Explanatory otes G eneral A l l weights and measures shown on invoice i l be governed by standards o f t h e respective specifications so off.ered Carehas been taken t o ensure that a l l data a n d information herein i s factual a nd that numerical values are accurate. To the best of o ur knowledge, a l l information contained In this handbook I s accurate a t the time of publication. Continental Hardware P t e Lt d assume no responsibility for errors in o r misinterpretation f the Information contained in this handbook o r in Its use. M aterial Sections T h e structural components referred to i n this handbook ar e of steel to BS 4360, 'Weldable structural steels' and/or i t s related equivalents. T h e univers-41 bOMikrid. columns and tees cut therefrom, t h e joists, . X c hannels, dgive aring piles a n d rolled tees are generally as listed in U B S 4: Part V universal bearing piles a n d rolled tees P!980 t s , U i n regular duBc are a d . N A .ifie unive .52' tape- e d f l " C olum,q core-i serial size 3$6m-.*. J I - f, i s section, isted separately, is rolled i n th e 0 - M appropriate o n e t o b e used a s 6 m '. It i . F ts . An hion r sedion than those rolled i s Dimensional nits T h e dimensioa-fifUt-tioni'..'are g i calculated properties (cent.6idal Lipp, moments o f inertia, e W , c enfinidttLý(qcbi).-'Uiitw,ASdrfaiee r e r ances o n dimensions and Other units r e s (mm) a n d t h e ectional areas, radii of i d plastic moduli) are given i n i n square metres M2) . F o r ference should be made o T he-units o f forcemass and acceleration are those of the Systeme International (SI). They are the Newton (N), the kilogramme k g ) a nd t h e metre per second per second m/s2) s o that 1 N- 1kgx ImA2. T h e acceleration d u e to gravity varies slightly from place t o place a n d f o r convenience a 'standare value o f 9.80665 m/s2has become enerally accepted i n structural engineering. With this convention, the force exerted b y a mass under action i s unit' o f 9.80665N. I n t h e same way 9.80665 kilonewtons (kN) i s the force exerted b y mass o f 1 tonne (1000kg) under ravity, a n d 1kN the force f r om a mass of 0.102 tonne.
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Al l w e i g h t s and measures shown o n i n v o i c e i l l b e g o v e r n e d b y s t a n d a r d s o f t h e
r e s p e c t i v e s p e c i f i c a t i o n s s o o f f . e r e d
Carehas been t a k e n t o e n s u r e t h a t a l l d a t a and i n f o r m a t i o n h e r e i n i s f a c t u a l andt h a t n u m e r i c a l v a l u e s a r e a c c u r a t e . T o t h e b e s t o f our k n o w l e d g e , a l l i n f o r m a t i o n
c o n t a i n e d I n t h i s handbook I s a c c u r a t e a t t h e t i m e o f p u b l i c a t i o n . C o n t i n e n t a l
Hardware P t e L t d assume no r e s p o n s i b i l i t y f o r e r r o r s i n o r m i s i n t e r p r e t a t i o n ft h e I n f o r m a t i o n c o n t a i n e d i n t h i s handbook o r i n I t s u s e .
Ma t e r i a l
S e c t i o n s
The s t r u c t u r a l components r e f e r r e d t o i n t h i s handbook a r e o f s t e e l t oB S 4 3 6 0 , ' W e l d a b l e s t r u c t u r a l s t e e l s ' a n d / o r i t s r e l a t e d e q u i v a l e n t s .
The u n i v e r s - 4 1 bOMikrid. columns and t e e s c u t t h e r e f r o m , t h e j o i s t s ,
. X
c h a n n e l s , d g i v e a r i n g p i l e s and r o l l e d t e e s a r e g e n e r a l l y a s l i s t e d i nU
B S 4 : P a r t V u n i v e r s a l b e a r i n g p i l e s and r o l l e d t e e sP ! 9 8 0 t s , Ui n r e g u l a r d u B c a r e a d .
NA . i f i e u n i v e
. 5 2 ' t a p e - ed f l "
C o l u m , q c o r e - is e r i a l s i z e 3 $ 6 m - . * .
