design of aluminium columns .pdf

8/10/2019 Design of aluminium columns .pdf

1/7

e s ig n o f a l u m i n iu m

c o l u m n s

Y F W L a i

Mitchel MacFarlane, Hong Kong

D A N e t h e r c o t

Department of Civil Engineering, U niversity o f Nottingham , UK

Received April 19 90; revised January 1991)

Theore t ica l resu l t s fo r the buck l ing o f a lumin ium co lumns hav ing

longi tud ina l and loca l t ransverse welds are presented. These are used

to assess the su i tab i l i t y o f the p rocedures g iven fo r co lumn des ign in

t h ~ '~ ra f t B r i t i sh S t a n d a rd f o r t h e u se o f s t ru c t u ra l a l u m in iu m

BS 81 18 . As a resu l t some m od i f i ca t ions to these p rocedu res a re

sugges ted .

Key word : a lum in ium s t ruc tu res , buck l ing , co lumns , s tab i l i t y ,

s t ruc tu ra l des ign , we ld ing

T h e n e w d r a f t B r i ti s h c o d e f o r t h e d e s ig n o f a l u m i n iu m

st ruc t u res BS 8118 I , wh i ch wi l l r ep l ace C P 1182 , has

recen t l y been c i r cu l a t ed fo r t he pu rpose o f i nv i t i ng

p u b l i c c o m m e n t .

A l t h o u g h t h e c o l u m n d e s i g n c u r v e s s u g g e s t e d i n

R e f e r e n c e 1 a r e b a s e d l a r g e ly o n t e s t da t a a n d a c c u r a t e

num erical s tudies 3 , thei r s ui tabi l i ty i s s t il l unce r tain for

s o m e t y p e s o f m e m b e r , e s p e c i a l l y w e l d e d c o l u m n s

and / o r co l um ns sub j ec t t o fl exu ra l - t o r s i ona l buck l i ng .

T h i s p a p e r p r e s e n t s t h e r e s u lt s o f a n e x t e n s i v e c o m -

p a r i s o n b e t w e e n t h e c o l u m n d e s i g n c u r v e s o f t h e d r a f t

BS 8118 and numer i ca l r esu l t s ob t a i ned by t wo f i n i t e

e l e m e n t p r o g r a m s I N S T A F a n d B I A X I A L 4. A ll c o m -

par i sons a r e r es t r i c t ed t o ' compact ' c ross - sec t i ons fo r

wh i ch no l oca l buck l i ng occu r s .

N o m e n c l a t u r e

A a r e a o f c r o s s - s e c ti o n

A * a r e a o f h e a t - a f fe c t e d z o n e ( H A Z )

C,, buck l i ng coef f i c i en t fo r f l exu ra l buck l i ng

Cr

buck l i ng coef f i c i en t fo r t o r s i ona l buck l i ng

E Y o u n g ' s m o d u l u s

L l e n gt h o f m e m b e r

L* l eng t h o f hea t - a f f ec t ed zone

L,r

cr i t i ca l r eg i on def i ned as a d i s t ance ex t end i ng

f r o m 0 . 2 5 L e i th e r s i d e o f p o i n t o f m a x i m u m c u r -

va t u re when f l exu ra l buck l i ng t akes p l ace

L, . t o ta l l eng t h wi t h i n c r i t ica l r eg i on ove r wh i ch

hea t - a f f ec t ed zone so f t en i ng occu r s

P , u l t imat e com press i v e s t r eng th g i ven by d raf t

B S 8 1 1 8

P~c c o m p r e s s i v e c a p a c i t y o f c r o s s - s e c t i o n

u l t c a l c u l a t e d 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

/5 n o n d i m e n s i o n a l m a x i m u m c o m p r e s s i v e s t re n g t h

o f m e m b e r ( =

Pult/Oo2A)

n k n e e f a c to r in R a m b e r g - O s g o o d f o r m u la

n * k n ee f a ct or f o r H A Z i n R a m b e r g - O s g o o d

f o r m u l a

r r ad i us o f gy ra t i on

0141 0296/92/030188 07

1992 Butterwor th Heinema nn Ltd

ro ry r ad i us o f gy ra t i on abou t x - and y -ax i s , r espec-

t i ve l y

h , X , s l e n d e rn e s s

L/rx, L/ry)

~ , ~ , nond i m ens i ona l i zed s l enderness r a t i o Xx/r E /

00.2) m , X,./Tr E/ao.2)1/2)

o no rmal s t r ess

a02 0 .2% p ro o f s t r ess

a *2 0 . 2 % p r o o f s t re s s o f H A Z

aul tens ile stren gth

w mat er i a l s t r eng t h r educ t i on f ac t o r fo r hea t -

a f f ec t ed zone mat er i a l p roper t i es .

