ISOPE-I-99-352_Load-Deformation Relationships for Gusset-Plate to CHS Tube Joints Under Compression Loads

8/12/2019 ISOPE-I-99-352_Load-Deformation Relationships for Gusset-Plate to CHS Tube Joints Under Compression Loads

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Proceedings of the Ninth 1999) International O ffshore and Polar Engineering C onference.Brest, France, May 3 0 - J u n e 4 1999Copyright 1999 by The International Society of Offshore an d Polar EngineersISB N 1-880653-39-7 Set); ISB N 1-880653-43-5 V ol. IV); ISSN 1098-6189 Set)

Load De for mat ion Re lat ionsh ips for Gusse t P la te to CHS Tube Jo in tsU n d e r C o m p r e s si o n L o a d sM . A r i y o s h i a n d Y . M a k i n oK u m a m o t o U n i v e r s i t yK u m a m o t o , J a p a n

A B S T R A C TG u s s e t - p l a t e t o C H S t u b e j o i n t s a r e c o n n e c t i o n s w h e r e t h e e n d o f ap l a t e i s d ir e c t l y w e l d e d t o t h e o u t e r s u r f a c e o f a t u b e . T h i s s t u d yp r o p o s e s e q u a t i o n s f o r u l t i m a t e a n d y i e l d s t r e n g t h i n i ti a l s t i ff n e s sa n d l o c a l d e f o r m a t i o n a t u l t i m a t e s t r e n g t h f o r t h e s e t y p e s o fc o n n e c t i o n s . T h e s e e q u a t i o n s a r e b a s e d o n a r in g m o d e l w i t h a ne f f e c t iv e w i d t h u s i n g m u l t i p l e n o n l i n e a r r e g r e s s i o n a n a l y s e s T od e s c r ib e t h e l o a d - d e f o r m a t i o n b e h a v i o r o f g u s se t - p la t e t o C H S t u b ej o i n t s e a c h l o a d - d e f o r m a t i o n c u r v e i s a p p r o x i m a t e d b y tw o s t r a i g h tl i n e s u s i n g t h e s e e q u a t i o n s .KEY WORDS: Effect ive Width, St rength Equat ion, Gusset -Plate toCHS Tube Joint , Load-Deformat ion Curve, Regression Analysis, RingModel

IN T R O D U C T IO NA database for gusset -plate to CHS tube joints has been compiled atKum amoto U niversi ty to provide other researchers wi th a starting pointfor thei r own work on gusset -plate to CHS tube joints. Many studieshave been carried out in Japan with resul ts publ ished in Japanesejournals and conferences. The language barrier has prevented theseresul ts from being found and subsequent ly ut i lized in research problemsoutside of Japan. Therefore, the authors compiled the Database of Testand Numerical Analysis Resul ts for Gusset -Plate to CHS Tube Joints(1998).This invest igat ion aims to produce simple load-deformat ionrelationships for the joints mentioned in the database. In this paper, theultimate and yield strength equations and the equations for initialstiffness and deformation values at ultimate strength for gusset-plate toCHS tube joints under compression loads are proposed. Each load-deformat ion curve is described by two st raight l ines as sho wn in Figure1. Functions fx and f2 are derived using the geometrical and materialparameters o f the connect ions. H ence, these relat ionships est imate loadsand deformat ions at yield and col lapse for gusset -plate to CHS tubejoints o f any given geometry.

5 4

i ewhere

N,Ny

N~L

F2

5y ~i,F n = f o N u , N y , 5 . , S y )N u = f l (~,13,~/, ) 8u = f2 (%13, )i y = f3 (ct,[~,~/,. ) 5y = f4(o%13, /,.

Figure 1 Load-deformat ion relat ionshipThe only exist ing study o f the st rength equat ions of gusset -plate to CHStube joints to the authors ' knowledg e is that of Makino (1984) / M akino(1986) in which equat ions for ul t imate st rength were developed.However, yield st rength, ini t ial st i ffness and deformat ion values werenot considered in Makino's paper because of insufficient test andanalysis data. Therefore in this paper, the equat ions are given not onlyfor ultimate strength but also for yield strength, initial stiffness anddeformat ion values. T he ul t imate goal o f this project i s to offer avai lablematerial on st rength and deformat ion and to acquire design formulae forevery type of gusset -plate to CHS tube joint .

CLASSIFICATION OF JOINT TYPESThe joints studied in this paper consist of gusset -plates and a CH S t u b eThe configurat ions are similar to tubular X or T-joints wi th weldedgusset -plates instead of braces. This paper deals wi th only thoseconfigurat ions where a st i ffener i s added to the CHS tube to resist shearand bending m oments across the cross-sect ion of the CHS tube. Otherconfigurat ions, where load-t ransmission is axial and the connect ionst rength is not dependent on the deformat ion o f the cross-section, are