J I -f,
i s s e c t i o n , i s t e d s e p a r a t e l y , i s r o l l e d i n t h e0 -M a p p r o p r i a t e o n e t o be used a s6m ' . I t i.
F t s.An h i o n r s e d i o n t h a n t h o s e r o l l e d i s
Dimensional n i t s
The d i m e n s i o a - f i f U t - t i o n i ' . . ' a r e g i
c a l c u l a t e d p r o p e r t i e s ( c e n t . 6 i d a l
L i p p , moments o f i n e r t i a , eW,
c e n f i n i d t t L ý ( q c b i ) . - ' U i i t w , A S d r f a i e e r e
ra n c e s on d i m e n s i o n s a n d
Other u n i t s
r e s (mm) a n d t h e
e c t i o n a l a r e a s , r a d i i o f
i d p l a s t i c m o d u l i ) a r e g i v e n i n
i n square metres M2) . F o r
ference should be made o
T h e - u n i t s o f forcemass and a c c e l e r a t i o n a r e t h o s e o f t h e S y s t e m e
I n t e r n a t i o n a l ( S I ) . They a r e t h e Newton ( N ) , t h e kilogramme k g ) a n d t h e
m e t r e p e r s e c o n d p e r second m / s 2 ) s o t h a t 1 N - 1kgx I m A 2 . Thea c c e l e r a t i o n due t o g r a v i t y v a r i e s s l i g h t l y f r o m p l a c e t o p l a c e and f o r
c o n v e n i e n c e a ' s t a n d a r e v a l u e o f 9 . 8 0 6 6 5 m/s2has b e c o m e e n e r a l l y
a c c e p t e d i n s t r u c t u r a l e n g i n e e r i n g . With t h i s c o n v e n t i o n , t h e f o r c ee x e r t e d by a m a s s o f l k g u n d e r t h e a c t i o n o f g r a v i t y i s t h e ' t e c h n i c a l u n i t '
o f 9 . 8 0 6 6 5 N . I n t h e same way 9 . 8 0 6 6 5 k i l o n e w t o n s ( k N ) i s t h e f o r c e
e x e r t e d by m a s s o f 1 t o n n e ( 1 0 0 0 k g ) under r a v i t y , and 1 k N t h e f o r c e
L , ý . . ý ' ' " l e n g t h of s p a n ýi n m i l l i m e t r e s . : ý h : ý ' ý : < ý ; ý , ý , . . . , . -
" W ý ý ý = t o t a l d i s t r i b u t e d o r p o i n t l o a d i n Ne w t ¢ h s : a t ý ' : ý ý .- ýW a 2 - p o i n t l o a d i n Newtons. ý ý ý ; '
y .
, . :
; , , ý ; ý . ý. , . . . ý:.,.ý'ý`s hýýaYim__um ending m o m e n t n Newton m i l l i m e t r e s .
E - r e s u l t a n t o f p o i n t l o a d s R Newtons. ý ý , '
ýs . R ý , e t c . - r e a c t i o n a t A , B , o r C t c , i n Newtons. ý ,F - shearing o r c e i n Newtons. .
m - a p p l i e d m o m e n t n Newton m i l l i m e t r e s .
Mx ý ý ý ý - bending moment n N e w t o n m i l l i m e t r e s
a t d i s t a n c e X f r o m t h e l e f t hand s u p p o r t A . ý '
a x _ - d e f l e c t i o n i n m i l l i m e t r e s .
._ . , ý x f'"ýPe m aaýans.
d e r t h e l o a d i n Newton m i l l i m e t r e s .ý . . . ^m i l l i m e t r e s .
i o n i n m i l l i m e t r e s : :
e f l e c t i o n i n m i l l i m e t r e s .
a n s :. 1 x 0 s N l m m z. . .
., ý ý
e r t i a ' o f uniform s e c t i o n b e a m i n m m ý. .
.
r d , . t e f t hand su p p a ti ' i cu i i r i of x t e r n a l l o a d s ý ý
. ,
r d .
d i a g r a m s ) when c a u s i n g
tans are i v e n , but the s i g n s d e p e n d
wh i c h s e c t i o n i s b e i n g c o n s i d e r e d ,
R a i n e d , b Y in s p e c t i o n .
