Residenual Strength of Damaged Steel Ships

7/22/2019 Residenual Strength of Damaged Steel Ships

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Residual Strength of D am ag ed S teel Shipsand O ffsho re StructuresD r C . S . Sm i t h * a n d M r R . S . D o w **ADMIRALTY MARINE TECHNOLOGY ESTABLISHMENT, DUNFERMLINE, SCOTLAND

S Y N O P S SA rev iew is made o f var ious for ms o f s t ruc tura l dama gewhich ma y occur in sh ips an d o f f shore s tee l s t ruc tures,with particular re ference to the influence of suchdama ge on s t i f fness a t td duc t i le st rength . Cons idera t ionis g iven to damage in a sh ip ' s bo t tom or s ide she l l asmay be caused by co l l i s ions , grounding , hydrodynamicimpac t or exp los ions and to the in f luence o f suchd m ge on hull-girder bending strength. Reference ismad e to the eJfec ts o f bending and dent ing o f tubularmembers in o f fshore p la t forms and o f co l li s ion dama gein ex te rnal ly pressur ized r ing-s t i f fened cy l inders asmay be employed in submers ib le s a t td large -d iame tertubulars. So me me thods are sugges ted fo r eva luat ion o fres idual s t i l lness a t td s t rength w i th emphasis onapprox imate analys is techniques which can be appl iedquick ly a tu l economieal ly to ob ta in an ear O, assessmen tof damage eJfects.I N T R O D U T I O NC o n s i d e r a b l e e f f o r t h a s b e e n d e v o t e d t o e s t i m a t i n g t h ee x t e n t o f d a m a g e c a u s e d i n s t ee l s t r u c t u r e s b y c o l li s io n sa n d o t h e r f o r m s o f a cc i d e n ta l o r a b n o r m a l l o ad .Eva lua t ion o f co l l i s ion da m ag e in sh ips ~ .- '~ i s , fo re x a m p l e , c o m m o n l y c a r r i e d o u t i n o r d e r t o c h e c k t h ew a t e r t ig h t n e s s o f hu ll c o m p a r t m e n t s , t h e c o n t a i n m e n to f d a n g e r o u s o r p o l l u t a n t c a r g o e s s u c h a s l i q u id g a s o rb u l k o il o r , in t h e c a s e o f n u c l e a r - p o w e r e d s h i p s , t h ei n t e g r i t y o f r e a c t o r c o m p a r t m e n t s . R e l a t i v e l y l i t t l ea t t e n t i o n s e e m s , h o w e v e r , t o h a v e b e e n f o c u s s e d o ne v a l u a t i o n o f t h e r es i d u a l s tr e n g t h o f d a m a g e ds t r u c t u r e s . C r i t i c a l i s s u e s o f s a f e t y , e c o n o m y a n d , i n t h ec a s e o f w a r s h i p s , m i l i t a r y e f f e c t i v e n e s s m a y d e p e n d o nc o r r e c t a s s e s s m e n t o f t h e a b il i ty o f a d a m a g e d s h i p t oc o n t i n u e n o r m a l o p e r a t i o n s e i t h e r u n t i l c o m p l e t i o n o fi t s im m edia te m is s ion or in the longe r t e rm un t i l as cheduled drydocking or re f i t . S im i la r ly , in the case o fo f f s h o r e p l a t f o r m s , i t i s o b v i o u s l y i m p o r t a n t t o b e a b l et o a s s e s s q u i c k l y a n d a c c u r a t e l y , a s a b a s i s f o r r e p a i rd e c i s io n s , a n y l o ss o f s t r e n g t h a n d s t if f n e s s i n d a m a g e dm e m b e r s t o g e t h e r w i t h t h e c u m u l a t i v e e f f e c t s o fe l e m e n t d a m a g e o n s t r e n g t h o f th e p l a t f o r m a s a w h o l e .

I n a d d i t io n t o c o l l is i o n s, p o s s i b l e c a u s e s o f d a m a g et o a s h i p ' s h u l l i n c l u d e h y d r o d y n a m i c i m p a c t ( s l a m -

m i n g ) , g r o u n d i n g a n d c a r e l e s s b e r t h i n g o r d r y d o c k i n g .T h e e f f e c t s o f i n t e r n a l g a s e x p l o s i o n s i n o il t a n k s o rm a c h i n e r y s p a c e s m a y r e q u i r e e v a l u a t i o n , a n d i n t h ec a s e o f w a r s h i p s c o n s i d e r a t i o n m u s t b e gi v e n tod a m a g e c a u s e d b y u n d e r w a t e r o r a t m o s p h e r i ce xp lo si on s~ JL D a m a g e t o t h e s t r u c t u r a l f r a m e w o r k o fo f f s h o r e s te e l p l a t f o r m s m a y o c c u r d u r i n g l a u n c h in g o ri n s t a ll a t i o n a n d i s c a u s e d f a i r ly f r e q u e n t l y b y m i n o rs u p p l y - b o a t c o l l i s i o n s a n d b y a c c i d e n t a l d r o p p i n g o fm a s s i v e o b j e c ts f r o m p l a t f o r m d e c k s . D a m a g e c a n a l sor e s u l t f r o m f o u n d a t i o n m o v e m e n t s , in c l u d in g i np a r t i c u l a r e a r t h q u a k e a c t i o n . ~4~ A f u r t h e r t y p e o fd a m a g e w h i c h m a y a f f e c t b o t h s h i p s a n d o f f s h o r es t ruc tures i s tha t cau sed by f i re , occu r r ing e i the r ins e r v i c e o r d u r i n g c o n s t r u c t i o n .

T h e a i m o f t h i s p a p e r i s t o e x a m i n e t h e i n f l u e n c e o fs o m e o f t h es e f o r m s o f d a m a g e in s h i p s, s u b m e r s i b le sa n d o f f s h o r e p l a t f o r m s a n d t o i n d i c a t e w h e r e p o s s i b l eh o w t h e r es i d u a l s t r e n g t h a n d s t if f n e s s o f d a m a g e ds t r u c t u r e m a y b e e s ti m a t e d . C o n s i d e r a t i o n i s l i m it e d tod u c t i l e d a m a g e a n d f a i l u r e p r o c e s s e s : t h e r e s i d u a ls t r e n g t h o f s h ip s a n d o f f s h o r e s t r u c t u r e s c o n t a i n i n gd a m a g e i n th e f o r m o f c r a c k s , a f f e c t i n g s u sc e p t i b i li t y tof a i l u r e b y f a t i g u e a n d f r a c t u r e , i s a n i m p o r t a n t t o p i cr e q u i r i n g s e p a r a t e d i s c u s s i o n .

D A M A G E E F F E C T S I N S H I P SD a m a g e c a u s e d b y c o l l i s i o n s , h y d r o d y n a m i c i m p a c t ,e x p l o s i o n s , e t c . u s u a l l y t a k e s t h e f o r m o f l a te r a l e l a s t o -p l a s t i c d e f o r m a t i o n o f s t i f f e n e d p a n e l s f o r m i n g t h eb o t t o m , s i d e s o r d e c k s o f a s h i p ' s h ul l. P o s s i b le c o n s e -q u e n c e s o f s u c h d a m a g e i n c lu d e :(a ) reduc t ion in s ti f fnes s and s t reng th o f she l l o r deck

p a n e l s u n d e r s u b s e q u e n t l a t e r a l l o a d s ;( b ) l o s s o f s t if f n e s s a n d s t r e n g t h u n d e r i n - p l a n e l o a d s

( p a r t i c u l a r l y l o n g i t u d i n a l c o m p r e s s i o n a s s o c i a t e dw i t h h u l l - g i r d e r b e n d i n g ) a n d c o n s e q u e n t r e d u c t i o ni n u l t i m a t e h u l l - g i r d e r b e n d i n g s t r e n g t h .

S t i f fn e s s a n d s t r e n g t h o f a d a m a g e d s t r u c t u r e w i l l b ei n f lu e n c e d n o t o n l y b y g e o m e t r i c d i st o r t i o n b u t a l s o b yr e s i d u a l s t r e s s e s r e s u l t i n g f r o m p l a s t i c d e f o r m a t i o nf o l l o w e d b y p r e d o m i n a n t l y e l a s t i c u n l o a d i n g .


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Residual Strength o f Dam aged Stee l Ships and Offshore Structures 3S t r e n g t h o f d a m a g e d s t r u c tu r e u n d e r la t e r all o a dI n th e c a s e o f l i g h t ly - p l a t e d , s t r o n g l y - s t i f f e n e d s h e l l st y p i c a l o f w a r s h i p s ) d a m a g e c a u s e d b y im p u l s iv e

h y d r o d y n a m i c p r e s s u r e m a y b e c o n f i n e d p r i m a r i l y t ot h e p l a t i n g , a s i l l u s t r a t e d i n F i g u r e 1 : i n d i v i d u a l p l a t e

Figure I Plating damage caused by hydrodynamic loadp a n e l s c o n t a i n e d b e t w e e n l o n g i t u d i n a l a n d t r a n s v e r s es t i f fene rs de form in to s ing le lobes wi th re la t ive ly l i t t l ed i s t o r t i o n o f th e s t i ff e n e r s . R e f e r e n c e t o l o a d -d e f o r m a t i o n c u r v e s f o r p l a t e s u n d e r l a t e r a l p r e s s u r e ~s u g g e s t t h a t t h is f o r m o f d a m a g e w i ll n o t c a u s e s i g -n i f i can t los s o f p la t ing s t i f fnes s o r s t reng th under subse -q u e n t a p p l i c a t i o n s o f l a t e r a l l o a d : ' s h a p e - h a r d e n i n g "e f f e c t s m a y i n f a c t c a u s e s o m e i n c r e a s e o f p la t es t i ffness .

D a t a f o r r e c t a n g u l a r p l a t e s u n d e r c o m b i n e d l a t e r a lp res su re and long i tud ina l co m p res s ion ~"1 sugg es t tha t inp l a t e s o f a s p e c t r a t i o a/b > 2 hav ing low or in te r -m e d i a t e s l e n d e r n e s s (b/t < 6 0 ) , s i n g l e - lo b e d a m a g ed e f o r m a t i o n s , w h i c h i n h i b it t h e p r e f e r r e d f o r m o f b u ck l -i n g in t o a p p r o x i m a t e l y s q u a r e h a l f - w a v e s , w i l l o n l ys l ig h t ly r e d u c e l o n g i t u d i n a l c o m p r e s s i v e s t r e n g t h ; t h ee f f e c t o f l a te r a l p r e s s u r e a n d t h e r e f o r e p r o b a b l y o fd a m a g e d e f o r m a t i o n i s m o r e m a r k e d i n s l e n d e r p l a t e s(b/t > 80) . F ur th e r inv es t iga t ion o f th i s case i s needed .