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F i g u re 3 De f i n i t io n o f y i e l d l o a d b y Ka m b a Fi g u re 4 De f i n i t i o n o f y i e l d l o a d b y Ku ro b a n e

e x c l u d e d f ro m t h i s p a p e r . Th e fo rms o f g u sse t -p l a t e t o C HS t u b e j o i n t sare XP a n d TP- j o i n ts , wh i c h c o r re sp o n d t o tu b u l a r X a n d T - j o i n t sre sp e c t iv e l y . Ea c h j o i n t t y p e i s c l a s s i f i e d i n t o f i v e t y p e s b y t h e sh a p e o ft h e j o in t s , a s sh o w n i n Ta b l e 1 . In a d d i t i o n , t wo t y p e s o f g u sse t -p l a t e sare d is t inguished: in one type the ex tension i s o rien ted la tera l ly , a r ib -p l a t e ; i n t h e o t h e r t y p e t h e e x t e n s i o n i s o r i e n t e d l o n g i t u d in a l l y , p a ra l l e lto the ax is o f tube , a gusse t -p la te .Ge n e ra l l y , j o i n t s a re su b j e c t e d n o t o n l y t o s i mp l e l o a d s b u t a l so t oc o m b i n e d l o a d s . In t h is p a p e r , o n l y j o in t s su b j e c t e d t o s i mp l ec o mp re ss i v e l o a d s a re c o n s i d e re d , a s p re se n t e d i n Ta b l e 1 . Th i s p a p e ru se s 8 5 t e s t s a n d a n a l y se s t o d e v e l o p t h e e q u a t i o n s . Th e n u mb e rs o fe a c h j o i n t t y p e a n d t h e p a ra me t e r r a n g e s a re sh o wn i n Ta b l e 2 .

D E F I N I T I O N S F O R U L T I M A T E A N D Y I E L D S T R E N G T H , I N I T IA LS T I FF N E S S A N D D E F O R M A T I O NU l t i m a t e S t r e n g t hA se v e re s t re s s c o n c e n t ra t i o n o c c u rs i n t h e c h o rd n e a r t h e we l d t o e o ft h e p l a t e . Th e c h o rd i n c u rs l o c a l b e n d i n g d e fo rma t i o n t h a t l e a d s t ofa i lu re . This paper i s l imi ted to those jo in ts underg oing fa i lu re in th isway. If an ax ia l fo rce i s appl ied to the p la te , the local deformat ion of thej o i n t u su a l l y c o n fo rms t o c u rv e A o f F i g u re 2 . In t h i s j o i n t , u l t i ma t es t re n g t h i s d e f i n e d a s t h e ma x i mu m v a l u e o f t h e p l a t e a x i a l fo rc e .C u rv e s B a n d C o f F i g u re 2 re fe r to jo i n t s wh e re i n so me re g i o n ss t i ffn e ss i n c re a se s a f t e r s e v e re d e fo rma t i o n o f t h e c h o rd . In c u rv e B ,a f t e r th e l o a d -d e fo rma t i o n re l a t io n sh i p re a c h e s i t s f i r s t ma x i mu m v a l u e ,t h e j o i n t b e c o me s u n s t a b l e . A f t e r a p e a k l o a d , t h e j o i n t sh o w s i n c re a s i n gst i ffness and becom es s tab le again . In th is case , ev en i f the jo in t i s

55


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su b j e c t e d t o l a rg e r a x ia l fo rc e s o n t h e p l a t e t h a n t h e fk s t ma x i mu m l o a d ,t h e f i r s t ma x i mu m l o a d i s d e fme d a s t h e u l t i ma t e s t r e n g t h . Fo r a j o i n tt h a t h a s a l o a d -d e fo rma t i o n re l a t i o n sh i p d e sc r i b e d b y c u rv e C , ap ra c t i c a l u l t i ma t e s t r e n g t h i s d e f i n e d a s t h e l o a d wh e re t h e s t i f fn e s sstart s to increase again .

Y i e l d S t r e n gt hKa mb a (1 9 9 8 ) d e f i n e d a t h i rd o f t h e i n i t i a l s t i f fn e s s a s t h e se c o n dst i ffness , and assu me d the y ie ld s t rength Ny.K~nb~, as the load whe re thes l o p e o f t h e l o a d -d e fo rma t i o n c u rv e i s e q u a l t o t h e se c o n d s t if fn e ss, a ssh o wn i n F i g u re 3 . On t h e o t h e r h a n d , a s s t a t e d b e lo w, y i e l d s t re n g t h c a na l so b e b a se d o n re su l t s o f t e s t s o n a c t u a l j o i n t s a n d r i n g mo d e l s a sp ro p o se d Ku ro b a n e (1 9 8 4 ) . A l o a d -d e fo rma t i o n c u rv e i s p l o t t e d o nd o u b l e l o g a r i t h mi c g ra p h p a p e r a s i l l u s t ra t e d i n C u rv e A o f F i g u re 4 , b u ti t i s a l so p o ss i b l e t o a p p ro x i ma t e t h e l o a d -d e fo rma t i o n c u rv e s b y t wost ra igh t l ines . The y ie ld s t rength N y K u r o b a n e i s defined as the load a t thein tersect ion of the two l ines , represen t ing a po in t o f maximum curvaturevaria t ion of the load-deformat ion curve . How ever, in cases wh ere the load-deformat ion curve can not be approximated by two s t ra igh t l ines , asi l lust ra ted in curve B o f Figure 4 , a sca t ter band o f 0 .25 com pared wi th thein i t ia l s lope of the load-deformat ion curve i s adopted . The load a t thein tersect ion of th i s l ine and the load-deformat ion curve i s defined as they ie ld s t rength . Com parisons of Ny,Kamua an d N y K u ro b an a r e sh o wn i n F i g u re5 . Th e y i e l d s t re n g t h s d e t e rmi n e d wi t h Ku ro b a n e ' s d e f i n i t i o n a resma l l e r t h a n t h e v a l u e s g i v e n b y Ka m b a ' s fo rmu l a a n d t h e fo rme r i sregar ded as safer va lues . In th is paper, Kuroba ne 's meth od i s adopted , andyie ld s t rength i s based on Kt t roban e 's defin i t ion .

