Design of RCC Slab Culvert

Name of the work:-Road from R&B Road to SC colony of Pedalanka.

Construction of 6.00mts span culvert at 6/0 KM of Vemuladeevi channel

Design Philosophy:-

The design of 1V-- 6.37m right span culvert is carried as per the procedure out lined

below:-

Step1:-

The design discharge was fixed after arriving discharge based on the following methods:-

and area by considering actual cross-section of the channel.

Step2:-

The vertical clearence and afflux are verified.

below the maximum scour depth

Step3:-

The structural components are desined in the following manner:-

and culverts of medium importance is selected.

designed as per the guide lines given in relevent IRC codes.

a.As per the hydraulic particulars furnished by the Irrigation department

b.By Area-Velocity method using Manning's equation for arriving at the flow velocity

a.Hydraulic particulars like HFL,OFL are obtained from Irrigation department.

b.Bottom of deck level was fixed based on HFL and road formation levels on both sides.

c.Ventway calculations are done for fixation of ventway.

d.Normal scour depth with reference to HFL was calculated using Lacey's equations

e.After arriving at the Maximum scour depth,bottom level of the foundation was fixed

After arriving at bottom of deck level,bottom of foundation level and required ventway,the dimensions of the bridge are finalised.

a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges

b.Load combination is selected as per IRC 6:2000

c.Based on the trial pit particulars and soil test reports,type of foundation was selected.

d.The structural components like Abutment,raft foundation are

e.The deck slab is proposed as per the MOST drawing Nos.BD 1-74&BD 2-74

f.The dirt wall is proposed as per the drawings given in Plate No.7.25 of IRC:SP20-2002(Rural roads manual)

Design of Abutments

I)Design Parameters:-

Clear Right Span = 6.00m

= 6.740m

Width of the carriage way = 5.50m

= 0.515m

= 0.075m

= 1.200m

Thickness of dirt wall = 0.30m

Sectional area of dirt wall = 0.360sqm

Thickness of RAFT footing = 0.50m

Height of abutments = 1.804m

(As per hydralic calculations)

Top width of abutments = 0.690m

Bottom width of abutments = 2.00m

Sectional area of abutment section = 2.426sqm

Bank side batter of abutment = 1.310m

Stream side batter of abutment = 0.000m

Width of 1st footing = 2.30m

Thickness of 1st footing = 0.30m

= 0.15m

Bank side offset of 1st footing wrt abutment = 0.15m

= 2.45m

= 0.30m

= 0.30m

Bank side offset of 2nd footing wrt abutment = 0.15m

Width of 3rd footing = 0.00m

Thickness of 3rd footing = 0.00m

Canal side offset of 3rd footing wrt abutment = 0.00m

Bank side offset of 3rd footing wrt abutment = 0.00m

Width of VRCC RAFT footing = 6.55m

= 0.60m

Type of bearings = No bearings proposed

= 25KN/cum

= 24KN/cum

= 18KN/Cum

= 10KN/Cum

Deck slab length

Thickness of deck slab as per MOST Dg.BD 1-74

Thickness of wearing coat

Height of railing

Canal side offset of 1st footing wrt abutment

Width of 2nd footing

Thickness of 2nd footing

Canal side offset of 2nd footing wrt abutment

Thickness of VRCC RAFT footing

Unit weight of RCC (yrc)

Unit weight of PCC (ypc)

Density of back fill soil behind abutments (y)

Unit weight of water (yw)

= 30

= 54.04

= 0

= 15

= 1.20m

= 2.577m

= 0.477m

= 1.477m

= -0.923m

= 6.00t/sqm

= 25.00N/sqmm

= 415.00N/sqmm

Cover to reinforcement = 50.00mm

II)General loading pattern:-

As per IRC:6---2000,the following loadings are to be considered on the bridge or slabculvert:-

1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Earth pressure9.Seismic force10.Water pressure force

As per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.

