Applied Ocean Research 31 (2009) 82-89
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Applied Ocean Research
j o u r n a l h o m e p a g e : wvwv.elsevier.conn/locate/apor
On the energy dissipation of jacket type offshore platforms w i t h different
pile-leg interactions
p. Alanjari^ B. Asgarian^'*, M.R. Bahaari^ M.R. Honarvar''
K.N.Toosi University of Teclinoiogy, Islamic Republic of Iran"School of Civil Engineering, University College of Engineering, University ofTeliran, Islamic Republic of Iran
A R T I C L E I N F O A B S T R A C T
Article history: Received 16 May 2008 Received in revised form 11 April 2009 Accepted 12 July 2009 Available online 26 July 2009
Keywords: Jacket Joint-can Energy dissipation Struts Joint fracture
In r e c e n t y e a r s , c o n s i d e r a b l e a m o u n t of effort has b e e n m a d e to design e a r t h q u a k e r e s i s t a n t offshore s t r u c t u r e s in s e i s m i c active areas. In o r d e r to a c h i e v e this objective, all c o m p o n e n t s of a typical s t r u c t u r e s h o u l d f u n c d o n p r o p e r l y to d i s s i p a t e s e i s m i c a l l y - i n d u c e d e n e r g y w i t h i n the m e m b e r s . A m o n g c o m p o n e n t s of an offshore i n s t a l l a t i o n , braces a r e of s i g n i f i c a n t i m p o r t a n c e as they c o n t r i b u t e s u b s t a n t i a l l y to total e n e r g y d i s s i p a t i o n of the s t r u c t u r e . B u c k l i n g in c o m p r e s s i o n and y i e l d i n g in t e n s i o n assist t h e p r o c e s s o f e n e r g y a b s o r p t i o n . N e v e r t h e l e s s , the f u n c t i o n a l i t y of b r a c e s is d e p e n d e n t u p o n their j o i n t s w h e r e j o i n t - c a n s are i n c l u d e d to avoid a n y brittle fracture a n d u n p r e d i c t e d f a i l u r e m e c h a n i s m s .
In this paper, s p e c i a l a t t e n t i o n is b e i n g p a i d to e n e r g y d i s s i p a t i o n of j a c k e t type offshore p l a t f o r m s w i t h t w o d i f f e r e n t p i l e - l e g i n t e r a c t i o n s . A c a s e study r e p r e s e n t i n g an offshore p l a t f o r m is s t u d i e d both a n a l y t i c a l l y a n d e x p e r i m e n t a l l y . A n a l y t i c a l m o d e l s are v a l i d a t e d step b y step b a s e d on a v a i l a b l e e x p e r i m e n t a l tests a n d o b s e r v a t i o n s o n i n d i v i d u a l m e m b e r s . S e v e r a l p a r a m e t e r s s u c h as c y c l i c b e h a v i o r , m a x i m u m b e a r i n g load a n d m o s t i m p o r t a n t l y energy d i s s i p a t i o n of t w o d i f f e r e n t 2 D f r a m e s are investigated. R e s u l t s p r o v i d e p r o m i s i n g insights into d e s i g n and f a b r i c a t i o n of f i x e d p l a t f o r m s w i t h d i f f e r e n t p i l e - l e g i n t e r a c t i o n s . © 2 0 0 9 E l s e v i e r Ltd. A l l rights r e s e r v e d . 1. I n t r o d u c t i o n P r o d u c i n g o i l a n d gas f r o m o f f s h o r e b y means o f f i x e d p l a t f o r m s has g a i n e d a t r e m e n d o u s m o m e n t u m i n t h e e n e r g y i n d u s t r y i n t h e past t e n years. D e s i g n o f s u c h s t r u c t u r e s is d e p e n d e n t u p o n l a t e r a l forces a p p l i e d b y e n v i r o n m e n t a l c o n d i t i o n s s u c h as w a v e s , c u r r e n t s , i m p a c t s as w e l l as s e i s m i c a l l y - i n d u c e d e x c i t a t i o n s . Severe l a t e r a l forces m a y cause c o n s i d e r a b l e d a m a g e t o l o a d c a r r y i n g m e m b e r s a n d e n d a n g e r o v e r a l l s t a b i l i t y o f t h e s t r u c t u r e . To c o u n t e r t h i s p r o b l e m , braces are d e s i g n e d t o w i t h s t a n d l a t e r a l e x c i t a t i o n s a n d dissipate e a r t h q u a k e i n p u t e n e r g y t h r o u g h b u c k l i n g i n c o m p r e s s i o n a n d y i e l d i n g i n t e n s i o n . Nonetheless, o b s e r v a t i o n s o f r e c e n t e a r t h q u a k e s f o r p o o r l y - d e s i g n e d o r d i n a r y s t r u c t u r e s p o i n t o u t t h a t j o i n t f r a c t u r e is e n c o u n t e r e d p r i o r to b u c k l i n g o f m e m b e r s a n d c o n s e q u e n t l y n o e n e r g y d i s s i p a t i o n occurs. T u b u l a r j o i n t s i n o f f s h o r e s t r u c t u r e s e x h i b i t d i f f e r e n t f a i l u r e m e c h a n i s m s s u c h as j o i n t r u p t u r e due t o t h e increase i n t h e size o f the h e a t a f f e c t e d zone (HAZ) and p u n c h i n g shear f a i l u r e d u e to excessive shear f o r c e s i n d u c e d i n c h o r d a n d brace i n t e r s e c t i o n . M o r e o v e r , l o c a l cyclic stresses m a y cause f a t i g u e p r o b l e m s i n j o i n t s
* Corresponding address: K.N.Toosi University of Technology, Department of Civil Engineering, Valiasr St., P.O.Box 15875-4416, 19967 Tehran, Islamic Republic of lran.Tel.:-r98 2188779623; fax:+98 2188779476.
E-mail address.-Asgarian®kntu.ac.ir(B. Asgarian).
V^ln^^Var' ' " ^ ^"""^ ""^^^^ ® 2 ° ° ^ ^isevier U d . All rights reserved. doi:10.1016/j.apor.2009.07.002 a n d r e s u l t i n g r a d u a l s t r e n g t h d e t e r i o r a t i o n o r s u d d e n f r a c t u r e o f c o n n e c t i o n s . I n o r d e r t o o v e r c o m e these d e f i c i e n c i e s , j o i n t - c a n s are i n c l u d e d to s t r e n g t h e n the j o i n t l o c a l l y so t h a t t h e w h o l e brace c a p a c i t y w i l l be u t i l i z e d . Recently, p i l e - l e g i n t e r a c t i o n has b e c o m e o f i n t e r e s t f o r m a n y designers i n o f f s h o r e i n d u s t r y [ 1 - 3 ] . S o m e t i m e s t h e gap b e t w e e n p i l e a n d l e g is f i l l e d w i t h g r o u t t o p r o v i d e a c o m p o s i t e s e c t i o n t e r m e d g r o u t e d s e c t i o n . On t h e o t h e r h a n d , t h e c o n n e c t i o n b e t w e e n p i l e a n d l e g m a y be p r o v i d e d t h r o u g h the use o f c o n n e c t i n g j o i n t s a n d s h i m plates a n d t h e r e b y an u n g r o u t e d i n t e r a c t i o n w o u l d be f o r m e d . H o n a r v a r et a l . [ 3 ] c o n d u c t e d an e x p e r i m e n t a l research i n w h i c h i t w a s s t a t e d t h a t u n g r o u t e d s t r u c t u r e is r e l a t i v e l y s u p e r i o r f r o m e n e r g y d i s s i p a r i o n p o i n t o f v i e w f o r p o o r l y - d e s i g n e d 2 D f r a m e s w h e r e j o i n t - c a n s w e r e n o t i n c l u d e d a n d braces w o u l d n o t c o n t r i b u t e i n t o t a l e n e r g y a b s o r p t i o n . T h e r e f o r e , m o r e i n v e s t i g a t i o n s o f the i n e l a s t i c b e h a v i o r o f g r o u t e d a n d u n g r o u t e d f r a m e s are n e e d e d .