D a m a g e o f t h e t y p e s h o w n i n F i g u r e 1 i s l ik e l y t oinduce m o re s ign i f i can t los s o f s t if fnes s and s t reng thu n d e r i n - p l a n e l o a d a p p l i e d i n t h e s h o r t e r d i r e c t i o n ,h e n c e c a u s i n g :( a ) a r e d u c t i o n o f h u l l- g i r d er b e n d i n g s t r e n g t h i n w a y

o f t r a n s v e r s e ly f r a m e d b o t t o m s he ll a n d d e c ks t r u c t u r e , a s c o m m o n l y e m p l o y e d i n t h e f o r e a n da f t reg ions o f a sh ip ' s hu l l ;

(b ) los s o f e f fec t ive f l cxura l s t i f fnes s in t ransve rsef ram es where the she l l p la t ing ac t s a s a f l ange tot h e f r a m e s , n o t a b l y i n d o u b l e - b o t t o m s t r u c t u r e s .

As i l lus t ra ted in F ig ure 2 , ~:b the bch av io ur o f a longr e c t a n g u l a r p l a t e u n d e r t r a n s v e r s e c o m p r e s s i o nd e p e n d s c r i t ic a l l y o n t h e r e l a t i v e f o r m o f i ni ti al d c f o fm a t i o n i n a d j a c e n t p l a t e p a n e l s : m u c h g r e a t e r l o s s o fs t i f f n e s s a n d s t r e n g t h o c c u r s w h e r e d e f o r m a t i o n i sa n t i s y m m e t r i c t h a n w h e r e d i s t o r t io n s h a v e a n

. / . . . . ~ L , = ~' / . / _ . . . . . . ~ , 6 ~ ~ A ~ ~ _ ~

I Z ] E EyFigure 2 Load-shortening curves fo r long, tranversety-compressedplates wi th symmetric and ant isymmetric deformat ionf ~a p p r o x i m a t e l y s y m m e t r i c , ' h u n g r y h o r s e ' f o rm .D a m a g e c a u s e d b y h y d r o d y n a m i c o v e r l o a d w i ll t e nd t oi n d u c e t h e la t t e r , m o r e f a v o u r a b l e f o r m o f d e f o r m a t i o n .T h i s e f f e c t h a s b e e n e v a l u a t e d a p p r o x i m a t e l y , f o r t h ecase o f a long s tee l p la te ( l a rge a/b) b y e x a m i n i n g t h eb c h a v i o u r o f a t r a n s v e r s e s t r i p o f p l a t in g s u b j e c t e d t o :( a ) a p p l i c a t i o n a n d r e m o v a l o f l a t e ra l p r e s s u r e c a u s i n g

e l a s t o - p l a s t i c d e f o r m a t i o n a n d a s s o c i a t e d r e s i d u a ls t re s ses ;

( b ) t r a n s v c r s e c o m p r e s s i o n u p to a n d b e y o n d c o ll a p s e .R e s u l ts w e r e o b t a i n e d u s i ng a c o m p u t e r p r o g r a m f o r

l a r g e d e t l e c ti o n e l a s t o - p l a s t i c a n a l y s i s o f f r a m e s b a s e do n i n c r e m e n t a l f in i te e le m e n t a n a l y s i s ~ k e a c h p l a t e s tr i pw a s d i v i d e d u p o v e r i ts le n g t h i n t o 3 0 u n i f o r m e l e m e n t sand ove r i t s dep th in to 21 f ib res to a l low for thep r o g r e s s i v e d e v e l o p m e n t o f p l a s t ic i t y . E l a s ti c a n de l a s t o p l a s t i c d e f o r m a t i o n s o f th e s t r i p w e r e a s s u m e d t oo c c u r u n d e r c o n d i t i o n s o f p l a n e s t r a i n : a m a t e r i a l w it hE /a v = 6 4 0 w a s a s s u m e d . A s s h o w n i n F i g u r e 3 a t w o -s p a n m o d e l w a s a d o p t e d , w i t h a p l a n e o f s y m m e t r y a tt h e c e n t r e o f e a c h s p a n b a n d a c o n d i t i o n o f si m p l esup por t a t the pos i t ion o f the long i tud ina l g i rde r .T r a n s v e r s e ( a x i a l) d i s p l a c e m e n t s o f th e p l a t e s t r ip w e r ea s s u m e d t o b e u n r e s t r a i n e d . A p p l i c a t i o n o f la t e ra lp r e s s u r e c a u s e d d e f o r m a t i o n s y m m e t r i c a l a b o u t t h es u p p o r t p o i n t B w i t h p e r m a n e n t s e t o f a m p l i t u d e 6 p a tA a n d C , a s s h o w n i n F i g u r e 3 ( a ) : u n d e r s u b s e q u e n ta p p l i ca t i o n o f c o m p r e s s i v e l o a d d e f o r m a t i o n s g r e wi n it ia l ly i n a s y m m e t r i c a l m a n n e r b u t " s n a p p e d t h r o u g h "t o u n s y m m e t r i c a l f o r m a t c o l l a p s e . T h e r e s u l t s a r e s u m -m a r i s e d i n F i g u r e 3 ( b ) in t h e f o r m o f c o m p r e s s i v e l o a d -s h o r t e n i n g c u r v e s f o r v a r i o u s b/t an d leve ls o f ~Sp. It isev iden t tha t fo r s l ende r p la te s in which the e la s t i cbuck l ing s t re s s i s subs tan t i a l ly lower than the y ie lds t r e ss , d a m a g e m a y c a u s e s i g n i fi c a n t l og s o f s t if f n e s sbu t has l i t t l e e f fec t on peak load ; in m ore s tocky p la te sw h i c h b u c k l e e l a s t o - p l a s t i c a l l y , d a m a g e w i l l c a u s e l o s so f b o t h t r a n s v e r s e s t i f fn e s s a n d s t r e n g t h .

M o r e g e n e r a l d a m a g e i n v o l v i n g c l a s t o - p l a s t i cb e n d i n g o f s t i ff e n e r s m a y a l s o r e s u l t f r o m l a t e r a l lo a d s .


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4 Jou rn a l o f Con s t r u c t i o na l S tee l Resea r ch . F b t. l , ~ b . 4. Septe.,n ber 1981

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6 . t~ yI igure 3 E/fe et c j syrnmetric damage on ~t iJ]hess and strength ofl ong p la t e s un de r t r ansve r se comp ressi on , fa ) M ode l adop ted inana l y s i s. ( b ) Load shor t en ing curves,A t y p i c a l l a t e r a l l o a d - d i s p l a c e m e n t c u r v e f o r a s t i f f c n e dp a n e l i s s h o w n i n F i g u r e 4 . T h e d e s i g n l o a d , i n d i c a t e db y p o in t B , c o r r e s p o n d s c o m m o n l y t o 2 / 3 o f t h e l o a dr e q u i r e d t o c a u s e f ir st y i e l d , i n d i c a t e d b y p o i n t C

( a l t h o u g h i n a s t r u c t u r e c o n t a i n i n g h i g h re s i d u a ls t r e s se s c a u s e d b v w e l d i n g o r c o l d - f o r m i n g , p r e m a t u r ey i e l d m a y c a u s e d e f o r m a t i o n a s in d i c a t ed b y t h e d o t t c dl in e t h r o u g h p o i n t D L D e f o r m a t i o n u n d e r a s t a ti c o r

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, //6 4 . . . . . . . . . . . . . . . .

A E G JFi,ure 4 L a t e r a l h ~a d i s p l a eemen t r e l a t i o n sh i p j b r sti j] 'enedp a n e ld y n a m i c o v e r l o a d i s li k e ly t o c o r r e s p o n d t o a c u r v e o ft h e f o r m A B C I I I , w i t h a p e a k a t p o i n t t l . P o s t - c o l l a p s er e d u c t i o n o f lo a d m a y b c c a u s e d b y :( a ) l o c a l s h e a r b u c k l i n g o f s t if f en e r w e b s a s s h o w n i n

F i g u r e 5 ( a ) ;( b ) t c a r i n g o f w c k l s , a l s o i l l u s t r a t e d ira F i g u r e 5 ( a )( c ) b u c k l i n g o f s h e l l o r d e c k p l a t i n g ( w h c r e th e p l a t i n g

a c t s a s a c o m p r c s s i o n f l a n g e t o t h e s t i f f e n c r s ) ;( d ) s t i f f c n e r t r ip p i ng ' , a s s h o w n i n F i g u r e 5 ( b ) , w h e r e

b e n d i n g c a u s e s o u t e r -l i b re c o m p r e s s i o n o f th es t i f f e n e r s .

(a)

( b )I.igure 5 (a) L oca l st i J fene r web buck l i ng a t td we ld tea rin g ~'~'. (h)St ( / fener t r ipping u n d e r l a t e r a l l o a d appl ied fro m xtiJyener ; ide ~ ~,.