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0 . 8~ 0 . 6

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X P j o i n tO T P - i o i n t

0 2 0 4 0 6 0 8 0 1 0 0D / r

Figure 5 Comparisons OfNy.Kuroban and Ny.Kamba

I n i t i a l S t i f f n e s sIn i t ia l s t i ffness i s defined as the s lope of a l ine tangent a t the orig in oft h e l o a d -d e fo rma t i o n c u rv e , a s sh o wn i n F i g u re 1 ,n o t b y a l i n e se c a n t.

t o t u b u l a r X a n d T- j o i n t s r e sp e c t i v e l y . I t i s a l so p o ss i b l e t o d e v e l o ps t re n g t h e q u a t i o n s o f g u sse t -p l a t e t o e l l S t u b e j o i n t s u s i n g t h e c o n c e p to f r i n g mo d e l s . T h e d e r i v a t i o n s o f r in g mo d e l s fo r X a n d T - j o i n t s a reg iven next .

R i n g M o d e l f o r a n X - j o in tAn X- j o i n t i s a p p ro x i ma t e d b y a r i n g wi t h a n e f fe c t i v e wi d t h B o , a sshown in Figure 6 (a) . Plast ic s t rength of the r ing No, i s ca lcu la ted usingp l a s t ic h i n g e t h e o ry a n d g i v e n b y Eq . (1 ) .

N : B e 1mT 2 ~ y R l d (1 )

DIn a m o re a c c u ra t e d e r i v a t i o n o f t h e p l a s ti c s t r e n g t h , i t b e c o m e s c l e a rt h a t t h e s t re n g t h a l so c h a n g e s wi t h D/ T . A ma t h e ma t i c a l mo d e l o fu l t i ma t e s t r e n g t h fo r r i n g s i s a s su me d a s i n Eq . (2 ) b y a d d i n g a t e rm D/ Tto Eq . (1) .

R N u e O 1~ = ~ ~ ~ - f - ) ~ (2 )T E o y D 1 131;2 DHe re , ~ i s a n e r ro r t e rm wh i l e , a n d a re re g re s s i o n c o e f f ic i e n ts .Th a t a re d e t e rmi n e d b y re g re s s i o n a n a l y s i s , Th e re su l t s a re p re se n t e d i nEq. (3). 4 4 9 3 0 o ,

TE~y D 1 _ 0 . 9 1 7 dD(3 )

Th e r i n g mo d e l me t h o d d e sc r i b e d a b o v e a n d mu l t i p l e n o n l i n e a rre g re s s i o n a n a l y se s o n a l a rg e n u m b e r o f t e s t r e su l t s p ro v i d e t h e b a s i sfo r t h e s t re n g t h e q u a t i o n s fo r t u b u l a r X, T , Y a n d K - j o i n t s su g g e s t e d b yM a k i n o e t a l (1 9 8 4 ) .

R i n g M o d e l f o r a T - j o i n tIn a T - j o i n t , o n l y two c o n c e n t ra t e d fo rc e s o p e ra t e o n t h e r i n g mo d e l a tt wo p o i n t s o u t s i d e t h e b ra c e d i a me t e r o f mo d e l , a s sh o w n i n F i g u re 6 (b ) .The r ing receives a shear force q as a react ion force . The T-jo in t i sre g a rd e d a s t h e r i n g m o d e l i n b e a m t h e o ry . Th e p l a s t i c f a i l u re lo a d o f ar ing w i th a wid th No, i s g iven in Eq . (4) .

T ~y RD e f o r m a t i o nIn t h i s p a p e r, d e fo rma t i o n i s d e f i n e d a s t h e l o c a l d e fo rma t i o n o f t h e j o i n t( i .e . i n d e n t a t io n ) , n o t a s t h e d e fo rma t i o n o f t h e w h o l e c h o rd .

1 c o s l 3l ,l + c o s 0 ) s , _ ( , _ + c o s , , s m 0

4 )

T E S T S O F R IN G M O D E L S A N D N O N L I N E A R A N A L Y S E SSi n c e ma n y i n v e s t i g a t i o n s o f t u b u l a r X a n d T- j o i n t s h a v e b e e nc o mp l e t e d , s t r e n g t h e q u a t i o n s o f t h e se j o i n t s u s i n g g e o me t r i c a lp a ra me t e r s h a v e b e e n su g g e s t e d . So me o f t h e se e q u a ti o n s a re b a se d o na n a l y t ic a l mo d e l , e .g . s i mp l e r in g m o d e l s . XP a n d TP - j o i n ts c o r re sp o n d

Here , s in 13=d/D and 7 i s an angle f orm ed in a p last ic h inge , y i s ob ta inedfrom Eq. (5) .

( 1 - 1 c o s - - [ 1 0 +cos+ c o s

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r yLi ) _ _ ; _ _ r . . . . .k- . - -_J

( a ) X - jo in t s

N/2

N/2

N ,';. N ~;. N ~;.w~ N ~ N ' 2 I - ~ - F F4-d-I~. . . i i 2 ~ N_ _ t . . . . I . . . . . N / / 2L J, , / 2 i - - ; - - 1 ] . . . . . j l q ~ Tk - . - - . . . . . .\ ] N/2 N/Z '~ INDICATESii ~" i , . o ~ , , ~ o , , o , "YIELDHINGE

(b ) T - jo in t sF i g u r e 6 R i n g m o d e l sE Q U A T I O N S T O D E S C R I B E L O A D - D E F O R M A T I O NR E L A T I O N S H I P SU l t i m a t e S t r e n g t h( 1 ) X P - j o i n t sI t is a s s u m e d t h a t a n X P - j o i n t u n d e r c o m p r e s s i o n c a n b e a p p r o x i m a t e dby a r ing w i th a n e f f e c t ive w id th Bo , a s s how n in F igu re 7 ( a ) . Am a t h e m a t i c a l m o d e l f o r e s t i m a t i n g t h e u l t i m a t e s t r e n g t h o f X P - j o i n t s i so b t a i n e d f r o m E q . ( 1 ) . A t e r m D / T i s a d d e d t o m a k e t h e e q u a t i o na pp l ic a b le fo r a l a rge r r a nge .