N u m e r i c a l r e s u l t s

Al l o f t he numer i ca l r esu l t s p resen t ed here i n w ere

o b t a i n e d b y u s i n g t h e p r o g r a m s I N S T A F f o r t w o -

d i m e n s i o n a l r e s p o n s e a n d B I A X I A L f o r t h r e e -

d i mens i ona l r esponse 4 . Bo t h p rog ram s perm i t t he fu l l

l oad def l ec t i on cu rve t o be t r aced up t o co l l apse u t i l iz i ng

56

soph i s t i ca t ed f i n i t e e l emen t app roaches ' , wh i ch permi t

t he e f f ec t s o f l ong i tud i na l an d / o r t r ansve r se w el ds t o be

a l l owed fo r . Bo t h have bee n ex t ens i ve l y ver i f i ed aga i ns t

t es t da t a and a l t e rna t i ve u l t i mat e s t r eng t h ana l yses fo r

bo t h a l um i n i um and s t ee l mem ber s 4 .

R e s u l t s h a v e b e e n o b t a i n e d f o r a l a r g e n u m b e r o f

ax i a l ly l oaded co l um ns , c over i ng t he r ange o f d i f f e r en t

t y p e s f o r w h i c h t h e d e s i g n a p p r o a c h o f R e f e r e n c e 1 is

in tended. T a b l e s l a and l b l i s t the individual cases

s t ud i ed , Al l oy t ypes a r e charac t e r i zed by t he paramet er

n u s e d i n t h e R a m b e r g - O s g o o d r e p r e s e nt a t io n o f t h e

s t r ess - s t r a i n cu rve , wi t h t he HAZ (hea t a f f ec t ed zone)

mat er i a l be i ng assumed t o possess p roper t i es

corr esp ond ing to 0 2 = 0 .500.2 and n* = 10. Al l c ol -

u m n s w e r e a s s u m e d i n it ia l ly b o w e d a b o u t t h e m i n o r a x i s

i n t h e f o r m o f a h a l f s i n e w a v e w i t h a m a x i m u m

a m p l i t u d e o f

L/IO00.

C o l u m n d e s i g n p r o c e d u r e o f d r a f t

B S 8 1 1 8

The f ac t o red ax i a l r es is t ance o f a co l um n , Pc , wh i ch i s

8 8

En g. Struct. 1992, V ol. 14, No 3


2/7


3/7

De s i g n o f a l u m i n i u m c o l u m n s : Y F W L a i a n d D A Ne t h e r c o t

T a b l e 2 F a c t o r s u s e d i n s e l e c t i o n o f c o l u m n c u r v e i n R e f e r e n c e 1

E x t e n t o f H A Z

Lw/ Lc , D e s i g n a p p r o a c h

0 I g n o r e p r e s e n c e o f t r a n s v e r s e

w e l d s

> 0 . 2 D e s i g n c o l u m n a s i f i t c o n s i s t e d

w h o l l y o f H A Z m a t e r i a l

Psc = a ~2A)

0 < Lw / Lc r < 0 . 2 I n t e r p o l a t e b e t w e e n t h e a b o v e

t w o c a s e s b a s e d o n a c t u a l

L w / L c , v a l u e

T a b l e 3 F a c t o r s u s e d i n s e l e c ti o n o f c o l u m n c u r v e i n R e f e r e n c e 1

A l l o y t y p e O u l t / O 0 . 2 O u l t/ O 0 . 2 > 1 . 2

h i g h n H ) l o w n L )

C r o s s - s e c t i o n y l / Y 2 * < 1 . 2 Y l / Y 2 > 1 .2

s y m m e t r i c s ) a y s y m m e t r i c A )

W e l d i n g n o n w e l d e d N W ) w e l d e d W )

* y l a n d y 2 a re p e r p e n d i c u l a r d i st a n c e s f r o m t h e a x i s o f b u c k l in g

t o t h e f u r t h e r a n d n e a r e r e x t r e m e f i b re s , r e s p e c t i v e l y

T a b l e 4

A l l o c a t i o n o f c a s e s t o c o l u m n d e s i g n c u r v e s

C l a s s D r a f t B S 8 1 1 8 P r o p o s e d

s e e T a b l e 1 ) C o n d i t i o n a l l o c a t i o n a l l o c a t i o n

A H - S - N W 1 1

B H - S - W 2 2

C H - A - N W 2 2

D H - A - W 3 3

E L - S - N W 3 2

F L -S -W 4 3

G L - A - N W 4 3

H L - A - W 5 4

Lw u n d e r g o i n g t h e l a r g e s t c u r v a t u r e s . T h r e e c a s e s a r e

i d e n t i f i e d a s i n d i c a t e d i n

Table 2.