Several researchers have i n v e s t i g a t e d t h e c y c l i c i n e l a s t i c b e h a v i o r o f steel o f f s h o r e p l a t f o r m s . Zayas et a l . [ 4 ] c o n d u c t e d e x t e n s i v e e x p e r i m e n t a l studies o n c y c l i c i n e l a s t i c p o s t - b u c k l i n g b e h a v i o r o f t u b u l a r braces as w e l l as o v e r a l l b e h a v i o r o f s m a l l -scale f r a m e m o d e l s [ 5 ] . F u r t h e r a n a l y t i c a l r e s e a r c h v e r i f i e d t h e i r e x p e r i m e n t a l e f f o r t s s u c h as K e y v a n i e t al. [ 6 ] a n d A s g a r i a n et a l . ( 2 0 0 5 ) [ 7 , 8 ] . G h a n a a t a n d C l o u g h [ 9 ] s t u d i e d the d y n a m i c elastic a n d i n e l a s t i c b e h a v i o r o f 5 / 4 8 t h scaled m o d e l o f a n
p. Alanjari et al./Applied Ocean Researcii 31 (2009) 82-89 83
Fig. 1. Comparison between analytical model and experimental test (strut 15 Blacker al. |12|); (a) analytical, (b) experimental.
Table 1
Geometric and material properties of the testspecimens of Zayas etal. |4) and Black etal. |12].
Strut / y ( M P a ) f 1st buckling load (kN) A(cm^) AISC buckling load (kN)
2 ( W 6 x 25) 290.76 40 1170.35 ' 47.35 1300 1 0 ( 2 - L 4 X 3 X 3 / 8 ) 286.62 120 432.54 34.45 470.05 15 (pipe 4 x 0.237) 327.27 80 489.5 18.08 592.29 2''(pipe 3.96 X 0.12) 213.59 54 194.46 9.41 185,56
Strut # 2 tested by Zayas et al, |4].
X - b r a c e d o f f s h o r e p l a t f o r m m a d e o f t u b u l a r braces. The e f f e c t s o f t u b u l a r j o i n t f l e x i b i l i t y o n t h e s t r u c t u r a l response o f o f f s h o r e s t r u c t u r e s w e r e e x a m i n e d b y B o u k a m p et a l . [ 1 0 ] . F u r t h e r m o r e , l o c a l SCF b e h a v i o r o f t u b u l a r j o i n t s w a s h i g h l i g h t e d b y B a h a a r i a n d M o l a e i [ 1 1 ] . H o n a r v a r et a l . [ 3 ] s t u d i e d t h e cyclic b e h a v i o r o f t w o s m a l l - s c a l e m o d e l s , r e p r e s e n t a t i v e o f a J a c k e t T y p e O f f s h o r e P l a t f o r m l o c a t e d i n t h e Persian Gulf, w i t h t w o d i f f e r e n t p i l e - l e g i n t e r a c t i o n s . T h e y also p r e s e n t e d a n a l y t i c a l m o d e l i n g o f p i l e - l e g i n t e r a c t i o n s as w e l l as b r i t t l e j o i n t b e h a v i o r a n d c o n c l u d e d t h a t j o i n t r u p t u r e is e n c o u n t e r e d i n g r o u t e d m o d e l p r i o r t o u n g r o u t e d f r a m e due t o g r e a t e r s t i f f n e s s a n d s t r e n g t h o f g r o u t e d legs. F o l l o w i n g t h e w o r k o f H o n a r v a r e t a l . [ 3 ] , e n e r g y d i s s i p a t i o n o f JTOPs are s t u d i e d i n t h i s paper. A n a l y t i c a l m o d e l s o f i n d i v i d u a l m e m b e r s are p r e s e n t e d a n d v e r i f i e d w i t h a v a i l a b l e e x p e r i m e n -t a l s-tudies i n -t h e l i -t e r a -t u r e . Special a -t -t e n -t i o n is p a i d -t o b u c k l i n g l o a d p r e d i c t i o n a n d e n e r g y d i s s i p a t i o n o f s t r u t s due t o t h e i r c o n t r i b u t i o n i n o v e r a l l b e h a v i o r o f JTOPs. V a l i d a t e d a n a l y t i c a l m o d -els are u s e d s u b s e q u e n t l y t o f o r m 2 D b r a c e d f r a m e s w i t h d i f f e r e n t p i l e - l e g i n t e r a c t i o n s . P r e v i o u s l y - d o n e e x p e r i m e n t a l r e s e a r c h [ 3 ] is a p p l i e d a c c o r d i n g l y t o r e a c h u s e f u l c o n c l u s i o n s a b o u t p e r f o r m a n c e o f g r o u t e d a n d u n g r o u t e d b r a c e d f r a m e s . 2 . B e h a v i o r of i n d i v i d u a l s t r u t s A n o f f s h o r e s t r u c t u r e is m a i n l y m a d e o f s t r u t s , piles, legs a n d j o i n t s . S t r u t s p l a y a n i m p o r t a n t r o l e i n t o t a l e n e r g y d i s s i p a t i o n a n d l a t e r a l l o a d c a r r y i n g c a p a c i t y o f t h e p l a t f o r m . T h e p u r p o s e o f t h i s s e c t i o n is t o s t u d y t h e b e h a v i o r o f i n d i v i d u a l s t r u t s u p o n b u c k l i n g i n c o m p r e s s i o n a n d y i e l d i n g i n t e n s i o n as w e l l as t h e i r a b i l i t y t o dissipate e n e r g y i n c o n s e c u t i v e cycles. Zayas et a l . [ 4 ] a n d Black et al. [ 1 2 ] c o n d u c t e d e x p e r i m e n t a l tests o n i n d i v i d u a l m e m b e r s w i t h v a r i o u s cross sections a n d p r o v i d e d s e v e r a l o b s e r v a t i o n s r e g a r d i n g cyclic b e h a v i o r , b u c k l i n g l o a d i n c o n s e c u t i v e cycles, e n e r g y d i s s i p a t i o n p e r cycle a n d c u m u l a t i v e d i s s i p a t e d energy. T h e i r w o r k m a y be u t i l i z e d as a v e r i f i c a t i o n f r a m e w o r k f o r s u b s e q u e n t a n a l y t i c a l s i m u l a t i o n s w h i c h w o u l d be used i n m o d e l i n g o f n o t o n l y o f f s h o r e p l a t f o r m s b u t also f o r a n y t y p e o f s t r u c t u r e . I n o r d e r t o s u m m a r i z e t h e i r results, o n e p i p e s p e c i m e n o u t o f s i x p i n - e n d e d s t r u t s tested b y Zayas e t a l . [ 4 ] , a n d 3 o u t o f 2 4 p i n - e n d e d s a m p l e s t r u t s (i.e. W s e c t i o n , d o u b l e a n g l e a n d p i p e s e c t i o n ) t e s t e d b y B l a c k et a l . [ 1 2 ] , w e r e m o d e l e d b y a n a l y t i c a l b e a m - c o l u m n e l e m e n t s [ 1 3 ] . Table 1 lists t h e s t r u t s a n d c o r r e s p o n d i n g p a r a m e t e r s i n c l u d i n g g e o m e t r i c a n d m a t e r i a l p r o p e r t i e s . I n o r d e r t o s t u d y t h e b e h a v i o r o f s t r u t s a n a l y t i c a l l y , r e l e v a n t f i n i t e e l e m e n t m o d e l s s h o u l d be c o m p o s e d o f r o b u s t a n d w e l l -t e s -t e d e l e m e n -t s -to e n s u r e r e a l i s -t i c responses. N o n l i n e a r f i n i -t e e l e m e n t p r o g r a m OpenSees [ 1 4 ] is u s e d h e r e i n t o s t u d y t h e b e h a v i o r o f t h e s t r u c t u r e a n d i t s c o m p o n e n t s . H o n a r v a r et al. [ 3 ] s u m m a r i z e d m o d e l i n g t e c h n i q u e s f o r s i m u l a t i n g the b e h a v i o r o f i n d i v i d u a l m e m b e r s a n d 2 D f r a m e s t o e n s u r e b o t h accuracy a n d e f f i c i e n c y . U n i a x i a l b e a m - c o l u m n e l e m e n t s i n c o m b i n a t i o n w i t h f i b e r sections are used h e r e a f t e r t o m o d e l t h e e x p e r i m e n t a l specimens. A d d i t i o n a l l y , c o r o t a t i o n a l t r a n s f o r m a t i o n is used t o a c c o u n t f o r g e o m e t r i c n o n l i n e a r i t i e s a n d m o d e l i n g o f p o s t -b u c k l i n g -b e h a v i o r o f s t r u t s as a c c u r a t e l y as p o s s i -b l e .
