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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 20 unit weight 25000
7 m 13.3
5 Steel fy 415 Tensile stress 230
6 Nominal Cover 25 mm Effective Cover 30 mm
Reinforcement
Main Top 16 3 Nos.
Anchor bars (Bottom ) 10 2 Nos.
Strirrups 8 120 to 300 mm c/c
400
350
2500
N/m3
σcbc N/mm2
N/mm2
mm Φ
mm Φ
mm Φ
3 nos.bars 16
2 nos.bars 16
0 720 1780
200
490 0 #REF! mm
###
10 mm 2 nos.anchor bars 8
120 mm c/c
8 300 mm c/c
(A) L- section
3 nos.bar of 16
2 nos.bars 16
8 300 mm c./c200
10
490 mm
250
mm
(C)Section at the end
250
mm φ
mm φ
mm φ 2 ldg strirrup
mm φ 2 lgd strps
mm φ
mm φ
mm φ 2 lgd strps
mm φ 2 nos.anchor bars
(B) section at support 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/ Or 12000 N per meter
Conrete M 20
Steel fy 415 Tensile stess = 230
7 m = 13.3
Nominal cover 25 mm Effective cover = 30 mm
1 Design Constants:- For HYSD Bars Cocrete M = 20
= 230 wt. of concrete = 25000
= 7 m = 13.3
m*c=
13.3x 7
= 0.28813.3
x 7 + 230
= 1 - 0.288 / 3 = 0.904
= 0.5 x 7 x 0.904 x 0.288 = 0.9116
2 Caculcation of B.M. :-
1. Let depth of beam at fixed end = span /7 = 2.50 / 7 = 0.36 mtrSay 400
effective depth of beam at fixed end = 400 + 2xcover = 400 + 2 x 25 = 450
Say = 500 mm
Let width of Beam at fixed end = 500 / 2 = 250 Say = 250 mm
Assume depth of Beam at free end = 500 / 2 = 250 say = 200 mm
N/mm2 N/mm2
σcbc N/mm2
σst N/mm2 N/mm2
σcbc
N/mm2
k=
m*c+σst
j=1-k/3
R=1/2xc x j x k
Let width of Beam at free end = = 250 mm
1x ( 0.50 + 0.20 ) x 0.25 x 2.50 x ### = 5469 N
2
Acting at0.5 + 2.00 x 0.20 x 2.50
= 1.070.50 + 0.20 3.00
= 5469 x 1.07 +12000 x( 2.50 43359
= 43.36 K N-m2.00 .= N m
Shear force at edge of support = 5469 + 12000 x 2.50 = 35469 N
2Design of setion :-
Effective depth required =ΒΜ
=
43.36 x
= 436 mmRxb
0.912 x 250
Let us take d = 440 = 440 +2 x
50 = 490
Assuming that ###
8 mm dia links and a nominal cover of =25
D =490 - 25 - 8
- 16 / 2 = 449 Hence ok.
Keep total depth at free end = 200 mm
4 Steel Reiforcement :-
Ast = =43.36 x
= 464.48
230 x 0.904 x 449
using ### mm bars A = =
3.14 x 16 x 16
= 2014 x100 4 x 100
Nomber of Bars = Ast/A = 464 / 201 = 2.31 say = 3 No.
Hence Provided 3 bars of 16
Also provide 2 x 10 mm anchore bars at bottom
having, Ast = 3 x 201 = 603
Since the bending moment decreases to zero at end, let us curtail few bars. Let
Let 1
the B.M. at this section may be approximately taken to eual to
x43.36 x = 6.938 x N-mm
2.50
∴ weight of Beam
m form fixed end
Max. possible Bending moment
)2
x 10 6
10 6
mm ∴ D =d+2xcover
mm Φ bar will be used. With
BM 10 6
mm2
σst x jx D
3.14xdia2
mm Φ bar,
mm2
Bars be curtailed at a distance x from the free end. Assuming the B.M.D.to parabolic,
2 x 10 6 106 x2
Area of rest bars= 2 x 201 = 402
∴ 402 =6.938 x
----------- (1)230 x 0.904 x
Total depth of section = 200 +490 - 200
x x2.50
= 200 +290
x x - 25 + 8 + 82.50
= 159 + 116 x ------------------------------------ (2)
Subsituting in (1), 402 =6.938 x
230 x 0.904 x( 159 + 116=
or 6.938 x = 402 x( 230 x 0.904 x( 159 + 116or 6937500 = 402 x( 208 x( 159 + 116 x)
divide by 402 than 17261 = 33057 + ### x
17261 - ### x - 33057 = 0
divide by 17261 than 1 - 1.40 x - 1.9152 = 0
a =or a = 1.397 1.95 -4x 1.00 x -1.9152
2 a 2 x 1
or a = 1.397 +( 1.95 - -7.660667439
2
or a = 1.397 +( 9.6129153
2 x 1
or a = 1.397 + 3.100
2
or a = 4.498 / 2
or a = 2.249 m say 2.30 mtrMinimum embedded requirement beyond this = = 12 x 16 = 192
or equal to dx = 159 + 116 x 2.30 = 426∴ Bars may be curtail at= 2.50 - 2.30 + 0.426 = 0.63 mtr
from the edge of the support. This should be grater than
= 45 x 16 = 720 mmHence bar can be curtailed at = 720 mm from the support.
