Design Of Cantilever Beam.xls 604o6z
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DESIGN OF CANTILEVER BEAM
1
Clear Span (opening )
2.50
mtr
2500
mm
2
Wall width
0.40
mtr
400
mm
3
Super imposed loads
12.00
kN per meter run
4
Conrete
M
cbc
5
Steel
fy
6
Nominal Cover
20 7
unit weight 25000 N/m3 m 13.3
N/mm2
415
Tensile stress
230
N/mm2
Effective Cover
30
mm
300
mm c/c
25
mm
Main Top
16
mm
3
Nos.
Anchor bars (Bottom )
10
mm
2
Nos.
Strirrups
8
mm
120
Reinforcement
400 350 2500
to
3 nos.bars
mm
16
2 nos.bars 0
720
mm
16
1780
200 490
0
#REF!
mm
10 mm 2 nos.anchor bars
8 mm 2 ldg strirrup
###
120 mm c/c mm 2 lgd strps
8
300
mm c/c
(A) L- section
3 nos.bar of
16 mm 2 nos.bars
8
mm 2 lgd strps
300
mm c./c
16
200
10 mm 2 nos.anchor bars 490
mm 250 mm (C)Section at the end 250
mm
(B) section at
pk_nandwana @yahoo.co.in
DESIGN OF CANTILEVER BEAM
Clear Span (opening )
2.50 m
2500 mm
Wall width
0.40 m
400 mm
Super imposed loads
12.00 kn/
Conrete
M
20
Steel
fy
415 N/mm2
cbc Nominal cover
7
Tensile stess
N/mm2
25 mm
cbc
230
N/mm2
7
N/mm2
m*c
k=
Effective cover
N per meter
=
230 N/mm2 13.3
=
30
Cocrete M =
20
mm
wt. of concrete = 25000 N/mm2
m 13.3 13.3
= 13.3
m*c+st
12000
m =
1 Design Constants:- For HYSD Bars
st
Or
x
x
7
j=1-k/3
1
-
0.288
/
3
R=1/2xc x j x k
0.5
x
7
x
0.904
7
=
0.288
=
0.904
x 0.288 =
0.9116
+
230
2 Caculcation of B.M. :-
1. Let depth of beam at fixed end
= span /7 =
effective depth of beam at fixed end =
Let width of Beam at fixed end Assume depth of Beam at free end
= =
400
500 500
2.50
/
+ 2xcover =
/ /
2 2
= =
7
=
400 +
250 250
0.36 mt Say
400
2
x
25
= 450
Say
=
500
mm
Say say
= =
250 200
mm mm
Let width of Beam at free end =
weight of Beam
x (
0.50
+
) x 0.25
x
2.50
x
###
0.5
+ 2.00 x 0.20 x 0.50 + 0.20 12000 x( 2.50 )2 43359 = 5469 x 1.07 + = 2.00 .= N m Shear force at edge of = 5469 + 12000 x Acting at
Max. possible Bending moment
2
0.20
=
250
=
5469 N
2.50 = 3.00
mm
m form
1.07 fixed end
43.36 x 10 6
K N-m
2.50 = 35469 N
Design of setion :-
Effective depth required Let us take d
= =
Rxb
43.36 x
=
= 0.912 x
D
436 mm
250
= 440 mm D =d+2xcover
### mm bar will be used. With
Assuming that
10 6
440 +
2
x
50
= 490
8 mm dia links and a nominal cover of =
=
490 25 Keep total depth at free end
=
16 8 200 mm
/
2
25
= 449 Hence ok.
4 Steel Reiforcement :BM
Ast =
43.36
=
st x jx D
230 x
using ### mm bars
A
x
10 6
0.904 x 3.14xdia2
=
=
464.48
449 3.14 x
=
16
x
= 201 4
464 /
201 =
2.31
x say
100 =
Hence Provided
3
bars of
16 mm bar,
Also provide
2
x
10
mm anchore bars at bottom
=
3
having, Ast
16
= 4 x100
Nomber of Bars = Ast/A
mm2
x
201 =
3
No.
603 mm2
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Since the bending moment decreases to zero at end, let us curtail few bars. Let Let 1 Bars be curtailed at a distance x from the free end. Assuming the B.M.D.to parabolic, the B.M. at this section may be approximately taken to eual to x 2 x 43.36 x 10 6 = 6.938 x 106 x2 2.50
N-mm
Area of rest bars=
2
x
201
=
6.938
402
=
230
x
200
+
mm2
402 x
10 6 x2
490 Total depth of section
=
dx
0.904 x -
Where dx effective depth at that section
----------- (1)
200 x
x
+
8
2.50 dx
=
200
+
dx
=
159
+
Subsituting in (1),
402
=
290 2.50
x
116 x 230
x
x
-
25
+
8
------------------------------------ (2) 6.938 x 10 6 x2 0.904 x( 159 +
116 x) =
or or 402
6.938 x 6937500 than divide by 17261 17261 divide by 17261 than 1
10 6 x2 = 402 x( 230 x 0.904 2 = 402 x( 208 x( 159 x x2 = 33057 + 24117 2 x - 24117 x 33057 1.40 x 1.9152 x2
x( 159 + + 116 x) x = 0 = 0
116
= 1.397 + 1.95 -4x 1.00 x -1.9152 x 2 1 or a = 1.397 +( 1.95 - -7.660667439 )1/2 2 or a = 1.397 +( 9.6129153 )1/2 2 x 1 or a = 1.397 + 3.100 2 or a = 4.498 / 2 2.30 or a = 2.249 m say mtr Minimum embedded requirement beyond this = 12. = 12 x 16 = 192 or equal to dx = 159 + 116 x 2.30 = 426 mm which ever more Bars may be curtail at= 2.50 - 2.30 + 0.426 = 0.63 mtr
a =
or
b +b2-4.a.c 2 a
a
from the edge of the . This should be grater than 45 x 16 = 720 mm Ld=45 = Hence bar can be curtailed at = 720 mm from the . 5 Check for shear and design of shear reinforcement :-
V
v
v For M ###
=
35469 N V
=
M
M tan d bxd
35469 =
grade concrete and
Hence from Table permissible shear (tc)for M
tan =
where
43.36 x 449 250 x 100Ast = bd 20
= 43.36 x 10 6
10 6
N-mm
490 - 200 = 0.116 2500
x 0.116
449 100 x 250 x
concrete, for
0.216 603 449
=
N-mm2
0.54 %
0.54 % steel
=
0.3 N/mm2
tv
here
tc
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Hence only nominal reinforcement is required. Given by the relation. Sv =
2.175 x Asv x fy
2.175
x
Asv
x
415 =
3.61 Asv
8
x
8
x
100
= b Using
250
8 mm 2-ldg. Strirrups Ast
=
2
x
3.14 x 4
Sv
=
3.61 x
100.5 =
Subject to maximum of 0.75d or b which ever is less.=
Hence provide the
8
this graually to
6
mm
x
0.75
=
100.5
mm2
363 mm 440
=
330
< 363
strirrups @ 300 mm c/c at s and reduce
0.75 x ( 200
-
25
-
8
-
8
)= 120 mm
Embedment of reinforcement in the s :In order develop full tensile strenth at the face of , each of must be embedded into by a length equal to Ld =45 F
=
45
3 x
bars
16 = 720
This could be best achieved by providing one bend of 90 0 where anchorage value of bend is = 8 x
7
=
8
x
16
=
anchorage in beam
=
490
-
anchorage in wall
= wall width - cover =
thus total anchorage value
=
128
908
>
720
Details of reinforcement:-
Shown in drawing
+
128 mm 2
430
Hence O.K.