III)Loading on the slab culvert for design of abutments:-

1.Dead Load:-

i)Self wieght of the deck slab = 238.64KN

ii)Self wieght of dirtwall over abutment = 49.50KN

iii)Self weight of wearing coat = 34.76KN

322.90KN

There is no need to consider snow load as per the climatic conditions

Angle of shearing resistance of back fill material(Q)

Angle of face of wall supporting earth with horizontal(In degrees)(in clock wise direction)(a)

Slope of back fill (b)

Angle of wall friction (q)

Height of surcharge considered (h3)

Road crest level (RTL)

Low bed level (LBL)

High flood Level (HFL)Bottom of foundation level (BFL) Safe Bearing Capacity of the soil (SBC)

Compressive strength of concrete for RCC Strip footing (fck)

Yield strength of steel (fy)

Self wieght of the abutments upto bottom most footing based on the preliminary section assumed:-

iv)Self wieght of the abutment section = 320.23KN

v)Self wieght of top footing = 91.08KN

vi)Self wieght of 2nd footing = 97.02KN

vii)Self wieght of 3rd footing = 0.00KN

viii)Self wieght of 4th footing = 0.00KN

508.33KN

ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment

S.No Description Load in KN Moment

1 155.97384 1.127 175.78

2 164.30832 0.345 56.69

3 0 0 0

320.28216 232.47

Location of resultant from toe of abutment = 0.73m

Distance of centroid of load from toe of abutment

Back batter(W1)

Centre portion(W2)

Front batter(W3)

W1W1

Eccentricity wrt centre of base of abutment = 0.270m

x)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footing


1 Back batter 155.97384 1.277 199.18

2 Centre portion 164.30832 0.495 81.33

3 Front batter 0 0 0

4 1st footing 91.08KN 1.15 104.74

411.36216 385.25


Eccentricity wrt centre of 1st footing= 0.210m

xi)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing

Distance of centroid of load from toe of 1st footing


1 Back batter 155.97384 1.427 222.57

2 Centre portion 164.30832 0.645 105.98

3 Front batter 0 0.3 0

4 1st footing 91.08KN 1.300 118.4

5 2nd footing 97.02KN 1.225 118.85

508.38216 565.8


Eccentricity = 0.115m

xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing


1 Back batter 0 1.427 02 Centre portion 0 0.645 03 Front batter 0 0.3 04 1st footing 0 1.00 05 2nd footing 0 0.92 06 3rd footing 0 0.00 0

0 0



2.Live Load:-

As per clause 201.1 of IRC:6--2000,the bridges and culverts of medium importance

GENERAL IRC Class-A loading Pattern

Distance of centroid of load from toe of 2nd footing

Distance of centroid of load from toe of 3rd footing

are to be designed for IRC Class A loading.

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

clauses 207.1.3&207.4

The ground contact area of wheels for the above placement,each axle wise isgiven below:-

Axle load Ground Contact Area(Tonnes) B(mm) W(mm)

11.4 250 5006.8 200 380

The IRC Class A loading as per the drawing is severe and the same is to be considered as per

Y

X

11.4t

11.4t

6.8t

6.8t

475

5500

Portion to be loadedwith 5KN/m² liveload

8000

3525

2.7 150 200

Assuming 0.475m allowance for guide posts/kerbs and the clear distance of vehicle from

the edge of guide post being 0.15m as per clause 207.1,the value of 'f' shown in the figure will

be 0.625m

0.625m

3.525m

4.15m

The total live load on the deck slab composes the following components:-

1.Wheel loads----Point loads 364.00KN

2.Live load in remaing portion(Left side)----UDL 21.06KN

2.Live load in remaing portion(Right side)----UDL 118.79KN

503.86KN

Resultant live load:-

Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)

Taking moments of all the forces w.r.t y-axis

S.No Distance from Y-axis Moment

1 57 0.875m 49.88KNm

2 57 0.875m 49.88KNm

3 57 2.675m 152.48KNm

4 57 2.675m 152.48KNm

5 34 0.875m 29.75KNm

6 34 0.875m 29.75KNm

7 34 2.675m 90.95KNm

8 34 2.675m 90.95KNm

9 21.0625 0.313m 6.58KNm

10 118.7925 4.688m 556.84KNm

Hence,the width of area to be loaded with 5KN/m2 on left side is (f) =

Similarly,the area to be loaded on right side (k) =

Wheel Load/UDL in KN

503.855 1209.52KNm

Distance of centroid of forces from y-axis

= 2.401m


Eccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)

Taking moments of all the forces w.r.t x-axis

S.No Load in KN Distance from X-axis Moment

1 57 9.005m 513.29KNm

2 57 9.005m 513.29KNm

3 57 7.805m 444.89KNm

4 57 7.805m 444.89KNm

5 34 3.505m 119.17KNm

6 34 3.505m 119.17KNm

7 34 0.505m 17.17KNm

8 34 0.505m 17.17KNm

9 21.06KN 4.690m 98.78KNm

10 118.79KN 4.690m 557.14KNm

503.855 2844.94KN

Distance of centroid of forces from x-axis

= 5.646m


Y

X5500

8000

Location of Resultant

2524

5574

Calculation of reactions on abutments:-

299.41KN

204.44KN

Hence,the critical reaction is Ra = 299.4KN

The corrected reaction at obtuse corner = 299.41KN

Assuming that the live load reaction acts at the centre of the contact area on the abutment,

Reaction due to loads Ra =

Reaction due to point loads = Rb =

Y

X5500

8000

Location of Resultant

2524

5574

300

300

185

815815

740

The eccentricty of the line of action of live load at bottom of abutment = 0.815m

----do----on top of 1st footing = 0.815m

----do----on top of 2nd footing = 0.740m

The eccentricity in the other direction need not be considered due to high section modulus in transverse direction.

