1
Valida ion o SCF Fo mulas o Join Mislaignmen s in Fa igue Design
Rules o he Coas Gua d and Na y
Ta a La kin1,2,
*
, Pingsha Dong1
1 Uni e si y o Michigan, Ann A bo , MI, USA
2 Uni ed S a es Coas Gua d Academy, New London, CT, USA
Abs ac . This s udy p esen s new SCF solu ions o axially misaligned bu welds be ween wo pla es, de i ed
using he “ASME B&PV Code” mesh-insensi i e s uc u al s ess me hod. Two-dimensional ini e elemen
models a e analyzed ac oss a ying bounda y condi ions and geome ies. A di ec analy ical app oach is also
aken and esul s in closed- o m solu ions co esponding o a ious pla e hickness and leng h combina ions.
Addi ionally, he solu ions a e alida ed by hose de i ed using he ene gy me hod by Xing and Dong (2018).
Resul s p o e ha cu en In e na ional Ins i u e o Welding (IIW) o mulas, along wi h o he indus y
s anda ds, con ain empi ical e ms ha lack physical basis, ha e limi ed applicabili y o ealis ic bounda y
condi ions, and gene ally p oduce un-conse a i e es ima es o s ess concen a ions—leading o o e -
p edic ion o a igue li e by up o se en imes o some misalignmen condi ions. The demons a ed inaccu acy
o IIW o mulas o simple misalignmen s, whe e analy ical solu ions a e easible, aises conce n o mo e
complex join s. The SCF solu ions p esen ed in his s udy a e mo e accu a e and b oadly applicable o
misaligned bu and c uci o m ille welds on na al essels, enable iden i ica ion o he c i ical weld oe o
a ge ed s uc u al heal h moni o ing, and can be ex ended o mo e complex join s. The me hods and solu ions
p esen ed a e also used o analyze he impac o ape ed ansi ions in welds o a ying hickness.
Keywo ds: s ess concen a ion ac o , misalignmen , ape
1 In oduc ion
Fa igue design o welded join s has been s udied o decades, ye p ema u e a igue ailu es con inue o plague
na al essels, including ecen U.S. Coas Gua d and Na y acquisi ions. No ably, he ini ial Na ional Secu i y
Cu e design o he Coas Gua d lacked su icien s uc u al a igue conside a ions, leading o ex ensi e s uc u al
enhancemen wo k on he i s wo hulls and signi ican edesign o subsequen hulls. To begin add essing hese
issues, he Coas Gua d launched he Fa igue Li e Assessmen P og am (FLAP) [1] o e alua e a igue design
p ocedu es, pa icula ly hose ou lined in he Na y’s Fa igue Design Guidance o Su ace Ships [2].
Indus y s anda ds, including he Na y’s guide, ou line h ee p ima y me hods o calcula e a igue li e: nominal
s ess, ho spo s ess, and he e ec i e no ch s ess[2], [3], [4], [5]. Each me hod de ines a s ess o calcula e,
applies a esul ing s ess concen a ion ac o o a welded connec ion no explici ly modeled, and classi ies he
join in o an app op ia e SN cu e. The nominal s ess me hod, despi e i s simplici y and widesp ead accep ance,
is challenging in applica ion. Nominal s ess is o en ill-de ined in complex s uc u es and he ca ego iza ion o
join s is ambiguous as join ype, geome y, and loading mode may no pe ec ly align wi h exis ing cu es. The
ho spo s ess and e ec i e no ch s ess me hods employ mo e de ailed ini e elemen models and equi e ewe
SN cu e ca ego ies. Howe e , hese me hods ha e been shown o be sensi i e o elemen ype and size [6]. The
In e na ional Ins i u e o Welding (IIW) guidance e en s a es a “high le el o expe ise is equi ed on he pa o
he FEA analys [5].” While he Na y ecognizes all h ee me hods, he nominal s ess app oach is equi ed unless
speci ic expe imen al c i e ia and app o als ha e been me [2].
Embedded wi hin he a igue design p ocess is a signi ican amoun o unce ain y. FLAP p edomina ely
ocused on he wa e loading and s uc u al esponse aspec s, which a e c i ical inpu s o de e mining he s ess
expec ed in a welded join o e he li e ime o he design. Wa e senso s and s ain gauges we e ins alled a c i ical
design loca ions on ac i e cu e s o assess he accu acy o cu en me hodologies. In addi ion, FLAP also
highligh ed o he c i ical a eas o unce ain y in he a igue design p ocess, such as cons uc ion impe ec ions [1].