x
+
30 400 350
=
430
-
2
=
x
908 mm
25 = 350
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mm mm
m form fixed end K N-m
mm
mm Hence ok.
mm2
.D.to parabolic,
ere dx effective h at that section
x)
mm mm which ever more
mm
mm
wall width 400
2500 3 -
16 mm bars 720
2 -
16 mm bars 1780
120 300
200
300
490
8 mm 2 ldge. Strirrups 8 mm 2 ldge. Strirrups 2 -
10 mm bars
Holding bars
@ 210 mm c/c
@ 120 mm c/c
250 250
3 -
16 mm main bars
mm 25 mm 8 mm 2 Lgd strirrups @ 120 mm c/c
` 8 mm 2 Lgd strirrups
200
@ 300 mm c/c
2 -
450 mm
10 mm anchor bars
25 mm
Section at end 2 -
10 mm anchor bars
section at
[email protected]
Pe
VALUES OF DESIGN CONSTANTS Grade 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
bd (N / mm2)
cbc N/mm2
5
7
8.5
10
11.5
13
m cbc
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
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
M 15
jc
0.89
0.89
0.89
0.89
0.89
0.89
M 20
Rc
0.732
1.025
1.244
1.464
1.684
1.903
M 25
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
M 30
kc
0.289
0.289
0.289
0.289
0.289
0.289
M 35
jc
0.904
0.904
0.904
0.904
0.904
0.904
M 40
Rc
0.653
0.914
1.11
1.306
1.502
1.698
M 45
Pc (%)
0.314
0.44
0.534
0.628
0.722
0.816
M 50
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
(a) st = 140 N/mm2 (Fe 250)
(b) st = 190 N/mm2
(c ) st = 230 N/mm2 (Fe 415)
(d) st = 275 N/mm2 (Fe 500)
Permissible shear stress Table v in concrete (IS : 456-2000)
Grade of concrete
100As bd
P
Permissible shear stress in concrete tv N/mm2 M-15
M-20
M-25
M-30
M-35
M-40
< 0.15
0.18
0.18
0.19
0.2
0.2
0.2
0.25
0.22
0.22
0.23
0.23
0.23
0.23
0.50
0.29
0.30
0.31
0.31
0.31
0.32
M 10
0.75
0.34
0.35
0.36
0.37
0.37
0.38
M 15
1.00
0.37
0.39
0.40
0.41
0.42
0.42
M 20
1.25
0.40
0.42
0.44
0.45
0.45
0.46
M 25
1.50
0.42
0.45
0.46
0.48
0.49
0.49
M 30
1.75
0.44
0.47
0.49
0.50
0.52
0.52
M 35
2.00
0.44
0.49
0.51
0.53
0.54
0.55
M 40
2.25
0.44
0.51
0.53
0.55
0.56
0.57
M 45
2.50
0.44
0.51
0.55
0.57
0.58
0.60
M 50
2.75
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
Maximum shear stress c.max in concrete (IS : 456-2000)
Grade of concrete
M-15
M-20
M-25
M-30
M-35
M-40
c.max
1.6
1.8
1.9
2.2
2.3
2.5
Grade of concrete
Shear stress tc
Reiforcement %
100As
100As M-20
M-20
0.15
0.18
0.18
0.15
0.16
0.18
0.19
0.18
0.17
0.18
0.2
0.21
0.18
0.19
0.21
0.24
0.19
0.19
0.22
0.27
0.2
0.19
0.23
0.3
0.21
0.2
0.24
0.32
0.22
0.2
0.25
0.35
0.23
0.2
0.26
0.38
0.24
0.21
0.27
0.41
0.25
0.21
0.28
0.44
0.26
0.21
0.29
0.47
0.27
0.22
0.30
0.5
0.28
0.22
0.31
0.55
0.29
0.22
0.32
0.6
0.3
0.23
0.31
0.23
0.32
0.24
0.35
0.75
0.33
0.24
0.36
0.82
0.34
0.24
0.37
0.88
bd
0.33 0.34
bd
0.65 0.7
0.35
0.25
0.38
0.94
0.36
0.25
0.39
1.00
0.37
0.25
0.38
0.26
0.39
0.26
0.42
1.25
0.4
0.26
0.43
1.33
0.41
0.27
0.44
1.41
0.42
0.27
0.45
1.50
0.43
0.27
0.46
1.63
0.44
0.28
0.46
1.64
0.45
0.28
0.47
1.75
0.46
0.28
0.48
1.88
0.47
0.29
0.49
2.00
0.48
0.29
0.50
2.13
0.49
0.29
0.51
2.25
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
0.4 0.41
1.08 1.16
0.58
0.31
0.59
0.31
0.6
0.32
0.61
0.32
0.62
0.32
0.63
0.32
0.64
0.32
0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74
0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34
0.75
0.35
0.76
0.35
0.77
0.35
0.78
0.35
0.79
0.35
0.8
0.35
0.81
0.35
0.82
0.36
0.83
0.36
0.84
0.36
0.85
0.36
0.86
0.36
0.87
0.36
0.88
0.37
0.89
0.37
0.9
0.37
0.91
0.37
0.92
0.37
0.93
0.37
0.94
0.38
0.95
0.38
0.96
0.38
0.97
0.38
0.98
0.38
0.99
0.38
1.00
0.39
1.01
0.39
1.02
0.39
1.03
0.39
1.04
0.39
1.05
0.39
1.06
0.39
1.07
0.39
1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
1.25
0.42
1.26
0.42
1.27
0.42
1.28
0.42
1.29
0.42
1.30
0.42
1.31
0.42
1.32
0.42
1.33
0.43
1.34
0.43
1.35
0.43
1.36
0.43
1.37
0.43
1.38
0.43
1.39
0.43
1.40
0.43
1.41
0.44
1.42
0.44
1.43
0.44
1.44
0.44
1.45
0.44
1.46
0.44
1.47
0.44
1.48
0.44
1.49
0.44
1.50
0.45
1.51
0.45
1.52
0.45
1.53
0.45
1.54
0.45
1.55
0.45
1.56
0.45
1.57
0.45
1.58
0.45
1.59
0.45
1.60
0.45
1.61
0.45
1.62
0.45
1.63
0.46
1.64
0.46
1.65
0.46
1.66
0.46
1.67
0.46
1.68
0.46
1.69
0.46
1.70
0.46
1.71
0.46
1.72
0.46
1.73
0.46
1.74
0.46
1.75
0.47
1.76
0.47
1.77
0.47
1.78
0.47
1.79
0.47
1.80
0.47
1.81
0.47
1.82
0.47
1.83
0.47
