Guide for ULSA of ships

A Guide for the Ultimate Longitudinal Strength Assessmentof Ships

Jeom Kee Paik1

The aim of the present paper is to establish a practical guide for the ultimate longitudinal strength assess-ment of ships The ultimate hull girder strength of a ship hull can be calculated using either the progressivecollapse analysis method or closed-form design formulas In the present paper both the progressivecollapse analysis method and the design formulas are presented A comparison between the progressivecollapse analysis results and the design formula solutions for merchant cargo ship hulls is undertaken Thetotal design (extreme) bending moment of a ship hull is estimated as the sum of the still-water andwave-induced bending moment components as usual The safety measure of a ship hull is then defined asa ratio of the ultimate longitudinal strength to the total design bending moment The developed guidelinesare applied to safety measure calculations of merchant ship hulls with respect to hull girder collapse It isconcluded that the guidance and insights developed from the present study will be very useful for theultimate limit state design of newly built ships as well as the safety measure calculations of existing shiphulls The essence of the proposed guide shall form ISO code 18072-2 Ships and Marine TechnologymdashShip StructuresmdashPart 2 Requirements of Their Ultimate Limit State Assessment

1 Introduction

DURING THE LAST FEW DECADES the emphasis in structuraldesign has been moving from the allowable (working) stressdesign to the limit state design because the latter approachhas many more advantages A limit state is formally definedas a condition for which a particular structural member or anentire structure fails to perform the function that it has beendesigned for From the special viewpoint of a structural de-signer four types of limit states are considered namely ser-viceability limit state (SLS) ultimate limit state (ULS) fa-tigue limit state (FLS) and accidental limit state (ALS) (Paikamp Thayamballi 2003)

The structural design criteria against the ULS are basedon plastic collapse or ultimate strength The design of manytypes of structures including merchant ship structures has inthe past tended to rely on estimates of the buckling strengthof components usually from their elastic buckling strengthadjusted by a simple plasticity correction This is representedby point A in Fig 1 In such a design scheme the structuraldesigner does not use detailed information on the postbuck-ling behavior of component members and their interactionsThe true ultimate strength represented by point B in Fig 1 istypically higher although one can never be sure of this

In design when the load level 2 shown in Fig 1 is appliedthe structure will be safe but if the load level 1 is applied thestructure will possibly collapse Arguably the ultimatestrength is a better basis for design but as long as thestrength level associated with point B remains unknown (asit is with traditional allowable stress design or linear elasticdesign methods) it is difficult to determine the real safetymargin Hence more recently the design of such structuresas those of navy ships as well as offshore platforms and land-based structures (eg steel bridges) has tended to be basedon the ultimate strength

The safety margin of a structure can be evaluated by a

comparison of its ultimate strength with the extreme appliedloads as depicted in Fig 1 To obtain a safe and economicstructure the ultimate load-carrying capacity as well as thedesign load must be assessed accurately The structural de-signer can perform a structural safety assessment in the pre-liminary design stage if there are simple expressions avail-able for accurately predicting the design loads loadcombinations and the ultimate strength A designer mayeven desire to do this not only for the intact structure butalso for structures with premised damage in order to assessand categorize their damage tolerance and survivability

In the present paper a guide for the ultimate longitudinalstrength assessment of ships is developed and is applied to

1 Professor of Ship Structural Mechanics Department of NavalArchitecture and Ocean Engineering Pusan National UniversityBusan Korea

Manuscript received at SNAME headquarters January 2004Fig 1 Structural design considerations based on the ultimate limit state (Paik amp

Thayamballi 2003)

Marine Technology Vol 41 No 3 July 2004 pp 122ndash139

122 JULY 2004 MARINE TECHNOLOGY0025-3316044103-0122$00000

safety measure assessment of existing merchant ship hullsagainst hull girder collapse as illustrative examples Becausethe essence of the proposed guide shall form ISO code 18072-2 Ships and Marine TechnologymdashShip StructuresndashPart 2Requirements of Their Ultimate Limit State Assessment theguide is written in a format similar to usual codes or regu-lations

2 Ultimate longitudinal strength criteriaof ships

21 Safety measure calculation

The ultimate longitudinal strengthndashbased safety measureof a ship can be calculated as follows

=Mu

Mt

where ultimate longitudinal strengthndashbased safety mea-sure Mt characteristic value of total extreme bending mo-ment Mu characteristic value of ultimate longitudinalstrength

22 Strength criterion

The safety measure defined in Section 21 should not beless than a target value involving the uncertainties associ-ated with the calculation models for Mt and Mu which mustbe greater than 10 Although the target safety measure canbe different depending on the types of ships it is often takenas 115 for newly built ships (eg NTS 1998) or 104 for agedships based on past experience the latter being equivalent to90 of newly built ships

3 Methods for calculating the ultimatebending moments

31 General

311 The ultimate bending moments of a ship in hoggingand sagging are to be calculated by the progressive collapseanalysis as will be described in Section 32 Alternativelythe ultimate strength calculations using the simplified de-sign formula defined in Section 33 may be accepted

312 In calculating ultimate bending moments of a shiphull all possible failure modes of structural componentssuch as buckling of plating between stiffeners flexural-torsional buckling (tripping) of stiffeners and buckling ofstiffener web should be accounted for

313 It is to be considered that individual structural ele-ments making up the ship hull have an average level of ini-tial imperfections in the form of initial deflection and weld-ing-induced residual stresses

314 For damaged ship hulls the effects of structural dam-ages need to be taken into account in the strength calcula-tions

32 Progressive collapse analysis

321 The aim of the progressive collapse analysis is toanalyze the detailed nonlinear response of ship structuresuntil and after the ultimate limit state is reached whichinvolves both geometric and material nonlinearities Theanalysis can be performed by either the conventional nonlin-ear finite element method or the idealized structural unitmethod (ISUM) the latter being with the analysis of largeplated structures

322 It is recommended to take the hull module betweentransverse bulkheads as the extent of the progressive col-

lapse analysis Alternatively a simpler model between thetwo adjacent transverse frames may also be adopted as longas the transverse frames are strong enough so that theywould not fail before the longitudinal members In the sim-pler model it is to be noted that transverse frame spacing ofbulk carriers may be different at deck side and bottomwhereas that of most merchant vessels is identical

323 When ISUM is employed ship structure is to be ide-alized as an assembly of plate-stiffener separation elementsas shown in Fig 2 Sample models for typical merchant ves-sel hulls between transverse frames are shown in Fig 3

324 One basic assumption of this simplified method for ahull module between the two adjacent transverse frames isthat the hull cross section remains plane up to the ultimatelimit state under bending moments To handle the conditionthat the hull cross section remains plane a displacementcontrol is usually applied so that any structural member issubjected to longitudinal axial displacement that is propor-tional to the associated member length or transverse framespacing as well as bending curvature As a result the distri-bution of longitudinal strains over the hull cross section islinear for both identical and different transverse frame spac-ing as those as long as the length of all structural members isidentical (Fig 4)

33 Simplified design formula

331 The simpler model that is a hull module between thetwo adjacent transverse frames is taken as the extent of the

Fig 2 Structural idealization as an assembly of plate-stiffener separation units

JULY 2004 MARINE TECHNOLOGY 123

simplified design formula analysis The ship hull is modeledas an assembly of plate-stiffener combination units or plate-stiffener separation units as shown in Fig 5 Sample modelsfor a double-skin tanker hull or a bulk carrier hull as anassembly of plate-stiffener combination units are shown inFig 6 and those for a double-skin tanker hull or a bulkcarrier hull as an assembly of plate-stiffener separation unitsare shown in Fig 3