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Residual Strength o f Damaged Steel Ships and Offshore Structures 5W h e r e d a m a g e h a s n o t p r o g r e s s e d b e y o n d p o i n t H

a n d w h e r e n o m a r k e d e v i d e n c e e x i s t s o f th e l o c a l fa i l u r em e c h a n i s m s l is t ed a b o v e , r e s id u a l s t r e n g t h u n d e r s u b s e -q u e n t l a t e r a l l o a d s i s l i k e l y t o r e m a i n a d e q u a t e .R e s i d u a l s t if f n e s s, a s i n d i c a t e d b y t h e s l o p e o f th eun load ing curve F G, i s un l ike ly to d i f fe r s ign i f i can t lyf r o m t h e o r i g i n a l s t i f f n e s s . P r o v i d e d t h a t t h e d a m a g e ds t r u c t u r e i s n o t r e q u i r e d t o w i t h s t a n d l a r g e i n - p l a n e( p a r t i c u l a r l y c o m p r e s s i v e ) l o a d s a n d t h a t o v e r r i d in gh y d r o d y n a m i c o r " a e s t h e t i c " r e a s o n s d o n o t e x i s t f o rr e s t o r i n g t h e o r i g i n a l g e o m e t r y , r e p a i r m a y b eu n n e c e s s a r y . I f c l e a r e v i d e n c e e x i s t s o f lo c a l f a i lu r e sa n d d a m a g e i s j u d g e d t o h a v e p r o g r e s s e d b e y o n d p o i n tH in F igure 4 , re s idua l s t reng th and s t i f fnes s a re l ike lyt o b e s u b s t a n t i a l l y r e d u c e d a n d d i f f i c u l t t o e s t i m a t ea c c u r a t e l y : e a r l y r e p a i r i s t h e n i n d i c a t e d .E f f e c t o f d a m a g e o n l o n g i t u d i n a l h u ll s t r e n g t hD a m a g e t o a s h i p ' s b o t t o m s h e l l o r d e c k s t r u c t u r e ,p a r t i c u l a r l y i n t h e m i d s h i p s r e g i o n , m a y h a v e a s e r i o u se f fec t on long i tud in a l s t r eng th , i .e . on the ab i l i ty o f thes h i p ' s h u l l t o w i t h s t a n d v e r t i c a l w a v e - i n d u c e d b e n d i n g .W h e r e d a m a g e i s s e v e r e , i n v o l v i n g h o l i n g o r g r o s sde form a t ion a s i l lus t ra ted in F igure 6 , the on ly s cns ib lcc o u r s e may bc t o a s s u m e t h a t t h e d a m a g e d s t r t . c t u r c isto ta l ly ine f fec t ive under in -ph ine loads and tha t hu l l -s e c t i o n p r o p e r t i e s a r c r e d u c e d a c c o r d i n g l y . W h e r ed a m a g e i s l e s s s e v e r e t h i s a s s u m p t i o n m a y b c t o o c o n .s c r v a t i v c i n w h i c h c a s e a r e a l i s t i c a s s e s s m e n t o fre s idua l s t i t ] ' ncs s and s t reng th i s neces sa ry .

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I i k 'u r e 6 G r o ~ d u m a g e t o s h i p ' s b o t t o m s t r u c t u r eI t h a s b e e n s h o w n ~ "' t h a t t h e m o s t l ik e l y f o r m o f

fa i lu re in f l a t pane l s o f o r tho gon a l ly s t i fl 'cned p la t ingform ing bo t tom she l l and deck s t ruc tures in sh ips i sc o l u m n - l i k e i n t c r f r a m c f l c x u ra l b u c k l i n g o f l o n g it u d i n alg i r d e r s w i t h a t t a c h e d p l a t i n g u n d e r l o n g i t u d i n a l c o m -pres s ion induced by hu ll bend ing . Th i s fo rm of fa ilu re ,w h i c h m a y b e s t ro n g l y i n f l u e n ce d b y c o m p r e s s i v es t i f fnes s o f the p la t ing , wi l l in m o s t p rac t i ca l ca sesp r e c e d e o t h e r c o l l a p s e m o d e s i n c l u d i n g l a t e r a l - to r s i o n a lb u c k l i n g o f g ir d e r s a n d o v e r a l l b u c k l i n g i n v o l v i n gb e n d i n g o f t r a n s v e r s e f r a m e s . T h e m o s t s i g n if i c an t f o r mo f d a m a g e i s t h e r e f o r e l ik e l y to b c l o c a l b e n d i n g o fl o n g i t u d i n a l g i r d e r s b e t w e e n t r a n s v e r s e f r a m e s .

Im per fec t ion s ens i t iv i ty s tud ies ~8.*:~ hav e sho wn tha tc o m p r e s s i v e s t r e n g t h o f st i ff e n e d p a n e l s m a y b e s u b -s t a n t i a ll y r e d u c e d b y i n it ia l d e f o r m a t i o n s o f th i s f o r ma n d m a y a l s o b e s t r o n g l y a f f e c t e d b y r e s i d u a l s t r e s s e sr e s u l ti n g f r o m e l a s t o - p l a s t i c b e n d i n g o f s t i ff e n e r s .

I n o r d e r t o i l l u s tr a t e t h e e f f e c t s o f s u c h d a m a g e , at y p i c a l l i g h t w a r s h i p h u l l s t r u c t u r e , a s s h o w n i n F i g u r e7 , h a s b e e n e x a m i n e d . E l a s t o - p l a s t i c d e f o r m a t i o n w a sa s s u m e d t o b e c a u s e d b y a p p l i c a t i o n o f a v e r t i c a l li nel o a d r u n n i n g t r a n s v e r s e l y a c r o s s t h e b o t t o m s t r u c t u r em i d - w a y b e t w e en a p a i r o f t r a n s v e r s e f r a m e s : d a m a g eo f th i s t y p e m i g h t a r i s e f r o m a b a d l y e x e c u t e d d r y d o c k -i n g . f r o m g r o u n d i n g , o r a s t h e l o c a l i n t e r f r a m e c o m -p o n e n t o f m o r e g e n e r a l d e f o r m a t i o n . T h e a n a l y s i s w a sca r r i ed ou t in th ree s t ages :( a ) s i m u l at i o n o f d a m a g e o c c u r r e n c e b y a p p l i c a ti o n

a n d r e m o v a l o f la t e r al l o a d t o p a r t o f t h e b o t t o ms t r u c t u r e ( e l e m e n t s n u m b e r e d 4 A , 4 B i n F i g u r e 7 )t o p r o d u c e p r e s c r i b e d l e v e l s o f c l a s t o - p l a s t i c d c f o fm a t i o n w i th c o r r e c t r e p r e s e n t a t i o n o f th ea s s o c i a t e d r e s i d u a l s t r e s s e s : t he s e v e r i t y o f d a m a g ew a s a s s u m e d t o v a r y a c r o s s t i l e b o t t o m s t r u c t u r e ,t h e a m p l i t u d e o f d c t \~ r m a t io n i n e l e m e n t s 4 B b e i n gt w i c e t h a t o f e l e m e n t s 4 A ( S t a n d 2 . 5 tr e s p e c t i v e l y ) :

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6 J o u r n a l o j ' C o n s t r u c t i o n a l S t e e l R e s e a r c h . {; ~l_ 1 , N o . 4 : S e p t e m b e r 1 9 8 1s iv e ) d i s p l a c e m e n t s to d a m a g e d a n d u n d a m a g e ds t i f f e n e d p a n e l s f o r m i n g t h e c r o s s - s e c t i o n i n o r d e rt o e s t a b l i s h a n e f f e c t i v e s t r e s s - s t r a i n c u r v e f o r e a c he l e m e n t :

( c} i n t e g r a t i o n o f e l e m e n t s t r e s s - s t r a i n c u r v e s o v e r t h ec r o s s - s e c t i o n to e v a l u a t e m o m e n t - c u r v a t u r er e l a t i o n s h i p s f o r t h e s h i p ' s h u l l a n d h e n c e t h eu l t i m a t e h u l l b e n d i n g s t r e n g t h u n d e r h o g g i n g a n d~ , u t L , l :s a ~ m E c o n d i t i o n s

T h e f ir s t t w o s t a g e s o f a n a l y s i s w e r e c a r r i e d o u t f o re a c h e l e m e n t o f t h e h u ll c r o s s - s e c t i o n u s i n g a n i n c r em e n t a l f in i te e l e m e n t m e t h o d ' < i n w h i c h( a ) t h e d e s t a b i t i s i n g in f l u e n c e o f c o m p r e s s i v e l o a d s in

e l e m e n t s ~ s a s r e p r e s e n t e d :b ) p r o g r e s s i v e d e v e l o p m e n t o f p l a s ti c i t y a l o n g t h e

l e n gt h a n d o v e r t i le c r o s s - s e c t i o n o f e a c h e l e m e n tw a s t r a c e d , i n c l u d i n g r e c o v e r y o f e l a s t i c s t i f fn e s s iny i e l d e d m a t e r i a l e x p e r i e n c i n g s t r a i n r e v e r s a l :

( c ) t h e cl T cc t s o f in i t ia l d e f o r m a t i o n a n d r e s i d u a l s t r e s sw e r e i n c l u d e d :

( d ) s t i ff n e s s o f th e p l a t i n g w a s d e f i n e d b v t h e s l o p c s o fl o a d s h o r t e n i n g c u r v e s l ia r r e c t a n g u l a r p l a t e s w i t hm o d e r a t e i n i t i al im p e r f e c t i o n s as s h o w n i n F i g u re8 . b a s e d a s d e s c r i b e d i n r e f e r e n c e 2 o n r e c e n tt h c o r c t i c a l a n d e x p e r i m e n t a l s t u d i e s o f p l a t es t i f f n e s s a n d s t r e n g t h .

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t \ ~ r m c d b y a r e p r e s e n t a t i v e s t i f f e n e r w i t h a n a t t a c h e ds t ri p o f p la t in g . T h r e e a d j a c e n t i n t c r f r a m e s p a n s w e r em o d e l l e d , , a it h a p l a n e o f s y m m e t r y : it t h e c e n t r e a n d ac o n d i t i o n o f s i m p l e s u p p o r t a s s u m e d a t e a c h t r a n s v e r s ef r a m e . T h e i d e a l i s c d s t r u c t u r e w a s s u b d i v i d e d a l o n g i tsl e n g t h i n t o e l c m c n t s a s s h o w n i n F i g u r e 9 , t h e e l e m e n t sb e i n g s u b d i v i d e d i n t o " f ib re ., ," o v e r t h e i r d e p t h . La r g ed e f l e c t i o n e f f e c ts w e r e i n c l u d e d i n t h e c o m p u t a t i o n a n da n i t e r a t i v e e q u i l i b r i u m c o r r e c t i o n w a s a p p l i e d a f t e re a c h i n c r e m e n t a l a p p l i c a t i o n o f l o a d o r d i s p l a c e m e n t .

P r c v i o u s p a r a m e t r i c s t u d ie s o F i m p e r f e c t i o neffe cts ~. " . ;:' h a v e c l e a rl y d e m o n s t r a t e d t h e i m p o r t a n ti n l l u c n c e o f b o t h r e s i d u a l s t r e s s e s a n d i n i ti a l d e l \ ~ r m a -t i o n s o n c o m p r e s s i v e s t i f f n e s s a n d s t r e n g t h o f s t i f fe n e dp a n e l s . I n a s s e s s i n g t h e c a p a c i t y ' o f a d a m a g e ds t r u c t u r e i t i s t h c r e t \ w c n e c e s s a r y t o c o n s i d e r t h e c f f e c to b o t h t h e s e q i , a n t i t i t c s : o n l y b y i n c l u d i n g i n t h c

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a n a l y s i s , a s d e s c r i b e d a b o v e , a s i m u l a t i o n o f t hed a m a g e p r o c e s s , c a n r e s i d u a l s t r e s s d i s t r i b u t io n s b ee s t a b l i s h e d a n d a c c o t m t e d f o r a c c u r a t e l y .