N . x _ c q- C (6)T2 y 1 + ~x - -

DF rom re g re s s ion a na lys e s , the fo l low ing u l t im a te s t r e ng th e qua t ion fo rX P 1 a nd X P 3- jo in t s i s ob ta ine d :

N u : - 1 . 9 6 ( D )' 2 7 3 _T 2 o y 1 - 0 8 5 7 c ( 7 )

Dn = 3 9 m e a n = 1 . 00 C o V = 0 . 0 9 0

In X P 3- jo in t s , the gus s e t -p la te p ro t rud ing ou t o f a f ib -p la te i s r e ga rde da s pa r t o f the loa de d e f f e c t ive w id th , s o the gus s e t -p la te c a n be ignore d .T h e e f f e ct i v e w i d t h o f X P 1 a n d X P 3 - j o i n t s i s c a l c u l a t e d b y c o n s i d e r i n gE q . (7 ) to be r e la te d to E q . (3 ) , a s fo l low s :

1- 0. 91 7 C 0.474D 1 - 0 . 8 5 7 C

DT h e X P 2 a n d X P 5 - j o i n ts c a n b e c o n s i d e r e d t o b e r e p r e s e n t e d b y a r i n gw i th a n e f f e c t ive w id th (Be +B) . A c hord l i e s be tw e e n tw o gus s e t -p la te sa nd e x te nds ou t s ide o f the gus s e t -p la te s . T he s e po r t ion s o f the c horda l s o c o l la bo ra te to t r a ns fe r the loa d a s s how n in F igu re 7 ( a ) . T he re fo re ,s t r e ng th e qua t ions fo r X P 2 a nd X P 5- jo in t s a r e ba s e d on the s t r e ng the qua t ion de r ive d fo r a r ing m ode l , E q . (3 ) .

4 4 9 ) 0 0 1T 2 ~ y D 1 _ 0 . 9 1 7 c ( 9 )

DBe q) i s c a lc u la te d us ing E q . (8 ) , s o tha t E q . (9 ) be c om e s :

if - - f - ' v

. . . . I ' - - 1i: :

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N ~.N / 2 ~ N / 2

N/2 N/2f iN I

( a ) X P - j o i n t s

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i

11 LOCATmNri, t~ Y I E L D H I N G E(b ) T P - j o in t s

F i g u r e 7 R i n g m o d e l s

N,,c, _ 1 .96 ~3273_ _ + - - - 4 . 49 ( D ) - 2 1T 2 ~ y 1 _ 0 . 8 5 7 D 1 _ 0 . 9 1 7 (1 0)

D Dn = 3 m e a n = 0 . 9 4 5 C O V = 0 . 0 3 0

C o f X P 2- jo in t s r e p re s e n t s the th ic kne s s o f the gus s e t -p la te a nd i s s m a l le nou gh to be s a f e ly ignore d . I t i s pos s ib le to ob ta in the u l t im a te s t r e ng thfo r X P 2- jo in t s u s ing the fo l low ing s im ple r e qua t ion :

- - 0 .2 7 3 - - - 0 . 2 0 1N u,c = 1 . 9 6 / D ) + 4 . 4 9 B / D 3 ( 11 )T 2 c r y

n = 12 m e a n = 1 .24 CoV = 0 .056T he s t r e ng th e qua t ion o f X P 4- jo in t s w i th tw o r ib -p la te s i s a s fo l low s :

N u c - 1 . 9 6 a n ( D 3 2 7 3T 2t ry 1_0 .857C__ (12 )

Dn = 6 m e a n = l . 1 6 C O V = 0 .0 7 8

T he r e la t ions h ip be tw e e n o~B a nd the ga p o f the tw o f ib -p la te s B , c a n befo rm ula te d a s fo l low s :

1 B~ B = 1 + - - . ~ 1 3 )4 DI f B i s l a rge e nough , i t i s e qua l to the s uppor t ing lo a d o f tw oinde pe nde n t f ig -p la te s , tha t i s o~B=2 . O n the o the r ha nd , i f B i s c lo s e toz e r o , t h e n t h e jo i n t i s e f f e c t iv e l y t h e s a m e a s X P l - j o i n t s , w h i c h m e a n stha t c ~B=l . T he e f f e c t s o f a gus s e t -p la te c a n be ignore d fo r the s a m ere a s on a s fo r X P 3- jo in t s .In F igu re s 9 ( a ) - ( c ) , a l though te s t a nd num e r ic a l r e s u l t s to p r e d ic t ionra t io s fo r X P 2- jo in t s a r e a l i t t le h igh , i t i s obs e rve d tha t the da ta a n d thep re d ic te d u l t im a te s t r e ng th va lue s a g re e w e l l . I t i s c onc lude d tha t thea s s um pt ions a bou t the e f f e c t ive w id th a r e a ppropr ia te .