332 Calculations using the plate-stiffener combina-tion models In this case the ship hull is modeled as anassembly of plate-stiffener combination units

332(a) The longitudinal bending stresses of individual

Fig 5 (Top) A typical stiffened plate structure (Middle) Plate-stiffener combina-tion units (Bottom) Plate-stiffener separation units

Fig 3 (Top two panels) A sample model of a double-hull tanker hull betweentransverse frames as an assembly of the plate-stiffener separation units (Bottomtwo panels) A sample model of a bulk carrier hull between transverse frames as an

assembly of the plate-stiffener separation units

Fig 4 (Top) Distributions of longitudinal strains and stresses for a ship hull withthe same transverse frame spacing at deck side and bottom (hogging) (Bottom)Distributions of longitudinal strains and stresses for a ship hull (eg bulk carrierhull) with different transverse frame spacing at deck side and bottom (hogging)

ULS = ultimate limit state

124 JULY 2004 MARINE TECHNOLOGY

plate-stiffener combination units are to be calculated withnegative sign in compression and positive sign in tensionuntil the tensioned flange of the hull (ie deck in hog bottomin sag) yields as follows

i =zi minus gD minus g

Yeqd for hogging

i =g minus zi

gYeqb for sagging

where i longitudinal bending stress of the ith element(see Fig 7) zi coordinate of the ith element measured fromthe base line to the deck with zi 0 at the base line g neutral axis which is given as

g = Aizi

Ai

where Ai cross-sectional area of the ith element calculatedconsidering the effective width of attached plating as will bedefined in Section 332(b) Yeqd Yeqb average equivalentyield stresses at upper deck or outer bottom panels D depth of the ship

332(b) The cross-sectional area of the units is to be calcu-lated considering the effective width of attached plating asfollows (for symbols used below see Fig 8)

A = bet + hwtw + bftf

where be effective width of attached plating which isgiven by

be = b for 1

b18

minus09

2 for 1 for compressed units

be = b for tensioned units

with b full width of attached plating

=btY

E

Y yield stress of attached plating E Youngrsquos modulus332(c) Following the concept of Fig 7 the longitudinal

bending stress value of plate-stiffener combination units de-fined in Section 332(a) should satisfy the following criterianamely

Yeq for tensioned units

u for compressed units

where Yeq equivalent yield stress which is given by

Yeq =Ybt + Yshwtw + bftf

bt + hwtw + bftf

Y Ys yield stresses of attached plating or stiffener u ultimate compressive stress of the unit as will be defined inSection 332(d)

332(d) The ultimate compressive stress of a plate-stiffener combination unit is to be calculated using the so-

Fig 6 (Top two panels) A sample model for a double-skin tanker hull as anassembly of plate-stiffener combination units (Bottom two panels) A samplemodel for a bulk carrier hull as an assembly of plate-stiffener combination units

Fig 7 Longitudinal stress distribution in a hull section at the ultimate limit stateas suggested by Paik and Mansour (1995) (Left) Sagging (Right) Hogging (Paik

amp Thayamballi 2003)


called Paik-Thayamballi formula (Paik amp Thayamballi 2003)as follows

u = minusYeq

0995 + 09362 + 01702 + 018822 minus 00674

and u Yeq

2

where Yeq as defined in Section 332(c) as defined inSection 332(b)

=a

rYeq

E

a length of the unit E Youngrsquos modulus

r = IA

A = bt + hwtw + bftf

I =bt3

12+ btzp minus

t22

+twhw

3

12+ hwtwzp minus

t2

minushw

2 2

+bftf

3

12+ bftfzp minus

t2

minus hw minustf

22

zp =05bt2 + hwtwt + 05hw + bftf t + hw + 05tf

A

333 Calculations using the plate-stiffener separationmodels In this case the ship hull is modeled as an assem-bly of plate-stiffener separation units

333(a) The longitudinal bending stresses of individualplate-stiffener separation units are again to be calculated asdescribed in Section 332(a) Cross-sectional area of eachunit will in this case be defined in Sections 333(b) and333(c)

333(b) The cross-sectional area of the plating of individualplate-stiffener separation units denoted by Ap is to be calcu-lated considering the effective width of plating as follows

Ap = bet

where be as defined in Section 332(b)333(c) The cross-sectional area of the stiffener of indi-

vidual plate-stiffener separation units denoted by As is to becalculated as follows

As = hwtw + bftf

333(d) The longitudinal bending stress value of the plate-stiffener separation units defined in Section 333(a) shouldsatisfy the following criteria namely

Y or Ys for tensioned units up or us for compressed units

where Y Ys yield stresses of plating or stiffener up us ultimate compressive stresses of the plating or stiffener ofthe unit as will be defined in Sections 333(e) and 333(f)

333(e) The ultimate compressive stress of the plating inan individual plate-stiffener separation unit is to be calcu-lated as follows

up = upl for ab 1upw for ab 1

where a length of the unit upl upw ultimate compres-sive stresses of plating for ab 1 and ab lt 1 respectivelywhich is given by

upl

Y= 00324 minus 00022 minus 10 for 15

minus1274 for 15 30minus12482 minus 0283 for 30

upw

Y=

ab

upl

Yminus

0475

2 1 minusab

where as defined in Section 332(b)

=at Y

E

with

upl

Y= 00324 minus 00022 minus 10 for 15


333(f) The ultimate compressive stress of the stiffener with-out attached plating in an individual plate-stiffener separa-tion unit is to be calculated as follows

us = minus1minuWu

T

where uW critical buckling stress of stiffener web as de-

fined in Section 333(g) uT critical flexural-torsional

buckling (tripping) stress as defined in Section 333(h)333(g) u

W is to be calculated as follows

uW =

EW for E

W 05Ys

Ys1 minusYs

4EW for E

W 05Ys

where EW is the elastic buckling stress of stiffener web

which is given by

EW = kw

2E

121 minus v2 tw

hw2

Fig 8 Typical types (flat bar angle bar and tee bar) of plate-beam combination units with theattached effective plating


and kw is the elastic buckling stress coefficient of stiffenerweb which is given by Paik and Thayamballi (2003)

kw = C1p + C2 for 0 p w

C3 minus 1C4p + C5 for w p 60C3 minus 160C4 + C5 for 60 p

for angle or T-stiffeners

kw = 0303p + 0427 for 0 p 11277 minus 1140p + 0428 for 1 p 6012652 for 60 p

for flat-bar stiffenerswith

w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f

2 + 140 for 0 f 011510f + 0860 for 01 f 10140f + 1814 for 10 f 3000724 for 30 f

C5 = minus1135f + 0428 for 0 f 02minus0299f

3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf

hwDw G = E21 + v v = Poissonrsquos ratio

Dw = Etw3121 minus v2 Jp =

01hwtw3

3 Jf =

bf tf3

3

333(h) uT is to be calculated as follows

uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys

where ET is the elastic tripping stress of stiffener as defined

in Sections 333(i) 333(j) or 333(k)333(i) For asymmetric angle stiffeners E

T is to be calcu-lated as follows (Paik amp Thayamballi 2003)

ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1

where it is approximated as be asymp 01hw and t asymp tw

C1 = 01hwtw + hwtw + bf tfIp minus Sf2

C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3

m22minus01hwtw + hwtw + bf tfGJw + Jf + EIzehw

2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2

S1 = minuszp minus hwtf bf minus 01hwtwzp minus hwtwzp minushw

2

S2 = minuszp minus hwtf hw2bf +

bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22

Ize = 01hwtwyoe2 + Awyoe

2 + Afyoe2 minus bf yoe +

bf2

3

Izye = 01hwtwzpyoe + Awzp minustw

2minus

hw

2 yoe + Afzp minustw

2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2

Aw = hwtw Af = bf tf

zp =05Awtw + hw + Af05tw + hw + 05tf

01hwtw + hwtw + bf tf

yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf

q equivalent line pressure (pbe m tripping half wavenumber of the stiffener p lateral pressure

