Box Culvert Chesirimion
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Transcript of Box Culvert Chesirimion
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1 In side diamentions 1.50 m x 1.50 m
2 Super imposed load 12000 N/m3
3 Live load 60000 N/m2
4 Wieght of soil 18000 N/m2
5 Angle of repose 25 Degree
6 Nominal cover top / bottom 50 mm Nominal cover side 50 mm
6 Cocrete M- 25 wt. of concrete 24000 kg/m3
scbc 7 N/m2 m 13
7 Steel 415 ater side sst 150 N/m2 sst 190 N/m2
8 Thickess of side wall 300 mm thickness of side wall is OK
Thickness of top slab 300 mm O.K.
Thickness of bottom slab 230 mm
9 Reinforcement
Top slab Main 16 mm F @ 230 mm c/c
Distribution 12 mmF
@ 310 mm c/cAt supports 16 mm F @ 200 mm c/c
Bottom slab Main 16 mm F @ 200 mm c/c
Distribution 12 mm F @ 370 mm c/c
At supports 12 mm F @ -580 mm c/c Through out slab at bottom
Vertical 20 mm F @ 300 mm c/c Both side O.K.
Distribution 12 mm F @ 310 mm c/c
16 mm F@ 460 mm c/c
12 mm F@ 200 mm C/C
16 mm F@ 310 mm C/c
300 16 mm F@
20 mm F@ 230 mm C/C
300 mm C/C
1.50
12 mm F@
310 mm C/C
16 mmF
@200 mm c/c
16 mm F@ 12 mm F
@ 16 mm F
@
400 mm c/c 200 mm C/C 310 mm C/c
300 1.50 300
DESIGN OF BOX TYPE CULVERT
300
230
Side vertical wall
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1 1/2
1+1/2 1+1/2
wL2 #### x 1.8 2=
12
wL2 #### x 1.8
2=
12
pL2 WL Where W is the total tringular earth pressure.
12 15
29266 x 1.82
+ #### x 1.8 1.815
pL2 WL
12 15
29266 x 1.8 2-- #### x 1.8 1.8
10
The Moment distribution is carried out as illustrate in table
Fixed End Moments
Member
The moment distribution carried out as per table 1 for case 1
Joint
Member
Distribution factore
Fix end moment A A
Balance
Carry over
balance 1.8 m
Carry over
balance
Carry over D D
balance 35960
Carry over
balanceCarry over
balance
Carry over
balance
Carry over
balance
Final moment
For horizontal slab AB, carrying UDL @ N/m2.
Vertical reactionat a and B = 0.5 x x 1.8 = N/m2
Similarly, for the Bottom slab DC carrying U.D.L.loads @ #### N/m2
Vertical reaction at D and C = 0.5 x x 1.80 = N
The body diagram for various members, including loading, B.M. And reactions are shown in fig.2
For the vertical member AD, the horizontal reaction at A is found by taking moments at D.Thus
( -ha x 1.80 ) + 14959 - #### + #### x 1.80 x 1.80 x 1/2
+ x x 1.80 x 1.80 x 1/3
-ha x 1.80 + + +
From which, ha =
Hence , hd =( 29266 + #### )x 1.80 - #### = N
79200 71280
71280
14959
18052
1986
19856
17117
84240
71280
-2 5
1/2
14959 -14959
-14
-18052
6
-4
-7
DA
-10035
AD
9325
35960
13170
0.9
14959
29266
0.9
-63
-149
18052
-7
-17 -33
21
188
50
21
5099
-5079 -10158
4020
-2680
1693
447-564
-1340
Distribution factore for AD and DA= = 2/3 = 1/3Distribution factore for AB and DC=
Fix end moments will be as under : =
Mfdc= + =
-21384 N - mMFAB=
N-m=
12
1225272 N - m
x
MFAD = +
MFAD = + 9325
+
25272
MFDA = - -
12 2
2MFDA = -
12
0.33
25272
D
DC
A
DC
AB
0.67
-10035
DA
= -10035-2133-7902=x
AD
-1129
447
-298
188
-125
0.67
9325
8039
-5079
3386
-1340
893
-564
376
-149
-63
42
-17
79200
11
2
47410.6
35960
7111.59
1693
93600
42435
84240
93600 84240
Fig 26
AB
-21384 28572
4020
-21384
28572
13170
-3093
28572
79200
0.33
18052
1495914959
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x 1.80 2=
8
Net B.M. at E = - =
x 1.80 2=
8
Net B.M. at F = - =
For vertical member AD , Simply supported B.M. At mid span
x 1.80
8+
2
3 Case 2 : Dead load and live load from out side and water pressure from inside.
In this case , water pressure having an intensity of zero at A and 9800 x 1.80 = N/m2
w = 79200 N/m2
Itensity = 29266 A E B
And = 42435 - 17640
= 24795
D F C
24795
w = 93600 N/m2
Fig 3
wL2 = #### x 1.80 2=
12
wL2 #### x 1.8
2=
12
pL2 WL Where W is the total tringular earth pressure.
