Box Culvert by B.C.punmia Example 30.2

DESIGN OF BOX TYPE CULVERT

1 In side diamentions 3.50 m x 3.50 m

2 Super imposed load 12000

3 Live load 45000

4 Wieght of soil 18000

5 Angle of repose 30 Degree

6 Nominal cover top / bottom 50 mm Nominal cover side 50 mm

6 Cocrete M- 20 wt. of concrete 25000

7 m 13

7 Steel 415 150 190

8 Thickess of side wall 330 mm thickness of side wall is OK

Thickness of top slab 320 mm O.K.

Thickness of bottom slab 350 mm

9 Reinforcement

Top slab Main 20 130 mm c/c

Distribution 8 130 mm c/c

At supports 8 200 mm c/c

Bottom slab Main 20 120 mm c/c


At supports 8 300 mm c/c Through out slab at bottom

Side vertical wall Vertical 20 300 mm c/c Both side O.K.


20 260 mm c/c

8 200 mm C/C

8 130 mm C/c

320

700 20

20 130 mm C/C

300 mm C/C

3.50

8

130 mm C/C

20

120 mm c/c

350

20 8 8

240 mm c/c 200 mm C/C 130 mm C/c

330 3.50 330

N/m3

N/m2

N/m2

kg/m3

scbc N/m2

Water side sst N/m2 sst N/m2

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @ mm F @ mm F @

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DESIGN OF BOX TYPE CULVERT

1 In side diamentions 3.5 x 3.5 m

2 Super imposed load 12000

3 Live load 45000

4 Wieght of soil 18000 wt. of water 9800

5 Angle of repose 30 Degree

6 Nominal cover top/bottom 50 mm Nominal cover Side 50 mm

6 Cocrete M - 20 wt. of concrete 25000

7 m 13

7 Steel Fy 415 190

150

1 Solution Genral

For the purpose of design , one metre length of the box is considered.

The analysis is done for the following cases.

(I) Live load, dead load and earth prssure acting , with no water pressure from inside.

(II) Live and dead load on top and earth pressure acting from out side, and water pressure acting from inside,

with no live load on sides

(III) Dead load and earth pressure acting from out side and water pressure from in side.

Let the thicness of Horizontal slab 330 mm = 0.33 m

Vertical wall thicness 320 mm = 0.32 m

Effective slab span 3.5 + 0.33 = 3.83 m

Effective Height of wall 3.5 + 0.32 = 3.82 m

2 Case 1 : Dead and live load from out side of while no water pressure from inside.

Self weight og top slab = 0.33 x 1 x 1 x ### = 8250

Live load and dead load = 45000 + ### = 57000

Total load on top = 65250

Weight of side wall = 3.82 x 0.32 x ### = 30560 N/m

65250 x 3.83 )+( 2 x ### )=81208.2

3.83

Ka =1 - sin 30

=1 - 0.5

=0.5

=1

= 0.331 + sin 30 1 + 0.5 1.5 3

p = ### x 0.333 = 19000

Latral pressure due to soil Ka x w x h = 0.333 x ### h = 6000 h

Hence total pressure = ### + 6000 h

Latral presure intencity at top = 19000

Latral pressure intencity at bottom = ### + 6000 x 3.82 = 41920

w = 65250

19000 19000

A E B

h 3.83

19000 3.82

6000 h

D F C

41920 19000 22920

w = 81208

Fig 1

N/m3

N/m2

N/m2 N/m3

N/m3

scbc N/m2

Out side sst N/m2

water side side sst N/m2

N/m2

N/m2

N/m2

\ Upward soil reaction at base = (N/m2

\ Latral pressure due to dead load and live load = Pv x Ka

N/m2

N/m2

N/m2

Fig 1 show the box culvert frame ABCD, along with the external loads, Due to symmetry, half of frame (i.e. AEFD) of box culvert is considered for moment distribution. Since all the members have uniform thickness, and uniform diamentions, the relative stiffness K for AD will be equal to 1 while the relative stiffness for AE and DF will be 1/2.

