design of 10m span rcc slab culvert

Construction of 10.00mts span culvert on Nathalova Drain at Saripalli

Name of the work:-

Design Philosophy:-

The design of 1V-- 10.37m 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 3-74&BD 4-74

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 = 10.00m

= 10.740m

Width of the carriage way = 5.50m

= 0.790m

= 0.075m

= 1.200m

Thickness of dirt wall = 0.30m

Sectional area of dirt wall = 0.440sqm

Thickness of RAFT footing = 0.70m

Height of abutments = 2.700m

(As per hydralic calculations)

Top width of abutments = 0.690m

Bottom width of abutments = 2.20m

Sectional area of abutment section = 3.902sqm

Bank side batter of abutment = 1.510m

Stream side batter of abutment = 0.000m

Width of 1st footing = 2.50m

Thickness of 1st footing = 0.30m

= 0.15m

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

= 2.65m

= 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 = 6.85m

= 0.70m

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 3-74

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

= 60.81

= 0

= 15

= 1.20m

= 3.665m

= 0.250m

= 2.200m

= -1.500m

= 8.00t/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 = 583.32KN

ii)Self wieght of dirtwall over abutment = 60.50KN

iii)Self weight of wearing coat = 55.38KN

699.20KN

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 Raft 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 = 515.06KN

v)Self wieght of top footing = 99.00KN

vi)Self wieght of 2nd footing = 104.94KN

vii)Self wieght of 3rd footing = 0.00KN

viii)Self wieght of 4th footing = 0.00KN

719.00KN

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

S.No Description Load in KN Moment

1 269.082 1.193 321.01

2 245.916 0.345 84.84

3 0 0 0

514.998 405.85

Location of resultant from toe of abutment = 0.79m

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 = 0.310m

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


1 Back batter 269.082 1.343 361.38

2 Centre portion 245.916 0.495 121.73

3 Front batter 0 0 0

4 1st footing 99.00KN 1.25 123.75

613.998 606.86


Eccentricity wrt centre of 1st footing= 0.260m

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 269.082 1.493 401.74

2 Centre portion 245.916 0.645 158.62

3 Front batter 0 0.3 0

4 1st footing 99.00KN 1.400 138.6

5 2nd footing 104.94KN 1.325 139.05

718.938 838.01


Eccentricity = 0.155m

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


1 Back batter 0 1.493 02 Centre portion 0 0.645 03 Front batter 0 0.3 04 1st footing 0 1.10 05 2nd footing 0 1.03 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

10000

35252925

11380

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 33.56KN

2.Live load in remaing portion(Right side)----UDL 189.29KN

586.86KN

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 33.5625 0.313m 10.49KNm

10 189.2925 4.688m 887.31KNm

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

586.855 1543.90KNm

Distance of centroid of forces from y-axis

= 2.631m


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 11.005m 627.29KNm

2 57 11.005m 627.29KNm

3 57 9.805m 558.89KNm

4 57 9.805m 558.89KNm

5 34 5.505m 187.17KNm

6 34 5.505m 187.17KNm

7 34 2.505m 85.17KNm

8 34 2.505m 85.17KNm

9 33.56KN 5.690m 190.97KNm

10 189.29KN 5.690m 1077.07KNm

586.855 4185.06KN

Distance of centroid of forces from x-axis

= 7.131m


Y

X5500

10000

Location of Resultant

2631

7131

11380

Calculation of reactions on abutments:-

367.74KN

219.12KN

Hence,the critical reaction is Ra = 367.7KN

The corrected reaction at obtuse corner = 367.74KN

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 =

300

300

185

815815

740

Y

X5500

10000

Location of Resultant

2631

7131

11380

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 0.269

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 0.1345

For the remaining portion,impact need not be considered.

4.Wind load:-

The deck system is located at height of (RTL-LBL) 3.42m

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 = 2.065

Breadth of the deck system = 11.38

Kg/m2.

300

300

185

815815

740

The effective area exposed to wind force =HeightxBreadth =

Hence,the wind force acting at centroid of the deck system = 6.97KN(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 raft footing = 5.97m

5.Water current force:-

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

26.286

(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 = 0.90KN

Point of action of water current force from the top of RCC raft footing = 4.47m

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

58.69KN

The location of the tractive force from the top of RCC raft footing = 5.67m

7.Buoyancy :-

P = 52KV2 = Kg/m2.

