reinforced concrete designers handbook 10th edition reynolds steedman
TRANSCRIPT
&FN SPONT ay l or &Francis G rou p
1 9 8 8
. shou l d
Copies
of
fi,
for
A sreq
A ctu al
Characteristic
T ransformed
K dS
Factors
fs2
'ey
W idth
U l timate
Nu mber Characteristic
Characteristic
L imiting
T otal
Depth
Shsu
T d
U'crit V
/ 3 , i/ i7 17 ns
pPi6 VPart I
E CONOM ICA L
a
no
by
to
W hen
be
A ccording
for
it
of the Desig n B u il ding s.
I
( pw) 2 ] ,
VS2 ,
ov er which =
by
T he
is
1 4Safetyfactors, l oads and pressu res
1 6 2 0are
l oads.
bel ow
Dh, whereis
k Dh, whereis
al so
is
1 6for
0 ) ,
9 0
\ l
Fh
H orizontal
( 1 sin
and those in section 1 0 . 3hav e been contribu ted byJ .G .M .W ood,
the
in
SING L E -SPA N
1 of
( or +
one
may
T his
and
and denote
from
and for
1 ) and
1 . 0 , 1 . 4 1 1 . 0
and from k 1 1 . 0 ;
H av ing
at
andE arl ier
and
+
+i. 6 Q k .
accou nt
g eneral
0 7 5 K
'tT his
etc. , +J 2 1 2
is I
F1 F3 -I-T he
where
to
and
which
fol l ows
can
where
( fifm) 2jI1where 1 1 / 2
H owev er,
( i. e. for
0 . 7 9 ( 1 is
=
( see
andof l . 6 4 s
or
is by Once
actu al l y
is
that
2 5 0 = =0 . 7 2 5 .
may 4 2 5
in
; fcr if; T he
1 ) .
mu st wherethe
g iv en
forand
for
with1 0
mu st
su fficient
Resistance
appl y
in
can
1 . 1 5 ,can
( 0 . 6 is
in
mu st
H owev er,
corresponding
4 6 0
set
of
and
0 . 1 :
0 . 5 , 0 . 1 ,
k 3 4 x
k 1 )
are
and
does
div ided
T he
For
may
M d/ bd2 ) for 1 5
is cal cu l ated
A ,,
and
M d/( d
1 0 0 0
I) ,2 0 0 / E r
; p)
g iv en of
1 3 6 ,the
is
1 3 7 .Since
ansformed
x ) / ( h x ) .
do
to
may
are
and
0 . 4 E vJ / 2
B rief
0 . 4 5
+
B y
k 1 x b + A ,2 fY d2Mk 2 x ) + d')+
are
O. 7 fcu / y m, k 2=0 . 5 0 . 6 0fcu / y rn,k 2=0 . 5
dc, O. 7 2 j ,
a
A 3 2
with1 d'/ h) .
In
and these and
Charts
of permitted
is
( h/ 2 )
h/ '2 )
h/ 2
bel ow
is
in
x
a'
4 / 9
=1 ( 7 N/ 6
( 2 / 3 )
M Y / M U Y
and
may can
acting M d/ Nd.T he
d')
1 5
and
is
+ f,,) / 3 3and and
and
=0
Nd3 8 1 / fi2 bd { ( fcrK i/ 2 )
1 5
[ fcr(
If
is
of
0 .
A tr J / A tr.
If
and
then
g reater
fl 2can
is
=bd/ 1 2 )fcr
If
T he
is
A n
N) NbaI) .
h d,7 ( h d') / l l
across
8
1 Nbal / bh)0
6 0 0
If
0 . 1 5 E ( h/ r) 2 .
0 . 6 E ( h/ r) 2 .
2 5 08 @ 2 5 0 3 7 5 6 @ 1 5 0 8 @ 2 0 0 8 @ 2 2 5
1 2 @ 2 7 52 2 51 2 @ 2 5 0
2 0 0 '
. 1 IA T 'l . . I I anu raii.aic Notes
T he
E x cept
+
of
and
6 . 9 3
in
T A ) k hc/ k C,
=
Pressu res behind wail sT he
where
T he
is
T he
is
2 F,,5 / 3 ,
neg ativ e
( 2 F,,5 / 3 )
otherwise.
k N
+
\ fl
M / FV.
situ
=K 0 . 5 x ,,.
E l ectronic
=3 01 . 5
at
1 0 0E l ectronic
Du ring
of
1 0 2E l ectronic
1 0 4E l ectronic
stru ctu ral
X 2 ( X ) 2 ,
iosFu tu re
1 0 6E l ectronic
P1
safetyfactors
fk / Y m for
_ _ _ _ _ _ _ _
1 . 4
0 . 81 . 0
.Shear
I 1 . 5
1 . 2 5 *M ax imu m+
ex cessiv e =1 . 0 5
characteristic
ends
TTL oads 1 . 6 Q ,,- remaining
on
fix ed
For
RS8 1 1 O:
on
+
A SFor
Vertical
throu g hou t
4 -. ,-o
5 ,,en 00U
corresponding
2
0000I-0a C
1 4 4 to
000a
00
0
G l ass-bl ock
2 . 6 3
3
1l b/ ft2
1 0 %
1 . 2 5 %
5 % 1 0 %
004
U ,U ,U ,'-40
00
42 . 5
U ,4 -0'a,a
E
c)-a
aa
a
metres
. 0Partition
1 0 0 0
1 2
( minimu m)A rea =0 . 4 3 3 1 2 h,=0 . 8 7 ( 1 h
1
9 ,
5-0E 'a, 0
8 . 2
. ,5 . 0
3 1 . 8
Notation D1 weig ht
9 8 0 7
v ol u me
=+hIf D1 ) :D,1 I
D1 h0 fi)+ =9 8 0 7 N/ rn3 6 2 . 4
I
'nil
3 . 6
.
.B ars,v estibu l es
nil
d). E
per )nil
, 3 . 0
.L ig ht
9 . 0
7
I-
4 . 5
} U ,
tL l
00
0 )
5 2 . 5 ' 1 2 0 . 9
}nil
l oad
U , . u 6 0 0 mm
1 1 8L oads
Fa
( 1 Fd( l
0a
00E
L5 6 ffmpl u s tender8
3 mpl u s tender
3 2 ft6 in( tank )4 . 7 m( tank )
y
T otal
-ao-B Oooi2 1 . 2 m 2 0 . 7 m1 5 . 2 m1 3 2 0
7 . 9 m 6 . 1m3 0 0
tons C0a
a
m
61 6ft1 . 8 3 m
2 . 4 4
8 5 08 5
'7 5I
T ractor
0 00 0
49 ft
1 . 3 5 m I '. I8 ffH 9 . 7 5 m
k N
3 2 0
. 2 . 7 4 m
9 l . 4 3 5 m l . 3 7 mG au g e driv ing
driv ing
dimensions
U nl ess
No
.From
H BDu e to v ehicl e as fol l ows:per wheel=2 5 0 0 /newtons ( where L imit of v ehicl ej = nu mber of u nits of H Bl oad)111mI O. 2 m. J( whichev er has most criticaleffect on member beingconsidered)
(* B u t
2 SOk N rn_ fi. 6rn_ fl . 6 mJ O. 8 rr 0
=
fh'
in =
J
f=
L oad =1 . 1N/ mm2
Dispersalof l oadconcrete sl ab. 1 / 6l oad transmittedbythis sl eeperDispersalof l oad throu g hasphal t etc.su rfacingI. .ov er which sl eeper_ _ _ _ _ _ _ _ _ _transmits l oad to bal l ast* aorDIspersalof concentrated l oad beneath sl eepers0 . 4m
1 1H A
U )
E I-
I- 0Ce
5 -.
U )
7 Smm. $3 7 5 mmDirection9 0 0 mm 3 fttrav elH
C)C)iB m
6 . 1m 1 . 8 mmm-u9 0 0 mmIi
mrnl _ f_9 0 0 mmtrav el CeO4 ---* - 3 ttmm2 0ft
0
C)
0U )
l oaddL rY ) 1 )Su rfacing/ /a=+I /i './ a contact l eng thB lb width of ty reI( = 7 5 1 0 4 5 0 mm or3 to l 8 in)I/I/'.W heel -l oad dispersion area =AxBC ov eral lwidth ( two sl eepers)1 l eng th of sl eeperA x l e-l oad dispersion area =AxB
1 2
2
area 2 5 %
1 / 5
ci,0 )C)CeCeI-0 )3 .0 E
2 0 2 1 . 8 60 2 0 0 8 5 02 . 5 86 - 1 1 5 1 3 0 1 0 0 1 0 3 . 0 1 00 1 8 0 2 0 0 2 1 5 1 8 2 0 2 1 . 5 2 . 0 699 . 52 0 0 2 0 3 . 2 1 06 3 1 0 3 1 3 3 2 . 3 76 2 8 0 1 1 may v ary du e3 0 0 3 0 3 . 6 1 20 4 6 0 4 8 0 5 1 0 4 6 4 8 5 1 2 . 6 861 2 tomak eand5 0 0 5 0 4 . 0 1 30 7 2 0 8 1 0 - 7 0 7 2 8 1 3 . 1 1 031 4 u seofcrane
E l ectric
7
1 5 0 0
Vsis 2 s3
1 . 1
0 . 9
1 3Rel ation
( m/ s)
B A SIC W IND SPE E D ( mis)5 41 01 21 41 61 8
I 1 0
E E 4 )
m 5 0 m
0 . 1 5 b,whichev er
are described in more detailin section 2 . 7 . 2 . FOR
1 4
6 b
i1a= h
1 0 + 0 . 7 0 . 6 0 . 7
0 . 6 + 0 . 6 0 . 5 0 . 8 0 . 8 -+ 0 ,8 0 . 7
C5 )
1 . 4 1 . 0
2 . 0 1 . 2
1 . 2 1 . 2 1 . 2 1 . 1 1 . 1 1 . 1 2 . 0 1 . 02 . 0 2 . 0 1 . 52 . 0 1 . 5 1 . 5 1 . 5
1 . 0 1 . 2 1 . 0 1 . 0 2 . 0 1 . 5 1 . 5 1 . 0 2 . 0 1 . 5
1 . 5 1 . 5 1 . 51 . 0 1 . 2 1 . 2'I,CV 5 )
ciI-5 )C
1 . 0 1 . 0
1 . 0 1 . 0 1 . 0 1 . 0 1 . 0
l . 0 ( 0 . 5 ) 1 . 0 ( 0 . 5 ) 1 . 0 ( 0 . 5 ) 0 . 9 0 . 6 0 . 2
0 . 8 0 . 6
1 . 0 ( 0 . 5 ) 1 . 0 ( 0 . 5 ) 1 . 0 ( 0 . 5 )
CV
5 ) C1 . 0 1 . 0 1 . 0 1 . 0
1 . 0 1 . 0 1 . 0 1 . 0
2 . 0 2 . 0 2 . 0 2 . 0 1 . 8 1 . 8 1 . 8 1 . 81 . 5 1 . 5 0 . 52 . 0 1 . 8 1 . 8 0 . 9 0 . 51 . 5 1 . 5 1 . 4 1 . 40 . 9
Ou tl ine of basic procedu re 1 .Cal cu l ate characteristic wind pressu re W kas indicated onT abl e Determine appropriate ex ternaland internalpressu re Co.efficients from T abl e 1 4or T abl e 1 5( top. and Centre) .3 .T otalwind force F on area Aof stru ctu re as a whol ew5 A ( C,,,5 where and are ex ternalpressu recoefficients on windward and l eeward faces respectiv el y .T otalwind force F on area Aof particu l ar face of stru ctu re=
wind force F on cl addingel ement =w5 Awhere C,,.andare ex ternaland internalpressu re co.efficients respectiv el y .T o obtain totalforce on entire stru ctu re, div ide stru ctu re intoparts, determine force on each part bysteps 1 3and then su mresu l ts v ectorial l y .Consider appropriate v al u e of Is for eachindiv idu alpart ( bu t for approx imate anal y sis, u se of sing l e v al u eof wkcorrespondingto heig ht to top of bu il dingerrs on side ofsafety ) .A l ternativ el y , first cal cu l ate characteristic wind pressu re.Nex t,obtain v al u e of force coefficient C1from T abl e ( bottom) .T hentotalwind force on area A=W 5 A C1 .For g reater accu racy ,su bdiv ide stru ctu re and su m indiv idu alresu l ts v ectorial l yasbefore.
0 . 6 0
0 . 2 5
0 . 7 0 0 . 7 0
+ 0 . 7 0
0 . 6 0
+ 0 . 8 0 0 . s0 0 . 8 0
0 . 7 0 0 . 8 0 0 . 5 00 . 5 0
5VA L U E S
0 . 7 0
0 . 6 0
0 . 5 0 0 . 2 0 0 . 5 0
0 . 81 . 0
! i heig ht
W ind
0 . 3 0 . 3
FOR
1 . 0
b 4 8 r B etween
H Ib 6 r
0 . 9
1 . 10 . 6
b1 2 r
1 . 1
b 6 r
0 . 7
Pressu res
1 0 . 1 . 1E ffect
=( k 2 D2+
+ +
k 2
1 6
=k Dh sin2
F ( 9 0Force F F1
0 ) : F1F;0 ;
ang l e
Incl inedIncl inedou twardsinwards
Vertical
( 01 >I-,enenI)0( 0I-U( 5
Cssin( fl k _ [ ( + l ) sin$ jsin2 fl
= tan sin
sinfl sin( / 3 0 )
sine+ sinfl j sin( fl O)1 2 sin 1
k( / 30 ) 1 2 C0 5
[ sin( 1 1 + $ ) sin( / 3 4 1 )
0C)Cs
--0
k 1 = kFsin( 9 F
k 3 = kk 1= cos2 0 =. . j [ sin=k=,J [ 2
0 ) : n
=0 ) : sin + 00 U
= 0 )
300)
30)
to
450
'I,4)I-C
4)4)0.
35)
24)
23)
24.5)
25)
30)
250
35
35
25
45
.
=1+k2L___(1_fl)]}
I
D1=62.41b/ft3
lOOfl)
Cohesion
IC,,0
4)0,4)0
0
4)4)
} l9
q2
I-(000= 0
9
50100
18'14 02'15
2+sinO
1
I-_____500
60
0.610
0.589
25
34'300
30'45
0.821
0.5 19
0.7810.7700,7600.7510.7430.7350.7270.7250.7110.699
0,300
0.556
0.5140.5530.53
0.4750.459
3341'linl.50.6920.2860.217
450
D1
D2
0.6
5560
= D1 h{ l +_ fl ) ] } +D1 h0= D( h0
is
q h/ q 0
8 4 0 0 2 5 .0 . 7 5 6 1 8 . 7 5
0 . 3 4 0
tan 4 7 . 0
( this
=( k 2 D24 - D,,,) ( h h1 .
