54225323 Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs
Transcript of 54225323 Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs
7/26/2019 54225323 Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs
http://slidepdf.com/reader/full/54225323-recommended-hot-spot-analysis-procedure-for-structural-details-of 1/8
Procee~ngs of the Eleventh 2001) International Offshore and Polar Engineering Conference
Stavanger, Norway, June 17-22, 2001
Copyright © 2001 by The International Society o f Offshore an d Polar Engineers
I S N 1-880653-51-6 Set); IS BN 1-880653-55-9 VoL IV); IS SN 1098-6189 Set)
R e c o m m e n d e d Ho t S p o t A n a l y s i s P r o c e d u r e f o r S t r u ct u r a l D e ta i ls o f F P S O s
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a n a l y s i s o f t y p i c a l s t r u c tu r a l d e t a i ls i n F P S O s ( F l o a t i n g P r o d u c -
t i o n , S to r a g e a n d O f f i o a d i n g U n i t s ) a s w e l l a s i n sh i p s . T h e p u r p o s e
o f t h i s s p e c i a l e ff o r t w a s t o d e v e l o p r e c o m m e n d a t i o n s o n a p p r o p r i -
a t e h o t s p o t s t r e s s m e t h o d s a n d S - N d a t a f o r f a t i g u e s t r e n g t h
d e s i g n . I n t o t a l , f iv e d e t a i l s w i t h d i f f e r e n t c h a r a c t e r i s t i c s , f r o m b o t h
g e o m e t r y a n d f a t i g u e l o a d i n g p e r s p e c t i v e s , w e r e s e l e c t e d f o r w h i c h
s t r e s s m e a s u r e m e n t s a n d f a t i g u e t e s t s a r e a v a i l a b l e . V a r i o u s f i n i t e
e l e m e n t m o d e l s w e r e d e v e l o p e d b y p a r t i c i p a n t s , u s i n g d i f f e r e n t
t y p e s a n d s i z e s o f e l e m e n t s , m o d e l l i n g a n d s t r e s s e v a l u a t i o n t e c h -
n i q u e s a s w e l l a s F E p r o g r a m s . C o m p a r i s o n s b e t w e e n t h e a n a l y s i s
r e s u l t s a n d m e a s u r e d s t r e s s e s n e a r t h e w e l d t o e s a l l o w c o n c l u s i o n s
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p r e d i c t i n g h o t s p o t s t r e s s e s a t t h e w e l d t o e s w e r e i n v e s t i g a t e d . T h e
r e s u l ti n g h o t s p o t s t r e s s e s , t o g e t h e r w i t h t h e e s t i m a t e d f a t ig u e l i v e s ,
a r e c o m p a r e d a g a i n s t t h e e x i s t i n g d e s i g n S - N c u r v e s p u b l i s h e d b y
t h e I n t e r n a t io n a l I n s t i t u t e o f W e l d i n g ( I I W ) . I t w a s c o n c l u d e d t h a t
t h e h o t s p o t s t r e s s e s p r e d i c t e d u s i n g t h e t h r e e s t r e s s e x t r a p o l a t i o n
t e c h n i q u e s , w h e r e t h e e l e m e n t s i z e s a n d s t r e s s e v a l u a ti o n p o i n t s a r e
d e t e r m i n e d b y t h e p l a t e t h i c k n e s s , c a n b e u s e d w i t h t h e c u r r e n t
d e s i g n S - N c u r v e s . M o s t s i g n i fi c a n t ly , o n e o f th e r e c o m m e n d e d
m e t h o d s r e q u i r e s n o s t r e s s e x t r a p o l a t i o n , w h i c h i s c o n s i d e r e d a n
a t t r a c t i v e a n d p r a c t i c a l a l t e r n a t i v e t o t h e e x i s t i n g p r a c t i c e s d e v e l -
o p e d b y c l a s s s o c i e t i e s . T h i s m e t h o d w i l l p r o v i d e s i g n i f i c a n t s a v i n g
o n a n a l y s i s e f f o r t s d u r i n g d e s i g n .
K E Y W O R D S : S t r e s s a n a ly s i s , h o t s p o t s t re s s , f i n i t e e l e m e n t m e t h o d ,
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I N T R O D U C T I O N
T h e h o t s p o t s t r e ss a p p r o a c h f o r t h e f a t i g u e s t r en g t h a s s e s s m e n t o f
w e l d e d j o i n t s i s b a s e d o n t h e a s s u m p t i o n t h a t t h e l o c a l s t r e ss i n c r e a s e a t
t h e w e l d t o e c a n b e s u b d i v i d e d i n t o t w o p a r t s , o n e g o v e r n e d b y t h e
s t ruc tura l ( i . e . m a c ro-ge om e t r i c a l ) s t r e s s inc re a se a nd the o the r c re a te d
b y t h e l o c a l i z e d n o t c h s t r es s d u e t o t h e w e l d t o e i t s e l f w h i c h i s r e st r ic t e d
t o a r e g i o n o f a p p r o x . 2 - 3 m m a r o u n d t h e t o e . F u r t h e r m o r e , i t i s
a s s u m e d t h a t t h e f a t i g u e a s s e s s m e n t c a n b e b a s e d o n t h e f i rs t p a r t, i . e .
t h e s t r u c t u r a l s t re s s a t t h e h o t s p o t , t o g e t h e r w i t h a n a p p r o p r i a t e S - N
c u r v e , w h i c h i m p l i c i t l y c o n s i d e r s t h e e f f e ct s o f t h e l o c a l i z e d
fur the rm ore , i s va l id for a c e r ta in c la s s of we ld sha pe s a nd
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s t r e s s out s ide the loc a l i z e d notc h-a f fe c te d z one to the we
a p p r o a c h w a s f i r st l y a p p l i e d i n t h e 1 9 7 0 s t o t u b u l a r j o i n t s
s t ruc ture s , whe re the inc re a se in s t ruc tura l s t r e s s c a n be ve ry
l o c a l b e n d i n g o f t h e t u b u l a r s h e l l c lo s e t o t h e c o n n e c t i o n b e
and chord (Almar-N~ess , 1 985) .
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s t ru c t u r es ( R a d a j , 1 9 9 0 ) b e i n g t y p i c a l f o r F P S O s ( F l o a t i n g
S t o r a g e a n d O f f l o a d i n g U n i t s ) a n d s h i p s. H e r e , t h r e e d i f f er
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a t t a c hm e n t sur fa c e ) .
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Fo r we ld toe s on a p la te or she l l sur fa c e , i . e . type s a )
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o f t h e s t re s s d i s t r i b u t i o n i n t h e t h i c k n e s s d i r e c t i o n ( N i e m i , 1
e ve r , a uniq ue de f in i t ion of the s t ruc tura l s t re s s a t p la te e dg
t y p e b ) , w h i c h c a n b e u s e d f o r f a t ig u e s t r e n g t h a s s e s s m e n t ,
b le . The re fore , e x t r a pola t ion of e dge s t r e s se s i s c ur re n t ly
t h e o n l y p r a c t ic a l w a y f o r t h e d e t e r m i n a t i o n o f h o t s p o t s t r es
T h e h o t s p o t s t r e ss a p p r o a c h h a s o f t e n b e e n c r i t i c iz e d . E s
p r o b l e m o f d e f i n i n g a p p r o p r i a t e r e f e r e n c e p o i n t s f o r
e x t r a p o l a t io n c r e a t ed m a n y d e b a t e s . S e v e r a l c o d e s a n d g
v a r i o u s i n d u s t r i a l se c t o rs r e c o m m e n d d i f f e re n t p r o c e d u
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7/26/2019 54225323 Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs
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d e t e r m i n a t i o n o f h o t s p o t s t r e s se s a n d S - N c u r v e s . E v e n i n t h e
s h i p b u i l d i n g a n d o f f s h o r e i n d u s t r y , th e p r o c e d u r e s e s t a b l is h e d b y t h e
c la s s i f i c a t ion soc ie t i e s a nd o the r a u thor i t i e s a re d ive rg ing . Unc e r ta in t i e s
a b o u t t h e s u i t a b i l i t y o f t h e h o t s p o t s t r e ss a p p r o a c h h a v e b e e n r a i s e d b y
r o u n d - r o b i n a n a l y s e s s u c h a s I S S C ( 1 9 9 7 ) s h o w i n g l a rg e s c a t te r a n d
di f f e re nc e s be twe e n a n a lys i s r e su l t s a nd m e a su re d s t r e s se s .