( 2 ) T P - j o i n tsA s fo r a n X P - jo in t , a T P - jo in t i s r e ga rde d a s a r ing w i th a n e f f e c t ivew id th Be , a s s how n in F igu re 7 (b ) . F o r th i s type o f jo in t , a n a x ia l f o r c ei n t h e b r a c e i s s u p p o rt e d a t b o t h e n d s o f t h e c h o r d , s o b e n d i n g m o m e n t sa c t ing on the jo in t de pe n d on the c hord l e ng th . I n a dd i t ion , s he l l - l ikem ove m e n t c ha nge s w i th the c hord l e ng th . T he re fo re , a func t ion (1 -0 .32m 0) tha t i s a r e duc t ion f a c to r fo r c ho rd m e m be r g loba l be nd inge f f e c t s i s a dde d to E q . (6 ) to inc lude the s e f a c to rs . T he u l t im a te s t r e ng thi s ob ta ine d a s fo l low s :

5 7


5/9

N , , ~ _ o q ( 1 _ 0 . 3 2m o )~ - ----------d (14)T2 'y 1 + a 2 DUl t i ma t e s t re n g t h s fo r TP1 a n d TP3 - j o i n t s a re e s t i ma t e d b y re g re s s i o nanalysis in Eq . (14).

N , , c _ 3 9.9 ( D ) ' 4 2 9 _ ( 1 - 0 . 3 2 m o )T2t~y 1 - 0 . 9 2 8 ( 1 5 )D

n = 1 6 m e a n = 1 . 0 1 C o V = 0 . 1 5 7TP4 - j o i n t s a re c o n s i d e re d i n a s i mi l a r wa y a s XP4 - j o i n t s . Th i s s t r e n g t hequat ion i s the fo l lowing:

N u , ~ _ 3 9 . 9 t ~ B (1 _ 0 .3 2m o )T2t~y 1 - 0 9 2 8 C ( 1 6 )D

n = 2 m e a n = 1 . 1 0 C o V = 0 . 0 8 6Th e b e h a v i o r o f TP2 a n d TP5 - j o i n t s c a n a l so b e a p p ro x i ma t e d b y a r i n gwi t h a n e f fe c t i v e wi d t h (B o + B ) s i mi l a r t o XP2 a n d XP5 - j o i n t s . Th e i ru l t imate s t rengths are pred ic ted using Eq. (4) .

N u ,c B ~ + B ( C (1 7 )In a d d i t i o n , t h e e f fe c t iv e wi d t h o f TP- j o i n t s i s o b t a i n e d u s i n g Eq s . (4 )and (15).

D/-0.4291_o.92aC 0 -0 32mo

e D 1 8 )39.9

Eq. (18) i s ra ther compl ica ted , so for p rac t ica l use i t i s s impl i f ied asfo l lows. Assign q = Bo(D/T)429/R(1-0 .32m0), and p lo t q versus C/D assh o wn i n F i g u re 8 . F ro m t h i s f i g u re , i t h a s b e e n d e t e rmi n e d t h a t i fC / D< 0 .9 t h e n q i s b e t we e n 2 1 .2 a n d 2 5 .0 a n d a l mo s t c o n s t a n t . Fo rC / D< 0 .9 , a s su m e q = 2 2 .3 a n d R = D/ 2 . C o n se q u e n t ly , Eq . (3 4 ) c a n b ere p re se n t e d a s fo l lo ws :

N u , ~ _ 3 9 .9 (1 _ 0 .3 2 m0 ) + BT 2 c y 1 _ 0 . 9 2 8 c l l . 2 D ( 1 9)D

n = 1 me an = 1.11Pa r t i c u l a r l y i n t h e c a se o f TP2 - j o i n t s , C c a n b e i g n o re d , b e c a u se t h evalue i s smal l . Hence , the s t rength equat ion can be s impl i f ied further .

N u '~ = 3 9 .9 ( 1 - 0 . 3 2 m 0 ) + ( 2 0 )TE{y y T 1 1 .2 Dn = 8 m e a n = 0 . 9 94 C o V = 0 . 1 1 0

Te s t r e su l ts fo r p re d i c t i o n ra t i o s fo r TP- j o i n t s a re a l m o s t a l l b e t we e n 0 .8a n d 1 .2 , a n d u l t i ma t e s t r e n g t h s a re p re d i c t e d we U, a s sh o wn i n F i g u re s10 (a)- (c) .

5 8

3 0e,t~. 2 5g 2 0

~ lO5o-

39.9/ 1-0i928C/D)f~

0 0 . 2 0 . 4 0 . 6 0.8 1C/DFi g u re 8 E f fe c t iv e w i d t h fo r TP- j o i n t s

Y i e l d S t r e n g t hUsi n g t h e c o n c e p t o f e f fe c t i v e wi d t h fo r a r i n g mo d e l ma k e s i t p o ss i b l et o e s t a b l i sh t h e u l ti ma t e s t r e n g t h e q u a t i o n s o n g u sse t -p l a t e t o C HS t u b ej o i n t s . Th e sa me r i n g mo d e l m e t h o d o l o g y u se d a b o v e fo r u l ti ma t es t re n g t h c a n b e u se d t o d e t e rmi n e t h e y i e l d s t re n g t h fo r b o t h XP a n d TP-j o i n t s . Th e e q u a t i o n s fo r y i e l d s t re n g t h a re sh o wn i n Ta b l e 3 , a n d Eq s .(2 1 ) - (2 8 ) . Th e t e s t a n d n u me r i c a l r e su l t s fo r p re d i c t i o n ra t i o s o f t h o see q u a t i o n s fo r XP a n d TP- j o i n t s a re p l o t t e d i n F i g u re s 1 1 (a ) - (c ) a n d 1 2a ) - c ) .