333(j) For symmetric tee-stiffeners ET is to be calculated

as follows (Paik amp Thayamballi 2003)

ET = minus1 min

m=123hellipminusa2GJw + Jf + EIfhw

2m22

Ipa2

+qa2

12S4

IeIp1 minus

3

m22where a length of the unit

S4 = minuszpminus hwtfhw2bf +

bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12

333(k) For flat-bar stiffeners ET is to be considered equal

to EW which is defined in Section 333(g)

34 Considering the concept of Fig 7 the ultimate bendingmoment of a ship hull with positive sign for hogging andnegative sign for sagging is to be calculated as follows (Paikamp Thayamballi 2003)

Mu = iAizi minus gu

where

gu = iAizi

iAi

i as defined in Sections 332 and 333 (with negative signin the compressed part and positive sign in the tensionedpart) considering hogging or sagging condition zi Ai asdefined in Section 332

Fig 9 (Top) Mid-ship section of the Dow frigate test ship (Middle) ALPSHULLmodel for the Dow frigate test hull (Bottom) Comparison of ALPSHULL with the

Dow test results varying the level of initial imperfections

Fig 10 Schematic representation of mid-ship section of a 113000 DWT floatingproduction storage and offloading unit (FPSO)

Fig 11 Progressive collapse behavior of the floating production storage andoffloading unit (FPSO) hull under vertical moment varying the level of initial im-

perfections as obtained by ALPSHULL


Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t


Methods for calculating the designbending moments

Design bending moment calculations

The design bending moments are to be estimated in bothhogging and sagging conditions as the sum of the correspond-

ing still-water and wave-induced bending moment compo-nents as follows

Mt = Msw + Mw

where Mt total bending moment Msw Mw still-waterbending moment as defined in Section 42 and wave-inducedbending moment as defined in Section 43 respectively

Table 2 A comparison of the hull property calculations obtained by the ALPSHULL and the closed-form design formula

Item

SHT DHT1 DHT2

(a) HULL (b) DF (b)(a) (a) HULL (b) DF (b)(a) (a) HULL (b) DF (b)(a)

Cross-sectional area (m2) 7858 7907 1006 5318 5331 1002 9637 9696 1006Height to neutral axis

from baseline (m) 12173 12169 1000 9188 9103 991 12972 12909 995I (m4)

Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011

Mp (GNm)Vertical moment 22615 22842 1010 11930 11942 1001 32481 32669 1006

Bulk1 Bulk2

(a) HULL (b) DF (b)(a) (a) HULL (b) DF (b)(a)

Cross-sectional area (m2) 5652 5671 1003 5786 5778 999Height to neutral axis

from baseline (m) 11188 11257 1006 10057 10093 1004I (m4)

Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007

Mp (GNm)Vertical moment 20650 21280 1031 15857 16081 1014

Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006


DF design formula ultimate hull girder strength obtained by the design formulas FPSO floating production storage and offloadingunit HULL ultimate hull girder strengths with average level of initial imperfections obtained by ALPSHULL


42(a) Msw is taken as the maximum value of the still-waterbending moment resulting from the worst load condition forthe ship considering both hogging and sagging The relateddetailed distribution of the still-water moment along the

shiprsquos length can be calculated by a double integration of thedifference between the weight force and the buoyancy forceusing the simple beam theory

42(b) For convenience the mean value of Msw may be

Table 3 A comparison of the ultimate hull girder strength calculations obtained bythe ALPSHULL and the closed-form design formula

Mu (GNm) (a) HULLSlight (b) HULLAverage (c) DF (c)(a) (c)(b)

SHTSag minus17508 minus16767 minus17921 1024 1069Hog 16626 15826 18457 1110 1166

DHT1Sag minus7949 minus6899 minus7848 987 1138Hog 9303 8485 8531 917 1005


Bulk1Sag minus15293 minus14281 minus14205 929 995Hog 16601 14434 15534 936 1076


Cont1Sag minus6965 minus6800 minus6684 960 983Hog 6793 5953 5501 810 924



FPSOSag minus8500 minus7282 minus8274 973 1136Hog 9654 8760 8566 887 978

ShuttleSag minus11760 minus11280 minus11638 990 1032Hog 12431 11404 11477 923 1006

Mean 963 1041COV 70 64

COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and offloading unit HULLSlight HULLAverage ultimate hull girderstrengths with slight or average level of initial imperfections obtained byALPSHULL

Table 4 Hull sectional properties of the existing double-hull tankers

Item DHT3 DHT4 DHT5 DHT6 DHT7 DHT8 DHT9 DHT10 DHT11

LBP (L m) 32000 31400 31500 26000 23800 23400 23300 17000 15200Breadth (B m) 5800 5800 5720 4600 4500 4200 4200 3000 2680Depth (D m) 3100 3100 3040 2330 2340 2100 2130 1620 1150Draft (d m) 2200 2220 2045 1560 1740 1430 1470 1020 700Block coefficient (Cb) 08135 08258 08408 08163 08072 08130 08232 08088 07983Design speed (knots) 1560 1500 1510 1500 1400 1440 1700 1450 1360DWT 300000 300000 278000 135000 125000 100000 105000 357000 175000Cross-sectional area (m2) 10401 10194 7524 6389 4800 5199 5309 2868 2128Height to neutral axis


Vertical 1406249 1403493 1122722 528777 425359 359272 360441 119728 47835Horizontal 4124232 4037184 2913590 1621094 1213897 1100777 1146983 326185 174565

Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804

YDeck HT32 HT32 HT36 HT32 HT32 HT32 HT32 MILD HT32Bottom HT32 HT32 HT36 HT32 HT32 MILD HT32 HT32 HT32



taken from an empirical formula that has been suggested fora first-cut estimation of the maximum allowable still-waterbending moment by some classification societies in the pastThat approximate formula amidships is given by (with posi-tive in hogging and negative in sagging)

Msw = minus 0065CL2BCb + 07 kNm) for sagging

+0015CL2B8167 minus Cb kNm) for hogging

where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

with L ship length (m) B ship breadth (m) Cb blockcoefficient at summer load waterline

43(a) For newly built ships Mw may be taken as the meanvalue of the extreme wave-induced bending moment whichthe ship is likely to encounter during its lifetime which isgiven amidships for unrestricted worldwide service by theInternational Association of Classification Societies (IACS)as follows (with positive in hogging and negative in sagging)

Mw = +019CL2BCb (kNm) for hogging

minus011CL2B(Cb + 07) (kNm) for sagging

where C L B Cb as defined in Section 32

43(b) For damaged ships a short-term analysis is to beundertaken considering specific sea states and operating con-ditions (significant wave height ship operating speed andsea-state persistence time) which are involved in the ship tobe assessed (Paik amp Thayamballi 2003) For this purpose theUSAS-L program which can be downloaded from httpssmlnaoepusanackr can be used

Application examples

The application examples illustrating the advantages ofthe guide developed in the present paper are now demon-strated USAS-L is used for calculating the still-water andwave-induced bending moment components and their sum asthe total bending moment based on the IACS design formu-lations USAS-L also calculates the wave-induced bendingmoment components based on a short-term response analysisinvolving the specific operating conditions and sea statesThe USAS-S program computes the ultimate hull girderstrengths of ships using the closed-form design formulasALPSHULL is a computer program for the progressive col-lapse analysis until and after a ship hull reaches the ultimatestrength