2 Ch IIC,. . ,-
1 9
9 . 8 1 0 . 6 D
--- . ( see
2
2 C
0C',4 )C-C',CO0 )C-0 . .4 )C. )
Dr/ tan8 4 0 04 7 . 0 2 r/ tan 3 / 0 . occu rs r/ tan1 . 5 / 0 ,2 6 8 5 . 6 0 1 0 . 8 3 / 8 . 8 20 . 3 4 0 1 e 3 4 0 . 2 8 8 .3 7 . 1 1 0 . 7 0
00FM2 00I-.00- k 2 N\g o =k 2 N[ d+( b1 2 )+h] ( 2 h a)'-0 5I-VEVV( d)Indefinite ex tent( e)L imited ex tentA ' =cross-Sectionalarea45 A '
B )F0 =n,h1= k 2 n ( force per u nitl eng th of wal l )approx ,NNote:pressu res du e earth retained bywal lto beaddedFor max ,, stope +0 :k=For mm sl ope Uk = k 3For v al u es of k 1 ,k 2 and see1 8 .a = +
2 1Pl anDr e hktantanG '
tan
k q ,,
d/ 4 .For
2 52 52 52 5 e the=hktan M u l tipl ier0 I, I I,aiil ai a a Ittiti t It I I i_ _ I I I I I( a)Core fl owT y pes ofE l ev ationof horizontal
Powdered 0 . 7 5 0o0 . 6 0 0 0
max , max max ' q h max q h max '
Dr
q hmax =
q , max=
max=Dr Dr
where1
i I I I I I III I I II''''II III I I I tI, I II0of h/ h0
du e
1 the
= +
Partial1 j 3 3 " \ )
3 0 / 1 1 1 shou l d
2B A SIC
l oads
rate
=rate
I jU
tO_ _ _ _ _ _U niforml ydistribu ted 0 5 U T tt-} 1 4 -! 0 . 5 1 1 1 1 1 1 1 1 10H IU ffl tt
dbdddcSddbdoodddddd. -Cantil ev er_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _0 . 1 0_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _+ VE_ _ _ _ _ _ _ _Propped cantil ev er y e4 -10 D51 1 1 1 1 1 1 1 Q 5 _ _ _ _ _ _0 . 0 5 I force( I l i/ l it I l il t!NA .( =coefficient xtotall oad)Il l l l l l Iil l l fl l Il l tl Il iIloIl '!1 1 1 1 1 1 1 1 1 IE nd span IJ _ l -1 4 + t IT U 't1 1 1B Menv el opes du e fo0 . 0 5 1 1 of l oad on span ortil l !on adj acent spans.( A ctu al_ _ _ _ _ _ _ _ _ _ _ _ _/ /env el ope depends on nu mberIl ljL I-I-Il l/of continu ou s spans andIl -Ft T hUi IA ' Ieq u al ityor ineq u al ityof spans)fl 4 l o. s+ v e( Il l Il l IlIII!Il il l Il l Il Il tIInterior span0 . 0 5_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _E nd conditions and_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _owIodooodddd. -B endingmoments ( =coetticient xtotall oad xspan)CRIT ICA L
opiu onaiT o
CP1 1 O:
For +
1
I
La(1a)J
t"Dzz
load = Fcsl..i7fluReactions:
Total load
a:
x
fi):
when
(1fi):=a
&Fl[x(la
=*(1 a+fl)(1afl) (1 a+fl)Fl atF13(la.+
a)4
x)
(lxfl)2]when
(fl2j
3
F13x(2_25fl)[9(l
= ____________________162E1
fl)
160E1(1afl)(
_________3
I
162E1
Total load = F
x
a:
a(1a)
x)s2MxIF1[
[{1
(4a25)2F13/{1920(1
Fla(la)
(F13(la)x/6E1)[a(2a)x2]when x >a:
(Ft3
x)/6E1)[x(2x)a2]
= F13a(l
a2)/3]
MLMR
L4,=MLMR
ML(lx)
[x(l
C
RR
Bending
4x(1
4F1
OR
(F13x/24E1)(1x)(l
x2)
5F13/384E1
RR 1
Bending
MR
4F7{x(1x)
F13x2(1x)2/24E1= F13/384E1
Shearing
(F/3)(26x
MR
x)(2x)
2F1/9
at
1/
2F12/45E1;OR =+
x(lx)(2x)(4 +
3x2)F13/1SOEI
Shearing
20x
Fl/10
F1/15
(Fl/30)(10x330x2
3)
F1/23.32
.jO.3)1 fromL
0
(F13/60E1)x2(lx)2(3 x) F13/382E1
$Reactions:
RR
when
vs
Bending
MR
o
a5
(F13/48E1)x(34x2)
F13/48E1
RR
4F
Bending
MR
M5
(F1/8)(4x1)
M5
(Fl/8)(34x)
R
Deflections:
a5
(Fl3
4x)
load = FF(xa)
(1afl)
0
r(xa)2
0
/3)2x]
+ a /3)2(1
a /3 4x)]
(xa)(lafl)[(1afl)
0
(xa)2
(1afl)F!3
--I 10x2(1+2a/3x)60E1
(xa)
(1afl)F!3
fl)2+iOxa3a2}(1+afl5x)]
(1_a_fl)2
0
(F13x2/&EI)(2
2$
2/3
3(1
(1 +a_fl)2(1 +a$Sx)]
ends
________F
F
Fl(ax)
x2(3ax)
a2(3xa)
F
z rDcM
cM
Total load = F
=F
1---L
0
when
if
ifz z z
IiIIIlIIIlIIIIIHIlMhIIIIlI
F(1x)
4F1(1x)2
0
0;
F12/6E1IDeflections:
(F13x2/24E1)(6
F13/8E1
1
F1/8;
0
4x)1]
9F1/128
5/8
OR
F12/48E1
(F13/48E1)
x)(32x)F13/185E1
0.5785
Apex at Ui. endShearing
F(1x)2
8R
F12/12E1
(F13x2/60E1)(10
+
Apex at r.h. endShearing
F(1x2)
0;
Ft2
Ai,ex at Vi. end41Reactions:
Shearing
2x
2F!/15;
lOx+2)(1
0;
F!2
Apex at r.h. endReactions:
x2)
0
.J0.45
0;
F!2/40E1
2x2)F13/120E1
F
Ft
F(lx)Slope:
Ft2
(3
F13/3E1
1
=
when
Bending
0
0;
F12/32E1
= x2(9
(F13/96E1)
1)(5x2lOx
F13/48
1
2 70 . 40 . 30 . 20 . 10 . 1 0 . 20 . 5 0 . 6 0 . 7 0 . 8 0 . 9T otal wl ( 1 -a-j 3 )WB endingmoment =coefficient xF!Position of max imu m moment= from l eft-hand su pport0 . 41 00 . 91 30 . 80 . 70 . 5T otall oad
B endingmoment =coefficient xF!Position of max imu m moment=if!from l eft-hand su pportO0 1 5 \/0 0 0 7and beams of one span_ _ _ _ _ _For=0 . 3 7 5and0 . 2 5 =0 . 1 0 4 W0 . 0 3 9 0 w!=0 . 3 7 5 w! ) .For0 . 7 5 0 :0 . 0 2 5 W0 . 0 0 3 1 w!=O. 2 5 w1 / 2 ) .For 0 ,6 2 5 =0 . 1 3 0 W=0 . 0 2 4 4 w!=( 1 / 2 ) 0 . 3 7 5 w! ) .=0 . 0 3 9 00 . 0 6 6 5 w! .Simil arl y , 0 . 2 5 0 . 3 7 5 : =0 . 1 2 9 W0 ,0 4 8 9 w! .For 0 . 6 2 5=0 . 0 4 9 W0 . 0 0 9 2 w! .0 . 7 5 0 :CRA 0 . 1 1 0 W0 . 0 1 3 8 w! . 0 . 0 4 8 90 . 0 7 0 . 3 7 50 . 0 9 7 W0 . 0 6 6 7 w! . 0 . 2 5 =0 . 3 7 5 , =0 . 1 0 4 W0 . 0 7
3u nits 3u nitsI2u nitS0 A l fi( C) A( d)AQcc= O6 2 5 00
9can
CA B IA B C8 4
M B A
CA B IA B CRA
FA B )=FRA )
CA B IA B CB A
FB AAC
A
D=
= _ or_ _ or_ or_ _ j =
z 'A S
CRA--a) F F! ) Fl ] F! j F! )$ 1 2 ( j +jfactor
0 . l 0 4 F
A nynu mber of l oads ( j ) spaced,+
O5 F 0 5 F
or u se
F( total )
Parabol ic'
L aiJ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _M IIIT II1 U U IIIIIIIU IIT IFIIIT T IT IT T T n,. . . _ =minu sA nynu mber of l oads 3 ( CA R
3 10 4 0 6 0 . 7 1 01D0 9 for CA B
to /0 1 4 8 2T otall oad F=wl ( 1B0 . 100 1 0 2 0 41 0fi for CA Bx
tothen FE M B A =CB Ax
0 1 1 1 9oad F = a / 1 )
beams
whil e where
3 2
=
=( F V. )
coefficient
5
M max
W 1 ST+ f] M ST
SF du e to restraint B M sSF du e to l oad ( if any )diag ram V7= +VM )
1 / 9 . 1
1 / 1 2 . 5
1 / 1 1 . 6
1 / 1 6 . 0
1 / 1 0
1 / 1 0
1 / 1 2 1 / 9 1 / 1 0 1 / 9 1 / 1 2 1 / 2 4
1 / 1 0 1 / 1 6
a
01 . 0 0 0 0 . 0 6 7
+ 1 . 2 6 7 + 1 . 0 0 0 +
1 . 0 0 0 0 . 0 0 5
1 . 0 0 0 . 1 . 0 0 01 . 0 0 0 + 1 . 0 0 01 . 0 0 0 + 1 . 0 0 0- 1 . 0 0 0 0 . 0 5 3 1 . 0 0 0
1 . 2 5 0 + 1 . 2 6 8 0 . 0 8 9 1 . 2 6 8 + 0 . 3 4 0 0 . 0 9 1 0 . 0 2 4 1 . 5 0 0 1 . 5 0 0 -+ 1 ,2 0 0
0 1 . 2 0 0 1 . 2 8 6 + 0 ,4 2 9 1 . 2 8 6 1 . 2 6 3
1 . 2 6 3 B f B f J fK tH tA dj u stment span
>.
0 . 1 0 1
[ 0 . 1 0 7 ] [ 0 . 0 7 1 1
=
A0 . 1 2 7
r
AdA E E 0 . 1 2 1
L .
4 1
max .
0
A
0 . 1 2 4A
0 . 0 8 9 0 . 1 3 30 . 1 3 1 0 . 0 9 8 0 . 0 9 8 0 . 1 3 1 A0 . 0 5 0A
A
A0 . 1 0 4-A0 . 1 2 7 0 . 1 2 7
[ 0 . 1 3 3 ] ( 0 . 1 3 3 ) 0 . 1 3 3 0 . 1 4 9AA0 . 1 3 2 0 . 1 0 9 0 . 1 0 9[ 0 . 1 3 1 ] ( 0 . 1 3 2 ) ( 0 . 1 3 2 ) ( 0 . 1 4 4 )0 . 1 4 9 0 . 1 3 8 0 . 1 3 8 0 . 1 4 9AA
A
A0 . 1 3 30 . 1 0 7 0 . 1 1 514Qo0 . 1 5 6A O. 0 9 5 0 . 0 9 5A
A
A 0 . 0 8 9 0 . 1 3 4A0 . 0 5 6A
A
A0 ,1 3 2 0 . 0 9 9 0 . 0 9 9 0 . 1 3 2A
0 . 1 4 6 0 . 1 3 6 0 . 1 0 4[ 0 . 1 3 4 ] [ 0 . 0 8 9 ] [ 0 . 1 3 4 ]( 0 . 1 4 5 ) ( 0 . 1 3 4 ) ( 0 . 1 4 5 )0 . 1 5 1 0 . 1 3 4 0 . 1 5 1A A0 . 1 1 1 0 . 1 1 1[ 0 . 1 3 2 ] [ 0 . 0 9 9 ] [ 0 . 0 9 9 ] [ 0 . 1 3 2 ]( 0 . 1 4 5 ) ( 0 . 1 3 3 ) ( 0 . 1 3 3 ) ( 0 . 1 4 5 )0 . 1 5 0 0 . 1 3 9 0 . 1 3 9 0 . 1 5 0A0 . 1 1 7A
A
A0 . 0 6 8A 0 . 1 0 50 . 1 3 5 0 . 1 0 9
0 .moa
0c000 . 1 8 8A
A 0 . 1 5 0A
A
A 0 . 1 0 7 0 . 1 6 1A
A
A
A
A 0 . 1 1 8 0 . 1 1 8 0 . 1 5 8A 0 . 1 8 8A
A 0 . 1 7 5A0 . 1 7 5A0 ,2 1 3A
[ 0 . 1 0 7 ] [ 0 . 1 6 1 ]( 0 . 1 7 4 ) ( 0 . 1 6 1 ) ( 0 . 1 7 4 )0 . 1 8 1 0 . 1 6 1 0 . 1 8 1A
A
A
A0 . 2 1 0A[ 0 . 1 1 8 ] [ 0 . 1 5 8 1( 0 . 1 7 4 ) ( 0 . 1 6 0 ) ( 0 . 1 6 0 ) ( 0 . 1 7 4 )0 . 1 7 9 0 . 1 6 7 0 . 1 6 7 0 . 1 7 9A A
A A
A0 . 1 3 2A 0 . 1 7 10 . 2 1 1 0 ,1 8 1a" a0
0 . 1 6 70 . 1 6 7
A0 . 1 3 9A 0 . 1 5 6A
A
A [ 0 . 0 9 5 ] [ 0 . 1 4 3 ]( 0 . 1 5 5 ) ( 0 . 1 4 3 ) ( 0 . 1 5 5 )0 ,1 6 0 0 . 1 4 4 0 . 1 6 0 A A
A 0 . 1 3 3 A
0 ,1 4 3 0 . 0 9 5 0 . 1 4 30 . 1 4 3 0 . 1 1 1[ 0 . 1 4 0 ] [ 0 . 1 0 5 ] [ 0 . 1 0 5 ] [ 0 . 1 4 0 ]( 0 . 1 5 5 ) ( 0 . 1 4 2 ) ( 0 . 1 4 2 ) ( 0 . 1 5 5 )0 . 1 5 9 0 . 1 4 8 0 . 1 4 8 0 ,1 5 9A0 . 1 0 8A
L A
A
A0 . 1 1 90 . 1 4 0 0 . 1 0 5 0 . 1 0 5 0 . 1 4 0A A
A0 . 0 5 0A
0 . 1 0 8( coefficient)
5 2 . 5 6 0 . 0 1 1 2 . 5 3 9 . 5 5 5 . 5 9 5 . 0 3 9 . 0 5 0 . 0 8 9 . 0 2 3 . 0 4 3 . 0 6 6 . Ok Nm 2 0 / 2 01 .
9 0 . 1 6 9 . 9
4 5 . 3
8 5 . 3
l Ok N/ m 2 Ok N/ m, l Ok N/ m 3 6 k N/ m.
2 6 . 3 1 0 4 . 4
1 3 0 . 7 2 0 . 0 9 6 . 3
1 1 6 . 3 1 9 . 5 9 0 . Ok Nm1 0 9 . 5 1 1 . 5 7 7 . 4
8 8 . 9
5
0 . 4 5 0
0 . 4 4 6
.V
J
=
VQ )
E 0
0 . 6 4 3
For anytrapezoidall oad.SF ( k +
0 . 5 , i0 . 5 ) ( 1 0 . 6 5 6 . 3 6 CP! 1 0
0 . 0 6 3 0 . 0 8 5 0 . 0 8 8 0 . 0 6 3 0 . 0 8 5 0 . 0 8 8
0 . 1 8 8 0 . 1 6 9 0 . 1 3 1 0 . 1 8 8 0 . 1 6 9 0 . 1 3 1 0 . 1 8 8 0 . 1 6 9
+ + . + + 0 . 0 5 0
0 . 0 7 4
0 . 0 7 0
0 . 0 5 0 0 . 0 7 4
0 . 0 8 2
+ + + 0 . 0 0 0
+ 0 . 0 3 3 +
0 . 0 9 4 ( 2 3 )
3 7
g iv e
U niform
+ + 0 . 0 5 3
0 . 0 7 6
0 . 0 7 4
0 . 0 5 4 0 . 0 7 6 0 . 0 8
+ +
0 . 0 7 9
0 . 1 2 2
0 . 0 7 9 0 . 1 2 2
0 . 1 2 2
oau s
+ 0 . 0 3 8 + 0 . 0 5 1 + 0 . 0 7 7
aE
0 . 0 8 3 0 . 0 7 5 0 . 0 5 8.0 . 0 8 3
0 . 0 7 5
0 . 0 5 8
0 . 1 0 6 0 . 0 9 5
0 . 0 7 4
0 . 0 6 3
0 . 0 8 1
0 . 0 8 8
0 . 0 6 3 0 . 0 8 1
coefficient
1 5 8 Continu ou s and
+
the
the
3 8factored dead l oad =factored imposed l oad=1 2 0 0u nits per span1 6 0Continu ou s
q
0 . 2 6 2 g 1 2 0 . 0 8 5 0 . 2 5 5 g 1 2( 0 . 2 6 2 0 . 2 5 5 ) x 2 . 5 % :
this
8 2
9Deformation
acentroid of A A S of
aA a8 ] 6 [ A A $ zA B Z B C) ] 6
=6 ( OB A 'A b 'A R +2 M B ( IA B M CIB C 6 [ A A B Z A D
K A A D K CCF
( A 8 0 Z 2
Ratio
2 8 % 1 5 /
moment moment 20one 4 0 % 2 0 % 8 %
1
l A B 1 2= =span
and l cD)
3 . 0 / 0 . 0 0 5 25 7 7 m3 ; 5 0
1 8 . 7=3 . 0 1 . 6 m.
