146065504 curved beam by b c punmia

38
Name of work:- 1 Radious of Beam 5 mtr 300 kN/m 2 Width of beam 500 mm 1000 mm 4 Conrete M 20 25000 N/m 3 s cbc 7 N/mm 2 m 13 Q 0.897 j 0.906 5 Steel fy 415 tesile stress 230 6 Nominal Cover 25 mm 45 degree 7 Reinforcement Maximum torsion Bottom 20 mm F 2 Nos bars top/ bottom 12 mm F 4 Nos bars Distirbution 10 mm F mm c/c Support section top 20 mm F 8 Nos bars Distirbution 10 mm f mm c/c Mid section Bottom 20 mm F 5 Nos bars Distirbution 10 mm F mm c/c 0 nos bars mm f mm F top bars 0 nos bars 0 mm F 25 mm cover mm F 0 mm c/c mm F 0 mm c/c 1000 1000 nos bars 0 mm F mm mm nos bars 0 mm F mm F 0 mm c/c mm cover 500 500 mm mm (a) supports section (B) Mid span section mm F 0 0 mm F 0 mm c/c each face 1000 mm F 0 mm c/c mm nos bars 0 mm F 500 © Section on to maximum torsion [email protected] Load on beam Design of circular beam Angle (between column) unit weight pkn Depth of beam

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Page 1: 146065504 Curved Beam by B C Punmia

Name of work:-

1 Radious of Beam 5 mtr 300 kN/m

2 Width of beam 500 mm 1000 mm

4 Conrete M 20 25000 N/m3

scbc 7 N/mm2 m 13

Q 0.897 j 0.906

5 Steel fy 415 tesile stress 230

6 Nominal Cover 25 mm 45 degree

7 Reinforcement

Maximum torsion Bottom 20 mm F 2 Nos bars

top/ bottom 12 mm F 4 Nos bars

Distirbution 10 mm F mm c/c

Support section top 20 mm F 8 Nos bars

Distirbution 10 mm f mm c/c

Mid section Bottom 20 mm F 5 Nos bars

Distirbution 10 mm F mm c/c

0 nos bars mm f mm F top bars

0 nos bars 0 mm F

25 mm cover

mm F 0 mm c/c

mm F 0 mm c/c 1000

1000 nos bars 0 mm F mm

mm nos bars 0 mm F

mm F 0 mm c/c

mm cover

#VALUE! 500

500 mm

mm

(a) supports section (B) Mid span section

mm F 0 0

mm F 0 mm c/c each face

1000 mm F 0 mm c/c

mm nos bars 0 mm F

500

© Section on to maximum torsion

[email protected]

Load on beam

Design of circular beam

Angle (between column)

unit weight

pkn

Depth of beam

Page 2: 146065504 Curved Beam by B C Punmia

Radious of Beam mtr

Width of beam mm

Conrete M- 20

scbc 7 N/mm2

Steel fy 415 N/mm2

Nominal cover 25 mm

Design Constants:-For HYSD Bars

sst = 230 N/mm2

scbc = 7 N/mm2

m = 13

k = 0.283 J = 0.906 R = 0.898

1 Design of Bottom circular ring beam B 2 :-

= x

Self weight = 0.50 x 1.00 x 1.00 x 25000

\

p

4

; C1 = 0.066 ; C2 = 0.030 ; C3 = 0.005

sin = 0.165 , cos = 0.986

p

4

Maximum -ve B.M. at support = M0 = C1.w R2.2f = 0.066 x

Maximum +ve B.M. at support = Mc = C2.w R2.2f = 0.030 x

Maximum torsion moment = Mtm = C3.w R

2.2f = 0.005 x

For HYSD Bars

sst = 230 N/mm2

scbc = 7 N/mm2

m = 13

k = 0.283 J = 0.906 R = 0.898

Mf x

b x R x

= 1000 mm from shear point of veiw, Let d=

Maximum shear force at supports, F0 =w.R.f = x 5.00

Shear force at any point given by, F = w.R(F-f) =

At f = fm, F = x 5.00 x( 22.50 - 9.5

B.M. at the point of maximum torsion moment (f = fm =9.5 ) is given by Eq.

