Deign of Slabs

DESIGN OF SLABS

Typically we divided the slabs into two types:

i. Roof Slab and ii.Floor Slab

In case of roof slab the live load obtained is less compared to the floor slab. Therefore we first design the roof slab and then floor slabs.

We have two types of supports. They are:

1. Ultimate support and

2. Penultimate support

Ultimate support is the end support and the penultimate supports are the in-termediate supports.

Wu x L2 Ultimate support tends to have a bending moment of 10

have W

u x L

2

12

Design of roof slab:

and the penultimate supports

It is a continuous slab on the top of the building which is also known as ter-race. Generally terrace has less live load and it is empty in most of the time except some occasions in case of any residential building. In case of office buildings it will be empty and live load act is very less.

According to the end conditions and the dimensions, the slabs are divided into 4 types. They are Roof S1, Roof S2, Roof S3 and Roof S4.

Slab

Dimensions (M x M)

Roof S1

8.62 X 3.05

Roof S2

8.62 X 3.05

Roof S3

5.78 X 3.05

Roof S4

5.78 X 3.05

10

We can observe the slab panels in the above figure and all the slabs are de-signed as one way slab for the easy arrangement of the reinforcement and ease of work.

Roof S1 and Roof S2 are the slabs with same dimensions but with different end conditions.

Roof S3 and Roof S4 are also the slabs with the same conditions as men-tioned above.

But the point to be noted is that all the Slabs have same shorter span and in the design of one way slab shorter span is of more importance. Therefore we design any two slabs with different end conditions and the remaining two slabs also follow the same design.

Design of Roof Slab S1:Calculation of Depth (D) by using modification factor:

Assume the percentage of the tension reinforcement (Pt) provided is 0.4% From IS456-2000, P38 Fig4, we get the modification factor (α) = 1.4

Required Depth (D) = rL

+ d1 a

11

Where, L

= Span

ra allowable

Ld

ratio

d1 = Centre of the reinforcement to the end fibre (= 20mm for slab) From IS456-2000, P39, Clause 24 & Clause 23.2 for continuous span we have

Span =

L = 26

Effective depth d

ra =26x1.4=36.4

3.05 x 103

Therefore, D = 36.4

+ 20 = 103.79mm say 110 mm

Effectivedepth(d)=D–d1 =110–20=90mm

Loads:Dead loads (From IS875 – Part 1):

= 2.5 KN/m2

=1x1xDx25= 110

x25 1000

= 2.75 KN/m2

= 1.5 KN/m2

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 6.75=10.125 KN/m2

Design moment: (for end panel)

Wu x L2 10.125 x (3.05)2

Mu = 10

= 10

=9.42KN-m

Terrace water proofing Selfweightoftheslab

Live loads (From IS875 – Part 2):

RoofTotal load (W) = 2.5 +2.75 + 1.5 = 6.75 KN/m2

12

Calculation of area of steel:

From IS456-2000, P96, Clause G-1.1 (b) we have

Mu = 0.87 x fy x Ast x d x (1 - fy x Ast

) fck x b x d

Or

Ast = 0.5 x fck

(1-(1-4.6 Mu

fy fck x b x d

)1/2) b x d

9.42x106 =0.87x415xAst x90x(1- 415xAst

) 20 x1000 x90

Ast = 312.4 mm2

Spacingof8mmφbars= ast x1000

=π

x82 x 1000

=160.9mm Ast 4 312.4

Therefore, Provide 8mm φ @ 150mm c/c. Distribution steel:

Ast = 0.12% of Ag

= 0.12

x110x1000=132mm2. 1000

Spacing of 8mm φ bars = π

x 82 x 1000

=380mm 4 132

Therefore, Provide 8mm φ @ 300mm c/c.