As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the 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 = 21.46Cum

ii)Volume of top footing = 4.13Cum

iii)Volume of 2nd footing = 4.37Cum

iv)Volume of 3rd footing = 0.00Cum

v)Volume of 4th footing = 0.00Cum

29.96Cum

Reduction in self wieght = 299.58KN

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*(62.46+30)/180] = 0.999Sin(a-q) = SIN[3.14*(62.46-15)/180] = 0.737Sina = SIN[3.14*(62.46)/180] = 0.886Sin(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*(62.46+0)/180] = 0.886

From the above expression,

0.6

The hieght of abutment above GL,as per the preliminary section assumed = 2.700m

Hence,maximum pressure at the base of the wall Pa = 29.16KN/sqm

Ka =

Ka =

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

Surcharge load = 12.96 KN/sqm

12.96

2.700

29.16 12.96

Area of the rectangular portion = 34.99Area of the triangular portion = 39.37

74.36

Taking moments of the areas about the toe of the wall

S.No Description Area Lever arm Moment

1 Rectangular 34.99 1.35 47.23652 Triangular 39.37 0.9 35.433

74.36 82.6695

Height from the bottom of the wall = 1.11m

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

0.69

44.192.700m

1.11m

60.81

2.200.62

Total earth pressure acting on the abutment P = 408.97KN

293.36KN

284.95KN

Eccentricity of vertical component of earth pressure = 0.48m

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 2.200m

3.70

BFL -1.500m

Horizontal component of the earth pressure Ph =

Vertical component of the earth pressure Pv =

37.00kn/sqm

Total horizontal water pressure force = 376.48KN

The above pressure acts at height of H/3 = 1.23m

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 699.20KN -0.740 0.00

2 Self wieght of abutment&footings 718.94KN 0.155 0.000

3 466.66KN -0.740 0.000

4 Impact load 0.00 0.00 0.00

1884.79

S.No Type of load Direction x or y

1 Wind load 16.50KN x-Direction 5.97

2 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 5.67

3 Water current force 0.90KN x-Direction 4.47

Check for stresses:-

About x-axis:-

Breadth of 2nd footing b = 6.25m

Depth of 2nd footing d = 2.45m

Area of the footing = A = 15.3125

Section modulus of bottom footing 6.25

about x-axis --Zx =

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)

m2

(1/6)bd2 = m3

For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.740 13.222 Self wieght of abutment&footings 718.94KN 0.155 53.943 Reaction due to live load with impact factor 466.66KN -0.740 8.834 Impact load 0.00KN 0.000 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 5.67 -53.22

22.77

S.No Type of load Eccentricity

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.740 78.12 Self wieght of abutment&footings 718.94KN -0.155 39.963 Reaction due to live load with impact factor 466.66KN 0.740 52.134 Impact load 0.00KN 0.000 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 5.67 53.22

223.41

Stress at heel = P/A(1+6e/b)+M/Z = 22.77 KN/Sqm>-2800KN/sqm.

Hence safe.

Stress at toe = P/A(1+6e/b)+M/Z = 223.41 KN/Sqm<5000KN/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 =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/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



S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Self wieght of abutment&footings 718.94KN 0.00 46.953 Reaction due to live load with impact factor 466.66KN 0.000 30.484 Impact load 0.00KN 0.00 0

Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 5.97 -6.186 Water current force 0.90KN 4.47 -0.25

116.66

S.No Type of load


Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 5.97 6.186 Water current force 0.90KN 4.47 0.25

129.52

Stress at up stream side P/A(1+6e/b)+M/Z = 116.66 KN/Sqm>-2800KN/sqm.edge =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 129.52 KN/Sqm<5000KN/sqmedge =

Hence safe.

i)On top of 2nd footing




S.No Type of load


2 Self wieght of abutment&cut waters 614.00KN 0.260 0.000

3 Reaction due to live load with impact factor 466.66KN -0.740 0.000

4 Impact load 0.00 0.000 0.00

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








About x-axis:-

Breadth of 1st footing b = 6.25mDepth of 1st footing d = 2.50mArea of the footing = A = 15.625

Section modulus of base of abutment 6.51

about x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 12.962 Self wieght of abutment&footings 614.00KN 0.26 43.223 Reaction due to live load with impact factor 466.66KN -0.74 8.654 Impact load 0.00KN 0.00 0


16.42




205.52

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)



Hence safe.


Hence safe.