R e f e r e n c e 1 d o e s n o t

r e c o g n i s e t h e p o s s ib i l it y o f t h e H A Z n o t e x t e n d i n g o v e r

t h e f u l l d e p t h o f t h e c r o s s - s e c t i o n .

F o r e n d - w e l d e d c o l u m n s f o r w h i c h t h e w e l d s e x t e n d

f o r l es s t h a n 0 . 0 5 L t h e e f f e c t o f t r a n s v e r s e w e l d s m a y b e

n e g l e c t e d . I n a l l c a s e s i t i s , h o w e v e r , n e c e s s a r y t o

e n s u r e t h a t t h e a x i a l l o a d d o e s n o t e x c e e d t h e c r o s s -

s e c t i o n a l c a p a c i t y P sc =

.2A.

A l l t h e c o l u m n c u r v e s a r e d e s c r i b e d b y a

P e r r y - R o b e r t s o n t y p e o f e q u a t io n w i t h th e s e l ec t io n f o r

a p a r t i c u l a r c o l u m n b e i n g b a s e d o n t h e f a c t o r s l i s te d i n

Table 3.

A s s e s s m e n t o n t h e b a si s o f

Table 3

p e r m i t s t h e

c o l u m n s t o b e g r a d e d i n to e i g h t c la s s e s a c c o r d i n g t o t h e

c o m b i n a t i o n s o f t h e s e c o n d i t io n s p r e s e n t a n d t h u s t o b e

r a t e d a c c o r d i n g t o t h e n u m b e r o f w e a k e n i n g c o n d i t io n s

a s i n d i c a t e d i n

Table 4.

T h e h i g h e r th e r a t in g n u m b e r t h e

w e a k e r i s th a t c l a ss o f c o l u m n .

C o m p a r i s o n b e t w e e n d e s ig n c o l u m n c u r v es o f

d r a f t B S 8 8 a n d n u m e r i c a l r e s u lt s

T h e a c c u r a c y o f t h e c o l u m n d e s i g n a p p r o a c h d e s c r ib e d

i n t h e p r e v i o u s s e c t i o n h a s b e e n a s s e ss e d b y m e a n s o f

s y s t e m a t i c c o m p a r i s o n s a g a i n s t t h e 2 9 s e t s o f n u m e r i c a l

r e s u l t s o f

Table 1.

Column curve 1 and class A columns

Figure i

s h o w s h o w f o r th e t w o s e t s o f n u m e r i c a l r e s u l t s

c o r r e s p o n d i n g t o th e m o s t f a v o u r a b l e cl a ss o f m e m b e r

c u r v e 1 r e p r e s e n t s a s a f e a n d r e a s o n a b l e d e s i g n b a s is

o v e r th e w h o l e r a n g e o f s l e n d e r n es s c o n s i d e r e d . F o r t h e

t o r s i o n a l l y w e a k e r n a r r o w f l a n g e s e c t i o n I I I t h e d e s i g n

c u r v e i s m o r e c o n s e r v a t i v e , p a r t i c u l a r l y a t m e d i u m

a n d h i g h s l e n d e rn e s s . F o r s t o c k y c o l u m n s t h e u s e o f th e

s q u a s h l o a d

P~,

= % 2 A m e a n s t h a t t h e b e n e f i c i a l

e f f e c t s o f t h e c o n t i n u o u s l y r i s i n g m a t e r i a l s t r e s s - s t r a in

c u r v e a r e n o t u t i l i z e d .

Column curve 1 and class B and C columns

S i x c a s e s o f lo n g i t u d i n a ll y w e l d e d m e m b e r s - t h r e e

e a c h w i t h s y m m e t r i c a l ly a n d n o n s y m m e t r i c a l ly

a r r a n g e d w e l d s - a r e c o v e r e d i n Figures 2 a n d 3 .

