DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.

55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:

M/S MJ CONSULTANCY
1 In side diamentions 4 x 4.555 m
2 Super imposed load 12000 N/m3
3 Live load 150000 N/m2
4 Wieght of soil 18000 N/m2 wt. of water 9800 N/m3
5 Angle of repose 30 Degree
6 Nominal cover top/bottom 50 mm Nominal cover Side 50 mm
6 Cocrete M- 25 wt. of concrete 25000 N/m3
scbc 7 N/m2 m 13
7 Steel Fy 500 Out side sst 230 N/m2
water side side sst 150 N/m2
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 580 mm = 0.58 m

Vertical wall thicness 580 mm = 0.58 m
Effective slab span 4 + 0.58 = 4.58 m
Effective Height of wall 4.555 + 0.58 = 5.135 m

2 Case 1 : Dead and live load from out side of while no water pressure from inside.
Self weight og top slab = 0.58 x 1 x 1 x 25000 = 14500 N/m2
Live load and dead load = 2E+05 + 12000 = 162000 N/m2
Total load on top = 176500 N/m2
Weight of side wall = 5.135 x 0.58 x 25000 = 74457.5 N/m
\ Upward soil reaction at base = ( 2E+05 x 4.58 )+( 2 x 74458 )=
209014.2 N/m2
4.58

Ka =
1 - sin 30
=
1 - 0.5
=
0.5 = 1
= 0.333
1 + sin 30 1 + 0.5 1.5 3
\ Latral pressure due to dead load and live load = Pv x Ka
p = 162000 x 0.3333 = 54000 N/m2
Latral pressure due to soil Ka x w x h = 0.3333 x 18000 h= 6000 h
Hence total pressure = 54000 + 6000 h
Latral presure intencity at top = 54000 N/m2
Latral pressure intencity at bottom = 54000 + 6000 x 5.135 = 84810 N/m2
Fig 1 show the box culvert w= 176500 N/m2

frame ABC D, along with the 54000 54000

external loads, Due to symmetry, A E B
half of frame (i.e. AEFD ) of box
culvert is considered for moment h 4.58
distribution. Since all the members
54000 5.14
have uniform thickness, and uniform
diamentions, the relative stiffness 6000 h
K for AD will be equal to 1 while the D F C
relative stiffness for AE and DF will 84810 54000 30810
be 1/2. w = 209014 N/m2
Fig 1

1 1/2
Distribution factore for AD and DA= = 2/3 Distribution factore for AB and DC= = 1/3
1+1/2 1+1/2

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 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
2 2
M/S MJ CONSULTANCY
wL 176500 x 5.135 =
Fix end moments will be as under : MFAB= = -387833 N-m
12 12

Mfdc= +
wL2
=
209014 x 5.135 2= 459277.8 N - m
12 12

MFAD = + pL2 WL Where W is the total tringular earth pressure.

+
12 15

MFAD = +
54000 x 5.135 2
+ 30810 x 5.135
x
5.135 = 145738 N-m
12 2 15
2
pL WL
MFDA = - -
12 15

MFDA = -
54000 x 5.135 2-
- 30810 x 5.135
x
5.135 = -118657 -40620 = -159277
12 2 10
The Moment distribution is carried out as illustrate in table
Fixed End Moments
Member DC DA AD AB 259567 176500 259567
459277.8 -159277 145738 -387833 134740

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

Joint D A 453163.75 453163.75

Member DC DA AD AB 134740
259567
Distribution factore 0.33 0.67 0.67 0.33 54000 203225

Fix end moment 459277.8 -159277 145738 -387833 A A

Balance -100000 -200000 161396 80698 259567 2.5675

Carry over 80698 -100000

106069
balance -26899 -53799 66667 33333 5.135 m
Carry over 33333 -26899
balance -11111 -22222 17933 8966 316538 2.5675

Carry over 8966 -11111 30810 D D

balance -2989 -5978 7407 3704 84810 183135 231508
316538
Carry over 3704 -2989
balance -1235 -2469 1993 996 478643 478643

Carry over 996 -1235 183135

balance -332 -664 823 412

Carry over 412 -332 209014

balance -137 -274 221 111 Fig 2

Carry over 111 -137
balance -37 -74 91 46
Final moment 316538 -316538 259567 -259567

For horizontal slab AB, carrying UDL @ 176500 N/m2.