. ,
. W h e r e space p e r m i t s , g e n e r a l equations o r Mx n d x .
. ' ý a t a ny o i n t o f t h e b e a m , , and a l s o t h e e q u a t i o n t o t h e
e l a s t i c l i n e (ý, hav e been i n c l u d e d . . ý .
. , ý ý ý Va l u a o r . S l o p e . T h e s e m a y be u s e d I n e v a l u a t i n g h e
. ý . , . . . . ý . . angle o f ý r o t a t i o n f o r , r ubber i e a r l n g s a n d ý s i m i t a r ý . ,
' ' ý " c o n s t r u c t i o n a l e l e m e n t s . '
Simply supported beam T w o concentrated m o v i n g l o a d s ( c o n t i n u e d )
L
f -- _ L _ - - - -
w' 2
A
IL i i -mi
W ,
-
- - I -
M, , I
n
I f m > , t h e Maximum Bending Moment t any s e c t i o n
always occurs under W , ( t h e h e a v i e r l o a d ) , whether W i s
o n o r o f f the s p a n .
F o r a s e c t i o n d i s t a n c e X from A :
X < ( I - m )
1 ý 4m a x
- (L- , - X)X
L (I- m ) < , X
Mrr.x ( L- X ) XW,
I f n <m < t h e Absolute Maximum Bending
n
Moment ccurs under W , wi t h W o n t h e s p a n .
I f n <m > n t h e Absolute Maximum Bending
n
Moment ccurs under W , a t mid-span w i t h W o f f t h e s p a n .
N o t e : When the two l o a d s a r e e q u a l (W, = W2 n d n = z )
t h e c r i t i c a l v a l u e o f Fn . 0 . 5 8 5 8 .
n
Simply supported b e a m s c a r r y i n g s e v e r a l m o v i n g concentrated l o a d s
T h e Maximum R e a c t i o n a n d t h e Maximum T h e Maximum Bending Moment d u e oShear d u e t o s e v e r a l m o v i n g concentrated s e v e r a l m o v i n g concentrated l o a d s occursl o a d s occur t o n e support w i t h o n e o f the under o n e o f t h e l o a d s when h a t l o a d andl o a d s a t t h a t s u p p o r t . T h e l o c a t i o n producing t h e g r a v i t y centre f a l l l o a d s are e q u i d i s t a n tthe Absolute Maximum must be f o u n d b y from mid-span. T h e Absolute Maximum mustt r i a l . be determined b y t r i a l .
JWCMP&(h-1-2C) R.-R"J i m b y a p p l y i n g f o r m u l a
i Li g i v e n i n N o . 8 t oR A
a >CR .
MD-L - ( A - 1 - 2a -P(
b+2.)
II e ach o a d .
8 - P I
. 4hP. P
.
1 ,
RAF-1
2 3P13- RA=RB=P d D3 " - 6 4 8 E I
I n c a s e o f beam s u b j e c t t o d i s t r i b u t e d l o a d s , l o a d s y m b o l , W, i n d i c a t e s t h e t o t a l l o a d o f t h e beam.' F o r e x a m p l e , I n c a s e o f a beam s u b j e c t t o u n i f o r m l y i s t r i b u t e d l o a d , w , W q u a l s wt where i ss p a n l e n g t h .
No. Load condition Bending moment R e a c t i o n f o r c e D e f l e c t i o n
a n d shear s t r e s s
1 1
1 2
P P P
MC=M8=D 16=5piAA AN 4 12
RAP
An
R A =RB2
d-53PI"
1296EI
1 9
20
W W fT -Lz; -> 1
RA RM
N "--JP- T t
R o - R e - I V 1 1 1 ' 7 . 1 1 - 4 0 1 - 4 0 12 WEi
m- \W
RA = R i r-- i
M A R A
-MA=-MB=MC=Lt MA=Jb=f8 2
I f i
d-
I d-
dmm-P1 3
1 92EI
I n c a s e - o f beam s u b j e c t t o d i s t r i b u t e d l o a d s , l o a d s y m b o l , I N , I n d i c a t e s t h e t o t a l l o a d o f t h e b e a m .
