Box Culvert

NAME OF WORK :-

PKN

DESIGN INPUT DATA : 1 2 3 4 5 6 7 8 9 # # # # # # # #

3.50 3.50 1 4.50 1.20 1.80 2.00 1.00 2.50 30 Fe 415 M 20 100.00 100.00 100.00 50

WIDTH OF EACH BARREL HEIGHT OF EACH BARREL NUMBER OF BARRELS LIVE LOAD DEAD LOAD UNIT WEIGHT OF DRY EARTH UNIT WEIGHT OF SATURATED EARTH UNIT WEIGHT OF SUBMERGED EARTH UNIT WEIGHT OF CONCRETE ANGLE OF INTERNAL FRICTION ( f ) GRADE OF STEEL GRADE OF CONCRETE BANK LEVEL DRAIN H.F.L. LEVEL AT TOP OF BARREL NOMINAL COVER REINFORCEMENT For TOP slab

Bottom slab

Vertical wall

20 10 20

20 10 20

20 10 20

10 10

Hench Corner 0.3

Face Dist Center Face Dist Center Face Dist Center

20 mm f @ 14.0 cm c/c

20 mm f @ 23.0 cm c/c

m m Nos. t/m2 t/m2 t/m3 t/m3 t/m3 t/m3

3500 3500

mm mm

4500 1200 1800 2000 1000 2500

kg/m2 kg/m2 kg/m3 kg/m3 kg/m3 kg/m3

14.00 17.00 23.00 11.00 17.00 18.00 20.00 17.00 -561.00 17.00 17.00

cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c cm c/c

Degree

m m M mm mm f mm f mm f mm f mm f mm f mm f mm f mm f mm f mm f

@ @ @ @ @ @ @ @ @ @ @

10 mm f @ 17.0 cm c/c

0.30 20

mm f @

20

cm c/c

20

mm f @

###

cm c/c

10

mm f @

17

cm c/c

m 20 mm f @

Corner

20.0 cm c/c 20 mm f @ -561.0 cm c/c 10 mm f @ 17 cm c/c

Hench

20 mm f @ 11.0 cm c/c

20 mm f @ 18.0 cm c/c

10 mm f @ 17 cm c/c [email protected]

DESIGN NAME OF WORK :-

PKN

DESIGN DATA : 1 2 3 4 5 6 7 8 9 # # # # 14 15

WIDTH OF EACH BARREL HEIGHT OF EACH BARREL NUMBER OF BARRELS LIVE LOAD DEAD LOAD UNIT WEIGHT OF DRY EARTH UNIT WEIGHT OF SATURATED EARTH UNIT WEIGHT OF SUBMERGED EARTH UNIT WEIGHT OF CONCRETE ANGLE OF INTERNAL FRICTION ( f ) GRADE OF STEEL GRADE OF CONCRETE BANK LEVEL DRAIN H.F.L. LEVEL AT TOP OF BARREL

16 NOMINAL COVER (1) Critical section of the barrel

3.50 3.50 1 4.50 1.20 1.80 2.00 1.00 2.50 30 Fe 415 M 20 100.00 100.00 100.00 50

m m Nos. t/m2 t/m2 t/m3 t/m3 t/m3 t/m3 Degree

m m m mm

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.

t

= =

100.00

m

0.30

m

= =

96.20

m

95.90

m

3.50 R.L. R.L. 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

resulting from chocking up of any of the barrels. 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. (iv)

Top slab :

(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. 0.3 m Thickness of top / bottom slab 0.3 m Thickness of side wall The effective length of horizontal member = 3.80 m The effective length of vertical member = 3.80 m Distribution factors At joint A For member AB

=

For member AD

=

For member DA

=

For member DC

=

3.8 3.8

3.8 + 3.8 +

3.8 3.8

=

0.50

=

0.50

=

0.50

=

0.50

At joint D

(i) Loads Consider one meter length of barrel Depth of dry earth over barrel = Depth of saturated earth = Weight of dry and saturard earth =