N/m2

N/m2

1= 2/3

1/2= 1/3

1+1/2 1+1/2

Fix end moments will be as under : =### x 3.82

-79346 N - m12 12

+ =### x 3.82

98751.9 N - m12 12

+ +WL Where W is the total tringular earth pressure.

12 15

+19000 x 3.82 ### x 3.82

x3.82

= 34254 N-m12 2 15

- -WL

12 15

-19000 x 3.82 ### x 3.82

x3.82

= -23105 -16723 = -3982812 2 10

The Moment distribution is carried out as illustrate in table

Fixed End MomentsMember DC DA AD AB 55075 65250 55075

98751.91 -39828 34254 -79346 46852

Joint D A 124627.5 124627.5

Member DC DA AD AB 4685255075

Distribution factore 0.33 0.67 0.67 0.33 19000 64569

Fix end moment 98751.91 -39828 34254 -79346 A A

Balance -19641 -39283 30061 15031 55075 1.91

Carry over 15031 -196417197

balance -5010 -10020 13094 6547 3.82 m

Carry over 6547 -5010

balance -2182 -4365 3340 1670 71023 1.91

Carry over 1670 -2182 22920 D D

balance -557 -1113 1455 727 41920 6981071023

77881

Carry over 727 -557

balance -242 -485 371 186 155514 155514

Carry over 186 -242 69810

balance -62 -124 162 81

Carry over 81 -62 81208

balance -27 -54 41 21 Fig 2

Carry over 21 -27

balance -7 -14 18 9

Final moment 71023 -71023 55075 -55075

For horizontal slab AB, carrying UDL @ 65250

Vertical reactionat a and B = 0.5 x 65250 x 3.82 = 124628 N/m2

Similarly, for the Bottom slab DC carrying U.D.L.loads @ ###

Vertical reaction at D and C = 0.5 x 81208.22 x 3.83 = 155514 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 3.83 ) + 55075 - ### + ### x 3.83 x 3.83 x 1/2

+ 1/2 x 22920 x 3.83 x 3.83 x 1/3

-ha x 3.83 + -15948 + 139355 + 56035.2

From which, ha = 46852

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Distribution factore for AD and DA= Distribution factore for AB and DC=

MFAB=wL2 2=

Mfdc=wL2 2=

MFAD =pL2

MFAD =2+

MFDA =pL2

MFDA =2--

The moment distribution carried out as per table 1 for case 1

N/m2.

N/m2


Hence , hd =( 19000 + ### )x 3.83 - ### = 69810 N

2

Free B.M. at mid point E =65250 x 3.83

119644 N-m8

Net B.M. at E = 119644 - 55075 = 64569 N-m

Similarly, free B.M. at F =81208.2245 x 3.83

148904 N -m8

Net B.M. at F = 148904.416 - 71023 = 77881 N-m

For vertical member AD , Simply supported B.M. At mid span

Simply supporetd at mid sapn =19000 x 3.83

1/16 x ### x 3.83 558528

Net B.M. =71023 + 55075

= 63049 - ### = 7197 N-m2

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 3.82 = 37436

w = 65250

19000 19000 19000

Itensity = 19000 A E B 14516

Net

latr

al p

ress

ure

diag

ram

And = 41920 - 37436

= 4484 3.83

3.82

D F C

41920 41920 4484

w = 81208

Fig 3

Fix end moments will be as under := ### x 3.83

-79762 N - m12 12

=### x 3.83

99269.6 N - m12 12

+ +WL Where W is the total tringular earth pressure.

12 10

+4484 x 3.83 ### x 3.83

x3.83

= 16128 N-m12 2 10

- -WL

12 15

-4484 x 3.83 ### x 3.83

x3.83

= -12579 N -m12 2 15

The moment distribution is carrired out as illustred in table.


