A Guide for the Ultimate Longitudinal Strength Assessment of Ships Jeom Kee Paik 1 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 progressive collapse analysis method or closed-form design formulas. In the present paper, both the progressive collapse analysis method and the design formulas are presented. A comparison between the progressive collapse analysis results and the design formula solutions for merchant cargo ship hulls is undertaken. The total design (extreme) bending moment of a ship hull is estimated as the sum of the still-water and wave-induced bending moment components as usual. The safety measure of a ship hull is then defined as a ratio of the ultimate longitudinal strength to the total design bending moment. The developed guidelines are applied to safety measure calculations of merchant ship hulls with respect to hull girder collapse. It is concluded that the guidance and insights developed from the present study will be very useful for the ultimate limit state design of newly built ships as well as the safety measure calculations of existing ship hulls. The essence of the proposed guide shall form ISO code 18072-2: Ships and Marine Technology— Ship Structures—Part 2: Requirements of Their Ultimate Limit State Assessment. 1. Introduction DURING THE LAST FEW DECADES, the emphasis in structural design has been moving from the allowable (working) stress design to the limit state design, because the latter approach has many more advantages. A limit state is formally defined as a condition for which a particular structural member or an entire structure fails to perform the function that it has been designed 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) (Paik & Thayamballi 2003). The structural design criteria against the ULS are based on plastic collapse or ultimate strength. The design of many types of structures including merchant ship structures has in the past tended to rely on estimates of the buckling strength of components, usually from their elastic buckling strength adjusted by a simple plasticity correction. This is represented by point A in Fig. 1. In such a design scheme, the structural designer does not use detailed information on the postbuck- ling behavior of component members and their interactions. The true ultimate strength represented by point B in Fig. 1 is typically higher, although one can never be sure of this. In design, when the load level 2 shown in Fig. 1 is applied, the structure will be safe, but if the load level 1 is applied, the structure will possibly collapse. Arguably the ultimate strength is a better basis for design, but as long as the strength level associated with point B remains unknown (as it is with traditional allowable stress design or linear elastic design methods), it is difficult to determine the real safety margin. Hence, more recently, the design of such structures as those of navy ships as well as offshore platforms and land- based structures (e.g., steel bridges) has tended to be based on the ultimate strength. The safety margin of a structure can be evaluated by a comparison of its ultimate strength with the extreme applied loads, as depicted in Fig. 1. To obtain a safe and economic structure, the ultimate load-carrying capacity as well as the design 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, load combinations, and the ultimate strength. A designer may even desire to do this not only for the intact structure, but also for structures with premised damage, in order to assess and categorize their damage tolerance and survivability. In the present paper, a guide for the ultimate longitudinal strength assessment of ships is developed and is applied to 1 Professor of Ship Structural Mechanics, Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, Korea Manuscript received at SNAME headquarters January 2004. Fig. 1 Structural design considerations based on the ultimate limit state (Paik & Thayamballi 2003) Marine Technology, Vol. 41, No. 3, July 2004, pp. 122–139 122 JULY 2004 MARINE TECHNOLOGY 0025-3316/04/4103-0122$00.00/0
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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)
JULY 2004 MARINE TECHNOLOGY 125
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
minus1274 for 15 30minus12482 minus 0283 for 30
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
126 JULY 2004 MARINE TECHNOLOGY
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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)
JULY 2004 MARINE TECHNOLOGY 125
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
minus1274 for 15 30minus12482 minus 0283 for 30
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
126 JULY 2004 MARINE TECHNOLOGY
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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)
JULY 2004 MARINE TECHNOLOGY 125
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
minus1274 for 15 30minus12482 minus 0283 for 30
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
126 JULY 2004 MARINE TECHNOLOGY
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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)
JULY 2004 MARINE TECHNOLOGY 125
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
minus1274 for 15 30minus12482 minus 0283 for 30
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
126 JULY 2004 MARINE TECHNOLOGY
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
minus1274 for 15 30minus12482 minus 0283 for 30
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
126 JULY 2004 MARINE TECHNOLOGY
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
201hwtw + hwtw + bf tf
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
JULY 2004 MARINE TECHNOLOGY 127
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
128 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
JULY 2004 MARINE TECHNOLOGY 129
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
Mp (GNm)Vertical moment 12451 12448 1000 15669 15726 1004
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
130 JULY 2004 MARINE TECHNOLOGY
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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)
COV coefficient of variation DF design formula ultimate hull girderstrength obtained by the design formulas FPSO floating production stor-age and off- loading 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
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
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
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
Table 8 Hull sectional properties of the existing container vessels
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
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
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
JULY 2004 MARINE TECHNOLOGY 135
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
136 JULY 2004 MARINE TECHNOLOGY
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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
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
JULY 2004 MARINE TECHNOLOGY 137
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
Table 11 Safety measure calculations for the 9 existing double-hull tankers
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
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
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
138 JULY 2004 MARINE TECHNOLOGY
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
JULY 2004 MARINE TECHNOLOGY 139
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