12 10
24795 x 1.8 2+ 4470 x 1.8 1.8
10
pL2 WL
12 15
24795 x 1.8 2- 4470 x 1.8 1.8
15
Fixed End Moments
Member
The moment distribution carried out as per table 1 for case 1
JointMember
Distribution factore 23412
Fix end moment A A
Balance
Carry over
balance 1.8
Carry over
balance
Carry over D D
1.80
29265.82278
4368
0.9
517 -670 24795
-670 -1340 1034 517 16743
4021 2010
2010 -1552
13887
-1552 -3103
0.9
4655 -6031
25272 -7178 7419 -21384
-6031 -12063 9310 4655
138870.33 0.67 0.67 0.33 29266 18189
DC
D A 71280 71280DC DA AD AB
25272 -7178 7419 -21384 23412
DA AD 13887
The moment distribution is carrired out as illustred in table.
AB 13887
MFDA = - x =12 2
-7178 N -m
= 7419 N-m12 2
MFDA = - -
MFAD = + +
MFAD = +
Mfdc= = 25272 N - m12
At D, is acting, in addition to the pressure
considered in case 1. The various pressures
are marked in fig 3 .The vertical walls will thus
be subjected to a net latral pressure of
N/m2At the Top
N/m2at the bottom
Fix end moments will be as under : MFAB=
Similarly, free B.M. at F =
79200
N-m
-
9360037908
18052 14959
79200Free B.M. at mid point E = 32076 N-m
32076 14959 17117
Netlatralpressurediagram
N -m
37908 18052 19856 N-m
29265.8228####
4470.38
N-mNet B.M. = = 16506
imply supporetd at mid sapn
#### =
1/16 x x 1.80 2=2+
14520
1.80
42435.44
17640
1986
-21384 N - m12
x
42435.443
29265.823 29265.82
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balance
Carry over
balance
Carry over
balance
Carry over
balance
Carry over
balanceFinal moment
For horizontal slab AB, carrying UDL @ N/m2.
Vertical reactionat a and B = 0.5 x x 1.8 = N/m2
Similarly, for the Bottom slab DC carrying U.D.L.loads @ #### N/m2
Vertical reaction at D and C = 0.5 x x 1.80 = N
The body diagram for various members, including loading, B.M. And reactions are shown in fig.3
For the vertical member AD, the horizontal reaction at A is found by taking moments at D.Thus
( -ha x 1.80 ) + 13887 - #### + #### x 1.80 x 1.80 x 1/2
+ x x 1.80 x 1.80 x 2/3
-ha x 1.80 + + +
From which, ha =
Hence , hd =( 24795 + #### )x 1.80 - #### = N
2
x 1.80 2=
8
Net B.M. at E = - =
x 1.80 2=
8
Net B.M. at F = - =
For vertical member AD , Simply supported B.M. At mid span
x 1.80
8+
2
4 Case 3 : Dead load and live load on top water pressure from inside no live load on side.
in this case, it is assume that there is no latral oressure due to live load . As before .