1.84
0.47
1.85
0.47
1.86
0.47
1.87
0.47
1.88
0.48
1.89
0.48
1.90
0.48
1.91
0.48
1.92
0.48
1.93
0.48
1.94
0.48
1.95
0.48
1.96
0.48
1.97
0.48
1.98
0.48
1.99
0.48
2.00
0.49
2.01
0.49
2.02
0.49
2.03
0.49
2.04
0.49
2.05
0.49
2.06
0.49
2.07
0.49
2.08
0.49
2.09
0.49
2.10
0.49
2.11
0.49
2.12
0.49
2.13
0.50
2.14
0.50
2.15
0.50
2.16
0.50
2.17
0.50
2.18
0.50
2.19
0.50
2.20
0.50
2.21
0.50
2.22
0.50
2.23
0.50
2.24
0.50
2.25
0.51
2.26
0.51
2.27
0.51
2.28
0.51
2.29
0.51
2.30
0.51
2.31
0.51
2.32
0.51
2.33
0.51
2.34
0.51
2.35
0.51
2.36
0.51
2.37
0.51
2.38
0.51
2.39
0.51
2.40
0.51
2.41
0.51
2.42
0.51
2.43
0.51
2.44
0.51
2.45
0.51
2.46
0.51
2.47
0.51
2.48
0.51
2.49
0.51
2.50
0.51
2.51
0.51
2.52
0.51
2.53
0.51
2.54
0.51
2.55
0.51
2.56
0.51
2.57
0.51
2.58
0.51
2.59
0.51
2.60
0.51
2.61
0.51
2.62
0.51
2.63
0.51
2.64
0.51
2.65
0.51
2.66
0.51
2.67
0.51
2.68
0.51
2.69
0.51
2.70
0.51
2.71
0.51
2.72
0.51
2.73
0.51
2.74
0.51
2.75
0.51
2.76
0.51
2.77
0.51
2.78
0.51
2.79
0.51
2.80
0.51
2.81
0.51
2.82
0.51
2.83
0.51
2.84
0.51
2.85
0.51
2.86
0.51
2.87
0.51
2.88
0.51
2.89
0.51
2.90
0.51
2.91
0.51
2.92
0.51
2.93
0.51
2.94
0.51
2.95
0.51
2.96
0.51
2.97
0.51
2.98
0.51
2.99
0.51
3.00
0.51
3.01
0.51
3.02
0.51
3.03
0.51
3.04
0.51
3.05
0.51
3.06
0.51
3.07
0.51
3.08
0.51
3.09
0.51
3.10
0.51
3.11
0.51
3.12
0.51
3.13
0.51
3.14
0.51
3.15
0.51
Permissible Bond stress Table bd in concrete (IS : 456-2000) M-10
M-15
M-20
M-25
M-30
M-35
M-40
M-45
M-50
--
0.6
0.8
0.9
1
1.1
1.2
1.3
1.4
Development Length in tension
Plain M.S. Bars
H.Y.S.D. Bars
bd (N / mm2)
kd = Ld
bd (N / mm2)
kd = Ld
0.6
58
0.96
60
0.8
44
1.28
45
0.9
39
1.44
40
1
35
1.6
36
1.1
32
1.76
33
1.2
29
1.92
30
1.3
27
2.08
28
1.4
25
2.24
26
2.0
Modification factore
1.4
1.2
0.8
0.4
Modific
0.4
Permissible stress in concrete (IS : 456-2000) Permission stress in compression (N/mm2) Bending cbc
(N/mm2)
Kg/m2
Direct (cc) (N/mm2)
Kg/m2
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
(N/mm2)
in kg/m2
--
--
3.0
300
2.5
250
5.0
500
4.0
400
0.6
60
7.0
700
5.0
500
0.8
80
8.5
850
6.0
600
0.9
90
10.0
1000
8.0
800
1.0
100
11.5
1150
9.0
900
1.1
110
13.0
1300
10.0
1000
1.2
120
14.5
1450
11.0
1100
1.3
130
16.0
1600
12.0
1200
1.4
140
0.0
0.4
0.8
Percentage of tension reinforcement
1.2
1.6
2
2
2.4
2.8
Perm
VALUES OF DESIGN CONSTANTS Grade 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
bd (N / mm2)
cbc N/mm2
5
7
8.5
10
11.5
13
m cbc
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
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
M 15
jc
0.89
0.89
0.89
0.89
0.89
0.89
M 20
Rc
0.732
1.025
1.244
1.464
1.684
1.903
M 25
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
M 30
kc
0.289
0.289
0.289
0.289
0.289
0.289
M 35
jc
0.904
0.904
0.904
0.904
0.904
0.904
M 40
Rc
0.653
0.914
1.11
1.306
1.502
1.698
M 45
Pc (%)
0.314
0.44
0.534
0.628
0.722
0.816
M 50
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
(a) st = 140 N/mm2 (Fe 250)
(b) st = 190 N/mm2
(c ) st = 230 N/mm2 (Fe 415)
(d) st = 275 N/mm2 (Fe 500)
Grade of concrete
Permissible shear stress Table v in concrete (IS : 456-2000) 100As bd
Pe
Permissible shear stress in concrete tv N/mm2 M-15
M-20
M-25
M-30
M-35
M-40 Grade of concrete
Grade of concrete
< 0.15
0.18
0.18
0.19
0.2
0.2
0.2
0.25
0.22
0.22
0.23
0.23
0.23
0.23
0.50
0.29
0.30
0.31
0.31
0.31
0.32
M 10
0.75
0.34
0.35
0.36
0.37
0.37
0.38
M 15
1.00
0.37
0.39
0.40
0.41
0.42
0.42
M 20
1.25
0.40
0.42
0.44
0.45
0.45
0.46
M 25
1.50
0.42
0.45
0.46
0.48
0.49
0.49
M 30
1.75
0.44
0.47
0.49
0.50
0.52
0.52
M 35
2.00
0.44
0.49
0.51
0.53
0.54
0.55
M 40
2.25
0.44
0.51
0.53
0.55
0.56
0.57
M 45
2.50
0.44
0.51
0.55
0.57
0.58
0.60
M 50
2.75
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
Maximum shear stress c.max in concrete (IS : 456-2000)
Grade of concrete
M-15
M-20
M-25
M-30
M-35
M-40
c.max
1.6
1.8
1.9
2.2
2.3
2.5
Shear stress tc
Reiforcement %
100As
100As M-20
M-20
0.15
0.18
0.18
0.15
0.16
0.18
0.19
0.18
0.17
0.18
0.2
0.21
bd
bd
0.18
0.19
0.21
0.24
0.19
0.19
0.22
0.27
0.2
0.19
0.23
0.3
0.21
0.2
0.24
0.32
0.22
0.2
0.25
0.35
0.23
0.2
0.26
0.38
0.24
0.21
0.27
0.41
0.25
0.21
0.28
0.44
0.26
0.21
0.29
0.47
0.27
0.22
0.30
0.5
0.28