I n i t i a l S t i f f nes sKa mb a (1 9 9 8 ) su g g e s t e d d e sc r i b i n g t h e p h y s i c a l q u a n t i t y a s a n o n -d i me n s i o n a l p ro d u c t o f a l l t h e i n d i v i d u a l q u a n t i t ie s r e l a t e d t o i t . Fo r t h ein i t ia l s t i ffness of a connect ion , the phy sica l quant i t ies are the mate ria l s 'p ro p e r t i e s a n d t h e s i z e o f t h e me mb e rs . Yo u n g ' s mo d u l u s i s s e l e c t e d tore p re se n t t h e ma t e r i a l s ' p ro p e r t i e s w h e re a s t h e t h i c k n e ss o f t h e c h o rd i st a k e n t o re p re se n t t h e s i z e o f a me m b e r . T h e i n i t i a l s ti f fn e ss i s o b t a i n e das fo l lows:

= e t 1 ~ (2 9 )E TTh e fo l l o wi n g s t re n g t h e q u a t i o n fo r XP1 a n d XP3 - j o i n t s i s o b t a i n e da f t e r u s i n g Eq . (2 9 ) a s a b a s i s fo r r e g re s s i o n a n a l y s i s .K 'c = 7 .45 (30)E T

n = 3 6 me a n = 1 .0 4 C OV= 0 .3 4 2Th e s t re n g t h e q u a t i o n fo r XP4 - j o i n t s i s s i mi l a r t o Eq . (3 0 ) a f t e r a d d i n g at e rm a B .Kn'c - 7.45ctB (3 1 )E T

n = 2 m e a n = l . 3 0 C O V = 0 . 2 9 8Th e XP 2 a n d XP 5 - j o i n t s a re b a se d o n t h e c o n c e p t o f th e e l a s t i cd e fo rma t i o n a s a r e su l t o f a p o i n t l o a d a c t i n g o n a c y l i n d r i c a l sh e l l a ssh o wn i n F i g u re 7 (a ) . Th e d e fo rma t i o n o f a mo d e l l o a d e d b y a p o i n tl o a d i s c a l c u l a t e d u s i n g t h e fo l l o wi n g fo rmu l a .

p R 38 = 0 . 1 4 9 ~ ( 32 )E IFro m Eq . (3 2 ) , t h e i n i t i a l s t i f fn e s s o f t h i s mo d e l i s r e p re se n t e d a s


6/9

fo l lows:R K n = 8 . 9 5 ( 3 3 )ET

As the funct ion in Eq. (33) i s considered insuffic ien t to be appl ied to thein i t ia l s t iffness of XP2-jo in ts , a second term includ ing D/I i s added toEq. (33):

( D ) - 2 ( n ) ( D ) 0 .4 09Kn'~ - 8 .95 .0 .876 (34)E Tn = 1 0 mean = l .0 1 C O V = 0 .12 3

For XP 5-jo in ts , the in i t ia l s ti ffness i s considered to be the sum of thev a l u e s ca l cu l a t ed u s i n g Eq . (3 0 ) an d t h e i n i t i a l s t i f fn e ss o f a mo d e ll o ad ed b y t w o p o i n t l o ad s a s sh o w n i n F i g u re 7 (a ) . Th e d e fo rma t i o neq u a t i o n o f t h e mo d e l i s a s fo l l o w s :

5 = 0 . 0 76 - 0 . 9 7 6 E ITh ere fo re , t h e i n i t ia l s t i f fn e ss o f X P5 - j o i n t s i s p red i c t ed u s i n g t h e su mo f Eq s . (3 0 ) an d (3 5 ) , a s sh o w n h e re :

_ \ - 1 . 3 2 / - - x l . 0 8 - 2 B C - 2K,,,,:ET 7 4 5 ( T ) / D ) + 8 7 8 ( D ) ( - ~ - )( - ~ - - 0 .9 7 6 ) ( 36 )

From Figures 13 (a)-(c) , i t i s observed that in i t ia l s t i ffnesses obta inedare accura te except for one data poin t of an XP 1-jo int . In a s imi lar way,eq u a t i o n s fo r TP- j o i n t s a re e s t ab l ish ed , an d sh o w n i n T ab l e 4 , a s Eq s .(37)-(40) and Figures 14 (a)-(c) .

D e f o r m a t i o n a t U l t i m a t e S t r e n g t hSimi lar to in i t ia l s t i ffness , the deformat ions values a t u l t imate s t rengtha re p re sen t ed i n n o n -d i men s i o n a l fo rm b y d i v i d i n g t h e ac t u a ld e fo rma t i o n s b y t h e ch o rd d i ame t e rs . R e fe r r i n g t o a ma t h ema t i ca l m o d e lfor a r ing , as in Eqs. (41) or (42), i t i s possib le for the local deformat ionat u l t imate s t rength to be calcu la ted .~ S u c ( D ) ~ 2 ( C ) ~3 ( 4 1)~ ' = O I ;1 [ ;D~3u'~ - a 1 ~ (42 )D

Th ere a re few t e s t an d an a l y s i s d a t a fo r so me t y p es o f j o i n t s i n t h i sp ap e r . Th e re fo re , eq u a t i o n s fo r d e fo rma t i o n v a l u e s a t u l t i ma t e s t ren g t ha re ap p l i ed t o Eq . (4 1 ) i n X P1 an d TPl - j o i n t s , an d Eq . (4 2 ) i n X P2 an dTP2 - j o i n t s re sp ec t i v e l y . Th e eq u a t i o n s a re sh o w n i n Tab l e5 , an d Eq s .(4 3 ) - (4 6) . Th e t e s t an d n u m er i ca l r e su l ts fo r p red i c t i o n ra t i o s o f t h o seeq u a t i o n s fo r X P an d TP - j o i n ts a re p l o t ted i n F i g u re s 1 5 (a ) - (b )

n = 3 mean = 0 .8 5 5 C O V = 0 .1 5 4Tab le 3 Ec~uations for ~ield stren gthT y p e II Y i e l d S t r e n g t h F o r m u l a e I N o . I T y p II Y i e l d S t r e n g t h F o r m u l a e N o .X P 1X P 3