N/m2
and the bottom slab is subjected to a load w = 79200 N/m2
Itensity = 93600 N/m2
A E B
1/3 x 12000 = N/m2
1/3 x 18000 = 6000 N/m2
4000 + 6000 h D F C
Earth pressure intensity at top = 4000 17640 w= 93600 N/ 17640
Fig 5
Earth pressure intensity at Bottom= 4000 + 6000 x 1.80 = N/m2
In addition to these, the vertical wall lslab subjectednto water pressure of intensity ZERO at top an
N/m2 at Bottom, acting from inside . The lateral pressure on vertical walls Is shown in fig 5 and 6
N/m2
14800
17640
25244
Netlatralpressurediagram
4470.379747
The top slab is subjected to a load of '=
1.80
79200
Lateral pressure due to dead load =
4000
Lateral pressure due to soil =
Net B.M. =16743
15315
Hence earth pressure at depth h is =
4368 N-m
4000 4000
2= 10947
13887= - #### =
N-m
imply supporetd at mid sapn24795.443 2+
1/16 x 4470 x 1.80
Similarly, free B.M. at F =93600
37908 N -m
37908 16743 21165
25244
Free B.M. at mid point E =79200
32076 N-m
32076 13887 18189 N-m
1/2 4470
-2856 40168.6 4828.01
23412
79200
79200 71280
93600 84240
16743 -16743 13887 -13887
6 -8
-2 -4 6 3
93600
-8 -17 13 6 Fig 4
25 -19
-19 -38 50 25
57 -74 25244
-74 -149 115 57 84240 84240
21165
223 -172
-172 -345 447 22316743
4000
1.80
14800 14800
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wL2 #### x 1.80 2=
12
wL2 #### x 1.8
2=
12
pL2 WL Where W is the total tringular earth pressure.
12 15
4000 x 1.8 2- 4470 x 1.8 1.8
15
pL2
WL 1080 - 48312 10
4000 x 1.8 2- 4470 x 1.8 1.8
10
Fixed End Moments
Member
The moment distribution carried out as per table 1 for case 1
Joint
Member
Distribution factore
Fix end moment A A
Balance
Carry over
balance 1.8
Carry over
balance
Carry over D D
balance
Carry over
balance
Carry over
balanceCarry over
balance
Carry over
balance
Final moment
For horizontal slab AB, carrying UDL @ N/m2.
Vertical reactionat a and B = 0.5 x x 1.8 = N
Similarly, for the Bottom slab DC carrying U.D.L.loads @ #### N/m2
Vertical reaction at D and C = 0.5 x x 1.80 = N
The body diagram for various members, including loading, B.M. And reactions are shown in fig.6
For the vertical member AD, the horizontal reaction at A is found by taking moments at D.Thus
( ha x 1.80 ) + 10477 - #### + 4000 x 1.80 x 1.80 x 1/2
- x x 1.80 x 1.80 x 1/3
-ha x 1.80 + + -
From which, ha =
Hence , hd =( 4470 x 1.80 )- 4000 x 1.80 - -673 =
2
x 1.80 2=
8Free B.M. at mid point E =
7920032076 N-m
1/2 4470
-2855 6480 2414
-673
79200
79200 71280
93600 84240
13332 -13332 10477 -10477
10 -11
-3 -6 8 4
93600
-11 -23 19 10 Fig 4
34 -29-29 -57 68 34
86 -103 -673
-103 -205 171 86 84240 84240
24576
308 -257
-257 -513 615 308 447013332
0.9
770 -923 0
-923 -1846 1540 770 13332
5537 2768
2768 -2310
10477 0.9
6929 -830511190
-2310 -4619
25272 -356 598 -21384
-8305 -16611 13857 6929
104770.33 0.67 0.67 0.33 4000 21599
D A 71280 71280
DC DA AD AB
79200 10477
25272 -356 598 -21384 =
The moment distribution is carrired out as illustred in table.
DC DA AD AB 10477
= -356 N -m12 2
MFDA = - +
MFDA = - x
x = 598 N-m12 2
MFAD = + -
MFAD = +
12
Mfdc= = 25272 N - m12
-2504
Fix end moments will be as under : MFAB= = -21384 N - m
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Net B.M. at E = - =
x 1.80 2=
8
Net B.M. at F = - =
For vertical member AD , Simply supported B.M. At mid span
x 1.80
8
+
2
5 Design of top slab :
Mid section
The top slab is subjected to following values of B.M. and direct force
The section will be design for maximum B.M. = N -m
for water side force
sst = = 150 N/mm2 = #### N/m3
scbc = = 7 N/mm2 = 9800 N/mm2
m = 13 for water side forcex
13 x 7 + 150
j=1-k/3 = 1 - 0.378 / 3 = J =
R=1/2xc x j x k = 0.5 x 7 x 0.87 x 0.378 = R =
= 300 mm so effective thicknesss = 250 mm
Mr = R . B .D2
= 1.155 x 1000 x 2502= > O.K.