1 8 . 7 5 7 7 0 4 . 5 / 0 . 0 0 7 87 5 l 2 6 k Nm per metre width;z2 =4 . 5 / 22 . 2 5 m.w,= 5 Ok N/ mw2k N/ mw3 = 6 Ok N/ m1 ,= 3 mAI,= O. 0 0 5 2 m41 2= 4 . 5 m1 2 = 0 . 0 0 7 8m4D! 3 3 . 6 m1 30 0 0 6 5m4D
4 0
1 / 1 K A B / ( K A B 0 . E FE M u nbal anced
IU niform moment of inertiaA
where is are 0=0 . 5 .
for
'PA B W B A
1 . E FE M
Distribu tion factors3 B 25 1 54 c35 5Fix ed-end momentsFirst distribu tion1 St carry -ov er00 2 0 3 + 2 0 301 2 20 0 0 02 nd distribu tion2 nd carry -ov er3 rd distribu tion3 rd carry -ov er6 1 + 1 1 24 th distribu tion 1 3 + 9 + 6 - 6 4 + 2 + 2 0Su mmations 0 + 1 5 2 -1 5 2 3 3 + 3 3 + 1 60ARel ativ e stiffnesses4 - 43 0k N/ m9 r4- U niform moment of inertiaDContinu ityfactors00 . 2 1 50 3 0 00 . 2 3 70 3 0 50 . 3 3 30 2 2 00 . 5 0 0Distribu tion factors 1 . 0 0 0 0 5 6 9 0 . 4 3 1 0 . 5 6 7 0 . 4 3 3 0 . 3 7 1 0 . 6 2 9 0Fix ed-end moments 2 0 3 + 2 0 3Distribu tion carry -ov er c 8 8 i 3 6 + 3 6Su mmations 0 + 1 5 0 1 5 0 + 1 0 9 1 0 9 3 6 + 3 6 + 1 81 6 4 Continu ou s
1 2 63 6 5 1 0 k N/ m23 . 6 / 0 . 0 0 6 55 5 4 6 0 3 2 . 43 . 61 . 9 2 z3 ) / 1 3 1 33 2 . 49 5 7 0 M D 0 .
6 ( 5 7 7 0 6 ( 3 6 2 5 3 2 7 6 4 :
8 5 2 2 4 0 : 1 0 0 ,6 k Nm
8 4 . 8
al teration '
Pi)
4 1
=0 . 3 3 3 ( 1 2 1 k ) ; x 30 . 3 3 3 ( 1 3x 40 . 3 3 3 ( 1 41 3 )etc. ,
6 A 2 ( 1 2 CN3 / 1 2 / 1 2 .CNF1 2 / 4 .CN3 F1 2 / 8 . a) ( 2 ct) Fl 2area=distancetotal
p2 ( CN
see _ _ _ _ _ _ _ '2
T he
tabu l ated
which
fu rtherk '2 can
0 . 5 8 / 1 20 . 6 6 7 .1 . 51 . 6 6 7 , 5 / 90 . 5 5 6 . 0 . 3 4 7 0 . 4 1 7 ; 1 . 2 9 6 1 . 1 1 1 ; 0 . 7 4 1 0 . 5 5 6 .T hu s From 0 . 0 5
0 . 0 4 9 3 . 6 8=1 7 . 0 11 7 . 0 18 5
=1 6 6 . 7 1 5 1 6 . 7 +
4 2
E 2 P2zero E 2 E 2 P2x
a)
P3 H P3 J 1 ) .
( b)A u x il iarydiag ramF'71 6 8Continu ou s k 1 F1 l 1k 2 F2 l 2 0 . 0 4 6 x 0 . 0 6 5
1 5 7 1 . 4 0 . 0 6 6 7 M r 1 6 0 5 . 6 k Nm 1 6 1 8 . 4 k Nm.
===
u nity
su pport
U u nity
k 1 , 4 3
1 . 2 5
1 . 3 3 0 1 6 7 FfF FFFA nynu mber of l oads( 1 )eq u al l yspaced
8 '\ 1 + j JOdd IF!8 \/ I
Q 4Q c U2U ; se ItA lSP fl=u nity -- - . -t I. . -- - - 0 . 0 6 2 5 . ----
1
-
AB 1 =u nityJspank 2B ase U s 0 . 5 Y U c=
5 1 -- H ( x t t I tA l l
ri 1 ( I I-I k spanA B u nity0 0 6 7 0
. + 0 . 0 1 3 4 U 5 ]
x = k 1 + ly = k 1+ k 3z k 2 + k 3
H 1 = 1 4 k 1 Y
0 . 0 4 9 1 0 . 0 5 3 6I U B ]I ff 0 . 0 0 4 5 2 H 4 ( 4 x y
5( 1 )C. ) C) LU -2 2II C) C. ) 02. 2In IIII-.U -ii II .IIU2 :I IIIIIIIINNNNC0000 0 2 /I I l iii I I Io 0 0 0 00C 0 CD U S 0 U S C 0 U S 0 U S C) 0o 0 0 0 U S 0 U S U S N U S U S U S U S C c-s C C'J C')U S CD C') ,- ,- 0 0 0 000CD 0 0 0 0 C) C0 0 0 0 0 0 C) 0 0 0000 CD C) 0 0 CD 0o o 0 0 00 00OOooO 0 00 0 0 Cj o)
forcontinu ou s
-- ( 0 . 0 8 2
+
( 0 . 0 8 2
+ ( 0 . 0 3 5 1 0 x 2 2 4 0 x 2 0 )
= 6 5 ,6 k Nm + 2 8 . Ok Nm
3 6 8 0 0 l bft + l S7 0 0 l bft 2 1 4 6
( ordinate F0 . 40 30
0/AC4 )00 . 10 1Ol E0 . 1 05 )0 . 1 5BShort span L 1-D 1 : 2a
0 1 .B1 . 1A BShort span L 1 C_ _ _ _ _ _ DL ongspan L 2 . E0C -l : 2 j-C 1 : 1a
CdeCsCsI-0CsCsVCsCs0 .C,,00 2 00 2 5g h/k
acefg hI
4 7
00 .Q )
Ca 0 0 500 .030 2 0ciL ong spanL 20I-0E 000 '0Caa 5 )Ul B D &Sk ort span L 1 B ' N9 hkjm
acefg jm n
1 : 1 . 5 : 1
( ordinate
I/
-B Short Span115:0 Cl0.10 00)a C0.100.10U,0ci00.100.200.250.05(Uo00.0.100)a C0.20abCdeIILong spanShort span L1Influence lines for bending moments at midspan B of span AC andmidspan D of span CE
t'ghI
IBi:1 i:11B'LongspanL2ImnHbAShortspanL1BdehIIAl
CIIIEIID'LongspanL,IC'1ICfillIIII B'Short span L1A' Ib
nInfluence lines for bending moments at penultimate support C__________Long span L2EpeIELongspanL,ID'I
j
Short spanL,lEt'"Influence lines for bending moments__________________________________________at central supportEII
nU)V CSI-C
abcdefg
p:z rD
mnp
lines marked 1: I:1:can be used directly (diagram of asuccession
(ordinate
(end span L1) x FCentral1: 1: 1: 10.0120.0210.0270.0270.0180.0280.0580.0800.0850.0610.0850.0800.0580.026supportE1:1.5:1.5:11:2:2:10.0100.0080.0170.0150.0220.0190.0220.0190.0150.0130.0380.0460.0820.1040.1160.1500.1240.163.0.0910.1210.1240.1630.1160.1500.0820.1040.0220.019
C z0a0.1
SupP0flI 1/II
'p'IbCdII
..Third-pointpoint
a
cdeI.mnpfqhjk
mnp
Midspan
pq
(ordinate
1
g ,,k 4 / ( k 41the
and 2 .
=
=
which 1 0 . 8 3 T he M arcu s's
B ending -moment
and
+
+ and are
0Condition
0 . 5 0 0
l ongspan =Conditions: edg e torsional
=middl e
=edg e total
Ratio w
M , =+ =M ,j k 2Corners ++ ++M ,/ k 2
M ,4
diameter) .
bey ond
torsional
cross-sectional cross-sectional
1 8 0 =0 . 2 7 7 k 2 / ( l+
Span +
=+
4 6 3 . 03 . 7 5m.
==1 . 2 5 .( i) 0 . 7 0 9=0 . 2 9l Ok N/ m2 .
1 0 0 . 2 9 15 . l 2 k Nm
( 1 . 4 1 5 . 2
1 2 . 1 8
CP1 1 O
andand and
Span
5 . 0 2
M iddl e 1 0 . 6 7 / 2
7 . 7 0 / 2
withou t torsional restraint at corners op p/( at corners V0 0 6
I5 )_ . . 4with torsional _ _ _ _ _ _ _ _ _ _. 9 _ _ _ _ _ _ _ _ _ _ _ _ I I I I -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _0 0 2withou t torsional0 1 2 1 4 1 6 1 8 2 0 1 0 1 2 1 4 l b 1 8 2 0 1 0 1 2 1 4 1 8Ratio ot spans N I I I IH Iii0 0 2 fl y 1fl y 10 0 0 8
fl y i fl y )Imy yfl y 1fl y i fl y i0 1 . 2 1 . 4 1 6 1 . 8 2 0 1 ,0 1 . 2 1 6 1 8 1 0 1 2 1 . 4 1 . 6 2 . 0Ratio of spansedg e which continu ou sB ending -moment
1 0 . 2 6 / 2 = 5 . l 3 k Nm
0 . 0 3 6+ 7 . 7 0 / 23 . 8 5
1 0
8 . O7 k Nm 6 . 1 6 / 23 . 0 8
+ 3 . 8 5 k Nm 0 . 0 2 4 5 . 1 3
0 . 0 4 1 . +5 . 6 1 7 . 3 9 k Nm 5 . 6 1 / 2 2 . 8 1
+ 3 . 8 Sk Nm 0 . 0 2 4 5 . 1 3 1 ) 0 . 0 4 5 0 . 0 2 5 .1 0 1 1 2 . 5
x 1 5 . 2 1 7 1
( 0 . 0 4 5+ + +
T he
1
rev erse 1 .0 . 8 0 . 2 ,0 . 0 7 2 ; 0 . 2 0 . 8 , =0 . 1 0 3 .
0 . 1
58 . 5
3 . 3 k NmTI
0 . 3 3 / 2 . 1 50 . 1 5 0 . 5 5 / 2 . 1 50 . 2 6 , =0 . 2 3=0 . 1 2 . 2 76 . 8 6 8 . 8 8
6 . 8 4 2 7 [ ( 0 . 2 4 . 4 8
0 . 6 7 ( 2 . 1 5 2 . 2 0 m 2 7 / 2 . 21 2 . 3 ( 1 / 4 ) 1 2 . 3 [ 2 . 1 5 ( 1 / 2 ) 0 . 3 3 ]6 . 0 8
0 . 5 5 1 / 2 ) ]1 . 8 4 m.
x7 . 2 8
7 . 1 6
3 . 7 5 / 3 . 01 . 2 5 ;0 . 5 2 5 / 3 . 00 . 1 7 5 ;1 . 0 5 / 3 . 7 50 . 2 8 . =0 . 1 9 =0 . 1 2 . 1 . 2 5 ,0 . 4 5 0 . 1 7 .
1 . 2 5 ,1 ; and being
3 4 . 2 4 3 . 5 33 7 . 7 7
2 5 . 2 8 2 . 5 22 7 . 8 0
0 . 5 2 5 0 . 9 7 5 0 . 5 2 5 m.
1 ) . 2 ( 0 . 5 2 5 3 . 01 . 0 5
3 . 0 / 3 . 01 . 0 5 / 3 . 7 50 . 2 8 .1 . 2 5 , =0 . 0 7 3 0 . 0 6 3 ; 1 . 5 0 . 0 7 3 0 . 1 0 9 ; 0 . 0 6 30 . 0 9 5 . 21 . 9 51 . 0 51 . 9 5 / 3 . 0 0 . 6 5 ;1 . 0 5 / 3 . 7 50 . 2 8 . =0 . 1 0 =0 . 0 8 8 ; 0 . 1 00 . 0 9 8 ; 0 . 0 8 6 .
=0 . 1 0 9 0 . 0 1 1 ; 0 . 0 8 6 0 . 0 0 9 ;2 F
mu st
C000Cci)E0E0 )CDCci)horizonta' moment at-M axpositiv e v erticalmoment1 . 0Vertical coefficient 1 8 6 Sl abs
2 0 0 / 0 . 5 2 53 8 2
3 8 2 1 ( 0 . 24 . 2 8
0 . 9 5 4 . 6 5 0 . 2 5 1 . 2 3
g iv en
1 . 0 7
= 1
u / v .
dv / dx
( i) 2 }which
\ l y /
1 2 ]1 2
( T he
Simil arl y
sin ( A s
the
A
l x i. .
4 m,3 / 2 0 ,
6 =1 / 2 , 1 / 2 0 ,
7 . 0 3 m
} 2c J r( 3 . 1 0 \ 2 1= O. 7 2 6 n
[ \ / { 3
[ ,J ( 1
=i1 )+ +
( \ / ( 1 c 3 +x rt
I Find
( iii)
a C
C.
L IUL ufor
( iii)
2 x a,.
( iii)
a,
a, 2 y ,
( iii)
2 ( a,1 +x ) ( a,1+ y ) .( ii) a1= 2 x 2 y ,
and ( v )
-C
( C) ( d)( e)( 1 )( g ) ( h) ; kk 11 . 0 , k 1
( or k 1 0 . 7 0 ; 0 . 8 50 . 2 5 ; 0 . 9 5 ; 0 . 9 5
a
C
aSpanU nsu pported edg eU nsu pported edg ez+ a/ 2 1L X J 4SpanSpanFor 1 1 / 2 , where xa,/ 2 )
I (1 fl1 )I.where
L \ 1 II\ 2 1 ,ij
_ _ )y = z+ a,+ 1 . 2 e( 1 _ 7 ) For 1 1 / 2 , where x
( 1 ,
a, z a,
4 n/ 3 . 1 / 2 .
2 M
2 M .2 M . 4 n/ 3 ,2 / 3 . 1 / 3 .
3
=3 . 7 5 n 3 . 7 5 n =Sn
6 M . 5 / 60 . 8 3 3 . 0 . 7
1 . 3 3 3 n 5 . 0 0 0 n=0 . 6 6 7 n 3 . 0 0 0 n
6 . 0 0 0 M2 . 0 0 0 M
1 0 . 0 0 0 n1 4 . 0 0 0 M
4 n.
0 . 7 1 4 .
mu st 1 . 4 6 2 .