*
Co espondence o: [email p o ec ed]
16 h In e na ional Symposium on P ac ical Design o Ships and O he Floa ing S uc u es PRADS 2025
Ann A bo , MI, USA, Oc obe 19 h – 23 d 2025
2
Misalignmen s a e common impe ec ions in shipya d welds ha educe a igue li e by inducing a seconda y
bending momen . Some ep esen a i e axial misalignmen s a e shown in Figu e 1, whe e ep esen s hickness,
and e is he misalignmen caused by he o se o he cen e lines o wo adjoining pla es. The impac o he induced
seconda y bending momen is assessed h ough a s ess concen a ion ac o , 𝑘𝑚, shown in he gene al o m in
equa ion (1). The memb ane s ess, 𝜎𝑚, e e s o he uni o m h ough- hickness s ess, and he bending s ess, 𝜎𝑏
is he linea ly a ying s ess g adien . Fo he geome y o a bu join , his equa ion can be ea anged in o equa ion
(2), whe e 𝜆 is a ac o p o ided in indus y s anda ds. Depending on he e e ence, some 𝑘𝑚 equa ions only
conside he seconda y bending momen e ec s ( 𝜎𝑏
𝜎𝑚), a he han he o al e ec ep esen ed by equa ion (1). Fo
cla i y and di ec compa ison, equa ions in ha o m ha a e discussed in his pape ha e been adjus ed.
𝑘𝑚=𝜎𝑚+𝜎𝑏
𝜎𝑚
(1)
𝑘𝑚=1+𝜆𝑒
𝑡
(2)
Figu e 1. Misalignmen in a (a) bu weld [7] (b) bu weld wi h pla es o a ying hickness, and (c) ille weld[7]
Indus y’s end owa d ligh weigh ing and s uc u al op imiza ion has inc eased he p e alence o
misalignmen s, esul ing om welding-induced dis o ions [8], making i impe a i e o c i ically assess associa ed
design guidance. Highe s eng h, hinne pla es a e mo e suscep ible o dis o ion, and equi e join s wi h hickness
ansi ions, which inhe en ly ha e misalignmen s. The Na y ecen ly d a ed a newe e sion o hei Fa igue
Design Guidance o Su ace Ships, ci ing majo s uc u al ailu es ac oss h ee di e en classes o ships and
issuing a wa ning abou he ligh weigh ing end [2],[8]. Despi e his wa ning, he upda ed d a ails o p o ide
any addi ional discussion on misalignmen s, and s ill simply sugges s ini e elemen analysis o he Ame ican
Bu eau o Shipping’s (ABS) 1996 e e ence wi h equa ion (2), whe e 𝜆=1.5.
Ex e nal design i ms con ac ed by he Coas Gua d ha e no been equi ed o s ic ly adhe e o Na y design
s anda ds, and ha e been pe mi ed o iden i y and apply compa able indus y s anda ds. When shipya d
misalignmen s we e disco e ed in he p oduc ion o a ecen Coas Gua d acquisi ion, IIW guidance was ollowed
[10], which p o ides addi ional de ails compa ed o he Na y guidance. IIW s ess concen a ion ac o o mulas
o axially misaligned bu welds a e p esen ed in equa ions (3) and (4), wi h hei applica ion explained in Table
1.
𝑘𝑚= 1+𝜆 𝑒∙𝑙1
𝑡(𝑙1+𝑙2)
(3)
𝑘𝑚= 1+6𝑒
𝑡1∙𝑡1
𝑛
𝑡1
𝑛+𝑡2
𝑛
(4)
In IIW guidance, he SN cu es a e i led by he a igue assessmen (FAT) ca ego y ha he join is classi ied
by. Each FAT cu e al eady assumes a ce ain amoun o 𝑘𝑚 as an accep able misalignmen . This alue is 1.30
o bu join s, when using he nominal s ess me hod and i s associa ed FAT cu e, and only 1.05 o he ho spo
and e ec i e no ch s ess me hods. The e o e, equa ions (3) and (4) only need o be applied when a misalignmen
exceeds wha is assumed in he FAT cu e. When his is he case, an e ec i e 𝑘𝑚 should be calcula ed using
equa ion (5). Addi ionally, IIW s a es ha a minimum 𝑘𝑚,𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒, dependen on join ype, mus always be
applied o nume ically de e mined 𝑘𝑚 alues ha did no explici ly include a misalignmen in he model. Ta as e
al [6] concluded his o be essen ial, and ha cu en indus y s anda ds lacks cla i y and su icien guidance.
