torsional rigidities of open stiffeners to compression flanges.pdf

7/30/2019 Torsional Rigidities of Open Stiffeners to compression flanges.pdf

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J . C o n s t r u c t . S t e e l R e s e a r c h 20 (1991) 65-74

Torsional R igidities of O pen Stiffeners toCom pression Flanges*I o a n n i s V a y a s

Na t io n a l T e c h n i c a l Un iv e r s i ty o f A th en s , 4 2 P a t i s s io n S tr ., G R- 1 0 6 8 2 A th e n s , Gr e e c e

A B S T R A C TA cr i t i ca l r ev iew o f code pr ov i s ions and o ther p r opos a l s concer n ing the r equ i r em en t sfo r to r s iona l r ig id i t ie s o f f la t s t i ff ener s to com pr e s s wn f lang es i s m ade . T h e r e levan tr u les a r e inves t iga ted by m eans o f 65 t e s t s on com pr es s ed , s t i f f ened p la tes w i thvar ious load ing and s uppor t ing condi tions . A new des ign r u le fo r the d e ter m ina t iono f the d im ens ions o f f la t s t i f f ener s, bas ed on the i r u l t im a te s t r es s and the u l t im a tes t r es s o f the s t i f f ened p la te , i s p r opos ed and r e levan t des ign char t s a r e g iven .

I N T R O D U C T I O NT h e o r e t i c a l a n d e x p e r i m e n t a l r e s e a r c h o n a x i a l ly l o a d e d p l a te s , st if fe n e do n o n e s id e b y o p e n s ti ff e ne r s h a v e s h o w n , t h a t t w o m o d e s o f f a il u r e a r eposs ib l e ( F ig . 1 ) :

- - p l a t e f a i l u r e , c a u s e d b y p l a t e b u c k l i n g , w h e r e t h e d e f o r m a t i o n s a tf a i lu r e c o n s i s t o f a g l o b a l , o v e r a l l d e f l e c t io n t o w a r d s t h e s t i f fe n e r a n dloc a l bu c k le s o f t he p l a t e ( F ig . l ( a )) ;- - s t if fe n e r f a il u r e, c a u s e d b y l a t e r a l t o r s i o n a l b u c k l i n g o f t h e s t i ff e n er s ,w h e r e t h e d e f o r m a t i o n s a t f a i lu r e c o n s i s t o f a g l o b a l , o v e r a l l d e fl ec -

t i o n t o w a r d s t h e p l a t e a n d l o c a l b u c k l e s o f t h e s t i ff e n e rs ( F i g . l (b )).T h e l o a d c a r r y i n g b e h a v i o u r o f t h e s e p l a t e s d e p e n d s l a r g e l y o n t h ef a il u r e m e c h a n i s m a s e x p e r i m e n t a l 1'2 a n d t h e o r e t ic a l r e s e a rc h 3 h a s s h o w n .

P l a t e s w i t h s t i f f e n e r f a i l u r e b e h a v e a l m o s t l i n e a r l y u p t o f a i l u r e , s i n c e o n l ys e c o n d - o r d e r e f f e c t s a r e r e l e v a n t , w h e r e a s t h e i r l o a d - c a r r y i n g c a p a c i t y*Presented a t the International Colloquium on Stability of Steel Structures h eld in Budapest,Hungary, 1990.

65J . C o n s t r u c t . S t e e l R e s e a r c h 0143-974X/92 /$05 .00 1992 E lsev ie r Sc ience Pub l i she rs L td ,E n g l a n d . P r i n t e d i n Gr e a t Br i t a i n


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Fig . 1 . F a i lu r e m od es o f ax i a l l y com pr ess ed , s t i f f ened p la t e s . (a ) P l a t e f a i l u re ; ( b) S t if f ene rfa i lure .