T h e i n d u s t r y , h o w e v e r , c o n s i d e r s t h e h o t s p o t s t r e s s a p p r o a c h a s a
v e r y p r a c t ic a l a p p r o a c h , o f f e r i n g a b e t t e r a l t e r n a t i v e c o m p a r e d t o t h e
t r a d i t io n a l n o m i n a l s tr e s s a p p r o a c h f o r t h e a s s e s s m e n t o f i n d i v i d u a l
j o i n t g e o m e t r i e s i n s h i p s a n d F P S O ' s , w h i c h v a r y f r o m d e ta i l to d e t a i l
d u e t o d i f f e r e n t s c a n t l i n g s a n d g e o m e t r i c a l c o n f i g u r a t i o n s . A s l a r g e
di f f e re nc e s in f a t igue a s se s sm e nt proc e dure s a s we l l a s unde r -pre dic te d
f a t ig u e l i v e s c a n n o t b e t o l e r at e d , m u c h e f f o rt h a s b e e n s p e n t i n t o f u r t h e r
i n v e s t i g a t i o n s o f t h e h o t s p o t s t r e s s a p p r o a c h w i t h i n t h e J o i n t I n d u s t r y
P r o j e c t ( J IP ) F P S O F a t i g u e C a p a c i t y w i t h 1 8 p a r t n e r s, c o o r d i n a t e d b y
D e t N o r s k e V e r i t as . W i t h i n t h i s p r o j e c t , a s p e c i a l t as k g r o u p p e r f o r m e d
i n v e s t i g a t i o n s t o a n s w e r t h e f o l l o w i n g q u e s t i o n s :
1 . W h i c h w a y s o f m o d e l l i n g y i e l d h o t s p o t s t r e ss e s w i t h s u f fi c i e n t
a c c ura c y for typ ic a l s t ruc tura l de ta i l s ?
2 . H o w c o r r e l at e c e rt a i n t y p e s o f s tr e s s e x t r a p o l a t i o n w i t h S - N c u r v e s
a v a i l a b l e ?
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o f t y p i c a l d e t a i ls w h e r e l o c a l s t r a i n m e a s u r e m e n t s a n d f a t ig u e t e s t d a t a
a r e a v a i l a b le , a l l o w i n g c o m p a r i s o n w i t h s t r e ss a n d l i f e c a l c u l a ti o n s . I n
t o t al , n i n e p a r t n e r s h a v e p a r t i ci p a t e d i n t h e w o r k , o f f e r i n g a w i d e r a n g e
o f m o d e l l i n g a n d e v a l u a t i o n t e c h n i q u e s a s w e l l a s f i n i t e e l e m e n t
a n a l y s i s p r o g r a m s . A s c e r t a i n p r o c e d u r e s a n d i d e a s a b o u t s t r e s s
d e t e r m i n a t i o n a n d e v a l u a t i o n e x i s t , it w a s d e c i d e d t o i n c l u d e a l l o f t h e m
i n t h e a n a l y s i s r a t h e r t h a n s y s t e m a t i c a l l y v a r y i n g c e r t a i n m o d e l l i n g
pa ra m e te r s . Insofa r , the rou nd - rob in s t r e s s a na lys i s r e f l e c t s c ur re n t
t e c h n i q u e s f r o m w h i c h r e c o m m e n d a t i o n s f o r a p p r o p r i a t e p r o c e d u r e s
c a n b e d e r i v e d . F u r t h e r q u e s t i o n s a r i s i n g f r o m t h e a n a l y s i s a r e i n t e n d e d
t o b e i n v e s t i g a t ed i n P h a s e I I o f t h e p r o j ec t .
I t s h o u l d b e n o t e d t h a t t h e i n v e s t i g a t i o n i s f o c u s s e d o n t h e f a t i g u e
a s s e s s m e n t o f w e l d t o e s o n l y a n d n o t o n p o s s i b l e c r a c k s o r i g i n a t i n g
f r o m t h e r o o t o f w e l d s w i t h i n c o m p l e t e p e n e t r a t i o n w h i c h a r e u s u a l l y
a s s es s e d o n t h e b a s i s o f t h e n o m i n a l s tr e s se s i n t h e w e l d t h r o a t . A l s o t h e
a s s e s sm e n t o f s t r e s s p e a k s a t r o u n d e d p l a t e e d g e s a r e o u t s i d e t h e s c o p e
of th i s pa pe r .
S E L E C T IO N O F S T R U C T U R A L D E T A I L S
T h e s t r u c tu r a l d e t a i l s w e r e s e l e c te d c o n s i d e r i n g t h e f o l l o w i n g
cri ter ia :
• a l l t h r e e t y p e s o f h o t s p o t s s h o w n i n F i g . 1 s h o u l d b e i n c l u d e d
• p l a t e b e n d i n g c a u s e d b y t h e a tt a c h m e n t s h o u l d b e i n c lu d e d , w h i c h
i s q u i te t y p i c a l fo r d e t a i l s i n s h i p s a n d F P S O ' s
• s t r a in m e a s u r e m e n t s a n d f at i g u e t e st s s h o u l d b e a v a il a b l e ; m o d e l s
t e s te d w i t h i n t h e J I P a r e p r e f e rr e d b e c a u s e d e t a i l ed o r a d d i t i o n a l
i n f o r m a t i o n i s a v a i l a b l e
F i v e d e t a i ls h a v e b e e n s e l e c te d f o r t h e r o u n d - r o b i n h o t s p o t s t re s s
a n a l y s i s, w h i c h a r e s h o r t l y d e s c r i b e d i n t h e f o l l o w i n g :
D e t a i l l : I S S C M o d e l
T h e f i r s t d e t a i l , t h e m o d e l f o r t h e s t u d y o f I S S C ( 1 9 9 7 ) a l r e a d y
m e n t i o n e d a n d f u r t h e r d e s c r ib e d b y l w a h a s h i e t a l . ( 1 9 9 8 ) , i s t h e c o n -
n e c t i o n o f a b u c k l i n g s t i ff e n e r 1 0 0 x 1 2 t o t h e f l a n g e o f a T - s h a p e d l o n -
g i t u d i n a l (w e b 3 5 0 x 1 2 , f l a n g e 1 5 0 x 2 0 ) . T h i s m o d e l b e i n g t y p i c al fo r
F P S O a n d t a n k e r s t r u c t u r e s w a s t e s te d e x p e r i m e n t a l l y i n t h e J a p a n e s e
re se a rc h pro je c t SR 219 so tha t loc a l s t r a in m e a sure m e nts a re a va i l a b le ,
h o w e v e r n o f a t i g u e t es t d a t a , a s t u r n e d o u t l a t e r . T h e f i n i t e e le m e n t
m o d e l s h o w n i n F i g . 4 g i v e s a n i m p r e s s i o n o f t h e s t r u ct u r e . T h e l o n g i -
t u d i n a l i s s u b j e c te d t o b e n d i n g a n d s h e a r, c r e a t i n g a n i n c r e a s e d h o t s p o t
s t re s s a t t h e w e l d e d c o n n e c t i o n w i t h t h e b u c k l i n g s t i f fe n e r . I t s h o u l d b e
n o t e d t h a t t h e f i l le t w e l d h a s a n i n c r e a s e d l e g l e n g t h o f 1 3 m m t o a v o i d
root f a i lure . Th e hot spo t be lon gs to type a ) in F ig . 1 .
Detai l 2: Gusse t s on Plat e Edge
T h e s e c o n d m o d e l , g u s s e t s o n p l a t e e d g e s s h o w n i n F i g . 2 a ,
t a k e n f r o m t e s t s p e r f o r m e d b y H H I i n t h e I I P ( K i m , 1 9 9
1 5 0 m m l o n g a n d I 0 m m t h i c k g u s s e t s, r e p r e s e n t i n g f a c e b
ta pe re d e nd s , a r e f i ll e t -we lde d to the e dge s o f a p la te s t r ip 60
whic h i s subje c te d to t e ns i l e s t r e s se s . The c r i t i c a l we ld toe b
type b) in F ig . 1 .