R e s i d u a l s t r e s s e s h a v e b e e n i n c l u d e d i n a l l c a s e s e x c e p t

f o r u n s y m m e t r i c a l w e l d s a n d

A*/A

= 0 . 5 . D e s i g n c u r v e

2 i s s a f e f o r a ll b u t a f e w c a s e s o f v e r y s t o c k y m e m b e r s ;

e v e n t h e r e i t o v e r e s t i m a t e s s t r e n g t h b y o n l y a f e w p e r

c e n t . H o w e v e r , a s s l e n d e r n e s s i n c r e a s e s t h e d e s i g n

1 . 0

0 .5

0 . 0 I

0 0

~ - , ~ ' - ~ / ~ c -A -2 ~B , A x , A , i

~ ,

l l l l i

0.5 I .0 1 .5

i x o r

F i g u r e 1 C o m p a r i s o n b e t w e e n d e s i g n c o l u m n c u r v e 1 a n d

t h e o r e t i c a l c o l u m n c u r v e s c l a s s A c o l u m n s ) . ) , t h e o r e t i c a l

c u r v e s ; - - - ) , d r a f t B S 8 1 1 8

1 0

. .. . -~ -- -~ C-B-I

_ _ _ ~ \ ~ C-B-2

-~- ~.-- ~ -.~ - ~

0 0 I I I I I i l t l i l J i I I l I I

0 0 0.5 I .0 I .5

Y

F i g u r e

2 C o m p a r i s o n b e t w e e n d e s i g n c o l u m n c u r v e 2 a n d

t h e o r e t i c a l c o l u m n c u r v e s c la s s B c o l u m n s , w i t h s y m m e t r i c

l o n g i t u d i n a l w e l d s ) . ) t h e o r e t i c a l c u r v e s b ia x i a l ); - - - ) ,

d r a f t B S 8 1 1 8

190 Eng. Struc t. 1992 Vol. 14 No 3


4/7

D e s i g n o f a l u m i n i u m c o / u m n s : Y F W L a i a n d D A N e t h e r c o t

1.0 __ __ .< = ~_ . ._ \ / c B .

IO,. 0 . 5 - - ' ~ ' ~ ~ ~

0 . 0 I I I I I P I I I I I I I I I I

0 . 0 0 . 5 1 . 0 1 . 5

Y

Figure C o m p a r i s o n b e t w e e n d e s i g n c o l u m n c u r v e 2 a n d

t h e o r e t i c a l c o l u m n c u r v e s ( c l a s s B c o l u m n s , w i t h a s y m m e t r i c

l o n g i t u d i n a l w e l d s ) . ( ) , t h e o r e t i c a l c u r v e s ( b i a x i a l ) ;

( - - - ) ,

d r a f t

B S 8 1 1 8

C urve 2 i s a l so appl i cabl e t o asymmet r i c nonw e l ded

c o l u m n s a n d F i g u r e s h o w s t h a t w h e n d e s i g n i s c o n -

t ro l l ed by f l exura l buckl i ng s ec t i on I I) t he des i gn pro-

c e d u r e b e c o m e s u n s a f e w h e n Xx f a ll s b e l o w 0 . 6 5 b u t is

qui t e conservat i ve over m uch o f t he range. W hen t or -

s i ona l buckl i ng cont ro l s s ec t i on IV ) the des i gn curv e i s

a l w a y s s a f e , p o s s i b l y e x c e s s i v e l y s o o v e r m u c h o f t h e

range .

Co l umn c u r v e

and class D and E

co l umns

C urve 3 i s appl i cabl e t o e i t her symmet r i ca l , unw e l ded

s h a p e s o f l o w n - m a t e r i a l o r t o w e l d e d , a s y m m e t r i c

s h a p e s . B o t h t y p e s h a v e b e e n c o n s i d e r e d a n d a s s h o w n

in F i e u r e s 5 and 6 t h e des i gn curve genera l l y under -

pred icts the s trength, part icularly for the mor e s lender

members . T hi s w oul d appear t o be due t o t he re l a t i ve

l ack o f y i e l ded m at er ia l present a t f a il ure f or such ca ses .

c u r v e b e c o m e s i n c r e a s i n g l y c o n s e r v a t i v e , l a r g e l y

b e c a u s e i t i s n o t n e c e ss a r y t o m a k e m u c h , i f a n y ,

a l l o w a n c e f o r H A Z a s s l e n d e r n e s s i n c r e a s e s a n d t h e

appl i ed l oads become i nsuf f i c i ent t o i nduce s t res ses

approachi ng trY .2 over mu ch o f t he mem ber .

Co l umn c u r v e

4 and class F and G

co l umns

T he t hree s e t s o f re su l ts cover i ng w e l ded , sym met r i ca l ,

l o w n - m a t e ri a l m e m b e r s a n d n o n w e l d e d , a s y m m e t r i c a l,

l ow n- mat er i a l members present ed i n F i g u r e s 7 and 8 ,

1 . 0

I~-

0 . 5

0 . 0

0 . 0

C - C - I I N S T A F )

~ , . ~ - - ~ Z C - 2 ( B IA X I A L)

I I I I I I I I I I I I 1 I 1 5 I

0 . 5 1 . 0 1 .