2.1. Cyclic behavior
A n i n c r e m e n t a l c y c l i c l o a d p a t t e r n is a p p l i e d o n a l l m o d e l s a n d results are p r e s e n t e d h e r e i n . To s u m m a r i z e t h e results, o n l y s t r u t 15 (i.e. t u b u l a r s e c t i o n ) is c o m p a r e d t o a n a l y t i c a l m o d e l . Figs. 1(a) a n d ( b ) i l l u s t r a t e t h e e x c e l l e n t a g r e e m e n t a n d s u p e r b a b i l i t y o f a n a l y t i c a l m o d e l t o s i m u l a t e t h e b e h a v i o r o f e x p e r i m e n t a l s p e c i m e n . B u c k l i n g i n c o m p r e s s i o n a n d y i e l d i n g i n t e n s i o n , s t r e n g t h d e t e r i o r a t i o n d u e t o B a u s c h i n g e r e f f e c t a n d p a r t i a l y i e l d i n g o f t h e cross s e c t i o n is m o d e l e d a c c u r a t e l y .
2.2. Prediction of buclcling load
T h e p e r f o r m a n c e o f a s t r u t s u b j e c t e d to c y c l i c l o a d i n g , is a f f e c t e d b y d e t e r i o r a t i o n o f c o m p r e s s i v e s t r e n g t h o f m e m b e r . B a u s c h i n g e r e f f e c t is r e s p o n s i b l e f o r t h i s p h e n o m e n o n . A n a l y t i c a l m o d e l is able t o c a p t u r e t h i s e f f e c t t h r o u g h t h e use o f s u i t a b l e steel s t r e s s - s t r a i n c u r v e i n w h i c h B a u s c h i n g e r e f f e c t is i n c o r p o r a t e d .
Fig. 2 i l l u s t r a t e s t h e a b i l i t y o f c u r r e n t m o d e l t o p r e d i c t b u c k l i n g l o a d i n c o n s e c u t i v e cycles. B u c k l i n g loads o f s t r u t 10 are p l o t t e d a g a i n s t cycle n u m b e r a n d c o m p a r e d t o t h e e x t r a c t e d b u c k l i n g loads f r o m a n a l y t i c a l b e a m - c o l u m n e l e m e n t [ 1 4 ] cyclic p l o t . I t is o b s e r v e d t h a t m o d e l p r e d i c t i o n s f a i r l y agree w i t h t h e b u c k l i n g loads o f t h e e x p e r i m e n t a l s p e c i m e n . I t s h o u l d be n o t e d t h a t t h e f i r s t b u c k l i n g l o a d o c c u r r e d i n test w a s 4 3 2 . 5 4 1 k N , w h e r e a s AISC f o r m u l a [ 1 5 ] p r e d i c t s t h e a m o u n t o f 4 7 0 . 0 5 k N based o n a c t u a l y i e l d i n g stress (i.e. Oy = 2 8 6 . 6 2 4 M P a ) a n d a n a l y t i c a l m o d e l p r e d i c t i o n is 4 5 0 . 2 5 1 k N w h i c h p r o v e s t h e r e a s o n a b l e accuracy o f t h e b e a m - c o l u m n e l e m e n t . M o r e o v e r a p o s t - b u c k l i n g analysis w a s p e r f o r m e d f o r a series o f d o u b l e angle s t r u t s w i t h d i f f e r e n t ' s l e n d e r n e s s r a t i o s a n d b u c k l i n g loads w e r e also c a l c u l a t e d a c c o r d i n g t o AISC f o r m u l a [ 1 5 ] . Fig. 3
84 P. Alanjari et al./Applied Ocean Researcii 31 (2009) 82-89
3 4 5 Cycle no.
10
- T e s t Analytical model]
Fig. 2. Buckling loads inconsecutive cycles for strut 10 Black etal. 112|.
300 ^ 250 ^ 200 w w OJ ^ 150 D I
I
100 m 50 0 0 20 40 60 80 100 120 140 160 180 KLVr| - ^ A I S C fonnuia -=^-Analylical model]
Fig. 3. Prediction of buckling load by analytical model and AISC formula |15|.
RIGID P L A S T I C
S T R U T
Fig. 4. Comparison o f p - S curves for a rigid plastic element and an axially loaded strut (Zayas e t a l . | 4 | ) .
s h o w s t h e b u c k l i n g loads p r e d i c t e d b y b e a m - c o l u m n e l e m e n t a n d AISC f o r m u l a [ 1 5 ] . I t is o b s e r v e d t h a t t h e b u c k l i n g loads are p r e d i c t e d a c c u r a t e l y b y t h i s e l e m e n t .
2.3. Energy dissipation
As m e n t i o n e d earlier, e n e r g y d i s s i p a t i o n c o n t r i b u t e s s i g n i f i c a n t l y i n inelastic c y c l i c b e h a v i o r o f s t e e l s t r u t s since these m e m -bers are m a i n l y d e s i g n e d to dissipate e a r t h q u a k e energy. One can c a l c u l a t e e n e r g y d i s s i p a t e d d u r i n g a l l l o a d i n g cycles f o r a n a x i a l l y l o a d e d m e m b e r f r o m i t s a x i a l l o a d a x i a l d i s p l a c e m e n t g r a p h . D i v i d i n g e n e r g y d i s s i p a t i o n per cycle b y e n e r g y d i s s i p a t i o n o f n o n -b u c k l i n g , r i g i d - p e r f e c t l y plastic e l e m e n t , "RP", n o r m a l i z e d energy d i s s i p a t i o n w o u l d be o b t a i n e d . T h e r i g i d - p e r f e c t l y plastic e l e m e n t (Fig. 4 ) , has t h e same y i e l d loads a n d c y c l e d t h r o u g h the same d i s -p l a c e m e n t s .
Zayas et a l . [ 4 ] r e f e r to this n o r m a l i z e d q u a n t i t y as e n e r g y d i s s i p a t i o n e f f i c i e n c i e s o f a s t r u t and d e f i n e i t as a m e a n s o f q u a n t i f y i n g t h e d e t e r i o r a t i o n o f t h e capacity o f a s t r u t t o d i s s i p a t e e n e r g y w i t h cycles. To o b t a i n t h e energy d i s s i p a t e d per cycle f o r r i g i d - p e r f e c t l y plastic m a t e r i a l , t h e f o l l o w i n g e q u a t i o n is u s e d [ 4 ] .