X P 2

X P 4

X P 5

N y c _ 1 . 2 0 / D ) 0 3 95T 2 ~ y 1 _ 0 . 7 9 5 CD

n = 3 6 m e a n = l . 0 1 C o y = 0 . 1 1 0

T P 1(2 1 ) T P 3

n = 1 0 m e a n = 0 . 8 9 3 C o v = 0 . 1 4 6(2 2 )

N y , c _ 1 . 2 0 a n I D ) 3 9 5 _T 2 f f y 1 - 0 . 7 9 5 cD

1 Ba B = 1 + - - . ~4 Dn = 2 m e a n = l . 1 3 C o v = 0 . 1 6 4

23)

N . v , , : _ 1.20 __ + 1 .75T 2 ~ y 1 - 0 . 7 9 5 C

Dn = 3 m e a n = l . 0 8 C o v = 0 . 0 4 5(2 4 )

T P 2

T P 4

T P 5

N y , ~ 14 4 ( TD../-91T E r r y 1 _ 0 . 8 2 8 C ( 1 - 0 3 2 m )D

n = 1 5 m e a n = l . 0 2 C o v = 0 . 1 8 8( o )N v : = 1 4 4 ( 1 - 0 . 3 2 m 0 ) +r o f f jn = 8 m e a n = l . 1 7 C o v = 0 . 1 1 9

B3 5 . 2 D _ i

N y , c _ 1 4 4 a n ( D ) - 9 ~T 2 C r . v 1 _ 0 . 8 2 8 C ( 1 - 0 3 2 m )D

1 Bo~n = 1 4 . . .4 Dn = 1 mean = 1 .39

N y , c _ 1 4 4 h _ 0 .3 2 m 0 ~ + 3 5 .2 DT 2 ~ y 1 - 0 . 8 2 8 cD - -n = l m e a n = 0 . 9 6 6

25)

(2 6 )

(2 7 )

28 )

59


7/9

Table 4 Ec~uat ions for in i t ia l s t i ffnessT y p e 1] I n i t i a l S t i f f n e s s F o r m u l a e

T P 1T P 3

T P 2

T P 4

T P 5

. . . . = 2 .0 4ET

n = 1 5 m e a n = l . 0 4 C o v = 0 . 2 8 9Knc ( T / - 2 1 B ) I D ) 4 4 4 ( B / -0 9 8 0

. . . . =8 .49 -1 .09ETn = 8 m e a n = l . 0 0 C o v = 0 . 0 6 50 :C / T M.... = 2 . 0 4 ~ mET

1 Bo~ B = 1 + - . m4 Dn = l m e a n = l . 0 8

n c D / - 0 . 7 1 8C )1 ,2 6 D /- 2 B ) c )- 1. .. . = 2 . 04 + 0 . 6 6 7 1 5 . 1 - - - 0 . 6 3 6ETn = 1 mean = 2 .3 1

Table 5 Eciuat ions for deformat ion a t u l t imate s t rengthT y p e D e f o r m a t i o n a t U l t i m a t e S t r e n g t h F o r m u l a e N o . I T y p e

X P 1

X P 2

~ ' :D '=0.163( -~) - 421C 0 8 9 -n = 3 3 m e a n = l . 0 2 C o v = 0 . 1 8 38 CD' = 0 .0 1 7 ( D ) 32s (DB---)22

n = 9 m e a n = l . 0 0 C o v = 0 . 0 5 2

( 4 3 ) T P 1

( 4 4 ) T P 2

N o .

(3 7 )

3 8 )

3 9 )

( 4 0 )

D e f o r m a t i o n a t U l t i m a t e S t r e n g t h F o r m u l a e [ N o .~ u c ( -- 0 2 64 C / ' 4 4 3

n = 1 4 m e a n = l . 0 1 C o v = 0 . 1 4 7~ ) u c 0 . 0 0 2 ( D ) ' 8 7 7 ( B ) 0 294

n = 8 m e a n = l . 0 1 C o v = 0 . 1 5 9

(4 5 )

(4 6 )

1.61.41.20.80.60.40.20

0

1.61.4 - | i o x P 2 1 1 w e ; / ]1 3 ~ | I~XP3 [ ~ o . s

ioxP4 l z 0.6I~


8/9

1.41.2

10.8

~ 0 . 60.40.2

020 40

D ~a ) against D/T

I . x P , I; IOXP21I~XP3ixP41I~


9/9

1 6 1 41 41 2 I I 0 I 1 2 D ~

o.s - | xvz l ~ 0 .6~ 0.60 4 0 40 2 0 2

0 00 2 0 4 0 6 0 0 2 0 4 0 6 0 8 0 1 0 0

T P 1 ]oTr~l

D/T D/T(a) XP - joints (b) TP- jointsF igu r e 15 T es t and numer i ca l r e su l t s t o p r ed i c t ion r a t i o s f o r de f o r mat ion a t u l t ima te s t r eng th