Detai l 3 Doub l ing Plat e
T h e t h i r d d e t a i l i s t h e d o u b l i n g p l a t e s h o w n i n F i g . 2 b , w
c r i t i c a l we ld toe on the p la te sur fa c e be longs to type c ) in F i
m o d e l c o n s i d e r e d h e r e w a s i n v e s t i g a t e d i n t h e J a p a n e s e r e s e ar c
S R 2 0 2 ( Y a g i e t a l . , 1 9 9 1 ) , s o t h a t s t r a i n m e a s u r e m e n t s a n d f a t
a r e a v a i l a b l e . W h e n t h e p a r e n t p l a t e i s s u b j e c t e d t o t e n s i o n ,
s i d e d d o u b l i n g p l a t e c a u s e s s e c o n d a r y b e n d i n g . T h i s h a s t o b
e r e d i n t h e a n a l y s i s , c r e a t i n g s o m e m o d e l l i n g p r o b l e m s i n c
wi th she l l e l e m e nts .
In the c ou r se of the a na lys i s , r e la t ive ly l a rge d i f f e re nc e s be
J a p a n e s e m e a s u r e m e n t s a n d t h e a n a l y t i c a l r e s u l ts w e r e f o u n d .
m o s t l i k e l y c a u s e d b y a n g u l a r d i s t o r t i o n d u r i n g t h e w e l d i n
d o u b l i n g p l a t e o n t h e p l a t e s tr i p . A s p r o n o u n c e d s t r es s m a g
d u e t o m i s a l i g n m e n t s h a l l b e c o n s i d e r e d i n t h e a p p l i e d s t r es s r a
i n t h e d e s i g n S - N c u r v e , a s t r es s m a g n i f i c a t i o n f a ct o r K m =
c e r ta in s t r e s s gra die nt we re e s t im a te d for the loc a l s t r e s s on th
a d d i t i o n a l t e s ts a n d c a l c u l a t io n s p e r f o r m e d .
D e t a i l 4 : H o p p e r C o r n e r M o d e l
T h e f o u r t h d e t a i l i s th e h o p p e r c o m e r s h o w n i n F i g . 2 c w
a l s o t e st e d i n t h e J I P . T h e c r i ti c a l w e l d i s l o c a t e d a t t h e t r a n s i
t h e 1 0 m m t h i c k f l a n g e t o t h e s l o p e d h o p p e r p l a te . T h e s t
s u b j e c t e d t o a v e r t i c a l f o r ce , p r o d u c i n g b e n d i n g a n d s h e a r i n
T h e s t re s s i n c r e a s e w i l l b e r e f e r r e d t o t h e n o m i n a l b e n d i n g s t r
k n u c k l e u n d e r t h e a s s u m p t i o n o f f u l l e f f e c t i v e b r e a d t h . T h e
be lo ngs to type c ) in F ig . 1 .
Detai l 5: Load Carry ing Fi l l e t Welds
Th e la s t de ta i l i s a ga in a m o de l t e s te d in the J IP , i . e .
w e l d e d c o n n e c t i o n b e t w e e n a v e r t i c a l I - b e a m a n d a v e r t ic a l p l a
r e p r e s en t s a s t i f f e n e r c o n n e c t i o n b e i n g s u b j e c t e d t o s h e a r a n d
se e F ig . 2d . Re fe re nc e s t r e s s i s a ga in the nom ina l be n din g s tr
u p p e r e d g e o f t h e v e r t i c a l p l a te . T h e w e l d t o e a t t h e h o t s p o t b
t y p e b ) i n F i g . 1 .
c D e t a i l 4
d O
F i g u r e 2 . D e t a i l s 2 - 5 s e l e c t e d f o r R o u n d R o b i n A n a
( D e t a i l 1 is s h o w n i n F i g . 4 )
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F I N I T E E L E M E N T M O D E L L I N G A N D S T R ES S E V A L U A T I O N
I n o r d e r t o f i n d a p p r o p r i a t e t e c h n i q u e s f o r m o d e l l i n g w e l d e d s t r u c -
t u r e s a s w e l l a s e v a l u a t i n g t h e h o t s p o t s t r e ss i n c r e a s e d u e t o s t r u c tu r a l
e f fe c ts , a g r e a t v a r i e t y o f m o d e l s a n d w a y s o f e v a l u a t i o n w a s t a k e n i n t o
c o n s i d e r a t i o n . I n p r i n c i p l e , t h e d i f f e r e n t t y p e s o f m o d e l l i n g c a n b e
d i v i d e d i n t o t w o g r o u p s , i l l u s t r a t e d i n F i g . 3 :
* u s i n g p l a t e o r s h e l l d e m e n t s w i t h o u t w e l d r ep r e s e n t a t i o n ; t h e
e l e m e n t s a r e l o c a t e d i n t h e m i d - p l a n e o f t h e a s s o c i a t e d p l a t e; i n
I n m o s t c a s e s, t h e e l e m e n t l e n g t h a n d b r e a d t h s c l o s e t o t h
we re c hose n a s t x t t = p la te th ic kne ss ) . F ig . 4 e xe m pl i f i e s
l i n g b y D e t a i l 1 . S m a l l e r e le m e n t d i m e n s i o n s t y p i c a l l y t / 2 o
s e l e ct e d f o r m e s h e s i n d i c a t e d b y
2Solid2Ow(f) and 4Solid8w .
r e m a r k s o n s p e c i f i c m o d e l l i n g a s p e c ts a r e g i v e n i n t h e f o l l o w i
She l l e lem ents
t w e l d s F / 4 = 9 8 k N - - -
. o 0 e
i i i i
w = at tachmentwidth w
• S y m m e t r y
F i g u r e 3 . T y p i c a l F i n i t e E l e m e n t M o d e l s f o r th e W e l d e d J o i n t
She l l
odel
s o m e c a s e s t h e w e l d i s i n c l u d e d i n a s i m p l i f i e d w a y
u s i n g s o l i d e l e m e n t s w i t h t h e p o s s i b i l i t y to m o d e l t h e f i l l e t w e l d s
Detail
S h o w n i n F ig . 1
V a r i a t i o n s a r e s e e n i n d i f f e r e n t e l e m e n t t y p e s o f f e r e d b y t h e f i n i t e
e l e m e n t p r o g r a m s a s w e l l a s e l e m e n t s i z e s c h o s e n b y t h e a n a l y s t . T h e
f o l lo w i n g d e m e n t t y p e s w e r e c o n s i d e r e d i n t h e i n v e s t i g a t io n , u s i n g
s p e c ia l s h o r t n a m e s a s m e n t i o n e d b e l o w :
1Sol id20w and 2So l id20w
2 0 - n o d e d i s o p a r a m e t r i c s o l i d e l e m e n t , u s e d w i t h e i t h e r o n e o r t w o
e l e m e n t l a y e rs o v e r f u l l o r h a l f p l a t e t h i c k n e s s m o d e l l e d p r e f ix 1 a n d 2 ,
r e s p e ct i v e ly ) . T h e w e l d s a r e g e n e r a l l y i n c l u d e d s u f f ix w ) , i n s o m e
m o d e l s v e r y s i m p l y d i s r e g a r d i n g t h e r o o t g a p s e e F i g . 3 ) .
4Sol id8w
8 - n o d e d s o l i d e l e m e n t , n o r m a l l y u s e d w i t h f o u r l a y e r s o v e r t h e p l at e
t h i c k n e s s. T h e w e l d s a r e i n c l u d e d i n t h e m o d e l s s u f f ix w ) .
olidpw
H i g h e r - o r d e r s o l i d e le m e n t s g e o m e t r i c p - e l e m e n t s ) w i th r e f i n e d
m e s h a n d o p t i m i s e d s h a p e f u n c t i o n i n t h e c r i t i c a l a r e a . T h e w e l d s a r e
i n c l u d e d i n t h e m o d e l s s u f f i x w ) .
Shell Shell8r and Shell8p
8 - n o d e d s h e l l e l e m e n t w i t h o u t w e l d r e p r e s e n t a t i o n . I n c a s e o f o f f -
s e ts , e it h e r r i g i d l i n k s s u f f i x r ) o r a p l a t e c o n n e c t i o n b e t w e e n t h e m i d -
p l a n e s o f t h e p la t e s s u f f i x p ) a r e a r r a n g e d .
Shell4, Shell4r and Shell4p
S a m e a s a b o v e , b u t w i t h 4 - n o d e d s h e l l e l e m e n t s , p a rt l y h a v i n g c o n -
s t a n t s t r es s s t at e c s s ) a n d p a r t ly i m p r o v e d i n - p l a n e b e n d i n g b e h a v i o u r .
