Box Culvert

Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Box Culverts Design Example Design a reinforced concrete box culvert under a drain for the following data: Properties of the drain:

Q  300 cumec ,W 1  8 m ,W 2  15 m , d n  3.5 m , side slopes  2H :1V , b  75 m and bed level  201 m Properties of channel:

Q  60 cumec , b  30 m ,side slopes  2H :1V , water table in the region  200 m , d 1  2 m , hb1  5.5 m , f b1  3.5 m ,freeboard above channel water surface  0.4 m . Bed reduced level (B.R.L.) = 200 m

 c  2.4T / m 3 Design the same transition type for both inlet and outlet. Draw the details of your design.

Figure 1: Profile of the box culvert.

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Solution Drain waterway For the drain check the waterway

Pmin  4.83 Q  4.83 300  83.65 m Applied wetted parameter Papp .  75  2  3.52   3.5  2 

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 90.65 m  83.65 m O.K. Channel waterway For the channel, V 

60  0.8823 m s  30  2  2   2

Maximum channel fluming is 40%, 0.4  30  12 m take 12.05 m Let the channel waterway be reduced from 30 m to 12.05 m. Take 4 vents 2.75 1.9 m each

1.9 m

2.75 m

12.05 m 12.75 m

Figure 2: Box culvert vents.

V  Fr 

60  2.87 m s  3 m s OK 4  2.75 1.9 2.87  0.66  1 OK 9.811.9

Length of expansion 

30  12.05  3  26.925 m 2

Length of contraction 

30  12.05  2  17.95 m 2

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Pucca Floor Length of u.s. pucca floor 

17.95  8.975 m say 9 m 2

3 Length of u.s. pucca floor   26.925  20.20 m 4 Design of Transitions a. Expansion transition B c B f Lf Bx  Lf B c  x  B c  B f



B c  30 m , B f  12.05 m , L f  26.925 m

Bx 

542.2 45  x x (m) Bx (m)

0 12.05

5 13.56

10 15.49

15 18.07

20 21.69

26.925 30.00

b. Contraction transition Bc  30 m , B f  12.05 m , Lf  17.95 m

Bx 

361.49 30  x x (m) Bx (m)

0 12.05

5 14.46

10 18.07

15 24.10

17.95 30.00

Uplift Pressures a. Seepage pressure Seepage head   201  3.5  200  4.5m Total seepage path  0.98  2  1.9  0.35  0.35 1   33.95  20.2   13  22.61m Depth of earth at inside edge  0.6  75  0.005  0.98m 1. At bottom of barrels L  1.96  2.6  4.56 4.5 h 18.05  3.59 m 22.61 Uplift at the base of the barrels  3.59  2.58  6.17 t m 2

say 6.2 t m 2 2. At d.s. end of barrels 4.5 h  6.73  1.34 m 22.61 3

Hydraulic Structures – Box Culverts

Printed: May 27, 2011

3. At 5 m from d.s. end of floor h

4.5  5     0.33 m 22.61  3 

4. At 10 m from d.s. end of floor 4.5  10  h    0.66 m 22.61  3  5. At 15 m from d.s. end of floor 4.5  15  h    0.99 m 22.61  3 

Figure 3: Seepage head at different points under the pucca floor.

b. Static head 1. At bottom of barrels floor Elevation of bottom of barrels floor  201   0.98  0.35  1.9  0.35  197.4 m Static head  200  197.4  2.58m Weight of earth, water and concrete  3.5  00.98  2   0.35  0.35   2.4 0.35 1.9  5  2.4 12.75  7.76 m of water  6.2 m O.K. 