= 872 mm2
150 x 0.874 x 250
3.14xdia2
3.14 x 16 x 164 x100 4
Spacing of Bars = x1000/Ast 201 x 1000 / 872 = 231 say = mm
mm F Bars @ mm c/c
1000 x 201 / 230 = 874 mm2
Bend half bars up near support at distance of L/5 = 1.80 / 5 = 0.40 m
0.1 x( 300 - 100 %
450 - 100
Ast = 0.24 x 300 x 10 = 729 mm2
area on each face= # mm2
3.14xdia2 3.14 x 12 x 12
4 x100 4
Spacing of Bars = 113 x 1000 / 365 = 310 say = mm
Hence Provided # mm c/c on each face
Section at supports :-
Maximum B.M.= N-m. There is direct compression of N also.
But it effect is not considered because the slab is actually reinforced both at top and bottom .
Since steel is at top sst = 190 N/mm2 concrete M 20
k = 0.324 J = 0.89 R = 1.01
190 x 0.892 x 250
Provide over all thickness
72202327 28572000
230230
= 0.24
201 mm2mm F bars A = =
Ast = BMx100/sstxjxD=28572000
using 16
Ax1000/Ast =
16
using 12 mm F bars
0.874 0.874
1.155 1.155
=
Area of distributionn steel = 0.3 -
Acual Ast provided
Hence Provided
= 0.378 K = 0.378m*c+sst
Case B.M. at ends (A)
28572
wt. of concrete
wt of water
B.M. at Center (E) Direct force (ha)
17117 2857214959
k=m*c
=13 7
18189
(i)
1047721599
23412
-673
(II)
(II)
13887
Simply supporetd at mid sapn =4000 2+
1/16 x 4470 1.80
11190 N-m=
N-m
N-m
x 2= -714.7
Net B.M. =13332 10477
= 11905 + -715
Similarly, free B.M. at F =93600
37908 N -m
37908 13332 24576
32076 10477 21599
230
mm2
310
310mm F Bars @
== 113
= 354 mm2
= =A
14959 28572
\ Ast =14959000
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Area available from the bars bentup from the middle section = / 2 = 437 mm2
354 < 436.9
6 Design of bottom slab:
The bottom slab has the following value of B.M. and direct force.
The section will be design for maximum B.M. = N -m
for water side force
sst = = 150 N/mm2 = #### N/m3
scbc = = 7 N/mm2 = 9800 N/mm2
m = 13 for water side force
x
13 x 7 + 150
j=1-k/3 = 1 - 0.378 / 3 = J =
R=1/2xc x j x k = 0.5 x 7 x 0.87 x 0.378 = R =
1000 x 1.155
230 mm so that d = mm
= 1524 mm2
150 x 0.874 x 180
3.14xdia2 3.14 x 20 x 20
4 x100 4
Spacing of Bars = x1000/Ast 314 x 1000 / 1524 = 206 say = mm
mm F Bars @ mm c/c
1000 x 314 / 200 = 1570 mm2
Bend half bars up near support at distance of L/5 = 1.80 / 5 = 0.40 m
0.1 x( 230 - 100
450 - 100Ast = 0.26 x 230 x 10 = 605 mm
2area on each face= mm
2
3.14xdia2 3.14 x 12 x 12
4 x100 4
Spacing of Bars = 113 x 1000 / 303 = 373 say = mm
Hence Provided # mm c/c on each face
Section at supports :-
Maximum B.M.= N-m. There is direct compression of N also.
But it effect is not considered because the slab is actually reinforced both at top and bottom .
Since steel is at top sst = 190 N/mm2 concrete M 20
k = 0.324 J = 0.89 R = 1.01
190 x 0.892 x 180
Area available from the bars bentup from the middle section = / 2 = 785 mm2
Additional reinforcemet required = -193 mm2
3.14xdia2 3.14 x 12 x 12
4 x100 4
Spacing of Bars = 113 x 1000 / -193 = -586 say = mm
Hence Provided # mm F Bars @ -580 mm c/c throught out the slab, at its bottom.
Provide thickness of bottom slab D=
mm2
Ax1000/Ast = -580
using 12 mm bars A = = = 113
874874
Hence these bars will serve the purpose. However, provide 8 mm dia.