She l l8w
8 - n o d e d s h e l l m o d e l w i t h s i m p l i f i e d w e l d r e p r e s e n t a t i o n b y a r r a n g -
i n g a r e i n f o r c e d p l a t e s t r i p a t t h e f o o t o f t h e a t t a c h e d p l a t e , h a v i n g t h e
t h i c k n e s s i n c r e as e d b y o n e l e g l e n g t h a n d e x t e n d i n g t o t h e a c tu a l w e l d
t o e p o s i t io n . T h e e n d i n g s a r e s l o p e d , m e e t i n g t h e w e l d t o e p o s i t i o n o n
the pa re n t p la te .
F i g u r e 4. T y p i c a l F i n i t e E l e m e n t M o d e l l i n g
I n
Detail 1 (ISSC-Model) ,
the r e inforc e d f i l l e t we ld a t t
t i o n a l s t re s se s w h i c h i s c o n s i d e r e d i n o n e s h e l l m o d e l c o n
w e l d i n a s i m p l i f i e d w a y (ShellSw). I n a l m o s t a l l s h e l l m o d e
2 (Gusse t on P la te Edge) the gusse t s we re a r r a nge d d i r e c t ly
o f t h e l o n g i t u d i n a l p l a te e d g e e x c e p t f o r o n e m o d e l w h e r
e l e m e n t s w e r e a r r an g e d i n t h e m i d - p l a n e o f t h e g u s s e t a n d c o
a r e inforc e d p la te s t r ip w i th s lope d e nds
(She l l8w) . De ta i l 3
Doubl ing P la te ) w a s g e n e r a l l y m o d e l l e d t a k i n g t h e o f f s e t i n
In c a se of she l l e l e m e nts , e i the r r ig id l inks or ve r t i c a l p la
we re a r r a nge d , s e e F ig . 5a .
a ) D o u b l i n g F '
r i g id l i n k s o r
p l a t e
e l e m e n t s
b ) H o p p e r C o r n e r
F i g u r e 5 . M o d e l l i n g o f O f f s e ts i n S h e l l M o d e l
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O n e s p e c if ic p r o b l e m o f
Detail 4 Hopper Corner Mod el)
i s t he o f f -
s e t b e t w e e n t h e i n t e r s e c t in g h o r i z o n t a l , v e r t i c a l a n d s l o p e d p l a t e a t t h e
c r i t i ca l po in t . T h i s i s au tomat i ca l l y accoun ted f o r i n so l id mode l s , wh i l e
i t i s c o n s i d e r e d o n l y i n p a r t o f t h e s h e l l m o d e l s b y a p l a t e c o n n e c t i o n
b e t w e e n t h e t w o i n t e r s e c t i o n p o i n t s , s e e F i g . 5 b . T h e s e m o d e l s a r e
d e n o t e d b y Shell8p and Shell4p. A n add i t i ona l s t udy showed tha t t h i s
o f f se t r educes t he s t resses i n t he ac tua l s t r uc tu r e by up to 10 in t he
v i c i n i ty o f t h e h o t s p o t . F o r Detail 5 Load Carrying Fillet Welds),
a g a i n o n e s h e l l m o d e l c o n t a i n s t h e w e l d i n s i m p l i f ie d f o r m Shell8w).
T h e s t re s s e s w e r e e v a l u a t e d w i t h t w o o b j e c t i v e s , (a ) t o c o m p a r e t h e
c o m p u t e d s t r es s e s w i t h m e a s u r e d v a l u e s i n t h e a r e a c l o s e t o th e h o t s p o t
a n d ( b ) t o e x t r a p o l a t e t h e s t r e s s e s t o t h e h o t s p o t u s i n g c o m m o n t e c h -
n i q u e s , f r o m w h i c h t h e f o l l o w i n g t h r e e w e r e s e l e c t e d :
1 . L inear ex t r apo la t i on ove r r e f e r enc e po in t s 0 .5 and 1.5 x p l a t e
t h i c k n e s s t a w a y f r o m t h e h o t s p o t ( t e c h n i q u e p r e f e r r e d b y m o s t
c l ass i f i ca t i on soc i e t i e s )
2 . L inear ex t r apo la t i on ove r r e f e r enc e po in t s 0 .4 and 1 .0 x p l a t e
t h i c kn e s s t a w a y f r o m t h e h o t s p o t ( t e c h n i q u e r e c o m m e n d e d b y t h e
I n t e r n a ti o n a l I n s t i tu t e o f W e l d i n g , s e e H o b b a c h e r , 1 9 9 6)
3 . No ex t r apo la t i on , bu t con s ide r in g the s t ress va lu e a t 0 .5 x p l a t e
th i ckness t a s t he r e l evan t ho t spo t s t r ess
T yp ica l s t r e ss eva lua t ion pa ths a r e i nd i ca t ed i n F ig . 3 . F i r s t compar i -
s o n o f t h e a n a l y s i s r e s u l t s s h o w e d t h a t a b e t t e r a g r e e m e n t b e t w e e n t h e
r e s ul t s f r o m t h e d i f f e r e n t m o d e l s a n d f r o m t h e m e a s u r e m e n t s i s
a c h i e v e d i f t h e d i s t a n c e o f t h e r e a d - o u t -p o i n t s ( R O P ' s ) i s m e a s u r e d t o
t h e h o t s p o t a s m o d e l l e d , i . e . t o th e w e l d t o e i f t h e w e l d i s m o d e l l e d o r ,
e l se , to t he s t r uc tu r a l i n t e r sec t ion po in t , i f t he we ld i s no t mod e l l ed . T he
s a m e a p p l i e s t o t h e p o i n t w h e r e t h e s t re s s i s e x t r a p o l a te d t o . T h e j u s t i f i -
ca t i on f o r t h i s p r ocedur e , wh ich a f f ec t s t he r esu l t s f o r sheU mode l s
wi thou t we ld r ep r esen t a t i on , i s t ha t t he s t r ess a t t he f i c t i t i ous we ld t oe
p o s i t i o n i s i n m a n y c a s e s t o o l o w d u e t o t h e r e d u c e d s t if f n es s c o m p a r e d
to t he r ea l s t r uc tu r e . T h i s means on the o the r hand , t ha t t he p r oposed
e x t r a p o la t i o n t o t h e s t r u ct u r a l i n t e r s e c t io n p o i n t m a y y i e l d c o n s e r v a t i v e
r esu l t s - a tr i bu t e t o s imple mod e l l i ng .
A g r ea t va r i ab i l i t y ex i s t s i n se l ec t i ng t he t ype o f s t r ess and in eva lu -
a t i ng t he s t r esses a t t he des i r ed l oca t ions . T he se l ec t ed de t a i l s do no t
show s ign i f i can t d i f f e r ences be tween p r inc ipa l and d i r ec t i ona l s t r e ss
( pe r pend icu l a r t o t he we ld t oe ) so t ha t t he t ype o f s t r ess does no t a f f ec t
t he r esu l t s he r e . E i the r noda l s t r esses o r e l emen t s t r esses a r e eva lua t ed ,
t h e l a t t e r n o r m a l l y e x t r a p o l a t e d l i n e a r l y f r o m t h e i n t e g ra t i o n p o i n t s t o
t h e p l a t e s u r f a c e o r e d g e a n d i n s o m e c a s e s a v e r a g e d t o o b t a i n a m i d -
s ide s t r ess . Pa r t i cu l a r ly f o r 4 - noded she l l e l emen t s , d i f f e r en t r e su l t s
w e r e o b t a in e d d e p e n d i n g o n t h e s h a p e f u n c t i o n a n d t h e c o n s i d e r a ti o n o f
i n - p l a n e s t r e s s c o m p o n e n t s . B y c o m p a r i n g a l l r e s u l t s , c o n c l u
d r a w n w i t h r e s p e c t to a p p r o p r ia t e w a y s o f d e t e r m i n i n g h o t s p o
P R E S E N T A T I O N A N D D I S C U S S I O N O F T H E R E S U L T S
T he eva lua t ed s t r esses a r e sum mar i z ed in F igs . 6 - 10 , w
t h e m e a s u r e d s t r e s s e s a r e s h o w n . T h e n o m i n a l s t r e s s h a s b e
un i ty f o r de t a i l s 2 - 5 , so t ha t t he r esu l t s a r e ac tua l ly ho t sp
c o n c e n t r a t i o n f a c t o r s ( S C F ' s ) . I t s h o u l d b e k e p t i n m i n d t h a t
m e a s u r e d s t re s s e s c o n t a i n s o m e u n c e r t a i n t i e s w h i c h w a s r e v e a
t es t s by sca t t e r ing s t r a ins ob t a ined f r om d i f f e r en t compar ab le
and t e s t mode l s . T he r i gh t pa r t o f the f i gu r es show s the s t r esse
o u t - p o i n t s ( R O P ' s ) s e l e c t e d b y t h e p a r t i c i p a n t s . T h e s e R
loca t ed a t ce r t a in d i s t ances f r om the ho t spo t mode l l ed ( i . e . we
s t r u ct u r al i n t e r s e c t i o n p o i n t , i f t h e w e l d i s n o t m o d e l l e d , s e e
chap te r ) and can b e i den t i f i ed as noda l o r e l emen t s t resses ( a t
o r i n t e g r a ti o n p o i n t s ) i n t h o s e c a s e s w h e r e t h e e l e m e n t l e n g t h e
p l a t e t h i c k n e s s t ( e x c e p t i o n s a r e f i n e r m e s h e s d e n o t e d b y 2S
4Solid8w and Solidpw). The l e f t pa r t g ives t he s t r esses ex t r ap
t h e h o t s p o t a c c o r d i n g t o t h e t h r e e m e t h o d s m e n t i o n e d a b
s t r esses a t t he r e f e r ence po in t s wer e i n t e r po la t ed by the pa r t i c
cu r ve f i t ti ng .