About y-axis:-



about y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



107.94

S.No Type of load



119.9

Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 107.94 KN/Sqm>-2800KN/sqm.

m2

(1/6)bd2 = m3


For M20 grade of concrete permissible tensile stress in bending tension is -2N/mm2

Intensity in KN (P)



Intensity in KN (P)



Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 119.9 KN/Sqm<5000KN/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 699.20KN -0.815 0.002 Self wieght of abutment&footings 515.00KN 0.310 0.0003 Reaction due to live load with impact factor 466.66KN -0.815 0.000

4 Impact load 0.00 0.000 0.00


1 Wind load 16.50KN x-Direction 5.372 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 5.073 Water current force 0.90KN x-Direction 3.87


About x-axis:-

Breadth of abutment b = 6.25mDepth of abutment d = 2.20mArea of the footing = A = 13.75


about x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)


Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



1 Reaction due to dead load from super structure 699.20KN -0.82 11.072 Self wieght of abutment&footings 515.00KN 0.31 42.523 Reaction due to live load with impact factor 466.66KN -0.82 7.394 Impact load 0.00KN 0.00 0


1.96




236.46


Hence safe.


Hence safe.

About y-axis:-

Breadth of abutment b = 2.20mDepth of abutment d = 6.25mArea of the footing = A = 13.75


about y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 50.852 Self wieght of abutment&footings 515.00KN 0.00 37.453 Reaction due to live load with impact factor 466.66KN 0.000 33.94

Intensity in KN (P)


m2

(1/6)bd2 = m3



Intensity in KN (P)



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

5 Wind load 16.50KN 5.37 -6.196 Water current force 0.90KN 3.87 -0.24

115.81

S.No Type of load



128.67



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 718.94KN

Reduction in self weight due to buoyancy -299.58KN

2 Net self weight 419.35KN 0.155 0.000

3 Vertical component of earth pressure 284.95KN 0.480 0.000

Intensity in KN (P)




Intensity in KN








4 Horizontal load due to earth pressure 293.36KN y-Direction 1.71

5 Water pressure force 376.48KN y-Direction 1.23


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, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 13.222 Net self wieght of abutment&footings 419.35KN 0.16 31.463 Vertical component of Earth pressure 284.95KN 0.48 27.18

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 293.36KN 1.71 -80.315 Water pressure force 376.48KN 1.23 74.3

65.81


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.74 78.12 Net self wieght of abutment&footings 419.35KN -0.16 23.313 Vertical component of Earth pressure 284.95KN -0.48 10.03

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 293.36KN 1.71 80.315 Water pressure force 376.48KN 1.23 -74.3

117.49


Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


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, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Net self wieght of abutment&footings 419.35KN 0.00 27.393 Vertical component of Earth pressure 284.95KN 0.00 18.61


85.23



Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 5.97 6.185 Water pressure force 0.90KN 4.47 0.3

98.09



Hence safe.

m2

(1/6)bd2 = m3



Intensity in KN (P)


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

Intensity in KN (P)


ii)On top of 2nd footing




S.No Type of load


Self wieght of abutment&footings 718.94KN











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 =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load


Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)





65.17




130.1


Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load


Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 5.67 -6.25

Intensity in KN (P)


m2

(1/6)bd2 = m3



Intensity in KN (P)



5 Water current force 0.90KN 4.17 -0.391.13




104.13



Hence safe.

iii)On top of 1st footing




S.No Type of load


Self wieght of abutment&cut waters 614.00KN








Intensity in KN (P)



Intensity in KN




Intensity in KN





About x-axis:-



about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



54.76




117.05


Hence safe.


Hence safe.

About y-axis:-

m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)




about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



80.26




91.56



Hence safe.

V)Check for stability of abutments:-

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



m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)