Mf = w.R2 (Fsin f +F cot F.cosf -1) sagging

= 359019 x 5.00 2x( p / 8 x sin 9.5 + p / 8

= 359019 x 25.00 x( 0.393 x 0.165 + 0.393

= x( +

= 8975475 x( +

= 8975475 x

= 3006 N-m (hogging)

The tosional moment at any point is given by Eq.20.6

Mtf = w.R

2 (Fcos f - F cot F.sinf -(F-f) At the support,f=

22.50 = M1f = w.R

2 (Fcos f -F cot F.sinf -1) '=

Uniformaly distributed load

0.90500

0.935356

degree 452f

9.5

w R2 . 2f

7045748

7045748

1000

Cocrete M -

wt. of concrete

Depth of beam

m

7045748

7045748

f

Angle

Cocrete M -

9.5

==

Assuming the size of beam

45

500

Design of circular beam

Tensile stess

wt. of concrete

5

500

Total load on beam w

465019

2x =

0=

1000

wt. of concrete

359019 x

However, keep total depth

5.0

Required depth= =

=

359019

359019

-0.0646437

At the mid span, f =F= p/8 rad.,

0.000335

0.064979

0.064979

Page 3: 146065504 Curved Beam by B C Punmia

Hence we have the following combinations of B .M. and the torsional moment.

(A) At the supports,

Mo = N-M (Hogging or negative);

(B) At mid span , Mc = N-m (sagging or positive)

(C ) At the point of max. torsion. 9.5 )

Mf = 3006 N-m hogging

Mf = -3006 N-m Sagging

Main and Longitudinal reinforcement.;-

(a) Section at point of maximum torsion.

T=Mtmax = 35229 N-m Mf '=M, Me1 =

1+D/b 1+ 1.00 / 0.50

1.7

\ Me1 = -3006 + 62169 = N-m

Me1 x

sst. j.d 230 x 0.906 x 950

3.14xdia2

3.14

4 x100

No.of hoop Bars = 299 / 314 = 1 No.

However Provided minimum 2 No. 20 mm F bar,

Since MT > m \ Me2 = MT -M = #### - -3006

Me2 x

sst. j.d 230 x 0.906 x 950

3.14xdia2

3.14

4 x100

No.of Bars = 329 / 113 = 3 No.However Provided minimum 4 No. 12 mm F bar, Thus,

4 x 12 mm f bars each at top and bottom.

(b) Section at maximum hogging B.M. (support)

M0 = N-m Mt0

Me2 x

sst. j.d 230 x 0.906 x 950

3.14xdia2

3.14

4 x100

\ No.of Bars = 2350 / 314 = 8 No.

Hence provided 6 Nos. of 20 mm f bars in one layer and 2 Bars in second layer.

Thes will be provided at the top of section, near supports.

(c ) Section at maximum hogging B.M. (mid-span)

Mc = N-m Mtc

For posotive B.M., steel will be to the orther face, where stress in steel (sst) can be taken as

190 The constants for M- 20 concrete having

k = 0.324 J = 0.892 R = 1.011

Mc x

sst. j.d 190 x 0.892 x 950

3.14xdia2

3.14

4 x100

No.of Bars = 1313 / 314 = 5 No.

Hence the scheme of reinforcement will be as follows: the supports, provide

and 2 Nos of 20 mm f bars in second layer . Continues these upto the section of maximum

=

=using 20 mm bars =A

Where Mt= T

211372

Ast = =

299

465019

(f = fm =

3006

1.7

M+Mt, D=

6216935229 =

1000

59163

=

= =

59163

using 20 mm bars A

Ast1 = =

mm bars A

329Ast2 = =65175 1000

=

At a point of maximum torsion, provide

465019

= =using 12

Ast2 = =465019 1000

= 2350

211372

= 1313

using 20 mm bars A

N/mm2

1000211372

= =

Page 4: 146065504 Curved Beam by B C Punmia

torsion (i.e.at fm = 9.5 = 0.166 rad.)) at a distance = Rfm

or equal to Ld =52 f = 52 x 20 = 1040

4 bars while continue the remaining bars.

mm f at the bottom, throughout the length. T̀hese bars will take care of both the maximum positive B.M. as well

as maximum torsional moment.

Transverse reinforcement ;-

(a) At point of maximum torsional moment; At the point of max. torsion.V =

Ve = V+1.6xT/b Where T= Mtm,\ ; b

35229

500

V

b xd 500 x 950

100 x As 100 x 4 x 314

b x d 500 x 950

Since Tve < Tc, Shear reinforcement required

b1.d1.ssv

where b1 = 500 - 2 x 25 - 20 = 430

d1 = 1000 - 2 x 25 - 20 = 930

\ Asv x

Sv 430 x 930 x 230 2.5 x 930

Asv tve-tc

Sv ssv

\ Asv 0.857 - 0.210

Sv

3.14xdia2

3.14

or Sv = 452 / 1.41 = 321

However , the spacing should not exceed the least of x1,

x1 = short dimension of strirrups = 430 + 20

y1 = Long dimension of strirrups = 930 - 20

x1 +y1 460 + 900

4

Hence provided 12 mm f 4 lgd strirrups @

(b) At point of maximum shear (supports):

