146065504 curved beam by b c punmia
DESCRIPTION
rc beamTRANSCRIPT
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
Load on beam
Design of circular beam
Angle (between column)
unit weight
pkn
Depth of beam
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
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
= =
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
(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
=
= 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
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
= 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
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
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.
N/mm2For HYSD bars , fy = 415
lgd strirrups @
201 mm2=
100
mm2= 314
100
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
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
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
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
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
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
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
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
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
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
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
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)
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
fs =190 =fy328
fs =240 =fy415
fs = 290 =fy500
2.8 3.21.6 2.42.0
3.2