S.No Type of load

1 Reaction due to dead load from super structure 699.20KN 0.82 0.00

2 Self wieght of abutments 515.06KN 0.310 0.000

3 Reaction due to live load with impact factor 466.66KN 0.82 0.000

4 Vertical component of Active Earth pressure 284.95KN 0.480 0.00

1965.87KN




3 Horizontal Active Earth pressure force 293.36KN y-Direction 1.11

368.54KN

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 = 315.14Kn-m

Moment due to active earth pressure force = 326.14Kn-m

Total overturning moment = 641.28Kn-m

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

Moment due to self weight of abutment = 726.23Kn-m

Moment due to live load reaction on abutment = 893.65Kn-m

Moment due to super structure load reaction on abutment = 1338.96Kn-m

Moment due to vertical component of active earth pressure = 450.23Kn-m

Total Restoring moment = 3409.07Kn-m

Factor of safety = 5.31601172 > 2.0 Hence safe


Intensity in KN




Intensity in KN


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

Check for stability against sliding:-

1965.87KN

368.54KN

Coefficient of friction between concrete surfaces = 0.80

4.26734705 > 1.5 Hence safe


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 699.20KN 0.82 0.00

Self wieght of abutments 515.06KN

-214.60KN

2 Net self wieght 300.46KN 0.310 0.000

3 Vertical component of Active Earth pressure 284.95 0.480 0.00




3 Active Earth pressure force 293.36KN y-Direction 1.11

4 Force due to water pressure 376.48KN y-Direction 0.63

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 = 326.14Kn-m

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


Total overturning moment = 326.14Kn-m

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

Moment due to self weight of abutment = 423.65Kn-m

Moment due to water pressure force on the abutment = 238.43Kn-m

Moment due to super structure load reaction on abutment = 1338.96Kn-m

Moment due to vertical component of active earth pressure = 450.23Kn-m

Total Restoring moment = 2451.27Kn-m

Factor of safety = 7.51593077 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)

Check for stability against sliding:-

961.89KN

293.36KN

Coefficient of friction between concrete surfaces = 0.80

2.62312913 > 1.5 Hence safe


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 Nathalova Drain at Saripalli village

Abutment

Abutment

Length of the Raft:- = 15.00m

Width of the Raft:- = 6.85m

Total load on the Raft:-

Dead Load:-

Wt.of Deck slab = 1166.63Kn

Wt.of wearing coat = 110.76Kn

Wt.of bed blocks over abutments = 121.00Kn

Wt.of abutments

Footing-I = 198.00KnFooting-II = 209.88KnWt.of abutments = 1030.12Kn

Total 2836.39Kn

Dead load stress = 27.60Kn/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 3.000 2.875

0.625

15.00m

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 = 13.31Kn/Sqm

Min.stress = -4.27Kn/Sqm

Total stress due to dead load and live load

Max.Stress = 40.91Kn/Sqm

Min.Stress = 23.33Kn/Sqm

Assuming the depth of raft as 70cm

Stress due to self weight of raft = 17.50Kn/Sqm

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

Hence,the Max.stress on the soil = 65.61Kn/Sqm

Which is less than 8t/sqm(Soil testing report)

Hence safe.

Net Max.upward pressure acting on Raft = 40.91Kn/Sqm

Net Min.upward pressure acting on Raft = 23.33Kn/Sqm

The design stress = 32.12Kn/Sqm

Hence,the UDL on the raft = 32.12Kn/m

Design of Raft:-

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

1.475 11.85 1.475

UDL of 32.12Kn/m

After analysis the bending moment diagram is as given below:

822

189

Max.Negative bending moment Mu = 822.00KNm

Max.Positive bending moment Mu = 189.00KNm

Effective depth required d = 488.12mm

Over all depth provided = 700.00mm

Effective depth provided(Assuming 50mm cover) d = 637.50mm

Top steel:-

2.023

From table 3 of SP 16,percentage of steel required = 0.627

Area of steel required = 3997.13sqmm

Bottom steel:-

0.465

From table 3 of SP 16,percentage of steel required/Minimum steel = 0.133


Hence provide 12mm dia HYSD bars@ 100mm c/c spacing at bottom and provide 25mm bars at 120mm c/c at top

4088.54sqmm

1130.40sqmm

Provide distribution reinforcement of 0.12% both at top and bottom

Area = 840.00sqmm

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 = 134.57mm

Hence provide 12mm dia bars @ 125mm c/c spacing at top& bottom as distribution steel

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 65.610t/Sqm

The raft is treated as simply supported beam with over hangs

42.33t-m

2.95t-m

Max.negative moment = 2.950t-m

Max.positive moment = 42.330t-m

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

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

Hence,the design moment = 42.330t-m

74.144471 7.7x100

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

300-50-6 = 24.4

94.70sqcm 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

6.60sqcm 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

1.1304

1.1304

0.785

12mm bars@250mm c/c

DESIGN OF CANTILEVER RETAINING WALL

Data:-

Height of wall above G.L=Height of wall below G.L=

Grade of concrete =Grade of steel =Ground water Table level =

(in clock wise direction)

(Assumed)Characteristic compressive strength =Tensile strength of steel =Unit weight of RCC =Unit weight of PCC =

Coefficient of active earth pressure by Coulomb's theory

Sin(a+Q)


sin(a+b)