99269.61 -12579 16128 -79762 23451

Joint D A 124627.5 124627.5

Member DC DA AD AB45069

Distribution factore 0.33 0.67 0.67 0.33 19000 23451 73951

Fix end moment 99269.61 -12579 16128 -79762 A A

Balance -28897 -57794 42423 21211 45069 1.91

Carry over 21211 -2889730523

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2=

2=

2+2=

N/m2

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/m2

N/m2 At the Top

N/m2 at the bottom

N/m2

MFAB=wL2 2=

Mfdc=wL2 2=

MFAD =pL2

MFAD =2+

MFDA =pL2

MFDA =2-



balance -7070 -14141 19265 9632 3.8230523


balance -3211 -6422 4714 2357 58813 1.91

Carry over 2357 -3211 4484 D D

balance -786 -1571 2141 1070 2140458813

89315


balance -357 -714 524 262 155108 155108

Carry over 262 -357 21404

balance -87 -175 238 119

Carry over 119 -87 81208

balance -40 -79 58 29 Fig 4

Carry over 29 -40

balance -10 -19 26 13

Final moment 58813 -58813 45069 -45069


Vertical reactionat a and B = 0.5 x 65250 x 3.82 = 124628 N/m2


Vertical reaction at D and C = 0.5 x 81208 x 3.82 = 155108 N



( -ha x 3.82 ) + 45069 - ### + 4484 x 3.82 x 3.82 x 1/2

+ 1/2 x 14516 x 3.82 x 3.82 x 2/3

-ha x 3.82 + -13744 + 32716.16 + 70607.8


Hence , hd =( 4484 + ### )x 3.82 - ### = 21404 N

2


119020 N-m8

Net B.M. at E = 119020 - 45069 = 73951 N-m

Similarly, free B.M. at F =81208 x 3.82

148128 N -m8

Net B.M. at F = 148127.862 - 58813 = 89315 N-m



1/16 x ### x 3.82 214188

Net B.M. =58813 + 45069

= 51941 - ### = 30523 N-m2

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 .

The top slab is subjected to a load of '= 65250

and the bottom slab is subjected to a load w = 65250

Itensity = 81208 4000 4000

Net

latr

al p

ress

ure

diag

ram

Lateral pressure due to dead load = A E B 4000

1/3 x 12000 = 4000

Lateral pressure due to soil = 3.83

1/3 x 18000 = 6000 3.82

Hence earth pressure at depth h is =

4000 + 6000 h D F C

26920 26920 14516

N/m2.

N/m2

2=

2=

2+2=

N/m2

N/m2

N/m2

N/m2

N/m2

Earth pressure intensity at top = 4000 37436 w= 81208 37436

Fig 5

Earth pressure intensity at Bottom= 4000 + 6000 x 3.82 = 26920

In addition to these, the vertical wall lslab subjectednto water pressure of intensity ZERO at top and 37436

N/m2 at Bottom, acting from inside . The lateral pressure on vertical walls Is shown in fig 5 and 6

Fix end moments will be as under : =### x 3.83

-79762 N - m12 12

=### x 3.83

99269.6 N - m12 12

+ -WL Where W is the total tringular earth pressure.

12 15

+4000 x 3.83 ### x 3.83

x3.83

= -2209 N-m12 2 15

- +WL 4890 - 7098

12 10

-4000 x 3.83 ### x 3.83

x3.83

= 5757 N -m12 2 10

The moment distribution is carrired out as illustred in table.


99269.61 5757 -2209 -79762 =

Joint D A 124627.5 124627.5

Member DC DA AD AB35902

Distribution factore 0.33 0.67 0.67 0.33 4000 83742

Fix end moment 99269.61 5757 -2209 -79762 A A

Balance -35009 -70018 54647 27324 35902 1.91

Carry over 27324 -3500948748

balance -9108 -18216 23339 11670 3.82


balance -3890 -7780 6072 3036 49646 1.91

Carry over 3036 -3890 0 D D

balance -1012 -2024 2593 1297 1451649646

99258


balance -432 -864 675 337 155108 155108

Carry over 337 -432 5200

balance -112 -225 288 144

Carry over 144 -112 81208

balance -48 -96 75 37 Fig 4

Carry over 37 -48

balance -12 -25 32 16

Final moment 49646 -49646 35902 -35902


Vertical reactionat a and B = 0.5 x 65250 x 3.82 = 124628 N


Vertical reaction at D and C = 0.5 x 81208 x 3.82 = 155108 N



( ha x 3.82 ) + 35902 - ### + 4000 x 3.82 x 3.82 x 1/2

N/m2 N/m2

N/m2

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MFAB=wL2 2=

Mfdc=wL2 2=

MFAD =pL2

MFAD =2-

MFDA =pL2

MFDA =2-


N/m2.

