Box Culvert

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NAME OF WORK

:-DESIGN INPUT DATA :

1 WIDTH OF EACH BARREL

3.50

m 3500 mm

2 HEIGHT OF EACH BARREL

3.50

m 3500 mm

3 NUMBER OF BARRELS

1

Nos.

4 LIVE LOAD

4.50

t/m2 4500 kg/m2

5 DEAD LOAD

1.20

t/m2 1200 kg/m2

6 UNIT WEIGHT OF DRY EARTH

1.80

t/m3 1800 kg/m3

7 UNIT WEIGHT OF SATURATED EARTH

2.00

t/m3 2000 kg/m3

8 UNIT WEIGHT OF SUBMERGED EARTH

1.00

t/m3 1000 kg/m3

9 UNIT WEIGHT OF CONCRETE

2.50

t/m3 2500 kg/m3

# ANGLE OF INTERNAL FRICTION ( f )

30

Degree

# GRADE OF STEEL Fe

415

# GRADE OF CONCRETE M

20

# BANK LEVEL

100.00

m

# DRAIN H.F.L.

100.00

m

# LEVEL AT TOP OF BARREL

100.00

M

# NOMINAL COVER

50

mm

# REINFORCEMENT

For TOP slab Face

20

mm f @ 14.00 cm c/c

Dist

10

mm f @ 17.00 cm c/c

Center 20 mm f @ 23.00 cm c/c

Bottom slab Face

20

mm f @ 11.00 cm c/c

Dist

10

mm f @ 17.00 cm c/c

Center 20 mm f @ 18.00 cm c/c

Vertical wall Face

20

mm f @ 20.00 cm c/c

Dist

10

mm f @ 17.00 cm c/c Center 20 mm f @ -561.00 cm c/c Hench

10

mm f @ 17.00 cm c/c Corner

10

mm f @ 17.00 cm c/c 0.3 20 mm f @ 20 mm f @ 10 mm f @ 14.0 cm c/c 23.0 cm c/c 17.0 cm c/c 20 mm f @ Corner 20 mm f @ 20 cm c/c 20.0 cm c/c 20 mm f @ 20 mm f @ ### cm c/c -561.0 cm c/c 10 mm f @ Hench 10 mm f @ 17 cm c/c 17 cm c/c 20 mm f @ 20 mm f @ 10 mm f @ 11.0 cm c/c 18.0 cm c/c 17 cm c/c [email protected] 0.30 m PKN

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NAME OF WORK

:-DESIGN DATA :

1 WIDTH OF EACH BARREL

3.50

m

2 HEIGHT OF EACH BARREL

3.50

m

3 NUMBER OF BARRELS

1

Nos.

4 LIVE LOAD

4.50

t/m2

5 DEAD LOAD

1.20

t/m2

6 UNIT WEIGHT OF DRY EARTH

1.80

t/m3

7 UNIT WEIGHT OF SATURATED EARTH

2.00

t/m3

8 UNIT WEIGHT OF SUBMERGED EARTH

1.00

t/m3

9 UNIT WEIGHT OF CONCRETE

2.50

t/m3

# ANGLE OF INTERNAL FRICTION ( f )

30

Degree

# GRADE OF STEEL Fe

415

# GRADE OF CONCRETE M

20

# BANK LEVEL

100.00

m

14 DRAIN H.F.L.

100.00

m

15 LEVEL AT TOP OF BARREL

100.00

m

16 NOMINAL COVER

50

mm

(1) Critical section of the barrel

The barrel shall be subjected to maximum loading under the bank at the lowest possible level of the barrel as indicated below in the following

section:-Bank level 100.00 m Saturation line 100.00 m R.L. = 100.00 m t = 0.30 m R.L. = 96.20 m R.L. = 95.90 m 7.90 (2) Design features

Following cosiderations have been made in the design of barrels :

(i) Bottom slab : This design is for uplift pressure and reaction from soil resulting from the loading on the foundations. Theoretically, the soil reaction is not uniform but for simplification it is assumed uniform.

(ii) side walls : Side walls would be tested in the following two critical conditions (a) High flood in the drain while barrels are empty (b) No water in the drain while barrels are full

(iii) Partition walls : The partition walls are subjected to equal pressures on either side, and therefore,no reinforcement is required. Nominal reinforcement is, however, provided to take care of contingency arising due to unequal pressures 3.50

PKN

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resulting from chocking up of any of the barrels. (iv) Top slab : The loads considered for design of top slab are :

(a) Earth load,

(b) Weight of water below saturation line

As there is no roadway along the drain, no live load due to traffic shall be considered.

(3) Design

As the barrels are rigidly joined, they should be designed as a continuous structure. Hardy Cross method of moment distribution shall be used for design.