Sin(a+Q) = SIN[3.14*(85.58+30)/180] = 0.88Sin(a-q) = SIN[3.14*(85.58-15)/180] = 0.943Sina = SIN[3.14*(85.58)/180] = 0.997Sin(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*(85.58+0)/180] = 0.997


Ka = 0.33

Dimensions of the Cantilever wall(Assumed for preliminary design):-

Thickness of base slab =Width of the heel slab =Thickness of stem at bottom =Thickness of stem at top =Length of the toe =

Height of Retaining wall(h) =

Density of back fill soil&material in toe portion(y) =

Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)

Slope of back fill(b) =Angle of wall friction (q) =Undrained Cohesion ( c) =Safe bearing capacity(SBC) =Surcharge over the back fill(s) =

Ka =

5.13m

F G

C1.20m 3.20m

Pressure distribution is as shown below:-

356.4

5.13m

3400.7 356.4

Area of the rectangular portion = 1826.55Area of the triangular portion = 8714.17

10540.72

Taking moments of the areas about the toe of the wall

S.No Description Area Lever arm Moment

1 Rectangular 1826.55 2.5625 4680.532 Triangular 8714.17 1.708333333333 14886.7

10540.72 19567.2


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

0.15

18.86

5.125m

Earth pressure at top including surcharge = Kays =

Earth pressure at bottom including surcharge = Kay(s+h) =

1.86m

86.14

0.50m0.13

Total earth pressure acting on the wall per 1m length P = 10540.72Kg

Eccentricity of vertical component of earth pressure =

Total earth pressure =

It acts at a hieght offrom the base

Stability calculations:-Load(Kg)

Weight of the rectangular portion of stem = 1921.88Kg

Weight of the rectangular portion of stem = 2242.19Kg

Wieght of base slab = 5500.00Kg

Wieght of soil on heel including surcharge = 29626.88Kg

Vertical component of earth pressure = 3405.70Kg

42696.65Kg

Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.

Horizontal earth pressure force = 9975.37

Lever arm x = M = 2.03m

V

Eccentricuty e = b/2-x = 0.17m <b/6 Hence there is no uplift

Maximum stress = P/A(1+6e/b) = 11953.3 < SBC



Minimum stress = P/A(1-6e/b) = 7454.27

Coefficient of friction between soil and footing u = 0.5

2.14 >1.5 Hence,the structure is safe

Moment of overturning force,ie,Horizontal component of earth pressure about toe 'C' =

Moment of restoring forces about toe 'C' =

Factor of safety against overturning = 5.69 >2.0 Hence safe.

Design of heel:-

Length of heel = 2.70m

Downward load intensity due to self weight of base slab = 5500.00Kg/m

Downward load intensity due to soil including surcharge = 29626.88Kg/m

TOTAL 35126.88Kg/m

The upward pressure distribution below the base slab is as given below:-

F G7454.27Kg/sqm

11953.3

1.20m 0.50m 2.70m

The upward pressure intensity at point 'F' is = 10726.29Kg/sqm

The upward pressure intensity at point 'G' is = 10215.04Kg/sqm

Total upward pressure force on heel portion due to soil reaction = 23853.57Kg/m

The distance of centroid of upward soil reaction from 'G' is = 1.28m

The distance of centroid of downward load intensity from 'G' is = 1.35m

Resultant moment = 16896.14Kg-m/m

Factored bending moment Mu = 25344.21Kgm

Factor of safety against sliding =(uFxW)/Ph =




1.297



Hence provide 12mm dia HYSD bars@ 150mm c/c spacing

753.60sqmm

Check for shear:-

The critical section for beam shear is at distance of 'd' from the face of the support

169.10KNat a distance 'd' from the face of the support

0.38N/sqmm <2.8 N/sqmm(As per Table 20 of 1S 456)

Hence,the section is safe from shear point of view

Assumed percentage area of the steel reinforcement = 0.17%

The design shear strength of concrete for the above steel percentage from Table 19 of IS 456 is

0.39

0.39>0.28

Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.

Provide temperature re inforcement @ 0.15%

Area required = 750.00sqmm

Taking 10mm dia HYSD bars,the spacing comes to 104.76mm

Hence provide 10mm dia bars @ 150mm c/c

Mu/0.138fckb =

Mu/bd2 =

Hence Ast provided =

Hence,the factored design shear force VFd =

Nominal shear stress Tv =

Design of wall or stem:-





4.743




1130.40sqmm

Check for shear:-







0.474

0.474>0.24

Hence,the depth provided is safe from beam shear point of view

Hence,no shear reinforcement is required.