N/m2


- 1/2 x 14516 x 3.82 x 3.82 x 1/3

-ha x 3.82 + -13744 + 29184.8 - 35304


Hence , hd =( 14516 x 3.82 )- 4000 x 3.82 - 5200 = 7245.6

2


119644 N-m8

Net B.M. at E = 119644 - 35902 = 83742 N-m

Similarly, free B.M. at F =81208 x 3.83

148904 N -m8

Net B.M. at F = 148904.416 - 49646 = 99258 N-m



1/16 x ### x 3.83 5973.98

Net B.M. =49646 + 35902

= 42774 + 5974 = 48748 N-m2

5 Design of top slab :

Mid section

The top slab is subjected to following values of B.M. and direct force

Case B.M. at Center (E) B.M. at ends (A) Direct force (ha)

(i) 64569 55075 46852

(II) 73951 45069 23451

(II) 83742 35902 5200

The section will be design for maximum B.M. = 83742 N -m

for water side force

= 150 wt. of concrete = ###

= 7 wt of water = 9800

m = 13 for water side force

m*c=

13 x 7= 0.378 K = 0.378

13 x 7 + 150

= 1 - 0.378 / 3 = 0.874 J = 0.874

= 0.5 x 7 x 0.87 x 0.378 = 1.155 R = 1.155

Provide over all thickness = 320 mm so effective thicknesss = 270 mm

= 1.155 x 1000 x 270 84216794 > 83742000 O.K.

Ast =83742000 = 2365

150 x 0.874 x 270

using ### A = =3.14 x 20 x 20

= 3144 x100 4

Spacing of Bars =Ax1000/Ast 314 x 1000 / 2365 = 133 say = 130 mm

Hence Provided 20 130 mm c/c

Acual Ast provided 1000 x 314 / 130 = 2415

Bend half bars up near support at distance of L/5 = 3.83 / 5 = 0.80 m

Area of distributionn steel = 0.3 -0.1 x( 320 - 100

= 0.24%

450 - 100

= 0.24 x 320 x 10 = 759 ###

using 8 A = =3.14 x 8 x 8

= 504 x100 4

Spacing of Bars = Ax1000/Ast = 50 x 1000 / 380 = 132 say = 130 mm

Hence Provided 8 130 mm c/c on each face

2=

2=

2+2=

sst = N/mm2 N/m3

scbc = N/mm2 N/mm2

k=m*c+sst

j=1-k/3

R=1/2xc x j x k

Mr = R . B .D2 2=

BMx100/sstxjxD=mm2

mm F bars 3.14xdia2

mm2

mm F Bars @

mm2

Ast mm2 area on each face= mm2

mm F bars 3.14xdia2

mm2

mm F Bars @

Section at supports :-

Maximum B.M.= 55075 N-m. There is direct compression of 46852 N also.

But it effect is not considered because the slab is actually reinforced both at top and bottom .

Since steel is at top = 190 concrete M 20

k = 0.3238 J = 0.892 R = 1.011

=55075000

= 1204190 x 0.892 x 270

Area available from the bars bentup from the middle section = 2415 / 2 = 1208

1204 < 1208

6 Design of bottom slab:

The bottom slab has the following value of B.M. and direct force.