At supports, Fo =

500 x 950

100 x As 100 x 8 x 314

b x d x

Tv > Tc shear reinforcement necessary

Vc = 0.300 x 500 x 950 =

\ F0 - Vc = -

3.14xdia2

3.14

ssv . Asv . D 230 x 452

=

+T . Sv

The area of cross section Asv of the strirupps is given by =

407200.7328= 0.857 <

35229

407201 N

\ tve = =

= 0.264 \ Tc

\ Ve = =407088 + 1.6 x

1.8

At this point, discontinue

>

Hence depth

=100035229

Maximum transverse reinforcement given by =

+407088.00

x

using 12 =

=230

500 = 1.407

mm f 4 lgd strirrup, Asv =100

(x1+y1)/4,

=4

= 340

704575

tv =704575

= 1.48

At supports, =500

142500

950= 0.529

100

704575 142500

lgd strirrup, Asv = =The spacing of

=SvVs

12 mm f 4

=562075

Page 5: 146065504 Curved Beam by B C Punmia

(c ) At mid point :

At mid span S.F. is Zero ,Hence provide minimum /nominal shear reinforcement, given by

Asv 0.400 Asv 0.4. b

b . Sv fy Sv fy

Asv 0.40 x 500

Sv

3.14xdia2

3.14

or Sv = 314 / 0.48 = 652 mm, maximum permissible spacing 0.75 d =

or 300 mm which ever is less. Hence provide 10 4

Side face reinforcement:-

Since depth is > than 450 mm, 0.1 % reinforcement is necessary.

0.10

100

3.14xdia2

3.14

4 x 100 4

\ No.of Bars = 500 / 201 = 3 No.

Total area = 4 x 201 = mm2

4 Nos . Bars of 16 mm f on each face ,

using

Hence Provided

x 1000 )= 500At =

= =

x( 500

16 mm f bars Area

> or =

lgd strirrup, Asv =

For HYSD bars , fy

0.482415

=

100

\ =

using 10 mm f 4

mm f bars lgd strirrups @

mm2

803.84

=

Page 6: 146065504 Curved Beam by B C Punmia

= kN/m2

= mm

= N/mm3

= 13

= 230 N/mm2

= 45 degree

= 20

= N/mm3

mm

=

= N/m

= N/m

p

8

; fm = 9.5

, cot =

= N-m

= N-m

= N-m

20

= N/mm3

1000 - 50 = 950 mm

x p / 8 = N

)x p /180 = N

x( cot22.5 x cos9.5 - 1))

x( 2.414 x 0.986 - 1))

- 1

0 \ wR2 (F-F)= 0

0

2.414

211372

12500

359019

704575

mm

465019

35229

407088

0.935356

22.5

25000

N-m

7045748

= 1017

7045748

25000

7045748

= =22.5

Design of circular beam

300.00

1000

25000

300000

-0.0646437

Page 7: 146065504 Curved Beam by B C Punmia

Mt0 = 0

Mtc = 0

Mtm = N-m

Hogging or negative

1000 mm, b = 500 mm

x 20 x 20

4 x

say 2 No.

= N-m

x 12 x 12

4 x

say 4 No.

= 0

x 20 x 20

4 x

say 8 No.

= 0

For posotive B.M., steel will be to the orther face, where stress in steel (sst) can be taken as

C= 7 N/mm2, and m= 13

x 20 x 20

4 x

6 Nos 20 mm bars in top layer,

mm f bars in second layer . Continues these upto the section of maximum

mm2

mm2

mm2= 314

100

35229

N-m

299

M+Mt, D=

62169

mm2

= 314 mm2

100

65175

329

mm2

100= 113

2350 mm2

1313

mm2

100= 314

Page 8: 146065504 Curved Beam by B C Punmia

= 0.0 x 0.17 = 0 m

mm from supports.

Similarly, provide 4 bars 20

These bars will take care of both the maximum positive B.M. as well

N

= 500 m

2.5 d1. ssv

mm [email protected]

mm

x 230

x 12 x 12

mm

and 300 mm

+ 10 = 460 mm

- 10 = 900 mm

mm

N

= N

x 12 x 12

x 950

407088.00

V . Sv

= 0.210 < Fail

safe, for M 20 concrete

0.857

Hence depth

b

407088.00= 1.14

= 1.41

= 452 mm2

100

300

704575

= 0.3 N/mm2\ tc%

mm2

100

562075

= 452

562075= 176 mm

Page 9: 146065504 Curved Beam by B C Punmia

At mid span S.F. is Zero ,Hence provide minimum /nominal shear reinforcement, given by

x 10 x 10

713 mm

300 mm c/c

x 16 x 16

x

say 4 No.

