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T h i s m a r k e t l e a d i n g s t u d e n t t e x t c o v e r s t h e d e s i g n o fs t r u c t u r a l s t e e l w o r k t o 5 5 5 9 5 0 P a r t 1 .t h e s u b j e c t I n t w o p a r t s , t h e f i r s t d e a l s w i t h d e s i g n a ta n e l e m e n t a r y l e v e l f a m l i l a r i s l n g t h e r e a d e r w i t hB S 5 9 5 0 . P a r t t w o t h e n p r o c e e d s t o c o v e r a l l a s p e c t so f t h o d e s i g n o f w h o l e b u i l d i n g s , h i g h l i g h t i n g t h ei n t e g r a t i o n o f ' e l e m e n t s ' t o p r o d u c e e c o n o m i c , s a f es t r u c t u r e s .
T h o s e c o n d e d i t i o n h a s b e e n t h o r o u g h l ya n du p d a t e d t o t a k e a c c o u n t o f r e c e n t r e s e a r c h a n d d e s i g nd e v e l o p m e n t s a n d a n e w c h a p t e r o n p l a t e g i r d e r s h a sb e e n a d d e d . T h e r e v i s e d t e x t r e t a i n s a l l t h e p o p u l a r
f e a t u r e s o f t h e o r i g i n a l w o r k . I n p a r t i c u l a r , r e a d e r s v . i l lf i n d t h a t t h e o u t h o r s : e x p l a i n c o n c e p t s c l e a r l y u s e a n e x t r e m e l y p r a c t i c a l a p p r o a c h. i n c i u d o n u S i e r o S v o v k S e x a m p l e s a n d r e a l
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1 1 . 5 D e s i g n o f s t i f f e n e d p l a t e g i r d e r1 1 . 6 E x a m p l e 2 3 . D e s i g n o f s t i f f e n e d p l a t e
g i r d e r e x c l u d i n gt e n s i o n f i e l d a c t i o nI 1 . 7 D e s i g n o f g i r d e r m c h i d i n g t e n s i o n f i e l d
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D e s i g n o f p u r l i n s a n d s h e e t i n g r a i l sD e s i g n o f l a t t i c e g i r d e rD e s i g n o f c o l u m n m e m b e r sO v e r a l l s t a b i l i t y o f b u i l d i n gD e s i g n o f g a b l e p o s t sD e s i g n o f c o n n e c t i o n sD e s i g n o f f o u n d a t i o n b l o c k
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I n 1 9 6 9 , t h e U n t is h S t a n d a r d s I n s t i t u t i o n C o m m i t t eB S4 4 9 , a p e r m i s s i b l e s t r e s s s n - u c t u r a t s t e e t w o r k d ep r e p a r a t i o n o f a n e w d r a f t c o d e b a s e d o n l i m i t s l ai n c o r p o r a t t n g t h e l a t e s t r e s e a r c h 1 0 1 0 t h e b e h a v i o ua n d c o m p l e t e s t r u c t u r e s . T h e d r a f t w a s i s s u e d f o ra n d a t t r a c t e d c o n s i d e r a b l e a d v e r s e c o m m e n t f r o m a c q u a i n t e d w i t h t h e s i m p l e r d e s i g n m e t h o d s i n 1 1 5
I t w a s r e a l i z e d b y t h e n e w l y c o n s t i t u t e d E S ! C or e d r a f t o f t h e 1 1 / 2 0 d o c u m e n t w o u l d b e n e c e s s a r ya c c e p t a b l e t o t h e c o n s t r u c t i o n i n d u s t r y . T h e w o r ku n d e r t a k e n b y C o n s t r a d o , p a r t l y f b n d e d b y I b e E uC o m m u n i t y , a n d t h e t a s k w a s g u i d e d b y a s m a l l s tt h e i n t e r e s t s o f c o n s u l t i n g e n g i n e e r s , s t e e t w o r k f a bD e p a r t m e n t o f t h e E n v i r o n m e n t .
P o o r t o t h e c o m p l e t I o n o f t h e r e d r a f t , c a l i b r a t i o nB u i l d i n g R e s e a r c h E s t a b l i s h m e n t t o d e n v e s u i t a bm a t e n a l f a c t o r s , a n d d e s i g n e x e r c i s e s t o c o m p a r e ts t r u c t u r e s t o t h e d r a f t c o d e w i t h d e s i g n s t o U S 4 4C o n s t r a d o . T h e o b j e c t o f t h e s e s t u d i e s w a s t o a s s e sr e c o m m e n d a t i o n s t o b e c o n t a i n e d w i t h i n t h e n e w s t r u c t u r a l d e s i g n s w h i c h w o u l d b e n o l e s s s a f e t h aw o o l d g i v e a n i m p r o v e m e n t I n o v e r a l l e c o n o m y .
T h e r e s u l t i n g c o d e o f p r a c t i c e , 1 1 5 5 9 5 0 : P a r t I ,c o v e n n g t h e d e s i g n i n s i m p l e a n d c o n t i n u o u s c o n ss e c t i o n s , a n d P a r t 2 , d e a l i n g w i t h t h e s p e c i h c a t t o ta n d e r e c t i o n , a c h i e v e d t h e g r e a t e r s i m p l i c i t y s o u ga l l o w i n g t h e d e s i g n o f b u i l d i n g s t r u c t u r e s l o b e b aa p p r o a c h o f l i m i t s t a t e t h e o r y t h a n t h e p e r m i s s i b l e sP a r t 3 , w h i c h i s i n t h e c o u r s e o l p r e p a r a t i o n , w i l l d e s i g n i n c o m p o s i t e c o n s t r u c t I o n .
W h i l e U S 5 9 5 0 : P a r ti s e x p l i c i t i n i t s d e s i g n r e c o m m e n d ai s i n t e n d e d t o b e u s e d b y a p p r o p n a t e l y q u a l i f i e d p et o s t r u c t u r a l s t e e l w o r k d e s i g n a n d c o n s t r u c t t o n . T h e
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a t e x t f o r u n i v e r s i t y a n t i c o l l e g e s t u d e n t s e n g a g e d o n c o u r s e s i n c i v i l a n ds t r u c t u r a l e n g i n e e n n g w h i c h g i v e s c l e a r g u i d a n c e o n t h e a p p l i c a t i o n o f t h ec o d et o t y p i c a l b u i l d i n g s t r u c t u r e sb y w o r k e d e x a m p l e s w h i c h s e t o u t t h ec a l c u l a t i o n su n d e r t a k e n i n t h e d e s i g n o ff c e .T h i s i s a c h i e v e d i n t h i sb o o kt h r o u g h e x p l a n a t o r y t e x t , f l l c a l c u l a t i o n s a n d r e f r e n c e t o t h e B S 5 9 5 0 :P a r tI c l a u s e s .
T h e f i r s t p a r t o f t h e b o o k d e a l s w i t h t h e d e s i g n o f v a n o u s t y p e s o f
s t r u c t u r a l m e m b e r s a n d t h e s e c o n d p a r t d e a l s w i t h c o m p l e t e d e s i g n s o f t h em o s t c o m m o n l y e n c o u n t e r e d s t r u c t u r e s , n a m e l y , s i n g l e - s t o r e y i n d u s t n a lb u i l d i n g s a n d m u l t i - s t o r e y o f f i c e b l o c k s . A p a r t f r o m t h e r e l e v a n t c o d e s a n ds t a n d a r d s , r e f e r e n c e s a r e g i v e n t o w e f l e s t a b h s h e d p u b l i c a t i o n s c o m m o n l yf o u n d i n t h e d e s i g n e r s o f f i c e . T h e b o o k s h o u l d a l s o b e u s e f u l t o t h e d e s I g ae n g i n e e r r e q u i n n g a n u n d e r s t a n d i n g o f t h e a p p l i c a t i o n o f t h e l i m i t s t a t e c o d e .
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A s i m p l e b a s i s f o r d e s i g n i s t o c o n s i d e ra s t r u c t u r a l f r a m c w o r k c o m p on u m b e r o f e l e m e n t s c o n n e c t e d t o g e t h e r . L o a d s
a r e s u s t a i n e d b y t h e e l e ma n d i t s r e a c t i o n s t r a n s f e r r c d t o o i l i e r e l e m e n t sv i a t h e c o n n e c t i o n s . I n t hs i m p l e c o n c e p t f o r d e s i g n i t i s e s s e n t t a l t h a t t h e o va c t i o n o f t h ef r a m e w o r k i s c o n s i d e r e d . T h e r e f o r e a n i n t r o d u c t i o n t h e c o n c e p t o f o v e r a l ls t a b i l i t y o f t h e s t r u c t u r e i s g i v e n i n t e r m s o f b r a c i ns y s t e m s .
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S t r u c t u r a ls t e e l w o r k c a n b e e i t h e r a s i n g l e m e m b e r o r an u m b e r o f s t e e l s e c t i o n s c o n n e c t e d t o g e t h e r i n s u c h
s p e c i f i e d f u n c t i o n . T h e f u n c t i o n r e q u i r e d b y a c le n o r m o u s l y h u t m a y i n c l u d e :
b u i l d i n g f r a m e s b y w h i c h l o a d s m u s t b e s u pw i t h o u t u n d u e m o v e m e n t , a n d t o w h i c h a w em u s t b e a t t a c h e d ;
c h e m i c a l p l a n t s u p p o r t s b y w h i c h l o a d s m u sw h i c h c o m m o n l y r e n t n r e n o e x t e r n a l e n v e l o p
c o n t a i n e r s w h i c h w i l l r e t a i n l i q u i d s , g r a n u l a ra n d w h i c h m a y a l s o b e e l e v a t e d a s a f u r t h e r
m a s t s w h i c h m u s t s a f e l y s u p p o r t m e c h a n i c a l
e q u i p m e n t a t s p e c i f i e d h e i g h t s a n d i n w h i c h v i b r a t t o n s a n d f a t i g u e m u s t b e c o n t r o l l e d ; c h i m n e y s w h i c h w i l l s u p p o r t f l u e s c a r r y t o g w
h e t g h t s ; b r i d g e s w h i c h m u s t s u p p o r t t r a f f i c a n d o t h e r
v a r y i n g s p a n s a n d f o r w h i c h d e g r e e s o f m o vp e r m i t t e d ;
t e m p o r a r y s u p p o r t s u s e d d u r i n g t h e c o n s t r u cs t r u c t u r e , w h i c h m a y b e o f s t e e l w o r k . c o n c r ei tw h i c h s a f e t y f o r s h o r t p e n o d s a n d s p e e d o f a s s
i t w i l l b e n o t i c e d t h a t b o t h s a f e t y a n d m o v e m e n t oa r e i m p o r t a n t f o r p r o p e r f u n c t t o n a n d , t o g e t h e r w it h e m a i n c o n s i d e r a t i o n s w h e n d i s c u s s t n g t h e d e s t g nn o t e d t h a t t h e d e s i g n o f o n l y s o m e o f t h e a b o v e s tB S 5 9 5 0 a n d h e n c e d i s c u s s e d i n t h e l a t e r c h a p t e r s .