CSF-5 7diameter
4 h2 )
wh2 / 3 0
1 x < 1 y1 y 2
l y or C)CeC)C)C. )( I,0Ctj h4
a
distance distance l . 0 7 7 h
- ( 1 4 n/ M , I v ) ( 1 1
M r
hal f su bstitu te d'= ,5 / ( 1 . 6 d2 + t2 ) 0 . 6 7 5 t
T herefore, since the workdone bythe moments remainsu nchang ed, the rev ised ratio of M / n 4 . 5 5 6 / 60 . 7 5 9 . M / n ag ain proportionalto the corrected v al u e ofx2 . 5=2 . 4 2 4 .7 .Recal cu l ate the indiv idu alv al u es of internaland ex ternalworkdone and draw u p another tabl e:8 .Repeat this cy cl ic procedu re u ntilreasonabl e ag reementbetween the ratios of M / n obtained.T his then g iv es thev al u e of M correspondingto a l oad n. the ex ampl e, the ratios g iv enbythe second cy cl e are q u ite satisfactory .Note that,al thou g h some of the dimensions orig inal l yg u essed werenot particu l arl yaccu rate, the resu l tingerror in M / n capacityof the sl ab is not g reatl yinfl u enced bytheaccu racyof the arbitrarydimensions.Concentrated l oads and l ine l oads occu rringat bou ndariesbetween sl ab shou l d be div ided eq u al l ybetween theareas that theyadj oin, and their contribu tion to the ex ternalworkdone assessed as described in section 1 4 . 7 . 5 .A s in al ly iel d-l ine theory , the abov e anal y sis is onl yv al idii the pattern of y iel d l ines considered is the criticalone.Ifreasonabl e al ternativ es are possibl e, both patterns shou l d beinv estig ated to determine which is critical .1 4 . 7 . 9T ests and el astic anal y ses of sl abs show that the neg ativ emoments al ongthe edg es redu ce to zero near the cornersand increase rapidl yawayfrom these points.In sl abs thatare fix ed or continu ou s at their edg es, neg ativ e y iel d l inesthu s tend to form across the corners and, in conj u nctionwith pairs of positiv e y iel d l ines, resu l t in the formation ofadditionaltriang u l ar sl ab el ements k nown as corner l ev ers,as shown in diag ram ( i) ( a)on T abl ethe sl ab is freel ysu pported a simil ar mechanism is indu ced, cau singthecorner to l ift ( diag ram ( i) ( b) ) . If these mechanisms aresu bstitu ted for the orig inaly iel d l ines ru nninginto thecorners of the sl ab, the ov eral lstreng th of the sl ab iscorresponding l ydecreased, the amou nt of this decreasedependingprincipal l yon the v ariou s factors l isted onT abl e For a corner hav ingan incl u ded ang l e of not l ess than9 0 , the redu ction of streng th is u nl ik el yto ex ceed 8to 1 0 % .Su ch cases can therefore be treated q u ite simpl ybyneg l ectingcorner-l ev er action, increasingthe amou nt of main reinforce-ment sl ig htl y , and prov idingtop steelat the corners torestrict crack ing .T he recommendations of the Swedish Codeof Practice ( see ref.3 4 )for this reinforcement are shown indiag ram ( ii)on T abl e acu te-ang l ed corners, the decrease in streng th is moreseriou s.For a triang u l ar sl ab A B C where no corner ang l eis l ess than 3 0 , J ohansen ( ref. 1 8 )su g g ests div idingthecal cu l ated streng th withou t corner l ev er action bya factor k g iv en bythe approx imation( 7 . 4sin A sin Bsin C) / 4T hu s for an eq u il ateraltriang l e, kT he determination mathematical l yof the tru e criticaldimensions of an indiv idu alcorner l ev er inv ol v es mu chcompl extrialand adj u stment.Fortu natel ythis is u nneces-sary , as J ones and W ood ( ref.2 1 )hav e dev ised a direct desig nmethod that establ ishes corner l ev ers hav ingdimensionswhich are su ch that the resu l tingadj u stment in streng th issimil ar to that du e to the tru e mechanisms.T his desig nprocedu re is su mmarized in the l ower part of T abl e il l u strated bythe ex ampl e bel ow.T he formu l ae deriv ed byJ ones and W ood and on whichthe g raphs on T abl ebased are as fol l ows:W ith fix ed edg es:k 1
=cos ( 0 / 2 ) cot sin ( 0 / 2 )where K j = . . J { 4 + 3 cot2 ( 0 / 2 ) ] 1 cot 1 ) tan( 0 / 2 ) .W ith freel ysu pported edg es:+ =cos ( 0 / 2 ) cot ,/ ' sin ( 0 / 2 )where K 21 cot2( 0 / 2 ) the resistance of the 5 m sq u are sl abwith fix ed edg es shown on T abl e neg ativ e resistance-moment coefficient i of 1at the fix edcorrected v al u es of x2 . 4 6 7x2 . 5xn( 1 / 2 )x( 2 . 0 7 1+1 . 4 6 2 )x2 . 5x( 1 / 3 )xn4 . 5 5 6 nA rea E x ternalworkdone Internalworkdone B al anceM / n
C
x4x( 1 / 3 )1 . 3 8 1 n[ ( 2 . 4 6 7x2 . 4 2 4x1 / 2 )+ x4 . 4 1 8 n x1 . 4 6 2x4x( 1 / 3 )xn0 . 9 7 5 n x1 . 5 7 6x1 / 2 )+( 1 . 5 7 6x3 . 5 3 3x( 1 / 2 )x( l / 3 ) ) ] n2 . 8 7 2 n 1 . 9 3 1 M6 [ ( 3 M / 2 ) 6 . 1 8 8 M x( M / 2 ) / 1 . 4 6 21 . 3 6 8 M xM / l . 5 7 6 =3 . 8 0 7 M
0 . 7 5 4T otal s =9 . 6 4 6 n =1 3 . 2 9 4 M 0 . 7 2 65 8
fix ed
prov ided
Val u es of M ini,20 1 1 0 . 1 2 0 . 1 2 5I ii III IiI7 89 1 0 1 52 0 5 0Val u es ofv al u e
etc.
( i)( a) ( if ( b)Distribu ted l oad =n T ransformed distribu ted l oad =nConcentrated l oad F concentrated l oad =( iv ) ( a)Orthotropical l yreinforced sl ab ( iv ) ( b(A ftine isotropic sl abT y picaly iel d-l ine patterns( v ) ( a)Sk ew sl ab ( v ) ( b)A ffine rectang u l ar sl ab0 . 0 41 7II1 00 0 5II1 . 4( v i) ( a)Continu ou s sl ab ( v i) ( b)A ftine freel ysu pported sl ab0 . 0 6 0 . 0 7 0 . 0 8 0 . 0 9 0 1 0I III I I I Il iiiI IIiIIII I III I I I4 56 l y rI',
1 9 6Sl abs i)=3 . 5 4 m.
1 . 1 T hu s 0 . 7 9 43 . 0 3 2 .
0 . 8 5 8 . [2 . 5
I
0 ,5 6 8 n,
are
5 9
jstab edg esx xFreel ysu pported. 1 BI-II-I-1 2 0 1 4 01 6 01 8 0Corner ang Ie 8Fix ed stabedg esNeg ativ e y iel d l ineSl ab corner tends to l ift,.across cornerpiv otingon this l ine
to resist moment ofper u nit width( ii)
Neg ativ e defl ection =0 8 5 8Indiv idu alA l ldimensions in metresObtu se-ang l ed
0a 2 ,xa2 ,4 -----. . \ -. = =k l . ,J ( M / n) -'i I iiA k IIi - i- I I \ /-r - 1 2 -:0 8: :o: / -1 J 1 L U Lil -1 _ J
1 10 2 5 3 0 3 5 4 04 55 0 6 0 7 0 8 0 9 0tOO
1 . 5 .
0 . 0 5 3
0 . 0 1 5 5 . 3
+
6 0-43
Section 1 -1 Section 3 -34 L oadingIrn 1 T n1 4Section 3 -3( iv )- ' reference
direction a4
A v erag e across strip 2B Mdiag ram( J I l It 1 1 1 1 1 1 I l iii It l iiiL oadingSection 1 -1+ I 4 L oading
I, Itl il Il il itilL oadingSection 3 -3+( i)4 L oading
Section 4 -4( iii)Ln-4 4 --4
L oadingSection 1 -14 4 L oadingSection 2 -21 1 1 1 1 1 1 1 1 1 1 l il t!ii til t II4 L oadingSection 3 -34 L oadingSection 1 -14( ii)4 4L oadingSection 2 -2
and
p1 3 determinei3 )
\ / ( 1
from
4 k 2 [ 1+1 4 ] _ 4 k [ 1 4 ( 1 +1 4 ) +
1 . 5 , 9 . 3 8 + 2 . 5 Ok Nm ++
9 . 3 8 / 2 . 5=3 . 7 5 ; 2 . 6 4 / 2 . 51 . 0 6 ; 1 3 6 . 6 8 / 2 . 6 42 . 5 3 .22 . 0 =2 . 0 / 2 . 50 . 8 .
0 . 8 3 . 7 5 ,0 . 0 1 2 .
3 . 0 1 1 . 2 5 k Nm3 . 08 . 0 5
SU PPORT ING
)
from
Failure mode 1Failure mode 2
2(i2i4)x=l ii\1L3
1+Recommended dispositionof strips
144x
97
31/20!f4
LiPWM5LoadMoment LoadMoment
2+/////////////////////////)///////%
dispositionof stripsil/J ILoadCOC')Load on horizontal stripa U,('3C-)'3)> C 0Load on horizontal strip 4-5-6Moment on horizontal strip 4-5-6C')0 C a
a CO('3C)'3)> C 01-(1 s3)fLoadC')Ca
a (0a
a)>
.....on horizontal strip 4-5-6Loan on horizontal strip 7-8-9C 0
+shou l d
8 S8 1 1 0 : 4 1 2 / 3. 4 :
a)C)a)0C)a)C)0Ca)a)0 )a)a)EU )Ca)C)a)0C)IL0 )Ca)0a)0C)IL( 0D6 2_ _ _ _ _ _ _ _ _ _ _ _ edg e which is discontinu ou s or which is cast monol ithical l ywithL oad is considered to be transfersed from sl ab to beam ov er centrall eng th of 07 5 1su pportas shown bel ow,edg e which is continu ou sT hese coefficients onl yappl yto rectang u l ar panel s consistingof sol id sl abs spanningin two directions at rig ht ang l es carry ingu niform l oads onl yand desig ned u singcoefficients prov ided on T abl e 5 1Coefficients and appl yto shearingforce actingon short span at continu ou sedg e and discontinu ou s edg e respectiv el y .L oad per u nit l eng th transferred from sl abto su pportingbeam ( i. e.spanningin direction =Coefficients and appl yto shearingforce actingon l ongspan 1 , at Continu ou sedg e and discontinu ou s edg e respectiv el y ,, L ongper u nit l eng th transferred from sl abto su pportingbeam ( i. e.spanningin direction =Ratio of spans k=Ratio of spans k=1 4Ratio of spans k=fin!2 0 4Sl abs spanningin
of can
is
T he
+If the resu l tingshearingstress ex ceeds 0 . 8times the v al u e
k > i:= = x = fl = R1 ( max . )
R3 / 3=1 / 2 k
=R4=k l ong ershorter
total
3 / 8 =5 / 8 ( max . )NIU t0 .0 .Ic3 / 8 k =5 / 8 k( max . ) 5 / 8( max . )
a / 3 = 5 / 8 k=5 / 8( max . )
ShorterspantRiR4R3R2I0 ) cIce_ J cO
appropriate
FB A A / i.
3 E K A B OA ( FA R 4 E K A COA4 E K A DOA 6 K A C
E OA ( 3 K A B ( FA B 0 FA B
3 K A BM A CK( M A C 2 E K A COAM A CI2M DA= M A D! 2 l . 5 A A B / IA B
Col u mn
b0 . 0 3 9 0 5
0 . 0 3 1 2 5
g0 0 4 0 0 0
h 0 . 0 4 1 2 5
0 . 0 0 5 0 0
drops
0 . 0 1 3 7 5
may
n 1 . 4 g b
col u mns M ax imu m
0 . 1
one-hal f
distance
to resist shear
k Y ,.1 . 1 5
V,) / u d,
Vdij . fu d/ 0 . 8 7 f,,,,,( v v ,)
5 A I penu l timate perimeterpu nchingperimeter Bshearperimeter CH II3 d( B S8 11 0 )with drop panelandcol u mn hadeffectiv ediameterof col u mn
L LCriticalsections
-t4 omrr
W idth drop ( if prov ided) 4 : 1 / 3-Sl ab withou t drop paneland col u mnCritical( col u mn perimetersections forperimeterpu nchingperimeter
2L Criticalsection for shear ( CPI1 O)
2 0 8Frame
FT S K sr( OT S
FT U ) -- FST ) FT U )
K ST
FT S)DT s) ( FST FSR) ] FSR) Frs) ]
and
K RSOSR
FSR DST DT S FT S) FSR) ]
FSR) Ff5 ) ] 6 5 z
l A B For
=2 A A B J A B / l A D = J A B )
FB A=0 a -
2 E K A S( 2 0 A FA R: '_ _ _ _ _ _ _ _ _ _ _ _ B 3 E K A B OA( FA B
B FA B F4 8 ( FA D
_ _ _ _ _ _ _ _ _2 E K A B ( 2 0 B .4 E K A B OB " fD?P= FA B 1A ny A nyjA ny , o fi =FA D+DI4 ,B I
A
BB
ciCondition
for mm.Ej M 4 8 M A D-2 K A CA 4 5 -- K 4 0 O. 5 M A C( M A C +
K A 1 / 2 C_ F4 8 1
0
E
B )
K A C FA D
su pport
either
F4 8
B asic formu l ae ( sl ope defl ection)M A D A B
I' 3 a\M 4 8= 2 0 A+0 8 ) FA R'A D7 3 a\2 E K A D( \ 2 0 D 6 A
M B A)
al lu pper col u mns'ST = 'T U =2 0 . 1 6 x 1 0 9 mm4
g k _ 8 k N/ m2 1 ,8 5xl O9 mm' 4 m1 1 1 1 1 1 1 1 I Il l 1 1 1 1 1 1 1 1 I H I III II I U III 1 1 1 1 1 1 1 1 1 1 WIR ST U4 m6m8mIfor al l col u mnsT he l ] ( FST FSR)
FT S 4 Frs 0 . 1 3 2 [ 0 . 9 5 3 ( Fsr FsR)
FSR0 . 0 8 3 =2 4
= =
and 0 . 0 8 3 3 4 2 . 7
FSR
8 1 0 ) 8 2 1 4 5 . 1
M ax imu m
0 . 5 1 . 3 7
=0 . 5 3 1 4 5 . 1
[ 1 . 1 1 6 ( 1 4 5 . 1 1 4 5 . 1 )
1 4 5 . 11 1 7 . 3 k Nm
2 . 7 3 0 . 4 7 1 1 4 5 . 1 ) 1 4 5 . 1 1 3 1 . 6 2 . 7 3 0 . 4 9 7
8 1 . 6 ) 1 4 5 . 1 ) ]
Ff5 ) 1 4 5 . 1 8 . 01 5 3 . 1
6 6
4 0 ) .1 .
K , 1 1 /where and
are
4 ,]is & )of b,)2 K j 3 , =1 / 2 :if 'W B CW CRare DFB A DFac.
'/ . 'RL ) . 3 0 8 1 . 1
Continu ityfactore . m q l '0 1 4 30 . 2 7 10 3 4 40 3 0 1' 0 . 3 5 30 3 6 80 . 2 8 70 . 5 0 0Distribu tion factors 0 . 1 2 4 0 1 2 8 0 . 7 4 4 0 . 4 7 6 a0 8 : 1 1 0 & 0 . 3 4 6 0 4 4 3 0 . 1 1 0 0 1 1 0 0 3 3 7 0 3 0 2 ) 1 0 0 0 . 1 0 0 0 . 4 9 8Fix ed-end moments 2 0 3 + 2 0 3Distribu tionCarry -ov erSu mmations 8 8:[ -4 -9 7 + 1 8+ 4+ 1 6+ 1 2 0 1 2 2+ 1 8+ 4-4 -2 2+ 7 0 9 0 3 1 + 2 1 1 6 4+ 1 3 4 2 2 4 2 6 2 2 4 2 6 8 2+ 4+ 4+ 4+ 4+ 2 2+ 1 14 ! m3 0k N/ m,-U niform moment ofinertia for beamsBC IAm9m 1 2rnU C L Cof inertiaof col u mns =1 / 1 0that of beamsE lU C L CU C L CU C L CDistribu tion factorsFix ed-end moments0 1 1 5 0 1 1 5 0 7 7 0 0 5 0 8 0 0 7 6 0 0 7 1 0 3 4 0 0 4 5 50 1 0 20 . 1 0 20 . 3 4 10 3 2 3j O. 0 9 70 0 9 70 4 8 3 2 0 3 + 2 0 31 st distribu tion 9 2 2 1 2 1 6 91 st carry -ov er2 nd distribu tion e 6+ 3 + 3 + 1 6+ 12 nd carry -ov er3 rd distribu tion 1 1 1 0 5 + 4+ 1 2 0+ 2+ 1+ 2+ 1I+ 2 2+ 2 2 ,+ 2 2 1 1 6 4 + 1 3 4 11 1 2 6 8 2+ 2 2 + 1 3 0+ 1+ 4+ 1+ 4+ 2+ 2 2+ 1 03 rd carry -ov er4 th distribu tionSu mmations 1 8 1 8 + 1 6[ For detail s of stru ctu re and l oading see diag ram abov eU C u pper col u mn L C l ower col u mnU C L CU C L C I U C L CU CRel ativ e stiffnesses1 / 4 01 / 4 0 1 / 6 1 / 4 01 / 4 0 1 / 9 1 / 4 0 1 / 4 0 1 / 1 2 1 / 4 0L C1 / 4 0 1 / 8
1 4 5 . 1 1 4 5 . 1 ) ] 1 4 5 . 1 1 5 . 2 =
1 4 5 . 1 ) =1 4 5 . 1 1 0 6 . 4 1 4 5 . 1 0 . 1 3 2 2 4 . 0 ) 1 4 5 . 1 ) ] 1 4 5 . 1 1 1 2 . 6
( 1 . 5 2 1 7 . 6 1 0 8 . 1 0 . 8 6 / 5 . 8 00 . 1 4 8 0 . 5 3 / 5 . 8 0
4 =2 3 . 1
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _4 2 4 . 0 ) ]=1 4 . 2
4 . 4 4
5 3
1 2 1 . 1
6 7
( 1 / 4 )
FE M RL )
( 0 . 7 0 8 4 00 . 6 9 6 F1 4 0 .