T h e r e s tt l ts a r e s u m m a r i s e d i n F i g u r e 1 0. w h i c hs h o w s e f f e c t i v e s t r e s s - s t r a i n c u r v e s tk ~r d a m a g e d a n du n d a m a g e d e l e m e n t s o f t h e h u ll c r o s s s c c t i o n ( l a b e l l e dm a c c o r d a n c e w i t h F i g u r e 7 ) . I t i s e v i d e n t f r o m c u r v c s4 , 4 A a n d 4 B i n F i g t, r c I O t h a t d a m a g e o f a m p l i t u d c2 . 5 t a n d 5 t c a u s e s r e d u c t i o n s o f 1 3 p e r c e n t a n d 3 7 p e rc c n t r e s p e c t i v e l y i n t h e c o m p r e s s i v e s t r c n g t h o f th eb o t t o m s t r u c t u r e : s o n ic lo s s t) l" t e n s i l e s t i f f n e s s ~.lnds t r c n g t h i s a l s o e v i d e n t .

T h e f o r m o f ti le a v e r a g e s t r e s s s t r a i n c u r v e s : , h o w nm F i g u r c 1 0 r e q u i re s s o m e c o m m e n t . T h c " d o u b lch u m p " s h a p e o f m o s t o f t h e s e c u r v e s i n th e c o m p r e s s i v er a n g e , i n w h i c h a n i n i t i al p e a k o r s h o u l d e r i s l ' o lt o w c db y a s e c o n d a r y d r o p i n lo a d , i s a f e a tu r e o f m u l t i .s p a ns t i ff e n e d p a n e l s i n w h i c h p l a s t i c i t y s p r e a d s t h r o u g h f ir s to n e a n d t h e n a n a d j a c e n t s p a n o f th c i d c a li s c ds t ru c t u re : d e v d o p m e n t o f a c o l la p s e m e c h a n i s mr e q u i r e s f o r m a t i o n o f a v i r t u a l p l a s t i c h i n g e at t h ec e n t r e o f e a c h a d j a c e n t s p a n a n d b e c a u s e o f th e u n s y mm e t r i c a l s h a p e o f t h e c r o s s - s e c t i o n a n d f o r m o f in i t ia ld e R ~ r m a t io n t h e s e ' h i n g e s ' d o n o t o c c u r s i m u l t a n e o u s l y .I n t w o e a s e s ( c u r v e s 2 a n d 4 i n F i g u r e 1 0 ) u n s t a b l ep o s t - c o l l a p s e b e h a v i o u r w a s e n c o u n t e r e d a n d i t w a sr l c e c s s a r y t o f o l l o w t h e n u m e r i c a l p r o c e d u r e d e s c r i b e din r e f e r e n c e 1 3, r e q u i r i n g i n c r e m e n t a t i o n o f l a t e r a ld i s p h i c c m e n t i n t h e p o s t c o l l a p s e r a n g e , i n o r d e r t oc t u n p u t c n o t i o n a l s t a t i c u n l o a d i n g b e h a v i o u r i n v o l v i n ga t e m p o r a r y r e v e r s a l o f e n d - s h o r t e n i n g d i s p l a c e m e n t s( s h o w n b y t h e s o l i d li n e s m F i g u r e 1 0 ): p o s t c o l l a p s eb c h a v i o u r o f m o s t p r a c t i c a l s t r u c t u r a l c o m p o n e n t s .i n c l u d i n g s t i f fe n e d p a n e l s i n a s h i p ' s b o t t o m s h e ll a n dd e c k s , w i l l h o w e v e r be i n t l t , c n c e d b y t h c a x i a l e l a s t i cs t i ff n e s s o f th e s u r r o u n d i n g s t r u c t u r e l e a d i n g in th e c a s co f u n s t a b l e s y s t e m s t o u n l o a d i n g c t, r v e s a s i l l u s t r a t e db y t h e d o t t e d l i n e in F i g u r e 1 0 w h e r e u n l o a d i n g f r o mp o i n t P t o p o i n t Q o c c u r s d y n a m i c a l l y . A s d e m o n st r a t c d i n r e f e r e n c e 13 u n s t a b l e p o s t c o l l a p s e b e h a v i o u rof c o l u r n n l i k e s t r u c t u r e s i s c o n f i n e d t o c a s e s i n , a h i c h


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A n e f f e c ti v e l o n g i t u d in a l s t r e s s - s t r a i n c u r v e h a v i n gb e e n e s t a b l i s h e d f o r e a c h e l e m e n t o f th e h u l l c r o s s -s e c t i o n , t h e f in a l s ta g e o f t h e a n a l y s i s w a s c a r r i e d o u tfo l lowing a s im ple p ro ced ure (14) in wh ich :( a ) v e r t i c al c u r v a t u r e o f t h e h u ll w a s a s s u m e d t o o c c u r

i n c r e m e n t a l l y : c o r r e s p o n d i n g i n c r e m e n t a l e l e m e n ts t r a i n s w e r e c a l c u l a t e d o n t h e a s s u m p t i o n t h a tp l a n e s e c t i o n s r e m a i n e d p l a n e a n d t h a t b e n d i n go c c u r r e d a b o u t t h e i n s t a n t a n e o u s e l a s t i c n e u t r a la x i s o f t h e c r o s s - s e c t i o n ;

( b ) e l e m e n t i n c r e m e n t a l s t r e s s e s w e r e d e r i v e d f r o mi n c r e m e n t a l s t r a i n s u s i n g t h e s l o p e s o f s t r e s s - s t r a inc u r v e s ( e f f e c ti v e t a n g e n t m o d u l i ) a s s h o w n i nF i g u r e 1 0 : i n t h e c a s e o f u n s t a b l e p o s t - b u c k l i n gb e h a v i o u r ( c u r v e s 2 a n d 4 ) u n l o a d i n g p a t h sc o r r e s p o n d i n g t o t h e d o t t e d l i n e s w e r e a d o p t e d ;c e r t a i n a r e a s o f t h e c r o s s - s e c t i o n , o c c u r r i n g a tin te rs ec t ion s o f deck s wi th the s ide shel l o rl o n g i tu d i n a l b u l k h e a d s a n d l a b e ll e d ( I ) i n F i g u r e 7 ,w e r e a s s u m e d t o r e s i s t b u c k l i n g a n d t o f o l l o w t h em a t e r i a l s t r e s s - s t r a i n c u r v e u p t o a n d b e y o n dc o l l a p s e :

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( c ) e l e m e n t st r e s s i n c r e m e n t s w e r e i n t e g r a t e d o v e r t h ec r o s s - s e c t i o n t o o b t a i n b e n d i n g m o m e n t i n c r e -m e n t s , t h e s e t o g e t h e r w i t h i n c r e m e n t a l c u r v a t u r e sb e i n g s u m m e d t o p r o v i d e c u m u l a t i v e v a l u e s o fb e n d i n g m o m e n t M a n d c u r v a t u r e 4 .

S h e a r f o r c e s a n d s h e a r l a g e f f e c t s i n t h e m i d s h i p sr e g i o n o f a s h i p ' s h ul l a r e u s u a l l y s m a l l a n d h a v e b e e ni g n o r e d .

C o m p u t e d m o m e n t - c u r v a t u r e r e l at i o n sh i p s a r es h o w n i n F i g u r e 11 f o r e a c h o f th e f o l l o w i n g c a s e sCa s e A : U n d a m a g e d h u l l, b u c k l i n g e f f e c t s i g n o r e d ( al le l e m e n t s f o l l o w m a t e r i a l s t r e s s - s t r a i n c u r v e ) ;Case B: U n d a m a g e d s t r u c t u r e ; e l e m e n t c o m p r e s s i v e

s t r e s s - s t r a i n c u r v e s f o l l o w t h o s e s h o w n i nF i g u r e I 0 u p t o p e a k l o a d s a n d t h e r e a f t e rr e m a i n h o r i z o n t a l , i . e . p o s t - b u c k l i n g l o a dr e d u c t i o n i s i g n o r e d ;

Case C: U n d a m a g e d s t r u c t u r e ; c l e m e n t s t r e s s - s t r a i nc u r v e s f o l l o w t h o s e s h o w n i n F i g u r e I 0i n c l u d i n g p o s t - b u c k l i n g l o a d r e d u c t i o n s ;Case D: D a m a g e d h u l l , o t h e r w i s e s a m e a s c a s e C .

C o m p a r i s o n o f c a s e s C a n d D i n F i g u r e I 1 i n d i c a t e s alos s o f 15 pe r cen t and 3 pe r cen t in hu l l s t reng th und erh o g g i n g a n d s a g g i n g l o a d c o n d i t i o n s r e s p e c t i v e l y a s ar e su l t o f d a m a g e t o t h e b o t t o m s t ru c t u r e . T h e c u r v e sshown in F igure I I a l so conf i rm prev ious f ind ings (14~ :


7/14

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p a r t i c u l a r l y u n d e r a s a g g i n g l o a d c o n d i t i o n , i sl ike ly to be subs tan t i a l ly l e s s than the fu l ly p la s t i cs t r e n g t h M p a s a r e s u l t o f l o c a l c o m p r e s s i v e f a i lu r e ( 2 )o f s t if f e n e d b o t t o m s h e ll o r d e c k p a n e l s ;

(b ) tha t u l t im a te hu ll s t reng th i s s t ron g ly in f luenced (3 )n o t o n l y b y t h e b u c k l i n g s t r e n g t h b u t a l s o b y t h ep o s t - c o l l a p s e b e h a v i o u r o f s t i ff e n e d p a n e l s f o r m i n gthe hu l l c ros s -sec t ion .

