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.

DESIGN OF CANTILEVER CHAJJAName of work :- pkn

1 Cear Span 1.25 mtr 1250 mm

2 Wall width 0.30 mtr 300 mm

3 1800 1.80

4 Concrete M - 20 wt.of concrete 25000

7 m 13.3

5 Steel fy 415 Tensile stress 230

6 Assume average thickness 100 mm 0.10 mtr

7 Nominal Cover 20 mm Effective Cover 30 mm

8 Reinforcement Main Top bars 8 300 mm

Distribution bars 8 300 mm

3001250

8 300 mm c/c8 300 mm c/c

100mm

150mm

(A) X - section

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Super imposed loads (with finishing) N/m2 or kN/m2

N/m3

scbc

N/mm2

mm F

mm F

mm f .bars mm f bars

DESIGN OF CANTILEVER CHAJJA

Cear Span 1.25 mtr 1250 mmWall width 0.30 mtr 300 mm

Super imposed loads (with finishing) 1800 N/m2 or Or 1.80Assume average thickness 100 mm Or 0.10 mtrConcrete M 20Steel fy 415 N/mm2 Tensile stess = 230 N/mm2Nominal cover 20 mmEffective cover 30 mm

1 Design Constants:- For HYSD Bars Cocrete M = 20

= 230 wt. of concrete = 25000

= 7

m = 13.33m*c

=13.33 x 7

= 0.28913.33 x 7 + 230

= 1 - 0.289 / 3 = 0.904

= 0.5 x 7 x 0.904 x 0.289 = 0.9130

2 Caculcation of B.M. :-

= 0.10 x 1 x 1 x ### = 2500 NSuper imposed loads (with finishing) = = 1800 N

= Total weight = 4300 N

= =4300 x( 1.25 3359

= 3.359 K N-m2 2 .= N m

= wL = 4300 x 1.25 = 5375 N2 Design of setion :-

=3.359 x

= 61 mm0.913 x 1000

From stiffness (i.e. deflection) point of view, L/d = 7for a cantilever where L=l+d/2 == 1250 + 50 = 1300

Hence modification factore for HYSD bars W 1.30 mm Hence d = L/ 1.300 x 7 = 1300 /( 1.30 x 7 )W 143 mm

However, this is a structure of minor importance keep D = 150 mm at the support.

Keeping nominal cover of = 20 mm

and using 8 = 150 - 20 - 4 = 126 mm

Reduce D = 100 mm at free end4 Steel Reiforcement :-

Ast = =3.36 x

= 128sst x j x D 230 x 0.904 x 126

using 8 mm bars A = = 3.14 x 8 x 8= 50.24 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 8 300 mm c/c .

1000 x 50.2= 167

300

kN/m2

sst = N/mm2 N/mm2

scbc = N/mm3

k= m*c+sstj=1-k/3

R=1/2xc x j x k

Dead weight, per m2

Max. possible Bending moment

wL2 )2

x 10 6

Vmax.

Effective depth required =

ÖBM/Rxb10 6

mm say For M20-Fe415 combination p1.lim'=0.44%

mm F bars, D

BM 10 6

mm2

3.14xdia2

mm2

mm F bar, @

Actual Ast= mm2

5 Embeded of reinforcement in supports.:- In order to devlopfull tensile strength at face of support, each bars should be embeded

45 x 8 = 360 mm.

= 8 x 8 = 64 mm. Thus total anchorage achieved value

= 300 - 20 + 64 +( 150 - 2.00 x 20 - 4 )'= 450 mm

= 450 > Hence O.K. = 360

6 Check for shear :-

Neglecting the taper and taking an average d=( 150 + 100 )- 20 = 105 mm

2

V = 5375 N b = 1000 mm d = 105 mm

=V

=5375

= 0.051bxd 1000 x 105

0.18 x 1.30 = 0.234For M 20 grade concrete and

p' =100Ast

=100 x 167

= 0.16 %bd 1000 x 105

20 concrete, for 0.16 % steel = 0.18

here < Hence safe

7 Distribution reinforcement:- Avrage depth = 125 mm

= 0.12 x b x D=

0.12 x 1000 x D= 1.20 D

100 100"= 1.20 x 125 = 150 mm

Using 8 =3.14 x 8 x 8

= 50.24 x 100

pitch s=###

=1000 x 50.2 = 335 mm

150

However, provied these @ 300 mm c/c .

