3 design of reinforce concrete slab
DESCRIPTION
REINFORCED CONCRETETRANSCRIPT
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Fig. 3.9 Moment and deftection coefficients for uniformly loaded two-way element with three edges simply supported and one edge free.IHI
lo()
{]01 v ' I L I 1--f'"
H = IJrH 2 v I XO = yrH 4 I I
I I I I
In, I I ri I I
07
O
0002
0001
00007
00005
OOOOJ
00002
0001 .OOOOI K> 7-0 so 1'0 2o 100"7 0-S O> 02 OI
HIL
c:::"
1-0
07
OS
0'3
02
OI
07
OS
CO
02
OI
007
OOS
OQ)
002
001
0007
0005
000>
0002
Fig. 3. t t Moment and deflection coefficients for uniformly loaded two-way element with two adjacent edges simply supported. one edge fixed and one edge free.l"I
I 2 v
{IQ J v
'
/
I / -
/ v
0-1
.07
OS
OJ
H = IJrH2 XO:: J
LJ._/ IJ2 I lj
I /1J1 v
J J I I I
v v I J J I
I/ I J I
I I
.
I v / I I
I IT I
) I
-02
01
OC1
005
00>
002
001
0007
0005
0002
0002
0001
0000'7
00005
000
-
Fig. 3.12 Moment and deflection coefficients for uniformly loaded two-way element with all edges fixed.1111
0-1 I I
-07 ,, .. n, .rn2 Ol
Ot:ll
005 -OS
03
'()l
01
'()(YI
00$
003
c;; 002 .. ~ .; 001
eS Xf1 i -ooos
C:>
'OOCll
ooo:i
0001
00007
oooos
OOOOJ
00002
00001
/.
~ 1 '/1 I
I j
/
I
/J V/ ....
h 11/ '// 1 1
J I 1 1 l!J ,/ '/ I I
J J I I
I I
J
I I
-v ~fllV/Yt
I-. ~ I v ~ n1H I ""-
H : flrH2 XO :: y rH
i{;:g
OO>
002
001
000?
ooos
000>
0 0 0 2
0001
OOOC1I
C>OOOS
0000>
-00002
00001
00000 7
ooooos
000003
000002
10 7-0 6'0 l'O 20 lO 0.7 0-6 o-3 0-2 000001
()ol
HI L
~ ,: ~
>:: .; ~
'' o q 0 5
OJ
02
OI
01
Of
OJ
02
OI
001
OOS
OOJ
002
00 1
-o:xY7
-ooos
OOOlt
-0002
Fig. 3.13 Moment and deflection coefficients for uniformly loaded two-way e lement with two opposite edges fixed and two edges simply supported .1111
- r. .... ""'
I -I
n2
0 1
. Ot:17
OOll
00>
002
001
/
1/ 000?
OOOS fl1v '
/1 ,, ~
I I 7 I / I
I// 'I
I ) f
I f J I I
v V/-1\. I :-..... i..._ floH
H = flrH1 XO" Yr H"
{J[TII l 2 I I L I
0003
0002
0001
OOOt:ll
00005
0000)
00002
00001
000007
000005
000001
000002
0001 000001 10 7-0 6 0 >O 2 0 lO 0'7 OS 03 0'.I 0 1
HIL
1.0
0 7
o.s
0.J
C>2
OI
07
OS
03 .. Oii ~
tS 01 i!::
-.;:: .~ .001
a OOS ~
00)
002
001
-oocn OOOS
OOOJ
0002
0 001
Fig. 3.14 Moment and deflection coefficients for uniformly loaded two-way element with three edges fi xed and one edge simply supported .1111
{{;g v I/
rn= 01 Ofl7 OOS
'()OJ
o()C)I
H = OrH2
XO= y r H" J I /,
JI! ///
/, r; J ,......._ f l I >-- n, I I I l!J I
/, '/ J
/, ~ I J rh I I I I
J" I
v,
~~
... ~ ,
I .......