I n o r der t o f ac i l i t a t e t he i n t e r p r e t a t i on o f t he r esu l t s , d i f f e r
o f s y m b o l s w e r e c h o s e n f o r t h e r e su l t s f r o m s o l i d a n d s h e l l m o
s y m b o l s h a v e b e e n c o n n e c t e d b y s t r a i g h t d o t t e d l i n e s w i t h s m
f or she l l mode l s . T hese s t r a igh t l i nes appear t o i nc r ease t h
h o w e v e r , r e l e v a n t a r e o n l y t h e s y m b o l s . T h e m e a s u r e m e n t r e
p l o t t e d u s i n g c o n t i n u o u s l i n e s . T h e y h a v e n o t b e e n e x t r a p o l a
m e s h s o l i d m o d e l s w i t h h i g h e r - o r d e r e l e m e n t s , w h i c h p l a y
r o l e , c a n b e r e c o g n i z e d b y :
* o p e n s q u a r e s ( p - e l e m e n t s Solidpw)
• f u l l squar es 2Solid20w 39)
I n t he f o l l owing , t he r esu l t s a r e d i scussed in de t a i l t b r t he
m o d e l s .
Detail I ISSC-M odel), Fig . 6
T h e m e a s u r e m e n t s h o w s a s t r e ss o f a p p r o x . 1 4 0 M P a a t a
1 0 m m a w a y f r o m t h e h o t s p o t ( I S S C , 1 9 9 7 ). O n l y o n e c o a
m o d e l i s i n c l u d e d 1Solid2Ow), y ie ld ing s l i gh t ly h igher s t r ess
the r esu l t s a r e somewhat a f f ec t ed by the s ingu la r i t y a t t he
a l t h o u g h t h e s t r es s w a s a v e r a g e d o v e r t h e a t ta c h m e n t w i d t h
s t i ff e n e r p l us w e l d s ) b y a r r a n g i n g r e l a t i v e l y w i d e s o l i d e l e m e n
con t r a r y , t he ve r y f i ne so l id mes h
2Solid2Ow f))
show s smal l e
wi th a s t eep s t r ess i nc r ease t o t he ho t spo t .
2 2 0 , 2 2 0
2 0 0 2 0 0
~ 1 8 0 ~ 1 8 0
~ 1 6 0
r 6 o
~ 1 4 0 ~ E 1 4 c
~ 1 0 0 ~ 1 0 ¢
80 - 8C
Re~ P~ . (t=2Omm)
i i i r r
0 1 0 2 0 3 0
~ E x p e r i m e n t
• , , - I -- ,S he l l4
• ~ - . S h e l l 8
- . 0 - . S h e l l 8 w
- ~ - . S h e l l 8
- - I - - . S h e l l 4
- ~ - . S h e l l 8
- , o - . S h e l l 4 ( c s s )
- - ( - - . S h e U 4
1 S o l i d 2 0 w
~ 2 S o l i d 2 O w ( f l
4 0 5 0 6 0
distance ROP s to hot spot [mm ]
F i g u r e 6 . S t r es s R e s u l t s f o r D e t a il 1 ( I S S C - M o d e l )
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T h e r e s u l ts o f t h e s h e l l m o d e l s a r e f a i r ly s c a t te r e d . L o o k i n g a g a i n a t
t h e l o c a t i o n 1 0 m m a w a y f r o m t h e h o t s p o t , t h r e e r e s u lt s a r e r e l a ti v e l y
c l o s e t o t h e m e a s u r e d o n e s , w h i l e f o u r o t h e r s a r e r e m a r k a b l y l o w e r . T h e
r e a s o n f o r t h i s c o u l d n o t b e c l a r i fi e d a s t h e s t r e s s e v a l u a t i o n p o i n t s a n d
methods a r e qu i t e d i f f e r en t ( a t nodes , a t e l emen t cen t r es , and ex t r apo-
l a t e d f r o m i n t e g r a t i o n p o i n t s t o t h e e l e m e n t e d g e ) .
T h e g e n e r a l t r e nd , t h a t s o l i d e l e m e n t s o v e r e s t i m a t e a n d s h e l l e l e -
men t s under es t ima te t he s t r esses , has been obse r ved a l so i n o the r s tud -
i es (e . g . I SSC, 2000) . P ou t i a in en and N iemi ( 2000) show ed tha t t h i s
h a p p e n s i n t h o s e c a s e s w h e r e a w e b i s a r r a n g e d b e l o w t h e p l a t e w i t h a
l o n g i t u d i n a l a t t a c h m e n t . I n o r d e r t o l i m i t t h e u n d e r - e s t i m a t i o n o f
s t re s s e s, t h e i n - p l a n e b e n d i n g b e h a v i o u r o f p la t e s s h o u l d b e i m p r o v e d
( t h e 4 - n o d e d e l e m e n t s s h o w i n g t h e l o w e s t r e s u l t s h a v e o n l y c o n s t a n t
s t r ess s t a t e ( css ) ) and the e l emen t wid th migh t have t o be r es t r i c t ed .
N i e m i ( 1 9 9 5 ) p r o p o s e d t h e ' a t t a c h m e n t w i d t h ' ( t h ic k n e s s o f a t t a c h m e n t
p l u s t w i c e w e l d l e g l e n g t h ) f o r t h e b r e a d t h o v e r t h e t w o e l e m e n t s i n
f r o n t o f t h e w e l d . F u r t h e r m o r e , t h e c o n s i d e r a t i o n o f t h e r e l a t i v e l y t h i c k
W h e n l o o k i n g a t t h e h o t s p o t s t r es s e s e x t r a p o l a t e d o v e r 0 .
s c a t te r i s m o d e r a t e w i t h i n ± 1 0 ( 1 5 2 M P a ± 1 5 M P a ) . I t i
t he ex t r apo la t i on i s pe r f o r med over 0 .4 t / 1 .0 t . T h i s i s obv ious
o f t h e r e l a t i v e l y c o a r s e m e s h e s , m a t c h i n g b e t t e r t h e f i r s t e x
t e c h n i q u e .