-8 0 0 . 8 4 8 F28 0 .++
+ 0 . 8 9 9 8 8 . 8
M odified stiffnessDistribu tion factors1 / 1 4B1 26 / 7 1 / 1 4C1 / 1 31 21 2 / 1 3Fix ed-end moments 8 0 . 0 8 0 . 0 4 0 0 4 0 . 01 st distribu tion + 8 . 6 +1 0 2 . 8 + 8 . 6 . + 3 . 1 + 3 6 . 91 st carry -ov er 8 . 6 3 . 1 8 . 62 nd distribu tion + 0 . 2 + 2 . 7 + 0 . 2 + 0 . 7 + 7 . 92 nd carry -ov er 0 . 2 0 . 7 0 . 23 rd distribu tion + 0 . 1 + 0 . 1 + 0 . 2Su mmations 8 8 . 8 7 1 . 1 + 1 0 6 . 0 3 4 . 9 4 5 . 0 + 4 5 . 0For detail s of stru ctu reand l oading s seediag ram bel owC K = 24 Ok NK = 1! < = 1 4 m4 Ok N_ _ _ _ _ _ _ _ _A B C A B0 1 / 5 3 / 5+ 0 6 0 01 / 5 1 / 4 3 / 4 Distribu tion factors 0 1 / 5 3 / 5 1 / 5 1 / 4 3 / 4 1 . 0 0 0 1 . 0 0 0Fix ed-end moments 10 0 0 10 0 0. l . O. 2 0 0 > . < 0 2 5 00 1 0 0+ 0 . 7 5 0 1 st distribu tion1 st carry -ov er,. . _ + 0 ,2 0 0+ 1 0 0 0 . 0 7 5 0 . 0 7 5 2 nd distribu tion 0 0 7 52 nd carry -ov er+ 0 . 0 8 9 + 0 . 1 7 8+ 0 . 6 0 0 0 . 0 0 1+ 0 . 5 3 0+ 0 . 0 0 3 + 0 . 0 0 3 + 0 0 0 9 3 rd distribu tion 0 . 8 9 9 0 . 7 9 7 1 + a6 0 6 10 0 0 1+ 0 . 1 9 1 + 0 . 0 7 6 o. ooi 0 . 7 0 8 0 . 6 8 3 0 . 0 0 1+ 0 6 8 33 rd carry -ov er4 th distribu tionSu mmationsCDistribu tion correspondingto 1 st deg .ot swayfreedom Distribu tion correspondingto 2 nd deg .of swayfreedomFinalmoments1 8 8 . 8 7 1 . 2 1 1 0 6 . 1 I 3 4 . 9 + 4 5 . 1A B C.
and
Dead loadAll
loadAll
load Maximum
loadMaximum
HKI I Iboth
AB'A8I/,G'8 0z,,II---2 0 0- - .
h
5 03 04 0 2 0 1 0-1 1 0Perceniag e redistribu tion ot rnon,ent at section+2 0
and
V1
1 4 0M onol ithic with su pportingmemberContinu ou sto CE l l O onl y )
end su pport0 1 1orr\ .M onol ithic with su pportingbeam or wail
E ffectiv edepth dSu pportL esser of:1 / 2width of su pport;or1 / 2effectiv e depthA nchorag e eq u iv al ent toto be prov ided bey ond this pointA 5 1. 4 :end su pportinterior su pport4 : O3 1 ----. 1 4 : O1 1 W ith tree su pportContinu ou s'A w depends onfix ityprov ided:g eneral l ysu fficientend su pportf.interior su pportf4 : 0 . l 5 I. /4 : 0 . 3 1/ / su pport
B S8 11 0specifies shear stresshere mu st not ex ceed one-hal fmax imu m permitted v al u eCP1 1 O specifies l ocal -bondstress here mu st not ex ceedone-hal f max imu m permittedv al u eG reater of:5 / 6width of su pport;or1 / 2width of su pport +3 0 mm
2 0 0 mm
where is
B ecau se
oncentratedCriticalperimeter forshearingu+3 thW hen
3 h/ 2
'hairpins' formingshearingreinforcementwel ded to horizontal'ring s'/I'-. -H orizontal'ring s'that 'hairpins' arepositioned correctl y( b)Centroid of
Ii.0I J
1 4 1In tension zone,IA ctu altermination pointprov ide fu l lanchorag e-bondIterminationl eng th u nl ess req u irementspoint3 0 )or 3 ( u )( bel ow)are metdFu l ll eng th from point ofmax imu m stressCompl iance with l ocal -bondreq u irements need check inghere u nl ess anchorag e-bondl eng th of continu ingbars,measu red from here,is 5 / 4times minimu m l eng threq u ired
a! 2( M L+
hmin/ 3 )where
for
for
If it
0 . 8 x 1 y 1
T / 0 . 8 x 1 y 1
or
V/ bd
V1
obtained
assu med
v , may
su pport mu st
more3 9-1 1 6
Shearing
2 1 ---4 . 0 0
0 . 3 4
4 . 0 0
3 . 0 2
E ffectiv e depth ( mm)
-1 1 3-1 1 2
z0 7
-1 0 5
1 . 0 1
2 0 0 3 5 0 mm
3 5 0 2 0 8 1 2 . 5=3 0 9mm ( 2 8
( 0 . 7 7
1 . 5 0 )
( 1 / 3 ) 2 0 0 ]
2=
T 0 FrT = M 0 sint/ J + T 0 cos,I,+ V0 r( 1 coscl l ) Fr[ 1 cos( i4 'V V0
is
k 3 k 8-k 5 k 6K 2 ,1 t4 1 t8k 4 k 6 k 3 k 7
where 1 ) sin 1 ) cos sin2K ( cos k 2 1 ) sin
l ) cos = 1 ) sin
( K 1 ) 1 )
First
a)
0CaC0 )C00C000 .0Sl ab modify ingConcrete g rade or moreShearing
Vtmj n
1 )+ Z ero 4 0 0 .
+ 1 )
k N K ( l hand 0 ( cosand
If=4 5 0 , h/ b 1 ,=3 0 ,0 . 0 1 5 , 0 . 0 0 5 3k 8 1 ) sin 0 . 0 6 7 1 4 6 .
0 . 0 1 5 1 2 0 0 0
M 0 3 0 )
1 2 0 0 0 2 0 0 1 5 8
T 0 cos4 5 1 2 0 0 0 K 4 nr2 , 0 . 7 0 7 ) 0 . 9 6 6 ) 6 0 7 0 Nm
l 8 6 0 0 0 N
M 0 V0 r
1 3 4 0 0 3 2 4 0 0 Nm M 0+ cos 1 2 0 0 0
4 2 2 0 1 4 7 , with=14 5 ,+ 0 . 0 8 6 , 0 . 2 3 ,0 . 0 1 7 5 +2 3 4 0 .
n it 3 1
K 4 nr2+ 4 2 4 3 8 0 0 =2 3 . 1 / h2 . K 6 nr20 . 0 1 7 5 8 9 0 0 0 / 2 0
K 1 nr2+1 1
\binders resistneg ativ e E Min sl abSl ab reinforcementCompression reinforcem6 ntin beamDou bl e sy stemof l ink sd0tan 9 / 2=0 4 1d0when 9=4 5 0=0 . 2 7 d0when 0=3 0 fi 9d0 ( tan\ 2 sin0 2= 0 . 2 9 d0when0=4 5 =0 . 2 8 d0when( 9 0 9 / 2 )=6 7 5 0 0=4 5 0 =d0 / 2sin 0 ;=7 5 0when 0=3 0 / 9 0 0 / 2
3 0 0
2 5 0=4 2 5=4 6 0 =2 5 0=4 2 5N/ mm2 =4 6 0
dou bl e 8 0 . 55 8 . 1 3 5 5 . 6 B ars in L ink s In rectang u l ar beamL ink s inL ink s In T -beamsbent downT op l inknarrow ribSl abY lreinforcementE q u alstress in straig ht and incl ined partss =d0 / sin 0=14 1 when 0==2 d0 when 0 = 3 0 Redu ced stress in incl ined partsFor common arrang ement of barsC,'Acot 9 sin sin + 0 / 2sin sin3 3 8 Resistance
k 1 [ h
reqthe
2 5 0
1 9 3 8 mm2 2 5 0 2 52 . 56 2 5
0 . 7 ( 8 0 0 0 . 3 5 2 8 3 mm 3 0 0 mm.
5 2 8 9 7
0 . 8 7 7
3 . 3 9 A 1 9 1
2 5 0
j
.H ig h-y iel d 4 6 0
2 0 02 2 52 5 02 7 53 0 0
5 0 2 7 8 5 1 1 3 0
1 4 6 2 2 7 3 2 81 8 8 3 3 5 5 2 3 7 5 37 0 1 2 5 1 9 5 2 8 11 6 1 2 8 7 4 4 8 6 1 1 0 9 1 7 ! 2 4 61 4 1 2 5 1 3 9 2 5 6 5 1 2 5 2 2 3 3 4 9 4 9 1 3 6 1 9 71 1 3 2 0 1 3 1 4 4 5 2 1 7 91 0 2 1 8 2 2 8 5 4 1 14 1 7 3 1 1 4 1 6 49 42 6 1 3 7 7
2 4 8 3 8 7 5 7 83 1 4 5 5 8 8 7 21 2 5 61 1 9 2 1 2 3 3 2 4 7 82 6 9 4 7 8 7 4 8 1 0 7 71 0 4 1 8 6 2 9 0 4 1 82 3 5 4 1 8 6 5 4 9 4 29 32 5 8 3 7 12 0 9 3 7 2 5 8 1 8 3 78 3 1 4 8 2 3 2 3 3 41 8 8 3 3 5 5 2 3 7 5 41 3 5 2 1 1 3 0 4 3 0 4 4 7 6 6 8 51 2 4 1 9 3 2 7 91 5 7 2 7 9 4 3 6 6 2 8 1 7 0 8 1 1 3 9 1 6 4 01 2 3
3 9 3 1 4 6 2 2 7 3 2 82 0 5 3 6 4 5 6 9 8 2 07 0 1 2 5 1 9 5 2 8 11 7 5 3 1 2 4 8 8 7 0 26 1 1 0 9 1 7 1 2 4 61 5 3 2 7 3 4 2 7 6 1 55 42 1 81 3 6 2 4 3 3 7 9 4 9 1 3 6 1 9 71 2 3 2 1 8 3 4 1 4 9 24 41 7 91 1 1 1 9 8 3 1 0 4 4 77 31 6 41 0 2 1 8 2 2 8 4 4 1 0
1 3 4 02 0 9 5
2 6 8 4 1 9 6 0 33 7 5 6 7 01 0 4 71 5 0 71 2 9 2 2 9 3 5 9 3 2 2 5 7 2 8 9 71 2 9 21 1 3 2 0 1 3 1 4 4 5 22 8 2 5 0 2 7 8 5 1 1 3 01 0 0 1 7 8 2 7 9 4 0 22 5 0 4 4 51 0 0 59 0 1 6 0 2 5 1 3 6 22 2 5 4 0 0 6 2 7 9 0 58 2 1 4 6 2 2 8 3 2 92 0 5 3 6 5 5 7 0 8 2 27 52 0 9 3 0 11 8 7 3 3 57 5 2
1 2 '1 62 02 02 52 52 5 s =3 / 4 d 2 5 6 2 03 6 9 0 0 1 5 6 8 02 7 8 8 04 3 5 6 06 2 7 3 0 9 2 2 01 6 4 0 0 2 5 6 2 0 3 6 9 0 0 1 6 9 7 03 0 1 7 04 7 1 5 06 7 8 9 0
0 5)CS>
= 9,
K4nr2
of (1
Id 9 '\ Id1 \ 1 / [ d
[ j For
Id 1 '\ 1 I[ d 9
[( 0 . 4 fcu A l thou g h
of
k 1 x b A s2 fY a2 k 2 x ) d') 0 . 0 0 8
shou l d
d')
k2
main
V1)
AA,
F/2//i(CriticaI
crack and natural/
Vpath
0.35a1)
0.35a1)f1b
0.35aa1)f1b
2.
However,
3 4 6 Col u mns
A 5 2 x ) + d')+A 5 2fY d2 ( dT hese
0 . 7 2 iV,1A 5 2f5 2iVI0 . 7 2 d')
is =+
=0 ; h, increases
prov ideddiN.
and
N
f5 2( d =Pi/ 2 , and 0 . l h N
is
i\ 1 7 1 d" \N which 0 . 9 5 ,
h/ 2 ) N, ( d h/ 2 ) N,
h/ 2
A 5 2 : bel ow
d h/ 2 ,
d h/ 2 ,
I
1 63 0 03 5 04 0 04 5 0
5 5 06 0 01 0 3 5 1 1 1 2 1 2 3 1 1 4 4 21 4 3 7 1 5 5 6 1 7 6 71 8 1 2 1 9 3 1 2 1 4 2 2 4 4 82 2 3 7 2 3 5 6 2 5 6 7 2 8 7 3l ess 2 7 1 2 2 8 3 1 3 0 4 2 3 3 4 8than 3 2 3 7 3 3 5 6 3 5 6 70 4 % 3 9 3 1
1 4 9 6 2 4 4 9 2 6 8 7 3 1 1 0 3 7 2 12 7 7 1 2 9 2 4 3 1 6 2 3 5 8 5 4 1 9 63 2 9 6 3 4 4 9 3 6 8 7 4 1 1 0 4 7 2 13 8 7 1 4 0 2 4 4 2 6 2 4 6 8 5=3 0
4 0 04 5 05 0 05 5 06 0 01 2 1 2 1 2 8 7 1 4 0 3 1 6 / 01 6 7 7 1 7 9 3 2 0 0 02 1 2 7 2 2 4 3 2 4 5 0 2 7 4 92 7 5 3 2 9 6 03 2 0 7 3 3 2 3 3 5 3 0 3 8 2 9than 3 9 5 3 4 1 6 0 4 4 5 90 . 4 % 4 6 4 3
Rcmt ex ceeds1 7 3 5 3 0 7 7 3 4 9 1 4 0 8 83 4 1 4 3 6 4 7 4 0 6 1 4 6 5 83 8 9 5 4 0 4 4 4 2 7 7 4 6 9 1 5 2 8 84 5 8 5 4 7 3 4 4 9 6 7 5 3 8 1 5 9 7 82 5 03 0 03 5 04 0 04 5 05 0 05 5 06 0 01 5 9 0 1 6 3 7 1 7 4 9 1 9 4 62 1 5 7 2 2 6 9 2 4 6 62 7 5 7 2 8 6 9 3 0 6 6 3 3 5 1 3 4 3 7 3 5 4 9 3 7 4 6 4 0 3 1l ess 4 1 9 7 4 3 0 9 4 5 0 6 4 7 9 1thanL5 1 4 9 5 3 4 6 5 6 3 10 4 %16 0 6 9
2 2 1 3 3 4 9 3 3 6 3 5 3 8 5 8 4 2 5 3 4 8 2 34 2 5 3 4 3 9 5 4 6 1 8 5 0 1 3 5 5 8 35 0 9 3 5 2 3 5 5 4 5 8 5 8 5 3 6 4 2 36 0 1 3 6 1 5 5 6 3 7 8 6 7 7 3 7 3 4 31 2 6 1 9 7 3 0 9 5 0 6 7 9 1 2 5 3 3 9 5 6 1 8 1 0 1 3 1 5 8 3
5 0 0
6 0 0 1 2 8 2 1 4 0 0 / 6 / 0 1 9 8 2 2 1 0 0 2 3 1 0 2 6 1 3l ess 2 5 1 6 2 7 2 6 3 0 2 9-than 2 8 5 7 2 9 7 5 3 1 8 5 3 4 8 80 . 4 % . 3 4 7 8
2 1 9 2 2 4 2 9 2 8 4 9 3 4 5 52 4 5 6 2 6 0 8 2 8 4 5 3 2 6 5 3 8 7 12 9 1 6 3 0 6 7 3 3 0 4 3 7 2 4 4 3 3 03 4 1 9 3 5 7 0 3 8 0 7 4 2 2 7 4 8 3 3 3 0f5 = 2 5 03 0 0 1 0 7 9 1 1 5 5 1 2 7 3 1 4 8 3 1 4 2 0 1 4 9 6 1 6 1 5 / 8 2 5 1 8 1 4 1 8 9 0 2 0 0 8 2 2 1 8 Rcmt 2 3 3 6 2 4 5 5 2 6 6 5 2 9 6 85 0 0 l ess 2 8 3 5 2 9 5 3 3 1 6 3 3 4 6 65 5 0 than 3 3 8 6 3 5 0 5 3 7 1 5 4 0 1 86 0 0 0 . 4 % 4 1 0 8ex ceeds1 5 5 5 6 % 2 5 4 7 2 7 8 4 3 2 0 3 3 8 1 02 8 9 4 3 0 4 5 3 2 8 2 3 7 0 2 4 3 0 83 4 4 5 3 5 9 7 3 8 3 4 4 2 5 3 4 8 6 04 0 4 9 4 2 0 0 4 4 3 7 4 8 5 7 5 4 6 34 03 0 03 5 04 0 04 5 05 0 05 5 06 0 01 3 9 4 1 4 7 0 1 5 8 8 1 7 9 81 9 2 5 2 0 4 3 2 2 5 32 4 5 0 2 5 6 8 2 7 7 8 3 0 8 13 0 4 5 3 1 6 3 3 3 7 3 3 6 7 6l ess 3 7 1 0 3 8 2 8 4 0 3 8 4 3 4 1than 4 4 4 5 4 5 6 3 4 7 7 3 5 0 7 60 . 4 % 5 3 6 8
ex ceeds1 9 8 4
3 9 2 0 4 1 5 7 4 5 7 7 5 1 8 34 5 0 4 4 6 5 5 4 8 9 2 5 3 1 2 5 9 1 85 3 0 9 5 4 6 0 5 6 9 7 6 1 1 7 6 7 2 31 1 3 1 7 6 2 7 6 4 5 2 7 0 7 2 2 6 3 5 3 5 5 2 9 0 5 1 4 1 4 g iv en in ital ics indicate l ess-practicabl e arrang ementseig htl arg e bars in smal lcol u mns or fou r bars in l arg e col u mns) .Inbeen
3 4 8
+is
+
and and is
are and [ M x
( 2 b
5 5 0 2 5 0 5 5 mm) . 2 5 0 0 . 0 2 8 .