r ap id ly d ec r ease s a f t e r f a i lu r e (F ig . l ( b ) ) . P l a t e s w i th p l a t e f a i lu r e b eh av e ,b e f o r e f a il u re , l a r g e l y n o n l i n e a r l y b e c a u s e o f p l a st i c s t re s s r e d i s t r i b u t i o n sa n d s e c o n d - o r d e r e f f e c t s a n d t h e y p o s s e s s a h i g h l o a d - c a r r y i n g c a p a c i t yaf te r fa i lu re (Fig . l (a ) ) .I t is , t h e r e fo r e , d e s i ra b l e ( a n d s e v e r a l C o d e s d o it) to p r e s c r i b e m i n i m u mto r s io n a l r ig id i t i e s o f t h e s t i ff en e rs in o rd e r to a v o id l a t e r a l t o r s io n a lb u c k l i n g , a n d c o n s e q u e n t l y a s ti ff e ne r m o d e o f fa i lu r e fo r t h e p l a te . I n t h ep r e s e n t w o r k t h e p r o v i s i o n s f o r fi a t s ti ff e ne rs o f t h e D r a f t C o d e D I N18 8 0 0 Pa r t 3 : 1 98 9, 4 BS 5 4 0 0 P a r t 3 :1 9 8 2 3 an d p r ev io u s p ro p o sa l s m ad eb y V a y a s 6 a r e e x a m i n e d t h r o u g h t e st r e s u l t s o n c o m p r e s s e d s t if fe n e dp la t e s , an d n ew ru le s th a t f i t b e s t t o th e t e s t s a r e p ro p o sed .

R E Q U I R E M E N T S F O R F L A T S T I F F E N E R SI n a u n i f o r m l y c o m p r e s s e d , s t i f f e n e d p l a t e t h e s t r e s s d i s t r i b u t i o n i n t h ec ro ss - se c t io n i s i n i t i a l ly co n s tan t (F ig . 2 ( a) ). Th i s r em a in s so a s lo n g a s th es t if fn esses o f t h e p l a t e b e tw een th e s t if f en e r s an d th o se o f t h e s t i f fen e r s a r eeq u a l . A t l a rg e r s t r e sse s (o r s t r a in s ) t h e s t i f f n ess o f o n e o f th e twoco m p o n e n t s i s d ec r ea s in g ( in F ig . 2 (b ) th e s t if fn ess o f t h e p l a t e ). Th i s r e su l t si n a d o w n w a r d s o r u p w a r d s ( as in F i g . 2) m o v e m e n t o f th e c e n t r o i d S , s ot h a t t h e s t i f f e n e d p l a t e i s n o l o n g e r c o m p r e s s e d c e n t r i c a l l y , b u t e x -c e n t r i c a U y . B e c a u s e o f t h e e x c e n t r i c a l c o m p r e s s i o n t h e s t i f f e n e d p l a t e i sd e f l ec t ed to ward s th e s t i f f en e r o r t h e p l a t e an d i t f a i l s b y p l a t e o r s t i f f en e r


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Torsional Rigidities of Open Stiffeners to Compression Flanges 67

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f a il u re . T he d i f fe r e n t C o de p r ov i s i ons a n d p r op os a l s f o r t o r s i on a l r i g id -i t io n a r e d e r i v e d f ro m t h is b a c k g r o u n d .

T h e p r o v i s i o n s o f t h e D r a f t C o d e D I N 18 8 00 : P a r t 3 : 1 9 8 9 4 h a v e b e e nba s e d o n t he a s s u m pt i on t ha t t he s tiff ne ss r e du c t i on o f t he p l a t e o r t hes t i f fene r i s s t a r t i ng when the cor re sponding c r i t i c a l buck l ing s t re s se s t rp~a nd tr,~ a r e r e a c he d . T a k i ng i n t o a c c o un t t he r e l e va n t s a fe ty f a c to r s a ga i n s tp l a t e a n d c o l u m n b uc k l i ng o f 1 .5 a nd 1 . 7 , r e spe c ti ve ly , t h is l e a ds t o t hef o l lo w i n g c o n d i t i o n :

1.5~si ~ -~ Gpi ( 1 )T h e p r o po r t i ons o f t he s ti ff e ner s w i t h t he no t a t i on o f F ig . 2 s hou l d t h e nbe such tha t (F ig . 3 ) :

h~ < 1 bpt, 1"3 tp (2 )

