CHAPTER 03

DESIGN OF STRUCTURAL ELEMENTS

3.1 DESIGN OF SLAB

The total slab is divided into number of panels and the design procedure is followed for
number of panels

Fig 3.1: slab panels

Panel 1:
l x = 2.89m

l y = 3.0m

l y 3.0
= = 1.03<2
l x 2.89

Hence, slab is to designed as two way slab

Thickness of slab:
 clear span 2890
Effective depth = = = 103.21mm
28 28

Adopt effective depth = 110mm

Overall depth = 110+20 = 130mm

Effective span:

l x = 3.12m

l y = 3.23m

l y 3.23
= = 1.03
l x 3.12

Loads:

Self weight of the slab = 0.13 x 25 = 3.25KN/m2

Live load = 3KN/m2 (From IS 875 part for residential building)

Floor finish = 1KN/m2

Total load = 7.25 KN/m2

Factored load:

Factored load wu = 1.5 x 7.25 = 10.875KN/m2

Calculation of moment and shear force :

From IS 456 : 2000 the moment coefficients are :

Two adjacent edges are discontinuous

α x = 0.047 & αy = 0.035

Slab spanning in two directions (Continuous)

α x = 0.064 & αy = 0.062

α x (-ve) = 0.064 α x (+ve) = 0.049

αy(-ve ) = 0.062 αy(+ve) = 0.035

+ve B.M. at mid span in shorter direction:

Mux (+ve) = α x (+ve)wl x 2 = 0.049 x 10.875 x (3.12)2 = 5.19KN-m

-ve B.M. at continuous edges in shorter direction

Mux (-ve) = α x (-ve)wl x 2 = 0.064 x 10.875 x (3.12)2 = 6.78KN-m

-ve B.M. at mid span in longer direction:

Muy(-ve) = αy(-ve)wl x 2 = 0.062 x 10.875 x (3.12)2 = 6.57KN-m

+ve B.M. at continuous edges in longer direction

Muy(+ve) = αy(+ve)wl x 2 = 0.035 x 10.875 x (3.12)2 = 3.71KN-m

W u l 10.875 x 3.12
Vu = = = 17 KN
2 2

Minimum depth required:

Mu = 0.138fck bd2

6.78 x 106 = 0.138 x 20 x 1000 x d2

6.78 x 106
dreq =
√ 0.138 x 20 x 1000
= 49.56mm<110mm
dpro > dreq therefore, provided depth is adequate

Reinforcement:

Along shorter span ( X- Direction )

f y A st
Mux = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 6.78 x 106 = 0.87 x 500 x Ast x 110 x [1- ]
20 x 1000 x 110

1.5 x 6.57 x 106 = 47850Ast - 10.875 Ast2

Ast = 223.936mm2

Using 8mm diameter bars

ast
S= x 1000
A st

π 2
∗8
= 4 x 1000
223.93

S= 224.4mm = 200mm

Provide 8mm dia bars @ 200mmc/c along shorter span

Along longer span (Y- Direction)

f y A st
Muy = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 6.57 x 106 = 0.87 x 500 x Ast x 102[1- ]
20 x 1000 x 102
9.86x 106 = 43500Ast - 10.875 Ast2

Ast = 241.08mm2

Using 8mm diameter bars,

ast
Spacing (S) = x 1000
A st

π 2
x8
S= 4 x 1000 = 208.51mm = 200mm
241.08

Provide 8mm dia bars @ 200mm c/c

Torsional reinforcement:

1. Edge strip :

3 A st x 3
At = = X 223.96 = 167.97mm2
4 4

1l x 1
= x 3120 = 630mm
5 5

Using 6mm bars, spacing

π 2
6
S= 4 x 1000 = 168.3mm
167.97

Provide 6mm bars at 150mm c/c as Torsional reinforcement at edge strip

2. Middle strip

1 3 1 3
At = x A st x = x x 223.96 = 84mm2
2 4 2 4
Using 6mm dia bars

π 2
6
S = 4 x 1000 = 336.6mm
67.5

Provide 6mm bars at 330c/c as Torsional reinforcement at middle strip

Check for deflection:

l
( ) = 28
d provided

f s = 0.58 x f y = 0.58 x 500 = 290N/mm2

From fig 4 of IS 456 : 2000

The modification factor K = 1.3

l
( ) max = k x 28 = 1.3x 28 = 36.4
d

l l
( ) provided < ( ) max
d d

Hence safe

Reinforcement detailing diagram :