C O N C L U S I O N S RTI n th i s paper , r i ng mode l s wi th t he e f f ec t i ve wid th and r eg r ess ionZ 1, Z 2, Z 3, . . . O~ana lyses has been used to es t ab l i sh equa t ions f o r u l t ima te and y i e ld 8u

strength, ini t ial st i f fness and deformat ion values at ul t imate st rength for 8u cgusse t - p l a te t o CHS tube j o in ts . T he p r ed i c t i ons us ing those equa t ions sa r e accu r a t e f o r bo th XP and T P- jo in t s , and a r e as we l l a s va lues Uyobser ved in t he r esu l t s o f te s t s and ana lyses i n t he da t abase. T her e a r emany types o f gusse t - p l a t e t o CHS tube j o in t s ; never the l ess , on ly a f eware deal t wi th in this paper . How ever , i t i s jud ged that the equat ionsdeve loped in t h i s paper may be app l i ed t o o the r gusse t - p l a t e t o CHStube jo in t s a s we l l . Unf o r tuna t e ly , f o r some types o f jo in t s no t e s t o ranalysis data are avai lable. Th erefore, i t is judg ed tha t the data are notadequa te f o r deve lop ing app l i ca t i ons f o r a l l t ypes o f j o in t s .

S Y M B O L SBBoCDdEF1, F2, F 3 . . . . F n~ ~ ~ .....IK.I~oLM0m0NcN ~N ~RN u

RN~ c

Nyy, c

n

wid th o f gusse t - p l a teef fect ive widthwid th o f r i b - p l at echor d d i amete rb r ace d i amete rY o u n g ' s m o d u l u sfunct ionsfunct ionsgeomet r i ca l mom en t o f i ne r t iaini t ial st i ffness unde r axial forceest imated ini t ial st i f fness by regression analysisini t ial sti f fness under axial force of r ing mod elchor d l eng thbend ing m ome nt i n chor d a t cen t e r o f j o in tf u ll p l as ti c mom ent capac i ty in chor d me mbe rbend ing m omen t r a ti o ( Mo/Mp)plast ic st rengthu l t ima te capac i ty o f j o in t m easu r ed as ax i a l l oades t ima ted u l t ima te capac i ty by r eg r ess ion ana lys isu l t ima te capac i ty o f r i ng mode l m easu r ed as ax i a ll oades t ima ted u l t ima te capac i ty o f r i ng mode l byr eg r ess ion ana lys i sy i e ld capac i ty o f j o in t m easu r ed as ax i a l l oad ingusset-platees t ima ted y i e ld capac i ty by r eg r ess ion ana lys isn u m b e r o f d a t a

chor d r ad iuschor d t h i cknesspar amete r s o f r eg r ess ion ana lys isloca l de f o r mat ion o f j o in t r eached a t u l t ima te s t r eng thes t ima ted loca l de f o r mat ion by r eg r ess ion ana lys i se r r o r t eam in r eg r ess ion ana lys i sy i e ld s t r ess o f chor d m ate r i a l

A C K N O W L E D G E M E N T ST he au tho r s wou ld l i ke t o t hank G. J . van de r Veg te and Y Mine har a f o rthe i r a ss i s t ance and con t r ibu t ions t o t he wor k r epor t ed he r e . Wi thou tthe i r suppor t , th i s paper wo u ld no t have been poss ib l e .

R E F E R E N C E SKam ba T ., and T ac lendo C. , ( 1998). CHS co lum n connec t ions wi thou tst i f fener , Proc. of 8 h Int . Sym posiu m on Tubular Structures ( ISTS ) ,S ingapor e , pp .567- 576Kur oban e Y. , Ma k ino Y. , and Och i K . , ( 1984) . U l t ima te Res i s t ance o fUns t i f f ened T ubu la r Jo in t s, Jou r na l o f S t r uc tu ra l E ng ineer ing , P roc . o fthe Am er i can Soc i e ty o f Civ i l E ng ineer s ( ASC E ) , U .S .A. , Vo l . 110 , No .2 ,pp .385- 400Lu L. H., de Winkel G. D., Yu Y., and Wardenier J . , (1994) .

Def o r m at ion l im i t f o r t he u l t ima te s t r eng th o f ho l low sec t ion jo in t s .P r oc . o f 64 I n t . Sym pos ium on T ubu la r S t r uc tu r es ( IST S) , A us t r a li a ,pp .341- 347Makino Y. , ( 1984) . E xper imen ta l S tudy on Ul t ima te Capac i ty andDef o r ma t ion fo r T ubu la r Jo in t s , Doc to r a l Di sse r t a t i on , Osa kaUniver s i t y ( i n Japanese )Mak ino Y. , and Kur obane Y. ( 1986). Recen t Resea r ch in Kum amo toUniver s i t y in T ubu la r Jo in t Des ign , I I W Doc . XV- 615- 86 / XV- E - 86-108, Japan, pp. 1-28Makino Y. , Ar iyosh i M . , M inehar a Y . , van de r Veg te G . J . , Wi lmshur s t S .R . , and Choo Y. S . ( 1998) . Da tabase o f T es t and Numer i ca l Ana lys i sResu l t s f o r Gusse t - P l a t e t o CHS T ube Jo in t s , I 1W Doc . XV- E - 98- 237 ,S ingapor eYur a J. A . , Z e t t l emoyer N . , and E dw ar d I . F . , ( 1980). U l t ima teCapac i ty E qua t ions f o r T ubu la r Jo in t s , P r oc . o f Of f shor e T echno logyCon ference (OT C), USA , Vol . 1 , No. 36 90, pp. 113-127

6 2

ISOPE-I-99-352_Load-Deformation Relationships for Gusset-Plate to CHS Tube Joints Under Compression Loads

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