0 . 0 2 83 8 5 0
2 5 01 . 84 0 0 3 8 5 0 mm2
5 5 02 5 0 0 . 2 =0 . 5 5 ,
4 4 5 0 mm2 1 . 8
2 7 5 ) 2 5 1 0 . 0 60 . 4 5 5 3 .
4 2 5 0 . 4 7 6 . ==1 6 1 6 mm2
d')
1 0 . 0 6 x 0 . 4 7 6 x 2 5 0 x 4 9 7
3 6 9 . 6
2 5 0 6 7 6 2 2 9 8
A 5 2 .
1 0
Size of sq u are [ = 2 5 0
2 9 5 9 1 2 4 9
2 0 4 1
2 5 6 4
3 0 3 9
4 4 4 2
1 4 9 4
L = 2 5 O
1 7 3 9 2 3 4 1 2 5 7 8 2 9 9 82 6 8 1 * 1
3 4 2 1 3 6 5 8
0
1 4 1 5
1 9 0 0
2 6 0 0 1 0 9 9 > 6 % 1 6 5 9
=2 5 0
9 0 8
1 8 8 32 2 5 4
3 4 0 1l cssthan 3 6 3 3
3 9 0 4
2 1 4 9 2 3 6 ! 2 7 3 73 2 8 02 4 2 9
3 2 3 6 3 6 1 24 1 5 5<
4 5 3 4 1 5 2 8 > 6 % 2 3 6 8 1
4 3 6 9 4 7 4 5 5 2 8 8
been d/ h=0 9 0K = 10d/ h =0 . 8 0
1 5 40 7Val u es of
562 00 1 0 21 80 : 0 40U )5 )( 5>0 51 60 641 21 040 80 6000 40 60 81 01 21 41 61 80 0 0 4 0 50 6Val u es of0 8
1 0 . 7 4
1 0 0
4 6 7
4 6 7 0 . 1 4 4 ,0 . 2 2 2 0 . 1 ,0 . 2 6 , =0 . 2 6
4 2 5Oncea 6 0 0 mm3 0 0 mm6 0 / 6 0 00 . 1 6 0 / 3 0 0 0 . 2 .3 0 00 . 0 9 2 6 , 1 0 0 1 . 51 0 6 1 ( 3 0 0 0 . 2 7 8 . 0 . 0 6 1 7 / 0 . 6 0 . 1 0 3 . 0 . 1 0 3 0 . 2 7 8 , 0 . 2 6 : =0 . 2 6 0 . 0 1 8 4 . 3 0 N/ mm2 , =4 2 5 =0 . 1 8 4 , 1 9 ,=0 . 2 7 80 . 4 4 . 0 . 6 =0 . 4 4 ,
shou l d 0 . 1 5 0 . 0 . 1 5 0 0 . 2 7 8 ,
0 . 3 6 :0 . 3 6 0 . 0 2 5 4 .
=0 . 0 2 2 =0 . 0 2 2 0 . 3 1 =0 . 2 7 8 ,0 . 1 20 . 0 6 1 7 / 0 . 1 20 . 5 2 9 .with =0 . 3 10 . 2 7 8 ,0 . 1 4 =0 . 0 9 2 6 / 0 . 1 40 . 6 6 2 . 4 2 59 . 3 5 ,2 0 . 5=0 . 2 7 80 . 4 0 6 . ( 5 / 3 ) 0 . 4 0 61 . 3 4 4 +0 . 5 2 9 1 =I,
1 . 2 6 7 . 0 . 1 4 5 0 . 2 7 8 ,0 . 3 10 . 0 2 2
and
1 5 ,
2 0 0 k N3 5 0 k N. 1 4 0 N/ mm2 ; fcr= 71 5 . 2 0 0 5 7 1 5 7 1 / 1 0 0 00 . 5 7 1 . 3 5 0 mm
8 2 4 . 2 7 8 0
1 3 61 5 , ( 1 5
( 1 5 x 2 8 2 6 ) + ( 2 2 0 . 5 x = 2 7 1 mm
f = 5d/ h=0 . 9 5d/ h=0 . 9 0
5 0 0
= 4 . 5 8
the
2 2 5 = 1 . 6 3
=6 7 5
Nd
= =1 1 . 5
8 0
+ ( 1 4 x 9 8 2 x 4 0 )
4 0 ) 26 2 7 3 0 d/ h=0 . 8 5d/ h=0 . 8 0
2 2 5
=3 . 8 3
3 . 8 3 [ ( 0 . 5
d'h\
d' 2
/ 'h \ x
=
=+Pt( 1 4 . 5 _
h
and
x ) / x
A
where, =
+ 1 ) Nd 1
>
/ /
2
2 r
l ) ] 2 it.
=
= x
= I) ]
0 . 6 7 ) 5 0 0=0 . 6 7=4 3 . 8 3 0 05 0 0 mm
4 0 5 0 mm, 0 . 9 . 5 0 / 5 0 080 . 0 1 7 .
4 . 0 7 6 1
fscmax=
= fscrnax =1 5 0 . 0 8 2
=1 4 00 . 93 0 0=1 0 0 5 0 05 0 0 / 5 0 01 .
0 . 4 1
2 0 0
x 1 5 2 . 4 = x ) ,
0 . 4 3 . 0 . 4 3 , 0 . 0 1 5 5 .0 . 0
3 4 8 mm l OOk N9 8 2 1 4 7 3
1 4 7 3 6 3 . 8 9 8 2 =6 . 1 9
7 1 5 . 1 0 0 / 1 0 0 0 0 . 1 ,1 . 5
2 2 . 8 6
0
b1 h1 Depth
M oment
=+ ( h,Compressiv e fNdM d( hX )f ( a1 h,) 1 5 A 1 , x ) fL 1 Nd]
2 0 mm ex tra Stripin 2 nd trial 3 5 0 k N2 0 0
01 1 )G O'4 ,'I,C) G O
E
ViV CO0 )CO0 )
a
0 )
G 0G O0 )
C)
( . . 1 ( a If x ) / E ( a x ) Position
1 '0 a, =1 3 6 mm ( 1 st trial )= 3 5 0mm ( 1 st tnal )bars
M 1/ 3 Nh
is
where shou l d
N) /
0 . 2
5 3 . 0 5
to
mark edl y
bd( a,
Stresses:=+f,. ,,,0 , = A ,,A ,
bx . =( =h/ 2
=+
d'\
1and =( a, )or
d'/ d) Nd] / A ,d/ ( 1 du e
1 ,, + f, and = f,,61r ,I,. J
0 . 6 0 0 . 7 0
factor
stresses
0 . 1 5
- 2 . 8
2 . 3
1 . 8
d/ h= O. 8 5=d/ h= O. 9 5Pi = ( i di! '0 . 7I0 . 8 0 . 9I i1 . 0i1 . 1I i I i i II I I I I I I I I I I II I I I I I I I I I I I I I II I I IIIII III I I I I I I1 . 5 1 . 4 1 . 3 1 . 2 1 . 1 1 . 0 0 . 8 0 . 7 0 . 6 0 . 51 31 2Ndrhtfcrii1 0987654320 read 1 6 5by M u l tipl ier for p10 . 5 1 . 0 2 . 0 2 . 5 3 . 0 3 . 5 4 . 5 5 . 0 M d5 . 5 6 . 0h1 / r=0 . 2 02 zrh,p1
M ,
h) .
= 0 . 0 0 3 5
where
3 0
4 6 0
5 6 / 5 0 00 . 1 1 2 . 5 0 0 0 / 2 5 02 0 , 2 0 ,0 . 2 0 ,
3 2 0 2 0 . 5 3 3 0 . 6 1 5
6
C.Ca
5 5 bars A ,1 ;
In
N4 ( z =z,A ,,
L 1 2 J 1 2 )0( I,C5 )a C. )5 )a C. )a
C) a
I) a 0C.
05 5C)
=N4 ( z, eInA ,2A ,
e]
=z,A ,
C-) C5 5a 0z
a, where
b,h, +( a, ---E ( x h) h ADepth _ _ _ _ _ _ _ _
a,( d x ) Ff,,M ax imu m ; J ,, j hj ,IA ,, h,) oA ,, > S LxFinal l y
a
2 .1 )
C. ) a 0a
C.E
5 )
C)
5 1 1
bx . ( K 1 x / 2 )
d'
Determine fIr$ 2 bd
txA x is throu g hcentroid ofNeu tralax is stressed/=M d/ Ndt,/ ;N,, ( tension)
5 )
and
-. T henfcr f,,
M d/ Nd and
000CS5 )0 5 )0
Cd,
nC
Cd,
2
L )
Cd,CM
C',5 )C',
C-
00CS5 )Cd,
V
67
abou t M dY
bendingStresses:
7 J y o/ \'C,T otalsteel=A ',_ _ _ _ _ _ _IBh,xNd- M d,= )- -(
= +fx( =
=
H _fCC
Cd)
. . J f,,)
0fpc +
f]
f,,]
68L imit ( u nbraced)L imit ( braced)8 S8 1 1 0sl enderness modifier f3for normaL . weig ht concrete0 . 0 5I II IFu l ll ines indicate tru e rel ationshipB rok en l ines indicate simpl ified rel ationshipsu g g ested in B S8 1 1 O1 4 1 6 1 8hI I I I I I5 5l a/ h6 00a>Ou tl ineVal u es of ( N/ mm2 )
2 . M 1
0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 ,0 1 . 2I i I ii I I IL imit0 1l tIl l Il l l tIl ItI{ ''IIIIIIIIIIIIIIIIIIIIIIIIIl1 0 1 52 0 2 5 3 0 3 5 4 0 4 5 ! 5 0ii 1 1 1 1 1 1 1 1 I I ,. . . " IIIIII l il t l Il t0 . 1 0 2 0 3 0 4 0 5 0 60 70 80 91 0 1 2 1 4 1 6 1 8 2 . 0L imrt ( al l )B S8 1 1 O sl enderness modifierflfor l ig htweig ht concreteCP1 1 O sl enderness modifier for normal -weig ht concrel e0 2 0 3 0 4 0 50 . 6I
IL mIt0 8 1 0 1 2 1 4 1 6
2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0iiiit iil i, iiiIIIIIII(IIIJ1JI I I IJ0 3 0 4 0 5 0 6 0 8 1 0 1 5CP1 1 O sl enderness modifier a for l ig htweig ht concrete
z
aa)a> . 42 0 2 5 3 0 3 5 4 0Val u es of
x 2 2 00 . 5 3 3 0 . 0 2 8
5 0 0 mm
0 . 2 1 ,
3 3 0
l a/ i l 2 / l OOi.
1 6 9U nbraced
ratios
I Iji I I I I I J5 0 1 . 1 . 5
II III I I III I I I9 0
1 ,/ i 0C. 10 . 9 51 . 0 0* *'a,C0t)> C0C-u
.Ic/ bis
2 0 2 0or or
I II
I I I I I I I I I I I I I I I I I i I I i i t i I i i i i I
1 7 0
0 . 3 5 f,,
W al l s
( 3 / 4 )
distance
0 3 ( 1 h 3 0 .
e
0 . 0 0 0 8 1 I IfLhor e 10 . 3 [ For 4 0
nominal
k 2 )
0 . 3 1 J
3 0 .
b, hd
T he
=cl ear
( 1 5 >3 / 2 ,
1 7 1NotesB raced and u nbraced wal l s:a braced
l oads
44 . < 4 ,<
If i+
0 8
j
W al l s
.W al l s
1 0 . ( 3 / 4 )
distancex
hA ppl icabil ity :for=3 0 .
1 For e, For 1 0 .=4 0
Desig n
and and may 1 0 2 .
Ii For 0 . 0 0 1 2 ( Al fL h JFor =3 0 .
E ffectiv e braced
E ffectiv e hd4 :h/ 2 0 )
P13 8 0J oints
bd23 5 0 d( J ( f. . ) =4 2 5
0 ) ,
A=bdA 1 6 . 3 M Uhd2
7 3 0 d(+ 2 4 . 5 J U NCT IONS B E T W E E N B E A M S A ND
1 7 2A deq u ate anchorag e-bondl eng th mu st be prov idedof action of l oad F:1 at ou ter edg e of bearingpad ( if prov ided) ;or2 at beg inningof chamfer( if prov ided) ;or3 at ou ter edg e of nib( If bearingpad or chamfer isnot prov ided, bars mu st beprov ided to prev ent cornerspal l ing )Form horizontalor v erticall oops here orwel d nib steelto l ong itu dinalbar of eq u alstreng th( If l oops are v ertical1 2mm. )M inimu m permissibl ecov erDesig n procedu reDetermine depth d fromconsiderations of shear2 .T hen prov ide A 5 =where is desig n stress in tensionFsteelcorrespondingto x / d ratioobtained from T abl e 1 0 4andsin3M inimu m al l owabl e 0 0 0 4 :max imu m =0 0 1 3Chamfer orrebatecornerProv ide horizontalstirru psg iv ingtotalarea 4hal f area ofmain reinforcementu pper two-thirds of dU ,z Nib reinforcement of area A s,,B SB 1 1 O:4 : 0 2 4 %of mil d steelor0 1 3 %of hig h-y iel d steelCP1 1 O:'4 : 0 2 5 %of mil d steelor0 . 1 5 %of hig h-y iel d steel( a)Verticall ink s
I'recommendations
1 . 1 ( b)H orizontall oopsCa>tension barsU ,5 )CUto crossbar or l ooped
Stru ctu res
2 0 6 0 .
cl ear
distance
Q5 )5 )a
CS1 7 3 T heoreticalstru t( criticalpl anefor crack ing )( 3 M 4 \ 2 1
/
A ,C/ 2 bCdC( d)( T his detailis Onl ysu itabl e wheremoments tend to cl ose corner)( b)( e)( c)L inkreinforcementA
T hru st in-col u mnbd/ l 0 0 ,
T ension in beamreinforcement
C. )V5 )a
C. )CSC)
Separate
0 . 4 2
2 . 7 1 . 4 l . 8 m,1 0 0 1 7 5 mm 3 0 .