D a m a g e c a u s e d b y s t ra i g h te n i n gA s u b t l e f o r m o f d a m a g e w h i c h m a y a f f e c t t h e c o m -p r e s s i v e s t r e n g t h o f s ti f f e n e d p a n e l s a n d h e n c e i n f l u e n ceh u l l - g i r d e r s t r e n g t h i s t h a t c a u s e d b y c o l d - s t r a i g h t e n i n go f d e f o r m e d s t r uc t u r e . W h e r e e x c e s si v e m i s a l ig n m e n to r w e l d - i n d u c e d d i s t o r t i o n o c c u r s d u r i n g f a b r i c a t i o n i na s h i p y a r d , i t i s n o t u n c o m m o n f o r t h e d e f o r m e ds t r u c t u r e t o b e f o r c e d i n t o a g e o m e t r y w h i c h w i l l p a s si n s p ec t io n b y u s e o f m e c h a n i c a l ' s t r o n g b a c k s ' o rh y d r a u l i c j a c k s . T h i s p r o c e d u r e i s i l l u s t r a t e d i n F i g u r e1 2 fo r t h e c a s e o f a st i f fe n e d p a n e l c o r r e s p o n d i n g t oe l e m e n t 4 o f t h e h u ll s e c t i o n s h o w n i n F i g u r e 7 . A t w o -s p a n m o d e l w a s e x a m i n e d a s s h o w n i n F i g u r e 1 2 (a ),s t i f f e n e r d e f o r m a t i o n s b e i n g a s s u m e d t o h a v e t h e f o r mo f u n i f o r m c u r v a t u r e w i t h a m p l i t u d e s ~ t a n d & a t t h ec e n t r e s o f a d j a c e n t s p a n s . T h r e e c a s e s w e r e c o n s i d e r e d :( I ) 6 , = -5~ = O . 001a (wi th in the to le ra nces

spec i f i ed by A P I ~ ls ) and D N V tl"~ fo r o f f sh ores t r u c t u r e s a n d b y B S 5 4 0 0 tI T) f o r b o x - g i r d e rb r i d g e s ) ;g t = - 0 . 0 0 1 a , ~ = 0 . 0 0 5 a ( w el l o u t si d e n o r m a lt o l e r a n c e s ) ;i n i t i a l d e f o r m a t i o n c o r r e s p o n d i n g t o c a s e 2 w a s' c o r r e c t e d ' b y a p p l i c a t io n a n d r e m o v a l o f a c o n -c e n t r a t e d l a t e ra l f o r c e P a t t h e c e n t r e o f th e r i g h t -hand span a s shown in F igure 12(a ) : the re su l t ingd e f o r m a t i o n , s h o w n b y a d o t t e d l i n e , i n v o l v e dv i r t u a ll y z e r o d i s p l a c e m e n t a t t h e c e n t r e o f t her i g h t - h a n d s p a n a n d w a s w e l l w i t h i n t o l e r a n c el im i t s; a pa t t e rn o f re s idua l s t re s s w as s e t up ,v a r y i n g a l o n g t h e l e n g t h o f t h e s t r u c t u r e a n dh a v i n g t h e f o r m s h o w n i n F i g u r e 1 2 ( b ) a t t h e p o i n to f a p p l i c a t i o n o f P .

I n e a c h c a s e c o m p r e s s i v e s t r e n g t h w a s e x a m i n e d b ya p p l i c a t i o n o f e n d - s h o r t e n i n g d i s p l a c e m e n t s , le a d i n g toload -sho r ten in g curv es a s sho wn in F igure 12(c ) . I t i se v i d e n t t h a t b e c a u s e o f th e r e s i d u a l s t r e s s e s i n d u c e d b yc o l d - b e n d i n g t h e e f f e c t o f s t r a i g h t e n i n g i s t o w e a k e nr a t h e r t h a n s t r e n g t h e n t h e s t r u c t u r e .E f f e c t o f o v e r a l l g r il la g e d e f o r m a t i o nW h e r e d a m a g e o f a s h i p 's b o t t o m s h el l o r d e c ks t r u c tu r e t a k e s t h e f o r m o f m o d e r a t e o v e r a ll d e f o r m a -t i o n i n v o l v i n g b e n d i n g o f t r a n s v e r s e a s w e ll a s


8/14

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A n e f f e c t iv e m e t h o d o f s o l v i n g t h e c o u p l e d d i f f e r e n -t ia l e q u a t i o n s i s t h a t s u g g e s t e d b y L e v y m i n w h i c h w0a n d w a r e e x p r e s s e d i n t h e f o r m o f a d o u b l e i n fi n it es e r i e s s a t i s f y i n g t h e s u p p o r t b o u n d a r y c o n d i t i o n s , i nc o n j u n c t i o n w i t h t h e A i r y s t r e s s f u n c t i o n F w h i c hs a t i s f i e s t h e d i f f e r e n t i a l e q u a t i o n s a n d b o u n d a r y f o r c e s ;t h e r e s u l t i n g n o n - l i n e a r s i m u l t a n e o u s a l g e b r a i c e q u a -t i o n s c a n t h e n b e s o l v e d i t e r a t i v e l y w i t h a c o m p u t e r .

T h i s a n a l y s i s t e c h n i q u e a l l o w s a n e s t i m a t e t o b em a d e f o r a n y m o d e r a t e l y l a r g e i n i t i a l d e f o r m a t i o n a n da n y c o m b i n a t i o n o f i n - p l a n e a n d l a t e r a l l o a d , o f :(a ) the e f fec t ive wid th o r in -p lane s t i f fnes s o f thed a m a g e d p a n e l a n d h e n c e i t s c o n t r i b u t i o n t o t h e

hu l l g i rde r s ec t ion m odulus ;(b ) l a t e ra l de f lec t ions and a s soc ia ted e la s t i c s t re s ses .I f on th i s bas i s s t re s s l eve l s a re foun d to be be low y ie ldp o i n t ( p o s s i b l y w i t h s o m e a l l o w a n c e f o r r e s i d u a ls t r e s s e s ) t h e a d e q u a c y o f t h e d a m a g e d s t r u c t u r e i sr e a s o n a b l y a s s u r e d .

S o m e n u m e r i c a l r e s u l t s , o b t a i n e d u s i n g a c o m p u t e rp r o g r a m d e v e l o p e d a t A M T E , z " a r e s h o w n in F i g u r e13 , i l lus t ra t ing the e f fec t o f an ove ra l l in i t i a l de form a-t i o n o n t h e e f f e c t i v e b r e a d t h a n d c e n t r a l d e f l e c ti o n o ft h e o r t h o t r o p i c p a n e l u n d e r t h e a c ti o n o f i n - p l a n eload ing .D A M A G E E F F E C T S I N O F F S H O R EP L A T F O R M ST h e s t r u c tu r a l f r a m e w o r k o f m o s t o f f s h o r e p l a tf o r m s i sf o r m e d b y l o n g u n s t i f f e n e d t u b u l a r m e m b e r s w h o s ed i a m e t e r / t h i c k n e s s r a t i o ( D / t ) i s usua l ly chosen to bel e ss t h a n 5 0 i n o r d e r t o a v o i d l o c a l b u c k l i n g o f t h e t u b ew a l l s . S u c h m e m b e r s a r e s u s c e p t i b l e t o d a m a g e i n t h ef o r m o f l a t e ra l e l a s t o - p l a s t i c b e n d i n g , p o s s i b l ya c c o m p a n i e d b y l o c a l i n d e n ta t i o n , c a u s e d f o r e x a m p l eb y s u p p l y - b o a t c o l l i s i o n s o r b y i m p a c t s d u r i n gl a u n c h i n g a n d i n s t a l l a ti o n . D a m a g e o f t h i s t y p e ,p a r t i c u l a r l y i n b r a c i n g m e m b e r s w h i c h c a r r y c o m p r e s -s i v e lo a d , m a y c a u s e s u b s t a n t i a l l o s s o f e l e m e n t


9/14

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s t i ffness and s t rength poss ib ly a f fec t ing the in t egr i ty o fa p l a t form as a whole . An ins t ance of seve re co l l i s iond a m a g e , i n w h i c h s e v e r a l m e m b e r s w e r e c a r r i e d a w a ywhi l e o the rs expe r i enced bending and den t ing , i s shownin Figure 14.

An ex tens ive theore t i ca l and exper imenta l i nves t iga -t io n o f d a m a g e e f f e c t s in t u b u l a r b r a c i n g m e m b e r s ,inc lud ing a se r i e s o f t e s t s on fu l l - sca l e and sma l l - sca l ebraces conta in ing s imula t ed co l l i s ion damage , i sdesc r ibed in re fe renc es 13 , 20 . As a re su l t o f t h i s s tudyt h e f o ll o w i n g o b se r v a t i o n s m a y b e m a d e .

a ) Sl igh t l a t e ra l bending de forma t ions in tubula rb r a c e s c a n c a u se s e r i o u s l o s s o f s tr e n g t h . A c c u r a t ee v a l u a t i o n o f su c h d a m a g e m a y b e c a r r ie d o u tus ing l a rge -de f l ec t ion , i ne l a s t i c beam-columna n a l y s i s, i n v o l v in g s i m u l a t io n o f t h e d a m a g ep r o c e s s b y a p p l i c a ti o n a n d r e m o v a l o f l at e ra l l o a d ,fo l lowed by appl i ca t ion of ax ia l l oad or end-s h o r t e n i n g d i s p l a c e m e n t u p t o a n d b e y o n dc o l l ap se . A n a p p r o x i m a t e e s t im a t e o f th e e f fe c t s o fb e n d i n g d a m a g e c a n b e o b t a i n e d d i r e c t ly , f o r t u b e so f a n y s l e n d e r n es s r a t i o ( L / r ) having any spec i f i ed


10/14

Residual Strength of Damaged Steel Ships and Offshore Structures I1

Figure 14 Severe collision dam age in an offshore platforms u p p o r t c o n d i t i o n s , b y i n t e r p o l a t i o n b e t w e e n t h ec u r v e s s h o w n i n F i g u r e 1 5. T h e a c c u r a c y o f t h i sa p p r o a c h h a s b e e n e x a m i n e d , a s in d i c at e d i n T a b l e1 , b y c o m p a r i s o n w i t h r e s u l t s o f f u l l - s c a l e a n ds m a l l - s c a l e t e s t s o n d a m a g e d t u b e s . ( u.2 ) T h e s ecurv es , base d on pa ram et r i c ana ly s i s , ~-~) re fe r tod a m a g e c a u s e d b y a c e n t r a l l a t e r a l ( c o l li s io n ) l o a d .I t h a s b e e n f o u n d , h o w e v e r , a s i l l u s t r a t e d i n T a b l e2 , t h a t t h e e f f e c t o f d a m a g e , w h i l e d e p e n d i n gs t r o n g l y o n t h e a m p l i t u d e ~ p o f l a t e r a l b e n d i n g , i sinsens i t ive to the pos i t ion x a long the tube a t whichla te ra l load i s app l ied ( in the rang e 0 .2 < x / L< 0 . 8 ) ; t h e c u r v e s s h o w n i n F i g u r e 1 5 m a yt h e r e f o r e b e u s e d w i t h r e a s o n a b l e a c c u r a c y w h e r ea c o ll i si o n o c c u r s a t a n y p o i n t i n t h i s r a n g e . W h e r ethe loca t ion o f a co l l i s ion i s c lose to e i the r end o f ab r a c e ( x / L < 0 . 2 , > 0 . 8 ) , the load requ i red toc a u s e p l a s t i c b e n d i n g i n c r e a s e s s u b s t a n t i a l l y a n dloca l inden ta t ion o f the tube wa l l i s l ike ly to be thed o m i n a n t c o m p o n e n t o f d a m a g e .