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= 5 2 1k N m= 6 7 6 k N
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A 1 B 2 C
A r r a n g e m e n t s o fl o a d i n g f o r m a x i m u mm o m e n t s a n df o r c e s :
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3 . 4 m
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M o m e n t s a n d f r c e s m a y b e f u n db y a n ya n a l y t i c a l m e t h o d , b u t f r e q u a ls p a n c a s e s c o e ff c i e n t s a r ew h e r e , f r e x a m p l e
= ( a i 1 + a 1 2 1 1 ' 2 ++ a 1 4 1 1 1 1 ) La n d M 1 ,R , , a n d5 a b a r e g i v e n b y s i m i l a r e x p r e s s i o n s .T h e c o e ff c i e n t s e m a y b e s u m m a n ze d :
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0 . 9 0 k N / m0 . 0 9 k N / m '0 . 7 5 k N / m '1 . 2 0k N / m '1 . 2 0k N / m '
W i n d p r e s s u r e s a r e b a s e d o n a b a s i c w i n d s p e e d oa l o c a t i o n i nS c o t l a n d .
F a c t o r g ' 5 , a n da r e b o t h t a k e n a s 1 . 0 a n d f c t o r s 3 a s 0 . 81 D m .
T h e d e s i g n w i n d s p e e d i s h e n c e 4 4 m / s . g i v i n g a dp r e s s u r e o f1 . 2 0k N / m ' .
P D F c o m p r e s s i o n , O C R , w e b - o p t i m i za t i o n
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I t i s p o s s i b l e t o u s e al o w e r w i n d p r e s s u r eb e l o w a h e i g h t o f S mb u tt h i sm a k e s t h e a n a l y s i s m o r e c o m p l e x f o r v e r y l i t t l e r e d u c t i o n i n f r a m e m o m e n t s .
( c ) P r e s s u r e c o e f f i c i e n t s
E x t e r n a l p r e s s u r e c o e f f i c i e n t s ( C , , , )m a yb e f o u n d a n d a r e s u m m a n z e d i n t h e
f o l l o w i n g t a b l e . T h e s e v a l u e s a r e o b t a i n e d f r o m r e f e r e n c e 1 2 ) .
C , , , f o r f r a m e m e m b e r
A D B C C D D E
W i n d o n s i d e 0 . 7 1 . 2 0 . 4 0 2 5W i n d o n e n d 0 . 5 0 . 6 0 . 6 0 . 5
D e a d l o a d o n r o o f i s c a l c u l a t e d o n t h e p r o j e c t e d a
S e l f w e i g h t = 0 . 9 x 1 9 . 3= 1 7 . 5 k NC l a d d i n g= 0 0 9 x 1 9 . 3 x 6 . 0 = l 0 . 5 k NT o t a l W d . = 2 8 . O N
D e a d l o a d o n w a l l s ( F g . 2 . 1 1 ) :S e l f w e i g h t = 0 . 9 x 5 . 5= 5 . 0 k N
CB
5 . 5
F g .2 . 1 0 F i g . 2 . 1 1
W i n d l o a d s f o r c a s e ( 1 ) o n s i d e + i n t e r n a l p r e s s u r c :
W i n d l o a d o n ' v a i l( F i g .2 . 1 3 ) = 0 . 5 x 1 . 2 0 x 6 . 0 x 5 . 5 =
W i n d p r e s s u r e o n r o o f i s d i v i d e d i n t o v e r t i c a l a n d( Fg . 2 . 1 4 ) ,
-
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A B B C C D D E
I . W i n d o n s i d e + i n I e m a t0 . 5 1 . 4 0 . 6 0 . 4 5p r e s s u r e
2 . W i n d o n s i d e + n i e m a l1 . 0 0 . 9 0 . 1 0 , 0 5s u c t i o n
3 . W i n d o n e n d + i n t e r n a l 0 . 7 0 . 8 0 . 8 0 . 7p r e s s u r e
4 . W i n d o n e n d + i n t e m a l 0 . 2 0 . 3 0 . 3 0 . 2s u c t i o n
Ve r t i c a l c o m p o n e n t 1 . 4 x 1 . 2 0 x 6 . 0 ' t 1 9 . 0 l 9 2 k Nl - l o n z o n t a l c o m p o n e n t= 1 . 4 x 1 . 2 0 x 6 . 0 x3 , 4 ' = 3 4 k N
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I t m a y b e n o t e d t h a t c a s e 4 i s s i m i l a r t o c a s e 3 , b u t hb e d i s c a r d e d .
M e m b e r l o a d s
I n t e r n a l p r e s s u r e c o e f f i c i e n t s ( C , , , ) s h o u l d b e o b t a i n e d t f l , a n d a r e t a k e n i nt h i s e x a m p l e a s + 0 . 2 ( m a x i m u m ) a n d 0 . 3 ( m i n i m u m ) w h i c h a r ec o m b i n e d a l g e b r a i c a l l y w i t h t h e v a l u e s o fa b o v e .
F g u r e 2 . 8 s h o w s t h e i n d i v i d u a l p r e s s u r e c o e f f i c i e n t s , a n d F g . 2 . 9 s h o w st h e v a n o u s c o m b i n a t i o n c a s e s .
a ) W i n d o n s i d e u I W i n d o n e n d
F g . 2 . 8
C l a d d i n g= 0 . 0 9 x 5 . 5 x 6 . 0T o t a l
= 3 . O c H= 8 . O N
I c ) I n t e r n a l p r e s s u r eI d ) l n t t r n s l s u c t i o n
F g . 2 . 9
C a s e I I n + b I C a s e 2 I n + d l C a s e 3 ) b ' + c I C a s e 4 l b + d l
W II I I H ( l ) i ) l l I I lI m p o s e d l o a d o n r o o f g i v e n o n p l a n a r e a ( a n d s e r vS n o w l o a d l F = 0 . 7 5 x 1 9 . 0 x 6 . 0 = 8 6 k M
F I g . 2 . 1 2
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F g . 2 . 1 6 B e n d i n gm o m e n t sf o r c o m b i n a t i o n
G r o u p I f , H . i A l 0 A l , ,I . 1 . 4 1 1 1 ,
+ 1 . 6 1 1 1 1 5 3 1 5 3 1 7 7 1 7 7 a 4 3 3 1 5 R 4 32 . 1 . 4 W , ,
+ I . 4 1 1 ' , t 1 3 4 1 1 7 1 9 0 1 1 6 7 1 3 2 3 9 7 1 33 . t . 2 1 1 1 ,
+ 1 . 2 0 1
+ I . 2 1 1 ' . , a 2 1 4 8 2 3 8 6 2 5 0 9 5 2 5 64 . t . D 0 ' , ,
+ I . 4 1 V , i 1 5 4 ' 1 2 7 2 0 ! 1 2 7 7 6 4 ' 2 5 9 7 6 4t O W ,
8 2 8 2 1 2 5 1 2 5 5 5 7 1 6 7 5 5 7
W h i l e t h e s e r a t t l e s a r e m a x i m a t o p p o s i i e n i g s ) l a m e g r o u p 4 c o n i b i n o m o n i t n s 5 9 3 0 ) s i t m a r o v e r 'p u a a n do v e n a n t u n g o n l y . ii i s u n e c e s s a o y , I r n w e v e r f o r a l l t h e e f f e c t s o f a l o a d c o r n b t n a m ' n n t o b e e o m n n l d e e e d ( n o r a l s oC h a p i e r l 2 )
M a x i m u m a n d m i n i m u m v a l u e s m a y b e s e l e c t e d f r o m t h e t a b l e . B e n d i n gm o m e n t d i a g r a m s m a y b e d r a w n a s s h o w n i n F g s . 2 . 1 6 a n d 2 . 1 7 .
2 . W i n d L o a d i n gB r i t i s h S t a n d a r d I n s t i t u t e C l ' ) , C h a n t e r3 . M o v i n g l o a d s e f f e c t sM a r s h a l l W . T . & N o t i o n n . M . ( 1 9 9 0 )
a n d i n f lu e n c e l i n e s , S r n s c n , r e s ,p p .7 9 i 0 6 . L o n g m a n4 . M o v m n g l o a d e f f e c t sW a n g C . K . ( 1 9 8 3 ) I n f l u e n c el i n e sf u r s t a t i c a l l y
d e t e r m i n a t eb e a m s , i n t e r n i e d i n a m e S t n , c : u r a lp p . 4 5 9 6 7 . M c G r a w 4 l i I l
5 . I n f l u e n c e l i n e sC o a t e s I L C . . C o u l i e M . C . & K o n g FM u e l l e r . B r e n l a u ' s p n n c i p l e . M o d e l a n. 9 n o l v s t s , p p . 1 2 7 3 1 . V a n N o s t r a n d R
6 . I n f l u e n c e l i n e sW a n g C . K . ( 1 9 8 3 ) I n f l u e n c e l i n e s f u rd e t e r m i n a t e b e a m s . ) n r e r n n e d i o , e S ! n sp p . 4 9 6 5 0 3 . K l c G r a w - l - I i l l
7 . B M a n d S F c o e f f i c i e n t s( 1 9 9 2 ) D e s i g n t h e o r y . S t e e l D e s i g n e r rp p . 1 0 5 1 4 . B l a c k w e l l
8 . B M a n d S F c o e f f i c i e n t s( 1 9 9 2 ) D e s i g n t h e o r y S t e e / D e r : g r i e r s p p . 1 0 8 0 9 7 . B l a c k w e l l
F I g . 2 . 1 7 B e n d i n gm o m e n t s
f o r c o m b i n a n o n 2
2 5 2
F n a l l yt h e e f f e c t o f w a l l d e a d l o a d c a n b e a d d e d , i f a x i a l f o r c e i n t h ec o l u m n s i s r e q u i r e d ( c o m b i n a t i o n 1 ) :
M a x i m u m a x i a l f o r c e a t A =1 7 7+ 1 . 4 x 8 . 2 =1 9 0k NM i m m u r n a x i a l f o r c e a t A = 2 0 9+ 1 . 0 x 8 . 2 = 2 0 1k N
T h e a l t e r n a t i v e m e t h o d o f a n a l y s t s i s b y a p p l i c a t i o n o f p l a s t t c t h e o r y t s e eC h a p t e r 1 3 ) . i n t h i s e l a s t i c a n a l y s i s o f a p o r t a l f r a m e , t h e l o a d i n gc o m b i n a t i o n sc a nb e a d d e d , b u t i n C h a p t e r 1 3e a c hl o a d c o m b i n a t i o np r o d u c e si t so w n u r n q u e c o l l a p s e m e c h a n i s m , i . e . e a c h l o a d c o m b i n a t i o nm u s t b e a n a l y s e d i n d e p e n d e a t l y w h e n a p p l y i n g p l a s t i c t h e o r y .