51 Progressive collapse analyses using ALPSHULL

ALPSHULL (Paik 2003) is a special purpose computerprogram for the progressive collapse analysis of ship hulls Itis based on the idealized structural unit method (ISUM)(Paik amp Thayamballi 2003) ALPS stands for nonlinearanalysis of large plated structures For the safety measureassessment it is essential to calculate the ultimate hullgirder strength of a ship hull accurately

Figure 9 shows a selected ALPSHULL comparison resultfor test models which pertain to the experiment of Dow(1991) who tested the 13 scale frigate hull model in saggingThe ALPSHULL model extends between web frames Al-though it would be more relevant to take the hull modulebetween transverse bulkheads as the extent of the analysisthe present simpler model between web frames may also beappropriate as long as the transverse frames are strongenough so that they would not fail before the longitudinalmembers

Figure 9 (bottom) shows the progressive collapse behaviorof the Dow test structure under sagging or hogging momentas obtained by ALPSHULL The Dow test result for saggingis also plotted In the ALPSHULL computations the mag-nitude of initial imperfections is varied Figure 9 (bottom)also plots the results of Yao et al (2000) as obtained using theso-called Smith method which models the structure as anassembly of only the plate-stiffener combinations It is seenfrom Fig 9 (bottom) that ALPSHULL provides quite accu-rate results when compared with the experiment Of interestthe computing time used was 2 minutes for the ALPSHULLanalysis using a Pentium III personal computer

As another example a 113000 DWT floating productionstorage and off-loading unit (FPSO) hull is now analyzedusing ALPSHULL Figure 10 shows a schematic of the mid-ship of the vessel In the ALPSHULL calculations it is con-sidered that individual structural units have fabrication-related initial imperfections (weld distortions and residualstresses) The longitudinal stiffeners have initial imperfec-tions which are considered to be wosx 00015a and rsx0where wosx maximum initial deflection of longitudinalstiffeners a length of the stiffener rsx residual stressof the stiffener For plating between longitudinal stiffenersthe level of initial imperfections is varied at the two types(ldquoslightrdquo and ldquoaveragerdquo levels) suggested by Smith et al(1988) as follows

Table 5 The computed ultimate hull girder strengths of the existingdouble-hull tankers

Mu (GNm) (a) HULLAverage (b) DF (b)(a)

DHT3Sag minus18384 minus19852 1080Hog 22299 20915 938









Mean 1000COV 74

COV coefficient of variation DF ultimate hull girder strengthobtained by the design formula HULLAverage ultimate hull girderstrength with average level of initial imperfections obtained byALPSHULL


Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4


bull Slight level wopl 00252t rcx minus005Ybull Average level wopl = 012t rcx minus015Y

In the ALPSHULL computations deck or bottom stiffenedpanels as well as vertical members (ie side shells and lon-gitudinal bulkheads) are modeled by the plate-stiffener sepa-ration models as assemblies of the ISUM rectangular plateunits and the ISUM beam-column units the latter beingused without attached plating as shown in Fig 5 (bottom)This modeling method more accurately represents the verti-cal bending stress distribution at vertical members or hori-zontal bending stress distribution at horizontal members(ie deck or bottom panels) whereas plating between longi-tudinal support members in typical merchant ship structuresmay normally not fail before longitudinal support members

Figure 11 represents the progressive collapse behavior ofthe considered ship hull under vertical hogging or saggingmoment varying the level of initial imperfections Some se-lected typical failure events are represented in the figuresFigure 11 shows that the collapse of the compression flangeof the tanker hulls takes place before the yielding of the ten-sion flange as in the design of usual ship structures Theinitial imperfections significantly affect the progressive col-lapse behavior of the ship hulls Also there is still some re-sidual strength even after buckling collapse of the compres-sion flange This is due to a shift of the neutral axis towardthe tension flange resulting from loss of effectiveness of thecollapsed compression flange

52 Ultimate hull girder strength calculations by thedesign formulas using the plate-stiffenercombination models

The accuracy of the ultimate hull girder strength designformulas when a ship hull is modeled as an assembly of theplate-stiffener combination units is checked by comparingwith the results obtained by the progressive collapse analy-ses using ALPSHULL It is noted that the ship hull is mod-eled as an assembly of the plate-stiffener separation modelsfor the ALPSHULL progressive collapse analyses

A total of the 10 typical merchant ships are considered asindicated in Table 1 The vessels considered herein are hy-pothetical although they have of course been designed fol-

Table 7 The computed ultimate hull girder strengths of the existingbulk carriers

Mu (GNm) (a) HULLAverage (b) SM (b)(a)

Bulk3Sag minus16338 minus17602 1077Hog 16599 15243 918












Mean 970COV 64


Table 8 Hull sectional properties of the existing container vessels

Item Cont4 Cont5 Cont6 Cont7 Cont8 Cont9 Cont10 Cont11 Cont12

LBP (L M) 29200 27700 26520 26300 26300 22400 17250 13200 11900Breadth (B m) 4000 3220 4030 4000 3710 3200 3020 2050 2000Depth (D m) 2420 2150 2410 2420 2170 1900 1640 1050 1070Draft (d m) 1400 1300 1400 1400 1360 1170 1050 735 740Block coefficient (Cb) 06410 06933 06108 06030 06096 06560 05999 06940 06957Design speed (knots) 2680 2400 2880 2820 2630 2220 2330 1750 1650TEU 6500 4024 5000 5550 4400 2700 2200 700 700Cross-sectional

area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473

Height to neutral axisfrom baseline (m)

12327 10331 10534 10887 9970 8248 6184 4252 4252

I (m4)Vertical 630496 312112 489533 472630 345418 195481 100394 23996 23996Horizontal 1584921 738743 1408825 1279941 989130 563300 353564 82768 82768

Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643

YDeck HT36 HT36 HT32 HT36 HT36 HT36 HT32 HT36 HT32Bottom HT32 HT32 HT32 HT32 HT32 HT32 MILD MILD MILD



lowing the rules of the classification societies Section 53 willdeal with real existing vessels Tables 2 and 3 represent thecomputed ultimate hull girder strengths

Figure 12 plots the correlation between ALPSHULL re-sults and the design formula predictions of the ultimatebending moments for 10 typical commercial ships The meanand coefficient of variation of the present closed-form expres-sion predictions against the ALPSHULL progressive col-lapse analyses for ship hulls considering both slight and av-erage levels of initial imperfections are 1002 and 0077respectively

53 Ultimate hull girder strength calculations by thedesign formulas using the plate-stiffenerseparation models

Some comparisons between the ALPSHULL progressivecollapse analyses and the design formula solutions for a totalof the 30 vessels (9 double-hull tankers 12 bulk carriers and9 container vessels) are now made when the ship hulls aremodeled as assemblies of the plate-stiffener separation mod-els for the use of both ALPSHULL and design formulas Thevessels considered herein are real existing ones

Tables 4 to 9 represent the sectional properties and thecomputed ultimate hull girder strengths for the double-hulltankers bulk carriers and container vessels consideredherein Figures 13 to 15 show correlation between ALPSHULL results and design formula solutions for the double-hull tankers bulk carriers and container vessels consideredherein Figure 16 shows correlation between ALPSHULLresults and design formula solutions for all 30 ships FromFigs 12 to 16 it is surmised that the design formula solu-

Table 9 The computed ultimate hull girder strengths of the existingcontainer vessels