[email protected]

N/mm2For HYSD bars , fy = 415

lgd strirrups @

201 mm2=

100

mm2= 314

100

Page 10: 146065504 Curved Beam by B C Punmia

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

18.67 13.33 10.98 9.33 8.11 7.18 tbd (N / mm2)

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

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 0.89

Rc 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

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

0.18 0.18 0.19 0.2 0.2 0.2

0.22 0.22 0.23 0.23 0.23 0.23

0.29 0.30 0.31 0.31 0.31 0.32

0.34 0.35 0.36 0.37 0.37 0.38

0.37 0.39 0.40 0.41 0.42 0.42

0.40 0.42 0.44 0.45 0.45 0.46

0.42 0.45 0.46 0.48 0.49 0.49

0.44 0.47 0.49 0.50 0.52 0.52

0.44 0.49 0.51 0.53 0.54 0.55

0.44 0.51 0.53 0.55 0.56 0.57

0.44 0.51 0.55 0.57 0.58 0.60

0.44 0.51 0.56 0.58 0.60 0.62

0.44 0.51 0.57 0.6 0.62 0.63

15 20 25 30 35 40

1.6 1.8 1.9 2.2 2.3 2.5

scbc N/mm2

(c ) sst =

230

N/mm2

(Fe 415)

m scbc

(a) sst =

140

N/mm2

(Fe 250)

VALUES OF DESIGN CONSTANTS

Grade of concrete

Modular Ratio

(b) sst =

190

N/mm2

(d) sst =

275

N/mm2

(Fe 500)