0.00 X t/m2 0 Weight of top slab 0.30 X Live load and dead load = 4.50 + Weight on the top slab including its own weight = = Weight of the barrels per metre of length =( 1 X 3.80 + 2 X = 8.55 t Total dead load/m length of barrels = = = Net upward pressure on the base slab = = = =

3.8 3.8

3.8 + 3.8 +

100.00 100.00 1.80 +

3.8

100.00 = 0.00 m 100.00 = 0.00 m 0.00 X 2.00

2.50 1.20 0 6.45

= + t/m2

3.80

)x

=

8.55 + 30.21 t 30.21 / 2 7.95 t/m

(ii) Earth pressure The earth pressure shall comprise of the following : (a) dry earth pressure above saturation line from R.L. (b) saturated earth pressure from R.L. Corresponding to f = 30 degree ,

3.8

0.75 5.70 0.75

0.30

t/m2 t/m2 +

X

5.70

2.50

0.00

X

3.80

+

3.80

=

7.95

t/m2

100.00 to 100.00 to Cp =

100.00 100.00 1/3

The pressure at A= Surcharge ( due to dry earth + Satured soil + live & dead load )

5.70

x

3.80

= Cp =

h1

1/3

X

2 1.90 t/m 1.90 +

= =

Pressure at D

X wd X

Cp

+ 1.80 X

Cp

X

ws X + Cp

0.00

+ +

ws

= 1.90 + 1/3 X 1.00 2 = 4.18 t/m Loads acting on different members are shown below :

X h2 W DL,LL x

1/3 X 1/3 X

X

h1

+

X

0.00

+

1.0 5.70 Cp

X 0.00

x

1/3

x

2 6.45 t/m 2 1.90 t/m

A

B

E

3.80

3.80

D

3.80

1.90 t/m

2

C

F 2 2.28 t/m

4.18 t/m

2

7.95 t/m

2

(iii) Fixing moments (i)

(ii) (iii)

wl2 12

2 X 3.8 On span AB = = 12 = 7.77 t-m 2 wl2 7.95 X 3.8 On span CD = 12 = 12 = 9.57 t-m On span AD fixed end moments in the wall at each end due to rectangular portion wl2 1.90 X 3.8 2 = 12 = 12 = 2.29 t-m Fixed end moments due to triangular portion 2.28 X 3.8 2 MAD = 30

MDA

6.45

= =

1.10 t-m 2.28 X

=

1.65

Total fixed end moments at A Total fixed end moments at D

20 t-m = = = =

3.8

2.29 3.39 2.29 3.94

2

+ t-m + t-m

1.10 1.65

(iv) Distribution of moments Joints C Member Distribution factore Fixed end -9.57 moments Balance Carry over -1.41 Balance Carry over -0.27

D

A

B

Dc 0.50 9.57

DA 0.50 -3.94

AD 0.50 3.39

AB 0.50 -7.77

-2.82

-2.82 1.10 -0.55 0.35

2.19 -1.41 0.70 -0.27

2.19

-0.55

7.77

1.10 0.70 0.35

wd

X

1.80 X

h2 3.80

Balance Carry over Balance Total

-0.18

0.14 -0.09 0.04

0.14

-0.03

-0.18 0.07 -0.03

6.00

-6.00

4.70

-4.70

-0.09

-11.34

0.07 0.04 9.29

(v) Net moments at centre and face Span AB 2 6.45 X 3.8 6.45 X 0.15 Sagging moments at face = ------------------X 0.15 - ----------------------------2 2 = 1.766 t-m 3.65 Fixing moments at face= 4.70 + ( 9.29 4.70 ) 3.8 = 9.104 t-m Net fixing moments at face = 9.104 1.766 = 7.338 t-m 2 Sagging moments at centre = 6.45 X 3.8 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 2 7.95 X 3.8 7.95 X 0.15 Sagging moments at face = -------------------X 0.15 ---------------------------2 2 = 2.176 t-m Fixing moments at face= 3.65 6.00 + ( 11.34 6.00 ) 3.8 = 11.13 t-m Net fixing moments at face = 11.13 2.18 = 8.95 t-m 2 Sagging moments at centre = 7.95 X 3.8 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 = = (a)