Cont4Sag minus17085 minus15786 924Hog 12667 13281 1048









Mean 975COV 44


Fig 12 (Top) Correlation between ALPSHULL progressive collapse analysesand the closed-form design formula predictions for a slight level of initial imper-fections (Middle) Correlation between ALPSHULL progressive collapse analysesand the closed-form design formula predictions for an average level of initial im-perfections (Bottom) Correlation between ALPSHULL progressive collapseanalyses and the closed-form design formula predictions varying the level of initial

imperfections FPSO = floating production storage and offloading unit


tions obtained by the plate-stiffener separation models aremore accurate than those obtained by the plate-combinationmodels that is showing similar features in the ALPSHULLprogressive collapse analyses

54 Safety measure calculations for ship hulls

The safety measure calculations for ship hulls under ver-tical bending moments are now undertaken following theprocedure described in Section 21 Both hypothetical andexisting vessels previously analyzed are considered In thisassessment is adopted the ALPSHULL progressive col-lapse analysis method to determine the ultimate hull girderstrengths

Tables 10 to 13 indicate the results of the safety measurecalculations of the ships It is seen from Tables 10 to 13 thatall vessels considered satisfy the class rule requirements interms of longitudinal strength because the section modulusZ is greater than the minimum required section modulusZmin in both sagging and hogging However it is consideredthat the ultimate limit state (ULS)ndashbased safety measure isnot enough for some vessels For instance the ULS-basedsafety measure of a typical double-hull tanker (DHT1) is1106 in sagging which is smaller than 115 as a requiredsafety measure for newly built ships previously defined inSection 22 This happens in most existing double-hull tank-ers and some existing bulk carriers in sagging

Traditionally the safety measure with respect to longitu-

Fig 13 Correlation between ALPSHULL progressive collapse analyses and thedesign formula predictions for the existing double-hull tankers

Fig 14 Correlation between ALPSHULL progressive collapse analyses and thedesign formula predictions for the existing bulk carriers

Fig 15 Correlation between ALPSHULL progressive collapse analyses and theclosed-form design formula predictions for the existing container vessels

Fig 16 Correlation between ALPSHULL progressive collapse analyses and theclosed-form design formula predictions for all 30 existing vessels considered


dinal strength of ships has been based on the section modu-lus In this case the safety measure may be defined as a ratioof the section modulus to the minimum required sectionmodulus namely ZZmin Figures 17 and 18 compare theULS-based safety measure calculations that is MuMtwith the section modulusndashbased safety measure calculationsIn this comparison the shiprsquos longitudinal strength was con-sidered only amidships

It is evident from Figs 17 and 18 that the section modulusndashbased safety measure does not correlate well with the ULS-based safety measure It is not surprising that the sectionmodulusndashbased approach evaluates the shiprsquos longitudinalstrength optimistically in some cases but pessimistically in

the other cases providing inconsistent level of safety Theinconsistency of the safety measure calculations by the tra-ditional approach is seen to be more serious for containervessels and some very large bulk carriers

Concluding remarks

In the present paper a guide for the ultimate longitudinalstrength assessment of ships was established The ultimatehull girder strengths of ships can be calculated by either theprogressive collapse analysis or the closed-form design for-mulations An elaborate description for calculating both theultimate hull girder strengths and the total bending mo-ments is made in the present study A comparison of theultimate hull girder strengths obtained by the progressivecollapse analysis and the design formulas is made for the 40existing ships

From the present study it is apparent that the safety mea-sure calculations by the traditional method based on the sec-tion modulus do not correlate well with those by the ULS-based method The former method optimistically evaluatesthe shiprsquos longitudinal strength in some cases but pessimis-tically in the other cases providing an inconsistent level ofsafety This indicates the disadvantage of the traditionalstructural design procedures for ships based on the allowablestress andor the sectional moduli The ultimate limit statedesign procedure can avoid such a problem because it caneasily determine the real safety margin of any economicallydesigned structure

It is concluded that the guide and insights developed in thepresent study will be very useful for the ultimate longitudi-nal strength design of ship hulls and also for condition as-sessment of existing ship hulls

Acknowledgments

Part of the present study was undertaken with supportfrom the Korean Register of Shipping (KRS) the American

Table 10 Safety measure calculations for the 10 typical vessels

Item SHT DHT1 DHT2 Bulk1 Bulk2 Cont1 Cont2 Cont3 FPSO Shuttle

Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175

Zmin (m3)Deck 60699 27814 73494 44040 38950 17252 26327 44042 26991 36992Bottom 60699 27814 73494 50516 42196 18689 28521 47712 26991 36992

ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329

Msw (GNm)Sag minus5058 minus2318 minus6125 minus4210 minus3516 minus1557 minus2377 minus3976 minus2249 minus3083Hog 5584 2559 6185 4673 3868 1943 3162 5107 2488 3409

Mw (GNm)Sag minus8560 minus3923 minus10365 minus7124 minus5951 minus2636 minus4022 minus6729 minus3806 minus5217Hog 8034 3682 9674 6661 5599 2250 3237 5597 3568 4891

Mt (GNm)Sag minus13618 minus6240 minus16489 minus11334 minus9467 minus4193 minus6399 minus10705 minus6056 minus8300Hog 13618 6240 16489 11334 9467 4193 6399 10705 6056 8300

Mu (GNm)Sag minus16767 minus6899 minus19136 minus14281 minus12165 minus6800 minus9571 minus16599 minus7282 minus11280Hog 15826 8485 23566 14434 12027 5953 9049 13075 8760 11404

MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374

Zmin minimum required section modulus specified by IACS Mt = Msw + Mw Mu ultimate vertical moment of ship hulls with averagelevel of initial imperfections but without structural damage as obtained by ALPSHULL FPSO floating production storage andoffloading unit

Fig 17 The section modulusndashbased safety measure versus the ultimate limitstatendashbased safety measure for the 10 hypothetical ships considered FPSO =

floating production storage and offloading unit ULS = ultimate limit state


Table 11 Safety measure calculations for the 9 existing double-hull tankers


Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804

Zmin (m3)Deck 73416 71600 65971 37514 30038 27018 26931 11844 6315Bottom 73416 71600 65971 37514 30038 34638 26931 9238 6315

ZZminDeck 1089 1116 1044 1080 1090 1124 1114 1125 1249Bottom 1427 1458 1207 1410 1361 1131 1442 1797 1394

Mt (GNm)Sag minus17946 minus17930 minus16745 minus9092 minus7344 minus6816 minus6730 minus2331 minus1769Hog 17946 17930 16745 9092 7344 6816 6730 2331 1769

Mu (GNm)Sag minus18384 minus18369 minus17104 minus9858 minus7349 minus7114 minus6928 minus2747 minus1793Hog 22299 24129 19421 12069 8758 7990 8402 3332 1937

MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095

Zmin minimum required section modulus specified by IACS Mt Msw + Mw Mu ultimate vertical moment of ship hulls with averagelevel of initial imperfections but without structural damage as obtained by ALPSHULL

Table 12 Safety measure calculations for the 12 existing bulk carriers

Item Bulk3 Bulk4 Bulk5 Bulk6 Bulk7 Bulk8 Bulk9 Bulk10 Bulk11 Bulk12 Bulk13 Bulk14

Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560

Zmin (m3)Deck 52581 52269 52330 33555 29801 16137 16486 16140 11207 9490 7122 6826Bottom 52581 56625 52330 36352 32285 17482 17860 17486 11207 9490 9892 6826

ZZminDeck 1008 1030 0998 0994 1011 1004 0989 1025 1199 0985 1131 1091Bottom 1172 1110 1135 1206 1221 1343 1323 1341 1731 1310 1248 1693

Mt (GNm)Sag minus12880 minus13084 minus12690 minus8108 minus7323 minus3937 minus3962 minus4019 minus2351 minus1635 minus1958 minus1671Hog 12880 13084 12690 8108 7323 3937 3962 4019 2351 1635 1958 1671

