design-of-one-way-slab.pdf

8/14/2019 Design-of-One-Way-Slab.pdf

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Design of one way slab

Classification of slab:-

a) On the basis of shape –square, circular, triangular etc.

b) On the basis of supporting condition –simply supported along

it edge continues slab running over number of support,

cantilever slab fixed at one end and free at other end, flat slab

directly supported by column

c) On the basis of spanning direction- one way slab (when the

main reinforcement is in one direction), two way (when themain steel is provided in two or orthogonal directions.

Lx

Ly

Ly

Lx >>22

Ly

One way

Lx

Ly

Ly

Lx <=2

Ly

Two way

. Effective Span (clause 22.2):-

a) simply supported slab

!he effective span of member that is not built integrally

with it support shall be the least of the following.

i. "lear span # d (effective depth of slab).



ii. "enter to center of support.

b) $or continues slab.

%f the width of support is less than &' of clear

span the effective span shall be as a).if the supportare wider than &' of the clear span or mm

which ever is less the effective span should be

ta*en as under.

i. $or end span with one end fixed and other

continues or for intermediate span.

+ffective span clear span between two

support

ii. $or end span with one end fixed and othercontinues

+ffective span clear span #half the effective

depth of slab or beam.

Or

+ffective span clear span #half the width of

discontinues support.

hich ever is less.

2. Trial Depth

epth of slab is governed by serviceability requirement of

deflections.

"alculate the depth of slab based on /&d ratio.

er effectiveratiod Lallowable

span D cov

&+=

0d ra

L D +=

bar of diaof half er d .cov0 +=

"over min. 'mm

!able clause '.1.' %213-'



4llowable /&d ratio ra basic /&d ratio 5 modification

factor (6)

7asic /&d ratio (%213-', "-'8.'.)

7asic values of span for effective depth ratio for span up to

m"antilever – 9m

2imply supported – 'm

"ontinues – 'm

:odification factors (6) depends upon ;t< =c-'8.'. (e)>

$or span above m, the value in (a) may be multiplied by

&span in meters, except for cantilever in which case

defection should be made.4st < the in (a) ? (b) shall be modified by multiplying

with the modification factor as per fig. given below.

M o d i f i c a t i o n

f a c t o r

Fs=145

Fs=120

provided steel of sc Areaof

required steel of scof Area fy Fs

&

&3@.=

8. oa!s:-

"alculate load in AB&m on m wide strip of the slab.



ead load self weight of slab # floor finish.

/ive load ' to '.3 (use %2@93-part %%)

!otal wor*ing load /#//

!otal ultimate load u .3 (/#//)

". Design #o$ents:-

$or simply supported slab :u u@

'l

$or continous slab :u ''l wl w ul l d ud α α +

here d uw .3 /

ul w .3 //

:oments and shear coefficient for continuous beam. ( !able '

and 8 )

$or moments at support where two unequal span meet or in

case where the span are not equally loaded, the average of

two values for the negative moment at the support may beta*en for the design.

"lause ''.3.'

Chec% for concrete !epth:-



2ince the depth of the slab is obtained from serviceability

consideration it is required to be chec*ed from bending

moment requirements.

"alculate maximum moment carrying capacity of the section

'

maxmax bd R M uur =

$or slab b mm

( maxu R for fe 13 .8@ fc* )

( maxu R moment of resistance factor)

%f maxur

M

C ur M

!hen the section is adequate from bending moment

requirements.

max

max

×

=∴

u

u

R

M d hich shall be less than the

provided

%f the above condition is not satisfied provide the depth

required from bending moment consideration.

#ain steelD-

4st bd bd Fck

Mu

Fy

Fck

−−

'

.1

3.

here b mm C 4st min4st min .'< bd for (#E2 bar)

($e 13 ? $e 3)

.3< bd for $e '3



Fequired spacing s Ast

ast

ast area of c&s of one bar

4st total area of steel required

!he spacing shall not exceed 8d or 8 mm whichever is less.