3.Impact of vehicles:-

As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment

of live load by a factor 4.5/(6+L)

Hence,the factor is 0.353

Further as per clause 211.7 of IRC:6--2000,the above impact factor shall be only

50% for calculation of pressure on piers and abutments just below the level of bed block.There

is no need to increase the live load below 3m depth.

As such,the impact allowance for the top 3m of abutments will be 0.1765

For the remaining portion,impact need not be considered.

4.Wind load:-

The deck system is located at height of (RTL-LBL) 2.10m

The Wind pressure acting on deck system located at that height is considered for design.

As per clause 212.3 and from Table .4 of IRC:6---2000,the wind pressure at that hieght is=

59.48

Height of the deck system = 1.790

Breadth of the deck system = 7.38

The effective area exposed to wind force =HeightxBreadth =

Kg/m2.

300

300

185

815815

740

Hence,the wind force acting at centroid of the deck system = 3.91KN(Taking 50% perforations)

Further as per clause 212.4 of IRC:6---2000 ,300 Kg/m wind force is considered to be

acting at a hieght of 1.5m from road surface on live load vehicle.

Hence,the wind force acting at 1.5m above the road surface = 16.50KN

The location of the wind force from the top of RCC strip footing = 4.79m

5.Water current force:-

Water pressure considered on square ended abutments as per clause 213.2 of IRC:6---2000 is

24.18

(where the value of 'K' is 1.5 for square ended abutments)

For the purpose of calculation of exposed area to water current force,only 1.0m

width of abutment is considered for full hieght upto HFL

Hence,the water current force = 0.51KN

Point of action of water current force from the top of RCC raft footing = 2.90m

6.Tractive,braking effort of vehicles&frictional resistance of bearings:-

The breaking effect of vehicles shall be 20% of live load acting in longitudinal

direction at 1.2m above road surface as per the clause 214.2 of IRC:6--2000.

As no bearings are assumed in the present case,50% of the above longitudinal

force can be assumed to be transmitted to the supports of simply supported spans resting on

stiff foundation with no bearings as per clause 214.5.1.3 of IRC:6---2000

Hence,the longitudinal force due to braking,tractive or frictional resistance of

bearings transferred to abutments is

50.39KN

The location of the tractive force from the top of RCC raft footing = 4.49m

7.Buoyancy :-

As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the

P = 52KV2 = Kg/m2.

dead weight of the abutment shall be reduced by wieght of equal volume of water upto HFL.

The above reduction in self wieght will be considered assuming that the back fill behind the abutment is scoured.

For the preliminary section assumed,the volume of abutment section is

i)Volume of abutment section = 13.34Cum

ii)Volume of top footing = 3.80Cum

iii)Volume of 2nd footing = 4.04Cum

iv)Volume of 3rd footing = 0.00Cum

v)Volume of 4th footing = 0.00Cum

21.18Cum

Reduction in self wieght = 211.80KN

8.Earth pressure :-

As per clause 217.1 of IRC:6---2000,the abutments are to be designed for a

surcharge equivalent to a back fill of hieght 1.20m behind the abutment.

The coefficient of active earth pressure exerted by the cohesion less back fill on

the abutment as per the Coulomb's theory is given by

'2Sin(a+Q)

sina sin(a-q) sin(Q+q)sin(Q-b)

sin(a+b)

Sin(a+Q) = SIN[3.14*(54.04+30)/180] = 0.961Sin(a-q) = SIN[3.14*(54.04-15)/180] = 0.875Sina = SIN[3.14*(54.04)/180] = 0.97Sin(Q+q) = SIN[3.14*(30+15)/180] = 0.707Sin(Q-b) = SIN[3.14*(30-0)/180] = 0.5Sin(a+b) = SIN[3.14*(54.04+0)/180] = 0.97