Mu (GNm)Sag minus16338 minus16667 minus16140 minus9782 minus8706 minus4331 minus4236 minus4659 minus2896 minus2024 minus2361 minus1836Hog 16599 16400 15176 10645 9362 5451 5514 5493 3448 2303 2451 2517

MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506

Zmin minimum required section modulus specified by IACS Mt = Msw + Mw Mu ultimate vertical moment of ship hulls with averagelevel of initial imperfections but without structural damage as obtained by ALPSHULL

Table 13 Safety measure calculations for the 9 existing container vessels

Item Con4 Con5 Con6 Con7 Con8 Con9 Con10 Con11 Con12

Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460



Bureau of shipping and the Korea Ministry of CommerceIndustry and Energy The author is pleased to acknowledgetheir support Also Dr C W Kim and Mr S J Hong of KRSand Dr B J Kim of Virginia Tech are appreciated for theirefforts regarding ALPSHULL and USAS calculations

ReferencesDOW R S 1991 Testing and analysis of 13-scale welded steel frigate

model Proceedings International Conference on Advances in MarineStructures May 21ndash24 Dunfermline Scotland 749ndash773

NTS 1998 Design of Steel Structures N-004 Norwegian TechnologyStandards Institution Oslo

PAIK J K 2003 ALPSHULL Userrsquos Manual A Computer Program forthe Progressive Collapse Analysis of Ship Hulls Ship Structural Mechan-ics Laboratory Pusan National University Busan Korea

PAIK J K AND MANSOUR A E 1995 A simple formulation for predict-ing the ultimate strength of ships Journal of Marine Science and Tech-nology 1 1 52ndash62

PAIK J K AND THAYAMBALLI A K 2003 Ultimate limit state design ofsteel-plated structures John Wiley amp Sons Chichester UK

SMITH C S DAVIDSON P C CHAPMAN J C AND DOWLING P J 1988Strength and stiffness of shiprsquos plating under in-plane compression andtension RINA Transactions 130 277ndash296

YAO T ASTRUP O C CARIDIS P CHEN Y N CHO S R DOW R SNIHO O AND RIGO P 2000 Ultimate Hull Girder Strength Report ofSpecial Task Committee VI2 International Ship and Offshore Struc-tures Congress Nagasaki Japan October vol 2 321ndash391

Fig 18 The section modulusndashbased safety measure versus the ultimate limit state (ULS)ndashbased safety measure for (top left) the 9 existing double-hull tankersconsidered (top right) the 12 existing bulk carriers considered (bottom left) the 9 existing container vessels considered and (bottom right) all 30 existing vessels

considered


safety measure assessment of existing merchant ship hullsagainst hull girder collapse as illustrative examples Becausethe essence of the proposed guide shall form ISO code 18072-2 Ships and Marine TechnologymdashShip StructuresndashPart 2Requirements of Their Ultimate Limit State Assessment theguide is written in a format similar to usual codes or regu-lations

2 Ultimate longitudinal strength criteriaof ships

21 Safety measure calculation

The ultimate longitudinal strengthndashbased safety measureof a ship can be calculated as follows

=Mu

Mt

where ultimate longitudinal strengthndashbased safety mea-sure Mt characteristic value of total extreme bending mo-ment Mu characteristic value of ultimate longitudinalstrength

22 Strength criterion

The safety measure defined in Section 21 should not beless than a target value involving the uncertainties associ-ated with the calculation models for Mt and Mu which mustbe greater than 10 Although the target safety measure canbe different depending on the types of ships it is often takenas 115 for newly built ships (eg NTS 1998) or 104 for agedships based on past experience the latter being equivalent to90 of newly built ships

3 Methods for calculating the ultimatebending moments

31 General

311 The ultimate bending moments of a ship in hoggingand sagging are to be calculated by the progressive collapseanalysis as will be described in Section 32 Alternativelythe ultimate strength calculations using the simplified de-sign formula defined in Section 33 may be accepted

312 In calculating ultimate bending moments of a shiphull all possible failure modes of structural componentssuch as buckling of plating between stiffeners flexural-torsional buckling (tripping) of stiffeners and buckling ofstiffener web should be accounted for

313 It is to be considered that individual structural ele-ments making up the ship hull have an average level of ini-tial imperfections in the form of initial deflection and weld-ing-induced residual stresses

314 For damaged ship hulls the effects of structural dam-ages need to be taken into account in the strength calcula-tions

32 Progressive collapse analysis

321 The aim of the progressive collapse analysis is toanalyze the detailed nonlinear response of ship structuresuntil and after the ultimate limit state is reached whichinvolves both geometric and material nonlinearities Theanalysis can be performed by either the conventional nonlin-ear finite element method or the idealized structural unitmethod (ISUM) the latter being with the analysis of largeplated structures

322 It is recommended to take the hull module betweentransverse bulkheads as the extent of the progressive col-

lapse analysis Alternatively a simpler model between thetwo adjacent transverse frames may also be adopted as longas the transverse frames are strong enough so that theywould not fail before the longitudinal members In the sim-pler model it is to be noted that transverse frame spacing ofbulk carriers may be different at deck side and bottomwhereas that of most merchant vessels is identical

323 When ISUM is employed ship structure is to be ide-alized as an assembly of plate-stiffener separation elementsas shown in Fig 2 Sample models for typical merchant ves-sel hulls between transverse frames are shown in Fig 3

324 One basic assumption of this simplified method for ahull module between the two adjacent transverse frames isthat the hull cross section remains plane up to the ultimatelimit state under bending moments To handle the conditionthat the hull cross section remains plane a displacementcontrol is usually applied so that any structural member issubjected to longitudinal axial displacement that is propor-tional to the associated member length or transverse framespacing as well as bending curvature As a result the distri-bution of longitudinal strains over the hull cross section islinear for both identical and different transverse frame spac-ing as those as long as the length of all structural members isidentical (Fig 4)