" !'...
n, I n, ~ 001
0007
- ' ooos fl1H I
OOOJ
0002
0001
OOOt:l1
00005
OOOClll
00002
00001
000007
ooooos
00000>
00()001
'>'=
10 '1o0 6'0 SO 20 10 7 0-S 0'3 0-2 0 1 000001
HI L
0 (0
"' '' 0 .... :x:i (0
s O' ~ 0.
g ::s 0 @ -(0 V> ;" ~ .... ~
-
Fig. 3.15 Moment and deflection coefficients for uniformly loaded two-way element with all edges simply supported.IHI
> ~-
lO
07
05
0 3
0'2
01
07
05
03
02
01 ~ 007 005
003
002
I j
v J
-,, //
//. I'-.... j, II
I If j
I I I I I
J ) I I r. I
r1 fJr{ --fJIH
001
0007
COOS
I H = fJrH 2 J I XC = YrH4
I I {101 0003 -0002 I L I
().I
07
05
03
02
01
007
005
003
-002
001
0007
-0005
0003
0002
0001
00007
00005
-00003
ooooa
0001 J
10 7'0 6'0 J-() 2'0 00001
l-0 0'7 05 0'3 02 C>I
HIL
1-0
07
0 6
0'3
0'2
o~
-07
05
-03
~ .OQ . IS >-::: 01 ~ 007 J 005
COS
002
"001
OO
-
Design of Reinforced Concrete Slabs 137
o~
L f Mv1> Jl/2 H lMwN Mw1>
1-0
0-9
01
0-7
0-6
OS
04
03
02
OI
Fig. 3.18 Location of yield Jines for two-way e lement with two adjacent edges supported and two edges free (values of x).1111
x/L
O"-~~~-'-~~....___.~~-'-~-'---'~~~~-'-~--'~__..~..._~_._~_,
OI o-6 OI 1-0 2 , 7 .,!.. [Mvw-+Mv1>]
112
H M~
Fig. 3.19 Location of yield lines for two-way element with two adjacent edges supported and two edges free (values of y).181
10
-
138 Reinforced Concrete
lo()
0-1
07
>
-
Y/H
Design of Reinforced Concrete Slabs 139
0-5 I . 'l~IAS al 'tfH I V.tuts of x/L
05
0 4
O
I I\ ~
11 f / / ~ %1 :
I'\ ./ ~ % >---, ' / v ,, L / ~
L
0 4 .
O
02
OI
v ' / ...... / ~~
02
0-1
0-1 0-2 0., 04 0-6 0-8 10 6 10
Fig. 3.22 Location of symmetrical yield lines for tw~way element with four edges supported. IHI
_!! ., hMHN> + M,rJ201 r&-1 ~ (j)/ \Cl. X1 M-+M ..
H I @ \ , \ l
1-0 ,..,,_ MvH.2 .
\ \\ \~ t-1000 \\ \ .\ "\ ~ 1-000,h, - 4 000 \ \ \ \'\ ~o~l '
\. :'\,. '\.. \ 0-~~J
0 ..
0-7
o ..
""'~" '"" ""~ ' L~2s~" >--. "'""-0 ~'" 0)$0-~~ '0 ::::~ loSOO ~ ~ ' ~ ~ ......
0-2
0-1 - ~-.;:: :::.;:;:;::: -0
C>I 0 5 O I 1-0 s 10 50 IO IOO
Yag. 3.23 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (X2/X1=0.1).181
-
140 Reinforced Concrete
0'2
0 0-1 02
' \ y
\
!!_.bMH'!S + MHP~t/2 = O) ~ tb-1
{ 1 \~j x, MHNI+ MHP ' @ \ ,' \ , .
I L I
M\fp
Mv'!2
\' ~::_us L /' "~o:,:;;, \. '\. '\. 'Y< ~7-000 ' f\. ""'"\. .""'\. ~ .~ l
""'\." t-.."'-'\0 ~~\;-. 't'...~~ ~ :::::~ ~ ~ ....... ~ ~ .........
~...::::: ~-......:::: ~-2 s a ' 20 SO 80 IOO
L r: MvP ]''2 H[!olH'!t+M..,. Fig. 3.24 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (X2/X1 =0.3).181
~ J'2 !!-, fl.
X2. MHN1+MHP : 05 Wt ' X1 MHNI .. MHP H I @ \ ~ I
I \
L i' 1-0
Myp
Mv'!2 08
\. \ '\. l~~ .::_125 L, ~ >~ ~sot_ 500
06
'\, ~ ""< ~oooL 2-0001 ""-"' ~ ""-~ ~~k
'"'"'"' ~ ~ ~ ~ ::::---:: ........ ~ ~ ..... ~ _;;:,-.....; ~ - -
01
0 C>I OS OI K> :z 10 20 so 80100
Fig. 3.25 Location of unsymmetrical yield lines for twoway element with three edges supported and one edge free (X2/X1 =0.5).1
81
-
0-9
O I
6
0 '4
0 I
Design of Reinforced Concrete Slabs 141
11. bMHl!J + Mttll~l/2 =075 ~ A
HD 1 ' X1 Mttttl + Mwp / @ \ I \ '
I.