Case B.M. at Center (F) B.M. at ends (D) Direct force (ha)

(i) 77881 71023 69810

(II) 89315 58813 21404

(II) 99258 49646 7246

The section will be design for maximum B.M. = 99258 N -m

for water side force

= 150 wt. of concrete = ###

= 7 wt of water = 9800

m = 13 for water side force

m*c=

13 x 7= 0.378 K = 0.378

13 x 7 + 150

= 1 - 0.378 / 3 = 0.874 J = 0.874

= 0.5 x 7 x 0.87 x 0.378 = 1.155 R = 1.155

=99258416

= 294 mm D = 344 mm1000 x 1.155

Provide thickness of bottom slab D= 350 mm so that d = 300 mm

Ast =99258416 = 2523

150 x 0.874 x 300

using ### mm bars A = =3.14 x 20 x 20

= 3144 x100 4

Spacing of Bars =Ax1000/Ast 314 x 1000 / 2523 = 124 say = 120 mm

Hence Provided 20 120 mm c/c

Acual Ast provided 1000 x 314 / 120 = 2617

Bend half bars up near support at distance of L/5 = 3.83 / 5 = 0.80 m

Area of distributionn steel = 0.3 -0.1 x( 350 - 100

= 0.23 %450 - 100

= 0.23 x 350 x 10 = 800 400

using 8 mm bars A = =3.14 x 8 x 8

= 504 x100 4


Hence Provided 8 120 mm c/c on each face

Section at supports :-

Maximum B.M.= 71023 N-m. There is direct compression of 69810 N also.

But it effect is not considered because the slab is actually reinforced both at top and bottom .

Since steel is at top = 190 concrete M 20

k = 0.3238 J = 0.892 R = 1.011

=71023000

= 1397

sst N/mm2

\ Ast mm2

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mm2

Hence these bars will serve the purpose. However, provide 8 mm dia. Additional bars @ 200 mm c/c

sst = N/mm2 N/m3

scbc = N/mm2 N/mm2

k=m*c+sst

j=1-k/3

R=1/2xc x j x k

\ d

BMx100/sstxjxD=mm2

3.14xdia2

mm2

mm F Bars @

mm2

Ast mm2 area on each face= mm2

3.14xdia2

mm2

mm F Bars @

sst N/mm2

\ Ast mm2


=190 x 0.892 x 300

= 1397

Area available from the bars bentup from the middle section = 2617 / 2 = 1308

1397 > 1308 Fail , hence additional reinforcement will provided.

Additional reinforcemet required = 88.67

using 8 mm bars A = =3.14 x 8 x 8

= 504 x100 4


Hence Provided 8 300 mm c/c throught out the slab, at its bottom.

7 Design of side wall:

The side wall has the following value of B.M. and direct force.

Case B.M. at Center (F) B.M. at ends (D) Direct force (ha)

(i) 7197 71023 155514

(II) 30523 58813 155108

(II) 48748 49646 155108

The section will be design for maximum B.M. = 71023 N -m, and direct force = 155514 N

Eccentricity =71023 x 1000

= 457 mm155514

proposed thickness of side wall '= 330 mm \ e / D 457 / 330 = 1.38 < 1.5 OK

thickness of side wall is OK

Let us reinforce the section with 20 300 mm c/c provided on both faces, as shown

in fig xxx . With cover of 50 mm and D = 330 mm

Asc = Ast =1000

x3.14 x 20 x 20

= 1047300 4

The depth of N.A. is computed from following expression:

n

3 3 n= e +

D- dt

b n + (m -1) Asc n - dc- m Ast

D - dt - n 2

n n

or

1000 n330 - 50 -

n+ 12 x

1047x n - 50 x -100

2 3 n

1000 n+12 x

1047x n - 50 - 13 x

1047x 330 - 50 - n

2 n n

500 n 280 -n

+ n - 50 x-1E+06

3 n= 457 + 115

500 n+12560

x n - 50 -###

x 280 - nn n

140000 n - 167 + -1256000 --62800000

n= 572

500 n + 12560 -628000

-3809867

+ ###n n

multiply by n

140000 n2 - 167 n3 + -1256000 n - -62800000= 572

500 n2 + 12560 n- 628000 - 3809867 + ### n

140000 n2 - 167 n3 + -1256000 n - -62800000= 0

\ Ast mm2

mm2

mm2

3.14xdia2

mm2

mm F Bars @

mm F bars @

mm2

b n D - dt - + (m - 1)Asc 1 (n - dc)(D - dt- dc)