From the above expression,

0.71

The hieght of abutment above GL,as per the preliminary section assumed = 1.804m

Hence,maximum pressure at the base of the wall Pa = 23.06KN/sqm

Ka =

Ka =

The pressure distribution along the height of the wall is as given below:-

Surcharge load = 15.34 KN/sqm

15.34

1.804

23.06 15.34

Area of the rectangular portion = 27.67Area of the triangular portion = 20.8

48.47

Taking moments of the areas about the toe of the wall

S.No Description Area Lever arm Moment

1 Rectangular 27.67 0.902 24.958342 Triangular 20.80 0.60133333 12.50773333

48.47 37.46607333

Height from the bottom of the wall = 0.77m

The active Earth pressure acts on the abutment as shown below:-

0.70

50.961.804m

0.77m

54.04

2.000.56

Total earth pressure acting on the abutment P = 266.60KN

168.01KN

206.99KN

Eccentricity of vertical component of earth pressure = 0.44m

9.Siesmic force :-

As per clause 222.1 of IRC:6---2000,the bridges in siesmic zones I and II need not be

designed for siesmic forces.The location of the slab culvert is in Zone-I.Hence,there is no need to

design the bridge for siesmic forces.

10.Water pressure force:-

The water pressure distribution on the abutment is as given below:-

HFL 1.48m

2.40

BFL -0.92m

Horizontal component of the earth pressure Ph =

Vertical component of the earth pressure Pv =

24.00kn/sqm

Total horizontal water pressure force = 158.40KN

The above pressure acts at height of H/3 = 0.80m

IV)Check for stresses for abutments&footings:-

a)Load Envelope-I:-(The Canal is dry,back fill scoured with live load on span)

i)On top of RCC raft

The following co-ordinates are assumed:-

a)x-Direction-----At right angle to the movement of vehicles

b)y-Direction-----In the direction of movement of vehicles

S.No Type of load

1 Reaction due to dead load from super structure 322.90KN -0.740 0.00

2 Self wieght of abutment&footings 508.38KN 0.115 0.000

3 405.10KN -0.740 0.000

4 Impact load 0.00 0.00 0.00

1236.38

S.No Type of load Direction x or y

1 Wind load 16.50KN x-Direction 4.79

2 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 4.49

3 Water current force 0.51KN x-Direction 2.90

Check for stresses:-

About x-axis:-

Breadth of 2nd footing b = 6.25m

Depth of 2nd footing d = 2.45m

Vertical forces acting on the abutment (P) composes of the following components

Intensity in KN

Eccentricty about x-axis(m)

Eccentricty about y-axis(m)

Reaction due to live load with impact factor---(Wheel loads+UDL)

Horizontal forces acting/transferred on the abutment (H) composes of the following components

Intensity in KN

Location(Ht.from the section considered).(m)

Area of the footing = A = 15.3125

Section modulus of bottom footing 6.25

about x-axis --Zx =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.740 6.112 Self wieght of abutment&footings 508.38KN 0.115 36.873 Reaction due to live load with impact factor 405.10KN -0.740 7.664 Impact load 0.00KN 0.000 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.49 -36.18

14.46

S.No Type of load Eccentricity

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.740 36.072 Self wieght of abutment&footings 508.38KN -0.115 29.543 Reaction due to live load with impact factor 405.10KN 0.740 45.254 Impact load 0.00KN 0.000 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.49 36.18

147.04

Stress at heel = P/A(1+6e/b)+M/Z = 14.46 KN/Sqm>-2000KN/sqm.

Hence safe.

Stress at toe = P/A(1+6e/b)+M/Z = 147.04 KN/Sqm<4000KN/sqm

Hence safe.

About y-axis:-

Breadth of 3rd footing b = 2.45m

Depth of 3rd footing d = 6.25m

Area of the footing = A = 15.3125

Section modulus of bottom footing about = 15.95

y-axis--Zy =

m2

(1/6)bd2 = m3

For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2

For M15 grade of concrete permissible tensile stress in bending tension is -2N/mm2

Intensity in KN (P)

Eccentricity/Lever arm

Stress at heelP/A(1+6e/b)

Intensity in KN (P)

Stress at toeP/A(1+6e/b)

m2

(1/6)bd2 = m3

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Self wieght of abutment&footings 508.38KN 0.00 33.23 Reaction due to live load with impact factor 405.10KN 0.000 26.464 Impact load 0.00KN 0.00 0

Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.79 -4.966 Water current force 0.51KN 2.90 -0.09

75.70

S.No Type of load


Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.79 4.966 Water current force 0.51KN 2.90 0.09

85.8

Stress at up stream side P/A(1+6e/b)+M/Z = 75.70 KN/Sqm>-2000KN/sqm.edge =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 85.8 KN/Sqm<4000KN/sqmedge =