8 1 . 8 6 3 5 . 8 7 8 1 . 8 9 3 5 . 6 7
n( k fl + k Ok l 2 )j 2 ( k 1 3 stiffness is
is
is k 1 1 l ) ( j 2 )1 ) ( j 2 ) ( j 3 )I _ II _ 1 1 ) ( j 2 ) 1 ) ( j 2 ) ( j 3 )1 ) _ 1
1 7 4tie-force( dimensionl ess)
av erag e
0
F, 0 0 2 6 7 ( g 5
T 0 . 4 ! 0
2 F,
desig ned, .A t
barsA l ternativ e means of prov idinganchorag eA l ternativ e means of prov idinganchorag e of peripherybetween internaland col u mn ties Col u mn to wal lties at each col u mn( or wal l ) / fl oorintersection
2 4 = 3 . S4 k N/ m2
[ ( 3 . 8 4 1 8 0 / 3 0 00 . 6 . 0 . 0 8 8 . 3 . 9 5 k Nm
5 . 7 3. 3 . 9 5 =
++ k 4 ) K 2 ) ( k 5=0
cos2 +
of
of of
of
1 . 5 m, 1 2 0 0 / 1 2 0 1 0 . 0 . 1 2 , 0 . 3 2 . 5 . 3 ( 3 1 . 5 23 3 . 4 k N
6 0 ,M ,,= 1 . 1 1k Nm,
1 6 . 7
acting
assu ming
1 7 5Free-standing( or scissor)stair( l andingu nsu pported)Indiv idu alprecast treadscantil ev ered from spinebeamH el icalstair 0
U sag e1 5 0
Priv ate
1 7 5
G eneral 6 0 0 mman notation
] / 2
1 tan
b1
respectiv el y
M h,
respectiv el y
b2 ) ] +4 ,
IAwhere
sec2 I B '1 B c H y j -n,by
M e
H x sin +{ M 0 b2 ) ] Sl abl ess ( Or sawtooth Simpl e straig ht stairL andingarrang ementor 'dog -l eg ')stairfor simpl e stair3 8 8 Stru ctu res
1 )
of
0 .
the
and
0 ) . 9 0 . and 9 0 ;
and
x x ) sin2
sin2 FY B=( gq ) r
= ( g
=05 ,I-aVSC0CS
nR1 H H
k 1 k 2 nR2
'i,'2second
total 1 7 6
niniconsidered asconcentratedl oads at mid-treadT y picalbending -moment diag ramT y picalshearing l orce diag ramU( b)Possibl e arrang ements of reinforcement Vertical M 0 cosI-.CaCeC-)zM rs =CCaCCaCaa0CO
4 / i)
Y 'x x cos
'x x = x2 Ornl=OrniT h
where
sheii.transmitted
1 7 8Seg mentaldome
wx_ _ _ _ _ _2 cos2 O
wh
a0. 2 0 .. 0Q A B , Q B C etc.
* NA B L 2 ; * NB CL 2 ,
2 FB
IB CIB C\
1 4 8 h4 5 1 4 83 1M 4 8 Ii. 1 2 ( )
0
I;[
N
cosec2 _ _ _ _ _ _ _ --2 irr
seg mentaldome ( approx . w8 aR 2 Rr
. N Conicaldome-o00. 00 .0. 0I-U aC)( bJ ( C)6 Sadl oad$$$$$$
of Md,4.
ys-I
99 z
'aI)-u
0-u
I)S..U,I)0-u
I-
.N,5=K1F312/y5
1.7
when
Iwhere
1.78
9.8
=yswhere
0.17
9
(.)Nib
9.25
8.45
8.60F1/u/i
Y5
Y
Ys
1
10.2
10.8wrC)C 0.(I)
= 0 . 0 2 1 4 F17 5 x1 6 mmCW I fl at4ciNormaiCross-sectionT og g l e hol e2 5 mm 2 5 mmL L in Six1 6 mmbarsH el icalbinding( ties)Clspacer fork s
+ a1 cn
H 1C. )0EEC. )
pN/ mm2
ptons/ in2
Short pil es:T og g l e hol es near head ( for g u iding )can g eneral l ybe u sed for l iftingwithou t produ cingex cessiv e bendingmomentsSoft g rou nd throu g hou t T hrou g h soft g rou nd toShape su itabl e forRockshoe( no shoe)moderatel yhard g rou nd ( no shoe)g rav el s and sands0-Ca0 vCa =
5 0 mm7 5 mm 1 0 0 mm -centres : Centres2 5 mmg as-pipe ferru l es formingtog g l e hol es1 0 0 mm centres-centres-rJ .i. i- r
Ll . rr5 0 mmcentresCast-Iron shoeLFou r mainwith W I straps( proportions su itabl ebarsfor fairl ysoft strata)Cross-sectionat head of pil e6 ,8orl ink sSpacersat approx1 . 2centresSix1 6 mm 0barswith hel icalbindingat head onl yI-( C; -C. )=
C. )
. 0
=0 ,0 , =3 Om, 0 . 8 0 0 ( 3 . 7 5 3 . 0 ) + 6 0 0 k Nm. 3 . 8 4 6 0 . 5 9 1 7 . 0 . 9 8 0 6 ( 2 0 8 5 2 )2 8 0 . 4 0 . 9 8 0 6 ( 2 0 8 1 3 0 5 2 )2 5 . 5 0 . 9 8 0 6 ( 2 0 81 3 05 2 )3 8 2 . 4 k N 0 . 9 8 0 6 ( 2 0 8 1 3 01 2 7 . 5
0 0 ;
1 9 4 ( 3 nhpv ri
0 .
pil e-cap dCriticalperimeter forpu nchingshear
proj ectinginto cap frompil esE l ev ation Section at criticalpl ane for normalshearbars for col u mn-L ink s for starter bars-Verticall ink s between barsex tendingfrom pil esH orizontall ink s arou nd u p-standingend of main bars.( Not l ess than 1 2 mm at3 0 0 mm centres, say )bars desig ned to resist tensil e force obtained fromtabl e bel ow E nds bent and carriedto top of cap as shown, Not l ess than 0 . 2 5 %of mil dsteelor 0 1 5 %of hig h-y iel d steel
0co0L a+++NI9 d
b2 3 a2 ) Paral l el b2 )Y
a2 ) h2 )
+3 0 0 a2 )Paral l el Notation h,, diameter of pil e: a, b dimensions of col u mn; e spacingfactor of pil es ( normal l ybetween 2and 3dependingon g rou nd conditions)4 2 1 1 9 5 row
E RJB 2 A l A E RJ1 +B 2 x 0
A B
x 0
x C)I-I)
noCtDC
=E a,,/ 2 )E nx 2
F,,e Fhh i/ E n;
=FV( eh x 0 )+ Y o =( E 2E 3E 1E 4 ) / kk = E 1 E 5
( 1B 1 )A 1 A 2( 1: B 2 ) ( I B ,,_1 )
0
C)
C)
DC
E X 0 +Nil
x + B 2 )k h= ( tanOE l E 2 ) / kk m= X / I= X / E 6 +
formu l ae
1 tan2 1 cot2 1sinOsin sinO coscos sin cos 1 tan 1 2 sin =2sin 4 ')cos 2
1 9 3 / 7 2 7 2 1 / 1 0 0 1 2 . 7 1 8
3 9 1 9 / 1 7 0 2 2 . 3 0 2 9 . 8 0 6 6 5 3 2 . 1 7 4
c:
c,a,
3 5 5 / 1 1 3 2 2 / 7 3 . 1 4 1
1 8 0 / it5 7 . 3 5 7 . 2 9 5 7 7 9 5
radiu s
5 / 9 ( t 3 2 ) / 1 . 8 C ( 1 . 8 t sin sin
2 = a) ( s b) ( s c) ]( a
2 bc
=0x =
1 .\ / ( l
( a) 2 0 :cot
=2 . 7 4 7 5 1 : 2 . 7 5 .( b) 1 0 :cot 5 ,6 7 1 3 1 : 5 . 6 7 .
0
= tan2 l
0
Y / XR
nn.3 23 ,,3 2 83 ',3 2 1 61 ',49 "3 2. 1 j ,1 6U ,,3 2
3 22 ,,.1 6 3 21 "29 j ;1 6 3 25 ,,82 1 ,,3 2 3 2 4
2 . 5 "3 2. 1 5 "1 6. 2 "82 . 9 . ! '3 21 5 "1 6. 5 . 1 "3 21J . _ "3 21 . _ L "1 6 L I.3 2A i_ 5 j '1 6i_ i"3 2 4i_ S. . "1 6 3 21 1 "81 . 1 5 "3 2itS"3 2ii"21 1 5 "3 2
AtY l 'iS"4') 2 5 "3 2i2 i"3 2 8i2 i"3 2'itS"1 63 _ L "3 2 1 62 1 "8AA Q 2 _ S_ "3 22 _ I! '1 6 3 2 3 2 1 6 3 2iS"8 1 62 1 5 "3 22 1 "2
4 2 6M etric/ imperial ft 0 " 1 " 2 " 3 " 4 " 5 " 6 " 7 " 8 " 9 " 1 0 " 1 1 "0 0 . 0 2 5 0 . 0 5 1 0 . 0 7 6 0 . 1 0 2 0 . 1 2 7 0 . 1 5 2 0 . 1 7 8 0 . 2 0 3 0 . 2 2 9 0 . 2 5 4 0 . 2 7 91 0 . 3 0 5 0 . 3 3 00 . 3 81 0 . 4 0 6 0 . 4 3 2 0 . 4 5 7 0 . 4 8 3 0 . 5 0 80 . 5 5 9 0 . 5 8 42 0 . 6 1 0 3 0 . 9 1 4 0 . 9 4 00 . 9 9 1 1 . 0 1 6 4 1 . 2 1 9 1 . 2 4 5 1 . 2 7 0 1 . 2 9 55 1 . 5 2 4 1 . 5 4 96 1 . 8 2 9 1 . 8 5 4 1 . 8 8 0 1 . 9 0 5 1 . 9 3 0 1 . 9 5 6 1 . 9 8 1 2 . 0 0 72 . 0 5 7 2 . 0 8 3 2 . 1 0 87 2 . 1 3 4 2 . 1 5 9 2 . 1 8 4 2 . 2 1 0 2 . 2 3 5 2 . 2 6 1 2 . 2 8 6 2 . 3 1 1 2 . 3 3 7 2 . 3 6 2 2 . 3 8 8 2 . 4 1 38 2 . 4 3 8 2 . 4 6 4 2 . 4 8 9 2 . 5 1 5 2 . 5 4 02 . 5 9 1 2 . 6 1 6 2 . 6 4 2 2 . 6 6 7 2 . 6 9 2 2 . 7 1 89 2 . 7 4 3 2 . 7 6 9 2 . 7 9 4 2 . 8 1 9 2 . 8 4 5 2 . 8 7 0 2 . 8 9 6 2 . 9 2 1 2 . 9 4 6 2 . 9 7 2 2 . 9 9 7 3 . 0 2 31 0 3 . 0 4 8 3 . 0 7 3 3 . 0 9 9 3 . 1 2 4 3 . 1 5 0 3 . 1 7 5 3 . 2 0 0 3 . 2 2 6 3 . 2 5 1 3 . 2 7 7 3 . 3 0 2 3 . 3 2 71 13 . 3 7 8 3 . 4 0 4 3 . 4 2 9 3 . 4 5 4 3 . 4 8 0 3 . 5 0 5 3 . 5 3 13 . 5 8 1 3 . 6 0 7 3 . 6 3 21 23 . 6 8 3 3 . 7 0 8 3 . 7 3 4 3 . 8 1 0 3 . 8 3 5 3 . 8 6 1 3 . 8 8 6 3 . 9 1 2 3 . 9 3 71 3 3 . 9 6 2 3 . 9 8 8 4 . 0 1 3 4 . 0 3 9 4 . 0 6 4 4 . 0 8 9 4 . 1 1 5 4 . 1 4 0 4 . 1 6 6 4 . 1 9 1 4 . 2 1 6 4 . 2 4 21 4 4 . 2 6 7 4 . 2 9 3 4 . 3 1 8 4 . 3 4 3 4 . 3 6 9 4 . 3 9 4 4 . 4 2 04 . 4 7 0 4 . 4 9 6 4 . 5 2 1 4 . 5 4 71 5 4 . 5 7 2 4 . 5 9 7 4 . 6 2 3 4 . 6 4 8 4 . 6 7 4 4 . 6 9 9 4 . 7 2 44 . 7 7 5 4 . 8 0 1 4 . 8 2 6 4 . 8 5 11 6 4 . 8 7 7 4 . 9 0 2 4 . 9 2 84 . 9 7 8 5 . 0 0 4 5 . 0 2 95 . 0 8 0 5 . 1 0 5 5 . 1 3 1 5 . 1 5 61 7 5 . 1 8 2 5 . 2 0 7 5 . 2 3 2 5 . 2 5 8 5 . 2 8 3 5 . 3 0 9 5 . 3 3 45 . 3 8 5 5 . 4 1 05 . 4 6 11 8 5 . 4 8 6 5 . 5 1 2 5 . 5 8 8 5 . 6 1 3 5 . 6 3 95 . 6 9 0 5 . 7 1 55 . 7 6 61 9 5 . 7 9 1 5 . 8 1 7 5 . 8 4 2 5 . 9 1 8 5 . 9 4 45 . 9 9 4 6 . 0 2 06 . 0 7 12 0 6 . 0 9 6 6 . 1 2 1 6 . 1 4 7 6 . 1 7 2 6 . 1 9 8 6 . 2 2 3 6 . 2 4 8 6 . 2 7 4 6 . 2 9 9 6 . 3 2 5 6 . 3 5 03 0 9 . 1 4 4 9 . 1 6 9 9 . 1 9 5 9 . 2 2 0 9 . 2 4 6 9 . 2 7 1 9 . 2 9 6 9 . 3 2 2 9 . 3 4 7 9 . 3 7 3 9 . 3 9 8 9 . 4 2 3 -4 0 1 2 . 1 9 2 1 2 . 2 1 7 1 2 . 2 4 3 1 2 . 2 6 8 1 2 . 2 9 4 1 2 . 3 1 9 1 2 . 3 4 4 1 2 . 3 7 0 1 2 . 3 9 5 1 2 . 4 2 1 1 2 . 4 4 6 1 2 . 4 7 15 0 1 5 . 2 4 0 1 5 . 2 6 5 1 5 . 2 9 1 1 5 . 3 1 6 1 5 . 3 6 7 1 5 . 3 9 2 1 5 . 4 1 8 1 5 . 4 6 9 1 5 . 4 9 41 0 . 3 2 mm1 9 . 8 4 mm. E 1 7 . 4 6 mm 2 3 . 8 1mm2 . 3 8 mm 5 . 5 6 mm 8 . 7 3 mm1 5 . 0 8 mm 1 8 . 2 6 mm 2 1 . 4 3 mm 2 4 . 6 1 j 3 1 5 3 7o
l . 1 9 6 y d2 3 . 2 80 . 3 0 4 80 . 4 0 4 7 1 6 3 9 0 mm30 . 6 2 1 4 3 5 . 3 1 0 . 0 2 8 3 2 0 . 0 0 1 6 4 5 . 2=1 . 3 0 8 y d30 . 7 6 4 6 l 0 . 7 6 ft2
0 . 2 2 4 8 1 bf=0 . l OO4 tonf= II1 0 1 6 1 . Ol 6 tonnell k g fI 0 . 0 6 8 5 20 . 1 0 2 00 . 0 3 0 6 0 . 1 0 2 011 . 4 8 8 1 3 . 3 3 3 0 . 6 7 210 . 3 0 0 0 I 1 4 5 . Ol bf/ in21 0 . 2 ok g f/ cm2I0 . 2 ok g f/ cm21 0 . 0 7 0 3 I1 5 7 . 5 1 4 . 2 2 I 0 . 0 0 6 I 0 . 0 2 0 8 9 1 bf/ ft29 . 3 2 4 tonf/ ft21 0 . 2 0 k g f/ cm2 1 4 . 8 8 211 . 0 9 4 0 . 2 0 4 8 11 0 . 0 0 60 . 1 0 2 0 . 0 0 2 0 . 1 0 2 0 1 1 6 . 0 2I3 5 ,8 8 0 . 0 6 2 4 I0 . 0 2 7 8 7I 0 . 0 0 3 6 8 4 0 . 1 0 2 0 1 2 7 . 6 8 0 . 0 3 6 1 8 . 8 5 1 0 . 7 3 7 6 0 . l O2 Ok g fm 1 0 . 0 8 3 3 3 0 . 0 1 1 l 2 l bfin1 0 . l 3 8 3 k g frn8 6 . 8 0 1
0 . 2 2 0 . 2 6 4 2U SA 11 . 2 0 10 . 8 3 2 7 1 6 2 . 42 4 0 01 4 0x 2 5 . 5
is Simpl y
bl ems
. Z eitu ng
Corn-
an
9 0 .