n2

286000 n2 + 14967333 n - 2538459733= 0

-146000 n2 - 13711333 n - -2475659733 = 167

-876 n2 + 82268 n - 14853958 =

Solwing this trial and error we get, n = 91.47 mm

( 500 x 91.47 +12 x 1047

( 91.47 - 50 ) -13 x 1047

91.47 91.47

x ( 330 - 50 - 91.47 )

or 45734 + 137.3 x 41.47 - 149 x 188.53 = 23383

=155514

= 6.65 < 7 Stress is less than permissiable 23383

Also stress in steel t =m c'

(D-dc-n) =13 x 6.65

x ( 330 - 50 - 91.47 )n 91.47

= 178.2 N/mm2 < 190 N/mm2 O.K.

Stress in steel is less than permissiable Hence section is O.K.

n3

n3

\ c'

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\ c' N/mm2


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Box culverts

20 260 mm c/c

8 200 mm C/C

8 130 mm C/c

320

700 20

20 130 mm C/C

300 mm C/C

3.50

8

130 mm C/C

20

120 mm c/c

350

20 8 8

240 mm c/c 200 mm C/C 130 mm C/c

330 3.50 330

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @

mm F @ mm F @ mm F @

Grade of co M-10 M-15 M-20 M-25 M-30 M-35 M-40

1.2 2.0 2.8 3.2 3.6 4.0 4.4

(N/mm2) (N/mm2) (N/mm2)M 10 3.0 300 2.5 250 -- --M 15 5.0 500 4.0 400 0.6 60M 20 7.0 700 5.0 500 0.8 80M 25 8.5 850 6.0 600 0.9 90M 30 10.0 1000 8.0 800 1.0 100M 35 11.5 1150 9.0 900 1.1 110M 40 13.0 1300 10.0 1000 1.2 120M 45 14.5 1450 11.0 1100 1.3 130M 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-40Modular 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 Grade of concrete M

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

0.867 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

0.329 0.329 0.329 0.329 0.329 0.329

0.89 0.89 0.89 0.89 0.89 0.89

0.732 1.025 1.244 1.464 1.684 1.903

0.433 0.606 0.736 0.866 0.997 1.127

0.289 0.289 0.289 0.289 0.289 0.289

0.904 0.904 0.904 0.904 0.904 0.904

0.653 0.914 1.11 1.306 1.502 1.698

0.314 0.44 0.534 0.628 0.722 0.816

Table 1.15. PERMISSIBLE DIRECT TENSILE STRESS

Tensile stress N/mm2

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)

Kg/m2 Kg/m2 in kg/m2

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

scbc N/mm2 tbd (N / mm2)

m scbc

(a) sst = 140

N/mm2 (Fe 250)

kc

jc

Rc

Pc (%)

(b) sst = 190

N/mm2

kc

jc

Rc

Pc (%)

(c ) sst = 230 N/mm2 (Fe 415)

kc

jc

Rc

Pc (%)