3
Table 1. IIW Misalignmen Guidance
𝑘𝑚,𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 =𝑘𝑚,𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑟𝑜𝑚 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠
𝑘𝑚,𝑎𝑠𝑠𝑢𝑚𝑒𝑑 𝑖𝑛 𝐹𝐴𝑇 𝑐𝑢𝑟𝑣𝑒
(5)
Many s udies ha e ques ioned he alidi y o 𝑘𝑚 equa ions, ye indus y s anda ds emain oo ed in
o mula ions by Be ge and Myh e om he 1970s [11], ha we e subsequen ly expe imen ally alida ed unde
speci ic loading condi ions [12]. In 1999, Cui e al [13] used pla e heo y o in es iga e equa ion (2), no ing
𝜆 o
a y amongs li e a u e, and concluding 𝜆 o depend on geome y and loading. The s udy speci ically p o ed he
ABS e sion o equa ion (2) wi h 𝜆=1.5, s ill e e enced by he new d a o he Na y a igue guidance, has no
jus i ica ion. In 2004, a Ship S uc u es Commi ee epo [14], ound exis ing guidance o be oo gene al, and
bounda y condi ions o be an impo an ac o ha needs o be add essed. Wi h indus y s anda ds la gely
emaining unchanged ollowing hese ea ly conclusions, mo e ecen s udies ha e eigni ed he issue and
ques ioned he exis ing app oaches. Ta as e al [6] assessed he nume ical me hods agains he nominal s ess
app oach o se e al cons uc ion impe ec ions. Xing e al [15] and Zhou e al [12] p esen ed new analy ical
solu ions o misalignmen s in welded join s, alida ed wi h FEA and expe imen al da a. Mancini [16] de eloped
hin pla e solu ions wi h expe imen al alida ion, and Rau iainen [17] assessed nume ical me hods o use on
complex join s. Amongs hese s udies, he ollowing issues ha e been aised ega ding a igue design guidance
o misaligned welds:
1. Limi ed Applicabili y - Bounda y condi ions ha e been ound o signi ican ly impac 𝑘𝑚, ye IIW
con ains ague classi ica ions, such as “ ully es ained”, “un- es ained”, and “ emo ely loaded”, wi hou
clea guidance o adjus ing o al e na e condi ions [9]-[12].
2. Empi ical Limi a ions – IIW o mula ions a e oo ed in empi ical o mula ions ha lack physical meaning
and we e de i ed unde speci ic condi ions. S udies ha e p o en o mula ions o be w ong in ce ain cases
[15], and ques ion he use o n=1.5 o di e en hickness combina ions, ha is “suppo ed by es s.”
3. Inconsis en Resul s – The h ee-indus y accep ed a igue design me hods p oduce di e en s ess esul s,
di ec use s o di e en FAT cu es, and ul ima ely lead o di e en a igue li e es ima es. E en wi hin
each me hod, ambiguous guidance, subjec i e join ca ego iza ion, and mesh sensi i i y yield a ying
esul s [6], [12], [14], [15], [17].
4. Non-conse a i e – IIW app oaches ha e been ound o unde es ima e s ess in many cases, leading o
o e es ima ed a igue li e, which is especially conce ning conside ing he issues abo e and he mul i ude
o o he ac o s o unce ain y in ol ed. [6], [12], [15], [16], [17]
5. Lack o c i ical weld loca ion in o ma ion in a join – cu en 𝑘𝑚 o mula ions do no iden i y he c i ical
oe, which is c i ical o s uc u al heal h moni o ing e o s, such as hose ini ia ed by FLAP, and e ec i e
design. The e is lack o cla i y on how a ape a a bu join be ween wo di e en hickness pla es educes
𝑘𝑚, as IIW simply c edi s ape ed ansi ions wi h an al e na e FAT ca ego iza ion.
Type o Misalignmen
Equa ion
No es
Axial misalignmen be ween la pla es
(3)
λ is dependen on es ain
λ = 6 o un es ained join s
Fo emo ely loaded join s assume 𝑙1 = 𝑙2
Axial misalignmen be ween la pla es o di e ing
hickness
(4)
𝑡2≥𝑡1
Rela es o emo ely loaded un es ained
join s.
The use o n=1.5 is suppo ed by es s.