S T U D Y R E F R E N C E S
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5 5 6 3 9 9 D e s i g n L o a d i n g f o r B u i l d i n g sP a r t 1 : D e a d a n d i m p o s e d l o a d s ( 1 9 8 4 )P a n 2 : W i n d l o a d s ( 1 9 9 5 )P a s t 3 : i m p o s e d r o o f l o a d s ( 1 9 8 8 )
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C o n n e c t i o n s m u s t b e p r o v i d e d a t j u n c t i o n s b e t w e e n m e m b e r s a n d m u s t
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C o n n e c t i o n s m u s t b e p r o v i d e d a t j u n c t i o n s b e t w e e n m e m b e r s a n d m u s ts a f e l y t r a n s m i t t h e c a l c u l a t e d l o a d s f r o m o n e m e m b e r t o t h e n e x t . A v a r i e t yo f c o n n e c t i o n d e t a i l s e x i s t f o r m o s t c o m m o n s i t u a t i o n s a n d a r e f u l l yd e s c r i b e d i n t h e S C ! h a n d b o o k t 4 1 . D e s i g n i n f o r m a t i o n f o r c o n n e c t i o n s i sg i v e n i n s e c t i o n 6 . B S 5 9 5 0 , w h i c h i n c l u d e s s o m e g u i d a n c e o n b o l t s p a c t a ga n d e d g e d i s t a n c e s . B o l t a n d w e l d . s i z e s a n d c a p a c i t i e s a r e g i v e n i nr e f e r e n c e ( 5 ) .
3 . 7 E X A M P L E 4 . B E A M S U P P O R T I N G C O N C R E T E F L O O R S L A B( R E S T R A I N E D B E A M )
( a ) D i m e n s i o n s
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B e a m s c e n t r e sS p a n ( s i m p l y s u p p o r t e d )C o n c r e t e s l a b ( s p a r m m g i n t w o d i r e c t t o n s )F i n i s h i n g s c r e e d
r - i
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.
F o r p r e l i m i n a r y c a l c u l a t i o n , a n e s t i m a t e d s e l f w e i g h t i s i n c l u d e d . A s s u m eb e a m t o b e 5 3 3 x 2 1 0 x 9 2 t I E ( g r a d e 4 3 A ) . I n s s u f f i c i e n t l y a c c u r a t e t o t a k eb e a m w e i g h t o f 9 2 k g i m = 0 . 9 2 k N / m . M e m b e r s i z e m u s t b e f i n a l l yc o n f i r m e d a f t e r a l l t h e d e s i g n c h e e k s h a v e b e e n e a r n e d o u t .
D e a d l o a d
I m p o s e d l o a d W ; :
2 3 . 7 x 0 . 2 5 02
= 0 . 9 0k N / j n 26 . 8 3 I N / r n 2
U l t i m a t e l o a d ( f a c t o r e d ) ( F i g . 3 . 4 ) :
( c ) B M a n d S F
I A x 7l . 4 x 5 7 + l . 6 x 4 2
I A x 1 2 3 + 1 . 6 x 9 0
M a x a n u m u l t i m a t e m o m e n t M , ( m i d - s p a n )
= I D x 7 . 4 / 8 + 2 3 2 x 3 . 0 1 5 8 x 1 . 7 7 4 x 1 0M a x i m u m u l t i m a t e s h e a r f o r c e F , =1 0 ) 2+ 2 3 2 =2 3 7k N
S h e a r c a p a c i t y= 0 . 6p ,= 0 . 6 x 0 . 2 7 5 x 5 3 1 . 1 x 1 0 . 2 = 5 9 7 k
T h e r e f o r e , a s F , / P ? < 0 . 6 , t h e r e w i l l b e n o r e d u c t i oI n m o m e n t c a p a c i t y (c l a u s e 4 . 2 . 5 ) .
( e ) M o m e n t c a p a c i t y
T h e c o n c r e t e s t a b p r o v i d e s f u l l r e s t r a i n t t o t h ec o m p r e s s i o n f l a n g e ( F i g .
a n d l a t e r a l t o r s i o n a l b u c k l i n g i s n o t c o n s i d e r e d . Ti s
S e l f w e i g h t
D e a d l o a d s l a bD e a d l o a d s c r e e d
0 . 9 2 x 7 A= 7 k N
A r e a o f s i a b s u p p o r t e d b y b e a m ( F i g . 3 . 3 ) :
r e c t a n g l e s2 x 1 . 4 x 3 . 0= 8 . 4m 2t r i a n g l e s4 x 3 . 0 x 3 . 0 / 2 =1 8 . 0 m 2
o n r e c t a n g l e s6 . 8 3 x 8 . 4= 5 7k No n t r i a n g l e s6 . 8 3 x 1 8 . 0 =1 2 3k N
6 . 0 m7 . 4 m2 S O m m t h i c k4 O m m t h i c k
M a i n b e a m
o n r e c t a n g l e s5 . 0 x 8 . 4= 4 2 k No n t u i a o g l e s5 . 0 x 1 8 . 0 =9 0 k N
4 0 m m s c r e e d\
u n i f o r m l y d i s t r i b u t e do n r e c t a n g l e so n t r i a n g l e s
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/I
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U s i n gt h e d e s i g n s t r e n g t h f r o m T a b l e 1 . 2 f o r g r a d e 4n o t i n g t h a tm a x i m u m t h i c k n e s s o f s e c t i o n i s 1 5 . 6 m m :
p , , = 2 7 5 N / m m 2
c l a u s e4 . 2 . 3
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C o n c r e t e s l a bS c r e e d ( 4 0 m m )I m p o s e d l o a d
2 3 . 7 I N / m 30 . 9 k N / m 25 . 0 k N / m 2
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3 0 S T R U O 1 U R A L S T E E L W O R K D E S I G N T O S I $ 0 5 0
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P a
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t , J 1 ' l $ n i1 . S m
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( a ) D i m e n s i o n s
M u mb e a m i s s i m p l y s u p p o r t e d a n d s p a n s 9 . 0 m ( F i g . 3 . 9 ) . B o i l e r s a r es u p p o r t e d s y m m e t n c a l l y o n s e c o n d a r y b e a m s ( A a n d B ) o f s p a n 6 . 0 m , w h i c ha r e a t 5 . 0 m c e n t r e s .
W i t h r e f e r e n c e t o F i g . 3 . 1 1
( c ) B M a n d S F
F i g . 3 . 9 P l a n t l o a d s
W i t h r e f e r e n c e t o F i g . 3 . 1 2 :
F l o o n n g o n b e a m B= 5 . 4k NI m p o s e d l o a d o n b e a m B =4 0 . 5k N
U l t i m a t e p o i n t l o a d W 4 =1 . 4 ( 4 . 0+ 7 . 2 ) + 1 . 6 ( 2 0 0 + 5 4 )= 4 2 2 k NU l t i m a t e p o i n t l o a d T V 8= 1 . 4 ( 4 . 0+ 5 . 4 ) + 1 . 6 ( 2 0 04 0 . 5 ) =3 9 8k N
U l t i m a t e s h e a r f o r c eF , =1 9 / 2x 4 2 2 x 6 . 0 / 9 . 0 + 3 9 8 x 1 . 0 / 9 . 0 = 3 3 5 k
U l t i m a t e s h e a r f o r c eF 2= 1 9 / 2x 3 9 8 x 3 . 0 / 9 . 0 4 2 2x 3 . 0 / 9 . 0 =5 0 4k N
U l t i m a t e m o m e n t= 3 3 5x 3 . 0 =1 0 0 5k N a ,U l t i m a t e m o m e n t M 0 = 5 0 4 x 2 . 0 = 5 0 4 k f l m
N o t e t h a t i n c a l c u l a t i n g t h e m o m e n t s , t h e s m a l l rd u e t o t h e s e l fw e i g h t i s i g n o r e d .
D e s i g n s t r e n g t hf rs t e e l 1 9 . 7 m m t h i c k ( g r a d e 4 3 A )= 2 6 5N / n u n 2 ( s e eT a b l e 1 . 2 ) .
= O . 6 x 2 6 5 x 6 0 9 6 x l 1 . 9 xk NS h e a r f o r c e= 3 3 5 k N
= 3 3 5 / 1 1 5 3 = 0 . 2 9
= 5 0 4 / 1 1 5 3= 0 . 4 4 0 . 6T h i s m a x i m u m c o e x i s t e n t s h e a r f o r c ei s p r e s e n t a t p o i n t B , w h i l e t hm a x i m u m m o m e n t o c c u r s a t p o i n t A .
( b ) L o a d i n g
B o i l e r l o a d i n g ( e a c h )O p e n s t e e l f l o o n n g ( c a r i i e d o n b e a m s A a n d B )I m p o s e d l o a d ( o u t s i d e b o i l e r a r e a )
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6 . 0
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S h e a r c a p a c i t y P . =0 . 6p r - i ,
T h e b o i l e r s p r o d u c e r e a c t i o n s o f I O U k N a t t h e e n d o f e a c h s e c o n d a r y b e a m .
A l l o w 4 . 0 k N f o r t h e s e l f w e i g h t o f e a c h s e c o n d a r y b e a m ( n o t d e s i g n e d h e r e ) .A s s u m e 6 1 0 x 3 0 5 x 1 4 9 1 W ( g r a d e 4 3 ) f o r m a i n b e a m .
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W i t h r e f e r e n c e t o F i g . 3 . 1 0 :
F l o o r i n g o n b e a m A= 0 . 3 x 4 . 0 x 6 . 0 =7 . 2k NI m p o s e d l o a d o n b e a m A =4 . 5x 3 . 0 x 4 . 0 =5 4 . 0k N
S h e a r f o r c e F 2= 5 0 4k N
( e ) M o m e n t c a p a c i t y
c l a u s e 3 . 5 . 2T h e c h o s e n s e c t i o n i s a p l a s t i c s e c t i o n ( b / T = 7 . 7 )
M o m e n t c a p a c i t y= 2 6 5, < 4 5 7 0 x= 1 2 1 0k N m
M o m e n t r a t i o M 4 / M c= l 0 0 5 / 1 2 1 0 = 0 . 8 3< IS e c t i o n i s s a t i s f a c t o r y .