DE CIDE . 4 3 2References
an
charts
fou ndation
g raphics
a
Nu mbers preceded by't' areT abl e Nu mbersA bu tments 7 7A g g reg ates 3 7 8A g ricu l tu ralsil os, see Sil osA ircraft ru nway s 1 2 2A nchorag e bond, see B ondA nnu l ar sections 6 6 , 8 4 , 3 6 0 2 ,ti 6 4 5A rches 3 3 5 , t7 5 8fix ed 3 4 , t7 6 8parabol ic 3 4 5 , 2 2 4 8 , t7 7stresses in 2 2 2 4 , t7 6thick ness determination 2 2 2 ,t7 6sy mmetricalconcrete 3 3 , ti 8 0three-hing ed 3 3 4 , t7 5two-hing ed 3 3 , 3 4 , t7 5 , 2 2 2 , t7 5see a/ so B ridg esA reas 4 9 , t9 8B al u strades 9B arscu rtail ment 6 0 , 3 2 2 , t1 4 1economic choice 4in compression 6 3 4 , t1 0 3in tension 6 3 , t1 0 3incl ined 6 0 , 3 2 8 , t1 4 4spacing3 2 2see a/ so ReinforcementB asements 9 1B eamsB S8 1 1 O desig n chart thU ilcantil ev ers, see Cantil ev erscement content 4concentrated l oads 3 2 8 3 0 ,ti 4 3continu ou s, see Continu ou sbeamsCP1 1 O desig n chart t1 1 2 1 4cu rv ed 6 0 , t1 4 6 7concentrated l oads 3 3 4 6 ,ti 4 6u niform l oads 3 3 6 , ti 4 7deep 6 0 1 , 3 3 6 8 , ti 4 8desig n shearingforce 3 3 8E u ropean ConcreteCommitteerecommendation 3 3 6main l ong ttu dinalreinforcement 3 3 6web reinforcement 3 3 6 8defl ections t2 3 4desig n of 4 9 5 0 , 2 8 8 9 4dou bl y -reinforced 4fix ed-end-moment coefficients1 3 8 4 6 , t2 9 3 1fl ang ed, see Fl ang ed beamsfreel ysu pportedmax imu m defl ections t2 8max imu m moments t2 7I- 2 9 4in tension 5 5 , t9 1j u nctions with ex ternalcol u mns3 7 8 , t1 7 3moments t2 3 4proportions and detail s of 5 5 6rectang u l ardetail ing6 0 , t1 4 0modu l ar-ratio method 5 4 5 ,2 8 8 9 4 , ti 1 7 1 9shears t2 3 4sing l e-span 1 8 , t2 4 9stru ctu ralanal y sis 1 8sl ender 2 3 4steel -beam theory5 5see a/ so Sl abs;Stru ctu ralmembersB earing s 7 8 ,3 9 0 , t1 9 1 , t1 8 1detail ing7 0 , ti 7 2fou ndations 8 9 , t1 9 1B endingbiax ial6 4 , 6 8 , 3 4 6 5 6 , t1 5 9 ,t1 6 7concrete desig n streng th 4 2permissibl e serv ice stress 4 3u niax ial3 4 4 6 , 3 5 6 6 2 , t1 6 0 1B endingmomentsbasic data t2 2combined base fou ndations 4 1 0continu ou s beams, seeContinu ou s beamsfl at sl abs 2 6 , 2 0 4fl ex ibl e retainingwal l8 8in wal lof y l indricaltank8 0 ,ti 8 4wind forces and 3 1 2see al so M oments;Stru ctu ralanal y sisB iax ialbending6 4 , 6 8 , 3 4 6 5 6 :t1 5 9 , ti6 7B l indingl ay er 8 9B ond 2 3 4 4 2anchorag e 4 7 , 2 3 4 3 6compression reinforcement4 7l eng ths t1 2 1minimu m t9 3mechanical4 7tension reinforcement 4 6 7 ,t9 2 4bars in l iq u idstru ctu res 4 7 , t1 3 2bearinginside bends 2 3 6 , t9 5between concrete andreinforcement 4 6 9 , t9 2 5B S5 3 3 7req u irements 2 4 2 , t1 3 2concrete 4 3l ocal4 7 , 2 5 4 6 , t9 2minimu m internalradii t9 5reinforcement t9 2 4B ow g irders, see B eams, cu rv edB ridg es 5 0 , 7 6 7 , t1 8 0deck7 6 7 , t1 8 0footbridg es and paths 7 7 , 1 1 4 ,till oads 1 0 , 7 6 , 1 1 4 , t8 1 1partialsafetyfactors 1 0 8piers and abu tments 7 7rail way1 0 , 1 1 5 2 2 , t9road 1 0ty pes 7 6 , t1 8 1weig hts of v ehicl es t8wind forces 1 3see a/ so A rchesB u il ding s stru ctu re 7 1 Shol l ow-bl ocksl abs 7 2 , t2imposed l oads t6 7l oad bearingwal l s 7 5 6 , ti 7 1opening s in sl abs 7 1 2panelwal l s 7 4 , t5 0precast concrete pu rl ins 7 3stabil ity7 1 , t1 7 4wind l oading1 3see a/ so Stru ctu re andfou ndationsB u nk ersel ev ated 8 2wind forces 3 1 2see a/ so Sil osCA DS software 1 0 0Cantil ev ers 1 8 , t2 4 9defl ections t2 5 6mu l tipl iers for ti 2 1moments t2 5 6shears t2 5 6tapered 3 1 8Cementcontent choice 4hig h-al u mina ( B S9 1 5 )3 7l ow-heat Portl and bl ast-fu rnace( B S4 2 4 6 )3 7l ow-heat Portl and ( B S13 7 0 ) 3 7masonry( B S5 2 2 4 )3 7ordinaryPortl and ( B S1 2 )3 6other 3 7Portl and bl ast-fu rnace ( B S1 4 6 )3 6Portl and pu l v erized fu el -ash( B S6 5 8 8 )3 7rapid-hardeningPortl and ( B S12 )3 6su l phate-resistant ( B S4 0 2 7 )3 6su per-su l phated ( B S4 2 4 8 )3 6 7Characteristic streng thconcrete 4 2reinforcement 4 5Chimney sdimensions 8 4l ong itu dinalstress 8 3 , t1 6 4 5transv erse stress 8 3wind forces 1 3Cl adding , wind pressu res andti 4 -1 5Cl ay s 1 5Cohesiv e soil s 1 5 , 4 0 4 , ti 9Col u mns 2 1 8annu l ar sections 6 6 , 3 6 0 2 ,t1 6 4 5biax ialbending6 4 , 6 8 , 3 4 6 5 6 ,t1 5 9 , t1 6 7braced, wind forces 3 1cement content 4col u mn head sl abs 2 0 4 , t6 4combined bendingand tension6 7 8 ,t1 6 6u niax ial 6 4 , t1 5 3 6combined bendingand thru st6 5 7 , ti 6 0 5u niax ial6 2 3 , t1 5 7 8compressiv e and tensil e stress6 7 , t1 6 0concentrical l yl oaded t1 6 9el ev ated bu nk ers 8 2el ev ated tank s 8 1 , 4 0 2 4 , t1 4ex ternal2 9 3 0 , 6 1 , t6 5 , t6 8 , t7 4j u nctions with beams 3 8 0 ,t1 7 3in bu il dingframescorner col u mns 3 0 1ex ternal3 0internal3 0irreg u l ar 6 3 4 , 6 5 , t1 0 3 , t1 6 0l oading9 , 6 1 2 , 3 4 0 4 , t6 , t1 2 ,t1 4 9 5 0massiv e su perstru ctu res 3 1neu tralax is position 6 8radii of g y ration 3 7 4 , t9 8 9 , t1 6 9rectang u l ar 6 2 , 6 5 6 , t1 6 1 3 ,tl6 5rig orou s anal y sis 6 2 , ti 1 5 1 6sy mmetrical l yreinforced 6 5 ,ti 6 2 3serv iceabil ity6 3short, see Short col u mnssl ender 6 9 7 0 , 3 6 4 7 4 , ti 6 8desig n procedu reB S8 1 1 O, 3 6 4 7 0 , t1 5 1 2CP1 1 O, 3 7 0 4 , t1 6 9rectang u l ar 6 2 , t1 6 8stresses in different directi ns6 8 9 , t1 6 2stru ctu ralanal y sis 2 9 3 2 , t6 5Compressionconcrete 4 0 , 4 2 , 4 3 , 1 5 4 , t7 9 8 0permissibl e serv ice stress 4 3 , 4 6reinforcements 4 5 , 4 6 , ti 0 3 4stress in col u mns, 6 7 , t1 6 0Compu ters 9 6 1 0 6CA DS software 1 0 0DE CIDEsy stem 9 8 9fu tu re dev el opments 1 0 5 6l nteg raph sy stem 9 7 8micros 1 0 0 2OA SY S software 9 9 -1 0 0prog rammabl gcal cu l ators1 0 0 -2writingsoftware 1 0 2 5prog ram l isting s 1 0 4prog rammingaids 1 0 4 5Concentrated l oads 2 1 , 1 1 4 , 1 9 0 ,t5 4 6beams 1 8 6 7 , t1 4 3cu rv ed 1 8 9 9 0 , t1 4 6dispersion 1 1 , 1 2 2 , tl O 1 1on bridg es tbsl abs 3 3 0 , t6 4Concreteaerated 4 0ag g reg ates 3 7 8air-entrained 4 0bond 4 3cel l u l ar 4 0cement 3 6 7characteristic streng th 4 2compression 4 0 , 4 2 , 4 3 , t7 9 8 0 ,2 3 0desig n streng ths 4 2 3 , 2 3 4bearingstresses 4 3bond 4 3in direct compression andbending4 2modification with ag e 4 3streng th in shear 4 2 3torsion streng th 4 3 , t1 4 3el astic properties 4 0 , 2 3 0fatig u e 4 1 2fibre-reinforced 4 2fire resistance 4 0 -1 , 4 8 , 2 3 2 4 ,1 8 1 3 , t8 1 4 , t8 1fl ex u ralstreng th 2 3 04 3 4 indexg rade 4 2l ig htweig ht 4 0 , 2 3 4 , 3 1 8 , 3 2 6 ,t8 0mix esbu l kredu ction 4 1cement to ag g reg ate 3 8du rabil ity3 9fine and coarse ag g reg ates 3 8per B S8 1 1 O 3 9per CP1 1 O 3 9q u antityof water 3 8 9permeabil ity4 1permissibl e serv ice stresses4 3 4bearingstresses 4 3 4bond 4 3compression du e to bending4 34 3tensil e streng th 4 3porosity4 1properties 3 9 4 2 , t7 9roads, see Roadsshrink ag e 4 1 , 5 7 , 2 3 2stress-bl ock s 5 0 , tl0 2parabol ic-rectang u l ar 5 0 , 6 2 ,2 6 0 4 , 3 4 0rectang u l ar 3 4 4 , 3 4 6stresses in 4 2 4 , 8 4 5tensil e streng th 4 0 , 4 3 , 2 3 0thermalproperties 4 0 1 , 8 4 ,2 3 2 , t8 1 4weig ht and pressu re 3 9 4 0 ,1 1 0 , t2see al so l ig htweig htsee al so ReinforcementConstru ction Indu stryCompu tingA ssociation 9 7Constru ctionalmaterialweig ht1 1 0 , t3 4Contained material s, see Retainedand contained material sContinu ou s beams t3 2bendingmomentsand shearingforces 1 8 1 9 ,t3 6 8diag rams t3 6 7eq u alspans 1 9 2 1 , 1 5 4 8 ,t3 3 4max imu m 1 5 0 4positiv e and neg ativ e in 1 5 0characteristic-points methodt4 2coefficient method t4 4 5criticall oadingfor t2 2eq u all oads on eq u alspans1 5 4 8 , t3 3 5fix ed points method 1 9 , 1 6 4 , t4 1frame anal y sis 2 0 6 1 2infl u ence l ines 1 7 22spans 2 1 , t4 63spans 2 1 , t4 74spans 2 1 , t4 85or more spans 2 1 , t4 9moment distribu tion anal y sis15 8 6 2 , t3 6 7H ardyCross 1 9 , t4 0precise moment 1 9 , t4 0moment of inertia 1 9non-u niform 1 6 4 , t3 9u niform t4 1mov ingl oads on 2 1shearingforces 1 5 0 4eq u alspans 1 9 2 0 , 1 5 4 8 ,t3 5sl ope defl ection 1 8 1 9su pport-moment-coefficientmethod 16 6 B , t4 3 5three-moment theorem 1 8 ,1 6 2 4 , t3 9u neq u alprismatic spans andl oads t4 3Conv ersion 3 7Corbel s 3 7 8 , t1 7 2Crack ing5 7 8crackwidth criteria ti 3 9l imit-state of 1 7 6 7l iq u id containingstru ctu res t1 3 2rig orou s anal y tic procedu re tI 3 8Cranes 1 1 , 1 1 8 , t1 2Creep 7 7 8 , t1 8 6bendingmoments in 7 8 ,ti 8 6l oads on 7 7 B , tb h, t1 6 2 0 ,t5 6pipe cu iv erts 7 7Cu rtail ment, see B ars, cu rtail mentCu rv atu re, see Defl ectionDE CIDEsy stem 9 8 9Deep containers, see Sil osDefl ection 5 6 7 , t2 2 , t1 3 6 7beams t2 3 4freel ysu pported t2 8cantil ev ers t2 5 6mu l tipl iers for tl2 1l ig htweig ht concrete 3 1 8l imit-state of 2 9 6modu l ar-ratio desig n 3 1 2rig orou s anal y sis 3 1 6 , t1 3 6simpl ified method 3 16 18 , t1 3 7Desig n charts ti 2 2 3 1Desig l i streng ths, see Concrete;ReinforcementDetail ing4 8bearing s 7 0 , t1 7 2intersections 7 0 , t1 7 3rectang u l ar beams 6 0 , t1 4 0Dispersion, see Concentratedl oadssee M arine stru ctu resDol phins, see M arine stru ctu resDomes, see RoofsDrainag e behind wal l s 8 7Drawing s 5 7E arthq u ak e resistant stru ctu res 3 2E conomicalconsiderations 3 5E l astic method, see M odu l ar-ratiomethodE l astic properties 4 0 , 2 3 0 2E l ectronic dev ices, see Compu tersE u ropean Concrete Committee3 3 6Fabric reinforcement 4 4 , t9 1Fatig u e 4 1 2Fibre-reinforced concrete 4 2Fire resistance 4 0 -1 , 2 3 2 4 ,t8 1 3 , t8 1 4reinforcement concrete cov er4 8 , t8 1Fix ed seating1 1 4Fix ed-end-moment coefficients1 3 8 4 6 , t2 9partialtriang u l ar l oads t3 0partialu niform and trapezoidall oads t3 1Fl ang ed beamsbreadth of rib 5 6modu l ar-ratio method, 5 5 , tl1 7properties of 4 9 , ti 0 1Fl ang ed sections, see Fl ang edbeams;Stru ctu ralmembersFl ex u ralstreng th 2 3 0Fl oorsg arag es 1 1 , 1 1 4 1 8 , tl limposed l oads 9 , t6indu strialbu il ding s 9stru ctu re 7 1Footpaths and foot bridg es 7 7 ,1 1 4 , 4Fou ndationsbal anced bases 9 0 -1 , 4 1 0 , tl9 0 ,ti 9 2basements 9 1bl indingl ay er 8 9combined bases 8 9 , 4 0 8 , t1 9 0 ,ti 9 2bendingmoments 4 1 0minimu m depth 4 1 0 , t1 9 1shearingforces 2 1 7 1 8eccentric l oads 8 9for machines 9 2 3fou ndation cy l inders 9 5imposed l oads 9 , 1 1 4 , t1 2inspection of site 8 8 9piers 9 1 2 , t1 9 1pil es, see Pil es;Reinforcedconcrete pil esrafts 9 1 ,4 1 0 1 4 , t1 9 0safe bearingpressu res 8 9 , t1 9 1separate bases 9 0 , 4 0 6 8 , t1 9 1strip bases 9 1 , t1 9 0 , t1 9 2tied bases 9 0 , t1 9 2wal lfooting s 9 2 , t1 9 2Framed stru ctu res 2 7 9 , t6 5 7 4B S8 1 1 O and CP1 1 Oreq u irements 2 7 8 , t6 8col u mns in bu il ding s 2 1 8continu ou s beams in 2 0 6 1 2g abl e frames t7 1 , t7 3l aterall oads 2 7 , t7 4members end conditions 3 2moment-distribu tion methodno sway2 8 , t6 6with sway2 8 , t6 7moments of inertia 3 1 2 ,2 16 -1 8portalframes 2 9 , t7 0 , t7 2shearingforce on members 2 9sl ope-defl ection method 2 8 9 ,2 0 6 , t6 5su b-frame 2 9 , 3 0 , t6 8three-hing ed frame 2 9 , t6 9wind forces 3 1 2see al so Col u mns;Stru ctu ralmembersG arag es 1 1 ,