Hence safe.

i)On top of 2nd footing




S.No Type of load



Intensity in KN (P)


Stress at upstream edgeP/A(1+6e/b)

Intensity in KN (P)


Stress at D/S edgeP/A(1+6e/b)

Vertical load acting on the abutment (P) composes of the following components

Intensity in KN




2 Self wieght of abutment&cut waters 411.36KN 0.210 0.000

3 Reaction due to live load with impact factor 405.10KN -0.740 0.000

4 Impact load 0.00 0.000 0.00






About x-axis:-

Breadth of 1st footing b = 6.25mDepth of 1st footing d = 2.30mArea of the footing = A = 14.375

Section modulus of base of abutment 5.51

about x-axis--Zx =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load



7.48


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 38.42

Horizontal load acting/transferred on the abutment (H) composes of the following components

Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


2 Self wieght of abutment&footings 411.36KN -0.21 22.853 Reaction due to live load with impact factor 405.10KN 0.74 48.24 Impact load 0.00KN 0.00 0


147.78


Hence safe.


Hence safe.

About y-axis:-



about y-axis--Zy =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load



74.22

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Self wieght of abutment&footings 411.36KN 0.00 28.623 Reaction due to live load with impact factor 405.10KN 0.000 28.18

m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)



4 Impact load 0.00KN 0.00 0Horizontal loads:- (Stress = M/Z)

5 Wind load 16.50KN 4.49 4.956 Water current force 0.51KN 2.60 0.09

84.3

Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 74.22 KN/Sqm>-2000KN/sqm.

Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 84.3 KN/Sqm<4000KN/sqm

Hence safe.

i)On top of 1st footing


a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehicles

S.No Type of load

1 Reaction due to dead load from super structure 322.90KN -0.815 0.002 Self wieght of abutment&footings 320.28KN 0.270 0.0003 Reaction due to live load with impact factor 405.10KN -0.815 0.000

4 Impact load 0.00 0.000 0.00


1 Wind load 16.50KN x-Direction 4.192 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 3.893 Water current force 0.51KN x-Direction 2.30


About x-axis:-

Breadth of abutment b = 6.25mDepth of abutment d = 2.00mArea of the footing = A = 12.5


about x-axis--Zx =

i.e, 4000KN/sqm


Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3


i.e, -2000KN/sqm

S.No Type of load



-5.43


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.82 46.042 Self wieght of abutment&footings 320.28KN -0.27 18.983 Reaction due to live load with impact factor 405.10KN 0.82 57.764 Impact load 0.00KN 0.00 0


169.82

Stress at heel = P/A(1+6e/b)+M/Z = -5.43 KN/Sqm>-2000KN/sqm.

Hence safe.


Hence safe.

About y-axis:-

Breadth of abutment b = 2.00mDepth of abutment d = 6.25mArea of the footing = A = 12.5


about y-axis--Zy =

i.e, 4000KN/sqm

i.e, -2000KN/sqm


Intensity in KN (P)



Intensity in KN (P)


m2

(1/6)bd2 = m3



S.No Type of load



78.46

S.No Type of load


Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.19 5.316 Water current force 0.51KN 2.30 0.09

89.26



Hence safe.

b)Load Envelope-II:-(The Canal is full,back fill intact with no live load on span)

i)On top of RCC Raft footing




S.No Type of load


Self wieght of abutment&cut waters 508.38KN

Intensity in KN (P)



Intensity in KN (P)




Intensity in KN



Reduction in self weight due to buoyancy -211.80KN

2 Net self weight 296.58KN 0.115 0.000

3 Vertical component of earth pressure 206.99KN 0.440 0.000





4 Horizontal load due to earth pressure 168.01KN y-Direction 1.37

5 Water pressure force 158.40KN y-Direction 0.80


About x-axis:-

Breadth of bottom footing b = 6.25mDepth of bottom footing d = 2.45mArea of the footing = A = 15.3125


about x-axis --Zx =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.74 6.112 Net self wieght of abutment&footings 296.58KN 0.11 21.513 Vertical component of Earth pressure 206.99KN 0.44 19.23

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.37 -36.895 Water pressure force 158.40KN 0.80 20.3

30.23


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 36.072 Net self wieght of abutment&footings 296.58KN -0.11 17.233 Vertical component of Earth pressure 206.99KN -0.44 7.81


Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.37 36.895 Water pressure force 158.40KN 0.80 -20.3

77.73


Hence safe.


Hence safe.