Provide 1/3rd of above reinforcement on earthen side = 162.50sqmm

Provide 8mm dia @ 200mm c/c on earthen side

Mu/0.138fckb =

Mu/bd2 =




Provide 2/3rd of above reinforcement on other side = 325.00sqmm

Provide 8mm dia @ 150mm c/c on other side

Provide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rods

Design of Toe:-

Length of toe = 1.20m

Downward load intensity due to self weight = 5500.00Kg/mDownward load intensity due to soil including surcharge = 0.00Kg/m

TOTAL 5500.00Kg/m

The upward pressure distribution below the base slab is as given below:-

F G7454.27Kg/sqm

11953.3

1.20m 0.50m 2.70m

The upward pressure intensity at point 'F' is = 10726.29Kg/sqm

The upward pressure intensity at end of toe is = 11953.30Kg/sqm

Total upward pressure force on heel portion due to soil reaction = 13607.75Kg/m

The distance of centroid of upward soil reaction from 'F' is = 0.61m

The distance of centroid of downward load intensity from 'G' is = 0.60m

Resultant moment = 5011.89Kg-m/m





1.284


Min.percentage of steel as per IS 456 = 0.15

Mu/0.138fckb =

Mu/bd2 =



565.20sqmm

Check for shear:-







0.402

0.402>0.24




Taking 10mm dia HYSD bars,the spacing comes to 104.76mm

Hence,provide 10mm dia bars @ 150mm c/c




DESIGN OF CANTILEVER RETAINING WALL

5.13m5.13m0.00m

1800Kg/CumM25

Fe415

30

86.14

015

1600Kg/sqm7500Kg/sqm

0.60m

25N/sqmm415N/sqmm2500Kg/Cum2400Kg/Cum

2

0.50m3.20m0.50m0.15m1.20m

356.4Kg/sqm

3400.7Kg/sqm

9975.37Kg

3405.70Kg

0.12m

10540.7Kg/m

1.86m

Lever arm about C Moment(Kg-m)

1.28 2450.40

1.47 3288.55

2.200 12100.00

2.80 82955.26

1.33 4529.57

105323.78

1.86m -18517.7686806.02

Hence there is no uplift

Hence safe

>1.5 Hence,the structure is safe

18517.76Kgm

105323.78Kgm

167.466666666667

334.933333333333

Provide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rods 287.085714285714

DESIGN OF PROTECTION WALL(WING WALL)

Data:-

Total height of Retaining wall =Height of tappered wall portion=Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Top width =Bottom width assumed =Width of 1st step =Thickness of 1st step =Width of 2nd step =Thickness of 2nd step =


Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =


Sin(a+Q)


sin(a+b)


0.7

Hence,maximum pressure at the base of the wall Pa =


Surcharge load = 693

693

5.165m

5965.58

Total earth pressure = 18985.45535


The active earth pressure acts on the wall as shown below:-


Slope of back fill(b) =Angle of wall friction (q) =

Ka =

Ka =

0.45

G.L

50.4

1.75m5.2

54.63.20m

0.60m 3.80m0.70m 4.40m C

Stability calculations:-

CASE:I(Earth on toe side is scoured):-

Load(Kg)

Weight of rectangular portion of the wall = 4174.20KgWeight of triangular portion of the wall = 12754.50KgWeight of step-I = 5472.00KgWeight of step-II = 7392.00KgWeight of the earth on heel(Part-I Triangular) = 8768.72KgWeight of the earth on heel(Part-II Rectangular) = 1913.18KgWeight of the earth on heel(Part-III Rectangular) = 2259.68KgVertical component of Active earth pressure= 14623.15Kg

57357.42Kg

Horizontal active earth pressure force = 12108.31

Lever arm x = M = 2.20mV


Maximum stress = P/A(1+6e/b) = 13035.78 < 1.5xSBC Hence safe



2.13 >1.4 Hence safe


Note:-From the factors of safety and also from the Max.&Min.stresses,it can be inferred that,though the section is safe



Factor of safety against sliding =(uFx0.9W)/Ph =

it is very uneconomical.