f b r e x a m p l e , i n c a s e o f a beam s u b j e c t o u n i k i r m l y i s t r i b u t e d l o a d , w , W q u a l s v 4 where i s
N o . Load c o n d i t i o n Bending m o m e n t . . . R e a c t i o n f o r c e D e f l e c t i o n
and s h e a r s t r e s s ' -
I n c a s e o f beam s u b j e c t t o d i s t r i b u t e d l o a d s , l o a d s y m b o l , W, i n d i c a t e s t h e i t o t a l l o a d o f t h e beam.F o r e x a m p l e , i n c a s e o f a beam s u b j e c t t o u n i f o r m l y d i s t r i b u t e d l o a d , w , W q u a l s w i , where i ss p a n . l e n g t h .
T h e v a l u e s g i v e n i n t h e s a f e l o a d t a b l e s a r e b a s e d on t h e a l l o w a b l e
s t r e s s e s i n BS 4 9 ' a s f o l l o w s :
T h i c k n e s s f m a t e r i a l Grade A l l o w a b l e s t r e s s e s NImM2)o f s t e e l
(mm) B e n d i n g S h e a r ( l ) B e a r i n g
Up t o a n d i n c l u d i n g 40 43 165 100 190
O v e r 40 150 90
Up o a n d i n c l u d i n g 65 so 2 30 140 260
O v e r 65 Y , / 1 . 5 2 ( 2 )
Up o a n d i n c l u d i n g 40 5 5 2 8 0 170 320
O v e r 40 2 6 0 160
N o t e s : 1 ) On n s t i f f e n e d w e b . ( 2 ) Ys- y i e l d ' s t r e s s , t o b e a g r e e d w i t h t h e
m a n u f a c t u r e r and n o t t o exceed 350NIm M 2 T h i s a p p l i e s o n l y t o u n i v e r s a l column
s e c t i o n s and p pound s e c t i o n s n d , i n t h i s handbook a f f e c t s c e r t a i n In i v e r s a l coluvw"Muspitly f o r which a v a l u e o f Ys- 325N/mM 2 h a s been
a s s u m e d .
t
I
we b s h a v e b e e n c a l c u l a t e d i n2 8 a ( i ) o f B S 4 4 9 , n a m e l y W-pctB
t r a t e d l o a d i n N , b u t t a b u l a t e d i n k N .
u t s a s g i v e n i n BS 4 4 9 , Clause 3 0 a .
3 ) / t , i n which
r o o t f i l l e t s
i n g s , i n w h i c h
o f s i m p l y s u p p o r t e d beams
la t eh s h a l l n o t be t a k e n a si m p l y s u p p o r t e d beams
f o r a n i n t e r m e d i a t e b e a r i n g o v e r
u s , u n l e s s t h e web i s s t i f f e n e d .