4
O no e, Lo sbe g [18] asks simila ques ions, bu concludes IIW o mulas o axially misaligned bu welds
o be su icien . Howe e , he s udy was conduc ed unde speci ic geome y and loading. This pape u ilizes he
“ASME B&PV Code” mesh-insensi i e s uc u al s ess me hod, e e ed he e as he nodal o ce me hod (NFM)
o wo-dimensional analyses, o add ess hese i e issues. The NFM is used o analyze join s wi h a ious
bounda y condi ions and geome ies. Di ec analy ical solu ions will also be ob ained when possible, including
speci ic o ms de i able om hose p esen ed in [12], [15]. These solu ions will be used o no only alida ing
he ele an IIW o mulas, bu also shed ligh on he egime o alidi y and co esponding bounda y condi ions.
The NFM is used o assess he e ec s o weld p esence in misaligned join s, which has been igno ed in analy ically
de i ed closed- o med solu ions, in addi ion o examining he alidi y o he empi ical n=1.5 e m and s udying
ape ed ansi ions in welded join s o a ying hickness.
2 SCF Analysis
To ep esen he ange o bounda y condi ions possible o a welded join on a na al essel, se e al cases we e
s udied, lis ed in Table 2. Cases 0 and 1 a e s a ically de e mina e cases. Cases 1 h ough 3 ma ch hose s udied by
Xing [15], enabling alida ion o he di ec analy ical app oach o e ed in his s udy wi h Xing’s ene gy me hod
solu ions. When compa ing agains IIW guidance om Table 1, i is assumed ha IIW’s “un es ained” and “ ully
es ained” a e mos like cases 1 and 2, espec i ely. Models o bu welded join s we e de eloped based on Figu e
1 (a) and (b) using hicknesses and misalignmen s p o ided in [10], wi h 𝑙1=10𝑡𝑚𝑎𝑥. To s udy he impac o
weld placemen , 𝑙2 a ied. All FEA esul s we e calcula ed using plane s ess elemen s in ABAQUS.
Table 2. Bounda y Condi ion Cases
Case
Le Bounda y Condi ion
Righ Bounda y Condi ion
0
Edge ixed wi h no o a ion
F ee
1
Pinned in x and y
Pinned in y
2
Edge ixed wi h no o a ion
Pinned in y wi h no o a ion
3
Edge ixed wi h no o a ion
Pinned in y
2.1 Nodal Fo ce Me hod in ASME B&PV Code
The “ASME B&PV Code” mesh-insensi i e s uc u al s ess me hod p esen ed in [19], add esses he
ambigui ies associa ed wi h s ess iden i ica ion and SN cu e ca ego iza ion in cu en indus y s anda d a igue
design me hods . This obus app oach, adop ed by ASME in 2007, is explained comp ehensi ely in [20]. Due o
he simple geome y o he misalignmen s in his s udy, he 2D s uc u al s ess de ini ion, he NFM, is u ilized.
Unlike he ho spo s ess me hod, which elies on a linea ex apola ion o su ace s esses o weld oe, he
NFM imposes equilib ium equa ions by using he nodal o ces ac ing on ei he side o he hypo he ical c ack plane
o yield mesh in-sensi i e esul s, ha co ela e well wi h expe imen al da a [12], [15], [19], [20]. Depic ed in
Figu e 2, a ee-body cu a he weld oe exposes elemen s (shaded in blue) and hei nodal o ces (NFORC in
ABAQUS). A summa ion o hese nodal o ces in he x-di ec ion, 𝐹𝑥𝑖, and nodal momen s yields he in e nal
o ce, N, and momen , M, as w i en in equa ions (6) and (7), whe e i =1, n and n is he numbe o nodes exposed
by he cu . Fo he example o h ee h ough- hickness elemen s, he e is a o al o six exposed 𝐹𝑥𝑖 o sum: one
each a he op and bo om nodes, and wo a each in e nal node. Mesh con e gence es s conduc ed h oughou
he s udy con i med he mesh-insensi i i y o his me hod.
Figu e 2. An example o he 2D NFM, wi h h ee h ough- hickness elemen s. The e is a o al o six 𝐹𝑥𝑖 o be summed along
he ed line, ep esen ing a ee-body cu a he hypo he ical c ack line a he weld oe [21].