~ o ~

x y

F i g u r e 4

Compa r is on be t w e e n a e s = gn c o lumn c urv e 2 a nd

theoret ica l colum n curves c lass C colum ns) . ) ; theoret ica l

c urve s ; - - - ) , d ra f t BS 8 1 1 8

la.

1 .0

0 5 r-

0 . 0

0 0

~ \ . j C - D - 1

I I I I I I I I I I I I I I I I

0 . 5 1 . 0 1 . 5

Y

F i g u r e

C o m p a r i s o n b e t w e e n d e s i g n c o l u m n c u r v e 3 a n d

t h e o r e t i c a l c o l u m n c u r v e s ( c l a s s D c o l u m n s ) . ( ), t h e o r e t i c a l

c u r v e s ( b i a x i a l ) ;

( - - - ) , d r a f t B S 8 1 1 8

la .

\

0 . 0 i I t 1 i I I I I 1 I I I I ] I I

0 . 0

0 . 5 1 . 0 1 . 5

o r

y

F i g u r e

C o m p a r i s o n b e t w e e n c l es i gn c o l u m n c u r v e 3 a n d

t h e o r e t i c a l c o l u m n c u r v e s ( c l a s s E c o l u m n s ) .

( );

t h e o r e t i c a l

c u r v e s ; ( - - - ) , d r a f t B S 8 1 1 8

1 . 0

IQ-

0 . 5

0 0 i

0 . 0

_

~ ~ \ \ C - F - I ( B I A X I A L )

- - ~ ~ ~ . .

I I I I I I I 1 I I I I I I I

0 . 5 1 . 0 1 . S

Y


t h e o r e t i c a l c o l u m n c u r v e s ( c l a s s F c o l u m n s ) .

( ),

t h e o r e t i c a l

c u r v e ;

( - - - ) , d r a f t B S 8 1 1 8

E n g . S t r u c t . 1 9 9 2 , V o l . 1 4 , N o 3 1 9 1


5/7

D e s i g n o f a l u m i n iu m c o lu m n s : Y F W L a i a n d D A N e t h e r c o t

1 0

0 5

0 . 0

0 . 0

\

\ \ . c c 1

~ \ . C G 2

I I I I I ~ i I I i I I I I I I

0 . 5 1 . 0 1 . 5

Y

F i g u r e 8 C o m p a r i s o n

b e t w e e n d e s i g n

c o l u m n c u r v e 4 a n d

t h e o r e t i c a l c o l u m n c u r v e s ( c la s s G c o l u m n s ) . ( ) , t h e o r e t i c a l

c u r v e s ( b ia x i al ); ( - - - ) , d r a f t B S 8 1 1 8

r e s p e c t i v e l y s h o w t h a t c u r v e 4 s i g n i f i c a n t l y u n d e r -

e s t i m a t e s s t r e n g t h i n a l l c a s e s . T h e d e g r e e o f c o n s e r -

v a t i s m is v a r i a b l e b u t a p p r o a c h e s 1 0 0 f o r t h e m o s t

s l e n d e r m e m b e r s .

Column curve 5 and c lass H co lumns

W h e n a l l a d v e r s e e f f e c t s a r e c o m b i n e d Figure 9 a g a i n

s h o w s t h e p r o p o s e d c o l u m n c u r v e t o b e e x c e s s i v e l y c o n -

s e r v a t i v e o v e r t h e w h o l e r a n g e . F r o m R e f e r e n c e 3 i t i s

c l e a r t h a t th e o r i g i n a l p o s i t i o n i n g o f c u r v e 5 w a s b a s e d

o n r e l a t i v e l y f e w n u m e r i c a l o r e x p e r i m e n t a l r e s u l t s .

Columns containing transverse welds

E l e v e n c a s e s o f t r a n s v e r s e l y w e l d e d c o l u m n s h a v e b e e n

c o n s i d e r e d a s d e t a i l e d in Table lb . I n a n ea r l i e r s tudy 4 ,

i t h a d b e e n s h o w n t h a t l o c a t i n g s u c h w e l d s a t c o l u m n

m i d - h e i g h t i .e . t h e r e g i o n o f g r e a t e s t c u r v a t u r e a n d

highes t s t r e s s , l ed to the l a r ges t r educ t ions in s t r eng th a s

c o m p a r e d w i t h a n e q u i v a l e n t u n w e l d e d m e m b e r .

F o r t h e t h r e e c a s e s o f c e n t r a l l y w e l d e d c o l u m n s

Figure 10

s h o w s t h e s t r e n g t h t o b e o n l y s l i g h t l y g r e a t e r

t h a n th a t o f a w h o l l y H A Z m e m b e r L*/L = 1 . 0 . Th e

d e s i g n p r o c e d u r e i i o f

Table 21

dea l s wi th th i s case

q u i t e w e l l a s t h e c o m p a r i s o n i n

Figure 10

s h o w s .