Detail 2 (Gussets on Pla te Edge), Fig. 7
T h e m e a s u r e m e n t s h o w s a m e a n s t r u c t u r al s t r e s s i n c r e a s e
l o c a t io n 5 m m a w a y f r o m t h e h o t s p o t , h o w e v e r w i t h a l a rg e s
I f t he two sm al l es t s t r e sses r esu l t i ng f r om the f i ne me
h i g h e r - o r d e r s o l i d e l e m e n t s
(2Solid2Ow(j ) and Solidpw )
a n d
the 4 - noded she l l e l emen t s wi th cons t an t s t r e ss s t a t e ( css ) a r e
the r esu l t s a r e f a i r l y c lose t oge the r . T h i s can a l so be seen in t
s t r e sses ex t r apo la t ed over 0 .S t /1 .5 t , wh ich a r e be tw een [ .85
i . e . _+6 . T he d i f f e r en t i dea l i sa t i ons o f t he r oo t gap an d s t r
t i o ns i n s o l i d m o d e l s ( a v e r a g e d o v e r t h i c k n e ss o r t a k e n a t c o
l i t t l e e f f ec t on t he r esu l t s . Ag a in , t he sca t t e r i s m uch h ighe r i
i s ex t r apo la t ed ove r 0 .4 t / 1 .0 t , wh ich i s due t o t he s t eep s t r ess
we ld s l igh t ly i nc r eases t he s t r ess ( by appr ox . 2 ) .
3 . 2
3 . 0
2 . 8
~ 2 . 6
2 . 4
~ 2.2
~ 2 . 0
~ 1 . 8
~ 1.4
1.2
1.(1
0.8
, , 3 . 2
3 . 0
2 . 8
( n 2 ' 6
~ 2 . 4
0 2 . 2
~ 2 . 0
1.4
1.2
1.0
0.8
R e f . P t s. ( t = 1 0 m m )
f r on t o f t he ho t spo t .
' ~ E x p e r i m e n t
1 S o l i d 2 0 w
- - ¢ ] - - S ol id p w
: 4 S o l id 8 w
0 4 S o l id 8 w
~ a ~ . - 2 S o l id 2 0 w
- - J k .- - 2 S o l i d 2 0 w
= 2 S o l i d 2 O w ( f )
- . 0 - . S h e l l 8 w
- . - t. . - .Sh el l4
I I - - I - - , S h e l l 4
:
1 0 5 2 0 2 5 3 0
d i s t a n c e R O P ' s t o h o t s p o t [ m m ]
Figur e 7 . S t r ess Resu l t s f o r De ta i l 2 ( Gusse t s on P l a t e E ~dge)
2 ,2 . , 2 .2
2 . 0 I 2 . 0
~ 1 . 8 ~ ) 1 . 8
'-- I::lZ
1 . 2 1 . 2
1 . 0 - - 1 . 0
Ref . Ots . ( t= 1gram)
I J - - O - - E x p e r i m e n t I
I i - - s o 2 o w j
I E ~ o l i d p w I
i ~ I - - e " 1 S ° l id 2 0 w
~ - )< - . S h e l l 4 r
\ . ' . / I . )K - 'Sh e l l 8 r I
• : ~ ' ~ ~ ~ , . o . ' S h e 4 r ( c s s )
~ t ~ ; . = . / I
- X S h e l l 4 r /
= . w ~ - - ~ ~ j - .
. . . . 5 . . . . 1 0 . . . . 1 5 . . . . 2 0 2 5 3 0 3 5 4 0
d i s t an c e R O P s t o h o t s p o t [ m m ]
Fig ur e 8 . S t r ess Resu l t s f o r De ta i l 3 ( Doub l in g P l a t e )
93
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Detail 3 One-Sided Doubling Plate), Fig. 8
T h e r e s u l t s a r e f a i r l y c l o s e t o g e t h e r a t t h e h o t s p o t a n d m a t c h t h e
m e a s u r e d v a l u e s c o n t a i n i n g t h e s t r e ss m a g n i f i c a t i o n f a ct o r K m
e x p l a i n e d e a rl i er . T h e s c a t te r i n t h e r e s u l ts i s m a i n l y d u e t o t h e p r o b l e m
o f c o r r e c t l y m o d e l l i n g t h e o f f s e t i n t h e s h e l l e l e m e n t m o d e l s . M o s t o f
t h e r e s u l ts o r i g i n a t i n g f r o m s h e l l m o d e l s w i t h c o n n e c t i o n s b y p l a t e s o r
r i g i d l i n k s a re s l i g h t l y a b o v e t h e o t h e r o n e s .
T h e r e m a i n i n g r e s u l t s f o r t h e c o a r s e s o l i d m o d e l s a r e v e r y c l o s e
toge the r , a l so whe n lo ok ing a t the e x t r a pola te d s t r e s se s.
Detail 4 Hopper Corner Model) , Fig. 9
At a f i r s t g la nc e , the r e su l t s a ppe a r r a the r s c a t t e re d . Only the m e a n
v a l u e f r o m t h e m e a s u r e m e n t , w h i c h a l s o s h o w e d a l a r g e s c a t te r , h a s
b e e n p l o t te d .
F i v e m o d e l s , w h e r e t h e m i s a l i g n m e n t i l l u s tr a t e d i n F ig . 5 b h a s n o t
b e e n c o n s i d e r e d Shell4 and Shell8) s h o w t h e h i g h e s t r e s u lt s a t 5 m m
dis ta nc e f rom the ho t spot . I f the se r e su l t s a s we l l a s those f rom the
m o d e l s w i t h h i g h e r - o r d e r s o l i d e l e m e n t s 2SoIid2Ow09 and So l
e xc lude d , the s c a t t e r i s f a i r ly sm a l l , r e su l t ing in a hot sp
i n c r e a s e b e t w e e n 1 . 9 6 a n d 2 . 1 6 i f e x t r a p o l a t ed o v e r 0 . 5 t / 1 . 5 t
f r o m t h e m e a n .
Detail 5 Load C arrying Fillet Welds), Fig . 10
Also for th i s m o de l , the r e su l t s r e ve a l a h igh sc a t t e r . As for
the s t r e s s s ingula r i ty p la ys a pa r t , inc re a s ing a dd i t iona l ly t
- v a l u es c l o s e to t h e h o t s p o t . I t is u n c l e a r w h y t h e m e a s u r e m e
ra the r sm a l l va lue s .
T h e s c a tt e r is m u c h r e d u c e d , i f t h e r e s u l ts f o r t h e f i n e m e s
h i g h e r - o r d e r s o l i d e l e m e n t s
2Solid2Ow D and Solidpw)
a s w
l o w e s t r e s u l t s f o r t h e 4 - n o d e d s h e l l e l e m e n t s w i t h c o n s t a n t s t
( c s s ) a re a ga in e xc lude d . The n the hot spot s t r e s s inc re a s
b e t w e e n 1 . 6 4 a n d 2 . 1 8 ( _+ 1 0 ) i f e x tr a p o l a t e d o v e r 0 . 5 t /1 . 5 t , w
l o w e s t r e s u l t re f er s t o a m o d e l w i t h s i m p l i f i e d w e l d r e p r e
Sh e l l Sw ) .
2 . 8 ~
2 . 6
2 . 4
2 . 2
2 . 0
~ 1 6
~ 1.4
~ 1 2
1 0
0 8
R e f . P t s . ( t= l O m m )
4
0 5
- - ( > - E x p e r i m e n t
-
- I - - , S h e l l 4
-
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-
~ . - , S h e l l S p
-
SK- ,She l l8
-
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-
- & - . S h e l l S p
.
. o . , S h e l l 4 ( c s s )
-
. -P - ,She l l4
1 S o l i d 2 0 w
,
. - - E l -. S o l i d p w
' . ¢ 4 S o l i d S w
~ k - - 2 S o l id 2 0 w
' ~ ¢ : ] ~ 1 ~ ~ - • : ~ . . - - - = - - 2 S o l i d 2 O w ( f )
~ i I i i I i I i ,,
0 1 5 2 0 2 5 3 0
distance ROP s to hot spot [mm]
F i g u r e 9 . S t r es s R e s u l ts f o r D e t a i l 4 ( H o p p e r C o m e r M o d e l )
3 . 2 •
2 8
2 6
1.0
0.8
u2. ~. m.
