362.151

10.0 400.07089 1202.9269 2951.0282 6202.6109 11549.765 19514.768


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Table 3

6.0 6.5 7.0 7.5 8.0 8.5

x3.4 2.7072930 2.7860296 2.8435006 2.8848968 2.9143737 2.9351534

3.6 3.3091769 3.4227189 3.5068819 3.5683780 3.6127563 3.6444349

3.8 4.0862382 4.2499746 4.3732287 4.4645858 4.5313993 4.5796937

4.0 5.0927767 5.3289023 5.5094075 5.6451272 5.7457193 5.8193455

Documents

Guidelines-no.19 Guidelines for Fatigue Strength of Ship Structure%2c 2007