Vertical reactionat a and B = 0.5 x 176500 x 5.135 = 453163.8 N/m2
Similarly, for the Bottom slab DC carrying U.D.L.loads @ 209014 N/m2
Vertical reaction at D and C = 0.5 x 209014.19 x 4.58 = 478642.5 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 4.58 ) + ##### - 316538 + 54000 x 4.58 x 4.58 x 1/2
+ 1/2 x 30810 x 4.58 x 4.58 x 1/3
-ha x 4.58 + -56971 + 566362.8 + 107713.8
From which, ha = 134740
Hence , hd =( 54000 + 84810 )x 4.58 - 134740 = 183135 N
2
176500 2
x 4.58 =
Free B.M. at mid point E = 462792 N-m
8
Net B.M. at E = 462792 - 259567 = 203225 N-m
209014.192 2
x 4.58 =
Similarly, free B.M. at F = 548045.7 N -m
8

2/8
 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY
Net B.M. at F = 548045.663 - 316538 = 231508 N-m
For vertical member AD , Simply supported B.M. At mid span
54000 x 4.58 2+
Simply supporetd at mid sapn = 1/16 x 30810 x 4.58 2= 181983
8
316538 + 259567
Net B.M. = = 288053 - 181983 = 106069 N-m
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 5.14 = 50323 N/m2
At D, is acting, in addition to the pressure
considered in case 1. The various pressures are
w= 176500 N/m2
marked in fig 3 .The vertical walls will thus be
subjected to a net latral pressure of 54000 54000 54000
Itensity = 54000 N/m2 At the Top 19513

Net latral pressure diagram

A E B
And = 84810 - 50323
= 34487 N/m2 at the bottom 4.58
5.14

D F C
84810 84810 34487
w = 209014 N/m2
Fig 3
2
wL = 176500 x 4.58 2=
Fix end moments will be as under : MFAB= -308528 N-m
12 12

Mfdc= wL
=
2
209014 x 4.58 = 365363.8 N - m
2

12 12

MFAD = + pL2 WL Where W is the total tringular earth pressure.

+
12 10

MFAD = +
34487 x 4.58 2
+ 19513 x 4.58
x
4.58 = 80751 N-m
12 2 10
MFDA = - pL2 WL
-
12 15

MFDA = -
34487 x 4.58 2- 19513 x 4.58
x
4.58 = -73928 N -m
12 2 15
The moment distribution is carrired out as illustred in table.
Fixed End Moments
Member DC DA AD AB 186701 176500 186701
365363.8 -73928 80751 -308528 113976

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

Joint D A 453163.75 453163.75

Member DC DA AD AB
186701
Distribution factore 0.33 0.67 0.67 0.33 54000 113976 395048

Fix end moment 365363.8 -73928 80751 -308528 A A

Balance -97145 -194290 151851 75926 186701 2.5675

Carry over 75926 -97145

61335
balance -25309 -50617 64763 32382 5.135
Carry over 32382 -25309
balance -10794 -21588 16872 8436 227625 2.5675

Carry over 8436 -10794 34487 D D

balance -2812 -5624 7196 3598 113215 461292
227625
Carry over 3598 -2812
balance -1199 -2399 1875 937 536644 536644

Carry over 937 -1199 113215

balance -312 -625 800 400

Carry over 400 -312 209014

balance -133 -267 208 104 Fig 4

Carry over 104 -133
balance -35 -69 89 44
Final moment 227625 -227625 186701 -186701

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 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY

For horizontal slab AB, carrying UDL @ 176500 N/m2.