Panel 2:

l x = 3.0m

l y = 3.83m

l y 3.83
= = 1.27<2
l x 3.0

Hence, slab is to designed as two way slab

Thickness of slab:

span 3000
Effective depth = = = 107.1mm
28 28

Adopt effective depth = 110mm

Overall depth = 110+20+ = 130mm

Loads:
Self weight of the slab = 0.13 x 25 = 3.25KN/m2

Live load = 3KN/m2

Floor finish = 1KN/m2

Total load = 7.25 KN/m2

Factored load:

Factored load wu = 1.5 x 7.25 = 10.875KN/m2

Effective span:

l x = 3.23m

l y = 4.06m

l y 4.06
= = 1.27
l x 3.23

Calculation of moment and shear force :

From IS 456 : 2000 the moment coefficients are :

Two adjacent edges are discontinuous

α x = 0.065 & αy = 0.049

Slab spanning in two directions (Continuous)

α x = 0.093 & αy = 0.055

α x (-ve) = 0.093 α x (+ve) = 0.065

αy(-ve ) = 0.055 αy(+ve) = 0.049

+ve B.M. at mid span in shorter direction:

Mux (+ve) = α x (+ve)wl x 2 = 0.065 x 10.875 x (3.23)2 = 7.38KN-m

-ve B.M. at continuous edges in shorter direction

Mux (-ve) = α x (-ve)wl x 2 = 0.093 x 10.875 x (3.23)2 = 10.56KN-m

+ve B.M. at mid span in longer direction:

Muy(-ve) = αy(+ve)wl x 2 = 0.049 x 10.875 x (3.23)2 = 5.56KN-m

+ve B.M. at continuous edges in longer direction

Muy(-ve) = αy(-ve)wl x 2 = 0.055 x 10.875 x (3.23)2 = 6.25KN-m

W u l 10.875 x 3.23
Vu = = = 17.56 KN
2 2

Minimum depth required:

Mu = 0.138fck bd2

10.56 x 106 = 0.138 x 20 x 1000 x d2

10.56 x 106
d=
√ 0.138 x 20 x 1000
= 61.85mm<110mm

dpro > dreq therefore, provided depth is adequate

Reinforcement:

Along shorter span ( X- Direction )

f y A st
Mux = 0.87 fy Ast d [1- ]
fck x bd
 500 A st
1.5 x 10.56 x 106 = 0.87 x 500 x Ast x 110[1- ]
20 x 1000 x 110

1.5 x 10.56 x 106 = 47850Ast - 10.875 Ast2

Ast = 360.58mm2

Using 8mm diameter bars

ast
S= x 1000
A st

π 2
∗8
= 4 x 1000
360.58

S= 139.40mm = 130mm

Provide 8mm dia bars @ 130mmc/c along shorter span

Along longer span (Y- Direction)

f y A st
Muy = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 6.25 x 106 = 0.87 x 500 x Ast x 102[1- ]
20 x 1000 x 102

9.4x 106 = 44370Ast - 10.875 Ast2

Ast = 224.17mm2

Using 8mm diameter bars

ast
S= x 1000
A st
 π 2
x8
S= 4 x 1000 = 224.2mm = 200mm
224.17

Provide 8mm dia bars @ 200mm c/c along longer span

Torsional reinforcement:

a) Edge strip

3 A st x 3
At = = X 360.58 = 270.5mm2
4 4

1l x 1
= x 3230 = 650mm
5 5

Using 6mm bars, spacing

π 2
6
S= 4 x 1000 = 104.5mm
270.5

Provide 6mm bars at 100mm c/c as Torsional reinforcement at edge strip

At corner where one edge discontinuous and one edge continuous

b) Middle strip

1 3 1 3
At = x A st x = x x 270.5 = 101.44mm2
2 4 2 4

Using 6mm dia bars

π 2
6
S= 4 x 1000 = 278.72mm
101.44

Provide 6mm bars at 270mm c/c as Torsional reinforcement at middle strip

Check for deflection:

l
( ) = 28
d provided

f s = 0.58 x f y = 0.58 x 500 = 290N/mm2

From fig 4 of IS 456 : 2000

The modification factor K = 1.3

l
( ) max = k x 28 = 1.3x 28 = 36.4
d

l l
( ) provided < ( ) max
d d

Hence safe

Reinforcement detailing diagram:

Panel 3:

l x = 2.89m

l y = 3.31m

l y 3.31
= = 1.13<2
l x 2.83

Hence, slab is to designed as two way slab

Thickness of slab:

span 2830
Effective depth = = = 103.31mm
28 28
Adopt effective depth = 110mm

Overall depth = 110+20= 130mm

Loads:

Self weight of the slab = 0.13 x 25 = 3.25KN/m2

Live load = 3KN/m2

Floor finish = 1KN/m2

Total load = 7.25 KN/m2

Factored load:

Factored load wu = 1.5 x 7.25 = 10.875KN/m2

Effective span:

l x = 3.12m

l y = 3.54m

l y 3.54
= = 1.13
l x 3.12

Calculation of moment and shear force :

From IS 456 : 2000 the moment coefficients are :

Two adjacent edges are discontinuous

α x = 0.053 & αy = 0.040

Slab spanning in two directions (Continuous)

α x = 0.074 & αy = 0.061

α x (-ve) = 0.074 α x (+ve) = 0.053

αy(-ve ) = 0.061 αy(+ve) = 0.040

+ve B.M. at mid span in shorter direction:

Mux (+ve) = α x (+ve)wl x 2 = 0.053 x 10.875 x (3.12)2 = 5.61KN-m

-ve B.M. at continuous edges in shorter direction

Mux (-ve) = α x (-ve)wl x 2 = 0.074 x 10.875 x (3.12)2 = 7.84KN-m

+ve B.M. at mid span in longer direction:

Muy(-ve) = αy(+ve)wl x 2 = 0.061 x 10.875 x (3.12)2 = 4.3KN-m

+ve B.M. at continuous edges in longer direction

Muy(-ve) = αy(-ve)wl x 2 = 0.040 x 10.875 x (3.12)2 = 6.5KN-m

W u l 10.875 x 3.12
Vu = = = 17.34 KN
2 2

Minimum depth required:

Mu = 0.138fck bd2

7.84 x 106 = 0.138 x 20 x 1000 x d2

7.84 x 106
d=
√ 0.138 x 20 x 1000
= 48.85mm<110mm

dpro > dreq therefore, provided depth is adequate

Reinforcement:

Along shorter span ( X- Direction )

f y A st
Mux = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 7.84 x 106 = 0.87 x 500 x Ast x 110[1- ]
20 x 1000 x 110

1.5 x 7.84 x 106 = 47850Ast - 10.875 Ast2

Ast = 259.86mm2

Using 8mm diameter bars

ast
S= x 1000
A st

π 2
∗8
= 4 x 1000
259.86

S= 193.30mm = 150mm

Provide 8mm dia bars @ 150mmc/c along shorter span

Along longer span (Y- Direction)

f y A st
Muy = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 6.5 x 106 = 0.87 x 500 x Ast x 102[1- ]
20 x 1000 x 102

9.75x 106 = 44370Ast - 10.875 Ast2

Ast = 233.0mm2
Using 8mm diameter bars

ast
S= x 1000
A st

π 2
8
= 4 x 1000 = 214.8mm = 200mm
223.0

Provide 8mm dia bars @ 200mm c/c along longer span

Torsional reinforcement:

a) Edge strip

3 A st x 3
At = = X 259.89 = 195mm2
4 4

1l x 1
= x 3120 = 630mm
5 5

Using 6mm bars, spacing

π 2
6
S = 4 x 1000 = 144.9mm
195

Provide 6mm bars at 140mm c/c as Torsional reinforcement at edge strip

At corner where one edge discontinuous and one edge continuous

b) Middle strip

1 3 1 3
At = x A st x = x x 259.89 = 97.46mm2
2 4 2 4

Using 6mm dia bars

 π 2
6
S= 4 x 1000 = 290.11mm
97.46

Provide 6mm bars at 20mm c/c as Torsional reinforcement at middle strip

Check for deflection:

l
( ) = 28
d provided

f s = 0.58 x f y = 0.58 x 500 = 290N/mm2

From fig 4 of IS 456 : 2000

The modification factor K = 1.3

l l l
( ) max = k x 28 = 1.3x 28 = 36.4 ( ) provided < ( ) max
d d d

Hence safe

Reinforcement detailing diagram:

Panel 4:

l x = 3.31m

l y = 3.83m

l y 3.83
= = 1.2<2
l x 3.31

Hence, slab is to designed as two way slab

Thickness of slab:

span 3310
Effective span = = = 108.31mm
28 28
Adopt effective depth = 110mm

Overall depth = 110+20+ = 130mm

Loads:

Self weight of the slab = 0.13 x 25 = 3.25KN/m2

Live load = 3KN/m2

Floor finish = 1KN/m2

Total load = 7.25 KN/m2

Factored load:

Factored load wu = 1.5 x 7.25 = 10.875KN/m2

Effective span:

l x = 3.54m

l y = 4.06m

l y 4.06
= = 1.2
l x 3.54

Calculation of moment and shear force :

From IS 456 : 2000 the moment coefficients are :

Two adjacent edges are discontinuous

α x = 0.060 & αy = 0.045

Slab spanning in two directions (Continuous)