( b ) D a m a g e i n t h e f o r m o f a s e v e r e d e n t o f su f f ic i e n td e p t h ( > 0 . 0 5 D , s a y ) t o c a u s e a s i g n i f i c a n t l o c a lr e d u c t i o n a n d e c c e n t r i c i t y i n t h e s e c t i o n a lp r o p e r t i e s o f a t u b e , m a y a l s o c a u s e s u b s t a n t i a ll o s s o f s t r e n g t h . I t h a s b e e n f o u n de x p e r i m e n t a l l y ( : ) t h a t , b e c a u s e o f l o n g i t u d in a l' p u l l - i n ' o f f ib r e s a s s o c i a t e d w i t h d e n t f o r m a t i o n ,s e v e r e d e n t s a r e a l w a y s l i k e ly t o b e a s s o c i a t e d w i t hs o m e o v e r a l l b e n d i n g d e f o r m a t i o n . I n o r d e r t oa c c o u n t a p p r o x i m a t e l y f o r d e n t e f f e c t s w i t h i n t h e

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l t 1 t001 0 02 00 3 0-0t .~pILFigure IJ Effects o f bending damage on compressive strength oftubular bracesT a b l e 1 S i m p l y - s u p p o r t e d t u b e s c o n t a in i n g b e n d in g d a m a g e : c o m p a r i s o n o f a p p r o x i m a t e s t re n g t h e st i m a t e s f r o mF i g u r e 1 5 w i t h e x p e r i m e n t a l d a t a

Amplitude Collapse strength ofTube D L L / ( av~ of bending damaged tube (au/oy)ident if icat ion 7- 7- 2 = ~ / ~-E] da m ag e6tJL Experimental From Fig. 15A4 (ref. 13) 29.0 98.9 1.09 0.005 0.5084 (ref. 13) 45.8 78.2 0.80 0.005 0.61E2 (ref. 20) 31.5 69.7 0.83 0.0032 0.73E25 (ref. 20) 30. I 69.6 0.82 0.0034 0.63

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Figure 16 l 'heoretical attd exper'mcnt(tl hind shortening curvesfor a dented br~wer a n g e 2 5 t o 6 0 a n d d e n t s o f d e p t h 0 . 0 2 D t o O . t 3 Dc a u s e d b y a k n i f e - e d g e a c t i n g a t r i g h t - a n g l e s t o t h et u b e a x i s , h a s s h o w n t h a t r e a s o n a b l y a c c u r a t er e s u l t s a r e o b t a i n e d b y t a k i n g E a n d es, o f f i b re s int h e d e n t z o n e e q u a l t o b e t w e e n 5 0 p e r c e n t a n d 7 5p e r c e n t o f t h e f ul l m a t e r i a l v a l u e s : a n e x a m p l e i ss h o w n i n F i g u r e 1 6. F u r t h e r s y s t e m a t i c c o r r e l a t io nw i t h t es t d a t a i s h o w e v e r r e q u i r e d b e f o r e t h ism e t h o d c a n b e a p p l i e d w i t h c o n f i d e n c e t o a n yd a m a g e s i tu a t io n . A n a l t e rn a t i v e a p p r o x i m a t er e p r e s e n t a t i o n o f d e n t e f f e c t s , i n v o l v i n gc h a r a c t c r i s a t i o n o f a d e n t a s a p l a s t i cm e c h a n i s m , ' :~ ' h a s a l s o b e e n t \ m n d t o c o r r e l a t e w e l lw i t h t e s t d a t a i n s o m e c a s e s .

W h e n t h e e ft 'e e l s o f d a m : t g e o n i n d i v i d u a l t u b u l a r e l em c n t s h a v e b e e n e s t a b l is h e d , th e p r o b l e m r e m a i n s o fa s s e s s i n g t h e i n fl u e n c e o f e l e m e n t d a m a g e o n s t i f f n e s s; tn d s t r e n g t h o f t h e p l a t f o r m a s a w h o l e . A s a f i rs t s t e p ,t h e o r i g in a l l i n e ar s p a c e - f l a m e a n a l y s i s o f t h e p k t t f o rmm a y b e r e p e a t e d a s s u m i n g t h a t d a m a g e d e l e m e n t s a r en o n e x i s t e n t : i f t h e r e s u l t s a r e a c c e p t a b l e t h e i n v e s t i g a -t i o n n e e d b e t a k e n n o f u r t h e r . I f t h e c o n t r i b u t i o n o fd a m a g e d e l e m e n t s p r o v e s e s s e n t i a l t h e r e d u c e d s t if f n es so f e a ch s u c h e l e m e n t m a y b e r e p r e s e n t e d b y a b i- l in e a r( o r i f n e c e s s a r y m u l t i - l i n e a r ) i d e a t i s a t i o n o f t h e c o r np u l e d l o a d - s h o r t e n i n g o r l o a d - e x t e n s i o n c u r v e : a n a l y s i so 1 t h e c o m p l e t e p l a t f o r m m a y t h e n b e r e p e a t e d o n ap i e c e w i s e li n e a r b a s i s w i t h a d i s c o n t i n u i t y i n t he c o n >p u t a t i o n c o r r e s p o n d i n g t o e a ch k n u c k l e i n a n c l e m e n ts t r e s s - s tr a i n c u rv e . A s i m i l a r a p p r o a c h h a s p r o v e d

e f f e c t iv e i n t h e a n a l y s i s o f e l a s t o - p l a s t ic c y c l i c r e s p o n s eo f p l a t f o r m s t o e a r t h q u a k e l o a d s . ~ ' C o n s i d e r a b l ee c o n o m y m a y b e ac h i e ve d b y e m p l o y i n g a s u b s tr u c t u r-i n g t e c h n i q u e i n w h i c h r e g i o n s o f a p l a t f o r mp a r t i c u l a r l y e x p o s e d t o d a m a g e , e .g . in t h e s p la s h z o n e .a re rep resen ted a s d i s t i n c t s u b s t r u c t u r e s : r e - a n a l y s i sa c c o u n t i n g f o r d a m a g e e f f e c t s m a y t h e n b e c o n f i n e de s s e n t i a ll y t o s u b s t r u c t u r e s c o n t a i n i n g d a m a g e d e l e -m e n t s .

E f f e c ts o f d a m a g e in s u b m e r s i b le s a n d o t h e rr i n g - s t i f f e n e d c y l i n d r i c a l s h e l l sR in g -s t i f f en ed cy l in d r ica l sh e l l s a re w id e ly em p lo y ed ins u b m e r s i b le s , m i l i ta r y s u b m a r i n e s a n d c o m p o n e n t s o fu n d e r w a t e r o r o f f s h o r e e n g i n e e r i n g s y s t e m s s u c h a ss t o r a g e o r t l o t a t i o n t a n k s w h i c h h a v e t o w i t h s t a n d h i g he x t e r n a l p r e s s u r e . F a i l u r e o f a r i n g - s t i f f e n e d c y l i n d e ru n d e r e x t e r n a l p r e s s u r e m a y o c c u r( a ) b y i n t e r f r a m e b u c k l i n g o f t h e s h e l l, w h i c h m a y b e

e i t h e r a x i s y m m e t r i c o r " l o b u l a r ' i n f o r m , i . e . m a yi n v o l v e e i t h e r , t s i n g l e l o b e o r s e v e r a l b u c k l i n gw a v e s r o u n d t h e c i r c u m f e r e n c e o f t h e sh e l l p l a t i n gb e t w e e n r i n g f r a m e s , o r

( b ) b y g e n e r a l i n s t a b i l i t y in v o l v i n g b e n d i n g o f r i n gf l a m e s .

T h e l b r m o f d a m a g e m o s t r e l e v a n t t o " I o b u la r 'i n t e r f r a m e f a i h i r i s i n d e n t a t i o n o f l en g t h a n d w i d t hs i m i l a r t o t h a t o f a b u c k l i n g h a l f - w a v e . I n v i e w o f t h er e l a t i v e l y lo w i m p e r f e c t i o n s e n s i t i v i t y o f e x t e r n a l l y p r e s -s u r i s e d c y l in d e r s ( c o m p a r e d w i t h a x i a l ly c o m p r e s s e dc y l i n d e r s ), f u r th e r r e d u c e d b y t h e p r e s e n c e o f f ra m e s ,a n d b e c a u s e s h o r t - w a v e l e n g t h i n d e n t a t i o n i s u n l ik e l y toe x t e n d f a r r o u n d t h e c i r c u m f e r e n c e , t h i s f b r m o fd a m a g e i s u n l i k e l y t o c a u s e s e r i o u s l o s s o f s t r e n g t h .P o s s i b l y o f g r e a t e r s i g n i f ic a n c e w o u l d b e d a m a g e in t h eR ) rm o f a x i s y t n m e t r i c i n te r f r a m c d e f o r m a t i o n , a s m i g h tb c c a u s e d i n t h i c k e r s h e l ls b y a c c i d e n t a l o v e r l o a d o r b yu n d e r w a t e r e x p l o s i o n s . S c o p e e x i s t s f o r p a r a m e t r i ce v a l u a t i o n o f t h e se t y p e s o f d a m a g e b y m e a n s o f li n it ee l e m e n t / f in i t e d if f e re n c e a n a l y s i s m e t h o d s ~ h i c h h a v ep r o v e d e f f e c t i v e f o r i n v e s t i g a t i o n o f p l a t e a n d s h e l ls t r e n g t h ( e . g . r e f e r e n c e 2 2 ) .