RPi = Py ( S E I + 2Sa + S ^ ) .
Figs. 5 ( a ) - ( c ) s h o w t h e e n e r g y d i s s i p a t i o n e f f i c i e n c i e s f o r s t r u t s 2 a n d 10 t e s t e d b y Black et al. [ 1 2 ] a n d s t r u t 2 t e s t e d b y Zayas et al. [ 4 ] , a l o n g w i t h t h e results p r o v i d e d b y c o r r e s p o n d i n g a n a l y t i c a l m o d e l s .
It s h o u l d be n o t e d t h a t at the f i r s t cycle o f t e s t i n g , t e s t s p e c i m e n s s h o w g r e a t e r a m o u n t o f e n e r g y d i s s i p a t i o n d u e t o n o n l i n e a r i t i e s t h a t n o r m a l l y occur u n d e r t h e e x p e r i m e n t a l c o n d i t i o n s u n l i k e t h e a n a l y t i c a l m o d e l i n w h i c h f i r s t cycles are a l m o s t l i n e a r . A l t h o u g h b o t h b u c k l i n g a n d tensile loads o f t h e test a n d t h e a n a l y t i c a l m o d e l are a l m o s t t h e same, n o n l i n e a r i t i e s i n t h e test s t r u t s have n o t b e e n c a p t u r e d t h r o u g h t h e use o f m o d e l i n g p r o c e d u r e . Fig. 5(c) p o i n t s o u t a n i n t e r e s t i n g p h e n o m e n o n r e g a r d i n g the c y c l i c b e h a v i o r o f s t r u t s h a v i n g s l e n d e r a n d s e m i - c o m p a c t cross sections. One can see t h a t as t h e n u m b e r o f cycles increases, e n e r g y d i s s i p a t i o n e f f i c i e n c i e s o f t h e t e s t s p e c i m e n d e t e r i o r a t e s d u e t o l o c a l b u c k l i n g d a m a g e r e s u l t i n g f r o m l o w - c y c l i c f a t i g u e . Since t h i s f a c t o r has n o t b e e n i n c l u d e d i n t h e a n a l y t i c a l m o d e l , s e p a r a t i o n o f t h e t w o curves o c c u r s i n last cycles. It s h o u l d be n o t e d t h a t n o r m a l l y f o r c o m p a c t o r s t o c k y cross sections, t h i s r a t e o f d e t e r i o r a t i o n is n o t obsei-ved [ 1 6 ] .
C u m u l a t i v e s u m o f cycle d i s s i p a t i o n e f f i c i e n c i e s m a y be c o m p u t e d to f a c i l i t a t e t h e s t u d y o f energy d i s s i p a t i o n . Figs. 6 ( a ) - ( c ) s h o w t h e a b i l i t y o f a n a l y t i c a l m o d e l t o p r e d i c t t h e a m o u n t o f c u m u l a t i v e cycle e f f i c i e n c i e s f o r a l l t h r e e s t r u t s . As can be seen, i n last cycles b o t h curves a l m o s t c o i n c i d e a n d FE m o d e l gives t h e s a m e a m o u n t w h i c h w o u l d have b e e n d i s s i p a t e d b y a real m e m b e r , i n a n average sense. Since c u m u l a t i v e cycle e f f i c i e n c y can be r e g a r d e d as a n i m p o r t a n t f a c t o r f r o m s t r u c t u r a l d e s i g n s t a n d p o i n t , i t can be c o n c l u d e d t h a t p r e s e n t FE m o d e l is able t o e f f e c t i v e l y p r e d i c t t h e real b e h a v i o r óf t e s t s p e c i m e n , b e f o r e d a m a g e d u e t o l o w - c y c l i c f a t i g u e can cause loss o f e n e r g y d i s s i p a t i o n . Zayas et al. [ 4 ] t e s t e d t u b u l a r s t r u t s w i t h f i x e d - e n d c o n d i t i o n s a n d e n c o u n t e r e d d a m a g e d u e t o l o w - c y c l i c f a t i g u e i n l a t e r cycles a n d c o n c l u d e d t h a t f i x e d - e n d c o n d i t i o n s m a y p r o d u c e a y i e l d p l a t e a u a n d d e l a y t h e d a m a g e . It can be i n f e r r e d f r o m t h e i r r e s u l t s t h a t a w e l l - d e s i g n e d m e m b e r w i t h l o w " D / f " r a t i o a n d p r o p e r e n d c o n d i t i o n s (i.e. f i x e d - e n d c o n d i t i o n s e q u i p p e d w i t h j o i n t - c a n s w h i c h n o r m a l l y e x i s t i n o f f s h o r e braced s t r u c t u r e s ) , c o u l d d e l a y t h e d a m a g e r e s u l t i n g f r o m l o w - c y c l i c f a t i g u e . As a r e s u l t , p r e s e n t m o d e l m a y be p r o p e r l y used f o r m o d e l i n g o f t u b u l a r s t r u t s i n o f f s h o r e p l a t f o r m s . 3. 2 D j a c l t e t f r a m e s A f t e r v e r i f i c a t i o n o f t h e b e h a v i o r o f i n d i v i d u a l s t r u t s w h i c h are basically r e s p o n s i b l e f o r c a r r y i n g l a t e r a l loads, o n e c a n use t h e m i n m o d e l i n g o f 2 D or 3 D s t r u c t u r e s . H o n a r v a r et a l . [ 3 ] c o n d u c t e d a n e x p e r i m e n t a l test o n t w o d i f f e r e n t 2 D f r a m e s n a m e l y g r o u t e d a n d u n g r o u t e d . T h e y d i d n o t d e s i g n j o i n t - c a n s i n b o t h f r a m e s d e l i b e r a t e l y t o e n c o u n t e r b r i t t l e f r a c t u r e o f t h e j o i n t s d u e t o p u n c h i n g shear f a i l u r e a n d / o r increase i n t h e size o f t h e H A Z . I n t h i s section, v u l n e r a b l e ( w i t h o u t j o i n t - c a n s ) f r a m e s o f H o n a r v a r e t al. [ 3 ] are c o m p a r e d w i t h f r a m e s r e i n f o r c e d w i t h j o i n t - c a n s (i.e. g r o u t e d a n d u n g r o u t e d ) , f o r w h i c h braces are capable o f b u c k l i n g a n d d i s s i p a t i o n o f e n e r g y .
To m o d e l t h e j o i n t - c a n s , b e a m - c o l u m n e l e m e n t s [ 1 4 ] (i.e. d a s h e d lines i n Fig. 7 ) are u s e d w h o s e t u b u l a r s e c t i o n s are d i s c r e t i z e d w i t h t h e a i d o f f i b e r e l e m e n t s a n d r e l e v a n t s t e e l s t r e s s - s t r a i n r e l a t i o n s h i p s are assigned a c c o r d i n g l y .
p. Alanjari et al./Applied Ocean Research 31 (2009) 82-89
Cycle no.
I^^Anaiyticaj models HK^-Test specimens |
Fig. 5. Energy dissipation efficiency; comparison between analytical and experimental models; (a) strut 2, (b) strut 10, (c) strut 2 (Zayas et al. |4]).
Cycle no. a
|-*-Analytical models - * - T e 5 t specimens]
86 P. Alanjari et al./Applied Ocean Research 31 (2009) 82-89
Table 2
Details of used sections in the experimental frames.
Member name Section O.D. (mm) W.T. (mm)
Fig. 7. Analytical modeling of joint-cans with the aid of fiber sections.