7 Details of reinforcement:- Shown in drawing

pk_nandwana@yahoo.co.in

into support by a length equal to Ld = 45 F =

This could be best achieved by providing one bend of 900 where anchor value of this bend=8F

Ld Ld

tv N/mm2

Permissible value of tc = N/mm2

Hence from Table permissible shear (tc)for M N/mm2

tv tc

Asd

mm F bars each having mm2

x As

Asd

pk_nandwana@yahoo.co.in

Name of work :- pkn

wall width 300

12508 mm bars @ 300 C/C 8 mm bars @ 300 C/C

100

150

VALUES OF DESIGN CONSTANTSGrade of concrete M-15 M-20 M-25 M-30 M-35 M-40 Grade of concrete

Modular Ratio 18.67 13.33 10.98 9.33 8.11 7.18

5 7 8.5 10 11.5 13

93.33 93.33 93.33 93.33 93.33 93.33

0.4 0.4 0.4 0.4 0.4 0.4

0.867 0.867 0.867 0.867 0.867 0.867

0.867 1.214 1.474 1.734 1.994 2.254

0.714 1 1.214 1.429 1.643 1.857

0.329 0.329 0.329 0.329 0.329 0.329

0.89 0.89 0.89 0.89 0.89 0.89

0.732 1.025 1.244 1.464 1.684 1.903

0.433 0.606 0.736 0.866 0.997 1.127

0.289 0.289 0.289 0.289 0.289 0.289

0.904 0.904 0.904 0.904 0.904 0.904

0.653 0.914 1.11 1.306 1.502 1.698

0.314 0.44 0.534 0.628 0.722 0.816

0.253 0.253 0.253 0.253 0.253 0.253

0.916 0.916 0.916 0.914 0.916 0.916

0.579 0.811 0.985 1.159 1.332 1.506

0.23 0.322 0.391 0.46 0.53 0.599

bd M-15 M-20 M-25 M-30 M-35 M-40

0.18 0.18 0.19 0.2 0.2 0.2

0.25 0.22 0.22 0.23 0.23 0.23 0.230.50 0.29 0.30 0.31 0.31 0.31 0.320.75 0.34 0.35 0.36 0.37 0.37 0.381.00 0.37 0.39 0.40 0.41 0.42 0.421.25 0.40 0.42 0.44 0.45 0.45 0.461.50 0.42 0.45 0.46 0.48 0.49 0.491.75 0.44 0.47 0.49 0.50 0.52 0.522.00 0.44 0.49 0.51 0.53 0.54 0.552.25 0.44 0.51 0.53 0.55 0.56 0.572.50 0.44 0.51 0.55 0.57 0.58 0.602.75 0.44 0.51 0.56 0.58 0.60 0.62

3.00 and above 0.44 0.51 0.57 0.6 0.62 0.63

Grade of concrete M-15 M-20 M-25 M-30 M-35 M-40

1.6 1.8 1.9 2.2 2.3 2.5

Reiforcement %

tbd (N / mm2)

scbc N/mm2

m scbc

(a) sst = 140

N/mm2 (Fe 250)

kc

jc

Rc

Pc (%)

(b) sst = 190

N/mm2

kc

jc

Rc

Pc (%)

(c ) sst = 230

N/mm2 (Fe 415)

kc

jc

Rc

Pc (%)

(d) sst = 275

N/mm2 (Fe 500)

kc

jc

Rc

Pc (%)

Permissible shear stress Table tv in concrete (IS : 456-2000)

100A s Permissible shear stress in concrete tv N/mm2

< 0.15

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

tc.max

Shear stress tc

M-20 M-20bd bd

0.15 0.18 0.18 0.150.16 0.18 0.19 0.180.17 0.18 0.2 0.210.18 0.19 0.21 0.240.19 0.19 0.22 0.270.2 0.19 0.23 0.3

0.21 0.2 0.24 0.320.22 0.2 0.25 0.350.23 0.2 0.26 0.380.24 0.21 0.27 0.410.25 0.21 0.28 0.440.26 0.21 0.29 0.470.27 0.22 0.30 0.50.28 0.22 0.31 0.550.29 0.22 0.32 0.60.3 0.23 0.33 0.65

0.31 0.23 0.34 0.70.32 0.24 0.35 0.750.33 0.24 0.36 0.820.34 0.24 0.37 0.880.35 0.25 0.38 0.940.36 0.25 0.39 1.000.37 0.25 0.4 1.080.38 0.26 0.41 1.160.39 0.26 0.42 1.250.4 0.26 0.43 1.33

0.41 0.27 0.44 1.410.42 0.27 0.45 1.500.43 0.27 0.46 1.630.44 0.28 0.46 1.640.45 0.28 0.47 1.750.46 0.28 0.48 1.880.47 0.29 0.49 2.000.48 0.29 0.50 2.130.49 0.29 0.51 2.250.5 0.30

0.51 0.300.52 0.300.53 0.300.54 0.300.55 0.310.56 0.310.57 0.310.58 0.310.59 0.310.6 0.32

0.61 0.320.62 0.320.63 0.320.64 0.320.65 0.330.66 0.33

100A s 100A s

0.67 0.330.68 0.330.69 0.330.7 0.34

0.71 0.340.72 0.340.73 0.340.74 0.340.75 0.350.76 0.350.77 0.350.78 0.350.79 0.350.8 0.35