Additional bars @ 200 mm c/c
Case B.M. at Center (F) B.M. at ends (D) Direct force (ha)
(i) 19856 18052 35960
(II) 21165 16743 25244
(II) 24576 13332 -2504
35960
wt. of concrete
wt of water
k=m*c
=13 7
= 0.378 K = 0.378m*c+sst
0.874 0.874
1.155 1.155
227 mmD =
180
20 200
Ast = BMx100/sstxjxD=35960000
using 20 mm bars A =
= 0.26
= = 314 mm2
200
%
303
using 12 mm bars A = = = 113
\ Ast =
18052000
= 592 mm2
18052
Acual Ast provided
\ d =35960000
=
Area of distributionn steel = 0.3 -
Hence Provided
177 mm
1570
Hence these bars will serve the purpose. However, provide 8 mm dia.
Additional bars @ 200 mm c/c
mm2
370
370
Ax1000/Ast =
mm F Bars @
35960
785
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or 56572 + 111 x 63.14 - 120 x =
m c' 13 x 1.79
n
= 28.11 N/mm2 < 190 N/mm2 O.K.
=\ c'84240
47124
47124136.86
113.14 )
Stress in steel is less than permissiable Hence section is O.K.
113.14x ( 300 - 50 -
= 1.79 7< Stress is less than permissiable
Also stress in steel t = (D-dc-n) =
N/mm2
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16 m F 460 mm c/c
12 mm F@ 200 mm C/C
16 mm F@ 310 mm C/c
300 16 mm F@
20 mm F@ 230 mm C/C
300 mm C/C
1.50
12 mm F@
310 mm C/C
16 mm F@
200 mm c/c
16 m F 12 mm F
@ 16 mm F
@
400 mm c/c 200 mm C/C 310 mm C/c
300 1.50 300
300
230
Box culverts
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Grade of co M-10 M-15 M-20 M-25 M-30 M-35 M-40
(N/mm2) Kg/m2 (N/mm2) Kg/m
2 (N/mm2) in kg/m2
M 10 3.0 300 2.5 250 -- --
M 15 5.0 500 4.0 400 0.6 60
M 20 7.0 700 5.0 500 0.8 80
M 25 8.5 850 6.0 600 0.9 90
M 30 10.0 1000 8.0 800 1.0 100
M 35 11.5 1150 9.0 900 1.1 110M 40 13.0 1300 10.0 1000 1.2 120
M 45 14.5 1450 11.0 1100 1.3 130
M 50 16.0 1600 12.0 1200 1.4 140
Grade of co M-10 M-15 M-20 M-25 M-30 M-35 M-40
Modular ra
Grade of concrete M-15 M-20 M-25 M-30 M-35 M-40
Modular Ratio 18.67 13.33 10.98 9.33 8.11 7.18 Grad
scbc N/mm2 5 7 8.5 10 11.5 13 t
m scbc 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
Table 1.15. PERMISSIBLE DIRECT TENSILE STRESS
Tensilestress 1.2 2.0 2.8 3.2 3.6 4.0 4.4
Table 1.16.. Permissible stress in concrete (IS : 456-2000)
Grade of
concrete
Permission stress in compression (N/mm2) Permissible stress in bond (Average) for
plain bars in tention (N/mm2)Bending acbc Direct (acc)
Table 1.18. MODULAR RATIO
31
(31.11)
19
(18.67)
13
(13.33)
11
(10.98)
9
(9.33)
8
(8.11)
7
(7.18)
Table 2.1. VALUES OF DESIGN CONSTANTS
(a) sst =
140
N/mm2
(Fe 250)
(b) sst =
190N/mm2
(c ) sst =
230
N/mm2
(Fe 415)
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100As 100As Degree sin cos tan
bd bd 10 0.17 0.98 0.18
0.15 0.18 0.18 0.15 11 0.19 0.98 0.19
0.16 0.18 0.19 0.18 12 0.21 0.98 0.21
0.17 0.18 0.2 0.21 13 0.23 0.97 0.23
0.18 0.19 0.21 0.24 14 0.24 0.97 0.25
0.19 0.19 0.22 0.27 15 0.26 0.97 0.27
0.2 0.19 0.23 0.3 16 0.28 0.96 0.29
0.21 0.2 0.24 0.32 17 0.29 0.96 0.31
0.22 0.2 0.25 0.35 18 0.31 0.95 0.32
0.23 0.2 0.26 0.38 19 0.33 0.95 0.340.24 0.21 0.27 0.41 20 0.34 0.94 0.36
0.25 0.21 0.28 0.44 21 0.36 0.93 0.38
0.26 0.21 0.29 0.47 22 0.37 0.93 0.40
0.27 0.22 0.30 0.5 23 0.39 0.92 0.42
0.28 0.22 0.31 0.55 24 0.41 0.92 0.45
0.29 0.22 0.32 0.6 25 0.42 0.91 0.47
0.3 0.23 0.33 0.65 30 0.50 0.87 0.58
0.31 0.23 0.34 0.7 35 0.57 0.82 0.70
0.32 0.24 0.35 0.75 40 0.64 0.77 0.84
0.33 0.24 0.36 0.82 45 0.71 0.71 1.00
0.34 0.24 0.37 0.88 50 0.77 0.64 1.19
0.35 0.25 0.38 0.94 55 0.82 0.57 1.43
0.36 0.25 0.39 1.00 60 0.87 0.50 1.73
0.37 0.25 0.4 1.08 65 0.91 0.42 2.14
0.38 0.26 0.41 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 2.130.49 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
Shear stress tc Reiforcement %
M-20 M-20
Value of angle