2. At d.s. end of barrels El. of end of barrels  201   0.6  0.35  1.9    75  33.95   0.005

 197.61m Assume floor thickness 3.0 m El. of lower point  197.61  3  194.61m Static head  200 194.61  5.39 Total head  1.33  5.39  6.72m 4

Hydraulic Structures – Box Culverts

Printed: May 27, 2011

6.72  3.05 m this is larger than the assumed 3.0 m, 2.2 Assume thickness  3.1m , therefore, Min. floor thickness 

El. of lower point  197.61  3.1  194.51m Static head  200  194.51  5.49 m Total head  5.49  1.33  6.82m

6.82  3.1 m  assumed thickness O.K. 2.2 3. At 5 m from d.s. end of pucca floor Assume thickness  2.5m Min. floor thickness 

El. of lower point  197.61  2.5  195.11m Static head  200 195.11  4.895m Total head  4.895  0.33  5.22m

5.22  2.37 m , this is smaller than the assumed 2.5 m thickness, 2.2 Assume thickness  2.3m Min. floor thickness 

El. of lower point  197.61  2.3  195.31m Static head  200  195.31  4.69 m Total head  4.69  0.33  5.02m

5.02  2.28 m  2.3 m O.K. 2.2 4. At 10 m from d.s. end of pucca floor Assume thickness  2.5m Min. floor thickness 

El. of lower point  197.61  2.5  195.11m Static head  200 195.11  4.895m Total head  4.895  0.66  5.55m

5.55  2.52 m  2.5 m not O.K. 2.2 Assume thickness  2.6 m Min. floor thickness 

El. of lower point  197.61  2.6  195.01m Static head  200  195.01  4.99 m Total head  4.99  0.66  5.65m

5.65  2.57 m  2.6 m O.K. 2.2 5. At 15 m from d.s. end of pucca floor Assume thickness  3.0 m Min. floor thickness 

El. of lower point  197.61  3.0  194.61m Static head  200  194.61  5.39 m Total head  5.39  0.99  6.38m

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

6.38  2.9 m  3.0 m not O.K., revise 2.2 Assume thickness  2.9 m Min. floor thickness 

El. of lower point  197.61  2.9  194.71m Static head  200  194.71  5.29 m Total head  5.29  0.99  6.28m Min. floor thickness 

6.28  2.85 m  2.9 m O.K. 2.2

Figure 4: Floor thickness at different points.

Upstream pucca floor Length of seepage path  0.6  2   0.35  1.9  0.35 1   23.55  9   13

 14.65m Seepage head  204.5  200  4.5m 1. U.S. end of barrels L  0.6  2  2.6 

23.55  11.65 m 3

4.5  3  0.92 14.65 Assume thickness = 0.8 m Total head  0.8  0.92  1.72 m h

1.72  0.78 m  0.8 m O.K. 2.2 2. At 5 m from u.s. end of floor 4.5 5 h   0.51 m 14.65 3 Assume floor thickness = 0.6 m Total head  0.6  0.51  1.11m Min. floor thickness 

Min. floor thickness 

1.11  0.505 m  0.6 m O.K. 2.2

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

PROFILE

PLAN Figure 5: Box culvert details.

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Structural Design Number of barrels Size of barrels Bank level Drain high flood level Uplift at base of barrel Unit weight of dry earth Unit weight of saturated earth Unit weight of submerged earth Angle of internal friction in all conditions Depth of earth cover

=4 = 2.75 m×1.9 m = 205.5 m = 204.5 m = 6.2 t/m2 = 1.6 t/m3 = 2.0 t/m3 = 1.0 t/m3 = 30º = 5.5 m

Figure 6: A cross-section of the proposed box culvert. Dimensions are in meters.