CASE:II(Earth on toe side is not scoured):-

Load(Kg)

Weight of rectangular portion of the wall = 4174.20KgWeight of triangular portion of the wall = 12754.50KgWeight of step-I = 5472.00KgWeight of step-II = 7392.00KgWeight of the earth on toe(Part-I) = 222.75KgWeight of the earth on toe(Part-II) = 519.75KgWeight of the earth on heel(Part-I Triangular) = 8768.72KgWeight of the earth on heel(Part-II Rectangular) = 1913.18KgWeight of the earth on heel(Part-III Rectangular) = 2259.68KgVertical component of Active earth pressure= 14623.15Kg

58099.92Kg

1.43

The distribution of passive earth pressure on toe side is as shown below:-

Location&Line of action of resultant

1.75m

4129.125

Total Passive Earth pressure force = 3612.98KgHeight from the bottom of the wall = 0.58m

Load(Kg)

Horizontal passive earth pressure force = 3612.98Horizontal active earth pressure force = 12108.31

Lever arm x = M = 2.21mV


Maximum stress = P/A(1+6e/b) = 13384.59 < SBC Hence safe



2.16 >1.4 Hence safe

Coefficient of Passive Earth pressure = Kp = 1/Ka =

Factor of safety against sliding =(uFx0.9W)/Ph =


Note:-From the factors of safety and also from the Max.&Min.stresses,it can be inferred that,though the section is safe it is very uneconomical.

Total Active earth pressure = 18985.46

Moment of the centroid of the above force about the base of the stem of theretaining wall =

35767.85 Kg-m

Design of Cantilever Wall:-

Adopting working stress method of design,

Effective depth required = 63.13cm

The over all depth provided = 37.50cm

Effective depth(Assuming 50mm cover and 12mm dia bars) = 31.90cm

53.81sqcm

Hence,the reinforcement provided is safe

Distribution steel of 0.15% is to be provided

Area of distribution steel = 5.63sqcm

The area of distribution steel provided on both the faces is safe

Ast required =

Design of beam:-

Moment of the centroid of the earth pressure force about the bottom of the beam =

41463.48 Kg-m

Load coming on beam:-

Weight of wall w1 = 3712.34KgWeight of earth w2= 813.49KgSelf weight of beam w3= 281.25Kg

4807.08Kg

Design for flexure:-

1922.83kgm

Equivalent bending moment due to twisting

43902.51 Kg-m

Total Bending moment = 45825.34kgm

Effective depth required = 71.46cm

The over all depth provided = 30.00cm

Effective depth(Assuming 50mm cover and 12mm dia bars) = 24.40cm

90.13sqcm

Hence,provide 2-12mm dia bars at top and bottom and provide 3-12mm dia bars to be cranked at pile locations and stirrups at 200mm c/c spacing

Design of piles:-

To be modified as per above values

Check for safety against sliding:-

Sliding force:-

Force due to active earth pressure on wall = 37970.92 KgForce due to active earth pressure on beam = 1316.7 KgForce due to active earth pressure on pile = 3573.2813 Kg

Total sliding force = 42860.901 Kg

Resisting force:-

Kp = 1/Ka = 1.43

Lateral passive earth pressure at the top of beam = 707.85Lateral passive earth pressure at the top of pile&bottom of beam = 1415.7Lateral passive earth pressure at the bottom of pile = 7314.45

Maximum B.M = wl2/10 =

MT =

Ast required =

Lateral resistance of beam = 637.065 KgLateral resistance of pile = 4092.2578125 Kg

4729.3228125 Kg

Factor of safety against sliding = 0.1103411892 > 1.5. Hence safe

Check for safety against overturning:-

Overturning moment about bottom of pile :-

Due to active earth pressure on wall = 177854.24 Kg-mDue to active earth pressure on beam = 3484.06 Kg-mDue to active earth pressure on pile = 3902.6367 Kg-m

Total 185240.94 Kg-m

Restoring moment about bottom of pile :-

Due to passive earth pressure on wall = 615.8295 Kg-mDue to passive earth pressure on beam = 1677.6045 Kg-mDue to passive earth pressure on pile = 3963.2227 Kg-m

Total 6256.6567 Kg-m

Factor of safety against overturning = 0.03 > 1.2 Hence O.K

DESIGN OF PROTECTION WALL(WING WALL)

5.165m3.865m3.415m1.75m

1650Kg/CumM15

0.45m3.20m3.80m0.60m4.40m0.70m

3054.6

015

0.60m8000.0Kg/Sqm

2

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

5965.58Kg/sqm

12108.31Kg/sqm

14623.15Kg/sqm


0.83 3443.721.97 25083.852.20 12038.402.20 16262.402.88 25283.143.95 7557.044.25 9603.623.38 49493.15