0.22
0.31
0.55
0.29
0.22
0.32
0.6
0.3
0.23
0.31
0.23
0.32
0.24
0.35
0.75
0.33
0.24
0.36
0.82
0.34
0.24
0.37
0.88
0.35
0.25
0.38
0.94
0.36
0.25
0.39
1.00
0.37
0.25
0.38
0.26
0.39
0.26
0.42
1.25
0.4
0.26
0.43
1.33
0.41
0.27
0.44
1.41
0.42
0.27
0.45
1.50
0.33 0.34
0.4 0.41
0.65 0.7
1.08 1.16
0.43
0.27
0.46
1.63
0.44
0.28
0.46
1.64
0.45
0.28
0.47
1.75
0.46
0.28
0.48
1.88
0.47
0.29
0.49
2.00
0.48
0.29
0.50
2.13
0.49
0.29
0.51
2.25
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
0.63
0.32
0.64
0.32
0.65 0.66 0.67
0.33 0.33 0.33
0.68 0.69 0.7 0.71 0.72 0.73 0.74
0.33 0.33 0.34 0.34 0.34 0.34 0.34
0.75
0.35
0.76
0.35
0.77
0.35
0.78
0.35
0.79
0.35
0.8
0.35
0.81
0.35
0.82
0.36
0.83
0.36
0.84
0.36
0.85
0.36
0.86
0.36
0.87
0.36
0.88
0.37
0.89
0.37
0.9
0.37
0.91
0.37
0.92
0.37
0.93
0.37
0.94
0.38
0.95
0.38
0.96
0.38
0.97
0.38
0.98
0.38
0.99
0.38
1.00
0.39
1.01
0.39
1.02
0.39
1.03
0.39
1.04
0.39
1.05
0.39
1.06
0.39
1.07
0.39
1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41
1.18 1.19 1.20 1.21 1.22 1.23 1.24
0.41 0.41 0.41 0.41 0.41 0.41 0.41
1.25
0.42
1.26
0.42
1.27
0.42
1.28
0.42
1.29
0.42
1.30
0.42
1.31
0.42
1.32
0.42
1.33
0.43
1.34
0.43
1.35
0.43
1.36
0.43
1.37
0.43
1.38
0.43
1.39
0.43
1.40
0.43
1.41
0.44
1.42
0.44
1.43
0.44
1.44
0.44
1.45
0.44
1.46
0.44
1.47
0.44
1.48
0.44
1.49
0.44
1.50
0.45
1.51
0.45
1.52
0.45
1.53
0.45
1.54
0.45
1.55
0.45
1.56
0.45
1.57
0.45
1.58
0.45
1.59
0.45
1.60
0.45
1.61
0.45
1.62
0.45
1.63
0.46
1.64
0.46
1.65
0.46
1.66
0.46
1.67
0.46
1.68
0.46
1.69
0.46
1.70
0.46
1.71
0.46
1.72
0.46
1.73
0.46
1.74
0.46
1.75
0.47
1.76
0.47
1.77
0.47
1.78
0.47
1.79
0.47
1.80
0.47
1.81
0.47
1.82
0.47
1.83
0.47
1.84
0.47
1.85
0.47
1.86
0.47
1.87
0.47
1.88
0.48
1.89
0.48
1.90
0.48
1.91
0.48
1.92
0.48
1.93
0.48
1.94
0.48
1.95
0.48
1.96
0.48
1.97
0.48
1.98
0.48
1.99
0.48
2.00
0.49
2.01
0.49
2.02
0.49
2.03
0.49
2.04
0.49
2.05
0.49
2.06
0.49
2.07
0.49
2.08
0.49
2.09
0.49
2.10
0.49
2.11
0.49
2.12
0.49
2.13
0.50
2.14
0.50
2.15
0.50
2.16
0.50
2.17
0.50
2.18
0.50
2.19
0.50
2.20
0.50
2.21
0.50
2.22
0.50
2.23
0.50
2.24
0.50
2.25
0.51
2.26
0.51
2.27
0.51
2.28
0.51
2.29
0.51
2.30
0.51
2.31
0.51
2.32
0.51
2.33
0.51
2.34
0.51
2.35
0.51
2.36
0.51
2.37
0.51
2.38
0.51
2.39
0.51
2.40
0.51
2.41
0.51
2.42
0.51
2.43
0.51
2.44
0.51
2.45
0.51
2.46
0.51
2.47
0.51
2.48
0.51
2.49
0.51
2.50
0.51
2.51
0.51
2.52
0.51
2.53
0.51
2.54
0.51
2.55
0.51
2.56
0.51
2.57
0.51
2.58
0.51
2.59
0.51
2.60
0.51
2.61
0.51
2.62
0.51
2.63
0.51
2.64
0.51
2.65
0.51
2.66
0.51
2.67
0.51
2.68
0.51
2.69
0.51
2.70
0.51
2.71
0.51
2.72
0.51
2.73
0.51
2.74
0.51
2.75
0.51
2.76
0.51
2.77
0.51
2.78
0.51
2.79
0.51
2.80
0.51
2.81
0.51
2.82
0.51
2.83
0.51
2.84
0.51
2.85
0.51
2.86
0.51
2.87
0.51
2.88
0.51
2.89
0.51
2.90
0.51
2.91
0.51
2.92
0.51
2.93
0.51
2.94
0.51
2.95
0.51
2.96
0.51
2.97
0.51
2.98
0.51
2.99
0.51
3.00
0.51
3.01
0.51
3.02
0.51
3.03
0.51
3.04
0.51
3.05
0.51
3.06
0.51
3.07
0.51
3.08
0.51
3.09
0.51
3.10
0.51
3.11
0.51
3.12
0.51
3.13
0.51
3.14
0.51
3.15
0.51
Permissible Bond stress Table bd in concrete (IS : 456-2000) M-10
M-15
M-20
M-25
M-30
M-35
M-40
M-45
M-50
--
0.6
0.8
0.9
1
1.1
1.2
1.3
1.4
Development Length in tension
Plain M.S. Bars
H.Y.S.D. Bars
bd (N / mm2)
kd = Ld
bd (N / mm2)
kd = Ld
0.6
58
0.96
60
0.8
44
1.28
45
0.9
39
1.44
40
1
35
1.6
36
1.1
32
1.76
33
1.2
29
1.92
30
1.3
27
2.08
28
1.4
25
2.24
26
Permissible stress in concrete (IS : 456-2000) Permission stress in compression (N/mm2)
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
Bending cbc
(N/mm2)
Kg/m2
Direct (cc) (N/mm2)
Kg/m2
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
(N/mm2)
in kg/m2
--
--
3.0
300
2.5
250
5.0
500
4.0
400
0.6
60
7.0
700
5.0
500
0.8
80
8.5
850
6.0
600
0.9
90
10.0
1000
8.0
800
1.0
100
11.5
1150
9.0
900
1.1
110
13.0
1300
10.0
1000
1.2
120
14.5
1450
11.0
1100
1.3
130
16.0
1600
12.0
1200
1.4
140
1
Clear Span (opening )
2.50
mtr
2500
mm
2
Wall width
0.40
mtr
400
mm
3
Super imposed loads
12.00
kN per meter run
4
Conrete
M
cbc
5
Steel
fy
6
Nominal Cover
20 7
unit weight 25000 N/m3 m 13.3
N/mm2
415
Tensile stress
230
N/mm2
Effective Cover
30
mm
300
mm c/c
25
mm
Main Top
16
mm
3
Nos.