Chec% for !eflection:-

"alculate ;t < 4st & bd

here 4st is the maximum area of steel required at mid span

assumed.

er effectived basicL

span D ser cov

&+

×=

α

"hec* that C ser D

&. Distribution of steel:-

Fequired 4st Db××

'. for $e 13

Db××

3. for $e '3

here b mm and is the overall depth

:aximum spacing ≤ csd or 13 m whichever is less

'. Chec% for shear:-

"alculate maximum shear Gu max as per table 8 (%213)

? v J Gu max area of cross section

Obtain design shear stress vc J corresponding to ;t 4st & bd

(from table H)

"alculate shear resistance of slab

%nternal stress A vc J

A – factor to increase in the resistance to shear due to membrane

action of slab and is given in table.



Overall

depth

of slab

in mm

8 or

more

'93 '3 ''3 ' 93 3 or

less

A . .3 . .3 .' .3 .8

%f c J v C maxv J the safe else increase the thic*ness of slab.

'. Chec% for !evelop$ent length:-

!he length of the bars provided for resisting –ve moment should

not be less than #ve development length given by

/d A bd J

fy

1

@9.



L 1

0 .1 5 L 1 0 .2 5 L 1 0 .2 5 L 2

A s t 1

0 . 5 A s t 2

D i s t r i ! t i on s t e e "

Ea$ple: - design a simply supported rcc slab for a roof of hall

1m x m (inside dimension) with '8mm wall all around.4ssume a live load of 1 AB& 'm and finish AB& 'm . Ise :'3 and

$e 13

Solution: - data given

Foom siJe 1 x m

all thic*ness '8

// 1 AB& 'm

$$ AB&'

mFequired – find depth, 4st.

Step *. Calculation of loa!.



4ssume d '@

span

'@

1 1'.@ ≈ 18 mm

('@'x.1'@)

!otal depth 18#3#'@≈

9ead load .9 x '3 1.'3 AB& 'm

$$ . AB& 'm

!otal ./ 3.'3 AB& 'm

// 1. AB& 'm

$actored design load .3(3.'3#1) 8.@93 AB& 'm

Span length of slab

2pan effective span # d 1#.18 1.18 m

+lti$ate $o$ent an! shear:-

KNmwl

M 99.'H@

[email protected]

@

''

=×

==

KNmwl

M 91.'@'

[email protected]

'=×==

,. Chec% the !epth for the ben!ing:-

:.8@ $c* b 'd

' '[email protected].'H d ×××=×∴

@ H.H ' =⟨=∴ d m md OA

". rough calculation for shear:-



)8.('. 1 8

9 1.' @cv

b d

vτ τ ⟨=

×

×==

cτ $or grade of concrete :'3 is .8

Kence OA for shear.

. Calculation of steel area:-

−=

fck bd

fy Ast d Ast fym

u@9.

'H.99 x

××

×

−×××= '318

13

1813@9.

Ast

Ast

38.3 4st -3.HH818 ' Ast

' Ast - @1.139@ 4st # 1H93.19

( )

'

19.1H931139@.@1139@.@1' ×−±

=∴ Ast

''=∴ Ast

. $ain steel:-

Ising bar.

2pacing cc &'3''

9@3≈

4st provided '@ 'mm

<1'.)<18H.)< ≈=∴ Ast

. chec% for central of crac%:-

:in pt .''

'1

9'.m As =

××=∴

Kence o* for crac* control

ia @

9'.'3Cmm provided o*.



:ax spacing not more than 8. o*

. rechec% for shear

p 1.18

'@ =××

<

Feference table H'&1H'. mm N

c =τ

&. chec% for !eflection

7asic span to depth ratio '

:ultiplying factor for 4st .1'< .1

4llowable /&d .1 x ' '@

4ssumed is also '@ hence o*

Kence safe in deflection

Secon!ary steel

4s ''1

9'.

'. mm Db =××=××

2pacing less than 3d or 13 mm

93 or 13 mm

Kence o*

DES/01 3 C1T/1++S S45S



esign the interior span of a continuous one way slab for an office

floor continuous over ! beams spaced at 1m centers.

$c* '3B& 'mm and $e 13 steel

*. Calculate factore! loa!