Ref. Pts. (t=lOmm)
\ \~ \ \ ,1
~ , ~ L
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- -+ - ,SheU4
-
- I - - , S h e l l 4
-
~ - . S h e l l 8
-
- ~ - , S h e l l 8
-
. o . , S h e l l 4 ( c s s )
, , , , , ~
5
- N.-,, 'Sh el l4
-
< > . S h e l l 8 w
~ IS o l i d 2 0 w
' - - 0 - - S o l i d p w
- - A - - 2 S o l i d 2 0 w
• - @ = - 4 S o l i d S w
~ 4 S o l i d 8 w
• ' = - 2 S o l i d 2 O w ( t )
t : = k
i i / i i i i
1 0 1 5 2 0 2 5 3 0
distance ROP s to hot spot [mm]
F i g u r e 1 0 . S t r e ss R e s u l t s f o r D e t a i l 5 ( L o a d - C a r r y i n g F i l l e t W e l d s )
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D E S I G N S - N C U R V E S
A v a i l a b l e f a t i g u e t e s t d a ta , i . e. f a t i g u e l i v e s o b t a i n e d f o r g i v e n l o a d
l e v e l s , c a n b e u s e d t o v e r i f y i f t h e c o m p u t e d h o t s p o t s t r e s s es c o r r e l a t e
wi th s t andar d S - N cu r ves . Fa t igue t e s t da t a a r e ava i l ab l e f o r de t a i l s 2 , 4
and 5 ( Kim , 1999) and a l so f o r de t a i l 3 ( Yag i e t a l . , 1991). I n add i t i on ,
m o d e l s s i m i l a r t o d e t a i ls 1 a n d 3 h a v e b e e n a n a l y s e d a n d t e s t e d b y H H I ,
w h i c h a r e i n c l u d e d i n t h e p r e s e n t a n a l y s i s a s
Mo del 1 Longi tudinal
Gusset s ) and Mo del 3 Two -Sided Doubl ing Plates ) . I t s h o u l d b e n o t e d
t h a t o n l y t es t s w i t h h i g h R - r a t io a r e t a k e n f r o m t h e d a t a b y K i m ( 1 9 9 9 ) .
T h e v e r i f i c a ti o n i s p e r f o r m e d o n t h e b a s i s o f l o w e r - b o u n d h o t s p o t
S C F s f r o m t h e a n a l y s i s. I n t h i s w a y t h e c o m p a r i s o n w i t h s ta n d a r d S - N
c u r v e s i s c o n s e r v a t i v e . A s d i s c u s s e d b e f o r e , t h e r e s u l t s f r o m t h e f i n e
m e s h e s w i t h h i g h e r - o r d e r s o l i d e l e m e n t s a s w e l l a s t h o s e f r o m t h e 4 -
n o d e d s h e l l s w i t h c o n s t a n t i n - p l a n e s t r e s s s t at e h a v e b e e n e x c l u d e d
w h i c h m e a n s t h a t S - N c u r v e s d e r i v e d a r e a s s o c i a t e d t o a n a l y s e s w i t h
c e r t ai n m o d e l l i n g a n d e x t r a p o l a t i o n t e c h n i q u e s .
T h e l o w e s t S C F - v a l u e s a r e m o s t l y d e t e r m i n e d b y s o l i d m o d e l s u s i n g
8 - n o d e d e l e m e n t s w i t h d i m e n s i o n s t / 4 x t / 4 x t /4 . T h e a d d i t i o n a l m o d e l s
1 an d 3 w e r e a l s o a n a l y s e d b y t h is t e c h n i q u e a n d a l s o b y s h e l l e l e m e n t s .
I t i s i n t e r es t i ng t o no t e t ha t t he r esu l t s f r om the ve r y f i ne so l id mod-
els
2Solid2Ow f)),
ex t r apo la t ed ov er 0 .4 t and 1 .0t , f i t qu i t e we l l w i th
t h e o t h e r v a l u e s e x t r a p o l a t e d o v e r 0 . 5 t / 1 . 5 t . H o w e v e r , t h e r e s u l t s
o b t a i n e d f r o m t h e p - e l e m e n t s a r e b e l o w t h e s e v a l u e s .
T he S - N p lo t i n F ig . 11 show s the f a t i gue l i ves i n r e l a t ion t o t he ho t
spo t s t r ess r ange f o r t he f i r s t ex t r apo la t i on t echn ique , i . e . nomina l
s t re s s r a n g e m u l t i p l ie d b y t h e l o w e s t c a l c u l a t e d h o t s p o t S C F s e x t r a p o -
l a te d o v e r 0 . 5 t/ 1 .5 t . T h e d e t a i l s 4 a n d 5 s h o w g e n e r a l l y h i g h e r li v e s
which a r e assumed to be due t o benef i c i a l r e s idua l s t r e sses f ound in
de t a i l 5 and to a f a i l u r e c r i t e r ion de f ined by a r e l a t i ve ly l ong c r ack .
Fur the r mo r e , t he r esu l t s f o r mod e l 1 and de t a i l s 2 - 3 a r e c lose r t o t he
l o w e r b o u n d d u e t o t h e f a c t th a t o n l y t h e w o r s t o f fo u r c o m p e t i n g h o t
spo t s i n t he mode l s a r e r ep r esen t ed .
I n a d d i ti o n , t h e S - N c u r v e F A T 1 00 , c h a r a c t e r i z e d b y a s lo p e e x p o -
n e n t m = 3 a n d a r e f e r e n c e v a l u e o f 1 0 0 M P a a t 2 m i l l i o n c y c l e s , is
p lo t t ed i n t he f i gu r e , r ep r esen t ing th e l owe r boun d o f a l l r e su l t s . T he
s a m e e v a l u a t i o n f o r t h e o t h e r e x t r a p o l a t io n t e c h n i q u e s , w h i c h a r e o m i t -
t e d h e re , s h o w s a l s o F A T 1 0 0 a s l o w e r b o u n d f o r th e r e s u l ts e x t r a p o -
l a te d o v e r 0 . 4 t / 1. 0 t , w h i l e F A T 9 0 i s t h e l o w e r b o u n d f o r t h e re s u l ts a t
0 .5 t . I t shou ld be no t ed t ha t a l l t e s t da t a u sed h e r e i s r e l a t ed to j o in t s
w i t h p l a t e th i c k n e s s r a n g i n g f r o m 1 0 to 1 5 m m .
R E C O M M E N D A T I O N S F O R H O T S P O T ST R E S S A N A L Y S I S
B a s e d o n t h e r e s u l t s o f t h e r o u n d - r o b i n f i n i t e e l e m e n t a n a l y s i s
d e s c r i b e d a b o v e , t h e f o l l o w i n g r e c o m m e n d a t i o n s c a n b e g i v e n .
H o t s p o t s t r e s s e s a r e c a l c u l a t e d a s s u m i n g l i n e a r m a t e r i a l b e h a v i o u r
u s i n g a n i d e a l i s e d s t r u c t u r a l m o d e l w i t h n o f a b r i c a t i o n - r e l a t e d m i s -
l
I 0 0
10
a l i g nm e n t . T h e l a t t e r h a v e t o b e c o n s i d e r e d i n c e r t a i n j o i n ts
p r o n o u n c e d m i s a l i g n m e n t e f f e c t s a r e p o s s i b le , s u c h a s p l a t e
c r uc i f o r m jo in t s an d t r ansv er se f i l l e t we lds on f r ee p l a t es , .b
a t e Kin- fac to r s d e f ined e . g . by H obb ache r ( 1996) . T he ex
l o c a l f i n i t e e l e m e n t m o d e l h a s t o b e c h o s e n s u c h t h a t e f f e
s t r uc tu r a l de t a i l cons ide r ed a r e su f f i c i en t ly smal l and r easona
a r y c o n d i t i o n s c a n b e f o r m u l a t e d .
I n p l a t e s t r uc tu res , t h r ee t ypes o f we ld t oes can b e i den t i
a r e exempl i f i ed i n F ig . I . T he r e l evan t ho t spo t s t r ess i s t h
s t r e s s o n t h e s u r f a c e o r a t t h e e d g e o f t h e p l a t e a c t i n g a p p
per pend icu l a r t o t he we ld t oe ( 45 to 90° ) .
M o d e l s w i t h t h i n p l a t e o r s h e l l e l e m e n t s o r a l t e r n a t i v e l y
e l e m e n t s m a y b e u s e d . I t s h o u l d b e n o t e d t h a t o n t h e o n e
ar r angemen t and type o f e l emen t s have t o a l l ow f o r s t eep s t
e n t s a s w e l l a s f o r t h e f o r m a t i o n o f p l a t e b e n d i n g , a n d o n
hand , on ly t he l i nea r s t r ess d i s t r i bu t ion in t he p l a t e t h i cknes
needs t o be eva lua t ed wi th r espec t t o t he de f in i t i on o f s t r uc t
T h e f o l l o w i n g m e t h o d s o f m o d e l l i n g a r e r e c o m m e n d e d , s e e a
Plate and Shel l Model s .