5 Check for shear and design of shear reinforcement :-
V = 35469 N M = 43.36 x N-mm
V -=
d where =
490 - 200= 0.116
b x d 2500
35469 -43.36 x
x 0.116=
4490.216
250 x 449
For M### grade concrete and =100 x 603
= 0.54 %bd 250 x 449
20 concrete, for 0.54 % steel = 0.3
mm2
10 6 x2
Where dx effective depth at that section dx
∴ dx
∴ dx
10 6 x2
x)
10 6 x2
x2
x2
x2
x2
b +√b2-4.a.c + √
)1/2
)1/2
12. Φmm which ever more
Ld=45Φ
10 6
M tan β
τv tan β
10 6
τv N-mm2
100Ast
Hence from Table permissible shear (tc)for M N/mm2
here tv
tc
Hence only nominal reinforcement is required. Given by the relation.
Sv = 2.175 x Asv x fy=
2.175 x x 415= 3.61
b 250
Using 8 mm 2-ldg. Strirrups
= 2 x3.14 x 8 x 8
= 100.5
4 x 100
Sv = 3.61 x100.5 = 363 mm
Subject to maximum of 0.75d or b which ever is less.=0.75
x 440 = 330 < 363
Hence provide the 8 mm strirrups @ 300 mm c/c at supports and reduce
this graually to 0.75 x ( 200 - 25 - 8 - 8 )= 120 mm
6Embedment of reinforcement in the supports :-
In order develop full tensile strenth at the face of support, each of 3bars
must be embedded into support by a length equal to Ld =45 F = 45 x 16 = 720
= = 8 x 16 = 128 mm
anchorage in beam = 490 -2
x 30 = 430
anchorage in wall = wall width - cover =400
- 2 x 25 = 350
thus total anchorage value = 128 + 430 +350
= 908 mm
908 > 720 Hence O.K.
7Details of reinforcement:- Shown in drawing
Asv
Asv
Ast mm2
This could be best achieved by providing one bend of 90 0 where anchorage value of bend is
8 x Φ
DESIGN OF CANTILEVER BEAM
mm
mm
K N-m
mm
mm
Hence ok.
m form fixed end
mm2
from the free end. Assuming the B.M.D.to parabolic,
x)
mm
Where dx effective depth at that section
mm which ever more
mm
mm
wall width
400
2500
3 - 16 mm bars 2 - 16 mm bars
720 1780
200120
300 300
490
8 mm 2 ldge. Strirrups
8 mm 2 ldge. Strirrups @ 120 mm c/c
2 - 10 mm bars @ 210 mm c/c
Holding bars
250
250 3 - 16
mm
25 mm
8
2 Lgd strirrups `
@ 120 mm c/c 8
2 Lgd strirrups 200
@ 300 mm c/c 450 mm
2 - 10 25 mm
Section at end
2 - 10
section at support
mm Φ main bars
mm Φ
mm Φ
mm Φ anchor bars
mm Φ anchor bars
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
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
Development Length in tension0.867 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
0.3290.329 0.329 0.329 0.329 0.329 M 15
0.890.89 0.89 0.89 0.89 0.89 M 20
0.732 1.025 1.244 1.464 1.684 1.903 M 25
0.433 0.606 0.736 0.866 0.997 1.127 M 30
0.289 0.289 0.289 0.289 0.289 0.289 M 35
0.904 0.904 0.904 0.904 0.904 0.904 M 40
0.653 0.914 1.11 1.306 1.502 1.698 M 45
0.314 0.44 0.534 0.628 0.722 0.816 M 50
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
Permissible Bond stress Table τbd
in concrete (IS : 456-2000)
τbd
(N / mm2)
σcbc
N/mm2
m σcbc
(a) σst =
140 N/mm2
(Fe 250)
kc
jc
Rc
Grade of concrete
Pc (%)
(b) σst =
190 N/mm2
kc
jc
Rc
Pc (%)
(c ) σst = 230
N/mm2 (Fe 415)
kc
jc
Rc
Pc (%)
(d) σst =
275 N/mm2 (Fe 500)
kc
jc
Rc
Pc (%)
Permissible shear stress Table τv in concrete (IS : 456-2000)
bdM-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 0.23
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
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
100A s Permissible shear stress in concrete tv N/mm2 Permissible stress in concrete (IS : 456-2000)
Grade of concrete
< 0.15
Maximum shear stress τc.max
in concrete (IS : 456-2000)
τc.max
Reiforcement %
M-20 M-20bd bd
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 0.230.33
0.65
0.31 0.230.34
0.7
0.32 0.24 0.35 0.75
0.33 0.24 0.36 0.82
0.34 0.24 0.37 0.88
Shear stress tc
100A s
100A s
0.35 0.25 0.38 0.94
0.36 0.25 0.39 1.00
0.37 0.250.4