4ssume d mm span

838

1

8==

!otal depth 83#3#'mm

ead load . x '31. AB& 'm

$loor finish . AB& 'm

!otal 3. AB& 'm

/ive load for office floor 8. AB& 'm

Fatio of //&/ . less than .93

(2eparate analysis of /#// not needed)

esign factored load .3(3#8) ' AB& 'm

2. +lti$ate $o$ents

4t interior support KNmwl '1'

'

''

=×=

4t interior span KNmwl

@'1

1'

'1

''

=×

=

,. Chec% !epth for $o$ent

:u .8@ fc* b 'd

d @ mm adopt d 83mm

". 6ough chec% for shear

G KN '1'

1'=

× 99.

83

'1=

××

=vτ



mincτ $or :'3

'&8. mm N c =τ OA

. Calculation of steel areas

4dopted depth is greater than required.Kence section is under reinforced.

4t support

×××

−×××=×83'3

138313@9. Ast

Ast

[email protected] 4st – 3.HH81 x ' Ast

' Ast - @88. 4st

HH81.3

=×

+

'

'

818'

HH81.3

1.@88.@88

mm=

××−±

∴

:in area of steel

'

H'

'.

'.mm

bD=××= OA

4t interior span H'min9''

818

''' <=== mm

Ast Ast

Kence provide minimum steel H' 'mm

:ain steel at support @ of e 8 c&c (4st8@1) (.'@1<)

4st interior @ of ' c&c (4stH') (.1'<)

7. Chec% for !eflection at $i!!le of slab

7asic /&d ratio '$ .3@ x fy H'

H'133@. ××=

Asp

Asr

'1.9

:odification factor '

2o allowable ratio is ' x ' 3'



Liven are 8 hence OA

. Chec% for crac%ing

2teel are greater than .'< OA

2pacing less than 8d 8 x 83 13

2pacing less than 8 OA

iameter of rod M &@ (&@ 'mm) OA

&. Chec% for shear

mincv thanlessveryis τ τ

OA

'. Chec% for top steel

$or !- beam action

the detailing arrangement provide more than < of main steel in

mid span of the slab as transverse steel OA

'. !evelop$ent length

/d bd

fy

τ

φ

1

@9.

:inimum embedment length into the support /d&8

/ength of bar embedment into the support

width of support- clear side cover



Ea$ple:-esign a cantilever porch of siJe '3 mm wide and

3 mm long is to be provided at a height of 8 m from floor level.

!he porch slab which overhangs '3 mm beyond the face of the beam into be cast in flush with the top face of the beam

4ssume live load .93 '&m KN

$loor finish .@ '& m KN

"oncrete :' and $e 13

Solution:-

. effective span

( )

−+

+'

''

'

'3 '33

!he trial depth /&d 9

:odification factor is '

$or

$e'3, fs.3@ x fy

.3@ x '3 13

;t < is .1

Kence allowable /&d is 9 x ' 1Fequired d '33&1 @

4ssuming bar effective cover 3 # &' ' mm

;rovide total depth of ' mm d '-'@ mm

/et the overall depth of the slab be reduced to mm at the

cantilever and where bending moment is Jero.

'. oa!s

"onsider m width of slab

2elf weight of slab (.'#.)&' x '3 8.93 AB&m

eight due to finish .@ AB&m

/ive load .93 AB&m



!otal 3.8 AB&m

Iltimate load per meter

u 3.8 x .3 9.H3 AB&m

:aximum bending moment (-ve) at the face of support:u u x KNm L @1.'1

'

3.'H3.9'&

''

=×=

1. Depth fro$ ben!ing $o$ent consi!eration

KNm KNm M ur

@1.'1'.H@H9.' '

max >>=×××=

)1H.(

'bd f ck =

Or'

H9.'@1.'1 d ××=×

d H.13MM d consider (@)

Kence o*

3. 4rea of steel

@@'

@1.'1.1

'3

'3.'

' ××

××××

−−×

= Ast

' mm=

Ising ) bar

mm spacin 9

3.9@ =×

=

;rovide ) N c&c

4rea provided x [email protected]& 98 'mm



Curtail$ent of steel

%t is proposed to curtail 3< of the steel required at the supportsince the depth of the slab is tapering and bending moment

variations parabolic the area of reinforcement will get reduced to

half at a distance greater than half the span from the free end.

7ending moment at . m

=×= 9.

