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