33 Simplified design formula

331 The simpler model that is a hull module between thetwo adjacent transverse frames is taken as the extent of the

Fig 2 Structural idealization as an assembly of plate-stiffener separation units













Yeqd for hogging

i =g minus zi

gYeqb for sagging


g = Aizi

Ai





be = b for 1

b18

minus09




=btY

E







bt + hwtw + bftf








u = minusYeq

0995 + 09362 + 01702 + 018822 minus 00674

and u Yeq

2


=a

rYeq

E


r = IA


I =bt3

12+ btzp minus

t22

+twhw

3

12+ hwtwzp minus

t2

minushw

2 2

+bftf

3

12+ bftfzp minus

t2

minus hw minustf

22


A




Ap = bet



As = hwtw + bftf







upl

Y= 00324 minus 00022 minus 10 for 15


upw

Y=

ab

upl

Yminus

0475

2 1 minusab


=at Y

E

with

upl

Y= 00324 minus 00022 minus 10 for 15



us = minus1minuWu

T





uW =

EW for E

W 05Ys

Ys1 minusYs

4EW for E

W 05Ys


which is given by

EW = kw

2E

121 minus v2 tw

hw2









w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f



3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf



01hwtw3

3 Jf =

bf tf3

3


uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys




ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1



C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3


2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2


2


bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22



bf2

3


2minus

hw


2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2




yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf




ET = minus1 min


2m22

Ipa2

+qa2

12S4

IeIp1 minus

3



bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered













Yeqd for hogging

i =g minus zi

gYeqb for sagging


g = Aizi

Ai





be = b for 1

b18

minus09




=btY

E







bt + hwtw + bftf








u = minusYeq

0995 + 09362 + 01702 + 018822 minus 00674

and u Yeq

2


=a

rYeq

E


r = IA


I =bt3

12+ btzp minus

t22

+twhw

3

12+ hwtwzp minus

t2

minushw

2 2

+bftf

3

12+ bftfzp minus

t2

minus hw minustf

22


A




Ap = bet



As = hwtw + bftf







upl

Y= 00324 minus 00022 minus 10 for 15


upw

Y=

ab

upl

Yminus

0475

2 1 minusab


=at Y

E

with

upl

Y= 00324 minus 00022 minus 10 for 15



us = minus1minuWu

T





uW =

EW for E

W 05Ys

Ys1 minusYs

4EW for E

W 05Ys


which is given by

EW = kw

2E

121 minus v2 tw

hw2









w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f



3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf



01hwtw3

3 Jf =

bf tf3

3


uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys




ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1



C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3


2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2


2


bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22



bf2

3


2minus

hw


2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2




yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf




ET = minus1 min


2m22

Ipa2

+qa2

12S4

IeIp1 minus

3



bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered




Yeqd for hogging

i =g minus zi

gYeqb for sagging


g = Aizi

Ai





be = b for 1

b18

minus09




=btY

E







bt + hwtw + bftf








u = minusYeq

0995 + 09362 + 01702 + 018822 minus 00674

and u Yeq

2


=a

rYeq

E


r = IA


I =bt3

12+ btzp minus

t22

+twhw

3

12+ hwtwzp minus

t2

minushw

2 2

+bftf

3

12+ bftfzp minus

t2

minus hw minustf

22


A




Ap = bet



As = hwtw + bftf







upl

Y= 00324 minus 00022 minus 10 for 15


upw

Y=

ab

upl

Yminus

0475

2 1 minusab


=at Y

E

with

upl

Y= 00324 minus 00022 minus 10 for 15



us = minus1minuWu

T





uW =

EW for E

W 05Ys

Ys1 minusYs

4EW for E

W 05Ys


which is given by

EW = kw

2E

121 minus v2 tw

hw2









w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f



3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf



01hwtw3

3 Jf =

bf tf3

3


uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys




ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1



C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3


2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2


2


bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22



bf2

3


2minus

hw


2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2




yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf




ET = minus1 min


2m22

Ipa2

+qa2

12S4

IeIp1 minus

3



bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered



u = minusYeq

0995 + 09362 + 01702 + 018822 minus 00674

and u Yeq

2


=a

rYeq

E


r = IA


I =bt3

12+ btzp minus

t22

+twhw

3

12+ hwtwzp minus

t2

minushw

2 2

+bftf

3

12+ bftfzp minus

t2

minus hw minustf

22


A




Ap = bet



As = hwtw + bftf







upl

Y= 00324 minus 00022 minus 10 for 15


upw

Y=

ab

upl

Yminus

0475

2 1 minusab


=at Y

E

with

upl

Y= 00324 minus 00022 minus 10 for 15



us = minus1minuWu

T





uW =

EW for E

W 05Ys

Ys1 minusYs

4EW for E

W 05Ys


which is given by

EW = kw

2E

121 minus v2 tw

hw2









w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f



3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf



01hwtw3

3 Jf =

bf tf3

3


uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys




ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1



C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3


2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2


2


bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22



bf2

3


2minus

hw


2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2




yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf




ET = minus1 min


2m22

Ipa2

+qa2

12S4

IeIp1 minus

3



bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered








w = minus0444f2 + 3333f + 10

C1 = minus0001f + 0303

C2 = 0308f + 0427

C3 = minus4350f

2 + 3965f + 1277 for 0 f 02minus0427f

2 + 2267f + 1460 for 02 f 15minus0133f

2 + 1567f + 1850 for 15 f 305354 for 30 f

C4 = minus670f



3 + 0803f2 minus 0783f + 0328 for 02 f 10

minus0016f3 + 0117f

2 minus 0285f + 0235 for 10 f 300001 for 30 f

p =GJp

hwDw f =

GJf



01hwtw3

3 Jf =

bf tf3

3


uT =

ET for E

T 05Ys

Ys1 minusYs

4ET for E

T 05Ys




ET = min

m=123hellipC2 + C2

2 minus 4C1C3

2C1



C2 = minusIpEIem

a 2

minusqa2

12S1

Ie1 minus

3


2m

a 2

minusqa2

12S2

Ie1 minus

3

m22 + 2SfEIzyehwm

a 2

minusqa12

S3

Ie1 minus

3

m22

C3 = EIcm

a 2

minusqa2

12S1

Ie1 minus

3

m22GJw + Jf

+ EIzehw2m

a 2

minusqa2

12S2

Ie1 minus

3

m22minus EIzyehwm

a 2

minusqa2

12S3

Ie1 minus

3

m222

Sf = minustf bf

2

2


2


bf3

3 minus hw3tw1

3zp minus

hw

4

S3 = zp minus hwbf

2tf

2

Ie =01hwtw

3

12+ 01hwtwzp

2 +twhw

3

12+ Awzp minus

tw

2minus

hw

2 2

+bf tf

3

12+ Af zp minus

tw

2minus hw minus

tf

22



bf2

3


2minus

hw


2minus hw minus

tf

2yoe minus

bf

2

Ip =twhw

3

3+

tw3hw

3+

bf3tf

3+

bf tf3

3+ Af hw

2




yoe =bf

2tf


Jw =13

tw3hw1 minus

192

5

tw

hw

n=135

1

n5tanhnhw

2tw

Jf =13tf

3bf1 minus192

5

tf

bf

n=135

1

n5tanhnbf

2tf




ET = minus1 min


2m22

Ipa2

+qa2

12S4

IeIp1 minus

3



bf3

12 minus hw3tw1

3zp minus

hw

4


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered


Ip =twhw

3

3+

tw3hw

12+

bf tf3

3+

bf3tf

12+ Afhw

2

If =bf

3tf

12




Mu = iAizi minus gu

where

gu = iAizi

iAi








Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered


Tab

le1

Hu

llse

ctio

nal

pro

per

ties

of

the

typ

ical

ship

s

Item

SH

TD

HT

1D

HT

2B

ulk

1B

ulk

2C

ont

1C

ont

2C

ont

3F

PS

OS

hu

ttle

LB

P(L

)31

30

m23

30

m31

50

m28

20

m27

30

m23

00

m25

80

m30

50

m23

06

m25

40

mB

read

th(B

)48

2m

420

m58

0m

500

m44

5m

322

m40

0m

453

m41

8m

460

mD

epth

(D)

252

m21

3m

303

m26

7m

230

m21

5m

242

m27

0m

229

m22

6m

Dra

ft(d

)19

0m

122

m22

0m

193

m15

0m

125

m12

7m

135

m14

15

m15

0m

Blo

ckco

effi

cien

t(C

b)