'

.13.9

'

Mu

!otal depth of slab at . m from free end

# .('-)&'.3 1 mmd 1 -' 11 mm

1111'

9..1

'3

'3.'

' ××

××××

−−×

= Ast

883 'mm M (98&') provided at support

istance from support '@-H

"urtail 3< of the bars at a distance greater of the following

a) H#' H#' ' mm

b) H# d H#11 11 mm

2o curtail 3< of steel at a distance 3 mm from support

. Distribution steel

4rea required .3 .3('#)&' ''3 'mm

2pacing x '@&''3 '1 mm;rovide N ' mm c&c

9. chec% for !eflection

;t (say) x & ( x @) .89 < M .1< OA



Or

;t provided x 8& ( x @) .1< OA

Fequired d '33& 9 x ' @

@. chec% for !evelop$ent length

/d mm1'.1

'3@9.=×

××

4vailable length H mm C /d



Continuous one way slab



# $ # $ # $

1 2 #

u '.3 AB& 'm

$c* 3 B& 'mm

$e- 13

3actore! loa!



*) 4ssume d 93.@@8.'

8

8.'≈=

×=

×= span

'

ead load .' x '3 8. AB& 'm

$loor finish . AB&'

m !otal 1. AB& 'm

/ive load '.3 AB& 'm

Fating //&/ '.3&1. .'3 M .93

2) $o$ents

:iddle of the end part (at

centre)

4st support

next to end

support

:id of mid span 4t support o

intermediat

span

/ // / // / // / //

'

'wl

'wl

)

H

(

'

'

H

3.1'

83.1 '

=×× 8.893 3.1 8.93 8.893 '.@'3 1.3 8.9

!otal 9.@93 H.3 .@93 @.'3



%.&%5 '.1&%5 %.&%5

().15 (&.25 ().15

* * *( ( ((

:u .8@ fc* 'bd

d mm938@.

3.H

=××

×

d '-3-3mm

,) rough chec% for shear

v '3.1'

83.)3.'1(

'=

××+=

× spanload total

'&1'3.

'3.1m N v =

××

=τ 3.

'@. =<bd

Ast for OA

") calculation of steel area

4st of middle leg and span



1313@9.@[email protected] ×

××

−××=× Ast Ast

' [email protected]@[email protected] Ast Ast −=×

H.HH@

@93.9113.8

' =

×+− Ast Ast

'

H.HH@

@93.91)113.8(113.8

'

×

××−±

= Ast

Chec% for !eflection of $i!!le span

) Chec% for crac%ing

4st greater than .'<2pacing less than 8d or 8 mm

ia of bar M &@

&) Chec% for shear

') Chec% for top steel for T-bea$ action



ne way slab

Syllabus- assign of simply supported, cantilever, continuous

over beam with %2 coefficient.

ue- design a one way slab continuous on four support

subPected to udl of '.3 AB& 'm . !a*e floor finish as .93 AB& 'm

. !he c&c distance between two successive supports is 8m. 4nd

it is constant for other spans also use m3 grade of concreteand steel grade concrete fe13

ue- a cantilever beam proPecting out ' m from the face of

the support carries an udl of '3 AB&m over its entire length

and a concentrated load of 3 AB at its free end. esign the

beam, using concrete :3 and steel fe13. 4ssume width of

beam width of support 8 mm. design also the shear

reinforcement (2-HH)

ue- a hall of dimension 'm x @ m effective is provided

with monolithic slab and beam floor with beams provided at

8.3 m c&c. the slab is ' mm thic* and carries a live load of

1 AB& 'm and finishing load of AB& 'm . esign an

intermediate beam if web width is '8 mm. also design the

shear reinforcement for the beam. 2*etch the reinforcement

details for the beam. Ise :' concrete and fe13 steel.

ue- a simply supported slab having an effective span of

8.3 m. the slab is '3 mm thic* and carries a live load of 1



AB& 'm . !he tension reinforcement is provided in the form of

' mm diameter bars at 93 mm c&c at effective cover of '3

mm. calculate the deflections for slab using %2 code method

%2 13-H9@ specifications. Ise :3 concrete and fe'3

steel.

ue- a hall of effective dimensions of 9 m x @ m is

provided with monolithic slab and beam floor with beams

provided 8 m c&c. the walls and beams are '8 mm thic*.

