Cantilever+Type++SLAB+(Chajja)

As per RCC design ( B.C. punmia ) page 184 example 7.6 DESIGN OF CANTILEVER CHAJJA A cantilever slab bends down wards, with the result that tension is devloped at the upper face. Hence reiforcement is provided at upper face, The span of slab is taken equal to the actual length.or over hang plus half the effective depth If the width of cantilever is long, 1meter length of the cantilever is taken for the design purpose. However, if the the width of cantilever is short, whole width may be taken as the width of slab for design purpose.

Name of work :-

DESIGN OF CANTILEVER CHAJJA pkn

1

Cear Span

1.25

mtr

1250

mm

2

Wall width

0.30

mtr

300

mm

3

Super imposed loads (with finishing)

1800

N/m2 or

1.80

kN/m2

4

Concrete

wt.of concrete

scbc

7

m

13.3

Tensile stress

230

N/mm2

30

mm

Steel

fy

6

Assume average thickness

100

mm

7

Nominal Cover

20

mm

8

Reinforcement Main Top bars

8

mm F

300

mm

Distribution bars

8

mm F

300

mm

415 0.10

mtr

Effective Cover

300 8 mm f .bars

1250 300

mm c/c 8 mm f bars

300

mm c/c 100 mm

150 mm

(A) X - section

pk_nandwana @yahoo.co.in

3

20

5

25000

N/m

M-

DESIGN OF CANTILEVER CHAJJA Cear Span Wall width Super imposed loads (with finishing) Assume average thickness Concrete M 20 Steel fy 415 N/mm2 Nominal cover 20 mm Effective cover 30 mm

1 Design Constants:- For HYSD Bars

sst = scbc = m

m*c

m*c+sst j=1-k/3 = 1 R=1/2xc x j x k = 0.5

mtr mtr N/m2 or Or mm Or

Tensile stess

Cocrete M =

= 230 N/mm2 N/mm3 = 7 = 13.33 k=

1.25 0.30 1800 100

=

1250 300 1.80 0.10

mm mm kN/m2 mtr

230 N/mm2

20

wt. of concrete

2 = 25000 N/mm

x 7

= 0.289

=

13.33 13.33 x

-

0.289

/

3

x

7

x

0.904

7 +

230

= 0.904 x 0.289 =

0.9130

2 Caculcation of B.M. :Dead weight, per m2 = Super imposed loads (with finishing) = = Max. possible Bending moment

=

wL2 2

0.10 x

1x

1

x #### = = Total weight =

4300 x( 1.25 )2 3359 = 2 .= N m Vmax. = wL = 4300 x

=

2500 N 1800 N 4300 N

3.359 x 10 6 1.25 =

K N-m

5375 N

2 Design of setion :Effective depth required =

Rxb

3.359 x

10 6

= 61 mm 0.913 x 1000 From stiffness (i.e. deflection) point of view, L/d = 7for a cantilever where L=l+d/2 = 1250 + 50 = 1300 mm say For M20-Fe415 combination p1.lim'=0.44% = W 1.30 mm Hence modification factore for HYSD bars 7 = 1300 /( 1.30 x 7 Hence d = L/ 1.300 x )W 143 mm = mm at the support. 150 However, this is a structure of minor importance keep D 20 mm Keeping nominal cover of = 20 4 = 126 mm and using 8 mm F bars, D = 150 Reduce D = 100 mm at free end 4 Steel Reiforcement :BM 3.36 x 10 6 = Ast = = 128 mm2 sst x j x D 230 x 0.904 x 126 2 using 8 mm bars A = 3.14xdia = 3.14 x 8 x 8 = 50.2 mm2 4 x100 4 x 100 Nomber of Bars = Ast/A = 128 / 50 = 2.55 say = 3 No. Maximum permissble spacing = 3 x d = 3 x 150 = 450 mm or 300 mm which ever is smaller. Hence Provided 8 mm F bar, @ 300 mm c/c . 1000 x 50.2 Actual Ast= = 167 mm2 300 [email protected]