~ M-n.2
'\. I'\ :'\.. '~ :f- o-1as b 0 250 I'\. x::-x ~iOOL
""'-"' ~~ 1-000
O~I
'-......""~ ~ ... ., 4000 L ,...., .oOO]
~ ~ ~ ~ A- er> I ~ --~ ~ ~ - -O S O I lO I IO 20 SO IO IOO
Fig. J.26 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (X2/X1 =0.75) .1111
lo()
0 -9
0 ..
OJ
OI
0
~ r f41 fl-!J. HN3 MHP , 125 [ ..D1 \~ Xo M1tt11 M ..
H @ \ / \ ~
' l
MVP MvH2
" ' ~~ ~ '
-
142 Reinforced Concrete
I'
0'9
0 ~
'5
0 " 0 )
0 '2
0 0
0-1
~ ]',, .!!; ~ ~: M...,+ MHP a l S HI :!>1 '.~ X1 MHHr MHP . / @ \ I \ I l I
Myp
MvH2
'"'-~ - 0-500 ~ ,........ ... l-000 -""'~~
2-000
~i:... -oooL....., ~'::>
0 t::::::~~ ,,..01 I r--.: ,....
0250
----~ r-.-so aoioo
Fig. 3.28 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (X2 /X1 = 1.5).181
f O
0 9
Oa
0 7
0 6
>
-
fo()
O Oa
04
0 01
I .
o~
Design of Reinforced Concrete Slabs 143
~-~]"2
20 ~ ~ X1 MtNM.., [17 ~ H /@ \_
I l I
'
Myp MvN2
1 ....... ,, - ---L~a~'~
200
- -o_,-ff'...: .... ~ k;;;;;;t_ ~---c;~ l i:.::.:; "'~ ~~ 1.r'
~ - i--.. - -2 5 I 10 50 IO IOO
J..[ MVI' ] 112 H ~N1H~-'J
Fig. 3.30 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (X2/X1 =2.0).1
111
~~N1+MH~l/2 rX-1
x "4t.a+M .. H[ 1@1 - ~HN1M;r2 ,,-&,,, ~ 1Y l I+ MHN2+Mij1> __L~ 1-0 v
/
I/ >IX /
0-4 v
0-1 01 --L---i--
./ ~
S ~o
Fig. 3.31 Location of unsymmetrical yield lines for two-way element with three edges supported and one edge free (values of y ) .181
-
144 Reinforced Concrete
0-5
04
X1
M111
-
Design of Reinforced Concrete Slabs 145
0.15,l 0.15,f 0.15 l ~454>
100"/.
!
Effective Effective S n I
Continuous Slab : Approximate equal spans
Si~ly ~orted Slab
l.1z TOOlo I ~45 >
Cantilever Slab
Fig. 3.34 Simplified detailing rules for slabs.
-
146 Reinforced Concrete
Table 3.1 Graphical summary of two-way elements to be used in conjunction with Figures 3.3 to 3.17
g {B :nCJ' I. L I Fig. 3.3 Fig. 3.4 Fig. 3.5 {g rd :1J81
I L .I Fig. 3.6 Fig. 3.7 Fig. 3.8
{ILJI {lg 1Jd I L I .t L I
Fig. 3.9 Fig. 3.10 . Fig. 3.11
L
:IJffi rm Fig. 3.12 Fig. 3.13 Fig. 3.14
~DI ~ 11 {B {II f I. L I L L I Fig. 3.15 Fig. 3.16 Fig. 3.17
Legend: Edge conditions
r: t=t E r://:-i Free Simple Fixed
-
Table 3.2 Ultimate unit resistance for two-way elements (symmetrical yield-lines) (to be used in conjunction with Figs 3.18 to 3.23).
Edge conditions
Two adjacent edges supported and two edges free
Three edges supported and one edge free
Four edges supported
Yield line locations
P-1 EJ
H I(;:,;;:,J ~ I. L I AA B ~
HIL;;i~Jn I L .1
~ YI ~=r HI~~ I L .I
Limits
x :s L
y :s H
L x :s -
2
y :s H
L xs -
2
H y s -
2
Ultimate unit resistance
5(MHN + MHP) 6L MVN + (5Mvp - MVN)X or
x2 H 2 (3L - 2x)
5(MVN + Mvp) 6H MHN + (5MHP - MHN)Y or
y2 L2(3H - 2y)
S(MHN + MHp) 2MVN(3L - x) + 10 x Myp or
x2 H2(3L - 4x)
5(MVN + Mvp) 4(MHN + MHP)(6H - y) y2
or L2{3H - 2y)
5(MHN + MHP) 8(MVN + Mvp)(3L - x) x2
or H2(3L - 4x)
S(MVN + Mvp) 8(MHN + MHp)(3H - y) or
y2 L2(3H - 4y)
Cl G VJ
-
Table 3.3 Ultimate unit resistance for two-way elements (unsymmetrical yield-lines) (to be used in conjunction with Figs 3.18 to 3.33).