Anchor bars (Bottom )
10
mm
2
Nos.
Strirrups
8
mm
120
Reinforcement
400 350 2500
to
3 nos.bars
mm
16
2 nos.bars 0
720
mm
16
1780
200 490
0
#REF!
mm
10 mm 2 nos.anchor bars
8 mm 2 ldg strirrup
###
120 mm c/c mm 2 lgd strps
8
300
mm c/c
(A) L- section
3 nos.bar of
16 mm 2 nos.bars
8
mm 2 lgd strps
300
mm c./c
16
200
10 mm 2 nos.anchor bars 490
mm 250 mm (C)Section at the end 250
mm
(B) section at
pk_nandwana @yahoo.co.in
DESIGN OF CANTILEVER BEAM
Clear Span (opening )
2.50 m
2500 mm
Wall width
0.40 m
400 mm
Super imposed loads
12.00 kn/
Conrete
M
20
Steel
fy
415 N/mm2
cbc Nominal cover
7
Tensile stess
N/mm2
25 mm
cbc
230
N/mm2
7
N/mm2
m*c
k=
Effective cover
N per meter
=
230 N/mm2 13.3
=
30
Cocrete M =
20
mm
wt. of concrete = 25000 N/mm2
m 13.3 13.3
= 13.3
m*c+st
12000
m =
1 Design Constants:- For HYSD Bars
st
Or
x
x
7
j=1-k/3
1
-
0.288
/
3
R=1/2xc x j x k
0.5
x
7
x
0.904
7
=
0.288
=
0.904
x 0.288 =
0.9116
+
230
2 Caculcation of B.M. :-
1. Let depth of beam at fixed end
= span /7 =
effective depth of beam at fixed end =
Let width of Beam at fixed end Assume depth of Beam at free end
= =
400
500 500
2.50
/
+ 2xcover =
/ /
2 2
= =
7
=
400 +
250 250
0.36 mt Say
400
2
x
25
= 450
Say
=
500
mm
Say say
= =
250 200
mm mm
Let width of Beam at free end =
weight of Beam
x (
0.50
+
) x 0.25
x
2.50
x
###
0.5
+ 2.00 x 0.20 x 0.50 + 0.20 12000 x( 2.50 )2 43359 = 5469 x 1.07 + = 2.00 .= N m Shear force at edge of = 5469 + 12000 x Acting at
Max. possible Bending moment
2
0.20
=
250
=
5469 N
2.50 = 3.00
mm
m form
1.07 fixed end
43.36 x 10 6
K N-m
2.50 = 35469 N
Design of setion :-
Effective depth required Let us take d
= =
Rxb
43.36 x
=
= 0.912 x
D
436 mm
250
= 440 mm D =d+2xcover
### mm bar will be used. With
Assuming that
10 6
440 +
2
x
50
= 490
8 mm dia links and a nominal cover of =
=
490 25 Keep total depth at free end
=
16 8 200 mm
/
2
25
= 449 Hence ok.
4 Steel Reiforcement :BM
Ast =
43.36
=
st x jx D
230 x
using ### mm bars
A
x
10 6
0.904 x 3.14xdia2
=
=
464.48
449 3.14 x
=
16
x
= 201 4
464 /
201 =
2.31
x say
100 =
Hence Provided
3
bars of
16 mm bar,
Also provide
2
x
10
mm anchore bars at bottom
=
3
having, Ast
16
= 4 x100
Nomber of Bars = Ast/A
mm2
x
201 =
3
No.
603 mm2
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Since the bending moment decreases to zero at end, let us curtail few bars. Let Let 1 Bars be curtailed at a distance x from the free end. Assuming the B.M.D.to parabolic, the B.M. at this section may be approximately taken to eual to x 2 x 43.36 x 10 6 = 6.938 x 106 x2 2.50
N-mm
Area of rest bars=
2
x
201
=
6.938
402
=
230
x
200
+
mm2
402 x
10 6 x2
490 Total depth of section
=
dx
0.904 x -
Where dx effective depth at that section
----------- (1)
200 x
x
+
8
2.50 dx
=
200
+
dx
=
159
+
Subsituting in (1),
402
=
290 2.50
x
116 x 230
x
x
-
25
+
8
------------------------------------ (2) 6.938 x 10 6 x2 0.904 x( 159 +
116 x) =
or or 402
6.938 x 6937500 than divide by 17261 17261 divide by 17261 than 1
10 6 x2 = 402 x( 230 x 0.904 2 = 402 x( 208 x( 159 x x2 = 33057 + 24117 2 x - 24117 x 33057 1.40 x 1.9152 x2
x( 159 + + 116 x) x = 0 = 0
116
= 1.397 + 1.95 -4x 1.00 x -1.9152 x 2 1 or a = 1.397 +( 1.95 - -7.660667439 )1/2 2 or a = 1.397 +( 9.6129153 )1/2 2 x 1 or a = 1.397 + 3.100 2 or a = 4.498 / 2 2.30 or a = 2.249 m say mtr Minimum embedded requirement beyond this = 12. = 12 x 16 = 192 or equal to dx = 159 + 116 x 2.30 = 426 mm which ever more Bars may be curtail at= 2.50 - 2.30 + 0.426 = 0.63 mtr
a =
or
b +b2-4.a.c 2 a
a
from the edge of the . This should be grater than 45 x 16 = 720 mm Ld=45 = Hence bar can be curtailed at = 720 mm from the . 5 Check for shear and design of shear reinforcement :-
V
v
v For M ###
=
35469 N V
=
M
M tan d bxd
35469 =
grade concrete and
Hence from Table permissible shear (tc)for M
tan =
where
43.36 x 449 250 x 100Ast = bd 20
= 43.36 x 10 6
10 6
N-mm
490 - 200 = 0.116 2500
x 0.116
449 100 x 250 x
concrete, for
0.216 603 449
=
N-mm2
0.54 %
0.54 % steel
=
0.3 N/mm2
tv
here
tc
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Hence only nominal reinforcement is required. Given by the relation. Sv =
2.175 x Asv x fy
2.175
x
Asv
x
415 =
3.61 Asv
8
x
8
x
100
= b Using
250
8 mm 2-ldg. Strirrups Ast
=
2
x
3.14 x 4
Sv
=
3.61 x
100.5 =
Subject to maximum of 0.75d or b which ever is less.=
Hence provide the
8
this graually to
6
mm
x
0.75
=
100.5
mm2
363 mm 440
=
330
< 363
strirrups @ 300 mm c/c at s and reduce
0.75 x ( 200
-
25
-
8
-
8
)= 120 mm
Embedment of reinforcement in the s :In order develop full tensile strenth at the face of , each of must be embedded into by a length equal to Ld =45 F
=
45
3 x
bars
16 = 720
This could be best achieved by providing one bend of 90 0 where anchorage value of bend is = 8 x
7
=
8
x
16
=
anchorage in beam
=
490
-
anchorage in wall
= wall width - cover =
thus total anchorage value
=
128
908
>
720
Details of reinforcement:-
Shown in drawing
+
128 mm 2
430
Hence O.K.