=

5 Embeded of reinforcement in supports.:In order to devlopfull tensile strength at face of support, each bars should be embeded into support by a length equal to Ld = 45 F = 45 x 8= 360 mm. This could be best achieved by providing one bend of 90 0 where anchor value of this bend=8F = = =

8 300 450

x >

8 20 Ld

= 64 mm. Thus total anchorage achieved value + 64 +( 150 - 2.00 x 20 4 )'= 450 mm Ld Hence O.K. = 360

6 Check for shear :Neglecting the taper and taking an average d=(

V

=

5375

N

b=

1000 mm

150 + 2

100 )-

d =

105 mm

20 =

105 mm

5375 V = = 0.051 N/mm2 bxd 1000 x 105 Permissible value of t c = 0.234 N/mm2 0.18 x 1.30 = For M 20 grade concrete and 100 x 167 100Ast p' = = = 0.16 % 1000 x 105 bd Hence from Table permissible shear (tc)for M 20 concrete, for 0.16 % steel = 0.18 N/mm2 tc tv here < Hence safe

tv

7 Distribution reinforcement:Asd = 0.12

=

Avrage depth = 125 mm 0.12 x 1000 x D = = 1.20 D 100 "= 1.20 = 150 mm 3.14 x 8 x 8 Using 8 = = 50.2 mm F bars each having 4 x 100 1000 x As 1000 x 50.2 = 335 mm pitch s= = Asd 150 However, provied these @ 300 mm c/c .

7 Details of reinforcement:-

[email protected]

x bxD 100 x 125

Shown in drawing

mm2

Name of work :-

pkn

wall width 300

8

1250 mm bars @ 300 C/C

8

mm bars @ 300 C/C

100 150

VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio

M-15 18.67

M-20 13.33

M-25 10.98

M-30 9.33

M-35 8.11

M-40 7.18

scbc N/mm2 m scbc

5

7

8.5

10

11.5

13

93.33

93.33

93.33

93.33

93.33

93.33

kc

0.4

0.4

0.4

0.4

0.4

0.4

(a) sst = 140 N/mm2 (Fe 250)

jc

0.867

0.867

0.867

0.867

0.867

0.867

Rc

0.867

1.214

1.474

1.734

1.994

2.254

Pc (%)

0.714

1

1.214

1.429

1.643

1.857

kc

0.329

0.329

0.329

0.329

0.329

0.329

jc

0.89

0.89

0.89

0.89

0.89

Rc

0.89 0.732

1.025

1.244

1.464

1.684

1.903

Pc (%)

0.433

0.606

0.736

0.866

0.997

1.127

kc

0.289

0.289

0.289

0.289

0.289

0.289

jc

0.904

0.904

0.904

0.904

0.904

0.904

Rc

0.653

0.914

1.11

1.306

1.502

1.698

Pc (%)

0.314

0.44

0.534

0.628

0.722

0.816

kc

0.253

0.253

0.253

0.253

0.253

0.253

jc

0.916

0.916

0.916

0.914

0.916

0.916

Rc

0.579

0.811

0.985

1.159

1.332

1.506

Pc (%)

0.23

0.322

0.391

0.46

0.53

0.599

(b) sst = 190 N/mm2 (c ) sst = 230 N/mm2 (Fe 415) (d) sst = 275 N/mm2 (Fe 500)

Permissible shear stress Table tv in concrete (IS : 456-2000) 100As bd < 0.15 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 and above

Permissible shear stress in concrete M-15 M-20 M-25 M-30 0.18 0.18 0.19 0.2 0.22 0.22 0.23 0.23 0.29 0.30 0.31 0.31 0.34 0.35 0.36 0.37 0.37 0.39 0.40 0.41 0.40 0.42 0.44 0.45 0.42 0.45 0.46 0.48 0.44 0.47 0.49 0.50 0.44 0.49 0.51 0.53 0.44 0.51 0.53 0.55 0.44 0.51 0.55 0.57 0.44 0.51 0.56 0.58 0.44 0.51 0.57 0.6

tv N/mm2 M-35 M-40 0.2 0.2 0.23 0.23 0.31 0.32 0.37 0.38 0.42 0.42 0.45 0.46 0.49 0.49 0.52 0.52 0.54 0.55 0.56 0.57 0.58 0.60 0.60 0.62 0.62 0.63