Thickness of top / bottom slab 0.3 m

Thickness of side wall 0.3 m

The effective length of horizontal member = 3.80 m The effective length of vertical member = 3.80 m Distribution factors At joint A 3.8 + 3.8 3.8 + 3.8 At joint D 3.8 + 3.8 3.8 + 3.8 (i)

Loads

Consider one meter length of barrel

Depth of dry earth over barrel = 100.00 - 100.00 = 0.00 m Depth of saturated earth = 100.00 - 100.00 = 0.00 m Weight of dry and saturard earth = 0.00 X 1.80 + 0.00 X 2.00

= 0 t/m2

Weight of top slab = 0.30 X 2.50 = 0.75 t/m2 Live load and dead load = 4.50 + 1.20 = 5.70 t/m2

Weight on the top slab including its own weight = 0 + 0.75 + 5.70 = 6.45 t/m2

Weight of the barrels per metre of length

=( 1 X 3.80 + 2 X 3.80 )x 0.30 X 2.50

= t

Total dead load/m length of barrels = = 8.55 + 0.00 X 3.80 + 5.70 x 3.80 = 30.21 t

Net upward pressure on the base slab = = 30.21 / 3.80 = 7.95 t/m2 7.95 t/m2

(ii) Earth pressure

The earth pressure shall comprise of the following :

(a) dry earth pressure above saturation line from R.L. 100.00 to 100.00 (b) saturated earth pressure from R.L. 100.00 to 100.00 Corresponding to f ₌ _{30 degree ,} Cp = 1/3

The pressure at A= Surcharge ( due to dry earth + Satured soil + live & dead load ) 8.55 0.50 For member AB = For member AD = = For member DA = 3.8 3.8 = For member DC = 3.8 = 0.50 0.50 0.50 3.8 =

(4)

= Cp X wd X h1 + Cp X ws X h2 + Cp x WDL,LL = 1/3 X 1.80 X 0.00 + 1/3 X 1.0 X 0.00 + 1/3 X 5.70 = 1.90 t/m2 Pressure at D = 1.90 + Cp X ws X h1 + Cp x wd X h2 = 1.90 + 1/3 X 1.00 X 0.00 + 1/3 x 1.80 X 3.80 = 4.18 t/m2

Loads acting on different members are shown below : 6.45 t/m2

1.90 t/m2 t/m2

F

2.28 t/m2 7.95 t/m2

(iii) Fixing moments

wl2 6.45 X 3.8 2 (i) On span AB = 12 = 12 = 7.77 t-m wl2 7.95 X 3.8 2 (ii) On span CD = 12 = 12 = 9.57 t-m

(iii) On span AD fixed end moments in the wall at each end due to rectangular portion wl2 1.90 X 3.82

= 12 = 12

= 2.29 t-m Fixed end moments due to triangular portion

2.28 X 3.82 MAD = 30 = 1.10 t-m MDA = 2.28 X 3.82 20 = 1.65 t-m

Total fixed end moments at A = 2.29 + 1.10 = 3.39 t-m Total fixed end moments at D = 2.29 + 1.65

= 3.94 t-m (iv) Distribution of moments

Joints C D A B Member Dc DA AD AB Distribution factore 0.50 0.50 0.50 Fixed end 9.57 -3.94 3.39 moments Balance -2.82 -2.82 2.19 Carry over 1.10 -1.41 Balance -0.55 -0.55 0.70 Carry over 0.35 -0.27 -1.41 3.80 0.70 7.77 1.10 0.35 -0.27 3.80 3.80 -9.57 0.50 1.90 2.19 4.18 t/m2 -7.77 B D A C E