Design Depth of dry earth cover  205.5  204.5  1m Depth of saturated earth  204.5  200  4.5m Weight of dry and saturated earth  11.6  4.5  2   10.6t m 3 Weight of top slab  0.35  2.4  0.84t m 2 Weight on top slab including its own weight  10.6  0.84  11.44t m 2 Weight of barrels per meter length  12.75  2  5 1.9   0.35  2.4  29.4t m Total dead load/meter of barrels  29.48  10.6 12.75  164.55t m Uplift/meter length  6.2 12.75  79.05t m 8

Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Net vertical load acting on foundation  164.55  79.05  85.5t m Pressure on foundation soil 

85.5  6.70 t m 2 12.75

Pressure acting on the base slab= soil reaction + uplift  6.7  6.2  12.9t m 2 Net upward pressure on the base slab  12.9  0.84  12.06 t m 2

say 12.1t m 2

Earth Pressure Cp 

1  sin 30 1  1  sin 30 3

Pressure at point (a)  C p   d 1  C p   s  204.5  199.825  w  204.5  199.825  6.770t m 2

1 Pressure at point (n)  6.77  1 2.25  1 2.25  9.77 t m 2 3

Figure 7: Loading on the culvert barrels.

Distribution Factors At joints a, e, f and n For ab, mn, ed and fg, distribution factor  For an, ef, distribution factor 

2.25 2.25   0.42 2.25  3.1 5.35

3.1  0.58 5.35

At joints b, c, d, g, h and m

I  2.25  3.1 3.1  6.975, D.F.  0.3 3.1 I I  2.25  3.1 3.1  6.975, D.F.  0.3 For bc  3.1 I I  2.25  3.1 3.1  9.61, D.F.  0.4 For bm  2.25 For ba

I



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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Fixing Moments 11.44  3.1   9.16 t  m 12 2

M

F ab

M

F nm

M

F an

6.77   2.25  3  2.25     2.86  0.506  3.37 t  m 12 30

M

F na

6.77   2.25  3  2.25     2.86  0.76  3.62 t  m 12 20

12.1  3.1   9.69 t  m 12 2

2

2

2

2

Figure 8: Fixed end moments in t∙m. Table 1: Finding moments using moment distribution method.

Joint

m

n

a

b

c

h

Member

mh

mb

mn

nm

na

an

ab

ba

bm

bc

cb

hm

D.F.

0.3 9.69

0.4 -

0.3 -9.69

0.42 9.69

0.58 -3.62

0.58 3.37

0.42 -9.16

0.3 9.16

0.4 -

0.3 -9.16

9.16

-9.69

-2.549

-3.521

3.358

2.432

1.679

-1.760

-0.974

1.021

0.739

-0.486

-0.365 -0.182

0.191

-0.094

0.089

-0.039

0.041

8.84

-9.37

F.E.M. Balance

-1.275

C.O. Balance

0.382

C.O. Balance

0.179

C.O. Balance

0.082

-0.705

1.216

0.510

0.382

-0.365

-0.243

-0.353

0.191

0.510

-0.487

-0.182

0.370

0.255

0.238

0.179

-0.295

-0.407

0.388

0.281

-0.187

-0.250

-0.125

-0.147

0.089

0.194

-0.203

-0.094

0.141

0.119

0.109

0.082

-0.119

-0.164

0.172

0.125

-0.078

-0.104

-0.187 -0.078

-0.052

-0.060

0.041

0.086

-0.082

-0.039

0.062

0.054

Balance

0.033

0.045

0.033

-0.053

-0.074

0.070

0.051

-0.035

-0.047

-0.035

Moment

10.37

0.48

-10.85

6.29

-6.29

5.85

-5.85

10.28

-0.46

-9.83

C.O.

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Figure 9: Design centerline moments in t∙m.

Design Moments Span ab, de At face: Sagging moment 

11.44  3.1 11.44  0.17 2  0.17   2.84 t  m 2 2

Fixing moment  5.85 

2.93 10.28  5.85  10.04t  m 3.1

Net fixing moment  10.01  2.84  7.2t  m At centre: Sagging moment  Fixing moment 

11.44  3.12  13.74 t  m 8

5.85  10.28  8.065t  m 2

Net sagging moment  13.74  8.065  5.68t  m Span bc, cd

11.44  3.1 11.44  0.17 2  0.17   2.84 t  m At face: Sagging moment  2 2 Fixing moment  8.84 