H o w e v e r , w h e n t h e e x t e n t o f t h e w e l d i n g f a ll s b e l o w

t h a t c o r r e s p o n d i n g t o c a s e i i

L * / L

= 0 . 0 5 , t h e n

Figure

11 s h o w s t h a t t h e u s e o f i n t e r p o l a t i o n a s p e r m i t t e d b y

case i i i o f

Table 2

l e a d s t o u n s a f e r e s u l t s f o r t h e m o r e

s t o c k y e n d o f th e r a n g e . T h e r e a s o n f o r t h i s is q u i te

1 . 0

0 . 5

0 . 0

0 . 0

\ \ C - H - I ( B I A X I A L )

\ \

I I I I I I I I I I I I I I I I

0 . 5 1 . 0 I . 5

Y


t h e o r e t i c a l c o l u m n c u r v e s ( c la s s H c o l u m n s ) . ( ) , t h e o r e t i c a l

c u r v e ; ( - - - ) , d r a f t B S 8 1 1 8

1 . 0 - - - - \

\

\

\ C-TW-6 ( L * / L = O . 0 5 )

0 5 ~ \\\ ~

0 . 0 I I I I I I I I I I I I I I I t I I

0.0 0.5 I .0 I .5

x

F i g u r e 1 1 C o m p a r i s o n w i t h t r a n s v e r s e l y w e l d e d c o l u m n c u r v e s

o b t a i n e d b y I N S T A F p r o g r a m ( L w l L c r = O . 1 ) . ( ) , t heo re t i c a l

c u r v e ( I NS T A F ); ( - - - ) , d r a f t B S 8 1 1 8

1 . 0

0 . 5

0 0

0 0

\

\

\

C-TW-1 { L * I L = 0.1 ) \X

, ~ C - T W - 2 ( L * I L = 0 . 2 ) , \

C - T W - 3 ( L * / L = 0 . 3 ) \

- _ = .

I I I I I I i I J J i I I I I I I

0 . 5 1 . 0 1 . 5

-2

F i g u r e 1 0

C o m p a r i s o n w i t h t r a n s v e r s e l y w e l d e d c o l u m n c u r v e s

o b t a i n e d w i t h I N S T A F p r o g r a m (Lw/Lcr > 0 . 2 ) . ( ) , t heo re t i c a l

c u r v e s (I N S T A F) ; ( - - - ) d r a f t B S 8 1 1 8

1 . 0 . . . . - = - ~ . ~ . ~ ~ \ / C - T W - 7 ( L * I L = 0 , 1

~ - ~ . ) ( a t b o t h e n d s )

, ~ \ \ \

~ / \ \ \ ,

0 .5

0 . 0 I I I I I I I I I I I I I I I I I I

0 . 0 0 . 5 1 . 0 1 . 5

~ v

F i g u r e 1 2

C o m p a r i s o n w i t h

t r a n s v e r s e l y w e l d e d

c o l u m n c u r v e s

o b t a i n e d b y I N S T A F p r o g r a m e n d - w e l d e d c o l u m n s ) . ),

t h e o r e t i c a l c u r v e s ( I N S T A F ); ( - - - ) , d r a f t B S 8 1 1 8

1 9 2 E n g . S t r u c t . 1 9 9 2 V o l . 1 4 N o 3


6/7

D e s i g n o f a / u m i n i u m c o /u m n s : Y . F . W . L a i a n d D . A . N e th e rc o t

s i mp l y t ha t t he c ross - sec t i ona l capac i t y / ' s t o f such

m e m b e r s i s s ti ll , o f c o u r s e , o n l y O ~ . and t ha t fo r

s t ocky co l um ns on l y a r e l a t i ve l y sm al l par t o f t he to t a l

l ong i t ud i na l s t r ess i s due t o bend i ng . Thu s m em bers f a i l -

i ng by ' squash ' as wel l as t hose fo r wh i ch l i t t l e bend i ng

occur s wi l l have t he i r s t r eng t h overp red i c t ed due t o t he

op t i mi s t i c va l ue o f P= , u sed i n t he des i gn p roc ess . Fo r

s l e n d e r m e m b e r s , i n c o m m o n w i t h s e v e r a l o t h e r c a s e s

c o n s i d e r e d h e r e i n , t h e d e s i g n m e t h o d o f R e f e r e n c e 1 is

c o n s e r v a t i v e s i n c e t h e a l l o w a n c e m a d e f o r H A Z d o e s

n o t r e d u c e i n a n a p p r o p r i a t e w a y .