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Balance -0.18 -0.18 0.14

Carry over 0.07 -0.09

Balance -0.03 -0.03 0.04

Total 6.00 -6.00 4.70

(v) Net moments at centre and face

Span AB

6.45 X 3.8 6.45 X 0.152

Sagging moments at face = --- X 0.15 -

---2 2

= 1.766 t-m 3.65

3.8 = 9.104 t-m

Net fixing moments at face = 9.104 - 1.766 = 7.338 t-m

Sagging moments at centre = 6.45 X 3.82 8

= 11.64 t-m Fixing moments at centre = 4.70 + 9.29

2 = 6.99 t-m

Net sagging moments at centre = 11.642 - 6.990 = 4.652 t-m

Span CD

7.95 X 3.8 7.95 X 0.152

Sagging moments at face = --- X 0.15 -

---2 2

= 2.176 t-m

Fixing moments at face= 3.65 3.8 = 11.13 t-m

Net fixing moments at face = 11.13 - 2.18 = 8.95 t-m

Sagging moments at centre = 7.95 X 3.82 8

= 14.35 t-m

Fixing moments at centre = 11.34 + 6.00 2

= 8.668 t-m

Net sagging moments at centre = 14.350 - 8.668

= 5.68 t-m

Span AD

(a) Due to rectangular portion

1.90 X 3.8 1.90 X 0.152

2 2

= 0.52 t-m (a) Due to triangular portion

( -11.34 -0.09 0.04 0.07 6.00 -( 9.29 -Fixing moments at face=

+ 4.70 + = ) ) -0.14 9.29 11.34 -4.70 X 0.15 4.70 6.00

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X 3.8 1 0.1 X 0.15

2 3 2

= t-m

Total sagging moments at face = 0.520 + 0.216 = 0.74 t-m

3.65 3.8 = 5.95 t-m Net fixing moments at face = 5.95 - 0.74

= 5.21 t-m

Sagging moments at centre

1.90 X 3.802 8 = 3.43 t-m 2.28 X 3.80 1 2 7.81 = 2.11 t-m

Total sagging moments at centre = 3.43 + 2.11 = 5.54 t-m

6.00 + 4.70 2

= 5.35 t-m Net sagging moments at centre = 5.54 - 5.35

= 0.19 t-m

The net moments at face and centre of the different spans are tabulated below :

AB 7.34 t-m (hogging) 4.65 t-m (sagging)

CD 8.95 t-m (hogging) 5.68 t-m (sagging)

AD 5.21 t-m (hogging) 0.19 t-m (sagging)

(vi) Thickness of members

The maximum moment in the barrels is 8.95 t-m For M 20 grade concrete and steel of Fe 415

Kg/cm2 1500 Kg/cm2 water side 1900 Kg/cm3 out side

The minimum effective thickness (d) required for bending moment

M 8.95 X 105

bQ 100 X 12

= cm

Adopt overall thickness of all the members = 31 cm

Then effective thickness = 26 cm

= 5.0 cm ) The reinforcement required at various points is given below :

(vii) Reinforcement 2.28 = 0.22 X = 27.84 = (a) Due to rectangular portion

Fixing moments at centre

0.05 X ) -6.00 0.15



=



At centre 4.70 X (

Fixing moments at face

-(b) Due to triangular portion =

= (clear cover X d j = 0.874 11.552 sst = X = MOMENTS 3.8 X 4.70 0.378 13 At face scbc = m = Span k = sst = + 70 R =

(7)

Span AB (Top Horizontal Slab)

Moments in t-m Reinforcement required

At face 7.34 t-m (hogging) A t = 21.53 Cm 2 Provide 20 mm bars @ 14.0 cm c/c At centre 4.65 t-m (sagging) A t = 13.65 Cm 2 Provide 20 mm bars @ 23.0 cm c/c

Distribution Provide 10 mm bars @ 17.0 cm c/c

Span CD (Bottom Horizontal Slab)

At face 8.95 t-m (hogging) A t = 26.26 Cm 2 Provide 20 mm bars @ 11.0 cm c/c At centre 5.68 t-m (sagging) A t = 16.67 Cm 2 Provide 20 mm bars @ 18.0 cm c/c

Span AD (vertical wall)

At face 5.21 t-m (hogging) A t = 15.28 Cm 2 Provide 20 mm bars @ 20.0 cm c/c At centre 0.19 t-m (sagging) A t = -0.56 Cm 2 Provide 20 mm bars @ -561.0 cm c/c

Hench 200 mm Provide 10 mm bars @ 17.0 cm c/c

corner Provide 10 mm bars @ 17.0 cm c/c

Nominal steel shall also be provided on the outer face of the walls for the condition when there is no water in the drain and barrels are running full. The details of reinforcement are shown below

20 mm f @ 14.0 cm c/c 20 mm f @ 14 cm c/c 10 mm f @ 17.0 cm c/c A 20 mm f @ 23 cm c/c B E C.C. M - 20 20 mm f @ -561 cm c/c 8 mm f @ 17.0 cm c/c 3.50 20 mm f @ 20 cm c/c D F 0.30 C 20 mm f @ 11 cm c/c _{clear cover =} _5.00 _cm 20 mm f @ 18 cm c/c 0.30 3.50 m 0.30 3.50 0.30

DETAILS OF REINFORCEMENT IN BARREL

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20 mm f @14.0 cm c/c 10 mm f @ 17.0 cm c/c 20 mm f @ 23 cm c/c 20 18 cm c/c 10 mm bars @ 20 20 cm c/c _{17 cm c/c} 10 mm bars @ 17 cm c/c 20 18 cm c/c 20 11 cm c/c _{10 mm bars @} 17 cm c/c 3.50 mm f @ mm f @ mm f @ mm f @ 0.30 0.30 3.50