0 IMMMOMM he d i r e c t i o n b e a r i n g s t r e s s a t t h er o o t o f t h e w e b s l i m i t e d t o t h e V a l u e s g i v e n i n B S 4 4 9 , T a b l e 9 and
i n c l u d e d i n t h e I
The l e n g t h o f w e b r e s i s t i n g b r u s h i n g i s ' d e t e r m i n e d o n h e ,a s s u m p t i o n t h a t t h e l o a d i s d i s p e r s e d t h r o u g h t h e f l a n g e and t h e b e a r i n g
a n d / o r f l a n g e p l a t e a t an a n g l e - o f 3 0 0 ( B S 4 4 9 , C l a u s e 2 7 e )
C l a u s e s 1 4
W e r e b e n d i n g and s h e a r s t r e s s e s , o r b e a r i n g , b e n d i n g and s h e a r s t r e s s e s ,a r e c o - e x i s t e n t , t h e b e a m s h o u l d b e ' C h e c k e d i n accordance i t h B S 4 4 9 ,
C l a u s e 1 5 t o B S 449 i n c l u d e s t h e r e q u i r e m e n i t h a t t h e m a x i m u m d e f l e c t i o n
I n a d d i t i o n t o t h e c r i t e r i a covered b y t h e u s e o f d i f f e r e n t t y p e f a c e s ,two o t h e r m a t t e r s r e q u i r e c o m m e n t ,
examined a s i n d i c a t e d above L i l l
d e f l e c t i o n e x c e e d i n g 1 / 3 6 0 t h
( a ) S h e a r c a p a c i t y . W h e r e t h e s h e a r c a p a c i t y o f t h e U n s t i f f e n e d w e b i s
l e s s t h a n t h e bending c a p a c i t y o f a b e a r n , t h e s a f e l o a d i s c a l c u l a t e d
on t h e a l l o w a b l e a v e r a g e s h e a r s t r e s s g i v e n i n BS 4 4 9 , T a b l e 1 1 , and
i n c l u d e d i n t h e t a b l e on page 2 2 . Such c a s e s a r e marked t i n t h e t a b l e s ,
t h a t t h e l e n g t h o f s t i f f b e a r i n g and t h i c k n e s s o f f l a n g e p l a t e o r p a c k i n g
( i f a n y ) p r o v i d e a s u f f i c i e n t a d d i t i o n a l l e n g t h o f w e b i n b e a r i n g ( s e epage 2 2 ) ,
exceed t h e b e a r n c o m p o n e n t o f t h e d i r e c t b e a r i n g c a p a c i t y o f t h e w e
a t i t s j u n c t i o n w i t h t h e f l a n g e . The d e s i g n e r s h o u l d t h e r e f o r e e n s u r eI
( b ) Web r u s h i n g . Many f t h e l o a d s t a b u l a t e d , i n t h e v a r i o u s t y p e
The a l l o w a b l e c o m p r I e s s i v e s t r e s s d u e t o bending about t h e x - x a x i s f o ru n i v e r s a l beams a n d columns, j o i s t s and channels s t h e l e s s e r o f t h e
v a l u e s O f Pb , g i v e n i n T a b l e s 2 and
'
3 a , b o r c (depending on t h e g r a d e o fs t e e l ) i n B S 449. The a l u e s i n ' F a b l e 2 a p p l y when the c o m p r e s s i o n flange
i s SO S u p p o r t e d that l a t e r a l i n s t a b i l i t y i s obviated. When th e c o m p r e s s i o n
O u t l a t e r a l r e s t r a i n t and having h e ends o f t h e c o m p r e s s i o n . f l a n g e
T a b l e 2 i s g i v e n a s L , w i t h t h e s a f e l o a d t a b l e s .
which m a y be u
T a b l e 3 a p p l i e s . Th
f l a n g e i s unsupported o r
E x a m p l e : F i n d the a l l o w a b l e s t r e s s ,Pb , ,
a nd t h es a f e
u n i f o r m l y
i s t r i b u t e d l o a d , W, f o r a 533 = 210 UB 82 i n g r a d e 4 3 s t e e l spanning 7 m
E f f e c t i v e l e n g t h = 0.85 x 7 00 = 595cm ( s e e BS 449, Cla use 2 6 )
p a r t i a l l y r e s t r
Li f f i c i e n t l y S u p p o r t e d l a t e r a l l y , t h e appropriate
D / T = 4 0 .
u m e f f e c t i v e l e n g t h o f compression f l a n g e
hout r e d u c t i o n o f t h e a l l o w a b l e bending s t r e s s e s i n
The s a f e u n i f o r m
From BS
d i s t r i b u t e d l o a d , W= f Z / L
= (8x1 19X 7
= 245kN
103/7000)N
L a t e r a l i n s t a b i l i t y i s n o t a c r i t e r i o n f o r t h e s e s e c t i o n s w h e n b e n t
about t h e y - y a x i s a n d t h e a l l o w a b l e s t r e s s e s i n T a b l e 2 a p p l y ,
N o t e ý T h e allowable s t r e s s e s i n B S 449, Table 2 are given o r ) p a g e 22 a n d Tables
3 a , b a n d c o f t h e standard are r e p r o d u c e d o r ) the following p a g e s ,