x
+
30 400 350
=
430
-
2
=
x
908 mm
25 = 350
[email protected]
mm mm
m form fixed end K N-m
mm
mm Hence ok.
mm2
.D.to parabolic,
ere dx effective h at that section
x)
mm mm which ever more
mm
mm
wall width 400
2500 3 -
16 mm bars 720
2 -
16 mm bars 1780
120 300
200
300
490
8 mm 2 ldge. Strirrups 8 mm 2 ldge. Strirrups 2 -
10 mm bars
Holding bars
@ 210 mm c/c
@ 120 mm c/c
250 250
3 -
16 mm main bars
mm 25 mm 8 mm 2 Lgd strirrups @ 120 mm c/c
` 8 mm 2 Lgd strirrups
200
@ 300 mm c/c
2 -
450 mm
10 mm anchor bars
25 mm
Section at end 2 -
10 mm anchor bars
section at
[email protected]
Pe
VALUES OF DESIGN CONSTANTS Grade 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
bd (N / mm2)
cbc N/mm2
5
7
8.5
10
11.5
13
m cbc
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
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
M 15
jc
0.89
0.89
0.89
0.89
0.89
0.89
M 20
Rc
0.732
1.025
1.244
1.464
1.684
1.903
M 25
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
M 30
kc
0.289
0.289
0.289
0.289
0.289
0.289
M 35
jc
0.904
0.904
0.904
0.904
0.904
0.904
M 40
Rc
0.653
0.914
1.11
1.306
1.502
1.698
M 45
Pc (%)
0.314
0.44
0.534
0.628
0.722
0.816
M 50
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
(a) st = 140 N/mm2 (Fe 250)
(b) st = 190 N/mm2
(c ) st = 230 N/mm2 (Fe 415)
(d) st = 275 N/mm2 (Fe 500)
Permissible shear stress Table v in concrete (IS : 456-2000)
Grade of concrete
100As bd
P
Permissible shear stress in concrete tv N/mm2 M-15
M-20
M-25
M-30
M-35
M-40
< 0.15
0.18
0.18
0.19
0.2
0.2
0.2
0.25
0.22
0.22
0.23
0.23
0.23
0.23
0.50
0.29
0.30
0.31
0.31
0.31
0.32
M 10
0.75
0.34
0.35
0.36
0.37
0.37
0.38
M 15
1.00
0.37
0.39
0.40
0.41
0.42
0.42
M 20
1.25
0.40
0.42
0.44
0.45
0.45
0.46
M 25
1.50
0.42
0.45
0.46
0.48
0.49
0.49
M 30
1.75
0.44
0.47
0.49
0.50
0.52
0.52
M 35
2.00
0.44
0.49
0.51
0.53
0.54
0.55
M 40
2.25
0.44
0.51
0.53
0.55
0.56
0.57
M 45
2.50
0.44
0.51
0.55
0.57
0.58
0.60
M 50
2.75
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
Maximum shear stress c.max in concrete (IS : 456-2000)
Grade of concrete
M-15
M-20
M-25
M-30
M-35
M-40
c.max
1.6
1.8
1.9
2.2
2.3
2.5
Grade of concrete
Shear stress tc
Reiforcement %
100As
100As M-20
M-20
0.15
0.18
0.18
0.15
0.16
0.18
0.19
0.18
0.17
0.18
0.2
0.21
0.18
0.19
0.21
0.24
0.19
0.19
0.22
0.27
0.2
0.19
0.23
0.3
0.21
0.2
0.24
0.32
0.22
0.2
0.25
0.35
0.23
0.2
0.26
0.38
0.24
0.21
0.27
0.41
0.25
0.21
0.28
0.44
0.26
0.21
0.29
0.47
0.27
0.22
0.30
0.5
0.28
0.22
0.31
0.55
0.29
0.22
0.32
0.6
0.3
0.23
0.31
0.23
0.32
0.24
0.35
0.75
0.33
0.24
0.36
0.82
0.34
0.24
0.37
0.88
bd
0.33 0.34
bd
0.65 0.7
0.35
0.25
0.38
0.94
0.36
0.25
0.39
1.00
0.37
0.25
0.38
0.26
0.39
0.26
0.42
1.25
0.4
0.26
0.43
1.33
0.41
0.27
0.44
1.41
0.42
0.27
0.45
1.50
0.43
0.27
0.46
1.63
0.44
0.28
0.46
1.64
0.45
0.28
0.47
1.75
0.46
0.28
0.48
1.88
0.47
0.29
0.49
2.00
0.48
0.29
0.50
2.13
0.49
0.29
0.51
2.25
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
0.4 0.41
1.08 1.16
0.58
0.31
0.59
0.31
0.6
0.32
0.61
0.32
0.62
0.32
0.63
0.32
0.64
0.32
0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74
0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34
0.75
0.35
0.76
0.35
0.77
0.35
0.78
0.35
0.79
0.35
0.8
0.35
0.81
0.35
0.82
0.36
0.83
0.36
0.84
0.36
0.85
0.36
0.86
0.36
0.87
0.36
0.88
0.37
0.89
0.37
0.9
0.37
0.91
0.37
0.92
0.37
0.93
0.37
0.94
0.38
0.95
0.38
0.96
0.38
0.97
0.38
0.98
0.38
0.99
0.38
1.00
0.39
1.01
0.39
1.02
0.39
1.03
0.39
1.04
0.39
1.05
0.39
1.06
0.39
1.07
0.39
1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
1.25
0.42
1.26
0.42
1.27
0.42
1.28
0.42
1.29
0.42
1.30
0.42
1.31
0.42
1.32
0.42
1.33
0.43
1.34
0.43
1.35
0.43
1.36
0.43
1.37
0.43
1.38
0.43
1.39
0.43
1.40
0.43
1.41
0.44
1.42
0.44
1.43
0.44
1.44
0.44
1.45
0.44
1.46
0.44
1.47
0.44
1.48
0.44
1.49
0.44
1.50
0.45
1.51
0.45
1.52
0.45
1.53
0.45
1.54
0.45
1.55
0.45
1.56
0.45
1.57
0.45
1.58
0.45
1.59
0.45
1.60
0.45
1.61
0.45
1.62
0.45
1.63
0.46
1.64
0.46
1.65
0.46
1.66
0.46
1.67
0.46
1.68
0.46
1.69
0.46
1.70
0.46
1.71
0.46
1.72
0.46
1.73
0.46
1.74
0.46
1.75
0.47
1.76
0.47
1.77
0.47