T h e p r o v i s io n s o f th e C o d e B S 5 4 00 : P a r t 3 : 1 9 8 2 s h a v e b e e n d e r i v e d f ro mthe req u i r em en t t ha t t he s l ende rn ess o f t he s t if fene r ~-~= x/ray~/tr,/ is l imitedt o 0 "673 , s o t h a t f o r t he c on s i de r e d buc k l i ng c u rve :1 0"22P ' ( 3 )


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* b p t p O ' yt? ~ = 2 0Fig. 3. Provisions for flat stiffeners (ay = 240 M Pa).

t h e u l t i m a t e s t re s s a ,= is n o t r e d u c e d d u e t o b u c k l i n g , w h e r eO 'us~ ---P say ( a y = = y i e l d s t r e s s o f t h e s t i f f e n e r )

T h e p r o p o r t i o n s o f t h e s t if fe n e rs s h o u l d b e s u c h t h a t ( F i g . 3 ):(4 )

h s ~ < 10 ( a y ~ i n M P a ) (5 )tsF o r s m a l l v a l u e s o f t h e s l e n d e r n e s s o f th e p l a t e b p / t p t h e s l e n d e r n e s s o f

t h e s t if f e ne r s c a n b e i n c r e a s e d d u e t o a c e r t a i n c l a m p i n g e f fe c t o f t h e p l a t e ,a s s h o w n i n F i g . 3 .

T h e p r o v i s i o n s o f t h e t w o c o d e s a r e c le a r ly c o n t r a d i c t i n g . D I N 18 8 0 0p e r m i t s g r e a t e r s t i f f e n e r s l e n d e r n e s s f o r g r e a t e r p l a t e s l e n d e r n e s s d u et o t h e p o s s i b l e p l a t e f a i lu r e , w h e r e a s B S 5 4 0 0 p e r m i t s g r e a t e r s ti f -f e n e r s l e n d e r n e s s f o r l o w e r p l a t e s l e n d e r n e s s , d u e t o t h e c l a m p i n ge f f e c t s .

I n a r e c e n t p r o p o s a l , V a y a s 6 d e r iv e s s t i ff e ne r p r o p o r t i o n s f r o m t h er e q u i r e m e n t t h a t t h e u l t i m a t e s t re s s o f t h e s t if f en e r au= is a t l e a s t e q u a l t ot h e u l t i m a t e s t r e s s o f t h e p l a t e a up . T h e r e l e v a n t c o n d i t i o n i s

O'us Psa ys ~< O'up pp O 'yp ( G y p = y i e l d s t r e s s o f t h e p l a t e ) (6 )


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Torsional Rigidities of O pen Stiffeners to Com pression Flanges 69w h e r e t h e r e d u c t i o n f a ct o r p , is d e t e r m i n e d f r o m t h e E u r o p e a n c o l u m nb u c k l i n g c u r v e c , a n d t h e r e d u c t i o n f a c t o r p p f r o m t h e b u c k l i n gcurve :

1 0 .22 '~p p = 1 . 1 3 ( 7 )

T h e r e l e va n t r e qu i r e m e n t f o r t he p r o po r t i ons o f t he s t if fe ne rs is s how n i nFig. 3 .I n t h e p r e s e n t p a p e r t h e s ti ff en e r p r o p o r t i o n s a r e p r o p o s e d t o b e d e r i v e df r om e qn ( 6 ), u s i ng a s r e du c t i on f a c to r s f o r t he s ti ff e ner s t he W i n t e r c u r vef o r s i m p l y s uppo r t e d p l a t e s on t h r e e e dge s :

0 .7ps= (8)a nd , f o r t he p l a t e , t he W i n t e r c u r ve f o r a p l a t e s uppo r t e d on f ou r e dge s(eq n (3) , bu t w i th pp, ~v ins tea d of p , , 2-s).T h e a b o v e r e q u i r e m e n t s l e a d a p p r o x i m a t e l y to t h e f o ll o w i n g c o n d i t io nfor t he p ropor t i ons o f t he s t i f fene rs (F ig . 3 ) :

h s a y p ~ _ _ l _ l b p + 4 . 0 ~ 1 2 . 9 a y _ _ _ ~t s O ' y s 4"6 tp O ' y p (9 )