5
𝑁= 𝜎𝑚𝑡=∑𝐹𝑥𝑖
𝑛
𝑖=1
(6)
𝑀= 𝜎𝑏𝑡2
6=∑𝐹𝑥𝑖 (𝑦𝑖−𝑡
2)
𝑛
𝑖=1
(7)
Addi ionally, his me hod enables calcula ion o an equi alen s uc u al s ess ange pa ame e , using equa ion
(8). The ac ion s uc u al s ess ange, Δ𝜎𝑆, is he sum o he anges o bending and memb ane s esses, m is 3.6,
and 𝐼(𝑟)1
𝑚 in Eq. (9) is a dimensionless li e in eg al by using a wo-s age g ow h model [22]. Using hese
de ini ions, a Mas e SN Cu e is de eloped, ha consolida es a ious SN cu es in o a single, uni ied cu e,
shown in Figu e 3. This app oach emo es he subjec i i y associa ed wi h FAT ca ego ies, o e ing consis en
and eliable esul s ac oss di e en weld ypes and join con igu a ions.
Δ𝑆𝑆=Δ𝜎𝑆
𝑡2−𝑚
2𝑚 𝐼(𝑟)1
𝑚
(8)
𝐼(𝑟)1
𝑚= 0.0011𝑟6+0.0767𝑟5−0.0988𝑟4+0.0946𝑟3+0.0221𝑟2
+0.014𝑟+1.2223
(9)
Figu e 3. Mas e SN Cu e wi h sca e bands ep esen ing 2 and 3 s anda d de ia ions om mean.
2.2 Analy ical SCF Solu ions
Di ec analy ical solu ions we e de i ed o alida e he NFM esul s. Figu e 4 ep esen s he ou cases ha
we e lis ed in Table 2, and hei esul ing momen dis ibu ions. The momen equa ion is lis ed o he le side o
he model, when ea ing he applied o ce, P, as a momen , M, applied a he weld, as in equa ion 10. Fo he
s a ically inde e mina e cases, cases 2 and 3, he eac ion o ces and momen s we e sol ed o by imposing
compa ibili y condi ions in addi ion o he equa ions o s a ic equilib ium.
𝑀= 𝑃∙𝑒
(10)
Fo mula ions o he s ess concen a ions a each oe, (𝑘𝑚)𝑖, a e p o ided in Tables 3 and 4, whe e an i alue
o 1 o 2 ep esen s he co esponding oe. These we e de eloped using equa ion (1) and by se ing x = li in he
espec i e momen equa ions. Solu ions a e p esen ed alongside IIW and modi ied e sions o Xing’s[15], ha
enable di ec compa ison. Xing’s o iginal exp essions had an al e na i e numbe ing o ma , only conside ed he
seconda y bending e ec , and used he memb ane s ess o he igh pla e, a he han he espec i e side. While
Xing did no di ec ly sol e o Case 0, his app oach yields iden ical esul s o he di ec analy ical solu ion. Fo
6
case 1, Xing had a ypo, whe e he inco ec ly lis ed 𝑡1 in he nume a o ins ead o 𝑡𝑖. Once co ec ed, he analy ical
solu ions o case 1 a e also equi alen . Compa ison o he solu ions o he s a ically inde e mina e cases is mo e
di icul due o he in oduc ion o highe o de e ms. Simpli ica ion o o mula ions o same hickness cases
p o es equi alency o he di ec analy ical me hod and Xing’s ene gy me hod, and e alua ion o esul s wi h model
geome y o e s addi ional alida ion o he wo me hods. The e o e, Table 4 and subsequen discussion o
analy ical solu ions e e ences a e singula .