Maximum shear stress tc.max in concrete (IS : 456-2000) Grade of concrete

tc.max

M-15 1.6

M-20 1.8

M-25 1.9

M-30 2.2

M-35 2.3

M-40 2.5

Grade of concrete tbd (N / mm2)

Shear stress tc 100As M-20 bd 0.15 0.18 0.16 0.18 0.17 0.18 0.18 0.19 0.19 0.19 0.2 0.19 0.21 0.2 0.22 0.2 0.23 0.2 0.24 0.21 0.25 0.21 0.26 0.21 0.27 0.22 0.28 0.22 0.29 0.22 0.3 0.23 0.31 0.23 0.32 0.24 0.33 0.24 0.34 0.24 0.35 0.25 0.36 0.25 0.37 0.25 0.38 0.26 0.39 0.26 0.4 0.26 0.41 0.27 0.42 0.27 0.43 0.27 0.44 0.28 0.45 0.28 0.46 0.28 0.47 0.29 0.48 0.29 0.49 0.29 0.5 0.30 0.51 0.30 0.52 0.30 0.53 0.30 0.54 0.30 0.55 0.31 0.56 0.31 0.57 0.31 0.58 0.31 0.59 0.31 0.6 0.32 0.61 0.32 0.62 0.32

Reiforcement % 100As M-20 bd 0.18 0.15 0.19 0.18 0.2 0.21 0.21 0.24 0.22 0.27 0.23 0.3 0.24 0.32 0.25 0.35 0.26 0.38 0.27 0.41 0.28 0.44 0.29 0.47 0.30 0.5 0.31 0.55 0.32 0.6 0.33 0.65 0.34 0.7 0.35 0.75 0.36 0.82 0.37 0.88 0.38 0.94 0.39 1.00 0.4 1.08 0.41 1.16 0.42 1.25 0.43 1.33 0.44 1.41 0.45 1.50 0.46 1.63 0.46 1.64 0.47 1.75 0.48 1.88 0.49 2.00 0.50 2.13 0.51 2.25

0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14

0.32 0.32 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4 0.4

1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66

0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46

1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18

0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50

2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70

0.50 0.50 0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15

0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

Permissible Bond stress Table tbd in concrete (IS : 456-2000) Grade of concreteM-10 -tbd (N / mm2)

M-15 0.6

M-20 0.8

M-25 0.9

M-30 1

M-35 1.1

M-40 1.2

M-45 1.3

Development Length in tension Plain M.S. Bars

H.Y.S.D. Bars

Grade of concrete

tbd (N / mm2)

kd = Ld F

tbd (N / mm2)

kd = Ld F

M 15

0.6

58

0.96

60

M 20

0.8

44

1.28

45

M 25

0.9

39

1.44

40

M 30

1

35

1.6

36

M 35

1.1

32

1.76

33

M 40

1.2

29

1.92

30

M 45

1.3

27

2.08

28

M 50

1.4

25

2.24

26

Permissible stress in concrete (IS : 456-2000) Grade of concrete M M M M M M M M M

10 15 20 25 30 35 40 45 50

Permission stress in compression (N/mm 2) Permissible stress in bond (Average) for Bending acbc Direct (acc) plain bars in tention (N/mm2) (N/mm2) 3.0 5.0 7.0 8.5 10.0 11.5 13.0 14.5 16.0

Kg/m2 300 500 700 850 1000 1150 1300 1450 1600

(N/mm2) 2.5 4.0 5.0 6.0 8.0 9.0 10.0 11.0 12.0

Kg/m2 250 400 500 600 800 900 1000 1100 1200

(N/mm2) -0.6 0.8 0.9 1.0 1.1 1.2 1.3 1.4

in kg/m2 -60 80 90 100 110 120 130 140

00) M-50 1.4