F o r c o l u m n s w e l d e d o n l y a t t h e i r e n d s R e f e r e n c e 1

p roposed neg l ec t i ng any r educ t i ons i n s t r eng t h . Figure

12 s h o w s t h i s t o b e c l e a r ly u n s a f e o v e r m u c h o f t h e

range . A s i m p l e p roced ure t o co r r ec t t h i s is g i ven i n t he

nex t sec t i on .

When f a i l u re i s due t o t o r s i ona l buck l i ng and t he

e x t e n t o f H A Z p r e s e n t i s s u f f ic i e n t fo r c a s e i i o f

Table

2 t o app l y ,

Figure 13

s h o w s t h e u s e o f

Cr

i n p l ace o f

Cc

t o be r easonab l e . Figure 14 shows t ha t fo r an end -

we l ded co l umn , l i mi ti ng t he s t r eng t h on t he bas i s o f P=c

c a l c u l a te d f o r t h e H A Z m a t e r ia l w o u l d p r o v i d e t h e b a s is

fo r a sa t i s f ac t o ry des i gn t r ea t men t .

roposed design improvements

Nonwe lde d r longitudinally welded 2t)

The r esu l t s p resen t ed i n Figures 1 9, c o r r e s p o n d i n g to

t h e 2 9 c a s e s o f n o n w e l d e d o r l o n g i tu d i n a ll y w e l d e d c o l -

umns l i s t ed i n

Table l a ,

s u g g e s t t h a t t h e n u m b e r a n d

s p r e a d o f d e s i g n c u r v e s p r o p o s e d i n R e f e r e n c e 1 is t o o

g rea t . Genera l l y speak i ng t he p roposa l s fo r t he more

favou rab l e c ases a r e sa t is f ac to ry ,_ i f r a t her t oo c onser -

va t i ve a t h igher s l endernesse s 0~ > 1 .0 ) , wh i l e t hose

r e q u ir i ng t h e u s e o f c u r v e s 4 a n d 5 a r e m u c h t o o c o n s e r -

v a t i v e o v e r t h e w h o l e r a n g e o f s l e n d e r n e s s e s . Table 4

t herefo re sugges t s an a l t e rna t ive a l l oca t i on o f cases

u s i n g j u s t 4 c o l u m n c u r v e s . F o r c l a s se s A - D t h e a l lo c a -

t io n i s a s b e f o r e ; c l a s se s E - H a ll m o v e u p o n e c u r v e ,

wi t h t he l owes t cu rve 5 be i ng d ropped .

Transversely welded

T h e p r o p o s e d m e t h o d d i s ti n g u is h e s b e t w e e n t h e 2 c a s e s

(1 ) P*_< P* , i n wh i ch P* = o*A i s the elast ic l imi t for

p u r e c o m p r e s s i o n

1.0

0.5

k

\ C-TW-8 (L* = 50 mm

~ / a t mid-height)

J ~ x C - T W - 9 ( L * = L )

, . , ,

0 0

I I I I I I I I I I I I I I / I I

0 0 0.5 1.0 1.5

Y

Figure 3

Com par i s on w i t h t r ans v e r s e l y we l ded c o l um n c u r v es

ob t a i ned by B I A X I A Lp r og r am ( c en t r a l ly - we l ded c o l um ns ) . ( ) ,

t heo r e t i c a l c u r v es ; ( - - - ) , d r a f t BS 811 8

(2) P * > P *

F o r t h e f i r st c a s e H A Z e f f e c ts m a y b e n e g l e c t e d . F o r t h e

second t wo var i an t s a r e r ecogn i sed :

i)

T h e H A Z i s l o c a t e d n e a r t h e e n d s w i t h in a d i s t a n c e

o f 0 . 2 5 L o f t h e s u p p o r t s. T h e c o l u m n i s d e s i g n a te d

' e n d - w e l d e d ' a n d m a y b e d e s i g n e d a s i f i t w e r e

n o n w e l d e d s u b j e c t t o a n u p p e r l i m i t g i v e n b y

P = 1 - (1 - w) A */A

( i i) I f cond i t ion ( i ) i s not sat i sf ied the colu m n is

d e s i g n e d a s i f it c o n s i s te d o f w h o l l y H A Z m a t e r ia l .

W h e n l o n g it u d in a l w e l d s a r e a l s o p r e s e n t t h e y s h o u l d b e

a l l owe d fo r w hen d e t e rmi n i ng P=c and t hus Pc*.