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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 0.320.64 0.32
0.65 0.33
0.66 0.33
0.67 0.33
0.68 0.33
0.69 0.33
0.7 0.34
0.71 0.34
0.72 0.34
0.73 0.34
0.74 0.34
0.75 0.350.76 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 0.370.89 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 0.391.01 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 0.4
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1.09 0.4
1.10 0.4
1.11 0.4
1.12 0.4
1.13 0.4
1.14 0.4
1.15 0.41.16 0.41
1.17 0.41
1.18 0.41
1.19 0.41
1.20 0.41
1.21 0.41
1.22 0.41
1.23 0.41
1.24 0.41
1.25 0.42
1.26 0.42
1.27 0.421.28 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 0.431.41 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 0.451.53 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
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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 0.461.68 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 0.471.80 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 0.481.93 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 0.492.05 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
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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 0.502.20 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 0.512.32 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 0.512.45 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 0.512.57 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
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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 0.512.72 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 0.512.84 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 0.512.97 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 0.513.09 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
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M-15 M-20 M-25 M-30 M-35 M-40
0.18 0.18 0.19 0.2 0.2 0.20.22 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
300 or more 275 250 225 200 175 150 or less
1.00 1.05 1.10 1.15 1.20 1.25 1.30
M-15 M-20 M-25 M-30 M-35 M-40
1.6 1.8 1.9 2.2 2.3 2.5
e of concre 10 15 20 25 30 35 40 45
d (N / mm -- 0.6 0.8 0.9 1 1.1 1.2 1.3
tbd (N / mm2) kd = LdF
M 15 60
M 20 45
M 25 40
M 30 36
M 35 33
M 40 30
M 45 28
M 50 26
Table 3.1. Permissible shear stress Table tc in concrete (IS : 456-2000)100As Permissible shear stress in concrete tc N/mm
2
bd
< 0.150.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00 and above
Table 3.2. Facor k
Over all depth of slab
k
Table 3.3. Maximum shear stress tc.max in concrete (IS : 456-2000)
Grade of concrete
tc.max
1.44
Table 3.4. Permissible Bond stress Table tbd in concrete (IS : 456-2000
Table 3.5. Development Length in tension
Grade of
concrete
Plain M.S. Bars H.Y.S.D. Bars
kd = LdF tbd (N / mm2)
1.92
0.6 58 0.96
0.8 44 1.28
0.9 39
2.08
1.4 25 2.24
1 35 1.6
1.1 32 1.76
1.3 27
1.2 29
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tan Degree sin cos
0.18 10 0.17 0.98
0.19 11 0.19 0.98
0.21 12 0.21 0.98
0.23 13 0.23 0.97
0.25 14 0.24 0.97
0.27 15 0.26 0.97
0.29 16 0.28 0.96
0.31 17 0.29 0.96
0.32 18 0.31 0.95
0.34 19 0.33 0.950.36 20 0.34 0.94
0.38 21 0.36 0.93
0.40 22 0.37 0.93
0.42 23 0.39 0.92
0.45 24 0.41 0.92
0.47 25 0.42 0.91
0.58 30 0.50 0.87
0.70 35 0.57 0.82
0.84 40 0.64 0.77
1.00 45 0.71 0.71
1.19 50 0.77 0.64
1.43 55 0.82 0.57
1.73 60 0.87 0.50
2.14 65 0.91 0.42
Value of angle
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23/26
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24/26
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25/26
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26/26