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= 5 0 4 / 5 = l 0 O . 8k N= M d , , , J 1 d 2= 2 5 . 3 x O . 2 0 / 2 ( 0 . 1 0 2 + 0 . 2 0 2 )
= 5 0 . 6 k M= 1 ( 1 0 0 . 8 2 + 5 0 6 2 )= 1 1 3 k N= 0 . 3 7 5 x2 x 3 0 3 = 2 2 7 k N= 2 2 x1 1 . 9x i . 0 3 5 = 2 7 1 l e N= 2 2 x1 1 . 9x 0 . 4 6 0 = 1 2 0k M C
2 4 3 k N
a
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B o w l i n g P . 3 . , K n o w l e s P . & O w e n s G . W . ( 3 9 8 8 )fS t r u c t u r a lS t e e l D e s i g n . S t e e l C o n s t r u c t i o n i n s t i t u t er
M a r s h a l ! W . T . & N e l s o n H . M . ( 3 9 9 0 ) E l a s t i c s t a b i l i t ya n a l y s i s . S t r u c t u r e , p p .4 2 0 5 2 .L o n g m a n
C o a t e s R . C . , C o u t i e M . G . & K o n g F . K . ( 3 9 8 8 )I n s t a b i l i t yo f s t r u t s a n d f r a m e w o r k s , S t r u c t u r a l A n a l y s i s ,p p . 5 8 7 3 .Va n N o s t r a n d R e i n h o l d
C r o x t o n P . L . C . & M a r t i n L i i . ( 1 9 9 0 ) A r e a - m o m e n tm e t h o d s o f a n a l y s t s , S o l v i n g P r o b l e m s i n S t r u c t u r e s.v o l .2 . p p . 2 3 4 7 .L o n g a n a n
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c l a u s e6 . 3 . 3 . 3 B e a r i n g c a p a c i t y / b o l tB e a r i n gc a p a c i t y o f w e b p l a t eP 5 ,h u t x 3 1 . 9x 0 . 4 6 0 / 2
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1 0 . D e f l e c t i o n M a r s h a l l W . T . & N e l s o n t i M . ( 1 9 9 0f u n c t i o n s , S t r u c t u r e s , p p . 2 3 3 8 . L o n g
I I . D e f l e c t i o n I l e a r n E l . ( 1 9 8 5 ) S l o p e a n d d e f l e c t i oM e c h a n i c s o f M a t e r i a l s v o l . 1 ,p p . 3 0 2 7 . P e r g a m o n
( i i i ) A N G L E C L E A T S D i r e c t i o no f1 1 3 t Nr e s u l l a n t
c l a u s e4 . 2 . 3
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S h e a rc a p a c i t y P . = 0 . 6 x 0 . 2 7 5 x8 2 0 8= 1 3 5 0l e NF V / P , = 5 0 4 / 1 3 5 0 = 0 . 3 7
C o n n e c t i o n c l e a t i s s a t i s f a c t o r y .
S T U D YR E F E R E N C E ST o p i c
I . L a t e r a l r e s t r a i n tB S 3 9 5 0
2 . S t r u t b e h a v i o u r
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6 . D e f l e c t i o n f o r m u l a e
7 . C o n n e c t i o n s
8 . M o m e n t - a r c s m e t h o d
( 3 9 9 3 ) J o i n t s i n S i m p l e C o n n e c t i o n s v o l . I . S t e e lC o n s t r u c t i o n I n s t i t u t e
( 1 9 8 5 ) S t e e l u ' a r k D e s i g n v o l .I , S e c t i o n p t o p e r u e s ,m e m b e r c a p a c i t i e s , S t e e l C o n s t r u c t i o n i n s t i t u t e
( 3 9 9 2 ) D e s i g n t h e o r y , S t e e l D e s i g n e r s ' M a n u a l .p p . 1 0 2 6 S O . B l a c i r w e l l
( 1 9 9 2 ) J o i n t s I n S i m p l e C o n n e c t i o n s v o l . 2 . S t e e lC o n s t r u c t i o n I n s t i t u t e
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P U R L I N S A N D S I D E f l A I L S5 10 S T R U C T U R A L S T E E L W O I < D E S I G N T O O 5 9 5 0
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l e n g t h o f n o t m o r e t h a n t w o s p a n s ( 1 2 m ) w o u l d b e a c c e p t a b l e ( t h e y c a n b ed e l i v e r e d b u n d l e d t o g e t h e r t o r e d u c e f l e x i b i l i t y ) . C o n u n r n t y c a n a l s o b eA = = 6 0 0 0 / 2 2 . 4 =2 6 8a r r a n g e d b y U s e o f s i t e c o n n e c t i o n s c a p a b l e o f t r a n s m i t t i n g b e n d i n g m o m e n t s .
T h e f a c t o r a i s o b t a i n e d f r o m E S t a b l e 1 6 f o r / 3 = A l / A l 0. j 0S u c h c o n n e c t i o n s a r e c o s t l y t o f a b n c a t e a n d t o a s s e m b l e a n d a r e r a r e l y u s e da s t h e e n d m o m e n t A l a n d s i m p l y s u p p o r t e d m o m ei n s m a l l s t r u c t u r a l e l e m e n t s s u c h a s p u r l i n s a n d s i d e r a i l s . U s i n g t h e s a m eo p p o s i t e s i g n ) , h e n c ee x a m p l e a s i n S e c t i o n 4 . 2 , t h e d e s i g n i s r e p e a t e d f o r a p u r l i n c o n t i n u o u s o v e r
t w o s p a n s o f 6 . 0 m . a 0 . 6 6i t t = 1 . 0i t = 0 . 9 0 2
( a ) D i m e n s i o n s A / x = 2 6 8 / 1 4 . 5 = 1 8 . 5
- w h e r e x i s t h e t o r s i o n a l in d e x .A s S e c t i o n 4 . 2 ( a ) .E S t a b l e1 4 = 0 . 4 9
= 0 . 6 6 x 0 . 9 0 2 ' < 0 . 4 9 x 2 6 8 = 7 8( b ) L o a d i n gE St a b l e 1 1 p j , = 1 7 0 N / r n m 2
A s S e c t i o n 4 . 2 : a s s u m e p u r l i n t o b e 1 5 2 x 7 6 c h a n n e l ,4 3 s t e e l : = 1 7 0 x 1 3 0 x= 2 2 . 1 k N m
= 2 . 8 8 k N I= 2 . 7 1
1 2 . 4 / 2 2 . 1 + 4 . 5 / ( 2 7 5 x 4 1 . 3 x= 0 . 9 61 1 ' d y = 0 . 9 9 k NU l t i m a t e l o a d r i ' , =1 6 . 5 k NU l t i m a t e l o a d I V, , =6 . 0 k W
( g ) D e f l e c t i o n
F o m E x a m p l e 6 . t h e i m p o s e d l o a d a t s e r v i c e a b i l i tc ) D I I a n d S F= 7 . 9 5 k W
W i t h r e f e r e n c e t o F g . 4 . 1 2 : & =7 . 9 5x 6 0 0 & / ( l 8 5 x 2 0 5 x 8 5 2 x= 5 . 3 m mM , k N m M a x i m u m u l t i m a t e m o m e n t ( a t c e n t r a l s u p p o d ) = 2 . 8 9 k W: > / 5 ' =1 4 . 5 m m= 1 6 . 5 x 6 . 0 / 8 = 1 2 . 4 k N m D e f l e c t i o n l i m i t G 0 0 0 / 2 0 0 = 3 Om m0 4
N F = 0 . 6 5 x 1 6 . 5= 1 0 . 4 k WS i . = 4 . 5 k W m
F g . 4 . 1 2 F , , =3 . 8 k W
( d ) S h e a r c a p a c i t y
S h e a r f o r c e i s l e s s t h a n 0 . 6 s h e a r c a p a c i t y , a s S e c t i o n 4 . 1 ( d ) .
( e ) M o m e n t c a p a c i t y
E St a b l e 7T h e 1 5 2 x 7 6 c h a n n e l i s a c o m p a c t s e c t i o n ( b / T =8 . 4 5 ) ,h e n c e
5 x 1 3 0 x 1 0 3 = 3 5 . 8 k N mv ! ' 7= 9 . O N m
I
1 2 . 4 / 3 5 . 8+ 4 . 5 / 9 . 0 = 0 . 8 5
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5 6 S T R U C T U R A L S T E E L W O R K D E S I G N T O a s S S S OC R A N E G I R D E R S5 7
D e a d l o a d d u e t o s e l f w e i g h to f g i r d e r ( 1 . 7 9 + 0 . 3 6 k N / m ) a n d r a i l ( e ) S h e a r c a p a c i t y( 0 . 2 5k N / m )i n c l u d i n g y , i s
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c l a u s e4 . 2 . 3 D e s i g ns t r e n g t h f o r c h o s e n s e c t i o n w i t h f l a n g e 2 2m mt h i c k :T a b l e 1 . 2 p , = 2 6 5N / m m 2J ' d 1 . 4 x 2 . 4 0 3
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( i ) W e b b e a r i n g
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F i g . 5 . 1 0
gb e c h e c k e d f r l o c a l( s e e F i g . 5 . 1 0 ) . I f n e c e s s a r y , b e a n n g s t i ff n e r s m u s t b e i n t r o d u c e d t op r e v e n tl o c a l c r u s h i n g o f t h e w e b .
c l a u s e 4 . 1 1 . 5L o a d d i s p e r s i o n u n d e r w h e e l =2 ( 7 5 + 4 3 . 6 +I 6 . S ) = 2 7 0 m m
D e a n n gc a p a c i t y= 2 7 0 x 1 4 . 1 x 0 . 2 6 5 = I O a 9 k NM a x i m u m w h e e l l o a d = 3 8 3 k N
R a i l ,' / 4 5 ' 1 5f a n g e
\- p l a t e . . - x 1 6 . 5U n d e r w h e e lo o t o l
f l l e tl i i
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1 A t s u p p o r t
L o a d d i s p e r s i o n a t s u p p o r t :
M i n i m u m s t i ff n 2 = ( 2 3 . 6 + l 6 . S ) 2 . S = l O O m mF 1 = 5 7 1k N ( s u p p o r t r e a c t i o n )b , = 5 7 1 / ( 1 4 . 1 x 0 . 2 6 5 ) 1 0 0 = 5 3 m m
W e bb e a n n g a t t h e s u p p o r tr e q u i r e s a m i n i m u m s t i f f b e a n n go f 5 3 m m ; c h e c kt h a t t h e s u p p o r t sp r o v i d et h i sm i m m u m s t i f f b e a n n gt o p r e v e n t w e b b e a n n gc a p a c i t yo f t h eg i r d e r f o m b e i n g e x c e e d e d ( s e e F i g5 . 1 0 ) .