α x = 0.084 & αy = 0.059

α x (-ve) = 0.084 α x (+ve) = 0.060

αy(-ve ) = 0.059 αy(+ve) = 0.045

+ve B.M. at mid span in shorter direction:

Mux (+ve) = α x (+ve)wl x 2 = 0.060 x 10.875 x (3.54)2 = 8.18KN-m

-ve B.M. at continuous edges in shorter direction

Mux (-ve) = α x (-ve)wl x 2 = 0.084 x 10.875 x (3.54)2 = 11.45KN-m

+ve B.M. at mid span in longer direction:

Muy(-ve) = αy(+ve)wl x 2 = 0.045 x 10.875 x (3.54)2 = 6.14KN-m

+ve B.M. at continuous edges in longer direction

Muy(-ve) = αy(-ve)wl x 2 = 0.059 x 10.875 x (3.54)2 = 8.05KN-m

W u l 10.875 x 3.54
Vu = = = 17.64 KN
2 2

Minimum depth required:

Mu = 0.138 fck bd2

11.45 x 106 = 0.138 x 20 x 1000 x d2

11.45 x 106
d=
√ 0.138 x 20 x 1000
= 64.85mm<110mm

dpro > dreq therefore, provided depth is adequate

Reinforcement:

Along shorter span ( X- Direction )

f y A st
Mux = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 11.45 x 106 = 0.87 x 500 x Ast x 110[1- ]
20 x 1000 x 110

1.5 x 11.45 x 106 = 47850Ast - 10.875 Ast2

Ast = 394.4mm2

Using 8mm diameter bars

ast
S= x 1000
A st

π 2
∗8
= 4 x 1000
394.4

S= 127.40mm = 120mm

Provide 8mm dia bars @ 120mmc/c along shorter span

Along longer span (Y- Direction)

f y A st
Muy = 0.87 fy Ast d [1- ]
fck x bd

500 A st
1.5 x 8.05 x 106 = 0.87 x 500 x Ast x 102[1- ]
20 x 1000 x 102

12.08x 106 = 44370Ast - 10.875 Ast2

Ast = 293.40mm2
Using 8mm diameter bars

ast
S= x 1000
A st

π 2
x8
= 4 x 1000 = 171.32.8mm = 150mm
293.40

Provide 8mm dia bars @ 150mm c/c

Torsional reinforcement:

a) Edge strip

3 A st x 3
At = = X 394.4 = 295.8mm2
4 4

1l x 1
= x 3540 = 710mm
5 5

Using 6mm bars, spacing

π 2
6
S= 4 x 1000 = 95.5mm
295.8

Provide 6mm bars at 90mm c/c as Torsional reinforcement at edge strip

At corner where one edge discontinuous and one edge continuous

b) Middle strip

1 3 1 3
At = x A st x = x x 394.4 = 147.9mm2
2 4 2 4

Using 6mm dia bars

 π 2
6
S= 4 x 1000 = 191.11mm
147.9

Provide 6mm bars at 150mm c/c as Torsional reinforcement at middle strip

Check for deflection:

l
( ) = 28
d provided

f s = 0.58 x f y = 0.58 x 500 = 290N/mm2

From fig 4 of IS 456 : 2000

The modification factor K = 1.3

l
( ) max = k x 28 = 1.3x 28 = 36.4
d

l l
( ) provided < ( ) max
d d

Hence safe

Reinforcement detailing diagram:

 Slab Results :

Table 3.1.1: Results of slab panels

Panel Dimensions Reinforcement Reinforcement Torsional

(M) Along X – Direction Along Y – Direction Reinforcement

1 3.23 x 3.12 224 mm2 242mm2 168mm2

8mm dia bars @ 8mm dia bars @ 6mm dia bars @
200mm c/c 200mm c/c 150mm c/c
2 3.23 x 4.06 360mm2 225mm2 270mm2
8mm dia bars @ 8mm dia bars @ 6mm dia bars @
130mm c/c 200mm c/c 100mm c/c
3 3.54 x 3.12 260mm2 233mm2 195mm2
8mm dia bars @ 8mm dia bars @ 6mm dia bars @
150mm c/c 200mm c/c 100mm c/c
4 3.54 x 4.06 395mm2 294mm2 296mm2
8mm dia bars @ 8mm dia bars @ 6mm dia bars @
120mm c/c 150mm c/c 90mm c/c
Analysis of slab:

S.no Panel Dimensions Bending Moment (KNm)

(m)
X - direction Y - Direction
1 3.12m x 3.23m 6.78 6.57

2 4.06m x 3.23m 10.56 6.25

3 3.12m x 3.54m 7.84 6.50

4 4.06m x 3.54m 11.45 8.05