2 0.52 t-m

Due to triangular portion

3.8

X

0.15

-

1.90 X 2

0.15

2

X 3.8 2 = 0.22 t-m Total sagging moments at face =

2.28

X

X

= =

Fixing moments at face

= = = =

Net fixing moments at face

1 3

4.70

+

0.15

0.1 X 2

-

0.520 + 0.74 t-m 3.65 X( 3.8

0.15

X 0.05

0.216

6.00

-

4.70

X

1 7.81

)

5.95 t-m 5.95 - 0.74 5.21 t-m

Sagging moments at centre (a)

(b)

Due to rectangular portion

=

1.90

= 3.43 X 3.80 Due to triangular portion = 2 = 2.11 t-m Total sagging moments at centre

X 8 t-m

2.28

3.80

X

3.8

= =

2

3.43 + 5.54 t-m

2.11

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 : Fixing moments at centre

=

MOMENTS

Span AB CD AD

7.34 8.95 5.21

At face t-m (hogging) t-m (hogging) t-m (hogging)

(vi) Thickness of members The maximum moment in the barrels is For M 20 grade concrete and steel of Fe Kg/cm2 scbc = 70 sst = m = 13 sst = k = j =

0.378 0.874

R =

4.65 5.68 0.19

8.95 415 1500 1900

Kg/cm2 Kg/cm3

(vii)

Reinforcement

water side out side

11.552



= 27.84 cm Adopt overall thickness of all the members Then effective thickness (clear cover The reinforcement required at various points is given below :

(sagging) (sagging) (sagging)

t-m

The minimum effective thickness (d) required for bending moment M 8.95 X d = = bQ 100 X



At centre t-m t-m t-m

= = =

105 12

31 26 5.0

cm cm cm )

Span AB (Top Horizontal Slab) Moments in t-m

Reinforcement required

At face

7.34 t-m (hogging)

At

At centre

4.65 t-m (sagging)

Distribution Span CD (Bottom Horizontal Slab) Moments in t-m

20

Provide Provide

20 10

mm bars @ mm bars @

8.95 t-m (hogging)

At centre

5.68 t-m (sagging)

Distribution Span AD (vertical wall) Moments in t-m

At

23.0 cm c/c 17.0 cm c/c

2 26.26 Cm

=

Provide

20

mm bars @ At =

11.0 cm c/c 2 16.67 Cm

Provide Provide

20 10

mm bars @ mm bars @

18.0 cm c/c 17.0 cm c/c

Reinforcement required 2 15.28 Cm 20.0 cm c/c 2 -0.56 Cm

At

5.21 t-m (hogging) Provide

At centre

2 21.53 Cm 14.0 cm c/c 2 13.65 Cm

Reinforcement required

At face

At face

Provide

= mm bars @ At =

= mm bars @ At =

20

0.19 t-m (sagging)

Provide 20 mm bars @ -561.0 17.0 Distribution Provide 10 mm bars @ 200 mm 17.0 Hench Provide 10 mm bars @ 17.0 corner Provide 10 mm bars @ 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

20 mm f @ 23

cm c/c

10 mm f @ 17.0 cm c/c A

B

E 0.30

20 mm f @ -561 cm c/c

C.C. M - 20

20 mm f @ 20

8 mm f @ 17.0 cm c/c

3.50

cm c/c

D

F 20 20 mm f @ 18

0.30

3.50 m

mm f @

C 11 cm c/c

clear cover =

5.00

cm

cm c/c

0.30

3.50

DETAILS OF REINFORCEMENT IN BARREL

0.30

0.30

cm c/c cm c/c cm c/c cm c/c

20 mm f @14.0

cm c/c 10 mm f @ 17.0 cm c/c

20 mm f @ 23 cm c/c

20

mm f @

18 cm c/c

20

mm f @

20 cm c/c

3.50

10 mm bars @

0.30

10 mm bars @ 17 cm c/c

17 cm c/c

20

mm f @

18 cm c/c

20

mm f @

11 cm c/c

3.50

10 mm bars @ 17 cm c/c

0.30