About y-axis:-

Breadth of bottom footing b = 2.45mDepth of bottom footing d = 6.25mArea of the footing = A = 15.3125


about y-axis --Zy =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Net self wieght of abutment&footings 296.58KN 0.00 19.373 Vertical component of Earth pressure 206.99KN 0.00 13.52


48.93



Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.79 4.965 Water pressure force 0.51KN 2.90 0.1

59.03


m2

(1/6)bd2 = m3



Intensity in KN (P)


Stress at U/S EdgeP/A(1+6e/b)

Intensity in KN (P)



Hence safe.

ii)On top of 2nd footing




S.No Type of load


Self wieght of abutment&footings 508.38KN











About x-axis:-

Breadth of 2nd footing b = 6.25mDepth of 2nd footing d = 2.30mArea of the footing = A = 14.375


about x-axis --Zx =


Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3


i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load



31.55




83.44


Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 4000KN/sqm

i.e, -2000KN/sqm


Intensity in KN (P)



Intensity in KN (P)


m2

(1/6)bd2 = m3



S.No Type of load



52.45




62.53



Hence safe.

iii)On top of 1st footing




S.No Type of load


Self wieght of abutment&cut waters 411.36KN




Intensity in KN (P)



Intensity in KN (P)



Intensity in KN











About x-axis:-



about x-axis --Zx =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load



29.23




77.89


Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 4000KN/sqm

i.e, -2000KN/sqm

S.No Type of load



48.85




58.25



m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


Hence safe.

V)Check for stability of abutments:-

a)Load Envelope-III:-(The Canal is dry,back fill intact with live load on span)




S.No Type of load

1 Reaction due to dead load from super structure 322.90KN 0.82 0.00

2 Self wieght of abutments 320.23KN 0.270 0.000

3 Reaction due to live load with impact factor 405.10KN 0.82 0.000

4 Vertical component of Active Earth pressure 206.99KN 0.440 0.00

1255.22KN




3 Horizontal Active Earth pressure force 168.01KN y-Direction 0.77

234.90KN

Check for stability against over turning:-

Taking moments of all the overturning forces about toe of the abutment wrt x-axis,

Moment due to tractive,braking&frictional resistance of bearings = 211.12Kn-m

Moment due to active earth pressure force = 129.87Kn-m

Total overturning moment = 340.99Kn-m

Taking moments of all the restoring forces about toe of the abutment wrt x-axis,,

Moment due to self weight of abutment = 406.69Kn-m

Moment due to live load reaction on abutment = 735.27Kn-m


Intensity in KN




Intensity in KN


Moment due to super structure load reaction on abutment = 586.05Kn-m

Moment due to vertical component of active earth pressure = 298.07Kn-m

Total Restoring moment = 2026.08Kn-m

Factor of safety = 5.94180648 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)

Check for stability against sliding:-

1255.22KN

234.90KN

Coefficient of friction between concrete surfaces = 0.80

4.27491751 > 1.5 Hence safe

(As per clause 706.3.4 of IRC:78-2000)

b)Load Envelope-IV:-(The Canal is running upto HFL with no live load on span)




S.No Type of load

1 Reaction due to dead load from super structure 322.90KN 0.82 0.00

Self wieght of abutments 320.23KN

-133.40KN

2 Net self wieght 186.83KN 0.270 0.000

3 Vertical component of Active Earth pressure 206.99 0.440 0.00




Total vertical load acting on the base of the abutment Vb =

Total sliding force,ie,horizontal load on the abutment Hb =

Factor of safety against sliding Fs =


Intensity in KN



Reduction in self weight due to buoyancy


Intensity in KN


3 Active Earth pressure force 168.01KN y-Direction 0.77

4 Force due to water pressure 158.40KN y-Direction 0.20

Check for stability against over turning:-

Taking moments of all the overturning forces about toe of the abutment wrt x-axis,

Moment due to tractive,braking&frictional resistance of bearings = 0.00Kn-m

Moment due to active earth pressure force = 129.87Kn-m

Total overturning moment = 129.87Kn-m

Taking moments of all the restoring forces about toe of the abutment wrt x-axis,

Moment due to self weight of abutment = 237.27Kn-m

Moment due to water pressure force on the abutment = 31.68Kn-m

Moment due to super structure load reaction on abutment = 586.05Kn-m

Moment due to vertical component of active earth pressure = 298.07Kn-m

Total Restoring moment = 1153.08Kn-m

Factor of safety = 8.87855106 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)

Check for stability against sliding:-

552.22KN

168.01KN

Coefficient of friction between concrete surfaces = 0.80

2.62940787 > 1.5 Hence safe

(As per clause 706.3.4 of IRC:78-2000)