T E S T S A N D T E S T E V A L U A T I O NI n o r d e r t o e xa m i ne t he d i f f er e n t r u l es d i s c us s e d i n t he p r e v i ous s e c t ion ,t he re su l t s o f 65 t e st s on s t if fened p l a t e s pe r f orm ed in t he Ins t i t u t e o f S t ee lS t r uc t u r e s a t t he T e c h n i c a l U n i ve r s i t y o f B r a uns c hw e i g , a n d r e po r t e d byB a r b r 6 e t a l . 1 a nd S c he e r a nd V a ya s 2 a r e u s e d .T h e t es t p r o g r a m m e i s s h o w n i n T a b l e 1. A l l p l at e s w e r e 7 m m t h ic k(nom ina l ly ) an d w ere s ti f fened by four , equ a l ly spaced bu lb s ti ffene rs . Th epa r a m e t e r s o f t he t e st s w e r e t he p l a t e s l e nde r ne s s b p / t p , t h e b e a m t h ic k n e s sl / i , t he s up po r t i n g c o nd i t i ons , t he s t re s s d i s t r i bu t i on a n d t he i m pe r f e c ti ons .T h e A m o d e l s w e r e p e rf ec t, th e B a n d D m o d e l s h a d g e o m e t r ic a l i m -pe r fec t i ons t ha t l ed t o p l a t e fa i l u re (B w i thou t , D w i th re s idua l s t re s se s du et o w e ld i ng ) , a n d t h e C a n d E m o d e l s h a d g e o m e t r ic a l i m p e r f e ct io n s t h a tl ed t o s t if fene r fa i lu re (C wi tho ut , E w i th re s idua l s t re sse s due t o we ld ing) .I n a na l o gy t o t he de f o r m a t i ons a t f a il u re , the i m pe r f e c t ions c ons i s t e d o f ag l oba l de f l e c t ion t ow a r ds t he p l a t e ( C a nd E ) o r t he s ti ff e ner ( B a nd D ) a n d


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l oca l s ti f fene r (C , E ) o r p l a t e (B , D) buckle s . The y a ll we re four t imes l a rge rt ha n t hos e p r e s c r i be d by t he Me r r i s on r u l e s .A l l t he t e s t e va l ua t i ons de s c r i be d i n t he f o l low i ng a r e ba s e d on t he

ac tua l p ro pe r t i e s o f t he sp ec im ens (wid ths , th i cknesses , y i e ld s t reng ths ,i m pe r f e c t i ons , e tc .). T he bu l b s ti ff e ner s ha v e be e n c on s i de r e d a s e qu i va l e n tp l a t e s h av ing the sam e c r i t ic a l s t re s se s trs~. In F ig . 4 , the p rov i s ions o f DI N18 800: Pa r t 34 a re c om pa red w i th t he re su l t s o f t he t e s ts . Fo r each t e s t,e q u i v a l e n t ( h s / t s ) e a n d ( b p / t p ) e r a t i o s h a v e b e e n d e t e r m i n e d a c c o r d i n g t ot he f o l l ow i ng p r oc e du r e . D ue t o t h e ov e r a l l i m pe r f e c t i on o f t he s t if f ene d