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

100As Permissible shear stress in concrete tv N/mm2

< 0.15

bd

0.25

0.50

0.75

1.00

1.25

1.50

2.50

1.75

2.00

tc.max

2.25

2.753.00 and above

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

Grade of concrete M

Page 11: 146065504 Curved Beam by B C Punmia

100As 100As % fy 200 250 328

bd bd 0.0

0.14 0.17 0.17 0.14 0.05

0.15 0.18 0.18 0.15 0.10

0.16 0.18 0.19 0.18 0.15

0.17 0.18 0.2 0.21 0.20

0.18 0.19 0.21 0.24 0.25 2

0.19 0.19 0.22 0.27 0.30 1.85

0.2 0.19 0.23 0.3 0.35 1.75

0.21 0.2 0.24 0.32 0.4 1.65

0.22 0.2 0.25 0.35 0.5 2.0 1.5

0.23 0.2 0.26 0.38 0.6 1.75 1.4

0.24 0.21 0.27 0.41 0.7 1.90 1.65 1.35

0.25 0.21 0.28 0.44 0.8 1.80 1.55 1.30

0.26 0.21 0.29 0.47 0.9 1.70 1.5 1.25

0.27 0.22 0.30 0.5 1.0 1.60 1.45 1.2

0.28 0.22 0.31 0.55 1.1 1.55 1.4 1.16

0.29 0.22 0.32 0.6 1.2 1.50 1.35 1.13

0.3 0.23 0.33 0.65 1.3 1.50 1.3 1.1

0.31 0.23 0.34 0.7 1.4 1.45 1.3 1.1

0.32 0.24 0.35 0.75 1.5 1.40 1.25 1.07

0.33 0.24 0.36 0.82 1.6 1.35 1.2 1.05

0.34 0.24 0.37 0.88 1.7 1.35 1.2 1.03

0.35 0.25 0.38 0.94 1.8 1.30 1.18 1.01

0.36 0.25 0.39 1.00 1.9 1.30 1.16 1.0

0.37 0.25 0.4 1.08 2.0 1.25 1.14 0.99

0.38 0.26 0.41 1.16 2.1 1.25 1.13 0.97

0.39 0.26 0.42 1.25 2.2 1.20 1.12 0.96

0.4 0.26 0.43 1.33 2.3 1.18 1.1 0.95

0.41 0.27 0.44 1.41 2.4 1.17 1.1 0.94

0.42 0.27 0.45 1.50 2.5 1.16 1.08 0.93

0.43 0.27 0.46 1.63 2.6 1.15 1.06 0.92

0.44 0.28 0.46 1.64 2.7 1.14 1.05 0.92

0.45 0.28 0.47 1.75 2.8 1.13 1.04 0.91

0.46 0.28 0.48 1.88 2.9 1.12 1.03 0.91

0.47 0.29 0.49 2.00 3.0 1.11 1.02 0.90

0.48 0.29 0.50 2.13 3.1 1.11 1.01 0.87

0.49 0.29 0.51 2.25 3.2 1.11 1.00 0.86

0.5 0.30

0.51 0.30

0.52 0.30

0.53 0.30

0.54 0.30

0.55 0.31 Degree sin Degree cos tan cot

0.56 0.31 1 0.017 1 1.000 0.017 57.295

0.57 0.31 1.5 0.026 1.5 1.000 0.262 56.300

0.58 0.31 2 0.035 2 0.999 0.035 28.644

0.59 0.31 2.5 0.044 2.5 0.999 0.044 22.913

0.6 0.32 3 0.052 3 0.999 0.052 19.083

M-20

Shear stress tc Reiforcement % modification factore Table

M-20

Value of angle

Page 12: 146065504 Curved Beam by B C Punmia

0.61 0.32 3.5 0.061 3.5 0.998 0.061 16.362

0.62 0.32 4 0.070 4 0.998 0.070 14.311

0.63 0.32 4.5 0.078 4.5 0.997 0.079 12.707

0.64 0.32 5 0.087 5 0.996 0.087 11.437

0.65 0.33 5.5 0.096 5.5 0.995 0.096 10.385

0.66 0.33 6 0.104 6 0.995 0.105 9.563

0.67 0.33 6.5 0.113 6.5 0.994 0.114 8.777

0.68 0.33 7 0.122 7 0.993 0.123 8.149

0.69 0.33 7.5 0.131 7.5 0.991 0.132 7.597

0.7 0.34 8 0.139 8 0.990 0.140 7.119

0.71 0.34 8.5 0.148 8.5 0.989 0.149 6.691

0.72 0.34 9 0.156 9 0.988 0.158 6.315

0.73 0.34 9.5 0.165 9.5 0.986 0.168 5.963

0.74 0.34 10 0.174 10 0.985 0.176 5.673

0.75 0.35 10.5 0.182 10.5 0.983 0.185 5.396

0.76 0.35 11 0.191 11 0.981 0.194 5.142

0.77 0.35 11.5 0.199 11.5 0.980 0.203 4.915

0.78 0.35 12 0.208 12 0.978 0.213 4.704

0.79 0.35 12.5 0.819 12.5 0.976 0.839 1.192

0.8 0.35 13 0.225 13 0.974 0.231 4.332

0.81 0.35 13.5 0.233 13.5 0.972 0.240 4.166

0.82 0.36 14 0.242 14 0.970 0.249 4.011

0.83 0.36 14.5 0.250 14.5 0.968 0.259 3.867

0.84 0.36 15 0.259 15 0.966 0.268 3.732

0.85 0.36 15.5 0.259 15.5 0.964 0.269 3.723

0.86 0.36 16 0.276 16 0.961 0.287 3.488

0.87 0.36 16.5 0.284 16.5 0.959 0.296 3.376

0.88 0.37 17 0.292 17 0.956 0.306 3.272

0.89 0.37 17.5 0.301 17.5 0.954 0.315 3.172