148765.32

1.88m -22811.57125953.75




0.83 3443.721.97 25083.852.20 12038.402.20 16262.40

0.450 100.240.150 77.962.88 25283.143.95 7557.044.25 9603.623.38 49493.15

148943.52

Location&Line of action of resultant


0.58m 2107.571.88m -22811.57

128239.52


Kg/sqmKg/sqmKg/sqm

DESIGN OF FLY WINGS

Data:-

Height of Fly wing wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Grade of steel =Ground water Table level =


Surcharge over the back fill in terms of height of back fill =

Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Length of the wing wall proposed =

Dimensions of the Fly wing(Assumed for preliminary design):-

Thickness of wing at support =Thickness of wing at end =


Sin(a+Q)


sin(a+b)


0.3

Hence,maximum pressure at the bottom of the wall Pa =


Pressure due toSurcharge load = 324

324

3.865m

2087.10

Total Active earth pressure force = 5285.58


Slope of back fill(b) =Angle of wall friction (q) =

Undrained Cohesion ( c) =

Ka =

Ka =


The active earth pressure acts on the wall as shown below:-

0.50

15

1.44m3.865

900.50

Design of wall :-





1.171




1607.68sqmm

Check for shear:-

Percentage of tension steel = 0.36

Maximum shear force on the member = 127.64KN

Factored Design shear force = 191.46KN

0.42 N/sqmm

Hence section is safe from shear strength point of view



Mu/0.138fckb =

Mu/bd2 =


Nominal shear stress tv =Vu/bd =


0.42 N/sqmm > 0.42




Provide 10mm dia @ 150mm c/c on earthen side

Provide 10mm dia @ 150mm c/c on other side in both directions

The reinforcement detailing is shown in the drawing

Check for serviceability:-

For cantilever walls,the span to effective depth ratio is 7

0.58fy x Area of cross-section of steel required Area of cross-section of steel provided

The stress level is 234.15N/sqmm

For percentage of tension steel provided is 0.36

The modification factor for ratio of span to effective depth is 1.5

Hence,the ratio is 10.5

The effective depth required = 0.24 <0.452 (Actually provided)

From Fig.4 of IS:456-2000, fs =

DESIGN OF FLY WINGS

3.865m3.865m0.00m

1800Kg/CumM25

Fe415

3090

015

0.60m

25N/sqmm415N/sqmm

2.50m

0.50m0.20m

2

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

2087.10Kg/sqm

5105.66Kg/m

1367.33Kg/m

<2.8 N/sqmm(As per Table 20 of 1S 456)

0.58fy x Area of cross-section of steel required Area of cross-section of steel provided

(Actually provided)

Hydraulic design

Hydraulic Particulars:-

1.Full supply Level 2.200

2.Ordinary Flood level

3.Lowest Bed level 0.250

4.Average bed slope 0.000067(1 in 15000)

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

6.Vertical clearence proposed 0.600(As per clause 15.5 of IRC:SP 13&as per profile)

6.Bottom of deck proposed 2.800(MFL+Vertical clearence)

7.Road Crest level 3.665(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 = 6.690Cumecs

2)Area Velocity method:-

Depth of flow w.r.t HFL = 1.950m

Bed width = 4.50m

Assuming side slopes 1:1.5 in clayey soils,top width at HFL = 7.425m

Wetted Area = 11.63sqm

Wetted perimetre = 10.02m

Hydraulic Radius R= Total area/Wetted perimeter = 1.16

Velocity V = 0.36m/sec

Discharge Q = AXV 4.19Cumecs

Design Discharge = 6.690Cumecs

Design Velocity = 0.337m/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.

12.42m

The actual top width is much less than the above regime width.Hence,the stream is quasi-alluvial in nature.As per IRC:SP--13,the ventway calculations for quasi-alluvial streams are as given below:-

Assuming afflux = x = 0.15m7.43m

Clear span = 10.00mEffective linear water way = 10.00m

Depth of flow = 1.95m

Head due to velocity of approach = 0.005m

Combined head due to Velocity of approach and 0.155mafflux

1.57m/sec

Linear water way required 2.19m

No.of vents required = = 0.219Say---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= 0.7425

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*6.690.5 =

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 80 KN/m2 at a depth of 1.75m below LBL

Hence open foundation in the form of raft is proposed at a depth of 1.75m 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 much less than the above regime width.Hence,the stream is quasi-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

8.90Cumecs

1.00

0.89

1.24m

1.86m

3.06m

-0.86m

1.110m

-1.500m

design of 10m span rcc slab culvert

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