083

30

833

082

30

826

083

740

6839

061

070

6503

083

050

831

Des

ign

spee

d15

0kn

ots

162

5kn

ots

155

knot

s15

15

knot

s15

9kn

ots

249

knot

s26

3kn

ots

266

knot

s15

4kn

ots

157

knot

sD

WT

orT

EU

254

000

DW

T10

500

0D

WT

313

000

DW

T17

000

0D

WT

169

000

DW

T3

500

TE

U5

500

TE

U9

000

TE

U11

300

0D

WT

165

000

DW

TC

ross

-sec

tion

alar

ea7

858

m2

531

8m

29

637

m2

565

2m

25

786

m2

384

4m

24

933

m2

619

0m

24

884

m2

683

2m

2

Hei

ght

tone

utra

lax

isfr

omba

selin

e

121

73m

918

8m

129

72m

111

88m

100

57m

872

4m

927

0m

116

14m

102

19m

105

68m

IV

erti

cal

863

693

m4

359

480

m4

134

609

7m

469

430

7m

450

831

7m

423

753

9m

439

764

7m

468

275

6m

439

362

5m

451

967

4m

4

Hor

izon

tal

205

044

3m

41

152

515

m4

385

564

1m

41

787

590

m4

153

095

4m

464

852

2m

41

274

602

m4

212

031

1m

41

038

705

m4

165

147

9m

4

ZD

eck

663

01m

329

679

m3

772

36m

344

354

m3

392

74m

318

334

m3

266

35m

344

376

m3

310

40m

343

191

m3

Bot

tom

709

50m

339

126

m3

103

773

m3

620

58m

350

544

m3

272

28m

342

894

m3

587

85m

338

520

m3

491

75m

3

YD

eck

HT

32H

T32

HT

32H

T40

HT

36H

T36

HT

36H

T36

HT

32H

T32

Bot

tom

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

HT

32H

T32

Mp V

erti

cal

mom

ent

226

15G

Nm

119

30G

Nm

324

81G

Nm

206

50G

Nm

158

57G

Nm

888

1G

Nm

121

79G

Nm

189

76G

Nm

124

51G

Nm

156

69G

Nm

Hor

izon

tal

mom

ent

312

02G

Nm

191

38G

Nm

544

65G

Nm

318

67G

Nm

267

14G

Nm

149

67G

Nm

217

63G

Nm

332

29G

Nm

190

30G

Nm

251

05G

Nm

I

mom

ent

ofin

erti

aZ

se

ctio

nm

odu

lus

Y

yi

eld

stre

ss

Mp

fu

lly

plas

tic

ben

din

gm

omen

t






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered






Mt = Msw + Mw



Item

SHT DHT1 DHT2




Vertical 863693 870490 1008 359480 360160 1002 1346097 1354800 1006Z (m3)

Deck 66301 66803 1008 29679 29527 995 77236 77457 1003Bottom 70950 71531 1008 39126 39567 1011 103773 104950 1011


Bulk1 Bulk2




Vertical 694307 715210 1030 508317 513750 1011Z (m3)

Deck 44354 45892 1035 39274 39805 1014Bottom 62058 63533 1024 50544 50902 1007


Cont1 Cont2 Cont3




Vertical 237539 232120 977 397647 402440 1012 682756 691580 1013Z (m3)

Deck 18334 17866 974 26635 27303 1025 44376 45551 1026Bottom 27228 26720 981 42894 42540 992 58785 58523 996


FPSO Shuttle Tanker




Vertical 393625 395080 1004 519674 522000 1004Z (m3)

Deck 31040 31202 1005 43191 43321 1003Bottom 38520 38590 1002 49175 49477 1006



















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered

















Mean 963 1041COV 70 64







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804







where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered





where

C = 00792L for L 90

1075 minus 300 minus L100 15

for 90 lt L 300

1075 for 300 lt L 350

1075 minus L minus 350150 15

for 350 lt L 500

























Mean 1000COV 74



Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered


Tab

le6

Hu

llse

ctio

nal

pro

per

ties

of

the

exis

tin

gb

ulk

carr

iers

Item

Bu

lk3

Bu

lk4

Bu

lk5

Bu

lk6

Bu

lk7

Bu

lk8

Bu

lk9

Bu

lk1

0B

ulk

11

Bu

lk1

2B

ulk

13

Bu

lk1

4

LB

P(L

)30

000

300

0030

000

259

0025

400

216

0021

700

216

0017

000

170

0017

000

158

00B

read

th(B

)50

00

500

050

00

430

041

00

322

032

30

322

027

60

231

026

00

262

0D

epth

(D)

257

025

70

257

023

80

229

019

10

190

019

10

170

014

50

136

013

80

Dra

ft(d

)18

00

180

018

00

173

016

00

139

013

75

139

012

05

106

59

709

90B

lock

coef

fici

ent

(Cb)

085

140

8390

084

080

8406

084

320

8427

084

920

8430

081

600

8430

080

300

7960

Des

ign

spee

d(k

not

s)13

50

135

013

60

144

313

00

146

014

30

164

014

90

154

015

00

128

0D

WT

207

000

207

000

207

000

135

000

126

000

730

0073

000

730

0039

700

295

0028

400

270

00C

ross

-sec

tion

alar

ea(m

2)

630

46

353

615

14

639

437

33

186

312

13

182

290

12

226

241

62

115

Hei

ght

ton

eutr

alax

isfr

omba

seli

ne

(m)

118

8211

859

120

2110

284

992

37

798

775

67

899

695

56

221

537

25

407

I(m

4)

Ver

tica

l73

225

374

510

571

416

345

089

239

100

718

306

018

330

618

524

013

495

877

368

663

0162

509

Hor

izon

tal

204

456

62

038

294

199

123

21

133

586

955

014

443

451

425

214

443

825

284

622

155

182

236

716

187

262

Z(m

3)

Dec

k52

994

538

3152

209

333

5930

130

161

9716

302

165

3713

436

934

58

058

744

8B

otto

m61

626

628

3359

409

438

4639

406

234

7523

635

234

5219

403

124

3612

342

115

60

YD

eck

HT

36H

T36

HT

36H

T36

HT

36H

T36

HT

36H

T36

MIL

DM

ILD

HT

36H

T32

Bot

tom

HT

36H

T32

HT

36H

T32

HT

32H

T32

HT

32H

T32

MIL

DM

ILD

MIL

DH

T32

Mp

(GN

m)

Ver

tica

lm

omen

t22

835

220

0921

686

142

5514

255

710

37

328

717

64

350

289

93

550

334

4






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered






















Mean 970COV 64





area (m2)5992 4310 5323 4940 4607 3552 2668 1473 1473


12327 10331 10534 10887 9970 8248 6184 4252 4252


Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643




















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered


















Mean 975COV 44


















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered















Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered





Concluding remarks




Acknowledgments




Z (m3)Deck 66301 29679 77236 44354 39274 18334 26635 44376 31040 43191Bottom 70950 39126 103773 62058 50544 27228 42894 58785 38520 49175


ZZmin

Deck 1092 1067 1051 1007 1008 1063 1012 1008 1150 1168Bottom 1169 1407 1412 1228 1198 1457 1504 1232 1427 1329





MuMtSag 1231 1106 1161 1260 1285 1622 1496 1551 1202 1359Hog 1162 1360 1429 1274 1270 1420 1414 1221 1446 1374







Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered




Z (m3)Deck 79986 79916 68892 40525 32732 30378 29997 13319 7885Bottom 104797 104421 79608 52878 40881 39166 38824 16605 8804





MuMtSag 1024 1024 1021 1084 1001 1044 1029 1179 1013Hog 1243 1346 1160 1327 1193 1172 1248 1429 1095




Z (m3)Deck 52994 53831 52209 33359 30130 16197 16302 16537 13436 9345 8058 7448Bottom 61626 62833 59409 43846 39406 23475 23635 23452 19403 12436 12342 11560





MuMtSag 1268 1274 1272 1206 1189 1100 1069 1159 1232 1238 1205 1098Hog 1289 1253 1196 1313 1278 1385 1392 1367 1466 1408 1251 1506




Z (m3)Deck 47050 24888 31779 32239 26739 16194 8721 3133 3050Bottom 51149 30212 46471 43413 34647 23701 16234 5643 5643





MuMtSag 1494 1534 1738 1617 1568 1449 1412 1405 1313Hog 1108 1188 1496 1281 1202 1273 1500 1381 1460













considered












considered


Documents

Guide for ULSA of ships