A s i m p l e m o d e l l i n g i s o f f e re d b y t h i n p l a t e a n d s h e l l e l e m
h a v e t o b e a r r a n g e d i n t h e m i d - p l a n e o f t h e s t ru c t u ra l c o m p
n o d e d e l e m e n t s a r e r e c o m m e n d e d p a r t i c u l a r ly i n c a s e o f s
g r ad i en t s . Car e shou ld be g iven to poss ib l e s t r ess unde
e s p e c i a l l y a t t y p e b ) w e l d t o e s i n c o n n e c t i o n w i t h 4 - n o d e d
w h i c h s h o u l d c o n t a i n a t l e a s t i m p r o v e d i n - p l a n e b e n d i n g m o d
T h e w e l d s a r e u s u a l l y n o t m o d e l l e d e x c e p t f o r s p e c i a l c
the r esu l t s a r e a f f ec t ed by h igh loca l bend ing , e . g . due t o
b e t w e e n p l a t e s o r d u e t o a s m a l l f r e e p l a t e l e n g t h b e t w e e
w e l d s . H e r e , t h e w e l d m a y b e i n c l u d e d b y v e r t i c a l o r i n c
e l e m e n t s h a v i n g a p p r o p r i a t e s t i f f n e s s o r b y i n t r o d u c i n g c
e q u a t i o n s t o c o u p l e t h e n o d e d i s p l a ce m e n t s . P a r t i c u la r l y f o
o f t ypes b ) and c ) , a s imp le a l t e r na t ive f o r we ld mode l l i ng i s
t he a r r angem en t o f a r e in f o r ced p l a t e s t r i p a t t he f oo t o f t he a
h a v i n g a t h i c k n e s s i n c r e a s e d b y o n e l e g l e n g t h a n d s l
ex t end ing to t he ac tua l we ld t oe pos i t i ons .
Sol id Element Model s :
A n a l t e rn a t i v e p a r t ic u l a r ly f o r c o m p l e x c a s e s i s o f f e r e d b
m e n t s w h i c h n e e d t o h a v e a d i s p l a c e m e n t f u n c t i o n a l l o w i n g
g r ad i en t s a s we l l a s p l a t e bend ing wi th l i nea r s t r ess d i s t r i bu
p la t e t h i ckness d i r ec t i on . T h i s i s o f f e r ed , e . g . , by i sopar amet r
e l e m e n t s ( w i t h m i d - s i d e n o d e s a t t h e e d g e s ) w h i c h m e a n s t h
e l e m e n t i n p l a t e t h i c k n e s s d i r e c t i o n n e e d s t o b e a r r a n g e d
e v a l u a t i o n o f t h e m e m b r a n e a n d b e n d i n g s t r e s s c o m p o n e n
p o s s i b l e i f a r e d u c e d i n t e g r a t i o n o r d e r w i t h o n l y t w o i n t e g ra
i n t h e t h i c k n e ss d i r e c t i o n i s c h o s e n . M o d e l l i n g o f t h e w e l d s i
r e c o m m e n d e d a n d e a s i l y p o s s i b l e a s s h o w n i n F i g . 3.
1 . 0 E + 0 4 1 . 0 E + 0 5 1 . 0 E + 0 6 1 . 0 E + 0 7
N c y c l e s )
F ig ur e 1 1 . F a t ig ue t e s t re su l t s v s . ho t spo t s t r ess r a ng e ba se d o n lo w e s t c a l c u la t e d SCF s e x t r a po la t e d o v e r 0 . 5 t /1 . 5 t
9 5
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Elemen t S i z es :
For both types o f modelling, the dimens ions of the first two or three
elements in front of the weld toe should be chosen as follows:
W e l d to e s o f t y p e s a a n d c : T h e
deme nt length should correspond
to the plate thickness. In the transverse direction, the plate thickness
may be chosen again for the breadth o f the plate elements. However, the
breadth over the first two elements should not exceed the 'attachment
width', i. e. the thickness of the attached plate plus 2 x the weld leg
length (in case of type c: the thickness of the web plate behind plus 2 x
weld leg length). This attachment width may also be taken for the width
of solid elements in front of the weld toe, see Fig. 3. Still open is the
question how the element size has to be defined e. g. for bulb profiles.
Furthermore it should be noted that a much finer mesh is needed in case
of 8-node solid elements.
Weld toes o f type b :
For weld toes at the plate edge, the plate thick-
ness is principally not a suitable parameter to determine the element
size and stress extrapolation points. A further study (Fricke and Bog-
dan, 2001) shows that fixed values can better be used to describe the
stress increase at in-p lane notches. From this s tudy and from details 2
and 5 of the current study it can be concluded that higher-order ele-
ments with element lengths of 10 x 10 mm together with a linear extra-
polation over the mid-side points yield conservative results. Therefore,
it is recommended to use element dimensions fixed to these dimensions .
St res s Eva luat ion:
The structural stress components on the plate surface should be
evaluated along the paths shown in Fig. 3 and extrapolated to the hot
spot. Recommended are stress evaluation points located at distances
0,5 t and 1.5 t away from the hot spot modelled, where t is the plate
thickness at the weld toe. I f the weld is not modelled, the hot spot is the
structural intersection point modelled. In case of type b) weld toes,
fixed distances of 5 mm and 15 mm are recommended.
If a relatively coarse mesh with the element sizes mentioned above is
chosen, the stresses may be evaluated as follows:
* In case of plate or shell elements the surface stress may be evalu-
ated at the corresponding mid-side points (i. e. taking the mean
value of the element stresses at the adjacent corners). At weld toes
of type c) the stress may be averaged over the width of the attach-
ment behind by taking the surface stress in the element centres as
also shown in Fig. 3.
* In case of solid elements the stress may be extrapolated l inearly to
the surface centre (usually after averaging the stress components at
each of the the two layers of integration points)
• At weld toes of type b), only part of plate bending obviously needs
to be considered. Further investigations are considered to be neces-
sary as such cases are outside the scope of the present analysis.
Fat igue Asses sment :
If the hot spot stress is evaluated by linear extrapolation in the way
described, the fatigue strength may be assessed with a usual design S-N
curve based on hot-spot stresses (e. g. Hobbacher, 1996).
Alternatively a simplified approach without any stress extrapolation
seems to be reasonable where the stress is taken at the location 0.5 t
(resp. 5 mm for weld toes of type b) away from the hot spot modelled
and assessed with a design S-N curve reduced by one fatigue class.
If the hot spot stress is evaluated from strain measurements or from
refined models with improved finite elements, a stress extrapolation
over reference points at distances 0.4 and 1.0 x plate thickness or a
quadratic extrapolation is recommended in line with Hobbacher (1996).
CONCLUDING R E M R K S
The present study has been used in the JIP together with other data
to derive a design hot spot S-N curve (Maddox, 2001). Here, a lower
S-N curve was found, which might be due to additional test data and in
particular to the inclusion of larger plate thickness (up to 25 ram).
The present study shows that further inves tigations are re
clarify especially the following items:
• Modelling and stress evaluation for very thick component
bulbs o f profiles
• Extent of plate bending to be considered at type b) weld toe
• Type of stress and evaluat ion in case of complex stress field
Finally it should be noted that root cracking at fillet we
covered by the hot spot stress analysis procedure. Approp
practical procedures for the analysis of the relevant stresses in
structures and their fatigue assessment are still to be developed
ACKNOWLEDGEMENTS
The JIP has been supported by 19 participants under coord
Det Norske Veritas. An overview over the project is given by
(2001). The present study has been managed by Germanisch
Hyundai Heavy Industries, as a participant of the JIP, perfo
fatigue tests with small scale specimens of typical fillet welded
ship structures, which was one of the main tasks in the JIP for
basis of the investigations described in the paper.
Nine participants contributed with great enthusiasm to th
robin analyses: Weimin Chen (Umoe Technology), Ben Fero
water), W.S. Kim (Hyundai Heavy Industries), Helena Po
(Lloyd's Register of Shipping), Philippe Rucho (Bureau
Armin S~ibel (Germanischer Lloyd), Tore Ull dand (Aker M
Richard Yee (American Bureau of Shipping) and also Y.-
(National University of Singapore). The author wishes to tha
them for their work and all participants of the JIP for their
comments and permission to publish the results.
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