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

pk_nandwana@yahoo.co.in

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

pk_nandwana@yahoo.co.in

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

pk_nandwana@yahoo.co.in

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

pk_nandwana@yahoo.co.in

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