1.08
0.38 0.260.41
1.16
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
0.58 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
0.650.33
0.660.33
0.670.33
0.680.33
0.690.33
0.70.34
0.710.34
0.720.34
0.730.34
0.740.34
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
1.080.4
1.090.4
1.100.4
1.110.4
1.120.4
1.130.4
1.140.4
1.150.4
1.160.41
1.170.41
1.180.41
1.190.41
1.200.41
1.210.41
1.220.41
1.230.41
1.240.41
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
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
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
Mo
difi
catio
n f
act
ore
2.01.3 27 2.08 28
1.4 25 2.24 261.4
1.2
0.8
0.4
Permissible Bond stress Table τbd
in concrete (IS : 456-2000)
τbd
(N / mm2) kd = L
d Φ τ
bd (N / mm2) k
d = L
d Φ
Mo
difi
catio
n f
act
ore
0.4
0.0
(N/mm2) (N/mm2) (N/mm2)
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
16.01600
12.01200
1.4140
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 αcbc Direct (αcc)
Kg/m2 Kg/m2
in kg/m2
0.4 0.8 1.2 1.6 2
Percentage of tension reinforcement
2 2.4 2.8
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
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
Development Length in tension0.867 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
0.3290.329 0.329 0.329 0.329 0.329 M 15
0.890.89 0.89 0.89 0.89 0.89 M 20
0.732 1.025 1.244 1.464 1.684 1.903 M 25
0.433 0.606 0.736 0.866 0.997 1.127 M 30
0.289 0.289 0.289 0.289 0.289 0.289 M 35
0.904 0.904 0.904 0.904 0.904 0.904 M 40
0.653 0.914 1.11 1.306 1.502 1.698 M 45
0.314 0.44 0.534 0.628 0.722 0.816 M 50
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
bdM-15 M-20 M-25 M-30 M-35 M-40
Permissible Bond stress Table τbd
in concrete (IS : 456-2000)
τbd
(N / mm2)
σcbc
N/mm2
m σcbc
(a) σst =
140 N/mm2
(Fe 250)
kc
jc
Rc
Grade of concrete
Pc (%)
(b) σst =
190 N/mm2
kc
jc
Rc
Pc (%)
(c ) σst = 230
N/mm2 (Fe 415)
kc
jc
Rc
Pc (%)
(d) σst =
275 N/mm2 (Fe 500)
kc
jc
Rc
Pc (%)
Permissible shear stress Table τv in concrete (IS : 456-2000)
100A s Permissible shear stress in concrete tv N/mm2 Permissible stress in concrete (IS : 456-2000)
Grade of concrete
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
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 %
M-20 M-20bd bd
0.15 0.18 0.18 0.15
0.16 0.18 0.19 0.18
0.17 0.18 0.2 0.21
Grade of concrete
< 0.15
Maximum shear stress τc.max
in concrete (IS : 456-2000)
τc.max
Shear stress tc
100A s
100A s
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 0.230.33
0.65
0.31 0.230.34
0.7
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 0.250.4
1.08
0.38 0.260.41
1.16
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
0.58 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
0.650.33
0.660.33
0.670.33
0.680.33
0.690.33
0.70.34
0.710.34
0.720.34
0.730.34
0.740.34
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
1.080.4
1.090.4
1.100.4
1.110.4
1.120.4
1.130.4
1.140.4
1.150.4
1.160.41
1.170.41
1.180.41
1.190.41
1.200.41
1.210.41
1.220.41
1.230.41
1.240.41
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
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
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 Bond stress Table τbd
in concrete (IS : 456-2000)
τbd
(N / mm2) kd = L
d Φ τ
bd (N / mm2) k
d = L
d Φ
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)
(N/mm2) (N/mm2) (N/mm2)
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
16.01600
12.01200
1.4140
Permissible stress in bond (Average) for plain bars in tention (N/mm2)
Bending αcbc Direct (α
cc)
Kg/m2 Kg/m2
in kg/m2
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