( J ) D e f e c t i o n
S e r v i c e a b i l i t y v e r t i c a l w h e e ll o a d e x c l u d i n g i m p a c t
1 9 1 . 4 k I N
M a x . d e f e c t i o n f r p o s i t i o n= a 3 / L 3 ) / 6 E J
a = ( L c ) / 2 = l . 5 m
D e f e c t i o n l i m j t = 6 5 0 0 / 6 0 0 = l O . 8 m m
T h e v e r t i c a lf r c e s a r e t r a n s m i t t e dt o t h e s u p p o r t i n g b r a c k e t b y d i r e( F i g . 5 . 1 1 ) . H o r i zo n t a l - r e a c t i o n s a r e p r e s e n t f o ms u r g e l o a d ( 1 3 . 3 k I N ) ah o r i zo n t a l b r a k i n g ( 1 5 . 3 k N ) . T h e s u r g e l o a d i s t r ab yt h e d i a p h r a g m ( F i g . 5 . 7 ) . T h e b r a k i n g f r c e w i l l b cn o m i n a lb o l t s ; p r o v i d e , s a y t w o M 2 0 b o l t s ( g r a d e 4 . 6 ) .
5 . 4 E X A M P L E J O . C R A N E G I R D E R W I T H L A
T h e d e s i g n i n S e c t i o n 5 . 3 m a y b e r e p e a t e d b u t i n c la l a t t i c e r e s t r a i n t t ot h e c o m p r e s s i o n f a n g e . I n p r a c t i c e s u c h a l a t t i c e gm a y h a v e b e e np r o v i d e d s p e c i f c a l l y f r t h i s p u r p o s e , o r t o s u p p o r t o rw a l k w a y s ( F i g . 5 . 1 2 ) . I n m o d e m U K p r a c t i c e i t i s s u c h a r e s t r a i n t i n o r d e r t o r e d u c e t h e b e a m s i ze , e xi n h e a v y m d u s t n a lb u i l d i n g s .
( a ) D i m e n s i o n s
A s S e c t i o n 5 . 3 .
( b ) L o a d i n g
A s S e c t i o n 5 . 3 ( m a k i n g n o c o r r e c t i o n f r t h e c h a n g
( c ) W h e e l t o a d s
A s S e c t i o o 5 . 3 .
C d ) B M a n d S F
A s S e c t i o n 5 . 3 , i . e .
M a x . I t ' , = 5 9 9 k N m ( 6 8 3 k N m w h e n a c t i n g a l o nM a x . I t ' . , = 1 5 . 8 k N m
( e ) S h e a r c a p a c i t y
A s m a l l e rU Bm a y b ec h o s e n a sl a t e r a lr e s t r a i n t i sp r o v i d e d .A s s u m e a5 3 3x 2 1 0 x 1 2 2 U Bw i t h n o p l a t ea d d e d .N o t et h a ti n t h e d e s i g n i n S e c t i5 . 3 w e b b e a n n g a n d b u c k l i n g w e r e c n t i c a t , h e n c e a as i m i l a r w e b t h i c k n e s s i s c h o s e n .
F i g . 5 . 1 2
I- - -- C 4D F c o m p r e s s i o n , O C R , w e b - o p t i m i za t i o n w
6 2 S T R U C T U R A L S T E E L W O K D E S I G N T O 5 5 5 9 5 0 C R A N E G I R D E R S 6 3
= O 6 x 0 . 2 6 5 x 5 4 4 . 6 x 1 2 . 8 = 1 0 8 k Nc l a u s e 1 . 2 . 3S h e a r c a p a c i t y p 5 = ( I ) C o n n e c t i o n
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( I ) M o m e n t c a p a c i t y
F / P , = 5 7 1 / 1 1 0 8 = 0 . 5 2
T h e c h o s e n U S i s a p l a s t i c s e c t i o n ( b I T = 5 . 0 )M o m e n t c a p a c i t y A l a =
B u t
S e c t io n i s s a t i s f a c t o r y .
( h ) D e f l e c t i o n
W h e e l l o a d = 1 9 1 . 4 k NC a l c u l a t i o n a s i n S e c t i o n 5 . 3 ( j ) g i v e s b = 9 . O mL i m i t = 6 5 0 0 / 6 0 0 = 1 0 . 5 m m
A s S e c t i o n 5 . 3 b u t t h e l a t t i c e t r a n s m i t s h o r i z o n t a l f o r ct h e d i a p h r a g m i s n o t n e e d e d .
T h e l a t t i c e g i r d e r w h i c h p r o v i d e s r e s t r a i n t t o t h e c rl o a d e d b y
( i ) t h e r e s t r a i n t f o r c e o f 1 1 . 4 5 1 1 4 ( 1 3 . 0 6 k N w h ec o n s i d e r e d t o b e d i s t r i b u t e d b e t w e e n t h e n o d e s o
( i i )i h e s u r g e l o a d o f 9 . 1 k N p e r w h e e l ( 1 0 . 4 t i N w h e n
2 8 . 6 k N i o t a i
I I I II1 2 3 4 5 6 7 8 9
T h e t r u s s i s a n a l y s e d b y g r a p h i c s , c a l c u l a t i o n , o r c of o r c e s a s t a b u l a t e d ( t i N ) :
P a n e l i o p c h o r dB o t t o m c h o r dD i a g o n a l P o s t
I 0 2 1 . 2 3 0 . 0 02 2 1 . 2 3 8 . 3 2 4 . 2 1 7 . 13 3 8 . 3 5 1 . 3 1 8 . 4 1 3 , 0
4 5 1 . 3 5 1 . 00 . 3 0 . 3
5 4 6 . 6 5 1 . 0 6 . 1 06 3 8 1 4 6 , 6 1 1 . 9 4 . 37 2 5 . 7 3 8 . 2 1 1 . 7 8 , 48 0 2 5 . 7 3 6 . 3 1 2 . 59 0
T h e a p p l i e d f o r c e s m a y a c t m e i t h e r d i r e c t i o n a n d hm a y b e e i t h e r t e n s i o n o r c o m p r e s s i o n . D e s i g n i n g t hc o m p r e s s i o n o f 5 1 . 3 t i N ; u s e a 3 5 x 4 5 x 6 e q u a l a n
A L 5 I r , , . t . 0 x 8 1 3 / 8 . 6 7 9 4p = I 3 5 N / m m 2
D e s i g n i n gt h e d i a g o n a l s f o r a c o m p r e s s i o n o f 3 6 . 2 t i N ua n g l e :
E f f e c t i v el e n g t h L e= 1 . 0 x 8 l 3 / c o s 4 5 = 1 1 5 0 m mA = 1 1 5 0 / 8 . 6 7 = 1 3 3
= 8 3 N / m m 2P r
( j ) L a t t I c e
6 2 3 m m
= 0 . 2 6 5 x 3 2 0 0 = 8 4 9 k N m
= I . 2 p , 4= 1 . 2 x 0 . 2 6 5 x 2 7 9 9 = 8 9 0 k N m= 6 8 3 / 8 4 9 = 0 . 8 0
c l a u s e 4 , 3 . 2T h e e f f e c t o f t h e l a t e r a l m o m e n t M , . i s c o n s i d e r e d l a t e r in p a r t U ) i nc o m b i n a t i o n w i t h a r e s t r a i n t f o r c e e q u a l 1 0 2 . 5 % o f t h e f l a n g e f o r c e . N o t e t h a tt h e v a l u e o f 1 % t n t h e i n i t i a l v e r s i o n b f c l a u s e 4 . 3 . 2 w a s c o n s i d e r e d l o b e t o os m a l l .
F a n g e f o r c e m a y b e e s t i m a t e d a s : 5 9 9 / 0 . 5 2 3 = 1 1 4 5 t i N ( 1 3 0 6 t i N w h e na c t i n g a l o n e ) ; s e e F g . 5 . 1 3 .R e s t r a i n t f o r c e = 2 8 . 6 t i N ( 3 2 . 6 t iN w h e n a c t i n g a l o n e )
F g ( g ) W e b b u c k l i n g / b e a r i n g
M i n i m u m s t i f f b e a n n g l e n g t h a i s u p p o r t t o r e s i s t r e a c t i o n o f 5 7 1 t i N .f t 5 4 4 . / 2 2 7 2 m mA = 2 . 5 x 4 7 7 / l 2 . 8 9 3
E S t a b / e 2 7 cP r = 1 3 4 N / m m 2M m . b e a n n g l e n g t h b , = 5 7 1 / ( 1 2 . 8 x O 1 3 4 ) 2 7 2 = 6 1 m m
n , = ( 2 l . 3 +1 2 . 7 ) 2 . 58 5 m mM m .b e a n n g l e n g t h b , = 5 7 l / ( 1 2 . 8 x 0 . 2 6 5 ) 8 5 = 8 4 m m
T h e r e f o r e , a s t i f f b e a n n g l e n g t h o f a t l e a s t 8 4 r u i n i s n e e d c d a t t h e s u p p o r t s t og i v e a d e q u a t c b e a r i n g s t r e n g t h f o r t h e g i r d e r .
F i g . 5 . 1 4
9 . 1 1 N 9 . 1 I N
4 5 .
8 b a y s a t 8 1 3 . 5 m m
E S t a b l e 2 7 cC o m p r e s s i o n r e s i s t a n c e= A g P r= 5 . 0 9 x l 3 5 x
E S t a b l e 2 7 c
P D F c o m p r e s s i o n , OC R , w e b - o p t i m i z a t i o n w
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7 4 S T R U C T U R A L S T E E L W O i < D E S I G N T O S 5 9 5 0 T R U S S E S 7 5
( I ) S t r u t( m e m b e r 1 0 )
M a x . c o m p r e s s i o n F = 2 3 . 9 k N
c l a u s e 4 . 8 . 3 . 2F / A g p , . + / t l , J & i , ,!
1 2 1 . 9 / ( 2 1 . 2 x 2 7 5 x 1 0 5 + 3 3 6 / 6 7 = 0 7 1
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( h ) B o t t o m c h o r d d e s i g n
M a xt e n s I O n = 1 I 3 . 0 k NM a xc o m p r e s s i o n3 9 . 2k N
U s e t w o 7 5 x 5 0 x 6 u n e q u a l a n g l e s s p a c e d 8 m m a p a r t ( s e m i - c o m p a c t )
E f f e c t i v ea r e aA , = a i + 5 a , a ,+ a , )a i = ( L t 1 2 ) t D t
= 1 7 5 3 ) 6 2 2 x6 = 3 0 0 m m 'a l l o w i n g f o ro n e2 2 m m d i a m e t e r h o l e i nc a l c u l a t i n gU I :
a 2 = 1 5 0 3 ) 6 = 2 8 2 m m 'A , = 3 0 0 + 5 x 3 0 0 x 2 8 2 1 ( 5 x 3 0 0 + 2 8 2 )= 5 3 7 m m ' / a n g l e
N o t e t h a t A , b e c o m e s n e t a r e a i f c l a u s e 4 , 6 . 3 , 3 i s s a t i s f i e d .