0.81 0.350.82 0.360.83 0.360.84 0.360.85 0.360.86 0.360.87 0.360.88 0.370.89 0.370.9 0.37

0.91 0.370.92 0.370.93 0.370.94 0.380.95 0.380.96 0.380.97 0.380.98 0.380.99 0.381.00 0.391.01 0.391.02 0.391.03 0.391.04 0.391.05 0.391.06 0.391.07 0.391.08 0.41.09 0.41.10 0.41.11 0.41.12 0.41.13 0.41.14 0.41.15 0.41.16 0.411.17 0.411.18 0.411.19 0.411.20 0.41

1.21 0.411.22 0.411.23 0.411.24 0.411.25 0.421.26 0.421.27 0.421.28 0.421.29 0.421.30 0.421.31 0.421.32 0.421.33 0.431.34 0.431.35 0.431.36 0.431.37 0.431.38 0.431.39 0.431.40 0.431.41 0.441.42 0.441.43 0.441.44 0.441.45 0.441.46 0.441.47 0.441.48 0.441.49 0.441.50 0.451.51 0.451.52 0.451.53 0.451.54 0.451.55 0.451.56 0.451.57 0.451.58 0.451.59 0.451.60 0.451.61 0.451.62 0.451.63 0.461.64 0.461.65 0.461.66 0.461.67 0.461.68 0.461.69 0.461.70 0.461.71 0.461.72 0.461.73 0.461.74 0.46

1.75 0.471.76 0.471.77 0.471.78 0.471.79 0.471.80 0.471.81 0.471.82 0.471.83 0.471.84 0.471.85 0.471.86 0.471.87 0.471.88 0.481.89 0.481.90 0.481.91 0.481.92 0.481.93 0.481.94 0.481.95 0.481.96 0.481.97 0.481.98 0.481.99 0.482.00 0.492.01 0.492.02 0.492.03 0.492.04 0.492.05 0.492.06 0.492.07 0.492.08 0.492.09 0.492.10 0.492.11 0.492.12 0.492.13 0.502.14 0.502.15 0.502.16 0.502.17 0.502.18 0.502.19 0.502.20 0.502.21 0.502.22 0.502.23 0.502.24 0.502.25 0.512.26 0.512.27 0.512.28 0.51

2.29 0.512.30 0.512.31 0.512.32 0.512.33 0.512.34 0.512.35 0.512.36 0.512.37 0.512.38 0.512.39 0.512.40 0.512.41 0.512.42 0.512.43 0.512.44 0.512.45 0.512.46 0.512.47 0.512.48 0.512.49 0.512.50 0.512.51 0.512.52 0.512.53 0.512.54 0.512.55 0.512.56 0.512.57 0.512.58 0.512.59 0.512.60 0.512.61 0.512.62 0.512.63 0.512.64 0.512.65 0.512.66 0.512.67 0.512.68 0.512.69 0.512.70 0.512.71 0.512.72 0.512.73 0.512.74 0.512.75 0.512.76 0.512.77 0.512.78 0.512.79 0.512.80 0.512.81 0.512.82 0.51

2.83 0.512.84 0.512.85 0.512.86 0.512.87 0.512.88 0.512.89 0.512.90 0.512.91 0.512.92 0.512.93 0.512.94 0.512.95 0.512.96 0.512.97 0.512.98 0.512.99 0.513.00 0.513.01 0.513.02 0.513.03 0.513.04 0.513.05 0.513.06 0.513.07 0.513.08 0.513.09 0.513.10 0.513.11 0.513.12 0.513.13 0.513.14 0.513.15 0.51

Grade of concreteM-10 M-15 M-20 M-25 M-30 M-35 M-40 M-45

-- 0.6 0.8 0.9 1 1.1 1.2 1.3

Development Length in tension

Plain M.S. Bars H.Y.S.D. Bars

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

(N/mm2) (N/mm2) (N/mm2)M 10 3.0 300 2.5 250 -- --M 15 5.0 500 4.0 400 0.6 60M 20 7.0 700 5.0 500 0.8 80M 25 8.5 850 6.0 600 0.9 90M 30 10.0 1000 8.0 800 1.0 100M 35 11.5 1150 9.0 900 1.1 110M 40 13.0 1300 10.0 1000 1.2 120M 45 14.5 1450 11.0 1100 1.3 130M 50 16.0 1600 12.0 1200 1.4 140

Permissible Bond stress Table tbd in concrete (IS : 456-2000)

tbd (N / mm2)

Grade of concrete tbd (N / mm2) kd = Ld F tbd (N / mm2) kd = Ld F

Permissible stress in concrete (IS : 456-2000)

Grade of concrete

Permission stress in compression (N/mm2) Permissible stress in bond (Average) for plain bars in tention (N/mm2)Bending acbc Direct (acc)

Kg/m2 Kg/m2 in kg/m2

M-50

1.4

in concrete (IS : 456-2000)