13

Design of Roof slab S2:

Depth D = 110mm Total load (W) = 6.75 KN/m2

Limit state load (Wu) = 1.5 x 6.75 = 10.125 KN/m2

Design moment: (for intermediate panel)

Wu x L2 10.125 x (3.05)2

Mu = 12

= 12

=7.85KN-m



) fck x b x d

7.85x106 =0.87x415xAst x90x(1- 415xAst

) 20 x1000 x90

Ast = 256.78 mm2


x 82 x 1000

4 256.78

= 195.75mm


Ast = 0.12% of Ag

= 0.12

x110x1000=132mm2. 1000


x 82 x 1000

=380mm 4 132


14

Design of Roof Slab S3 is same as Roof Slab S1. Design of Roof Slab S4 is same as Roof Slab S2. Area of steel at support next to end support:

From IS 456-2000, moment = Wu x L

2

10

Total Load acting on the support (Wu) = 10.125 KN/m

10.125 x (3.05)2

Therefore, Moment = 10

= 9.42 KN-m

Calculation of Ast:


) fck x b x d

9.42x106 =0.87x415xAst x90x(1- 415xAst

) 20 x1000 x90

Ast = 312.4 mm2

Area of steel available by bending up the alternate bars of mid span steel:

From Slab S1 = 12

x 312.4 = 160.7 mm2

From Slab S2 = 12

x 256.78 = 128.39 mm2

Total Ast (available) = 160.7 + 128.39 = 284.59 mm2

Therefore, extra bars required for Ast = 312.4 – 284.59 = 27.81 mm2

15

Area of steel at any other interior support:


2

12

Total Load acting on the support (Wu) = 10.125 KN/m

10.125 x (3.05)2


= 7.85 KN-m

Calculation of Ast:


) fck x b x d

7.85x106 =0.87x415xAst x90x(1- 415xAst

) 20 x1000 x90

Ast = 256.78 mm2


From Slab S2 = 12

x 256.78 = 128.39 mm2

From Slab S2 = 12

x 256.78 = 128.39 mm2

Total Ast (available) = 128.39 + 128.39 = 284.59 mm2 Therefore Ast (avail-able) = Ast (required)

No need of providing extra bars.

16

Design of Floor Slab:

It is the slab in which live load is more when compared to the roof slab. In this project the slab is divided into 9 types according to the end condition and function of slab.

S1 S2 S3 S4

- Toilet and WC’s

- Office

- Office sup dept.

- Assembly hall

S5(a),S5(b) - Officechamberandwaitingchamber S6(a),S6(b) - Office

S7

S8S9(a),S9(b) - Officerschamber

- Library

- Secretary Room

17

Floor Slab

Dimensions

S1 to S5 (b)

8.62 x 3.05

S6 (a) to S9 (b)

5.78 x 3.05

DESIGN OF FLOOR SLAB (S1):Calculation of Depth (D) by using modification factor:

Assume the percentage of the tension reinforcement (Pt) provided is 0.4% From IS456-2000, P38 Fig4, we get the modification factor (α) = 1.4

Required Depth (D) = rL

+ d1 a

Where, L

= Span

ra allowable

Ld

ratio

d1 = Centre of the reinforcement to the end fibre (= 20mm for slab) From IS456-2000, P39, Clause 24 & Clause 23.2 for continuous span we have

Span =

L = 26

Effective depth d

ra =26x1.4=36.4

3.05 x 103

Therefore, D = 36.4

+ 20 = 103.79mm say 120 mm



Floor finish = 1 KN/m2 Sanitary Blocks including filling = 2.5 KN/m2

18

Selfweightoftheslab =1x1xDx25= 120

x25 1000

= 3 KN/m2

Sanitary blocks public = 3 KN/m2 Corridor = 5 KN/m2

Maximum = 5 KN/m2 For Partition Wall = 1.5 KN/m2

Total load (W) = 1 + 2.5 +3 + 5 + 1.5 = 13 KN/m2

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 13



Wu x L2 19.5 x (3.05)2

Mu = 10

= 10

=18.14KN-m


From IS456-2000, P96, Clause G-1.1 (b) we have


) fck x b x d

=19.5 KN/m2

Or

Ast = 0.5 x fck

(1-(1-4.6 Mu

fy fck x b x d

)1/2) b x d

18.14x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 569.79 mm2

Spacingof10mmφbars= ast x1000

=π

x102 x 1000

=137.83mm

Ast 4

569.79

19


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


DESIGN OF FLOOR SLAB (S2):