Figu e 4. Rep esen a i e model and di ec analy ical momen dis ibu ion o cases 0 h ough 3, when ea ing he
misalignmen and applied axial o ce as a momen applied a he cen e
7
Table 3. Solu ion Compa ison – S a ically De e mina e Cases
Case 0
Case 1
IIW
𝑘𝑚= 1+6𝑒
𝑡𝑙1
(𝑙1+𝑙2)
o , wi h di e ing hickness:
𝑘𝑚= 1+6𝑒
𝑡1𝑡1
𝑛
𝑡1
𝑛+𝑡2
𝑛
whe e n=1.5
Di ec
Analy ical
(𝑘𝑚)1= 1+6𝑒
𝑡1
(𝑘𝑚)2= 1
C i ical Toe = le oe
(𝑘𝑚)𝑖= 1+6 𝑒∙𝑙𝑖
𝑡𝑖(𝑙1+𝑙2)
C i ical Toe = La ge 𝑙
𝑡
Xing
(𝑘𝑚)1= 1+6𝑒
𝑡1
(𝑘𝑚)2= 1
(𝑘𝑚)𝑖= 1+6 𝑒∙𝑙𝑖
𝑡𝑖 (𝑙1+𝑙2)
Table 4. Solu ion Compa ison – S a ically Inde e mina e Cases
Case
Case 2
Case 3
IIW
𝑘𝑚= 1+3𝑒
𝑡𝑙1
(𝑙1+𝑙2)
o , wi h di e ing hickness:
𝑘𝑚= 1+3𝑒
𝑡1𝑡1
𝑛
𝑡1
𝑛+𝑡2
𝑛
whe e n=1.5
Analy ical
[15]
(𝑘𝑚)𝑖=
1+ 6𝑒𝑡𝑖2𝑙1𝑙2(4𝑙𝑖3𝑡1
3𝑡2
3
𝑡𝑖3+3𝑙𝑖𝑙1𝑙2𝑡1
3𝑡2
3
𝑡𝑖3+𝑙1
3𝑙2
3𝑡𝑖3
𝑙𝑖3)
𝑙𝑖(𝑙2
4𝑡1
6+4𝑙2
3𝑙1𝑡1
3𝑡2
3+6𝑙2
2𝑙1
2𝑡1
3𝑡2
3+4𝑙1
3𝑙2𝑡1
3𝑡2
3+𝑙2
4𝑡1
6)
(𝑘𝑚)1=
1+ 3𝑒(2𝑙2
3𝑡1
4+3𝑙2𝑙1
2𝑡2
4+2𝑙1
3𝑡2
4)
(𝑙2
3𝑡1
4+3𝑙1𝑙2
2𝑡2
4+3𝑙2𝑙1
2𝑡2
4+𝑙1
3𝑡1
4)𝑡1
(𝑘𝑚)2=
1+ 9𝑒𝑡2
3𝑙1(2𝑙2+𝑙1)𝑙2
(𝑙2
3𝑡1
4+3𝑙1𝑙2
2𝑡2
4+3𝑙2𝑙1
2𝑡2
4+𝑙1
3𝑡1
4)
2.3 Compa ison
Resul s om he s a ically de e mina e cases, cases 0 and 1, p o ide impo an insigh s in o he IIW
o mula ions. Figu es 5 and 6 compa e FEA esul s agains he analy ical solu ion and cu en IIW equa ions o
a ying misalignmen , 𝑒
𝑡𝑚𝑖𝑛, and a ying weld posi ion, 𝑙1
𝑙1+𝑙2. These esul s indica e:
1. Valida ion o analy ical solu ion wi h NFM.
2. Bounda y condi ions ha e a signi ican impac . Igno ing hei e ec and blindly applying IIW o mulas
can unde p edic 𝑘𝑚. Case 0 ge s signi ican ly unde p edic ed by he IIW o mula ion whe e λ=6, and
he e is no clea guidance on how o ea his speci ic bounda y condi ions. Fo he wo s case analyzed,
whe e 𝑙1=0.25𝑙𝑡𝑜𝑡, he IIW li e p edic ion is 7 imes he FEA and analy ical li e p edic ion.
3. S a ically de e mina e cases do no need he hickness co ec ion e m. The inclusion o his empi ically
de i ed hickness e m, in he IIW o mulas, esul s in an unconse a i e p edic ion o 𝑘𝑚 o bo h
s a ically de e mina e cases. This indica es limi ed es ing condi ions in he o mula ion o he n=1.5 e m.
Despi e IIW o mula being de i ed like case 1, o weld posi ioning whe e 𝑙1<𝑙2, he IIW equa ion
seems inco ec . The e m should be 𝑙𝑖
𝑙1+𝑙2, ins ead o 𝑙1
𝑙1+𝑙2. Figu e 6 shows ha he IIW o mula ion only
conside s oe 1. When oe 2 is he c i ical oe, IIW is unconse a i e. Fo he wo s case analyzed, a case
1 join wi h 𝑙1=0.25𝑙𝑡𝑜𝑡, he IIW li e p edic ion is 4 imes he FEA and analy ical li e p edic ion.
4. Weld posi ioning impac s 𝑘𝑚. IIW con ains no guidance on he p ope use o he “ emo ely loaded”
assump ion. The “ emo ely loaded” is unconse a i e any ime 𝑙1≠𝑙2, .
8
Figu e 5. Km o a ying misalignmen , 𝑒
𝑡𝑚𝑖𝑛, based on IIW e sus analy ical and FEA solu ions o s a ically de e mina e
cases. FEA esul s alida e analy ical solu ions and show unde p edic ion by IIW.
Figu e 6. S ess concen a ion ac o s o a ying weld posi ion 𝑙1
𝑙1+𝑙2based on IIW o mula, IIW “ emo e loading” assump ion,
e sus de i ed solu ions and FEA esul s o s a ically de e mina e cases.