T e n s i o n c a p a c i t y F , = A , p , =2 x 5 3 7 x 0 . 2 7 5 = 2 9 5 1 6 4
C o m p r e s s i o n r e s i s t a n c e m u s t b e c h e c k e d a s s u m i n g l a t e r a l r e s t r a i n t t o t h eb o t t o m c h o r d a t t h e c h o r d b r a c i n g c o n n e c t i o n s , m a x i m u m s p a c i n g 4 . 6 4 m( F i g . 6 . 8 ) .
r , , 2 1 , 4 m mA , , , = 4 6 4 0 / 2 1 . 4 = 2 1 7A r = 5 8 0 / 1 0 . 8 = 5 4
( f o r c o n n e c t i o n s a t q u a r t e r p o i n t s , i . e . 0 . 5 8 m c e n t r e )
A , , = , / ( 2 l 7 ' + 5 4 ' )= 2 2 4M a x i m u m s l e n d e r n e s s= 2 5 0C o m p r e s s i o n s t r e n g t h P .= 3 4 N / m m 2C o m p r e s s i o n r e s i s t a n c e= A g P c
= 1 4 . 4 x 3 4x l 0 " = 5 0 . 4 3 6 4S e c t i o n i s s a t i s f a c t o r y .
pM a x . t e n s i o n= 1 0 , 3 k N
U s e 6 0 x 6 0 x 6 e q u a l a n g l e
1 8 . 2 m mL = L 7 2 m
0 . 8 5 L J r , ,= 1 2 5 o rA
C o m p r e s s i v es t r e n g t h P .= 9 1 N / m m ' f o r A =1 2 5C o m p r e s s i o n r e s i s t a n c e= A g P c
= 6 . 9 1x 9 1 xS e c t i o n i ss a t i s f a c t o r y .
C o n n e c t i o n
= 1 6 0 x 2 x 0 , 2 4 5= 7 8 k NH e a r i n g c a p a c i t y o f b o l t sF , , , , d t p , , , , = 2 x 2 0 x 6 x 0 . 4 5 03 0 8 k NB e a r i n g c a p a c i t y o f a n g l e s F , , , = d i p , , , = 2 x 1 0 8k Nb u t F , , ,e l p , , , / 2 = 4 0 x 6 x 0 , 4 5 0 / 2 = 5 4
C l e a r l y a b o l t s i z e o f a s l o w a sI 6 m m w o u l d b e p o s s i b l e .
G u s s e t p l a t e s t r e s s c a n b e b a s e d o n a n e f f e c t i v e 6 0 / c o s 3 0 ' 2 2 = 4 7 m m .
S e c t i o ns a t i s f a c t o r y .
B u c k l i n g r e s i s t a n c e m o m e n t o f t h e s e c t i o n m u s t b e c h e c k e d u s i n g :
S l e n d e r n e s s A
= 21 5 5 / 2 6 . 2 =8 2c l a u s e4 , 3 , 8 B u c k l i n gr e s i s t a n c e 4= 0 . 8x 2 7 5 x 2 4 . 3 x l 0 " 3 = 5 . 3 5 k N m
O v e r a l l b u c k l i n g c h e c k ( s i m p l i f i e d a p p r o a c h ) :
c l a u s e4 . 8 . 3 . 3 F A cP t+ m M J A I , ,I w h e r e n i =3 . 0
1 2 1 , 9 / 2 6 1 + 3 . 3 6 / 5 . 3 51 . 0 0
c l a u s e4 . 6 . 3 . 2
F i g . 6 , 5 a n dc l a u s e 4 . 7 . i O . 2 a
1 3 5 t a b l e 2 7 c
C h e c k t h e s t r e n g t h o f t h e c o n n e c t i o n j o t n t n g m eA s s u m e a n 8 m m t h i c k g u s s e t p l a t e a n d 2 0 m m b o l
M a x , f o r c e ( m e m b e r 1 3 ) = 3 L 3 k N
F o r c e c h a n g e b e t w e e n m e m b e r s 6 a n d 7 i s 3 2 . 2 k Nt o b e j o i n e d a t t h i s c o n n e c t i o n ( t o c h a n g e s i z e o rt h e n m a x i m u m f o r c e ( m e m b e r 6 ) w o u l d b e 9 6 . 9 k-
' 9
c l a u s e 4 7 . 3 . 2 b 5t a b l e 2 7 c
F i g . 6 . 1 4 2 2 m m h o l e s b r 2 0 m m b o i i a
c l a u s e 6 . 3 . 2S h e a r c a p a c i t y o f b o l t s ( d o u b l e s h e a r )
c l a u s e 6 . 3 . 3 . 2c l a u s e 6 . 3 . 3 . 3
P D F c o m p r e s s i o n , OC R , w e b - o p t i m i z a t i o n w
1 0 S T R U C T U R A L S T E E L W O ff ( D E S I G N T O E S 5 0 3 0 - i * S M T R U S S E S 7 7P l a t e s t r e s s = 3 2 . 3x 4 7 ) = 8 6 N / m i n 2( M a x i m u m v a l u e i s p , = 2 7 5N / m m 2 )
T h e r e m a i n i n g h - u s s m e m b e r s m a y b e d e s i g n e d i n t h e s a m ew a y , w i t h t h e
( c ) T r u s s f r c e s
A n a l y s i s o f t h e t r u s s t 1 2 1 u n d e r t h e n o d a l l o a d sg i v e s t h e m e m b e r f o r c e si n t h e t a b l e :
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c o m p r e s s i o n f o r c e u s u a l l y b e i n g t h e m a i n d e s i g n c n t e r j o n . I t s t i o u l d b e n o t e dt h a t i t i s g o o d p r n c t i c e t o l i m i t t h e n u m b e r o f d i f f e r e n t m e m b e r s i z e s b e i n gu s e d , p r o b a b l y n o t m o r e t h a n f o u r i n t o t a l . T h e d e f l e c t i o n o f a r o o f t r u s s i sn o tu s u a l l y c r i t i c a l t o t h e d e s i g n , a n d t h e e f f e c t s o f s a g u n d e r l o a dm a y b e o f f s e tb y p r e - c a m b e r i n g t h e t r u s s d u r i n gf b n c a t i o n
b y ,s a y ,
5 0 m mo r l O O m m . I ft h e d e f l e c t i o n i s r e q u i r e d t h e n h a n d o r g r a p h i c a lo r t h e v i r t u a lw o r k m e t h o d t 9 i O ) . o r a p p r o p n a t e p r o g r a m s m a y b e u s e d . I t s h o u l d b en o t e dt h a t d e f l e c t i o n d u e t o b o l t s l i p c a n b e s i g n i f i c a n t c o m p a r e d w i t h d e a d l o a de l a s t i c d e f i e c t i o n s .
( a ) D i m e n s i o n s
S e e F i g . 6 . 1 5 : l a t t i c e g i r d e r f a b n c a t e d f r o m t u b u l a r s e c t i o n s , s p a n 8 . 0 m ;s p a c i n g 3 . 5 m . ( d )
i n t h e t a b l e :
T o p c h o r d
M e m b e rF o r c e
B o t t o m c h o r d
M e m b e rF o r c e
D i a g o n a l s
M e m b e rF o r c e
I3
4
1 8 83 2 24 0 24 2 9
5
6
7
8
1 0 7 2 6 8 3 7 5 4 2 9
9
I DI I1 21 3
1 4
1 5
t o
1 5 2- 1 4 4
1 1 4 7 6
7 6
3 8
3 8
0
C o m p r e s s i o n f o r c e
B M i n t o p c h o r d
i s p o s i t i v e .
D e a d l o a d o n t i m b e r j o i s t :
f l o o r 0 . 5 x 3 . 5 x 0 . 5 = 0 . 8 S k Nf i n i s h e s0 . 2 x 3 . 5 x 0 . 5 = 0 . 3 5 k Nw e i g h t o f t r u s s ( e s t i m a t e d ) = 0 . 3 7 k NT o t a l l o a d I V , , = 1 . 6 0k N
I m p o s e d l o n d o n t i m b e r j o i s tI T ' , = 4 . 0 x 3 . 5 x 0 . 5 = 7 . O O k N
L o a d o n g i r d e r f r o m e a c h j o i s t =1 . 4 W ,,+ 1 . 6 W ,1 . 4 x 1 . 6 0 x 1 . 6 x 7 . 0 0 = l 3 . 4 k N
C o n c e n t r a t e d l o a d a t n o d e s = 2 6 . 8 k N
M a x . c o m p r e s s i o n F = 4 2 9 k NM a x . B M M X 1 . 6 S k N mU s e 9 0 x 9 0 x - 6 . 3 I 1 R S
r 3 4 . l m mS l e n d e r n e s s A = 0 . 8 5 x l 0 0 0 / 3 4 . i = 2 5
S t r u t t a b l e f o r R I - I S i s t a b l e 2 7 aC o m p r e s s i v e 2 7 0 N / m m 'C o m p r e s s i o n r e s i s t a n c eP c
= 2 0 . 9x 2 7 0xS e c t i o n c h o s e n i s p l a s t i c ( b I T1 4 )
M o m e n t c a p a c i t y
L o c a l c a p a c i t y c h e c k
F / A 5 ? S
4 2 9 / ( 2 0 . 9 x2 7 5x I . 6 8 ( 1 7 . 9 6 = O . 8 4
S e c t i o n i s s a t i s f a c t o r 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 n e e d n o t b e c o n s i d e r e dc o m p r e s s i o n f l a n g e i sp o s i t i v e l y r e s t r a i n e d c o n n e c t e d t o t h e t i m b e r j o i s to r f o r b o x s e c t i o n s( c l a u s e 8 . 2 . 6 . 1 ) .