I D
B r a c e s
Fig. 8. Joint-offset in connections of a frame.
U s i n g t h e s a m e a p p r o a c h b r i t t l e b e h a v i o r o f j o i n t s m a y be m o d -e l -e d w i t h t h -e a i d o f z -e r o - l -e n g t h -e l -e m -e n t s i n plac-e o f b -e a m - c o l u m n e l e m e n t s . U l t i m a t e s t r a i n is assigned t o s t r e s s - s t r a i n r e l a t i o n s h i p t h r o u g h t h e use o f e x p e r i m e n t a l data o f f a b r i c a t e d a n d tested s p e c i m e n s e x t r a c t e d f r o m j o i n t r e g i o n [ 3 , 1 6 ] . Because o f t h e r e l -a t i v e l y s m -a l l t h i c k n e s s o f t h e br-aces, incre-ase i n t h e size o f the H A Z a f f e c t t h e u l t i m a t e s t r a i n o f t h e m a t e r i a l . K n o w i n g t h i s fact, a s e g m e n t o f t h e w e l d e d x - j o i n t is e x p e r i m e n t a l l y t e s t e d a n d n e w steel s t r e s s - s t r a i n r e l a t i o n s h i p is e x t r a c t e d to be u s e d i n ana-l y t i c a ana-l i n o d e ana-l s u b s e q u e n t ana-l y . U s i n g e x p e r i m e n t a ana-l resuana-lts, H o n a r v a r e t al. [ 3 ] c o n c l u d e d t h a t this t y p e o f m o d e l i n g m a y be u t i l i z e d to m o d e l the f r a c t u r e o f j o i n t s a n d c o n s e q u e n t l y t o d e a c t i v a t e t h e braces i n e n e r g y d i s s i p a t i o n . It s h o u l d be n o t e d t h a t t h e e f f e c t s o f p r o g r e s s i v e o v a l i z i n g a n d local b u c k l i n g as w e l l as local j o i n t f l e x -i b -i l -i t y at j o -i n t s a n d plast-ic h-inges have n o t b e e n a c c o u n t e d f o r -i n t h e c u r r e n t s t u d y .
Each o f t h e s e m o d e l s is d i v i d e d i n t o g r o u t e d a n d u n g r o u t e d f r a m e s to s t u d y n o t o n l y the e f f e c t o f s t r u t s i n e n e r g y a b s o r p t i o n , b u t also t h e e f f e c t o f g r o u t o n response o f o f f s h o r e p l a t f o r m s i n g l o b a l sense. Some i m p o r t a n t c o r r e l a t i o n s t u d i e s are c a r r i e d o u t s u c h as c y c l i c b e h a v i o r , f r a m e m a x i m u m l a t e r a l l o a d c a p a c i t y t h r o u g h cycles, brace a x i a l loads a n d m o s t i m p o r t a n t l y , e n e r g y d i s s i p a t i o n f o r a l l f r a m e s . C o n c e n t r i c j o i n t s i n o f f s h o r e j a c k e t s m a y have a r e l a t i v e j o i n t o f f s e t . M o s t l y , i n t e r s e c t i o n o f brace a n d c h o r d c e n t e r l i n e s does n o t c o i n c i d e w i t h t h e n o m i n a l j o i n t l o c a t i o n . Fig. 8 d e p i c t s t h e l o w e r -l e f t c o n n e c t i o n o f the p -l a t f o r m w h i c h is t o be m o d e -l e d a n a -l y t i c a -l -l y . To a c c o u n t f o r t h i s e c c e n t r i c i t y , j o i n t o f f s e t o p t i o n is used i n FE m o d e l a n d r e l e v a n t o f f s e t o f each a n d e v e r y j o i n t is o b t a i n e d a n d i n t r o d u c e d t o t h e p r o g r a m . Pile Pipe 141 5 Leg Pipe 165 5
Lower brace Pipe 77 2
Upper brace Pipe 60 2
Deck Box (mm)
250 X 250 X 20
-
-Joint-can (Analytical model) Pipe , ^'^ Upper ^ Lower
64 81
4 4
Total deck weighl=521.5 kg
Fig. 9. Frame fabrication and details; units (mm).
3.3. Experimental setup A b r i e f d e s c r i p t i o n o f e x p e r i m e n t a l s e t u p is r e v i e w e d h e r e i n . T w o o n e - t w e l f t h scale m o d e l s o f a r e c e n t l y d e s i g n e d a n d i n s t a l l e d j a c k e t i n the Persian G u l f w e r e s i m p l i f i e d a n d a d j u s t e d as p e r a v a i l a b l e l a b o r a t o r y f a c i l i t i e s , c o n s t r u c t e d a n d t e s t e d u n d e r l a t e r a l quasi-static d i s p l a c e m e n t - c o n t r o l l e d histories, r e p r e s e n t a t i v e o f severe m o t i o n s [ 3 ] . O n l y a p l a n a r r o w w a s tested a n d t h e e f f e c t o f h o r i z o n t a l braces i n t h e p r o t o t y p e , p e r p e n d i c u l a r t o t h e m o d e l e d face, w a s c o n s i d e r e d as l a t e r a l (i.e. o u t o f p l a n e ) c o n s t r a i n t s o n legs. Table 2 s h o w s t h e d e t a i l s o f used sections i n s p e c i m e n f r a m e s .
A n a l y t i c a l m o d e l s o f f r a m e s r e i n f o r c e d w i t h j o i n t - c a n s are c o n d u c t e d and t e s t e d against e x p e r i m e n t a l a n d a n a l y t i c a l m o d e l s o f f r a m e s w i t h o u t j o i n t - c a n s . Table 2 also s h o w s t h e size a n d t h i c k n e s s o f d e s i g n e d j o i n t - c a n s t o be i n c l u d e d i n t h e m o d e l . Fig. 9 i l l u s t r a t e s a g e n e r a l v i e w o f t h e f r a m e i n w h i c h sizes a n d l e n g t h s o f t h e m e m b e r s are g i v e n . P i l e - l e g i n t e r a c t i o n is t r e a t e d i n t w o d i f f e r e n t w a y s as m e n t i o n e d p r e v i o u s l y . I n t h e case o f g r o u t e d f r a m e , t h e a n n u l u s b e t w e e n leg a n d p i l e m a y be f i l l e d w i t h g r o u t so n e w s e c t i o n is
p. Alanjari et al./Applied Ocean Researcii 31 (2009) 82-89 87 Ai(miu) 250 200 150 100 ^ 50 ^ 0 "^-50 - 1 0 0 - 1 5 0 - 2 0 0 - 2 5 0 1 -- 2 5 0 -- 2 0 0 -- 1 5 0 -- 1 0 0 -- 5 0 0 50 100 150 200 250 |—Frame with jolnlons —Frame v/iHiout joint-cans |
Fig. 10. Cyclic behavior; comparison between frames with antl without joint-cans (ungrouted models).
g e n e r a t e d to a c c o u n t f o r c o m p o s i t e a c t i o n o f t h e g r o u t e d p o r t a l . N o i n t e r n a l c o n s t r a i n t s are d e f i n e d i n t h i s case except f o r w e l d e d p i l e a n d l e g w h e r e a s c o n n e c t i o n b e t w e e n p i l e a n d leg is a v a i l a b l e t h r o u g h t h e use o f s h i m plates i n the case o f u n g r o u t e d i n t e r a c t i o n .