T a b l e 2 E f f e ct o f c o l l i s i o n l o c a t i o n : c o m p u t e d s t r e n g t h o f s i m p l y - s u p p o r t e d t u b e s c o n t a i n i n g b e n d i n g d a m a g eD / t - - 3 5 , E / a y = 6 3 8

I. Collision Amplitude o f bending dama ge Collapse strength er, ,'n.-r- locat ion ,~-~L . . . . .30 Mid span 0.037 0.5030 ~- span 0.037 0.5070 Mid span (1.0073 0.5470 1- span 0.0073 0.5370 .",lid span 0.023 0.3270 ~ span 0.023 0.33

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R e s i d u a l S t r e n g t h o f D a m a g e d S t e e l S h i p s a n d O f fs h o r e S t r u c t u r e s 1 3T h e f o r m o f d a m a g e l i k el y t o c a u s e m o s t s e r io u s l o s s

o f s t r e n g th i s t h a t i n v o l v i ng b e n d i n g d e f o r m a t i o n o fr i n g f r a m e s . P a r a m e t r i c s t u d i e s a n d e x p e r i m e n t s~8.za~h a v e c l e a r l y e s t a b l i s h e d t h e s e n s i ti v i t y o f g e n e r a lins tab i l i ty o f r ing-s t i f fened cy l inde rs to sm a l l in i t i a ld e f o r m a t i o n s a n d t o r e s i d u a l s t r e s s e s c a u s e d e i t h e r b yw e l d i n g o r b y c o l d - f o r m i n g o f th e f r a m e s : s m a l l l ev e l so f f r a m e d a m a g e m i g h t t h e r e f o r e b e e x p e c t e d t o c a u s es ign i f i can t los s o f buck l ing s t reng th .

I n o r d e r t o i l l u s tr a t e t h e e f fe c t s o f s u c h d a m a g e ,a n a l y s i s h a s b e e n c a r r i e d o u t f o r a t y p i c a l r i n g - s ti f f e n e dc y l i n d r i c a l s h e l l a s s h o w n i n F i g u r e 1 7 . D a m a g e , a sm i g h t r e s u l t f r o m a c o l l i s i o n o r g r o u n d i n g , w a sa s s u m e d t o b e c a u s e d b y a n e x t e r n a l c o n c e n t r a t e dr a d i a l f o r c e r e a c t e d b y a n o p p o s i n g ( i n e r t i a l o r g r a v i t a -t i o n a l ) f o rc e q d i s t r i b u t e d u n i f o r m l y r o u n d t h ec i r c u m f e r e n c e . A s d i s c u s s e d i n r e f e r e n c e 8 , a n a l y s i s o fa l o n g r i n g - s t i f f e n e d c y l i n d e r m a y b e c o n f i n e d t o as ing le f ram e w i th a s soc ia ted s t r ip o f she ll p la t ing : th i st w o - d i m e n s i o n al t r e a t m e n t o f t h e p r o b l e m , w h i c him pl ie s tha t a l l f ram es a re iden t i ca l ly dam aged , wi l lp r o v i d e a c o n s e r v a t i v e , l o w e r b o u n d e s t i m a t e o fs t r e n g t h f o r s h o r t c y l i n d e r s o r f o r s t r u c t u r e s i n w h i c hs o m e o f t h e f r a m e s a r e u n d a m a g e d o r l e ss s e v er e l yd e f o r m e d .

T a k i n g a d v a n t a g e o f s y m m e t r y t h e s t r u c t u r e w a ss u b d i v i d e d o v e r a 1 8 0 a r c i n t o 3 6 s t r a i g h t f r a m e e l e-m e n t s , c r o s s - s e c t i o n s b e i n g d i v i d e d u p i n t o 2 5 ' f i b r e s ' .T h e a n a l y s i s w a s c a r r i e d o u t u s i n g t h e m e t h o d a n dc o m p u t e r p r o g r a m d e s c r i b e d i n r e f e r e n c e 8 . A c o n -c e n t r a t e d r a d i a l lo a d P w a s f ir s t a p p l i ed a n d r e m o v e d i no r d e r t o s i m u l a t e v a r i o u s l e v e ls o f d a m a g e a s s h o w n i nF i g u r e 1 8 ( a ) . C o n s i d e r a t i o n h a s a l s o b e e n g i v e n t o t h eidea l r ig id -p la s t i c co l l apse o f a r ing f ram e under th i sf o r m o f l o a d , w h ic h o c c u r s b y f o r m a t i o n o f fo u r p l a s t i ch i n g e s a t p o i n t s A , B , C a n d D o n t h e c i r c u m f e r e n c e a sshow n in F igure 18(b) . The p os i t ion o f h inges B and Di s n o t o b v i o u s , b u t h a s b e e n f o u n d f r o m v i r t u a l w o r kc o n s i d e r a t i o n s t o o c c u r a t 0~ = 6 4 w i t h a c o r r e s p o n d -ing co l l apse load of P = 13 .8 M p / D ( f o u n d t o b ei n s e n si t iv e t o t h e a s s u m e d p o s i t i o n o f B a n d D , v a r y i n gby le s s than 6 pe r cen t ove r the range 60 < 0 , < 80) .T h e s e r e s u l t s a r e c o n s i s t e n t w i t h t h e c o m p u t e d d e f o r -m a t i o n s a n d l o a d - d i sp l a c e m e n t c u r v e s s h o w n inF igu res 18(a ) and (c ) . A typ ica l d i s t r ibu t ion o f re s idua ls t r e s s i n d u c e d i n t h e d a m a g e d s t r u c t u r e i s s h o w n i nFigure 18(d).

U s i n g a r e s t a r t f a c i l i t y i n t h e c o m p u t e r p r o g r a m , t h ec o l la p s e b e h a v i o u r w a s e x a m i n e d o f e a c h d a m a g e dc o n f i g u r a t i o n u n d e r u n i f o r m e x t e r n a l p r e s s u r e . T h en o n - c o n s e r v a t i v e n a t u r e o f h y d r o s t a t i c l o a d ( in w h i c h

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p r e s s u r e r e m a i n s n o r m a l t o t h e d e f o r m e d s u r f a c e ) w sr e p r e s e n t e d i n t h e a n a l y s i s . T h e r e s u l t s a r e s u m m a r i s e di n F i g u r e 1 9, i n t e r m s o f t h e c o l l a p s e p r e s s u r e p ~ a n d t h e' s q u a s h ' p r e s s u r e p ~ , s h o w i n g r e d u c t i o n i n c o l l a p s es t r en g t h c a u s e d b y v a r i o u s l e v e ls o f d a m a g e . A c o m -p a r i s o n i s m a d e w i t h t h e c o l l a p s e p r e s s u r e o f a nu n d a m a g e d c y l i n d e r, a s s u m e d t o b e f r ee o f re s id u a ls t r e s s , c o n t a i n i n g a ' c h a r a c t e r i s t i c ' i m p e r -f e c t io n i n t h e f o r m o f o v a l i s a t i o n w i t h( D ~ , , - m ~ , ~ ) / O . . . . = 0 . 0 1 .F IR E D A M A G EF i r e d a m a g e i s l i k e ' y t o i n c l u d e s e v e r e d i s to r t i o n s a n dres idua l s t re s ses in p la t ing and s t i f fene rs , toge the r wi thc h a n g e s i n m a t e r i a l p r o p e r t ie s w h i c h m a y b e c o m -p l i c a t e d b y f i r e - c o u n t e r m e a s u r e s s u c h a s w a t e rq u e n c h i n g . T h e f o l l o w i n g t e c h n i q u e s m a y p r o v e u s e f u li n a s s e s s i n g d a m a g e e f f e c t s .( a) A p p r o x i m a t e n o n - d e s t r u c t i v e e v a l u a t i o n o fre s idua l s t re s s l eve l s can be ca r r i ed ou t us ing the

hole -dri lling tec hn iqu e. ~-'4~( b ) T h e e x t e n t o f h e a t- ~ .f f e ct e d s t r u c t u r e a n d a n

e s t im a t e o f t e m p e r a t u r e s r e a c h e d c a n s o m e t i m e s b ed e d u c e d b y r e f e r e n c e t o c h a r r i n g , b l i s t e r i n g o rm e l t i n g o f p a i n t w o r k , p l a s t i c f i t ti n g s , e t c . ;s y s t e m a t i c h i g h - t e m p e r a t u r e t e s t s o n p a i n t e d p l a t e sa n d r e p r e s e n ta t i v e i te m s o f eq u i p m e n t m a y b ew o r t h w h i l e a s a m e a n s o f c a l i b r a t i n g s u c h d a t a .

( c ) A p p r o x i m a t e n o n - d e s t r u c t i v e i d e n t i f ic a t io n o fc h a n g e s i n m a t e r i a l s t r e n g t h c a n b e m a d e b yh a r d n e s s m e a s u r e m e n t u s i n g a V i c k e r s h a r d n e s ste s te r o r s im i la r dev ice . H igh-s t reng th s t ee l sub-j e t t e d t o h i g h t e m p e r a t u r e f o l l o w e d b y s l o wcool ing i s l ike ly to suf fe r los s o f y ie ld s t reng th andU T S , e v i d e n c e d b y a r e d u c t i o n i n h a r d n e s s ; c o n -v e r s e l y s t e e l w o r k s u b j e c t e d t o h i g h t e m p e r a t u r ef o l l o w e d b y r a p i d c o o l i n g ( e . g . q u e n c h i n g ) m a yg a i n in U T S a n d h a r d n e s s a t t he e x p e n s e o f s e r i o u se m b r i t t l e m e n t . C a r e f u l c a l i b r a t i o n o f h a r d n e s sm e a s u r e m e n t s i s n e c e s s a r y o n r e p r e s e n t a t i v em ate r ia l sub jec ted to a ra nge of he a t - t rea tm e nts . 2-~S u b s t a n t i a l c h a n g e s o f h a r d n e s s i n d i c a t e a n ee df o r r e m o v a l o f m a t e r i a l s p e c i m e n s f o r a c c u r a t ee v a l u a t i o n o f m e c h a n i c a l p r o p e r t i e s .

