3 Design of Reinforce Concrete Slab

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


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


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


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

" ' ~~ ~ '


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~


~-~]"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


0-5

04

X1

M111


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.


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

~ ~


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

Documents

3 Design of Reinforce Concrete Slab