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Torsional Rigidities o f Open Stiffeners to Com pression Flange s 71p l a t e t he i n i ti a l st re s s d i s t r i bu t i on a t t h e s t if fe ne rs i s no t un i f o r m . F o r t hea c t ua l s tr e ss d i s t r i bu t i on t he c r it ic a l s tr e ss a , i h a s b e e n d e t e r m i ne d a nde qu a t e d t o t he c r i ti c al s tr e ss o f a un i f o r m c om pr e s s e d p l a te , s i m p l ys u p p o r t e d o n t h r e e e d g e s h a v i n g a s l e n d e r n e s s o f ( h J t s ) e . T h e s a m ep r o c e d u r e h a s b e e n a p p l ie d in o r d e r t o d e t e r m i n e ( b p / t p ) e for t es t se r ies IVw he r e t he s tr e ss d i s t r i bu t i on o f t he p l a t e w a s no t un i f o r m .In F ig . 4 a p l a t e fa i l u re i s expec t ed t o occur be low the s t ra igh t l i ne anda s t i f fene r fa i l u re above i t . The t e s t r e su l t s show tha t i n 12 t e s t s i n t o t a lt he p r e d i c t e d m od e o f f a il u r e is i nc o rr e c t. I n e i gh t t es ts t he p r ov i s i ons o ft he D r a f t C o de g i ve c ons e r va t i ve r es u lt s, w he r e a s i n f ou r t e s ts w i t h pe r fe c tm ode l s t he r u l e s fo r t he s ti ff e ne r s a r e no t a de qu a t e .

I n F i g . 5 t he p r ov i s i ons o f B S 5400 , P a r t 35 a r e c om pa r e d w i t h ther e s u l t s o f t he t e s t s . T he e va l ua t i on o f t he e qu i va l e n t w i d t h - t o - t h i c kne s sr a t i o s h a s b e e n d o n e a c c o r d i n g t o t h e s a m e p r o c e d u r e d e s c r i b e d b e f o r e .T he t e s t r e s u l t s s how t ha t i n 21 t e s t s i n t o t a l t he p r e d i c t e d m ode o ffa i l u re i s i ncor rec t , a s s t i f fene r fa i l u re i s p red i c t ed whe reas p l a t e fa i l u reis a c t ua l ly t a k i ng p l ac e . I n F i g . 6 t he p r opo s a l o f V a ya s 6 is c o m pa r e dwi th t he re su l t s o f t he t e s t s . The s t i f fene rs a re cons ide red a s excen t r i c -a l l y c om pr e s s e d ba r s f i xe d a t t he p l a t e t ha t f a i l unde r l a t e r a l t o r s i ona lb u c k l i n g . A n e q u i v a l e n t s l e n d e r n e s s 2 , i s d e t e r m i n e d a c c o r d i n g l y a n dt he E u r o pe a n buc k l i ng cu r ve c is u s e d f o r t he e va l ua t i on o f t he u l ti -m a te s t re s s t r, s . Th e t e s t r e su l ts sho w th a t i n 22 t e s t s the p rop osa l i sc ons e r v a t i ve a nd i n on e t he d i m e ns i on s o f the s t if fe ne rs ar e n o ta d e q u a t e .

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F i g . 7 . C o m p a r i s o n o f th e p r e s e n t p r o p o s a l w i t h t h e te s t r es u lt s.


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Torsional Rigidities of O pen Stiffeners to Com pression Flanges 73I n F i g . 7 t he c u r r e n t p r op os a l i s c o m pa r e d w i t h t he r e su l ts o f t he t es ts .

I n 11 t es t s i n t o t a l t he p r e d i c t e d m od e o f fa i lu r e is inc o r r e c t a n d i n t w ot es t s w i t h pe r f e c t m od e l s t he d i m e ns i on s o f t he s t if fe ne rs a r e n o t a de qu a t e .

C O N C L U S I O N SF r o m t h e c o m p a r i s o n o f t h e c o n s i d e r e d 6 5 te s t r e su l ts w i t h t h e e x a m i n e dp r ov i s i ons f o r f i a t s ti ff e ner s t o c om pr e s s e d p l a te s t he f o l l ow i ng c onc l u s i onsc a n b e d r a w n :