Reiforcement % Value of angle

M-20 M-20Degree sin cos tan

bd bd 10 0.17 0.98 0.180.15 0.18 0.18 0.15 11 0.19 0.98 0.190.16 0.18 0.19 0.18 12 0.21 0.98 0.210.17 0.18 0.2 0.21 13 0.23 0.97 0.230.18 0.19 0.21 0.24 14 0.24 0.97 0.250.19 0.19 0.22 0.27 15 0.26 0.97 0.270.2 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 0.310.22 0.2 0.25 0.35 18 0.31 0.95 0.320.23 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 0.360.25 0.21 0.28 0.44 21 0.36 0.93 0.380.26 0.21 0.29 0.47 22 0.37 0.93 0.400.27 0.22 0.30 0.5 23 0.39 0.92 0.420.28 0.22 0.31 0.55 24 0.41 0.92 0.450.29 0.22 0.32 0.6 25 0.42 0.91 0.470.3 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 0.700.32 0.24 0.35 0.75 40 0.64 0.77 0.840.33 0.24 0.36 0.82 45 0.71 0.71 1.000.34 0.24 0.37 0.88 50 0.77 0.64 1.190.35 0.25 0.38 0.94 55 0.82 0.57 1.430.36 0.25 0.39 1.00 60 0.87 0.50 1.730.37 0.25 0.4 1.08 65 0.91 0.42 2.140.38 0.26 0.41 1.160.39 0.26 0.42 1.250.4 0.26 0.43 1.33

0.41 0.27 0.44 1.410.42 0.27 0.45 1.500.43 0.27 0.46 1.630.44 0.28 0.46 1.640.45 0.28 0.47 1.750.46 0.28 0.48 1.880.47 0.29 0.49 2.000.48 0.29 0.50 2.130.49 0.29 0.51 2.250.5 0.30

0.51 0.300.52 0.300.53 0.300.54 0.300.55 0.310.56 0.310.57 0.310.58 0.310.59 0.310.6 0.32

Shear stress tc

100A s 100A s

0.61 0.320.62 0.320.63 0.320.64 0.320.65 0.330.66 0.330.67 0.330.68 0.330.69 0.330.7 0.34

0.71 0.340.72 0.340.73 0.340.74 0.340.75 0.350.76 0.350.77 0.350.78 0.350.79 0.350.8 0.35

0.81 0.350.82 0.360.83 0.360.84 0.360.85 0.360.86 0.360.87 0.360.88 0.370.89 0.370.9 0.37

0.91 0.370.92 0.370.93 0.370.94 0.380.95 0.380.96 0.380.97 0.380.98 0.380.99 0.381.00 0.391.01 0.391.02 0.391.03 0.391.04 0.391.05 0.391.06 0.391.07 0.391.08 0.41.09 0.41.10 0.41.11 0.41.12 0.41.13 0.41.14 0.4

1.15 0.41.16 0.411.17 0.411.18 0.411.19 0.411.20 0.411.21 0.411.22 0.411.23 0.411.24 0.411.25 0.421.26 0.421.27 0.421.28 0.421.29 0.421.30 0.421.31 0.421.32 0.421.33 0.431.34 0.431.35 0.431.36 0.431.37 0.431.38 0.431.39 0.431.40 0.431.41 0.441.42 0.441.43 0.441.44 0.441.45 0.441.46 0.441.47 0.441.48 0.441.49 0.441.50 0.451.51 0.451.52 0.451.53 0.451.54 0.451.55 0.451.56 0.451.57 0.451.58 0.451.59 0.451.60 0.451.61 0.451.62 0.451.63 0.461.64 0.461.65 0.461.66 0.461.67 0.461.68 0.46

1.69 0.461.70 0.461.71 0.461.72 0.461.73 0.461.74 0.461.75 0.471.76 0.471.77 0.471.78 0.471.79 0.471.80 0.471.81 0.471.82 0.471.83 0.471.84 0.471.85 0.471.86 0.471.87 0.471.88 0.481.89 0.481.90 0.481.91 0.481.92 0.481.93 0.481.94 0.481.95 0.481.96 0.481.97 0.481.98 0.481.99 0.482.00 0.492.01 0.492.02 0.492.03 0.492.04 0.492.05 0.492.06 0.492.07 0.492.08 0.492.09 0.492.10 0.492.11 0.492.12 0.492.13 0.502.14 0.502.15 0.502.16 0.502.17 0.502.18 0.502.19 0.502.20 0.502.21 0.502.22 0.50