3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm



Floor finish Selfweightoftheslab

= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

= 4 KN/m2 = 5KN/m2


Office Corridor

20

Therefore, Maximum load = 5 KN/m2

For Partition wall = 1.5 KN/m2

Total load (W) = 5 +3 + 1 + 1.5 = 10.5 KN/m2

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 10.5

Design moment:

Wu x L2 15.75 x (3.05)2

Mu = 12

= 12

=12.21KN-m



) fck x b x d

=15.75 KN/m2

12.21x106 =0.87x415xAst x100x(1- Ast = 365.97 mm2


x 102 x 1000

4 365.97

415xAst )

20 x 1000 x 100

= 214.61mm


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


21

Area of steel at support next to end support (between S1 and S2):


2

10

Total Load acting on the support (Wu) = 13

+ 15.75

= 14.375 KN/m 22

14.375 x (3.05)2 Therefore, Moment = 10

Calculation of Ast:Mu = 0.87 x fy x Ast x d x (1 -

= 13.372 KN-m

fy x Ast )

fck x b x d

13.372x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 404.28 mm2


From Slab S1 = 12

x 569.79 = 284.895 mm2

From Slab S2 = 12

x 365.97 = 182.985 mm2




3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm

22



Design moment:


= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2


Private Corridor Maximum load

For Partition wallTotal load (W) = 5 +3 + 1 + 1.5 = 10.5 KN/m2


Wu x L2 15.75 x (3.05)2

Mu = 12

= 12

=12.21KN-m



) fck x b x d

12.21x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 365.97 mm2

= 2 KN/m2

= 5 KN/m2

= 5 KN/m2

= 1.5 KN/m2

=15.75 KN/m2

23


x 102 x 1000

= 214.61mm 4 365.97


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


Area of steel at any other interior support: (Between S2 and S3)

From IS 456-2000, moment = Wu x L2

12

Total Load acting on the support (Wu) = 15.75

+ 15.75

= 15.75 KN/m 22



= 12.21 KN-m

fy x Ast )

fck x b x d

12.21x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 365.97 mm2

24


From Slab S2 = 12

x 365.97 = 182.985 mm2

From Slab S3 = 12

x 365.97 = 182.985 mm2




3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm




= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

= 5 KN/m2

= 5 KN/m2

= 5 KN/m2

= 1.5 KN/m2


Assembly

Corridor Maximum load

For Partition wallTotal load (W) = 5 +3 + 1 + 1.5 = 10.5 KN/m2

25

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 10.5 =15.75 KN/m2

Design moment:

Wu x L2 15.75 x (3.05)2

Mu = 12

= 12

=12.21KN-m



) fck x b x d

12.21x106 =0.87x415xAst x100x(1- Ast = 365.97 mm2


x 102 x 1000

4 365.97

415xAst )

20 x 1000 x 100

= 214.61mm


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


26

Area of steel at any other interior support: (Between S3 and S4)

Same as between S2 and S3

DESIGN OF FLOOR SLAB (S5 (a)):

3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm




= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

= 4 KN/m2

= 2 KN/m2

= 1.5 KN/m2


Office chamber

Private For Partition wall

Total load (W) = 2 + 4 +3 + 1 + 1.5 = 11.5 KN/m2


Design moment:

Wu x L2 17.25 x (3.05)2

Mu = 12

= 12

=13.372KN-m



) fck x b x d

=17.25 KN/m2

27

13.372x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 404.27 mm2


x 102 x 1000

= 194.27mm 4 347.05


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


Area of steel at any other interior support: (Between S4 and S5 (a))