Total vertical load acting on the base of the abutment Vb =

Total sliding force,ie,horizontal load on the abutment Hb =

Factor of safety against sliding Fs =

DESIGN OF RAFT FOR THE SLAB CULVERT

Name of the work:-Slab culvert on Vemuladeevi Channel

Abutment

Abutment

Length of the Raft:- = 12.60m

Width of the Raft:- = 6.55m

Total load on the Raft:-

Dead Load:-

Wt.of Deck slab = 477.28Kn

Wt.of wearing coat = 69.51Kn

Wt.of bed blocks over abutments = 99.00Kn

Wt.of abutments

Footing-I = 182.16KnFooting-II = 194.04KnWt.of abutments = 640.46Kn

Total 1662.45Kn

Dead load stress = 20.14Kn/Sqm

Live Load:-

Taking IRC Class-A loading

Wheel width in the direction of movement =0.2+0.2+0.25/2 = 0.625m

11.4 11.4 6.8 6.8 6.8

1.2 4.3 3.0 3.0 0.475

0.625

12.60m

Centre of gravity of loading from 1st 11.4t load =

= 4.33m

Centre of gravity from the end of raft = 4.955m


Stress due to live load = 1xP(1+6e/b)(Taking single lanes) A

Max.stress = 11.45Kn/Sqm

Min.stress = -0.78Kn/Sqm

Total stress due to dead load and live load

Max.Stress = 31.59Kn/Sqm

Min.Stress = 19.36Kn/Sqm

Assuming the depth of raft as 60cm

Stress due to self weight of raft = 15.00Kn/Sqm

Stress due to wieght of base concrete = 7.20Kn/Sqm

Hence,the Max.stress on the soil = 53.79Kn/Sqm

Which is less than 6t/sqm(Soil testing report)

Hence safe.

Net Max.upward pressure acting on Raft = 31.59Kn/Sqm

Net Min.upward pressure acting on Raft = 19.36Kn/Sqm

The design stress = 25.48Kn/Sqm

Hence,the UDL on the raft = 25.48Kn/m

Design of Raft:-

The raft will be analysed as a continuous beam of 1m width with the loadingas shown below:-

1.30 10.00 1.30

UDL of 25.48Kn/m

After analysis the bending moment diagram is as given below:

517

37.5

Max.Negative bending moment Mu = 517.00KNm

Max.Positive bending moment Mu = 37.50KNm

Effective depth required d = 387.11mm

Over all depth provided = 600.00mm

Effective depth provided(Assuming 40mm cover) d = 542.00mm

Bottom steel:-

1.76

From table 3 of SP 16,percentage of steel required = 0.535

Area of steel required = 2899.70sqmm

Top steel:-

0.128

From table 3 of SP 16,percentage of steel required/Minimum steel = 0.12

Area of steel required = 650.40sqmm

Hence provide 12mm dia HYSD bars@ 150mm c/c spacing at bottom and provide 20mm bars at 110mm c/c at top