3.2. Hysteretic behavior
Cyclic a n d p r o g r e s s i v e l y - i n c r e a s i n g l a t e r a l load is a p p l i e d o n a n a l y t i c a l f r a m e m o d e l s (i.e. w i t h a n d w i t h o u t j o i n t - c a n s ) a n d results are s h o w n i n Fig. 10. As can be seen, t w o s i g n i f i c a n t s t i f f n e s s r e d u c t i o n s are d i s t i n g u i s h e d i n f r a m e w i t h o u t j o i n t - c a n s w h i c h c o r r e s p o n d t o t w o r e s p e c t i v e j o i n t f r a c t u r e s . It s h o u l d be n o t e d t h a t results o f a n a l y t i c a l m o d e l f o r f r a m e w i t h o u t j o i n t - c a n s h a v e b e e n v a l i d a t e d w i t h e x p e r i m e n t a l tests i n p r e v i o u s research [ 3 ] . F u r t h e r m o r e , n o a p p r e c i a b l e change i n o v e r a l l s t r e n g t h a n d s t i f f n e s s o f t h e f r a m e s c a n be seen p r i o r t o j o i n t f r a c t u r e b u t as s o o n as first f r a c t u r e is e n c o u n t e r e d , b o t h s t r e n g t h a n d s t i f f n e s s are r e d u c e d c o n s i d e r a b l y d u e t o e l i m i n a t i o n o f l a t e r a l l o a d c a r r y i n g e l e m e n t s . S m o o t h d e t e r i o r a t i o n o f s t i f f n e s s is o b s e r v e d i n t h e case o f f r a m e w i t h j o i n t - c a n s d u e t o b u c k l i n g o f braces a n d c o r r e s p o n d i n g d a m a g e r e s u l t e d f r o m c o n s e c u t i v e b u c k l i n g . I t s h o u l d be m e n t i o n e d t h a t o c c u r r e n c e o f l o c a l b u c k l i n g d u e t o l o w - c y c l i c f a t i g u e is l i k e l y i n t h i s m o d e l a n d m a y be a c c o u n t e d f o r t h r o u g h t h e use o f a s u i t a b l e d a m a g e m o d e l s p e c i a l i z e d f o r u n i a x i a l m a t e r i a l s a n d e l e m e n t s b u t t h e d e t e r i o r a t i o n o f s t r e n g t h is a s s u m e d t o be m i n o r i n t h i s s t u d y as discussed a n d r e a s o n e d i n p r e v i o u s sections. I n a n analogous w a y t o c o m p a r a t i v e studies o f H o n a r v e r et a l . [ 3 ] , one can i n v e s t i g a t e t h e e f f e c t o f g r o u t o n o v e r a l l b e h a v i o r o f t h e f r a m e s t h r o u g h c o m p a r i n g t h e c y c l i c response o f g r o u t e d a n d u n g r o u t e d f r a m e s . As can be seen i n Fig. 1 1 , g r o u t e d f r a m e is g e n e r a l l y s t i f f e r i n first f e w cycles. This coincides w i t h t h e r e s u l t s o b t a i n e d b y H o n a r v a r e t a l . [ 3 ] b u t as t h e a m o u n t o f i n p u t l a t e r a l d i s p l a c e m e n t is increased, n o s i g n i f i c a n t change i n s t i f f n e s s is seen. I n h i g h l a t e r a l d i s p l a c e m e n t s , c r u s h i n g occurs i n e n t r a p p e d g r o u t a n d i t does n o t c o n t r i b u t e i n s t i f f n e s s o f t h e s t r u c t u r e .
3.3. Frame maximum loaiis in consecutive cycles
Closer i n v e s t i g a t i o n is c a r r i e d o u t o n s t r e n g t h a n d l a t e r a l l o a d c a r r y i n g c a p a c i t y o f t h e f r a m e s i n c o n s e c u t i v e cycles. Fig. 12 s h o w s 4 g r a p h s r e p r e s e n t i n g t h e average m a x i m u m loads (i.e. average o f p u s h a n d p u l l i n each c y c l e ) t h a t t h e f r a m e s can c a r r y w h e n t h e y are s u b j e c t e d t o c y c l i c l o a d i n g . As can be seen, f r a m e w i t h o u t j o i n t - c a n s s h o w s s i g n i f i c a n t loss o f s t r e n g t h a f t e r t e a r i n g a n d
f r a c t u r e o f j o i n t s w h e r e a s f r a m e w i t h j o i n t - c a n s p r o v i d e s s m o o t h d e t e r i o r a t i o n o f s t r e n g t h as t h e l o a d increases. IVloreover, s t r e n g t h s o f b o t h f r a m e s are s i m i l a r b e f o r e b u c k l i n g o r f r a c t u r e takes place. I n a s i m i l a r f a s h i o n t o c y c l i c l o a d i n g , o n e can s t u d y t h e e f f e c t o f d i f f e r e n t p i l e - l e g i n t e r a c t i o n a n d observe t h a t a l m o s t t h e s a m e - 1 5 0 - 2 0 0 - 2 5 0 -250 - 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 50 100 150 200 250
Ungrouted frame - G r o u t e d frame
Fig. 11. Cyclic behavior; comparison between grouted and ungrouted frames (frames with joint-cans).
— -Grouled, v/ZojoinKans - - Ungrouted. w/o}Qlnt.cans ^ " G r o u t e d , w j o i n t - c a n s — U n g r o t i t e d . vr Joint-cans 25 30 Cycle no.
Fig. 12. Maximum lateral load carrying capacity of frames in consecutive cycles.
Fig. 13. Fracture of a joint in the frame without joint-cans (Honarvar et al. [2]).
Strength is o b t a i n e d i n last 10 cycles d u e t o c r u s h i n g o f g r o u t w h i c h h i g h l i g h t s the f a c t t h a t g r o u t does n o t c o n t r i b u t e i n o v e r a l l s t r e n g t h o f t h e p l a t f o r m w h e n excessive l a t e r a l loads are a p p l i e d . G e n e r a l l y g r o u t e d f r a m e is s t i f f e r n o t o n l y i n f r a m e w i t h j o i n t - c a n s w h e r e braces h a v e t h e c a p a b i l i t y t o b u c k l e i n c o m p r e s s i o n , b u t also i n f r a m e w i t h o u t j o i n t - c a n s f o r w h i c h f r a c t u r e o f j o i n t s takes place (Fig. 1 2 ) . This j o i n t f r a c t u r e can be seen i n Fig. 13.
3.4. Axial force in struts
As m e n t i o n e d earlier, s t r u t s c o n s t i t u t e t h e m a i n l a t e r a l l o a d c a r r y i n g m e m b e r i n a n o f f s h o r e p l a t f o r m . A x i a l f o r c e i n s t r u t s
88 P. Alanjari et ai. I Applied Ocean Research 31 (2009) 82-89
— Frame V/ )olnt-cans, lensloii — Frame v;/ololnl-cans, leiislon
— Frame v/jolrit-caiis, c o m p r e s s i o n — Frame vr/o joint-cans, c o m p r e s s i o n
Fig. 14. Brace axial force in brace no. 101-202; showing the effect of joint-cans (grouted frame). -150 — U n g r o u t e d - l e n s l o n — Grouted-tenslon *=^Unprouted-compresslon — Grouted-conipression
Fig. 15. Brace axial force in brace no. 101-202; showing the effect ofgi out (grouted and ungrouted-frames with joint-cans).