0.9 0.37 18 0.309 18 0.951 0.325 3.078

0.91 0.37 18.5 0.317 18.5 0.948 0.335 2.989

0.92 0.37 19 0.326 19 0.946 0.344 2.905

0.93 0.37 19.5 0.334 19.5 0.943 0.354 2.824

0.94 0.38 20 0.342 20 0.940 0.364 2.747

0.95 0.38 20.5 0.350 20.5 0.937 0.374 2.674

0.96 0.38 21 0.358 21 0.934 0.384 2.605

0.97 0.38 21.5 0.367 21.5 0.930 0.394 2.539

0.98 0.38 22 0.375 22 0.927 0.404 2.475

0.99 0.38 22.5 0.383 22.5 0.924 0.414 2.414

1.00 0.39 23 0.391 23 0.921 0.424 2.356

1.01 0.39 23.5 0.399 23.5 0.917 0.435 2.300

1.02 0.39 24 0.407 24 0.924 0.440 2.271

1.03 0.39 24.5 0.415 24.5 0.910 0.456 2.194

1.04 0.39 25 0.422 25 0.906 0.466 2.148

1.05 0.39 25.5 0.431 25.5 0.905 0.476 2.103

1.06 0.39 26 0.438 26 0.898 0.488 2.049

1.07 0.39 26.5 0.446 26.5 0.895 0.499 2.006

1.08 0.4 27 0.454 27 0.891 0.510 1.963

1.09 0.4 27.5 0.462 27.5 0.887 0.521 1.921

1.10 0.4 28 0.469 28 0.883 0.532 1.881

1.11 0.4 28.5 0.477 28.5 0.879 0.543 1.842

Page 13: 146065504 Curved Beam by B C Punmia

1.12 0.4 29 0.485 29 0.875 0.554 1.804

1.13 0.4 29.5 0.492 29.5 0.870 0.566 1.767

1.14 0.4 30 0.500 30 0.866 0.577 1.732

1.15 0.4 30.5 0.508 30.5 0.862 0.589 1.698

1.16 0.41 31 0.515 31 0.857 0.601 1.664

1.17 0.41 31.5 0.522 31.5 0.853 0.613 1.632

1.18 0.41 32 0.530 32 0.848 0.625 1.600

1.19 0.41 32.5 0.537 32.5 0.843 0.637 1.570

1.20 0.41 33 0.545 33 0.839 0.649 1.540

1.21 0.41 33.5 0.552 33.5 0.834 0.662 1.511

1.22 0.41 34 0.559 34 0.829 0.675 1.483

1.23 0.41 34.5 0.566 34.5 0.834 0.679 1.473

1.24 0.41 35 0.573 35 0.819 0.700 1.429

1.25 0.42 35.5 0.581 35.5 0.814 0.713 1.402

1.26 0.42 36 0.588 36 0.809 0.726 1.377

1.27 0.42 36.5 0.595 36.5 0.804 0.740 1.351

1.28 0.42 37 0.602 37 0.799 0.754 1.327

1.29 0.42 37.5 0.609 37.5 0.793 0.767 1.303

1.30 0.42 38 0.616 38 0.788 0.781 1.280

1.31 0.42 38.5 0.623 38.5 0.783 0.795 1.257

1.32 0.42 39 0.629 39 0.777 0.810 1.235

1.33 0.43 39.5 0.636 39.5 0.772 0.824 1.213

1.34 0.43 40 0.643 40 0.766 0.839 1.191

1.35 0.43 40.5 0.649 40.5 0.760 0.854 1.171

1.36 0.43 41 0.656 41 0.755 0.869 1.150

1.37 0.43 41.5 0.663 41.5 0.749 0.885 1.130

1.38 0.43 42 0.669 42 0.743 0.900 1.111

1.39 0.43 42.5 0.676 42.5 0.737 0.916 1.091

1.40 0.43 43 0.682 43 0.731 0.933 1.072

1.41 0.44 43.5 0.688 43.5 0.725 0.949 1.054

1.42 0.44 44 0.695 44 0.719 0.966 1.036

1.43 0.44 44.5 0.701 44.5 0.713 0.983 1.018

1.44 0.44 45 0.707 45 0.707 1.000 1.000

1.45 0.44 45.5 0.713 45.5 0.701 1.018 0.983

1.46 0.44 46 0.719 46 0.695 1.036 0.966

1.47 0.44 46.5 0.725 46.5 0.688 1.054 0.949

1.48 0.44 47 0.731 47 0.682 1.072 0.933

1.49 0.44 47.5 0.737 47.5 0.676 1.091 0.916

1.50 0.45 48 0.742 48 0.669 1.109 0.902

1.51 0.45 48.5 0.749 48.5 0.663 1.130 0.885

1.52 0.45 49 0.755 49 0.656 1.150 0.869

1.53 0.45 49.5 0.760 49.5 0.649 1.171 0.854

1.54 0.45 50 0.766 50 0.643 1.192 0.839

1.55 0.45 50.5 0.772 50.5 0.636 1.213 0.824

1.56 0.45 51 0.777 51 0.629 1.235 0.810

1.57 0.45 51.5 0.786 51.5 0.623 1.262 0.792

1.58 0.45 52 0.788 52 0.616 1.280 0.781

1.59 0.45 52.5 0.793 52.5 0.609 1.303 0.767

1.60 0.45 53 0.799 53 0.602 1.327 0.754

1.61 0.45 53.5 0.804 53.5 0.595 1.351 0.740

1.62 0.45 54 0.809 54 0.588 1.376 0.727

1.63 0.46 54.5 0.814 54.5 0.581 1.402 0.713

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1.64 0.46 55 0.819 55 0.574 1.428 0.700