2854.55sqmm

753.60sqmm

Provide distribution reinforcement of 0.12% both at top and bottom

Area = 720.00sqmm

Mu/0.138fckb =

Mu/bd2 =

Mu/bd2 =

Hence Ast provided at top =

Hence Ast provided at bottom =

Adopting 12mm dia bars,the spacing required is = 157.00mm

Hence provide 12mm dia bars @ 150mm c/c spacing at top& bottom

Effective depth = 300-50-6 = 0.244m

Clear span between abutments = 3.00-2x(0.125+2x(0.15)) = 2.150m

Effective span = 2.15+0.244/2 = 2.27m

For continuous slab,clear span will be the effective span,effective span =

The raft is proposed to be designed for the Max.stress of 5.47t/sqm

Assuming 1m width of raft,the UDL on the raft is 53.790t/Sqm

The raft is treated as simply supported beam with over hangs

34.71t-m

2.42t-m

Max.negative moment = 2.420t-m

Max.positive moment = 34.710t-m

Hence,the Max.positive moment = wl2/8 =

Max.Negative moment for over hangs = wl12/2 =

Hence,the design moment = 34.710t-m

67.140094 7.7x100

Hence provide overall depth of 30cm,the effective depth available is

300-50-6 = 24.4

77.65sqcm at centre 2000x0.916x24.4

Spacing of 12mm dia bars required = 1.13x100/7.9 = 14.303797468

However provide 12mm bars at 125mm c/c at centre

5.41sqcm for over hangs 2000x0.916x24.4

Spacing of 12mm dia bars required = 1.13x100/0.56 = 201.78571429

However provide 12mm bars at 250mm c/c

Provide distribution reinforcement of 0.12% both at top and bottom

Area = 3.60sqcm

Adopting 10mm dia bars,the spacing required is = 0.785x100/3.6 = 21.805556

Hence provide 10mm dia bars @ 175mm c/c spacing

The details of Reinforcement is as shown below:-

12mm bars@ 125 c/c(Curtail 50% of cranks at the centre of abutment

3.00m

12mm bars@250mm c/c

Depth required = 3.53x105

Area of steel required = 3.53x105

Area of steel required = 0.25x105

DESIGN OF RAFT FOR THE SLAB CULVERT

0.625 11.41.2 11.44.3 6.8

3 6.83 6.8

0.475

2.27m

1.1304

1.1304

0.785

12mm bars@250mm c/c

Hydraulic design

Hydraulic Particulars:-

1.Full supply Level 1.477

2.Ordinary Flood level ------

3.Lowest Bed level 0.477

4.Average bed slope 0.000059(1 in 17000)

0.020(As per table 5 of IRC:SP 13)

6.Vertical clearence proposed 0.510(As per clause 15.5 of IRC:SP 13&as per profile)

6.Bottom of deck proposed 1.987(MFL+Vertical clearence)

7.Road Crest level 2.577(Bottom of deck level+thickness of deck slab)

8.Width of carriage way 5.500

Discharge Calculations:-

1)From the data furnished by the Irrigation Department:-

Design discharge = 2.074Cumecs

2)Area Velocity method:-

Depth of flow w.r.t HFL = 1.000m

Bed width = 4.50m

Assuming side slopes 1:1.5 in clayey soils,top width at HFL = 6.000m

Wetted Area = 5.25sqm

Wetted perimetre = 7.33m

Hydraulic Radius R= Total area/Wetted perimeter = 0.72

Velocity V = 0.31m/sec

Discharge Q = AXV 1.63Cumecs

Design Discharge = 2.074Cumecs

Design Velocity = 0.31m/sec

5.Rugosity Coefficient(n)

1/nX(R2/3XS1/2)

Ventway Calculations(H.F.L Condition):-

Assuming the stream to be truly alluvial,the regime width is equal to linear waterway required for the drain.

6.91m

The actual top width is almost equal to the above regime width.Hence,the stream is almost truly alluvial in nature.As per IRC:SP--13,the ventway calculations for alluvial streams are as given below:-

Assuming afflux = x = 0.05m6.00m

Clear span = 6.00mEffective linear water way = 6.00m

Depth of flow = 1.00m

Head due to velocity of approach = 0.004m

Combined head due to Velocity of approach and 0.054mafflux

0.93m/sec

Linear water way required 2.24m

No.of vents required = = 0.3733333333333Say---1 Vent

In alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scour depth and expensive training works.

Hence No.of vents required as per the width of the stream at H.F.L= 1(6/6.00)

No.of vents to be provided 1Nos

No.of piers = 0Nos

Scour Depth Calculations:-

As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate margin of safety for foundations and protection works

Hence,the discharge for design of foundations = 1.30XDesign Discharge =

Discharge per metre width of foundations = q =

Hence,as per Lacey's silt theory,the regime width W = 4.8Q1/2 = 4.8*2.0740.5 =

Width of channel at H.F.L(b+h) =

di =

(Vmax2/2g)X[di/(di+x)]2

hi =

Velocity through vents Vv = 0.90X(2ghi)1/2 =

LWW = Qd/(VvXdi) =

LWW /LC

Lacey's Silt factor ' f ' = 1.76Xm1/2(For normal silt) =

Normal scour depth D = 1.34(q2/f)1/3 =

Bottom level of foundation =

Depth of foundation below low bed level =

The Minimum Safe Bearing capacity of the soil is considered as 65 KN/m2 at a depth of 1.50m below LBL

Hence open foundation in the form of raft is proposed at a depth of 1.85m below LBL,ie,at a level of

Cut-off walls and aprons are not required from scour depth point of view

Maximum scour depth Dm = 1.5XD =

Depth of foundation = Dm + Max.of 1.2m or 1/3 Dm =

Hydraulic design

The actual top width is almost equal to the above regime width.Hence,the stream is almost truly alluvial in nature.

In alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scour

As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate

2.76Cumecs

1.00

0.46

0.80m

1.20m

2.40m

-0.923m

1.400m

-0.923m

Date post:	23-Dec-2015
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Design of RCC Slab Culvert

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