1. T he t e s t e va l u a t i on t a ke s i n t o a c c oun t , a s de s c r i be d bef o r e, on l y t heg l oba l i m pe r f e c t i ons a nd no t t he l oc a l one s . T he l a t t e r a r e s o l a r ge ( f ou rt im e s t h o s e o f t h e M e r r i so n r ul es ) t h a t t h e y a r e n o t c o v e r e d b y a n ybuc k l i ng c u r ve s . T h i s e xp l a i n s t he f a c t t ha t t he f a i l u r e m e c ha n i s m o f s om a ny t e st s is p r e d i c t e d i nc o r r e c t ly by t he e xa m i ne d p r ov i s ions .2 . Th e p rop os a l o f Vayas 6 is ove r -c on se rva t ive fo r t h i s t ype of st if fene r ,a s i t doe s no t t a ke i n t o a c c oun t t he i r pos t buc k l i ng s t r e ng t h .3 . T h e p r ov i s i ons o f B S 5400: P a r t 35 a r e t oo c ons e r va t i ve fo r g r e a tp l a t e s l e nde r ne s se s , w h e r e a s t hos e o f D I N 18 800 : P a r t 34 a r e t oo c ons e r -va t i ve fo r l ow p l a t e s l e nde r ne s se s , bu t n o t s af e e no ug h f o r g r e a t one s .

4 . Th e pre se n t p rop osa l seem s to f it be s t wi th t he re su lt s . I t l e ads i n on lyt w o t es t s t o unc ons e r v a t i ve r e su l ts , bo t h o f w h i c h a r e ve r y ne a r t o t hes t a t ed c r i t e ri a . I t mus t , ho we ve r , be s t a t ed t ha t fo r g rea t e r s l ende rnesse s , anon l i ne a r be ha v i ou r o f t he s t i f f e ne r i s pos s i b l e , w h i c h , a c c o r d i ng t o t hed e s i g n m e t h o d o f B S 5 4 00 s h o u l d b e e x c lu d e d .

5 . T h e c o m pa r i s o n i nd i c a t e s tha t f o r l ow p l a t e s l e nde r ne s s i t is pos s ib l eto t ak e i n to a cco un t a ce r t a in c l am pin g e ffect o f the s t i ffene rs t o t h e p l a t e ,a l l ow i ng t hus e ve n l a r ge r s t if fe ne rs s l e nde r ne s s e s t ha n p r opo s e d , bu t t henu m be r o f te s ts c on s i de r e d doe s n o t a l low f o r c onc l u s i ve e v i de nc e .

6 . Fo r bu lb s t if fene rs i t is poss ib l e to use t he sam e ru l e s a s fo r t he f i ats ti ff e ner s by de t e r m i n i ng a n e qu i va l e n t (h f f ts )e r a t i o a s de s c r i be d i n t hep r e v i ou s s e c ti on .7 . O t he r t ype s o f op e n s t if fe ne rs a r e no t e xp e c t e d t o de ve l op pos t buc k -l i ng s tr e ng t h s o t ha t t he p r op os a l s o f V a ya s 6 c a n be u s e d , w h i c h t a ke i n t oacc ou nt t he bene f i c i a l e ffec ts o f wa rp ing .

R E F E R E N C E S1. Ba rbr 6, R., Schm idt, H. & Ricmann, S., Traglastvcrsuchc an 1/ingsgcstauchtcndurch Wulstflachst/ihlc vcrsteiften Blcchcn mit freicn L~ingsr/indern. D erStahlbau, 51 (1982) 321-32.


10/10

74 Ioannis Vayas2. Scheer, J . & Vayas, I . , Traglas tversuche an l / ingsgestauchten, vers t if tenRech teckp la t ten mi t a l l se i t iger Lagerung . Der Stahlbau, 52 (1983) 78-84.3 . Vayas , I. , Disse r ta t ion B raunschw eig , T ra g las tbe rech nun gen f i ir K on s t ruk -t ionen aus p la t tenar t igen Bau te i len , 1981 .4 . Sta hlba uten , Stabil it~itsf~il le , Pla t tenb eule n. D IN 18 800: P ar t 3 : 1987.5 . Br i t ish S tand ards Ins t i tu t ion , BSI, Lon don , 1982 . Co de o f Prac t ice fo r theD esign of Steel Bridges. BS 5400 : P ar t 3 .6 . Vayas , I ., M indes t s te i figke i ten und Bem essung von o ffenen S te ifen vers te i f te r ,gedr i ick te r P la t ten . Der Stahlbau, 58 (1989) 203-8.

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