2

12


+ 17.25

= 16.5 KN/m 22

16.5 x (3.05)2


= 12.79 KN-m

Calculation of Ast:


) fck x b x d

28

12.79x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 385 mm2


From Slab S4 = 12

x 365.97 = 182.985 mm2

From Slab S5 (a) = 12

x 404.27 = 202.135 mm2



DESIGN OF FLOOR SLAB (S5 (b)):

3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm




= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

= 4 KN/m2

= 2 KN/m2

= 1.5 KN/m2


Office chamber

Private For Partition wall

29

Total load (W) = 2 + 4 +3 + 1 + 1.5 = 11.5 KN/m2



Wu x L2 17.25 x (3.05)2

Mu = 10

= 10

=16.047KN-m



) fck x b x d

16.047x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 495.37 mm2


x 102 x 1000

= 158.55mm 4 495.37


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


=17.25 KN/m2

30

Area of steel at support next to end support (between S5 (a) and S5 (b)):


2

10


+ 17.25

= 17.25 KN/m 22



= 16.05 KN-m

fy x Ast )

fck x b x d

16.05x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 495.47 mm2



x 404.27 = 202.135 mm2

From Slab S5 (b) = 12

x 495.47 = 247.735 mm2



DESIGN OF FLOOR SLAB (S6 (a)):

3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm



Floor finish = 1 KN/m2

31

Selfweightoftheslab =1x1xDx25= 120

x25 1000

= 3 KN/m2

Office = 4 KN/m2 Total load (W) = 4 +3 + 1 = 8 KN/m2

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 8=12 KN/m2



Wu x L2 12 x (3.05)2

Mu = 10

= 10

=11.163KN-m

Calculation of area of steel:Mu = 0.87 x fy x Ast x d x (1 -

fy x Ast )

fck x b x d

11.163x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 332.06 mm2


x 102 x 1000

= 236.53mm 4 332.06


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144

32


DESIGN OF FLOOR SLAB (S6 (b)):

3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm




= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

= 4 KN/m2


OfficeTotal load (W) = 4 +3 + 1 = 8 KN/m2

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 8=12 KN/m2


Wu x L2 12 x (3.05)2

Mu = 12

= 12

=9.3025KN-m

33



) fck x b x d

9.3025x106 =0.87x415xAst x100x(1- Ast = 273.13 mm2


x 102 x 1000

4 273.13

415xAst )

20 x 1000 x 100

= 287.55mm


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


Area of steel at support next to end support (between S6 (a) and S6 (b)):


2

10

Total Load acting on the support (Wu) = 12 KN/m

12 x (3.05)2


= 11.163 KN-m

34

Calculation of Ast:


) fck x b x d

11.163x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 332.06 mm2



x 332.06 = 166.03 mm2

From Slab S6 (b) = 12

x 273.23 = 136.565 mm2




3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm



= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

Library = 10 KN/m2 Total load (W) = 10 +3 + 1 = 14 KN/m2



35

Ultimate load or limit state load or design load (Wu) = 1.5 x W = 1.5 x 14 =21 KN/m2


Wu x L2 12 x (3.05)2

Mu = 10

= 10

=19.54KN-m

Calculation of area of steel:Mu = 0.87 x fy x Ast x d x (1 -

fy x Ast )

fck x b x d

19.54x106 =0.87x415xAst x100x(1- 415xAst

) 20 x 1000 x 100

Ast = 621.3 mm2


x 102 x 1000

= 126.41mm 4 621.3


Ast = 0.12% of Ag

= 0.12

x120x1000=144mm2. 1000


x 82 x 1000

=349mm 4 144


36


3.05 x 103

D = 36.4

+ 20 = 103.79mm say 120 mm



= 1 KN/m2

=1x1xDx25= 120

x25 1000

= 3 KN/m2

Documents

Deign of Slabs