1.65 0.46 55.5 0.824 55.5 0.566 1.455 0.687

1.66 0.46 56 0.829 56 0.559 1.483 0.675

1.67 0.46 56.5 0.834 56.5 0.552 1.511 0.662

1.68 0.46 57 0.839 57 0.545 1.540 0.649

1.69 0.46 57.5 0.843 57.5 0.537 1.570 0.637

1.70 0.46 58 0.848 58 0.530 1.600 0.625

1.71 0.46 58.5 0.853 58.5 0.522 1.632 0.613

1.72 0.46 59 0.857 59 0.515 1.664 0.601

1.73 0.46 59.5 0.862 59.5 0.508 1.698 0.589

1.74 0.46 60 0.866 60 0.500 1.732 0.577

1.75 0.47 60.5 0.870 60.5 0.492 1.767 0.566

1.76 0.47 61 0.875 61 0.485 1.804 0.554

1.77 0.47 61.5 0.879 61.5 0.477 1.842 0.543

1.78 0.47 62 0.883 62 0.470 1.880 0.532

1.79 0.47 62.5 0.887 62.5 0.462 1.921 0.521

1.80 0.47 63 0.891 63 0.454 1.963 0.510

1.81 0.47 63.5 0.895 63.5 0.446 2.006 0.498

1.82 0.47 64 0.899 64 0.438 2.051 0.488

1.83 0.47 64.5 0.903 64.5 0.431 2.097 0.477

1.84 0.47 65 0.906 65 0.423 2.145 0.466

1.85 0.47 65.5 0.910 65.5 0.415 2.195 0.456

1.86 0.47 66 0.914 66 0.407 2.246 0.445

1.87 0.47 66.5 0.917 66.5 0.399 2.300 0.435

1.88 0.48 67 0.921 67 0.391 2.356 0.424

1.89 0.48 67.5 0.924 67.5 0.383 2.414 0.414

1.90 0.48 68 0.927 68 0.375 2.475 0.404

1.91 0.48 68.5 0.930 68.5 0.819 1.136 0.880

1.92 0.48 69 0.934 69 0.358 2.605 0.384

1.93 0.48 69.5 0.937 69.5 0.350 2.674 0.374

1.94 0.48 70 0.940 70 0.342 2.747 0.364

1.95 0.48 70.5 0.943 70.5 0.556 1.696 0.590

1.96 0.48 71 0.946 71 0.326 2.904 0.344

1.97 0.48 71.5 0.948 71.5 0.317 2.989 0.335

1.98 0.48 72 0.951 72 0.309 3.078 0.325

1.99 0.48 72.5 0.954 72.5 0.301 3.172 0.315

2.00 0.49 73 0.956 73 0.292 3.271 0.306

2.01 0.49 73.5 0.959 73.5 0.284 3.376 0.296

2.02 0.49 74 0.961 74 0.276 3.488 0.287

2.03 0.49 74.5 0.964 74.5 0.267 3.606 0.277

2.04 0.49 75 0.966 75 0.259 3.732 0.268

2.05 0.49 75.5 0.968 75.5 0.250 3.868 0.259

2.06 0.49 76 0.970 76 0.242 4.011 0.249

2.07 0.49 76.5 0.982 76.5 0.233 4.209 0.238

2.08 0.49 77 0.974 77 0.225 4.332 0.231

2.09 0.49 77.5 0.976 77.5 0.216 4.511 0.222

2.10 0.49 78 0.978 78 0.208 4.705 0.213

2.11 0.49 78.5 0.980 78.5 0.199 4.915 0.203

2.12 0.49 79 0.982 79 0.191 5.145 0.194

2.13 0.50 79.5 0.983 79.5 0.182 5.396 0.185

2.14 0.50 80 0.985 80 0.174 5.673 0.176

2.15 0.50 80.5 0.986 80.5 0.165 5.977 0.167

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2.16 0.50 81 0.988 81 0.156 6.315 0.158

2.17 0.50 81.5 0.989 81.5 0.148 6.691 0.149

2.18 0.50 82 0.999 82 0.139 7.178 0.139

2.19 0.50 82.5 0.991 82.5 0.131 7.597 0.132

2.20 0.50 83 0.993 83 0.122 8.145 0.123

2.21 0.50 83.5 0.994 83.5 0.113 8.777 0.114

2.22 0.50 84 0.995 84 0.105 9.517 0.105

2.23 0.50 84.5 0.995 84.5 0.096 10.389 0.096

2.24 0.50 85 0.996 85 0.087 11.431 0.087

2.25 0.51 85.5 0.997 85.5 0.078 12.716 0.079

2.26 0.51 86 0.998 86 0.070 14.302 0.070

2.27 0.51 86.5 0.998 86.5 0.061 16.362 0.061

2.28 0.51 87 0.999 87 0.052 19.083 0.052

2.29 0.51 87.5 0.999 87.5 0.044 22.913 0.044

2.30 0.51 88 0.999 88 0.035 28.637 0.035

2.31 0.51 88.5 1.000 88.5 0.026 38.299 0.026

2.32 0.51 89 0.9998 89 0.017 57.295 0.017

2.33 0.51 89.5 0.9999 89.5 0.009 114.931 0.009

2.34 0.51 90 1.000 90 0.000 1.000 0.000

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

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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

Page 17: 146065504 Curved Beam by B C Punmia

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

tbd (N / mm2) -- 0.6 0.8 0.9 1 1.1 1.2 1.3

M 15

M 20

M 25

M 30

M 35

M 40

M 45

M 50

(N/mm2) Kg/m2 (N/mm2) Kg/m

2

M 10 3.0 300 2.5 250

M 15 5.0 500 4.0 400

M 20 7.0 700 5.0 500

M 25 8.5 850 6.0 600

M 30 10.0 1000 8.0 800

M 35 11.5 1150 9.0 900

M 40 13.0 1300 10.0 1000

M 45 14.5 1450 11.0 1100

M 50 16.0 1600 12.0 1200

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

1.6 1.8 1.9 2.2 2.3 2.5

1 35 1.6

Development Length in tension

kd = Ld F

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

Grade of

concrete

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

tbd (N / mm2) kd = Ld F tbd (N / mm2)