Vertical reactionat a and B = 0.5 x 176500 x 5.135 = 453163.8 N/m2
Similarly, for the Bottom slab DC carrying U.D.L.loads @ 209014 N/m2
Vertical reaction at D and C = 0.5 x 209014 x 5.14 = 536643.9 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 5.14 ) + ##### - 227625 + 34487 x 5.14 x 5.14 x 1/2
+ 1/2 x 19513 x 5.14 x 5.14 x 2/3
-ha x 5.14 + -40924 + 454680.5 + 171507.7
From which, ha = 113976
Hence , hd =( 34487 + 54000 )x 5.14 - 113976 = 113215 N
2
176500 x 5.14 2=
Free B.M. at mid point E = 581749 N-m
8
Net B.M. at E = 581749 - 186701 = 395048 N-m
209014 x 5.14 2=
Similarly, free B.M. at F = 688916.7 N -m
8
Net B.M. at F = 688916.656 - 227625 = 461292 N-m
For vertical member AD , Simply supported B.M. At mid span
34487 x 5.14 2+
Simply supporetd at mid sapn = 1/16 x 19513 x 5.14 2= 145828
8
227625 + 186701
Net B.M. = = 207163 - 145828 = 61335 N-m
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 .
The top slab is subjected to a load of '= 176500 N/m2
and the bottom slab is subjected to a load w= 176500 N/m2

Net latral pressure diagram

Itensity = 2E+05 N/m2 4000 4000
Lateral pressure due to dead load = A E B 4000

1/3 x 12000 = 4000 N/m 2

Lateral pressure due to soil = 4.58

1/3 x 18000 = 6000 N/m2 5.14
Hence earth pressure at depth h is =
4000 + 6000 h D F C
34810 34810 19513

Earth pressure intensity at top = 4000 N/m2 50323 w= 209014 N/m 50323
Fig 5
Earth pressure intensity at Bottom= 4000 + 6000 x 5.14 = 34810 N/m2
In addition to these, the vertical wall lslab subjectednto water pressure of intensity ZERO at top and 50323
N/m2 at Bottom, acting from inside . The lateral pressure on vertical walls Is shown in fig 5 and 6

MFAB= wL2 176500 x 4.58 2=

Fix end moments will be as under : = -308528 N-m
12 12

Mfdc= wL2
=
209014 x 4.58 2= 365363.8 N - m
12 12

MFAD = + pL2 WL Where W is the total tringular earth pressure.

-
12 15

MFAD = +
4000 x 4.58 2
- 19513 x 4.58
x
4.58 = -6652 N-m
12 2 15
MFDA = - pL2 WL 6992.1 - 13644
+
12 10

MFDA = -
4000 x 4.58 2- 19513 x 4.58
x
4.58 = 13473 N -m
12 2 10
The moment distribution is carrired out as illustred in table.

4/8
 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY
Fixed End Moments
Member DC DA AD AB 143007 176500 143007
365363.8 13473 -6652 -308528 =
The moment distribution carried out as per table 1 for case 1
Joint D A 453163.75 453163.8
Member DC DA AD AB
143007
Distribution factore 0.33 0.67 0.67 0.33 4000 319785
Fix end moment 365363.8 13473 -6652 -308528 A A
Balance -126279 -252558 210120 105060 143007 2.5675

Carry over 105060 -126279

178562
balance -35020 -70040 84186 42093 5.135
Carry over 42093 -35020
balance -14031 -28062 23347 11673 183930 2.5675

Carry over 11673 -14031 0 D D

balance -3891 -7782 9354 4677 19513 364116
183930
Carry over 4677 -3891
balance -1559 -3118 2594 1297 536644 536644
Carry over 1297 -1559 14400
balance -432 -865 1039 520
Carry over 520 -432 209014
balance -173 -346 288 144 Fig 4
Carry over 144 -173
balance -48 -96 115 58
Final moment 183930 -183930 143007 -143007

For horizontal slab AB, carrying UDL @ 176500 N/m2.

Vertical reactionat a and B = 0.5 x 176500 x 5.135 = 453163.8 N
Similarly, for the Bottom slab DC carrying U.D.L.loads @ 209014 N/m2
Vertical reaction at D and C = 0.5 x 209014 x 5.14 = 536643.9 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 5.14 ) + ##### - 183930 + 4000 x 5.14 x 5.14 x 1/2
- 1/2 x 19513 x 5.14 x 5.14 x 1/3
-ha x 5.14 + -40923 + 52736.45 - 85754
From which, ha = 14400
Hence , hd =( 19513 x 5.14 )- 4000 x 5.14 - 14400 = 15159.6
2
176500 x 4.58 2=
Free B.M. at mid point E = 462792 N-m
8
Net B.M. at E = 462792 - 143007 = 319785 N-m
209014 x 4.58 2=
Similarly, free B.M. at F = 548045.7 N -m
8
Net B.M. at F = 548045.663 - 183930 = 364116 N-m
For vertical member AD , Simply supported B.M. At mid span
4000 x 4.58 2+
Simply supporetd at mid sapn = 1/16 x 19513 x 4.58 2= 15093.8
8
183930 + 143007
Net B.M. = = 163469 + 15094 = 178562 N-m
2