Figu es 7 and 8 include esul s om all 4 cases and compa e IIW and analy ical solu ions agains NFM esul s.
IIW does no ha e a solu ion o case 0. Cases 2 and 3 a e assumed o be he “ ully es ained” IIW condi ion. The
esul s om hese addi ional cases indica e:
1. Good co ela ion be ween NFM and analy ical solu ion o all cases.
2. Good co ela ion o IIW equa ion only o he same hickness case 1 condi ion. IIW unde p edic ed
c i ical oe o all o he scena ios es ed.
3. The IIW empi ical di e en hickness e m also unde p edic s s a ically inde e mina e cases, and is no
alida ed by o he p edic ion me hods. Fu he in es iga ion in o his e m is p o ided in sec ion 3.
4. The non-conse a i e na u e o IIW o mula ions is exace ba ed by a combina ion o e o s in geome ies
wi h di e en hickness combina ions and 𝑙1<𝑙2. Case 3 yielded IIW li e p edic ions 4.3 imes he
p edic ions om o he me hods.
9
Figu e 7. S ess concen a ion ac o s a each weld oe o s a ically de e mina e cases wi h di e en hickness combina ion o
𝑡1=5𝑚𝑚,𝑡2=9𝑚𝑚 o (a) same leng h and (b) 𝑙1=0.5𝑙2
Figu e 8. S ess concen a ion ac o s a each weld oe o s a ically inde e mina e cases wi h di e en hickness combina ion
o 𝑡1=5𝑚𝑚,𝑡2=9𝑚𝑚 o (a) same leng h and (b) 𝑙1=0.5𝑙2
2.4 C uci o m Join s
A c uci o m join wi h ou ille welds, shown in Figu e 9, was es ed wi h he bounda y condi ions o cases 0
h ough 3 applied o he ends o he ho izon al membe s. Resul s o hickness and leng h combina ions ma ching
hose s udied on he bu welds, p oduced iden ical esul s o Figu es 7 and 8, indica ing he analy ical solu ions
and NFM me hod a e alid o ille weld c uci o m join s, as well.
Figu e 9. Model o c uci o m join wi h ille welds.
NFM
(a)
(b)
NFM
NFM
NFM
NFM
NFM
NFM
NFM
NFM
(a)
(b)
NFM
NFM
NFM
NFM
NFM
NFM
NFM
NFM
16
manu ac u ing, i should no be gi en so much FAT ca ego iza ion “c edi ” o educing s ess concen a ion. IIW
cu en ly signi ican ly o e es ima es he educ ion o 𝑘𝑚 due o ape ing ansi ions o hickness in bu welds.
Fu u e ex ensions o his wo k include u he analysis o he ape o p oduce closed o m solu ions. Valida ion
will be done wi h a ailable published expe imen al da a, such as om a pape by Ta iq e al, p esen ed a he 2025
IIW Annual Assembly. This me hodology will also be ex ended o mo e complex join s and ul ima ely a emp o
de elop mo e obus a igue design p ocedu es o he Coas Gua d and Na y.
Re e ences
[1] K. S ambaugh, I. D ummen, C. Clea y, R. Sheinbe g, and M. Kaminski, “S uc u al Fa igue Li e Assessmen and
Sus ainmen Implica ions o a New Class o US Coas Gua d Cu e s”.
[2] M. W. Sie e, D. P. Kihl, and B. M. Ayyub, “Fa igue Design Guidance o Su ace Ships:,” De ense Technical In o ma ion
Cen e , Fo Bel oi , VA, No . 2000. doi: 10.21236/ADA389305.
[3] B i ish S anda ds Ins i u ion, Ed., Guide o me hods o assessing he accep abili y o laws in me allic s uc u es: B i ish
s anda d BS 7910:2019, Fou h edi ion. in BSI s anda ds publica ion, no. 7910. London: BSI, 2019.
[4] “DNV-RP-C203: Fa igue Design o O sho e S eel S uc u es,” 2011.
[5] A. F. Hobbache and J. Baumga ne , Recommenda ions o Fa igue Design o Welded Join s and Componen s. in IIW
Collec ion. Cham: Sp inge Na u e Swi ze land, 2024. doi: 10.1007/978-3-031-57667-6.