m a y be m e a s u r e d t o o b t a i n i n s i g h t s i n t o t h e a m o u n t o f t h e i r c o n t r i b u t i o n i n c a r r y i n g t o t a l i n p u t l o a d as w e l l as t h e rate o f l o a d d e t e r i o r a t i o n w h i c h w o u l d o c c u r d u r i n g r e p e a t e d l o a d i n g . Fig. 14 s h o w s axial f o r c e i n one o f t h e l o w e r p a n e l braces o f f r a m e s w i t h a n d w i t h o u t j o i n t - c a n s b o t h i n t e n s i o n a n d c o m p r e s s i o n . O b v i o u s l y , braces do n o t s h o w a n y resistance a f t e r cycle n o . 13 i n f r a m e w i t h o u t j o i n t - c a n s since t h e i r j o i n t s are f r a c t u r e d a n d c o n s e q u e n t l y t h e y do n o t c o n t r i b u t e i n o v e r a l l resistance o f t h e s t r u c t u r e w h e r e a s i n f r a m e w i t h j o i n t - c a n s , s m o o t h d e t e r i o r a t i o n i n a x i a l c o m p r e s s i v e r e s i s t i n g forces is o b s e r v e d w h i c h h i g h l i g h t s t h e b u c k l i n g l o a d d e t e r i o r a t i o n d u e t o B a u s c h i n g e r e f f e c t . E f f e c t o f g r o u t o n p l a t f o r m s t i f f n e s s m a y be f u r t h e r p r o n o u n c e d i n Fig. 15. H o w e v e r , as t h e s t r u c t u r e s are b o t h c y c l e d t h r o u g h excessive l a t e r a l d i s p l a c e m e n t , g r o u t e d a n d u n g r o u t e d f r a m e s t r a n s f e r a l m o s t t h e s a m e a m o u n t o f l o a d t o s t r u t s d u e t o t h e c r u s h i n g o f g r o u t . 3.5. Energy dissipation W h e n o f f s h o r e s t r u c t u r e s are s u b j e c t e d to l a t e r a l s e i s m i c forces, t h e y n e e d t o d i s s i p a t e i n p u t e n e r g y w i t h t h e aid o f e n e r g y d i s s i p a t i n g m e m b e r s . As m e n t i o n e d p r e v i o u s l y , s t r u t s are r e s p o n s i b l e f o r e n e r g y a b s o r p t i o n a n d w h e n t h e y d o n o t f u n c t i o n p r o p e r l y w h a t e v e r t h e cause, the e f f i c i e n c y o f t h e w h o l e s t r u c t u r e is e n d a n g e r e d . C o m p a r a t i v e s t u d y b e t w e e n f r a m e s w i t h a n d w i t h o u t j o i n t - c a n s m a y r e v e a l s o m e i m p o r t a n t facts a b o u t t h e e f f e c t o f b u c k l i n g o f braces. Fig. 16 i l l u s t r a t e s t h e s i g n i f i c a n t s u p e r i o r i t y o f f r a m e w i t h j o i n t - c a n s , due t o b u c k l i n g o f braces, o v e r f r a m e w i t h o u t j o i n t - c a n s , w h e r e braces lose f u n c t i o n a l i t y , a n d p o r t a l s (i.e. piles a n d legs) are m a i n l y i n charge o f e n e r g y d i s s i p a t i o n . Since a c c u r a t e e s t i m a t i o n o f energy d i s s i p a t i o n is
)•!
0 5 10 15 20 2 f t v c l e n c i ? 0
-\
Frame v/ joint-cans, grouted Frame vWo joinl-cans, grouted
— - Frame w joint-cans, ungrouted — -Frame w/o joint-cans, ungrouted
Fig. 16. Cumulative energy dissipation of frames.
Table 3
Cumulative energy dissipation of the frames (kJ).
Cycle no. Frame with joint-cans Frame without joint-cans
Grouted Ungrouted Grouted Ungrouted
0 0.00 0.00 0.00 0.00 1 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00 4 0.00 0.00 0.00 0.00 5 0.00 0.00 0.00 0.00 6 0.00 0.00 0.00 0.00 7 0.01 0.00 0.01 0.00 8 0.29 0.00 0.58 0.00 9 0.75 0.00 1,21 0-00 10 3.73 0.01 3.52 0.01 11 8.62 0.11 8.26 0.14 12 15.25 1.77 11.43 2.37 13 24.29 5.68 11.48 6.39 15 35.55 11.07 11.62 11.31 16 49.26 18.16 11.97 12.47 17 65.04 28.09 12.71 12.87 18 82.54 40.72 14,10 13.70 19 104.01 58.16 19.76 15.91 20 128.67 79.40 30.38 20.53 22 155.70 103.59 35.99 29.73 23 185.61 130.72 36.38 44.22 24 217.74 160.51 36.94 50,51 25 251.61 192.48 37.68 51,27 26 291.58 230.20 38.83 52.46 27 336.76 273.10 40,46 54.20 29 386.52 321.15 42.64 56,54 30 437.89 372.25 45.19 58,50 v e r y c r u c i a l , a n a p p r o p r i a t e a n a l y t i c a l s t r u t m o d e l s i m i l a r t o w h a t w a s i n t r o d u c e d i n p r e v i o u s sections [ 3 ] , m a y be u t i l i z e d t o c a p t u r e t h e a m o u n t o f energy d i s s i p a t i o n as a c c u r a t e l y as possible. C o r r e s p o n d i n g t a b u l a t e d data f o r energy d i s s i p a t i o n o f b o t h f r a m e s is s h o w n i n Table 3. D i s r e g a r d i n g t h e f i r s t f e w cycles, s i g n i f i c a n t i m p r o v e m e n t o f e n e r g y a b s o r p t i o n o f f r a m e w i t h j o i n t - c a n s is q u i t e m a r k e d . M o r e o v e r , c o m p a r i s o n b e t w e e n g r o u t e d a n d u n g r o u t e d m o d e l s o f f r a m e w i t h j o i n t - c a n s s h o w s t h e b e t t e r e f f i c i e n c y o f g r o u t e d m o d e l r a t h e r t h a n u n g r o u t e d p i l e - l e g i n t e r a c t i o n f r o m e n e r g y d i s s i p a t i o n p o i n t o f v i e w . As f o r f r a m e w i t h o u t j o i n t - c a n s , s i t u a t i o n is q u i t e d i f f e r e n t since u n g r o u t e d m o d e l s h o w s m o d e s t l y s u p e r i o r e f f i c i e n c y . This is i n a g r e e m e n t w i t h t h e r e s u l t s o b t a i n e d b y H o n a r v e r et a l . [ 2 ] i n w h i c h t h e y o n l y s t u d i e d t h e b e h a v i o r o f f r a m e w i t h o u t j o i n t - c a n s b o t h e x p e r i m e n t a l l y a n d a n a l y t i c a l l y . One can c o n c l u d e t h a t w h e n j o i n t - c a n s are i n c l u d e d a n d s t r u t s f u n c t i o n p r o p e r l y , a g r o u t e d f r a m e dissipates e n e r g y b e t t e r t h a n a n u n g r o u t e d one because i t s h o w s n o n l i n e a r b e h a v i o r sooner; h o w e v e r , i t s s u p e r i o r i t y is a b s o l u t e l y d e p e n d e n t u p o n t h e p r o p e r p e r f o r m a n c e o f braces. A p r o p e r l y d e s i g n e d s t r u t ( s t r u t w i t h a c o m p a c t cross s e c t i o n ) r e i n f o r c e d w i t h j o i n t - c a n s m a y d e l a y t o t a l
p. Alanjari et al./Applied Ocean Researcii 31 (2009) 82-89 89
brace f a i l u r e due t o l o w cyclic f a t i g u e a n d helps t h e d e f o r m a b i l i t y o f w h o l e s t r u c t u r e .