2.23 0.502.24 0.502.25 0.512.26 0.512.27 0.512.28 0.512.29 0.512.30 0.512.31 0.512.32 0.512.33 0.512.34 0.512.35 0.512.36 0.512.37 0.512.38 0.512.39 0.512.40 0.512.41 0.512.42 0.512.43 0.512.44 0.512.45 0.512.46 0.512.47 0.512.48 0.512.49 0.512.50 0.512.51 0.512.52 0.512.53 0.512.54 0.512.55 0.512.56 0.512.57 0.512.58 0.512.59 0.512.60 0.512.61 0.512.62 0.512.63 0.512.64 0.512.65 0.512.66 0.512.67 0.512.68 0.512.69 0.512.70 0.512.71 0.512.72 0.512.73 0.512.74 0.512.75 0.512.76 0.51

2.77 0.512.78 0.512.79 0.512.80 0.512.81 0.512.82 0.512.83 0.512.84 0.512.85 0.512.86 0.512.87 0.512.88 0.512.89 0.512.90 0.512.91 0.512.92 0.512.93 0.512.94 0.512.95 0.512.96 0.512.97 0.512.98 0.512.99 0.513.00 0.513.01 0.513.02 0.513.03 0.513.04 0.513.05 0.513.06 0.513.07 0.513.08 0.513.09 0.513.10 0.513.11 0.513.12 0.513.13 0.513.14 0.513.15 0.51

bd M-15 M-20 M-25 M-30 M-35 M-400.18 0.18 0.19 0.2 0.2 0.2

0.25 0.22 0.22 0.23 0.23 0.23 0.230.50 0.29 0.30 0.31 0.31 0.31 0.32

0.75 0.34 0.35 0.36 0.37 0.37 0.38

1.00 0.37 0.39 0.40 0.41 0.42 0.42

1.25 0.40 0.42 0.44 0.45 0.45 0.46

1.50 0.42 0.45 0.46 0.48 0.49 0.491.75 0.44 0.47 0.49 0.50 0.52 0.522.00 0.44 0.49 0.51 0.53 0.54 0.552.25 0.44 0.51 0.53 0.55 0.56 0.572.50 0.44 0.51 0.55 0.57 0.58 0.602.75 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

Over all depth of slab 300 or more 275 250 225 200 175 150 or less

k 1.00 1.05 1.10 1.15 1.20 1.25 1.30

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

Grade of concrete M10 15 20 25 30 35 40 45

-- 0.6 0.8 0.9 1 1.1 1.2 1.3

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

M 15 0.6 58 0.96 60

M 20 0.8 44 1.28 45

M 25 0.9 39 1.44 40

M 30 1 35 1.6 36

M 35 1.1 32 1.76 33

M 40 1.2 29 1.92 30

M 45 1.3 27 2.08 28

M 50 1.4 25 2.24 26

Table 3.1. Permissible shear stress Table tc in concrete (IS : 456-2000)100A s Permissible shear stress in concrete tc N/mm2

< 0.15

Table 3.2. Facor k

Table 3.3. Maximum shear stress tc.max in concrete (IS : 456-2000)

tc.max

Table 3.4. Permissible Bond stress Table tbd in concrete (IS : 456-2000)

tbd (N / mm2)

Table 3.5. Development Length in tension

Grade of concrete tbd (N / mm2) kd = Ld F tbd (N / mm2) kd = Ld F

Value of angle

tan Degree sin cos 0.18 10 0.17 0.980.19 11 0.19 0.980.21 12 0.21 0.980.23 13 0.23 0.970.25 14 0.24 0.970.27 15 0.26 0.970.29 16 0.28 0.960.31 17 0.29 0.960.32 18 0.31 0.950.34 19 0.33 0.950.36 20 0.34 0.940.38 21 0.36 0.930.40 22 0.37 0.930.42 23 0.39 0.920.45 24 0.41 0.920.47 25 0.42 0.910.58 30 0.50 0.870.70 35 0.57 0.820.84 40 0.64 0.771.00 45 0.71 0.711.19 50 0.77 0.641.43 55 0.82 0.571.73 60 0.87 0.502.14 65 0.91 0.42

150 or less

50

1.4

in concrete (IS : 456-2000)

Box Culvert by B.C.punmia Example 30.2

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