[6] A. Ta as and H. Un e wege , “Nume ical Me hods o he Fa igue Assessmen o Welded Join s: In luence o
Misalignmen and Geome ic Weld Impe ec ions,” Eng. S uc . Technol., ol. 9, no. 1, pp. 9–24, Ma . 2017, doi:
10.3846/2029882X.2017.1299968.
[7] B. Jonsson, “Imp o ing weld class sys ems in assessing he a igue li e o di e en welded join designs,” in F ac u e
and Fa igue o Welded Join s and S uc u es, Else ie , 2011, pp. 139–167. doi: 10.1533/9780857092502.2.139.
[8] C. Con a dy e al., “P ac ical Welding Techniques o Minimize Dis o ion in Ligh weigh Ship S uc u es”.
[9] NAVSEA, “Fa igue Design o Su ace Ships,” NAVSEA Design P ac ices and C i e ia Manual, D a T9070-AN-DPC-
100.
[10] “CDRL 085-110 Hull S uc u e Load_S eng h Analysis_154-WPC_110_433_2.”
[11] S. Be ge and H. Myh e, “FATIGUE STRENGTH OF MISALIGNED CRUCIFORM AND BUTT JOINTS,” 1977.
Accessed: Ap . 22, 2025. [Online]. A ailable: h ps://www.seman icschola .o g/pape /FATIGUE-STRENGTH-OF-
MISALIGNED-CRUCIFORM-AND-BUTT-Be ge-Myh e/38d7a4eee4deca 1e4 c8a8 03a3ac5070555a46
[12] W. Zhou and P. Dong, “An analy ical me hod o consis en ea men o axial and angula misalignmen s in a igue
e alua ion o welded join s,” Thin-Walled S uc ., ol. 173, p. 109003, Ap . 2022, doi: 10.1016/j. ws.2022.109003.
[13] W. Cui, Z. Wan, and A. E. Mansou , “S ess concen a ion ac o in pla es wi h ans e se bu -weld misalignmen ,” J.
Cons . S eel Res., ol. 52, no. 2, pp. 159–170, No . 1999, doi: 10.1016/S0143-974X(99)00019-X.
[14] A. Kend ick, “The E ec o Fab ica on Tole ances on Fa igue Li e o Welded Join s,” Ship S uc . Comm. Rep.-436, Dec.
2004.
[15] S. Xing and P. Dong, “An analy ical SCF solu ion me hod o join misalignmen s and applica ion in a igue es da a
in e p e a ion,” Ma . S uc ., ol. 50, pp. 143–161, No . 2016, doi: 10.1016/j.ma s uc.2016.07.006.
[16] F. Mancini, J. Sandg en, P. Leh o, and H. Remes, “Expe imen al alida ion o an analy ical s ess magni ica ion ac o
o hin pla es wi h welding-induced cu a u e,” Ships O sho e S uc ., pp. 1–11, Ma . 2025, doi:
10.1080/17445302.2025.2474118.
[17] M. Rau iainen, H. Remes, A. Niemelä, and J. Romano , “Fa igue s eng h assessmen o complex welded s uc u es wi h
se e e o ce concen a ions along a weld seam,” In . J. Fa igue, ol. 167, p. 107321, Feb. 2023, doi:
10.1016/j.ij a igue.2022.107321.
[18] I. Lo sbe g, “S ess concen a ions due o misalignmen a bu welds in pla ed s uc u es and a gi h welds in ubula s,”
In . J. Fa igue, ol. 31, no. 8–9, pp. 1337–1345, Aug. 2009, doi: 10.1016/j.ij a igue.2009.03.005.
[19] P. Dong, “A s uc u al s ess de ini ion and nume ical implemen a ion o a igue analysis o welded join s,” In . J.
Fa igue, ol. 23, no. 10, pp. 865–876, No . 2001, doi: 10.1016/S0142-1123(01)00055-X.
[20] “WRC 523 Mas e S-N Cu e.”
[21] ASME Boile and P essu e Vessel Code, Sec ion VIII, 2007.
[22] P. Dong, J. K. Hong, and Z. Cao, “S esses and s ess in ensi ies a no ches: ‘anomalous c ack g ow h’ e isi ed,” In . J.
Fa igue, ol. 25, no. 9, pp. 811–825, Sep . 2003, doi: 10.1016/S0142-1123(03)00130-0.
[23] “XIII-1180-85.”
[24] P. Dong, “A s uc u al s ess de ini ion and nume ical implemen a ion o a igue analysis o welded join s,” In . J.
Fa igue, ol. 23, no. 10, pp. 865–876, No . 2001, doi: 10.1016/S0142-1123(01)00055-X.