1.0 - - - - ~ -~ \ C-TW -10 ( L * = 0 )

~ ~ ~ , , ~ ' ~ C - T W - 1 1 ( L * = 30

~ ~ ~ N at both ends)

o . , _ _ _ _ . S

0 0 1 I I I I I I I I I I I I I I I I I

0 0 0.5 1.0 1.5

Figure 74

Com par i s on w i t h t r ans v e r s e l y we l ded c o l um n c u r v es

ob t a i ned by B I A X I A L p r og r am ( c en t r a l ly - we l ded c o l um ns ) . ( ) ,

t heo r e t i c a l c u r v es ; ( - - - ) , d r a f t B S 811 8 ( m od i f ied in c ase o f

e n d - w e l d e d c o l u m n )

o n c l u s i o n s

A se r i es o f numer i ca l r esu l t s fo r the f l exu ra l and

f l exu ra l - t o r s i ona l buck l i ng o f var i ous t ypes o f

a l u m i n i u m c o l u m n h a v e b e e n p r e s e n t e d . T h e c a s e s c o n -

s i d e re d w e r e s e l e c te d t o c o v e r t h e f u l l r a n g e o f e f f e c ts

t aken i n t o accoun t i n a l l oca t i ng co l umn t ypes t o

d e s i g n c u r v e s b y t h e d r a f t B S 8 1 1 8 . D e t a i l e d c o m -

par i sons be t ween t he numer i ca l r esu l t s and t he

a p p r o p r i a t e c o l u m n c u r v e s h a v e r e v e a l e d t h a t

T h e s t r e n g t h o f m o s t t y p e s o f c o l u m n i s s a f e l y

p r e d i c t e d b y t h e m e t h o d o f t h e d r a ft c o d e .

F o r a s y m m e t r i c c r o s s - s e c t i o n s o r m a t e r i a l w i t h

au ,/ . 2 > 1 .2 underes t i m at es o f s t r eng t h a r e poss i -

b l e , espec i a l l y fo r co l umns o f i n t e rmed i a t e

s l enderness .

E n g . S t r u c t . 1 9 9 2 , V o l . 1 4 , N o 3 1 9 3


7/7

De s i g n o f a l u m i n i u m c o lu m n s : Y F W L a i a n d D A Ne t h e r c o t

. As a genera l ru l e t he r educ t i ons i n l oad car ry i ng

capac i t y ob t a i ned by pass i ng t h rough t he d i f f e r en t

c a t e g o r i e s A - H a p p e a r s t o b e to o gr e a t. S o m e

u p w a r d r e v i si o n o f t he l o w e r d e s i g n c u r v e s c o u p l e d

wi t h som e r e -a l loca t i on o f c l asses wou l d appe ar t o

be j u s t i f i ed .

S u g g e s t io n s f o r i m p r o v e m e n t s t o t h e t r e a tm e n t o f

t r a n s v e r s e ly w e l d e d c o l u m n s p a r t ic u l a r ly w h e n th e

w e l d s a r e l o c a te d a t t h e c o lu m n e n d s h a v e b e e n

prov i ded .

cknowledgments

T h i s w o r k f o r m s p a r t o f a p ro j e c t f u n d e d b y

R . A . R . D . E . ; t h e a u t h o r s a r e g r a te f u l f o r a s s i st a n c e a n d

c o m m e n t s o n t h e s t u d i e s r e p o r t e d h e r e i n b y M r D .

W e b b e r an d D r P . S . B u l so n .

References

1 British Standards Institution Draft, British Standard BS 8118, Code of

practice for the design of aluminium structures , 1985

2 British Standards Institution, CP 118: 1969, The structural use of

aluminium

3 Hong, G. M. Aluminium column curves ,

Alumin ium s t ruc tures .

des ign and cons t ruc t ion R. Narayanan Ed., Elsevier Applied Science

Publishers, 1987, pp. 40- 49

4 Lai, Y. F. W. and Nethercot, D. A., Strength ofaluminium members

containing local transverse welds , Engineering Structures, (in press)

5 E1 Zanaty, M. H. Murray, D. W. and Bjorhovde, R. Inelastic

behaviour of multistorey steel frames, University of Alberta, Canada,

1980

6 El Khenfas, M. A. and Nethercot, D. A., Ultimate strength analysis

of steel beam-columns subjected to biaxial bending and torsion ,

Res.

M e c h a n i c a 1989, 28, (1-4), 307-360

7 Nethercot, D. A. Aspects of column design in the new UK structural

aluminium code , Alumin ium s t ruc tures : advances des ign and con -

s t ruc t ion R. Narayanan, Ed., Elsevier Applied Science Publishers,

1987, pp 50-59

1 9 4 En g . S t r uc t. 1 9 9 2 Vo l. 1 4 N o 3

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