2.93  9.82  8.84  9.77 t  m 3.1

Net fixing moment  9.77  2.84  6.93t  m

11.44  3.12  13.74 t  m At centre: Sagging moment  8 Fixing moment 

9.82  8.84  9.33t  m 2

Net sagging moment  13.74  9.33  4.41t  m

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Span nm, gf At face: Sagging moment 

12.1 3.1 12.1 0.172  0.17   3.02 t  m 2 2

Fixing moment  6.29 

2.93 10.85  6.29  10.6t  m 3.1

Net fixing moment  10.6  3.02  7.58t  m At centre: Sagging moment  Fixing moment 

12.1 3.12  14.54 t  m 8

10.85  6.29  8.57 t  m 2

Net sagging moment  14.54  8.57  5.97t  m Span mh, hg At face: Sagging moment  3.02t  m Fixing moment  9.37 

2.93 10.37  9.37   10.32t  m 3.1

Net fixing moment  10.32  3.02  7.3t  m At centre: Sagging moment 14.54t  m Fixing moment 

9.37  10.37  9.87 t  m 2

Net sagging moment  14.54  9.87  4.67t  m Span an, ef At face: Sagging moment a. Due to rectangular portion 6.77  2.25 6.77  0.17 2  0.17   1.197 t  m 2 2 b. Due to triangular portion 3  2.25 2 2.25R n    2.25 2 3 3  2.25 Rn  3 

3  2.25 2.77  0.17 2  0.17   0.343t  m 3 2 Total sagging moment 1.197  0.343  1.54t  m

Sagging moment 

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Hydraulic Structures – Box Culverts

Fixing moment  5.85 

Printed: May 27, 2011

2.08  6.29  5.85  6.26t  m 2.25

Net fixing moment  6.26  1.54  4.72t  m At centre: Sagging moment 14.54t  m a. Due to rectangular portion 6.77  2.25  4.28t  m 8 b. Due to triangular portion 3  2.25 2.25 1.5 1.13 1.13      0.95t  m 6 2 2 3 Total sagging moment  4.28  0.95  5.23t  m Fixing moment at centre 

5.85  6.29  6.07 t  m 2

Net sagging moment  5.23  6.07  0.84t  m

Reinforcement Use thickness of slab= 35 cm

d e  32.5cm Span ab, bc, cd, de At face (-ve steel)

At 

7.2 105  21.54 cm 2 6 1200  7  32.5

Use Ø16 mm bars, As  2 cm 2 Spacing 

100  9.3cm 21.54 2

Use Ø16 mm bars @ 9 cm c/c At centre (+ve steel)

At  Spacing 

5.68 105  16.99 cm 2 1200  76  32.5

100  11.77 cm 16.99 2

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Hydraulic Structures – Box Culverts

Printed: May 27, 2011

Use Ø16 mm bars @ 11.5 cm c/c Refer to Table 2 for the reinforcement of the rest of the members. Table 2: Steel Reinforcement.

Member ab,de bc, cd nm, gf mh, hg an, ef bm, dg

Fixing moment t∙m (-ve moment) 7.20 Ø16 mm bars @ 9 cm c/c 6.93 Ø16 mm bars @ 9 cm c/c 7.58 Ø16 mm bars @ 8.5 cm c/c 7.30 Ø16 mm bars @ 8.5 cm c/c 4.72 Ø16 mm bars @ 14 cm c/c 0.48 Ø12 mm bars @ 25 cm c/c

Maximum moment  7.58t  m

7.58 105 d   28.74 cm  32.5cm O.K. 100  9.18

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Sagging moment t∙m (+ve moment) 5.68 Ø16 mm bars @ 11.5 cm c/c 4.41 Ø16 mm bars @ 11.5 cm c/c 5.97 Ø16 mm bars @ 11 cm c/c 4.67 Ø16 mm bars @ 11 cm c/c -0.84 Ø12 mm bars @ 25 cm c/c -0.47 Ø12 mm bars @ 25 cm c/c