6 . 8 E X A M P L E 1 2 . L A T T I C E G I R D E R
J o i i i i o i d i 1 3 . 4 I N
6 . 1 6
l i m b e r l o u i s a t 0 . 5 m c e n i r e i
F i g . 6 . 1 5 L a t t i c e g i r d e r
( S e e F i g . 6 . 1 6 . )
( b ) L o a d i n g
T i m b e rj o i s tf o o rF l o o r f i n i s h e sI m p o s e d l o a d
( e )
3 M i n c o n t i n u o u s t o p c h o r d = W L / 8
T o p c h o r d
0 . 5 k N / m 20 . 2 k N / m 24 . 0 k N / m 2
= 1 3 . 4 x
F i g . 6 . 4E S t a b l e 2 5
E S t a b l e 2 7 a
c l a u s e 4 . 8 . 3 . 2
5 6 4 k N
= P J ,= 2 7 5x 6 5 . 3 x 1 7 . 9 6 k N m
P D F c o m p r e s s i o n , O C R , w e b - o p t i m i za t i o n
7 8 S T R U C T U R A L S T E E L W O I ( D E S I G N T O E S 5 9 5 0 T R U S S E S 7 9
( I ) B o t t o mc h o r d 2 . T r u s sa n a l y s i s C o a t e s f t C . , C o u t i e M . G . & K o n gF . K .( 1 9 8 8 )A n a l y s i s o f p l a n e t r u s s e s , S t r u c t u r a l A , i aVa n N o s t r a n d R e i n h o l dt v l a x . t e n s i o n F 4 2 9 k N
3 B o l t d e s i g n 1 1 9 9 1 ) S t e e l s r o r k D e s i g n v o l 4 p p 1 0 1 1
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3 . B o l t d e s i g n 1 1 9 9 1 ) S t e e l s r o r k D e s i g n v o l . 4 , p p . 1 0 1 1U s e 9 0 x 9 0 x S R I I S C o n s t r u c t io n I n s t i t u t e
T e n s i o n c a p a c i t y P A , p ,1 6 . 9 x 2 7 5 x 1 0 ' = 4 6 5
4 . W e l d i n g 1 1 9 9 1 ) S i e e l i s ' o r k D e s i g n v o l . 4 , p p . 1 1 / 1C o n s t r u c t io n i n s t i t u t e
5 . F i c t io n g a p b o l t s( 1 9 9 1 ) S t e e l w o r k D e s i g o v o l . 4 . p p . lO l S e c t i o n i s s a t i s f a c t o r y . C o n s t r u c t io n I n s t i s u i c
6 . W i n d p r e s s u r eO 6 3 9 9 D e s i g n L o a d i n g f o r B u i l d i n g s
( g ) D i a g o n a lc o e f f i c i e n t s P a n 2 : W i n d l o a d s ( 1 9 9 5 )
C h o r dI
7 . T r u s s d e f l e c t i o nM a r s h a l l W . T . & N e l s o n H . M . ( 1 9 9 0S l r u e t u r e s , S t n : c : u r e s , p p . 2 7 3 9 8 . L o n g( S e e F g . 6 . 1 7 . )
I S T r u s s d e f l e c t i o nW a n g C . K . ( 1 9 8 3 ) T h em e t h o d , J n t e n n e d i a t e
N \M a x . c o m p r e s s i o n F = 1 5 2 k N , S ; n i c n i r a l A n a l y s i s , p p 9 3 9 9 . P e r g a n s oM a x . t e n s t o n= l I 4 k N I 9 . Vi r t u a l w o r k l % l a r s l t a l l W . T . & N e l s o n 1 1 . M . ( 1 9 9 0
/ U s e S O 5 O 3 . 2 R H S a n d e n e r g y t s n n c t p l e s , S t r u c t u r e s , p p S O F g . 6 . 1 7 = 1 9 . 1 t r u s s t O Vi r t u a l w o r k C o a t e s f t C . , C o i s t i e M C . & K o n g F K
S l e n d e r n e s s A = 0 . 7 L 4 ' 5= 0 . 7 x 5 0 0 / 1 9 . 1 e o s 4 S ' = 2 6 A p p l i c a t i o n s o f t h e p n n e t p l e o f v i n u a l B S t a b l e 2 7 aC o m p r e s s i v e s t r e n g t h p .= 2 6 9 N / m m 2 A n a l y s i s , p p . 1 3 4 I S Va n N o s t r a n d R e i n
C o m p r e s s i o n r e s i s t a n c e= A g P r I I . C o n n e c t i o n o f P 1 4 5C I D E C T ( 1 9 8 5 ) W e l d e d j o i n t s . C o n s r n= 5 . 9 4 x 2 6 9 x I 0 " = 1 6 0 H o l l o w S t e e l S e c t io n s , p p .I 2 9 - 4 2 , B r i t i s h S l e e t
T e n s i o n r e s i s t a n c e P ,= 5 . 9 4 x 2 7 5 x I D _ i = 1 6 3 l e N C o r i o r n t t o n T u b e s D i v i s i o n
S e c t i o n i s s a t i s f a c t o r y .
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A l l w e l d e d j o i n t s w i t h e o n t m u o u s 4 m m w e l d s .
W e l d l e n g t h= 2 ( S 0 + 5 0 / e o s 4 S )= 2 4 1 m mc l a u s e 6 . 6 . 5 . 1D e s i g n s t r e n g t h P w = 2 1 5 N / n u n 2
W e l d r e s i s t a n c e= 0 , 7 x 4 x 2 4 1 x 2 1 5 = 1 4 5 k N
T h e m a x i m u m f o r c e s w h i c h m a y b e t r a n s m i t t e d b e t w e e n h o l l o w s t e e ls e c t i o n s a r e m o r e c o m p l e x a n d d e t a i l e d r e f e r e n c e s m a y b e c o n s u l t e d i fr e q u s r e d t i U
A s i n S e c t i o n 6 . 7 , t h e n u m b e r o f s e c t i o n s i z e s w o u l d b e l i m i t e d i n p r a c t i c e ,w i t h t h e a l l o w a b l e v a n a t i o n i n m e m b e r s i z e s d e p e n d i n g o n t h e d e g r e e o f
r e p e t i t i o n e x p e c t e d .
S T U D Y R E F R E N C E S
T o p i c R e f e r e n c e s
I . T r u s s a n a l y s i sM a r s h a l l W . T . & N e l s o n H . M .( 1 9 9 0 ) A n a l y s i so fs t a t i c a l l yd e t e r m i n a t e s t r u c t u r e s , S t r u c t u r e s , p p . 1 0 1 9 .L o n g m a n .
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8 4 r m u c m m A LS ' E E L W O R K D E S I G N T O E S 6 5 3 0 S I M P L EA N DC O M P O U N D C O L U M N S8 5L o a d i n g W ; 7 . 6 O VE R A L L B U C K L I N G
( W I + W 2 )
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o v e r a l lb u c k l i n g r e s i s t a n c e i n v o l v e s t h e s a m e f a c t o r s p r o c e d u r e s a s g i v ei n S e c t i o n 3 . 2 , b u t w i t h a n a d d i t i o n a l t e r m f o r a xa s i m p l i f i e d
W ,
a p p r o a c h ( c l a u s e 4 . 8 . 3 . 3 . 1 ) t h e o v e r a l l b u c k l i n g I S C o n s i d e r e d t o b es a t i s f a c t o r y i f t h e C o m b i n a t i o n r e l a t i o n s h i pi s s a t i s f i e u .
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w h e r e P r 1 5 t h e C o m p r e s s i v e s t r e n g t h ( S e c t i o n
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M 6 i s t h e b u c k l i n g r e s i s t a n c e ( S e c t i o n 3 . 5 )4 , i s t h e m i n o r a x i s e l a s t i c s e c t i o n m o d u l u s
A m o r e e x a c t a p p r o a c h ( c l a u s e 4 . 8 . 3 . 3 . 2 )m a y b e c a r r i e d o u t u s i n g 1 1 g . 7 . 6 R e s u l t a n t f o r c e ( M i +M , t h e b u c k l i n g m o m e n t s a b o u t m a j o r a n dm m o r a x e s i n t h er o o f t r u s s b o t i o m p r e s e n c e o f a x i a i l o a d . I n t h i s a p p r o a c h :c h o r d
n i x A I J A f g g + I
7 . 5 L O C A L C A P A C I T Y
7 . 7 E X A M P L E1 3 . C O L U M NF O R I N D U S T R I A L B U I L D I Nt a n y s e c t i o n I n a c o l u m n U s e s u m o f e f f e c t s o f a x i a l l o a d F a n d m o m e n t sa n d m u s t n o t e x c e e d t h e l o c a l c a p a c i t y . T h i s i s c o n s i d e r e d t o b e( a ) D i m e n s i o n ss a t i s f a c t o r y i f t h e c o m b i n a t i o n r e l a t i o n s h i p s a t i s f i e s t h e f o l l o w i n g i n t e r a c t i o n
e q u a t i o n :( S e e F i g .
O v e r a l l h e i g h t 1 2 . 5 ma ) f o r p l a s t i c a n d c o m p a c t s e c t i o n s :H e i g h t o f c r a n e r a i ll O O m. 1 1 3 , U C a n d j o i s t s e c t i o n sF r e e s t a n d i n g b r i c k w a l l2 . 5 mC r a n e n i l e c c e n t n c i t yO . 5 mC l a d d i n g e c c e n t n c i t y0 . 2 5 n i
R I - I S , C H S a n d s o l i d s e c t i o n s
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I R o o f t r u s s r e a c t i o n s I V , .D e a d l o a d
5 O k Nw h e r e M 0 , a r e t h e r e d u c e d p l a s t i c m o m e n t s i n d i e p r e s e n c e o fI m p o s e d l o a d 7 8 k Ma x i a l l o a d , a s d e f i n e d i n r e f e r e n c e ( 5 ) . W i n d l o a d ( s u c t i o n ) 9 0 k M
( b ) F o r s e m i - c o m p a c t a n d s l e n d e r s e c t i o n s , a n d a s a s i m p l i f i e d m e t h o d f o rC r a n e g i r d e r r e a c t i o n s ( v e r t i c a l )c o m p a c t s e c t i o n s i n ( a ) : D e a d l o a d ( g i r d e r s e l f w e i g h t )2 0 k N
C r a n e l o a d m d . i m p a c t l n e a r s i d e ) 2 2 0 k MF / A g p , + M 1 J M aI C r a n e l o a d ( f a r s i d e )1 5 0 k Mw h e r e A g i s t i l e g r o s s s e c t i o n a l a r e a a n d A - f , , , a n d A - f , , . a r e t h e m o m e n tC r a n e g i r d e r r e a c t i o n ( h i o n z o n t a l ) I t ' , , , .c a p a c i t i e s d e f i n e d i n S e c t i o n 3 . 4 . C r a n e s u r g e l o a d 6 k M
P D F c o m p r e s s i o n , O C R , w e b - o p t i m i za t i o n
8 6 S T R U C T U R A L S T E E L W O I < D E S I G N T O 8 5 5 9 5 0 S I M P L E A N DC O P O N D C O U M N S 8 7
W i n d o n s i d e o f b u i l d i n g W 8 .W i n d l o a d ( u . d , l . a b o v e b r i c k w o r k )5 5 k N
S e l f w e i g h t ( c o l u m n ) W 0D e a d l o a d l O k N
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D e a d l o a d l O k N
C l a d d i n g W D CD e a dl o a d t 6 k N
T h e r e s u l t a n t f o r c e ( J F k f o r w i n d ) d e p e n d s o n t h e d i f f e r e n c e b e t w e e n t h el o a d i n g o n t h e c o l u m n b e i n g d e s i g n e d a n d t h a t o n t h e s i m i l a r c o l u m n o n t h ef a r s i d e o f t h e b u i l d i n g ( F i g . 7 . 6 ) . I f t h e w i n d l o a d o n t h e f a r s i d e i s z e r o :
1 r 5 3 ( 5 + D ) 1 l 6T h er e s u l t a n t f o r c e ( l V i f o r c r a n e ) d e p e n d s o n t h e d i f f e r e n c e i n t h e c r a n e( v e r t i c a l ) l o a d i n g o n t h e n e a r a n d f a e s i d e c o l u m n s ( F i g . 7 . 6 ) :
1 5 0 ) 0 . 5 / ( 4 x 1 2 . 5 )= 1 0 . 2k N
T h e r e s u l t a n t f o r c ef o r d e a d l o a d ) d e p e n d s o n t h e c r a n e g i r d e r d e a d l o a dp r o d u c i n g m o m e n t s I n o p p o s i t e d i r e c t i o n s :
3 ( 2 0 + 2 0 ) 0 . 5 1 ( 4 x 1 2 . 5 )= 1 . 2k N
F l 9 . 7 . 7 N o t e t h a t t h e c r a n e s u r g e l o a d i n g ( h o r i z o n t a l ) p r o d u c e s n o r e s u l t a n t f o r c e mt h e t r u s s a s i t i n d u c e s e q u a l l o a d s i n b o t h c o l u m n s , a n d i n t h e s a m e d i r e c t i o n .