1.78
0.47
1.79
0.47
1.80
0.47
1.81
0.47
1.82
0.47
1.83
0.47
1.84
0.47
1.85
0.47
1.86
0.47
1.87
0.47
1.88
0.48
1.89
0.48
1.90
0.48
1.91
0.48
1.92
0.48
1.93
0.48
1.94
0.48
1.95
0.48
1.96
0.48
1.97
0.48
1.98
0.48
1.99
0.48
2.00
0.49
2.01
0.49
2.02
0.49
2.03
0.49
2.04
0.49
2.05
0.49
2.06
0.49
2.07
0.49
2.08
0.49
2.09
0.49
2.10
0.49
2.11
0.49
2.12
0.49
2.13
0.50
2.14
0.50
2.15
0.50
2.16
0.50
2.17
0.50
2.18
0.50
2.19
0.50
2.20
0.50
2.21
0.50
2.22
0.50
2.23
0.50
2.24
0.50
2.25
0.51
2.26
0.51
2.27
0.51
2.28
0.51
2.29
0.51
2.30
0.51
2.31
0.51
2.32
0.51
2.33
0.51
2.34
0.51
2.35
0.51
2.36
0.51
2.37
0.51
2.38
0.51
2.39
0.51
2.40
0.51
2.41
0.51
2.42
0.51
2.43
0.51
2.44
0.51
2.45
0.51
2.46
0.51
2.47
0.51
2.48
0.51
2.49
0.51
2.50
0.51
2.51
0.51
2.52
0.51
2.53
0.51
2.54
0.51
2.55
0.51
2.56
0.51
2.57
0.51
2.58
0.51
2.59
0.51
2.60
0.51
2.61
0.51
2.62
0.51
2.63
0.51
2.64
0.51
2.65
0.51
2.66
0.51
2.67
0.51
2.68
0.51
2.69
0.51
2.70
0.51
2.71
0.51
2.72
0.51
2.73
0.51
2.74
0.51
2.75
0.51
2.76
0.51
2.77
0.51
2.78
0.51
2.79
0.51
2.80
0.51
2.81
0.51
2.82
0.51
2.83
0.51
2.84
0.51
2.85
0.51
2.86
0.51
2.87
0.51
2.88
0.51
2.89
0.51
2.90
0.51
2.91
0.51
2.92
0.51
2.93
0.51
2.94
0.51
2.95
0.51
2.96
0.51
2.97
0.51
2.98
0.51
2.99
0.51
3.00
0.51
3.01
0.51
3.02
0.51
3.03
0.51
3.04
0.51
3.05
0.51
3.06
0.51
3.07
0.51
3.08
0.51
3.09
0.51
3.10
0.51
3.11
0.51
3.12
0.51
3.13
0.51
3.14
0.51
3.15
0.51
Permissible Bond stress Table bd in concrete (IS : 456-2000) M-10
M-15
M-20
M-25
M-30
M-35
M-40
M-45
M-50
--
0.6
0.8
0.9
1
1.1
1.2
1.3
1.4
Development Length in tension
Plain M.S. Bars
H.Y.S.D. Bars
bd (N / mm2)
kd = Ld
bd (N / mm2)
kd = Ld
0.6
58
0.96
60
0.8
44
1.28
45
0.9
39
1.44
40
1
35
1.6
36
1.1
32
1.76
33
1.2
29
1.92
30
1.3
27
2.08
28
1.4
25
2.24
26
2.0
Modification factore
1.4
1.2
0.8
0.4
Modific
0.4
Permissible stress in concrete (IS : 456-2000) Permission stress in compression (N/mm2) Bending cbc
(N/mm2)
Kg/m2
Direct (cc) (N/mm2)
Kg/m2
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
(N/mm2)
in kg/m2
--
--
3.0
300
2.5
250
5.0
500
4.0
400
0.6
60
7.0
700
5.0
500
0.8
80
8.5
850
6.0
600
0.9
90
10.0
1000
8.0
800
1.0
100
11.5
1150
9.0
900
1.1
110
13.0
1300
10.0
1000
1.2
120
14.5
1450
11.0
1100
1.3
130
16.0
1600
12.0
1200
1.4
140
0.0
0.4
0.8
Percentage of tension reinforcement
1.2
1.6
2
2
2.4
2.8
Perm
VALUES OF DESIGN CONSTANTS Grade 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
bd (N / mm2)
cbc N/mm2
5
7
8.5
10
11.5
13
m cbc
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
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
M 15
jc
0.89
0.89
0.89
0.89
0.89
0.89
M 20
Rc
0.732
1.025
1.244
1.464
1.684
1.903
M 25
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
M 30
kc
0.289
0.289
0.289
0.289
0.289
0.289
M 35
jc
0.904
0.904
0.904
0.904
0.904
0.904
M 40
Rc
0.653
0.914
1.11
1.306
1.502
1.698
M 45
Pc (%)
0.314
0.44
0.534
0.628
0.722
0.816
M 50
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
(a) st = 140 N/mm2 (Fe 250)
(b) st = 190 N/mm2
(c ) st = 230 N/mm2 (Fe 415)
(d) st = 275 N/mm2 (Fe 500)
Grade of concrete
Permissible shear stress Table v in concrete (IS : 456-2000) 100As bd
Pe
Permissible shear stress in concrete tv N/mm2 M-15
M-20
M-25
M-30
M-35
M-40 Grade of concrete
Grade of concrete
< 0.15
0.18
0.18
0.19
0.2
0.2
0.2
0.25
0.22
0.22
0.23
0.23
0.23
0.23
0.50
0.29
0.30
0.31
0.31
0.31
0.32
M 10
0.75
0.34
0.35
0.36
0.37
0.37
0.38
M 15
1.00
0.37
0.39
0.40
0.41
0.42
0.42
M 20
1.25
0.40
0.42
0.44
0.45
0.45
0.46
M 25
1.50
0.42
0.45
0.46
0.48
0.49
0.49
M 30
1.75
0.44
0.47
0.49
0.50
0.52
0.52
M 35
2.00
0.44
0.49
0.51
0.53
0.54
0.55
M 40
2.25
0.44
0.51
0.53
0.55
0.56
0.57
M 45
2.50
0.44
0.51
0.55
0.57
0.58
0.60
M 50
2.75
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
Maximum shear stress c.max in concrete (IS : 456-2000)
Grade of concrete
M-15
M-20
M-25
M-30
M-35
M-40
c.max
1.6
1.8
1.9
2.2
2.3
2.5
Shear stress tc
Reiforcement %
100As
100As M-20
M-20
0.15
0.18
0.18
0.15
0.16
0.18
0.19
0.18
0.17
0.18
0.2
0.21
bd
bd
0.18
0.19
0.21
0.24
0.19
0.19
0.22
0.27
0.2
0.19
0.23