4. C o n c l u s i o n
Cyclic i n e l a s t i c b e h a v i o r o f JTOPs a n d e n e r g y d i s s i p a t i o n o f 2 D o f f s h o r e f r a m e s w i t h d i f f e r e n t p i l e - l e g i n t e r a c t i o n w e r e s t u d i e d i n t h i s p a p e r . B u c k l i n g a n d p o s t - b u c k l i n g b e h a v i o r o f steel s t r u t s w e r e discussed a n d v a l i d a t e d against a v a i l a b l e e x p e r i m e n t a l tests. F o l l o w i n g p r e v i o u s r e s e a r c h [ 3 ] , s o m e g l o b a l and local b e h a v i o r o f g r o u t e d a n d u n g r o u t e d 2 D f r a m e s w a s i n v e s t i g a t e d a n d t h e f o l l o w i n g c o n c l u s i o n s c a n be r e a c h e d : • A p p r o p r i a t e a n d v a l i d a t e d a n a l y t i c a l m o d e l o f s t r u t s m a y be used t o c a p t u r e t h e n o n l i n e a r b e h a v i o r o f o f f s h o r e s t r u c t u r e s as p r e c i s e l y as p o s s i b l e . I t w a s s h o w n t h a t available n o n l i n e a r f o r c e d - b a s e d b e a m - c o l u m n e l e m e n t is capable o f e s t i m a t i n g t h e a m o u n t o f c u m u l a t i v e e n e r g y d i s s i p a t i o n o f steel s t r u t s q u i t e accurately. A l t h o u g h t h e accuracy o f the results p r o v i d e d b y u s i n g t h i s e l e m e n t is d e p e n d e n t u p o n t h e slenderness o f t h e cross s e c t i o n , i t w a s s h o w n t h a t f o r c o m p a c t a n d stocl<y cross sections, a n a l y t i c a l m o d e l is able t o c a l c u l a t e t h e a m o u n t o f e n e r g y d i s s i p a t i o n s a t i s f a c t o r i l y .
• W h e n j o i n t - c a n s are i n c l u d e d , s t r u t s are capable o f b u c k l i n g a n d t h e y c o n t r i b u t e s i g n i f i c a n t l y i n o v e r a l l l a t e r a l l o a d c a r r y i n g c a p a c i t y o f f r a m e s w h e r e a s w h e n j o i n t - c a n s are n o t d e s i g n e d , j o i n t s are s u s c e p t i b l e t o f r a c t u r e a n d s t r u t s are i m m e d i a t e l y e l i m i n a t e d f r o m t h e s t r u c t u r a l s y s t e m . • G r o u t e d p i l e - l e g i n t e r a c t i o n m a k e s t h e w h o l e s t r u c t u r e s t i f f e r a n d t h e r e b y b u c k l i n g o f s t r u t s a n d r e s u l t i n g n o n l i n e a r b e h a v i o r o f t h e f r a m e are e n c o u n t e r e d s o o n e r t h a n t h o s e o f u n g r o u t e d f r a m e , h o w e v e r , w h e n c r u s h i n g o f g r o u t takes place, b o t h f r a m e s behaves a n a l o g o u s l y a l m o s t i n e v e r y aspect. • A w e l l - d e s i g n e d f r a m e e q u i p p e d w i t h j o i n t - c a n s dissipates e n e r g y m u c h m o r e e f f e c t i v e l y i n c o m p a r i s o n w i t h a p o o r l y -d e s i g n e -d f r a m e w i t h o u t j o i n t - c a n s . F u r t h e r m o r e , c o n s i -d e r i n g a f r a m e w i t h j o i n t - c a n s , g r o u t e d m o d e l is m o r e e f f i c i e n t f r o m e n e r g y d i s s i p a t i o n p o i n t o f v i e w r a t h e r t h a n u n g r o u t e d s t r u c t u r e . The l a t t e r is s t r i c t l y d e p e n d e n t u p o n the d e s i g n o f s t r u t s a n d j o i n t - c a n s since i t d i r e c t l y a f f e c t s t h e d e f o r m a b i l i t y o f t h e s t r u c t u r e . T h a t is, i f a n e n g i n e e r is able to d e s i g n a s t r u t f o r w h i c h l o c a l b u c k l i n g d u e t o l o w - c y c l i c f a t i g u e is n o t e n c o u n t e r e d i n early l o a d i n g cycles, n o s t r e n g t h d e t e r i o r a t i o n o r d i s c o n n e c t i o n due t o a c c u m u l a t e d f a t i g u e d a m a g e is e n c o u n t e r e d a n d g r o u t e d p i l e - l e g i n t e r a c t i o n w o u l d be m o r e e f f e c t i v e f r o m s e i s m i c d e s i g n s t a n d p o i n t . R e f e r e n c e s
|1 j Etterdal B, Askhelm D, Grigorian H, Gladso R. Strengthening of offshore steel components using high-strength grout: Component testing and analytical methods. In: Proc OTC, Paper 13192. 2001.
|2] Honarvar MR, Bahaari MR, Asgarian B. Effect of grouting in jacket type offshore platforms pile-leg interaction in nonlinear range of deformation. Journal of Offshore Mechanics and Arctic Engineering 2007; Paper No. OMAE 07-1007, in press |doi:10.ni5/1.2904586].
| 3 | Honarvar MR, Bahari MR, Asgarian B, Alanjari P. Cyclic inelastic behavior and analytical modeling of pile-leg interaction in jacket type offshore platform. Journal of Applied Ocean Research 2008.
[4] Zayas VA, Popov EP, Mahin SA. Cyclic inelastic buckling of tubular steel Braces.
Report no. UCB/EERC-80/16. Berkeley (CA): University of California; 1980. [5] Zayas VA, Mahin SA, Popov EP. Cyclic inelastic behavior of steel offshore
struc-tures. Report no. UCB/EERC-80/27. Berkeley (CA): University of California; 1980.
[6| Kayvani K, Barzegar F. Modelling of tubular members in offshore steel
jackets under severe cyclic loading. UNICIV report no. R-324. School of Civil Engineering, The University of New South Wales; December 1993. |7] Asgarian B, Aghakouchak A, Bea R. Nonlinear analysis of jacket-type offshore
platforms using fibre elements. Journal of Offshore Mechanics and Arctic Engineering 2006; 128( August).
[81 Asgarian B, Aghakouchak A, Bea R. Inelastic post-buckling and cyclic behavior
of tubular braces. Journal of Offshore Mechanics and Arctic Engineering 2005; 127(August).
|9] Ghanaat Y, Clough RW. Shaking table tests of a tubular steel frame model.
Report no. UCB/EERC-82/02. Berkeley: Earthquake Engineering Research Center. Univ. of California; 1980.
(10) Bouwkamp JG. et al. Effects of joint fiexibility on the response of offshore towers. In: Proc. O T C Paper 3901.1980.
[11] Bahaari B, Molaei. Numerical analysis of stress concentration factors for KK multiaxial tubular connections. Journal of Faculty of Engineering 2003;37(1): 1-12. University of Tehran, Serial # 79.
[12| Black RG, Wenger WAB, Popov EP. Inelastic buckling of steel strut under cyclic load reversals. Rep. no. UCB/EERC-80/40. Berkeley (CA): Earthquake Engineering Research Center. Univ. of California; 1980.
[131 be Souza R. Forced-based finite element for large displacement inelasric analysis of frames. Ph.D. dissertation. Berkeley (CA): Univ. of California; 2000.
[14] Mazzoni S, McKenna F, Scott M, Fenves G. OpenSees command language
manual. 2006.
[15] American Institute of Steel. AISC specification for design and erection of structural steel for buildings. Chicago; 1969.
[161 Uriz Patxi. Towards earthquake resistant design of concentrically braced steel structures. Doctoral dissertation. Berkeley: Structural Engineering, Mechanics, and Materials, Department of Civil and Environmental Engineering, University of California; December 2005.