esign the slab as continuous slab as per %2 13-H9@. if it

has to carry live load of 8 AB& 'm and finishing load of AB&'

m . Ise :' grade of concrete and fe13 steel. 2*etchreinforcement.

ue- a hall of effective dimensions of 9 m x @ m is

provided with monolithic slab and beam floor with beams

provided 8 m c&c. the walls and beams are '8 mm thic*.

esign the slab as continuous slab as per %2 13-H9@. %f it

has to carry live load of 1 AB&

'm

and finishing load of AB&'m . Ise :' grade of concrete and fe13 steel. 2*etch

reinforcement.

ue- design a cantilever slab proPecting out of distance of

. m from a bric* wall of '8 mm thic*. !he slab is

subPected to a wor*ing live load of 3 AB& 'm and it also

carries a parapet wall of mm thic* with .93 m height.Ise :' mix and fe13. esign the slab for flexure and

chec* for development length only.



ue- design a roof slab for a room m x 8.3 m restrained at

all the degrees for a service load 1 AB& 'm . !hic*ness of wall

is 8 mm. use :' and fe13.

ue- a hall of dimension 3 m x .'3 m is provided withmonolithic slab beam floor with beams at 8.'3 m c&c. the

thic*ness of walls and beams is '8 mm. design the slab as

continuous slab as per %213-H9@. if it has to carry a live

load of 8 AB& 'm and finishing load of .3 AB& 'm . Ise :3

concrete and fe13 steel. 2*etch the reinforcement details of

slab.

ue- esign a rectangular slab panel having an effectivesiJe of 3.3 m x 8.3 m. the panel is continuous over two long

edges and carries superimposed load of 8 AB& 'm . Ise :3

grade concrete and fe13 grade of steel.

3ifth se$ester 5.E civil

Sub8ect 6.C.C structure (li$it state)9ractical assign$ent

Date of sub$ission

F.B 2pan in m /ive

load

AB&'m

$.$

load

AB&'m

Lrade

of

concrete

B& 'mm

Lrade

of

steel

B&'mm

2upport condition

/x /y

' 3 '.3 ' 13 2.2

' 8 .3 3 .93 ' '3 2.2

8 8 .3 8.3 .93 '3 13 +nd panel of



continous slab

1 ' 3 8.3 .3 '3 13 -Q-

3 8.3 9 ' . ' 13 -Q-

' 8.3 .3 3 13 -Q-

9 8 3 .3 .3 ' '3 "antilever slab@ '.3 3 .3 .3 ' 13 -Q-

H ' 3 .93 .3 ' 13 -Q-

' .3 3 13 -Q-

' .3 .3 ' '3 -Q-

' '.3 3 .93 .93 3 13 -Q-

8 8 3.3 .93 .3 ' 13 -Q-

1 8.3 1 .93 .3 '3 13 -Q-

3 '.@ .3 ' 3 -Q- '. 8 .3 ' 13 -Q-

9 '.'

3

1 .'3 ' '3 -Q-

@ '.3 8 %ntermediate

panel of continous

slab

H '.'

3

8.3 .'3 ' 13 -Q-

' 8 '.3 .93 3 '3 -Q-

' 8.'

3

' ' '3 -Q-

'' 8.8

@

.1

8.3 .'3 '3 '3 -Q-

'8 '.3 '.3 .93 ' '3 -Q-

'1 8.3 @ 8 .93 3 '3 -Q-

'3 1 H 8.3 '3 13 -Q-' 8 9 8 ' 13 -Q-

'9 1 H 8.3 .'3 ' 13 -Q-

'H ' ' .3 ' '3 -Q-

8 '.3 '.3 .93 ' '3 -Q-

8 8 9.3 8 .3 ' '3 -Q-



8' 8.3 @ 8.'3 ' 13 -Q-

88 1 @.3 1 ' 13 2.2

81 8 9 8.3 .3 ' 13 -Q-

83 3 8.3 ' 13 -Q-

8 8.3 9 '.3 .3 '3 13 -Q-89 8 .3 .93 '3 13 "antilever slab

8@ 8.3 .93 ' 13 -Q-

8H '.@ 3 ' .3 '3 13 -Q-

1 '.3 3 ' .3 ' 13 -Q-

1 1.3 8.3 '3 13 2.2

1' 1 8 .3 ' 13 -Q-

BO!+- in cantilever slab /x is the span of cantilever slab.