W h e n m a t e r i a l p r o p e r t i e s , d i s t o r t i o n s a n d r e s i d u a ls t re s s l eve l s have been e s tab l i shed , the duc t i l e s t reng tha n d s t i f f n e s s o f f i r e - a f f e c t e d s t r u c t u r e c a n b e e x a m i n e du s i n g m e t h o d s d e s c r i b e d i n p r e c e d i n g s e c t i o n s .CONCLUSIONSA r e v i e w h a s b e e n m a d e o f v a r io u s f o r m s o f s t r u ct u r a ld a m a g e w h i c h o c c u r i n s h i p s a n d o f f s h o r e s t r u c t u r e sa n d o f th e i n f l u e nc e o f s u c h d a m a g e o n s t if f n e s s a n ds t r e n g t h . S o m e m e t h o d s h a v e b e e n s u g g e s t e d f o re v a l u a ti o n o f d a m a g e e f fe c ts , w it h e m p h a s i s o na p p r o x i m a t e a n a l y s i s t e c h n i q u e s w h i c h c a n b e a p p l i e dq u i c k ly a n d e c o n o m i c a l l y to o b t a i n a n e a r l y a s s e s s m e n to f d a m a g e c o n s e q u e n c e s . I n m a n y c a s e s o f p ra c t ic a l


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( d )k'L~,,ure 18 (a) DeJbrmations under collision load. (b) Rig id plastie co llapse mechanism. (e) Collision load displacement relationship. (d)l~rpical residua l stres s distribution.impor tance use fu l lower -bound s t r ength e s t ima tes fordamaged p la te or she l l s t ruc tures can be made bys imple two-dimens iona l ana lys is . In o the r cases th ree -d imens iona l non- l inea r fin ite e lement she ll an a lys is m aybe the only e f fec t ive means of a ssessment : suchana lys is , which i s now poss ib le us ing commerc ia l lyava i lab le compute r programs, involves d i f f icu l t ie s ,d a n g e r s a n d h ig h c o s t s w h ic h s h o u ld n o t b eunderes t im a ted , bu t m ay we ll be jus t i f ied i f theeconomic and sa fe ty- re la ted s takes a re h igh enough. I tshould be r ecognised tha t in orde r to account fu l ly fordam age e f fects , inc luding pa r t icu la r ly r e s idua l s t r e ssesa s s o c i a t e d w i th d a ma g e d e f o r ma t io n , i t ma y b enecessa ry to inc lude a s imula t ion of the dam ageprocess in any ana lys is of r e s idua l s t i f fness andstrength.Mu ch scope remains for pa ram etr ic ana lys is ofdamaged s tee l s t ruc tures and for suppor t ing exper i -ments a imed a t p rovid ing da ta which w i l l a l low ins tan t

assessment of r e s idua l s t i f fness and s t r ength forcha rac te r i s t ic damage s i tua t ions . Areas in which apa r t icu la r need ex is t s for fur the r ana lys is and te s t da tainc lude eva lua t ion of dent damage in :

I % . . . . . . . . . C H A I ] A C T E R I S T I C C O L L A P S E S T I I E N C , T H

L ~ ~ to o z o o , . & , ; DFiA, re 19 Effect of dama.~e nn collap.~e pressure


14/14

Residua l Strength of D amaged Stee l Ships an d Of fshore Struc tures 5a) tubular braces an d pipe l ines:b ) th in -w a l l e d c y linde r s unde r a x ia l c o m pr e ss io n;c) r ing-st i ffened cyl inders;d) spher ical she l ls .

CKNO I l l /LED GEMEN TAcknowledgements are due to Mr W. C. Kirkwood forassistance in carrying out computation and plottingresults.

R E F E R E N E S1 JONES.N. A Literature Sz~rTey on the Collision and GroundingProtection of Ships. S h i p S t r u c t u r e C o m m i t t e e R e p o r t

S S C - 2 8 3 . 1 9 7 9 .2 R e p o r t s o f IS S C C o m m i t t e e 1 1 . 2 o n N o n - l i n e a r S t r u c t u r a lR e s p o n s e . P r o c e e d i n g s o f I n t e r n a t i o n a l S h i p S t r u c t u r e s C o n -

g r es s . B o s to n 1 9 7 6 . P a r i s 1 9 7 9 .3 KE IL . A . H . ' T h e R e s p o n s e o f S h i p s t o U n d e r w a t e r E x p l o s io n s . "Transactions of Society of Naval Architects attd AlarineEngineers. 1 9 6 1 . 6 9 .4 GA TF S. W. E.. MARStlALt,, P. w. a nd MA IIIN. S. A. AnalyticalMethods fi~r Determinhtg the Ultimate Earthquake Resistanceof Fixed Offvhore Structures. P r o c e e d i n g s o f O f f s h o r eT e c h n o l o g y C o n f e r e n c e , H o u s t o n . 1 9 77 .

5 C I .A R K SON , J ' A N ew A p p r o ach to th e D es ig n o f P l a t e s t oW i t h s t a n d L a t e r a l P r e s s u r e . " Transacthms of Rayal Institutionof Naral Architects, 1 9 5 6 . 9 8 .6 I)()WI,IN fL ' . J . an d OIleR.A F Strength of Ships Plating umh'rCombined Lateral t, oading and Biaxial Pressure. C E S L I CR e p o r t S P 6 . I m p e r i a l C o l l e g e , L o n d o n . S e p t e m b e r 1 9 7 8.7 S M I TI I . C . S . q m p cr f cc t io n F f f ec t s an d D es ig n T o le r a n ce s in

S h i p s a n d O f f s h o r e S t r u c t u r e s . " Transaction of In.~'titution ofEnghwers & Shiphuihh'rs in Scotland, 1981. 124.8 s s t l r l l . c . s . and KIRKW{)OD.W. ('. hifiuence oflni tht l Dt~Jrmation and Residual Stress on Inehlstie Fie.rural Buckling of

StiJfened Plates and Shells. P r o c e e d i n g s o f I n t e r n a t i o n a l C o n -f e r e n c e o n S t e e l P l a t e d S t r u c t u r e s , I m p e r i a l C o l l e g e , L o n d o n ,1976.9 CI.ARKSON, J. an d WAI.LACI~.G . " T r a n s v e r s e S t r e n g t h o f a L a r g e

S tee l F r ig a t e M o d e l . ' I'runsaetions of Royal Institution ofNaval Architects. 1967. 109.1 0 C t .A R K S Orq , J ' Tes t s o f F l a t P l a t ed G r i l l ag es u n d e r U n i f o r mP r es s u r e . " Transactions of Roya l Institution t~ NavalArchitects. 1963, 105.I I s %HI II , c . s . " C o m p r es s iv e S t r en g th o f Weld ed S tee l S h ipG r i l l ag es . ' Transactions of Royal Institution ~ NatalArchitects, 1975, 117.

12 MOOLANI, F. M. alld DOWLING. P. J. Ultimate Load Behaviour ofStiffened Plates in Compression. P r o c e e d i n g s o f I n t e r n a t i o n a lC o n f e r e n c e o n S t e e l P l a t e d S t r u c t u r e s . I m p e r i a l C o l l e g e ,L o n d o n . 1 9 7 6 .13 SM ITH . C. S.. KIRKWOO D. W. C. and SWAN. J. W. BucklingStrength and Post-Collapse Behaviour of Tubular BracingMembers including Damage Effects. C o n f e r e n c e o n B e h a v i o u r

o f O f f s h o r e S t ru c t u r e s (B O S S - 7 9 ) . L o n d o n . S e p t e m b e r 1 9 79 .14 SMIT H. C~ S Influence of Local Compressive Failure onLTtimate Longitudinal Strength of a Ship's Hull. P r o c e e d i n g so f I n t e r n a t i o n a l S y m p o s i u m o n P r a c t i c a l D e s i g n in S hi p b u i ld -

i n g ( P R A D S ) . T o k y o , O c t o b e r 1 9 7 7 .1 5 A M ER I C A NPETROLEUM INSTITUTE.Recommended Practice orPlanning. Designing and Constructing Fixed OffshorePlatforms. A P t R P 2 A . I l t h e d n . . T e x a s . 1 9 8 0 .1 6 D N V R u l e s f o r t h e D e s i g n . C o n s t r u c t i o n a n d I n s p e c t i o n o fF i x e d O f f s h o r e S t r u c t u r e s . D e t N o r s k e V e r i t a s. O s l o 1 9 77 .17 BRITISH STANDARD S INSTITUTION. Steel. Concrete and Com-posite Bridges. Part 6: Specification for Materials andWorkmanship. Steel. L o n d o n . B S 5 4 0 0 . 1 9 8 0 .18 LEv y. 5. Bending of Rectangular Plates with Large Deflections.N A C A R e p o r t N o . 7 3 7 . 1 9 4 2 .19 bOW . R. s Large-displacement Buckling and Bending ,4 nalysisof Initially Deformed Ship Grillages. U n p u b l i s h e d A d m i r a l tyM a r i n e T e c h n o l o g y E s t a b l i s h m e n t R e p o r t .20 SMII-H . C. S.. SOSlI-RVILLE. W. L. an d SWAN. J. W. ResidualStrength and Stiffness of Damaged Steel Bracing Members.P r o c e e d in g s o f O f f s h o r e T e c h n o l o g y C o n f e r e n c e . H o u s t o n .M a y 1 9 8 1 .21 RASH EI). S. %1. |t.. FAHY. J. an d M OAN . T. Fheoretical and Experi-mental Study of the Bchaviour of Damaged Tubular Atcmher~.

P r o c e e d i n g s o f F ir s t I n d i a n C o n f e r e n c e o n O c e a n F n g i n c e r i n g .1981,2 2 I I A R D I N G , J I- . ' Th e F , a s to - p l a s t i c A n a ly s i s o f h n p e r f ec tC y l in d e r s . " Proceedings of lnstituthm of Civil Engim.ers. P ar tI I . D e c e m b e r 1 9 7 8 . 6 5 . 8 7 5 - 9 2 .23 g.INI)RtCK. S B. The Influence ~ Shape lmperfi'etions andResidual Stresses on the Collapse of Stiff'ened C.rlinders.P r o c e e d i n g s o f C o n f e r e n c e o n S i g n i f i c a n c e o f D e v i a t i o n s fr o m

D e s i g n S h a p e , I n s t i t u t io n o f M e c h a n i c a l E n g i n e e r s . L o n d o n ,M a r c h 1 9 7 9 .24 HI iANI-Y. . S t. : rod PROCrOR. t '. 'A C r i t ica l Eva lua t ion of theC e n t r e t l o l e T e c h n i q u e f o r t h e M e a s u r e m e n t o f R e s i d u a lS tress ." Strain, J a n u a r y 1 9 7 4 .2 5 A LLA N . R . C . ; B I R D. J , U n p u b l i s h ed M ar in e Tcch *n o l o g y E s t a b l i s h m e n t R e p o r t s .

C o n t r i b u t i o n s d i s c u s s i n g t h i s p a p e r s h o u l d b e r e c e i v e d b y t h e E d i t o rb e f o re I J a n u a r y 1 9 8 2 .

H a v e y o u r e n e w e d y o u r s u b s c r i p t i o n f o r 9 8 2 ?P l e a s e h e l p u s b y r e n e w i n g y o u r s u b s c r i p t io n n o w

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Residenual Strength of Damaged Steel Ships