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) 203225 259567 134740
(II) 395048 186701 113976
(II) 319785 143007 14400

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 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY
The section will be design for maximum B.M. = 395048 N -m
for water side force
sst = = 150 N/mm2 wt. of concrete = 25000 N/m3
scbc = = 7 N/mm2 wt of water = 9800 N/mm2
m = 13 for water side force
m*c 13 x 7
k= = = 0.378 K = 0.378
m*c+sst 13 x 7 + 150
j=1-k/3 = 1 - 0.378 / 3 = 0.874 J = 0.874
R=1/2xc x j x k = 0.5 x 7 x 0.87x 0.378 = 1.155 R = 1.155
Provide over all thickness = 580 mm so effective thicknesss = 530 mm
Mr = R . B .D2 = 1.155 x 1000 x 530 2= 324506137 < 395048000 O.K.
395048000 = 5685 mm2
Ast = BMx100/sstxjxD=
150 x 0.874 x 530
3.14xdia2 3.14 x 25 x 25
using 25 mm F bars A = = = 491 mm2
4 x100 4
Spacing of Bars =Ax1000/Ast 491 x 1000 / 5685 = 86 say = 80 mm
Hence Provided 25 mm F Bars @ 80 mm c/c
Acual Ast provided 1000 x 491 / 80 = 6133 mm2
Bend half bars up near support at distance of L/5 = 4.58 / 5 = 1.00 m
0.1 x( 580 - 100 %
Area of distributionn steel = 0.3 - = 0.16
450 - 100
Ast = 0.16 x 580 x 10 = 945 mm2 area on each face= # mm2
2
3.14xdia 3.14 x 12 x 12
using 12 mm F bars A = = = 113 mm2
4 x100 4
Spacing of Bars = Ax1000/Ast = 113 x 1000 / 473 = 239 say = 230 mm
Hence Provided # mm F Bars @ 230 mm c/c on each face
Section at supports :-
Maximum B.M.= 259567 N-m. There is direct compression of 134740 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 = 230 N/mm2 concrete M 20
k = 0.283 J = 0.9055 R = 0.8985
259567000
\ Ast = = 2352 mm2
230 x 0.906 x 530

Area available from the bars bentup from the middle section = 6133 / 2 = 3066 mm2
2352 < 3066 Hence these bars will serve the purpose. However, provide 8 mm dia. Additional bars
@ 200 mm c/c
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) 231508 316538 183135
(II) 461292 227625 113215
(II) 364116 183930 15160