(prof. F.L 74%2)

ate-

Ea$ple on colu$n !esign



ueD-+xplain in detail the interaction diagram used for design of

column. %f such interaction diagram is not available, set up the procedure for design of column subPected to an axial load and

bending.

ueD- 4 F."." column 8 x mm is reinforced by 8 no.s of

'mm dia bars on each short side cover of 3mm to the centre of

steel. "oncrete used is :' ? steel is of grade $e13.

"alculate the ultimate axial force ? the corresponding

ultimate moment when the neutral axis is at .1@ from the

compression face ? is parallel to the shorter side.

ue- a rcc column 8 x 3 mm is equally reinforced on two

short faces with 3 bars of ' mm diameter of steel grade fe'3 on

each face. "oncrete used is :'.

"alculate the ultimate load and ultimate moment resisted by the

section if the column is Pust on the verge of crac*ing.

(ans pu 38 AB and :u H ABm)

ue- a F."." column 8 x mm is reinforced by 3 no of '3

mm diameter bar of grade $e13 on either short side with a cover

of mm to the center of steel. "oncrete grade :' is used.

"alculate ultimate load and ultimate moment corresponding to the

coeditors of maximum & compressive strain of .83 in concrete

and tensile strength of .' in the outermost layer of tension steel.

(ans- ;u 39.9 AB and :u 3H9.1 ABm)

ue- a F."." column of 8 x 3 mm is reinforced with 1 no bar

of 'mm diameter of grade $e13 on either short side with a cover

of 3 mm to the center of steel. "oncrete used is :'. calculate



the ultimate load and its eccentricity from the center of column for

an untrac*ed section with neutral axis .3 from the highly

comopressed edge. !he area of stress bloc* is .1'' fc* . and its

"L acting at .1@ from the highly compressed edge.

(ans ;u H1.9 AB and eccentricity ''. mm)

ue- a short F." column '3 x 1 mm carries an ultimate load of

8 AB. !he area of steel consist of @ bars of ' mm diameter

placed symmetrically along two short edges of column. !he

concrete :3 grade and steel $e13 grade is used. "alculate the

maximum ultimate moment about x axis, :ux (dividing the depth

of the column.) the column can carry when it is subPected toultimate moment about y axis equal to 1 ABm

(ans- :ux 99.@ ABm)

ue- a axially loaded short column of width '8 mm is subPected

to ultimate load of '' AB and ultimate moment of @1 ABm

bisecting the depth of column. esign the column using concrete

grade :3 and steel grade $e13.(ans- '8 mm x 9 mm, @ mm bars in 1 rows with ' bars in

each row.)

ue- design the column for the following dataD ultimate load

H ABm. Iltimate moment bisecting the depth H ABm.

"oncrete grade :'. 2teel grade fe13. idth of column'8 mm

(ans. 2iJe '8 mm x 1 mm, mm mm in 8 rows with ' bars in each row.)

ue- the corner column of a building of siJe '8 mm x 8 mm is

reinforced with four bars of ' mm diameter. %t is subPected to an



ultimate axial load of 81 AB and ultimate moments of 8 ABm

and ABm bisecting the depth and width of column respectively.

$or concrete grade :3 and steel fe13, chec* the safety of the

column.

(ans- the value of interaction equation is .@H M RR.safe)

ue - the circular diameter 8 mm is reinforced with @ bars of '

mm diameter of grade fe13. !he column braced and hinged at

both ends and carries an axial ultimate load of @ AB. !he length

of the column is m. the concrete grade used is :'. "hec* the

safety of the column. 4ssume effective length unsupported

length of m.(ans- the slender column is safe)

ue- solves ex. '.. by ta*ing effective length about x axis

equal to 1.H m other data remaining the same. "hec* the safety of

the column of siJe '3 x 1 mm reinforced with bars of ' mm

placed 8 bars on each face along the depth of column.

(ans- the interaction equation gives value of .3CRR.unsafe)

design-of-one-way-slab.pdf

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