0.3
0.21
0.2
0.24
0.32
0.22
0.2
0.25
0.35
0.23
0.2
0.26
0.38
0.24
0.21
0.27
0.41
0.25
0.21
0.28
0.44
0.26
0.21
0.29
0.47
0.27
0.22
0.30
0.5
0.28
0.22
0.31
0.55
0.29
0.22
0.32
0.6
0.3
0.23
0.31
0.23
0.32
0.24
0.35
0.75
0.33
0.24
0.36
0.82
0.34
0.24
0.37
0.88
0.35
0.25
0.38
0.94
0.36
0.25
0.39
1.00
0.37
0.25
0.38
0.26
0.39
0.26
0.42
1.25
0.4
0.26
0.43
1.33
0.41
0.27
0.44
1.41
0.42
0.27
0.45
1.50
0.33 0.34
0.4 0.41
0.65 0.7
1.08 1.16
0.43
0.27
0.46
1.63
0.44
0.28
0.46
1.64
0.45
0.28
0.47
1.75
0.46
0.28
0.48
1.88
0.47
0.29
0.49
2.00
0.48
0.29
0.50
2.13
0.49
0.29
0.51
2.25
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
0.63
0.32
0.64
0.32
0.65 0.66 0.67
0.33 0.33 0.33
0.68 0.69 0.7 0.71 0.72 0.73 0.74
0.33 0.33 0.34 0.34 0.34 0.34 0.34
0.75
0.35
0.76
0.35
0.77
0.35
0.78
0.35
0.79
0.35
0.8
0.35
0.81
0.35
0.82
0.36
0.83
0.36
0.84
0.36
0.85
0.36
0.86
0.36
0.87
0.36
0.88
0.37
0.89
0.37
0.9
0.37
0.91
0.37
0.92
0.37
0.93
0.37
0.94
0.38
0.95
0.38
0.96
0.38
0.97
0.38
0.98
0.38
0.99
0.38
1.00
0.39
1.01
0.39
1.02
0.39
1.03
0.39
1.04
0.39
1.05
0.39
1.06
0.39
1.07
0.39
1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41
1.18 1.19 1.20 1.21 1.22 1.23 1.24
0.41 0.41 0.41 0.41 0.41 0.41 0.41
1.25
0.42
1.26
0.42
1.27
0.42
1.28
0.42
1.29
0.42
1.30
0.42
1.31
0.42
1.32
0.42
1.33
0.43
1.34
0.43
1.35
0.43
1.36
0.43
1.37
0.43
1.38
0.43
1.39
0.43
1.40
0.43
1.41
0.44
1.42
0.44
1.43
0.44
1.44
0.44
1.45
0.44
1.46
0.44
1.47
0.44
1.48
0.44
1.49
0.44
1.50
0.45
1.51
0.45
1.52
0.45
1.53
0.45
1.54
0.45
1.55
0.45
1.56
0.45
1.57
0.45
1.58
0.45
1.59
0.45
1.60
0.45
1.61
0.45
1.62
0.45
1.63
0.46
1.64
0.46
1.65
0.46
1.66
0.46
1.67
0.46
1.68
0.46
1.69
0.46
1.70
0.46
1.71
0.46
1.72
0.46
1.73
0.46
1.74
0.46
1.75
0.47
1.76
0.47
1.77
0.47
1.78
0.47
1.79
0.47
1.80
0.47
1.81
0.47
1.82
0.47
1.83
0.47
1.84
0.47
1.85
0.47
1.86
0.47
1.87
0.47
1.88
0.48
1.89
0.48
1.90
0.48
1.91
0.48
1.92
0.48
1.93
0.48
1.94
0.48
1.95
0.48
1.96
0.48
1.97
0.48
1.98
0.48
1.99
0.48
2.00
0.49
2.01
0.49
2.02
0.49
2.03
0.49
2.04
0.49
2.05
0.49
2.06
0.49
2.07
0.49
2.08
0.49
2.09
0.49
2.10
0.49
2.11
0.49
2.12
0.49
2.13
0.50
2.14
0.50
2.15
0.50
2.16
0.50
2.17
0.50
2.18
0.50
2.19
0.50
2.20
0.50
2.21
0.50
2.22
0.50
2.23
0.50
2.24
0.50
2.25
0.51
2.26
0.51
2.27
0.51
2.28
0.51
2.29
0.51
2.30
0.51
2.31
0.51
2.32
0.51
2.33
0.51
2.34
0.51
2.35
0.51
2.36
0.51
2.37
0.51
2.38
0.51
2.39
0.51
2.40
0.51
2.41
0.51
2.42
0.51
2.43
0.51
2.44
0.51
2.45
0.51
2.46
0.51
2.47
0.51
2.48
0.51
2.49
0.51
2.50
0.51
2.51
0.51
2.52
0.51
2.53
0.51
2.54
0.51
2.55
0.51
2.56
0.51
2.57
0.51
2.58
0.51
2.59
0.51
2.60
0.51
2.61
0.51
2.62
0.51
2.63
0.51
2.64
0.51
2.65
0.51
2.66
0.51
2.67
0.51
2.68
0.51
2.69
0.51
2.70
0.51
2.71
0.51
2.72
0.51
2.73
0.51
2.74
0.51
2.75
0.51
2.76
0.51
2.77
0.51
2.78
0.51
2.79
0.51
2.80
0.51
2.81
0.51
2.82
0.51
2.83
0.51
2.84
0.51
2.85
0.51
2.86
0.51
2.87
0.51
2.88
0.51
2.89
0.51
2.90
0.51
2.91
0.51
2.92
0.51
2.93
0.51
2.94
0.51
2.95
0.51
2.96
0.51
2.97
0.51
2.98
0.51
2.99
0.51
3.00
0.51
3.01
0.51
3.02
0.51
3.03
0.51
3.04
0.51
3.05
0.51
3.06
0.51
3.07
0.51
3.08
0.51
3.09
0.51
3.10
0.51
3.11
0.51
3.12
0.51
3.13
0.51
3.14
0.51
3.15
0.51
Permissible Bond stress Table bd in concrete (IS : 456-2000) M-10
M-15
M-20
M-25
M-30
M-35
M-40
M-45
M-50
--
0.6
0.8
0.9
1
1.1
1.2
1.3
1.4
Development Length in tension
Plain M.S. Bars
H.Y.S.D. Bars
bd (N / mm2)
kd = Ld
bd (N / mm2)
kd = Ld
0.6
58
0.96
60
0.8
44
1.28
45
0.9
39
1.44
40
1
35
1.6
36
1.1
32
1.76
33
1.2
29
1.92
30
1.3
27
2.08
28
1.4
25
2.24
26
Permissible stress in concrete (IS : 456-2000) Permission stress in compression (N/mm2)
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
Bending cbc
(N/mm2)
Kg/m2
Direct (cc) (N/mm2)
Kg/m2
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
(N/mm2)
in kg/m2
--
--
3.0
300
2.5
250
5.0
500
4.0
400
0.6
60
7.0
700
5.0
500
0.8
80
8.5
850
6.0
600
0.9
90
10.0
1000
8.0
800
1.0
100
11.5
1150
9.0
900
1.1
110
13.0
1300
10.0
1000
1.2
120
14.5
1450
11.0
1100
1.3
130
16.0
1600
12.0
1200
1.4
140
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