The section will be design for maximum B.M. = 461292 N -m

for water side force
sst = = 150 N/mm2 wt. of concrete = 25000 N/m3
scbc = = 7 N/mm 2 wt of water = 9800 N/mm2
m = 13 for water side force
m*c 13 x 7
k= = = 0.378 K = 0.378
m*c+sst 13 x 7 + 150
j=1-k/3 = 1 - 0.378 / 3 = 0.874 J = 0.874
R=1/2xc x j x k = 0.5 x 7 x 0.87 x 0.378 = 1.155 R = 1.155
461291656
\ d = = 632 mm D = 682 mm
1000 x 1.155
Provide thickness of bottom slab D= 690 mm so that d = 640 mm
461291656 = 5497 mm2
Ast = BMx100/sstxjxD=
150 x 0.874 x 640
3.14xdia2 3.14 x 25 x 25
using 25 mm bars A = = = 491 mm2
4 x100 4
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 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY
Spacing of Bars =Ax1000/Ast 491 x1000 / 5497 = 89 say = 80 mm
Hence Provided 25 mm F Bars @ 80 mm c/c
Acual Ast provided 1000 x 491 / 80 = 6133 mm2
Bend half bars up near support at distance of L/5 = 4.58 / 5 = 1.00 m
0.1 x( 690 - 100
Area of distributionn steel = 0.3 - = 0.13 %
450 - 100
Ast 2 454 mm2
= 0.13 x 690 x 10 = 907 mm area on each face=
2
3.14xdia 3.14 x 12 x 12
using 12 mm bars A = = = 113 mm2
4 x100 4
Spacing of Bars = Ax1000/Ast = 113 x 1000 / 454 = 249 say = 240 mm
Hence Provided # mm F Bars @ 240 mm c/c on each face
Section at supports :-
Maximum B.M.= 316538 N-m. There is direct compression of 183135 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 = 230 N/mm2 concrete M 25
k = 0.283 J = 0.9055 R = 0.8985
316538000
\ Ast = = 2375 mm2
230 x 0.906 x 640
Area available from the bars bentup from the middle section = 6133 / 2 = 3066 mm2
Hence these bars will serve the purpose. However, provide 8 mm dia. Additional bars
2375 < 3066
@ 200 mm c/c
Additional reinforcemet required -691.4= mm2
2
3.14xdia 3.14 x 12 x 12
using 12 mm bars A = = = 113 mm2
4 x100 4
Spacing of Bars = Ax1000/Ast = 113 x 1000 / -691 = -163 say = -160 mm
Hence Provided # mm F Bars @ -160 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) 106069 316538 478643
(II) 61335 227625 536644
(II) 178562 183930 536644

The section will be design for maximum B.M. = 316538 N -m, and direct force = 536644 N
316538 x 1000
Eccentricity = = 590 mm
536644
proposed thickness of side wall '= 580 mm \ e/D 590 / 580 = 1.017 < 1.5 OK
thickness of side wall is OK
Let us reinforce the section with 20 mm F bars @ 110 mm c/c provided on both faces, as shown
in fig xxx . With cover of 50
mm and D = 580 mm
1000 3.14 x 20 x 20
Asc = Ast = x = 2855 mm2
110 4
The depth of N.A. is computed from following expression:
b n D - dt - n + (m - 1)Asc 1 (n - dc)(D - dt- dc)
3 3 n D
= e+ - dt
b n + (m -1) Asc n - dc D - dt - n 2
- m Ast
n n

1000 n n 2854.5
580 - 50 - + 12 x x n - 50 x -100
or 2 3 n
1000 n+ 2855 2854.5
12 x x n - 50 - 13 x x 580 - 50 -n
2 n n

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 DESIGN OF BOX TYPE CULVERT(SIZE 4mX4.55m) FOR AAI, BARAPANI, SHILLONG PREPARED BY:
M/S MJ CONSULTANCY
n -3425455
500 n 530 - + n - 50 x
3 n
= 590 + 240
34255 37109
500 n+ x n - 50 - x 530 - n
n n

-171272727
265000 n - 167 n2 + -3425455 -
n
= 830
1712727.3 19667818
500 n + 34254.5455 - - + 37109
n n
multiply by n
265000 n2 - 167 n3 + -3425455 n - -171272727
= 830
500 n2 + 34254.5455 n- 1712727.3 - 19667818 + 37109 n

265000 n2 - 167 n3 + -3425455 n - -171272727

= 0
415000 n2 + 59231818 n - 17745852727

-150000 n2 - 55806364 n - -17574580000 = 167 n3

-900 n2 + 334838 n - 105447480 = n3

Solwing this trial and error we get, n = 203.55 mm
12 x 2854.5 13 x 2855
\ c' = ( 500 x 203.55 + ( 203.55 - 50 )-
203.55 203.55
x( 580 - 50 - 203.55 )

or 1E+05 + 168.3 x 153.55 - 182.31 x 326.45 = 68103

536644 stress is more than permissiabl
\ c' = = 7.88 > 7 N/mm2
68103 Hence increase wall thickness
m c' 13 x 7.88
Also stress in steel t = (D-dc-n) = x( 580 - 50 - 203.55 )
n 203.55
= 164.3 N/mm2 < 230 N/mm2 O.K.
Stress in steel is less than permissiable Hence section is O.K.

8/8