A l l t h e u n f a c t o r e d l o a d s m a y ' b e s h o w n i n t h e l o a d m a t r i x [ i f ' ] k N :
D e a d I m p o s e dC r a n e C r a n e% V i n dl o a d l o a d l o a d l o a d l o a d
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( e ) C o e ff c i e n t s
B e n d i n gm o m e n t s a n d a x i a l f o r c e s a r e p r o d u c e db yt h e f a c t o r e d l o a d s . T oc a l c u l a t e a x i a l f o r c e a l l v e r t i c a l l o a d s a b o v e t h eb e i n g c h e c k e ds h o u l d b e a d d e d t o g e t h e r . T o c a l c u l a t e b e n d i n g m o m e n t s t h e p r o d u c t s o f
4 1
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g g pf o r c e a n d d i s t a n c e s h o u l d b e a d d e d t o g e t h e r . T h i s i s a g a i n u s e f u l l y s h o w ni n am a t r i x [ a ] , f o r a x i a l f o r c e F a n d b e n d i n g m o m e n t M . T h e B M v a l u e s a r e t o b ec a l c u l a t e d a t t h r e e p o s i t i o n s a s s h o w n i n F i g . 7 . 7 . T h e c o e f f i c i e n t s f o r E Ma r ei i i m e t r e s .
s o
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T h e c o e f f i c i e n t s f o r E M i n r e l a t i o n t o t h e l o a da l l o w f o r a r e d u c e d v a l u eo f a s w e l l a s a r e d u c e d d i s t a n c e i n c a l c u l a t i n g a f o r p o s i t i o n s 2 a n d 3 . F o re x a m p l e ;
( 7 . 5 / 8 0 ) x( 7 . 5 / 2 ) = 2 . 8 1 W 4
h e n c e a = 2 . 8 1 m .S i m i l a r l y t h e v a l u e o f t V o c d e c r e a s e s f o r p o i n t s 2 a a d 3 a a d t h i s i s r e f l e c t e d
i n t h e v a l u e o f a :M ' 2 a W a c ( 7 . 5 / I D ) x ( 0 . 2 5 ) 0 . 1 9 W a c
( 0 B M a n d a x i a l f r c e
A ss h o w n i n S e c t i o n 7 . 4 , t h e E M a n d a x i a l f o r c e m a t n x i s
[ F , M ] = [ W , ] T x [ a ]
U s e a 3 0 5 x 3 0 5 x 1 3 7 U C s e c t i o n ( g r a d e 4 3 ) . Ti s a p l a s t i c s e c t i o nB S t a b l e 6( b / T = 7 . 8 , c U t =1 7 . 9 )a n d h a s a d e s i g n s t r e n g t h p , = 2 6 5 N
M o m e n t c a p a c i t y A l a= p y
= 2 6 5 x 2 2 9 8 x 1 0 3 t 6 O 9 k N mA 1 p , = 1 7 4 . 6 x 2 6 5 x 1 0 = 4 6 3 0 k
C A S E ( i )
c l a u s e 4 . 8 . 3 . 2L o c a l c a p a c i t y c h e c k ( s i m p l i f i e d ) :
+ A I J I r I C . I
5 4 8 / 4 6 3 0 + 1 2 5 / 6 0 9 =0 . 3 2
C A S E ( i i )
L o c a l c a p a c i t y c h e c k :
5 9 2 1 4 6 3 0 + 1 4 2 / 6 0 9 = 0 . 3 6
C A S E ( i i i )
L o c a l c a p a c i t y c h e c k :
3 6 5 / 4 6 3 0 + 3 8 1 / 6 0 9 = 0 . 7 0
( I i ) O v e r a l lb u c k l i n g
F o r c o m p r e s s i v e s t r e n g t h , t h e s l e n d e r n e s s A i sn a n e f f e c t i v c l e n g t hL 5 .
L E Y I . 5 x l 2 . s % l 8 . 7 5 m , o rL 5 1 = 0 . 8 5 x 1 0 . 08 . 5 m
1 3 7P c = 8 6 N / i n n s 2
= 8 5 0 0 / 7 8 . 2 =1 0 9a l I O N / m m 2
F 5 M i M 3 M 3
C a s e ( 1 ) 5 4 8 4 9 8 7 1 2 5C a s e ( i i ) 5 9 2 4 0 5 0 1 4 2C a s e ( i i i )3 6 5 3 8 1 1 6 7 8 6
T h e E M d i a g r a m sf o r e a c h l o a d c a s e m a y b e d r a w n a s i n F i g . . 7 . 1 1 .
P D F c o m p r e s s i o n , O C R , w e b - o p t i m i za t i o n
9 0 S T R U C T U R A L S T E E L W O I c D E S I G N T O S 5 9 5 0
U s el o w c r v a l u eo f t o o b t a i n c o m p r e s s i o n r e s i s t a n c e :
A g p c y = 1 7 4 . 6x 8 6 x E S t a b l e s 1 6 , 1 7
S i M P L E A N D C O P O N D C O U M N9 1
$ = 8 6 / 3 8 1 = 0 . 2 3y = 3 8 1 / 6 7 = 5 . 7n = 0 . 7 !
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F o r m o m e n t r e s i s t a n c e , t h e b u c k l i n g s t r e n g t h i s a l w a y s b a s e do n t h e m i n o r E S t a b / e s1 1a x i ss l e n d e r n e s s :
, t , . L s / r , , =1 0 9x = 1 4 .( t o r s i o n a l i n d e x )
A k= 7 . 7N = 0 . 5
E S t a b l e1 4 v =0 . 7 1a = 0 . 8 5 1
C A S E( I )
S i m p l i f i e d o v e r a l l b u c k l i n g c h e c k :
3 6 5 / 1 5 0 0 + 1 . 0 x 3 8 1 / 5 4 7 = 0 . 9 4
S e c t i o n i s s a t i s f a c t o r y . U s i n g a s m a l l e r s e c t i o n ( 3i n t h e s i m p l i f i e d b u c k l i n g c h e c k > I .
E S t a b l e1 3 n = 1 , 0 ,i n 1 . 0 , a s t h e c o l u m n i s n o t l o a d e d a l o n g i t s l e n g t h f o r t h i sc o m b i n a t i o n .
E S r a b l e i SP = 4 9 / 1 2 5 = 0 . 3 9i n = 0 . 7 2
A L T i i i t VA= 1 . 0 x 0 . 8 5 1 x 0 . 7 ! x 1 0 9 = 6 6
E S t a b l e1 1 B u c k l i n g s t r e n g t h= 1 9 4 N / m m 2B u c k l i n g r e s i s t a n c e A l = P b
E S t a b l e1 8
S i m p l i f i e d o v e r a l l b u c k l i n g c h e c k :
F A C P C o & A I X I M b
5 4 8 / 1 5 0 0 + 0 . 7 2 x 1 2 5 / 4 4 6 = 0 . 5 7
C A S E ( i i )
A s f o r c a s e ( i ) n= 1 . 0 , i n I . 0 .
$ = 4 0 / 1 4 2 = 0 . 2 8a t = 0 . 4 8
= 1 9 4 x 2 2 9 8 x 1 r 3 = 4 4 6 l d 4 m
A s f o r c a s e ( f l ,b u c k l i n gr e s i s t a n c e =4 4 6k N mS i m p l i f i e d o v e r a l l b u c k l i n g c h e c k :
5 9 2 / l 5 0 0 + 0 , 4 8 x4 2 / 4 4 6 = 0 . 5 5
C A S E ( i i i )
E S t a b l e1 3 , n = t On < 1 . 0 ,a s t h e c o l u m n i s l o a d e d a l o n g i t s l e n g t h f o r i b i sc o m b i n a t i o n ,
F I g . 7 . 1 2
7 . 8 E X A M P L E 4 . L A C E D C O U M N FO I N D U S
( a ) D i m e n s i o n s
P n n c i p a ld i m e n s i o n s a r e a s S e c t i o n 7 . 7 ( a ) b u t t h e c r os h o w n ( F i g . 7 . 1 2 ) .
( b ) L o a d i n g
A sS e c t i o n 7 . 7 ( b ) .
C o m b i n e d f o r c e a n d S M
C o m b i n a t i o n s o f l o a d s m a y b e c o n s i d e r e d a s b e fu s i n g t h e s a m e v a l u e s o f W 4 t o W 5 i n c l u s i v e . Mf o r c e w i l l v a r y s l i g h t l y d w m g t o t h e r e v i s e d c r o s
C o n s i d e r c a s e ( i i i ) o n l y , i . e . 1 . 2 ( d e a u c r a n e
M a x . B M = 2 8 8 . 0 x 0 . 4 7 . 2 x 1 0 . 0 + 6 6 . 0 2 6 . 0 x 1 2 . 5 1 9 . 0 x 0 : 6 5 4 6 . 0 x O
A x i a l f o r c e4 6 . 0 2 8 8 . 0 1 2 . 0 1 9 . 0 = 3 6 5 k N
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c l a u s e 4 . 7 . 8T h e d e s i g n o f a l a c e d c o l u m n m a y b e e a r n e d o us i n g l e s n t e g r a l m e m b e r , a n d c h e c k i n g t h e d e s i g n
U s e t w o 3 0 5 x 1 2 7 x 3 7 L I D s e c t i o n s . T h e s e ( b I T =1 4 . 2