0.6 58 0.96 60

0.8 44 1.28

0.9 39 1.44 40

45

36

33

1.2 29 1.92 30

1.1 32 1.76

1.4

1.3 27 2.08 28

25 2.24 26

Permissible stress in concrete (IS : 456-2000)

Bending acbc Direct (acc)Grade of

concrete

Permission stress in compression (N/mm2) Permissible stress in bond (Average) for

plain bars in tention (N/mm2)

-- --

(N/mm2) in kg/m2

0.6 60

0.8 80

0.9 90

1.0 100

1.4 140

1.1 110

1.2 120

1.3

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

Grade of concrete

130

tc.max

Page 18: 146065504 Curved Beam by B C Punmia

415 500

2.00

1.80

1.65

1.90 1.50

1.80 1.40

1.70 1.35

1.60 1.30

1.50 1.20

1.40 1.16

1.30 1.08

1.20 1.00

1.15 0.95

1.05 0.90

1.02 0.86

1.20 0.84

0.98 0.82

0.96 0.81

0.94 0.80

0.92 0.79

0.91 0.78

0.90 0.77

0.89 0.76

0.86 0.75

0.86 0.74

0.85 0.73

0.84 0.72

0.83 0.72

0.83 0.72

0.82 0.71

0.82 0.71

0.81 0.71

0.81 0.70

0.81 0.70

0.81 0.69

0.81 0.69

0.81 0.68

0.81 0.68

Factors

H+dA 10 20 30 40 10 20

0.2 0.046 0.028 0.022 0.015 - 0.5

0.3 0.032 0.019 0.014 0.01 0.55 0.43

0.4 0.024 0.014 0.01 0.007 0.5 0.39

0.5 0.02 0.02 0.009 0.006 0.45 0.37

Valu

e o

f H

/D

F K1

Table Carpentors's coefficents for cylenlidrical tank (Reyolndhand book)

modification factore Table

Page 19: 146065504 Curved Beam by B C Punmia

1.0 0.012 0.006 0.005 0.003 0.37 0.28

2.0 0.006 0.003 0.002 0.002 0.3 0.22

4.0 0.004 0.002 0.002 0.001 0.27 0.2

Cofficent for bending moment and twisting moment in circular beam

No of support 2f C1 C2 C3

4 90 0.137 0.07 0.021

5 72 0.108 0.054 0.014

6 60 0.089 0.045 0.009

8 45 0.066 0.03 0.005

9 40 0.06 0.027 0.004

10 36 0.054 0.023 0.003

12 30 0.045 0.017 0.002

Cofficent for bending moment and twisting moment in circular beam

2f K1 K2 K3fm

4 90 0.0342 0.0176 0.0053 19.12

6 60 0.0148 0.0075 0.0015 12.44

8 45 0.0083 0.0041 0.0006 9.33

10 36 0.0054 0.0023 0.0003 7.3

12 30 0.0037 0.0014 0.0017 7.15

2.414

Angular

distance

for

maximum

torsionNo of

support

Negative

bending

moment

at

supporte

positive

bending

moment

at centr of

span

Maximum

twiting

moment

or torque

TABLE 20.1V

alu

e o

f H

/D

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Page 24: 146065504 Curved Beam by B C Punmia

M-50

1.4

fs = 120 =fy200

fs =145 =fy250

fs =190 =fy328

0

Modification factore

Fig 7.1

Fs= steel stress of service load =0.58fy

for steeel

fy 500 = Fs N/mm2

fy 415 = Fs N/mm2

fy 328 = Fs N/mm2

fy 250 = Fs N/mm2

fy 207 = Fs N/mm2

2.0

1.6

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

0.4

1.2

0.8

0.4 0.8 1.2

290

240

190

145

120

Page 25: 146065504 Curved Beam by B C Punmia

K2

30 40 10 20 30 40

0.45 0.4 0.32 0.46 0.53 0.5

0.38 0.33 0.35 0.53 0.6 0.66

0.35 0.3 0.44 0.58 0.65 0.7

0.32 0.27 0.48 0.63 0.69 0.73

K1

Table Carpentors's coefficents for cylenlidrical tank (Reyolndhand book)

Page 26: 146065504 Curved Beam by B C Punmia

0.24 0.21 0.62 0.73 0.74 0.83

0.19 0.16 0.73 0.81 0.85 0.88

0.17 0.14 0.8 0.85 0.87 0.9

Cofficent for bending moment and twisting moment in circular beam

fm

19.25

15.25

12.75

9.5

8.5

7.25

6.25

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Page 31: 146065504 Curved Beam by B C Punmia

fs =190 =fy328

fs =240 =fy415

fs = 290 =fy500

2.8 3.21.6 2.42.0

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3.2