Edge conditions
Two adjacent edges supported and two edges free
Three edges supported and one edge free
Four edges supported
Yield line locations
~
EJ HI0i
l L I
fJ1 ~ ~ r :~}:,,;,,,: ~
{L:;',lhln 1. L .1
~ A
t~t:3~TI x ,rfi:tJ!i '.L - -=r
1 L r Y2
Limits
x :S L
y :S H
L x :$ -
2
y ~ H
L x =:;;; -
2
y :$ !!._ 2
Ultimate unit resistance
Same as in Table 3.2
S(MHNI + MHpi) 5(MHN3 + MHP) 2 or 2
X1 X 2
(SMvp - MvN2)(X1 + X2) + 6MvN2L or
2 H (3L - 2X1 - 2X2)
(MHNt + MHr){6H - Y) (MHN2 + M1ip)(6H - Y) or
X2 (3H - 2Y) (L - X)2 (3H - 2Y)
5(MvN3 + Mvp) or y2
(MVNt + Mvp)(6L - X, - X2) (MvN2 + Mvp){6L - X 1 - X2) or
2 Y2 (3L - 2x. - 2X2) (H - Y) (3L - 2X, - 2X2)
5(MHNI + MHP) 5(MHN2 + MHp) 2 or 2
X 1 X2
S(MvNt + Mvp) S(MVN2 + Mvp)
Yr (MHNI + MHp)(6H - Y1 -
X 2 (3H - 2Y1 - 2Y2)
or y~
Y2) (MHN2 + MHP)(6H - Y1 - Y2) or
2 (L - X) (3H - 2Y1 - 2Y2)
.... &
~ :; O' g 0.
Q ::I
~ ~
-
Design of Reinforced Concrete Slabs 149
Table 3.4 Ultimate support shears for two-way elements (symmetrical yield-lines) (to be used in conjunction with Table 3.2). Edge conditions Yield line locations Limits Horizontal shear, VsH Vertical shear, Vsv
~ 3ruH( 2 - ~) D x :s L 3ruX Two adjacent 5 (6 - ~)
edges supported and two edges
3ruL (2 - ~) free HJ]f7;;,:,j 3 3ruy y :s H I L . I (6 - ~) 5
fl ~ L 3ruX 3ruH(l - ~) k:,,,:~I x :s - (3 - ~) 2 5 Three edges
supported and I-Li 3ruL(2-~) one edge free HIQ)n
y :s H 3ruy
1. L I 2(6 - ~) 5
fl f1 L 3ruX 3ruH( 1 - ~) tE:~11
x :s -
2(3 - ~) 2 5 Four edges
~ supported ~y 3ruL(l- ~) HI ::::r H 3ruy ::::r y :S -I L .( y 2 2(3 - ~) 5
-
Table 3.5 Ultimate support shears for two-way elements (unsymmetrical yield-lines) (to be used in conjunction with Table 3.3). -~ Edge Yield line locations limits Horizontal shear, V,H Vertical shear, V,v ::0
conditions 0 s i-!-i O' ~ D x s L 0 0. Two adjacent Q
edges supported Same as in Table 3.4 Same as in Table 3.4 = (') and two edges
HIL;';,;,J~ y s H ~ ....
free 0
1. l .1
~ A L 3xiru
Xi S -2 5
t:,2,,::J L 3x2ru 3ruH(2L - Xi - X2) Three edges x s - 6L - Xi - X2 supported and
~ 2 2 5
one edge free 3r .,x(2H - y) 3ruy
Hr~~7~]n y s H
6H - y 5
1. l I 3r.,x (L - x)(2H - y) 6H -y --
~ ~ L 3r .,Xi 3ruy(2L - Xi - X2)
x, s-5 6L - x, - X2 2
Four edges ~EJ~n L 3r.,x2 3ru(H - y)(2L - Xi - X2) supported x s -x
2 2 5 6L - Xi - X2 t-'"-1 YI H 3r.,x (2H - y , - Y2) 3raYi
[f!m::r y s -H ~_:::I I 2 6H - Yi - Y2 5 y2 H 3ru(L - x)(2H - Yi - Y2) 3ruY2 1. L 0 I Y2 s-
2 6H - y, - Y2 5